.... .1. nou~l1IU1 A -- nu. vuIIVIullu “WWII M. 1 v I.,-Ono .vo..w\ .‘IOoll‘ . H.4,..nvv..lqtd.y-..nu ,e If)! 11:4“- . .. . 1:11.... .. v .. o v .uvl n .11! toil-w: . u . I. .1»..~cdo.twd\uunoh.- v» Wick-IE. Jack?! . o» c n A . .v lg. . ,l livalh.‘ 6”, k". v. . . .Q r. v . w. . . _ :5»? u. .5 .7”me h... .. x, . 0r 1 v! v. I a . 1V 0 A a. ~l '1 flex- 1 O a . . .vo .9...” u u-.k\- .o v . '3 .x 1. “P I- opp? ‘fl glam/dun ’ ,.{ {.15. 'lm . . . . 7. v y : V . . c . r. u . .r J a x. . ‘ .V . A..uc .flv. u . 0-H . Hp . .. . . . o . ‘ c: 2 I n . c U .z u o . u . .-..‘ '0‘. (”In 1.1 . . . , I . n a. . u 4 v. .s b . I _r.-' . . ‘ a), ‘ :3 V... v. «vi-V an a 01.2. . mwwrnw . ‘p...vflo l I'DW‘IIP'U I: v..‘ 4. '10 .4. .7... . I) I n... ..... E. .. numrgrwnrw. . - ‘1! . 4..“ka . o. .1: . o ‘ I... . n . ‘1; . .l.’ll QVMJ...ovvllu - Al‘qllll- I. ll: INN [O’Kt I It '9\|‘¢|I.D\lln -.HII'IO l‘E'II‘IH'iCCIUIInnL . .04... in! . Huhuu .0 a It vii. y I} 380......» 1.11.. Ii 31.1.. . U100 O’u-Lioflu. . iii-OI! . r. . a. .4 0:0}... n .1‘.’ ‘hml.jc..fh!8u NI‘IIIJnt}- I“: “finial-0. . 1V . a», o NIB anIly‘L'K. Hv \l<. . .Ilw qufltlwfl .13..." .3 oluval‘lvluu.~as1¢ . Alfluhxtvl .1 .. . .... v u v v.- ‘r .....nuPn....uu . l 4,"?! H , .‘ ‘1 '1‘ why,» I;. . r' h Io 14:3031‘. . i- _ ll": ‘~v(.r; I! '1 o‘ii 1.9.1.3! . {or , “iii; titllll . . .5 n. t! o . a .v ”A?! MIQI‘IA'Iinu‘ t. .. ,r‘ I 1.. .. {{10‘13‘ $1 1‘ 0d...) g1. . Humiliaautu... . 51.. THESIS 00 ’llllllllllllllllll This is to certify that the thesis entitled Freeze Climatology of Michigan presented by Larry Jay Levitt has been accepted towards fulfillment of the requirements for Agricultural Engin— _M_degree meering Technology $9 Major professor Date $6. 2/, L9éz 0-7639 MSU RETURNING MATERIALS: Place in book drop to remove this checkout from LIBRARIES . III-KSIIII. your record. FINES w1ll be charged if book is returned after the date stampedabelow. is:- 9“ “hm I" "'9 I; ;,' 31 MAR 21294 9 FL: ""2 1‘7 '19 7-3“) {:9 f; , 2 9 ’o“ 03 1‘; P APR 2 1‘3 2001 CC? 0 “ 213 FREEZE CLIMATOLOGY OF MICHIGAN BY i Larry Jay Levitt \— C7//?77’ A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Agricultural Engineering Department 1981 ABSTRACT FREEZE CLIMATOLOGY OF MICHIGAN BV Larry Jay Levitt Knowledge of the freeze climatology of Michigan, 1950 through 1979, was augmented by computing the proba— bilities of freezes during spring and fall for selected agricultural weather stations in western Michigan, a data network which had not been analyzed prior to this study. The agricultural weather network, which was established in 1962, necessitated the estimation of minimum temperatures from the longer-term climatological network by the statistical technique of linear regression. A computer program provided by the Michigan Department of Agriculture/Michigan Weather Service was used to gener- ate freeze dates, assuming that the freeze dates were normally distributed. Vertical temperature profiles were monitored in two grape vineyards near Texas Corners, Michigan during the spring months of 1978, 1979 and 1980 by copper- constantan thermocouples attached to an instrumentation tower. Graphs depicting the temperature inversion between 1.0 and 15.2 meters, and between 1.0 and 17.4 meters, are reported. Larry Jay Levitt A minimum temperature forecasting scheme developed by the National Weather Service for agricultural weather stations in western Michigan was evaluated. The 4 p.m. temperature, dew point, cloud cover, and anticipated 850 mb temperature trend were used to predict the Grand Rapids minimum temperature. This prediction served as a basis to establish a forecast for 25 agricultural weather stations in western Michigan, provided that an average difference between Grand Rapids and the station in question, for different synoptic conditions, had been determined. The technique was tested for 1977 and 1978, with the results indicating that the method is a useful guide for forecasting nocturnal minimum temperatures in western Michigan. ACKNOWLEDGMENTS This thesis was written in response to the Michigan grape industry's freeze problems, and they provided the financial support. I would like to thank Dr. Dale Linvill, former Assistant Professor of Agricultural Engineering, Michigan State University, for initiating this project and co- ordinating the field research, and to whom I am grateful for introducing me to the discipline of agrometeorology. I would also like to express my appreciation to Dr. Jon Bartholic, assistant director of the Michigan Agricultural Experiment Station, and to Mr. Ceel Van Den Brink, advisory agricultural meteorologist (Agricultural Engineer— ing/Entomology), Michigan State University, for their use- ful comments. Mr. John Jensensius kindly provided the data from the TDL Agricultural Weather Guidance. I am grateful to Mr. Gary Connors and Mr. Al Shields, Agricul- tural Engineering, Michigan State University, for their assistance with the vineyard instrumentation. Finally, the owners of the two vineyards in which the research was conducted, Mr. Peter Dragecivich and Mr. Del Kellogg, must be thanked for their endless cooperation. ii The source of the data for the agricultural weather stations was the individual records from the Cooperative Weather Observers, which are on file at the Agricultural Weather Office, Room 230, Natural Science Building, Mich- igan State University. The climatological data are pub— lished by the National Climatic Center (NCC) through their series entitled "Michigan Climatological Data" (MCD), and is available at the Agricultural Weather Service Office, Documents Center, Main Library, Michigan State University, and the Michigan Weather Service, Room 240 Nisbet Building, 1407 S. Harrison, East Lansing. Finally, I would like to thank Dr. Fred Nurnberger, State Climatologist of Michigan (adjunct associate professor of Agricultural Engineering, Michigan State University), for his patience and for- bearance while serving as the major professor. iii LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS INTRODUCTION TABLE OF CONTENTS LITERATURE REVIEW . . . . . . . . 1. Freeze Climatology . . . . . 2. Freeze Protection with Wind Machines . A. Long Wavelength Radiation at Night . . . . B. Energy Budgets of Leaf and Fruit . . . . . . . 1. Radiation and the notion of effective sky temperature . . 2. Transfer of sensible and latent heat . . . 3. Determination of leaf temperature . . 4. Required energy for cold protection . . . . C. The Action of Wind Machines in Freeze Protection . . . . D. Empirical Minimum Temperature Forecasting Formulas . . . Formulas in Group 1 . . . Formulas in Group 2 . . . Formulas in Group 3 . . . E. Semi-Empirical and Theoretical Minimum Temperature Forecasting Formulas . . . . . F. Current Techniques of Minimum Temperature Prediction . . . Hygrometric Approach . . . Graphical Approach . . . Brunt and Reuter's Formulas . Multiple-Regression Equations iv Page vi ix xiii 11 ll 20 21 23 25 42 45 47 48 SO 54 54 55 55 57 Page METHODS AND DATA COLLECTION . . . . . 62 1. Freeze Climatology . . . . . 62 2. Vineyard Data Collection . . . . 65 3. Minimum Temperature Forecasting . . 66 RESULTS . . . . . . . . . . 69 1. Freeze Climatology of Selected Agri- cultural Weather Network Stations in Michigan . . . . . . . . 69 2. Vineyard Observations . . . . 98 A. Temperature Profiles . . . 98 B. Wind-Machine Trials . . . 124 3. Minimum Temperature Forecasting for Selected Agricultural Weather Stations in Western Michigan . . . . . 129 SUMMARY AND CONCLUSIONS . . . . . . 142 RECOMMENDATIONS . . . . . . . . 145 APPENDICES APPENDIX A. ACREAGE, YIELD (TONS), USES (TONS), AND RAW PRODUCT VALUES FOR MICHIGAN GRAPES, 1965-1976 . . . . . . . . . . 148 APPENDIX B. ESTIMATION OF WIND-MACHINE DESIGN FOR THRUST PER HORSEPOWER . . . . . . 149 APPENDIX C. FREEZE STATISTICS FOR THE AGRI- CULTURAL WEATHER STATIONS . . . . . . 150 APPENDIX D. TEMPERATURE-PROFILE PREDICTION MODEL . . . . . . . . . . . 168 BIBLIOGRAPHY . . . . . . . . . 175 Table 10. LIST OF TABLES Air Temperatures (Sheltered Thermometers) Endured for 30 Minutes or Less by Deciduous Fruits in Selected Stages of Development (Young, 1940) . . . . . . . . Total Counter Radiation at 0635 CST 8/31/53 O'Neill, Nebraska . . . . . . . Some Reported Values of Constants:h1Brunt%5 Nocturnal Radiation Equation for Clear Skies O I O O O O O O O 0 Area of Occurrence of a Temperature Rise of At Least 10 Precent of the Inversion Strength . . . . . . . . . Types of Freezes, Frequency, and Associated Temperature Characteristics (Spring Months, 1963 Through 1966) . . . . . . Results of Some Freeze Protection Tests in California . . . . . . . . Agricultural Weather Stations in Michigan Used in TDL Agricultural Forecast Guidance Mean Absolute Errors for the Minimum and Maximum Air Temperature Model Output Stat- istics Equations When Tested On One Growing Season of Independent Data (April-October, 1976) . . . . . . . . . . Climatic Network Stations Used in the Construction of 30 Year Freeze Climatology for Michigan . . . . . . . . Complete Listing of Predictive Equations Calculated to Estimate Minimum Temperatures for Selected Agricultural Weather Stations in Michigan . . . . . . . . vi Page 12 16 35 40 41 59 60 7O 91 Table Page 11. Results of Calculating the x2 Statistic for Use in Bartlett's x2 Test for the Homo- geneity of the Variances, for the Climato- logical Network, the Agricultural Weather Network, the Combined Climatological and Agricultural Set, a Climatological Subset, and the Combined Agricultural and Climat- ological Subset (a = .01) . . . . . 95 12. Distribution of Approximate 1 to 15 Meter Temperature Inversions According to 1 Meter Temperature (1978-1980) (Texas Corners, Michigan) . . . . . . . . . 98 13. Weather Conditions at Grand Rapids for Selected Nights During the Spring of 1979 . 118 14. Weather Conditions at Grand Rapids for Selected Nights During the Spring of 1980 . 119 15. Comparison of the Minimum Temperatures at Grand Rapids, Kalamazoo, and the Vineyard for Nights When Significant Temperature Inversions Were Occurring . . . . . 124 16. Ambient Temperatures Observed Before and During Wind-Machine Operation at 15 Loca- tions (Minimum Temperature Thermometers at the 1% Meter Level) in the Miller Vine- yard, South 6th Street, Near Texas Corners, MI, the Morning of May 4, 1979 (OF) . . 126 17. Average Difference in Minimum Temperatures Between the Indicated Station and Grand Rapids (April 15-June 15, 1967-1976) . . 133 18. Frequency Distribution of Weather Condi— tions at Grand Rapids, Michigan According to Minimum Temperature (April 15 Through June 15, 1967-1976) . . . . . . 134 19. Average Absolute Difference Between the Minimum Temperature Predictions Using the Soderberg Technique and the Observed Min- imum Temperature . . . . . . . 135 20. Comparison Between Minimum Temperature Forecasts Using the "Soderberg" Method Method and the "4 p. m. Dew Point" Method for Grand Rapids (1977 and 1978) . . . 137 Vii Table 21. 22. 23. Page Frequency Distribution of the Absolute Error of the Soderberg Prediction Method During 1977 and 1978 for Grand Rapids (Percentages of Total for Each Type of Temperature Change are Given in Paren- theses) . . . . . . . . . 138 Comparison Between the Average Absolute Error Using the MOS Forecast and the Soderberg Forecast for Selected Agricul— tural Weather Stations in Western Mich- igan (April Through June, 1978) . . . 139 Correlation Coefficient of the Minimum Temperatures at Selected Agricultural Weather Stations in Michigan as Compared With Grand Rapids, Michigan . . . . 141 viii LIST OF FIGURES Figure 1. Schematic Presentation of the Energy Flux Densities Emitted and Received by a Hor— izontal Leaf and By a Sphere. (Source: Businger, 1965) . . . . . . . Ratio of Long-Wave Sky Radiation (R) to the Black-Body Radiation 0T4 Corresponding to Air Temperature as a Function of Air Temperature as Screen Height. (Source: Businger, 1965) . . . . . . . Typical Air Flow Pattern Showing Direction of Air Movement Around the Turning Jet Based on Visual Observations and Temper- ature Patterns. (Source: Reese and Gerber, 1969) . . . . . . . Isotherms at the S-Foot Level Before Starting the Wind Machine. (Source: Reese and Gerber, 1963) . . . . . Isotherms at the 5-Foot Level with the Wind Machine Operating. (Source: Reese and Gerber, 1963) . . . . . Isotherms at 5-Foot Level with Wind Machine Operating. (Source: Reese and Gerber, 1963) . . . . . . . Area Influenced By Wind Machines of Different Thrusts (Source: Crawford, 1965) The Area of Protection of 1, 2, 3, and 40F That Can Be Expected at the Indicated In- version Strengths When Leaves Were Not Present on Trees. (Source: Reese and Gerber, 1969) . . . . . . . The Area of Protection of 1, 2, 3, and 40F That Can Be Expected at the Indicated In- version Strengths When Leaves Were Present on Trees. (Source: Reese and Gerber, 1969) . . . . . . . . . ix Page 13 19 29 30 31 32 36 38 39 Figure 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. Extent and Duration of Turbulence Created by the Wind Machine. (Source: Gerber and Busby, 1962) . . . . . . . . Locations of Stations Used in Freeze Climatology Study (1950 through 1979) . 50% Probability Date of Last 20°F in the Spring (1950 through 1979) . . . 50% Probability Date of First 20°F in the Fall (1950 through 1979) . . . . 50% Probability Date of Last 24°F in the Spring (1950 through 1979) . . . . 50% Probability Date of First 24°F in the Fall (1950 through 1979) . . . . . 5% Probability Date of Last 28°F in the Spring (1950 through 1979) . . . . 50% Probability Date of Last 28°F in the Spring (1950 through 1979) . . . . 95% Probability Date of Last 28°F in the Spring (1950 through 1979) . . . . 5% Probability Date of First 280F in the Fall (1950 through 1979) . . . . . 50% Probability Date of First 28°F in the Fall (1950 through 1979) . . . . 95% Probability Date of First 28°F in the Fall (1950 through 1979) . . . . . Length of 280E Growing Season, Days (1950 through 1979) . . . . . . . 5% Probability Date of Last 32°F in the Spring (1950 through 1979) . . . . 50% Probability Date of Last 32°F in the Spring (1950 through 1979) . . . . 95% Probability Date of Last 32°F in the Spring (1950 through 1979) . . . . 5% Probability Date of First 32°F in the Fall (1950 through 1979) . . . . . Page 43 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 Figure Page 27. 50% Probability Date of First 32°F in the Fall (1950 through 1979) . . . . . 87 28. 95% Probability Date of First 320E in the Fall (1950 through 1979) . . . . . 88 29. Length of 32°F Growing Season, Days (1950 through 1979) . . . . . . 89 30. Inversion Strength (OF) When 1 m Temp 5 45°F . . . . . . . . . . 100 31. Temperature (OF) at 1 m When Inversions of 3 10F Were Occurring . . . . . 101 32. Vineyard Temperature Profile on April 16- 17, 1979 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at Top . . . 102 33. Vineyard Temperature Profile on April 17- 18, 1979 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at TOp . . . 103 34. Vineyard Temperature Profile on April 18- 19, 1979 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at Top . . . 104 35. Vineyard Temperature Profile on April 19- 20, 1979 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at Top . . . 105 36. Vineyard Temperature Profile on April 22— 23, 1979 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction and Cloud Cover Indicated at Top . . . 106 37. Vineyard Temperature Profile on April 30— May 1, 1979 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at Top . . . 107 38. Vineyard Temperature Profile on May 1-2, 1979 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction and Cloud Cover Indicated at Top . . . . 108 39. Vineyard Temperature Profiles on May 3-4, 1979 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at Top . . . . 109 xi Figure Page 40. Vineyard Temperature Profile on April 30- May 1, 1980 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at Top . . . 110 41. Vineyard Temperature Profile on May 6-7, 1980 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at Top . . . . 111 42. Vineyard Temperature Profile on May 8-9, 1980 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at Top . . . . 112 43. Vineyard Temperature Profile on May 9-10, 1980 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at Top . . . . 113 44. Vineyard Temperature Profile on May 14, 1980 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at Top . . . . 114 45. Vineyard Temperature Profile on May 14-15, 1980 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at TOp . . . . 115 46. Vineyard Temperature Profile on May 15-16, 1980 at Texas Corners, Michigan. Grand Rapids Wind Speed, Wind Direction, and Cloud Cover Indicated at Top . . . . 116 47. Minimum Temperature (OF) for Non-Advection Nights When Cloud Cover at 4 p. m. Ranges from 0 Through 5/10. Data from April 15 through June 15, 1967 through 1976 . . 131 48. Minimum Temperatures (OF) for Non-Advec— tion Nights When Cloud Cover at 4 p. m. Ranges from 5/10 to 10/10. Data from April 15 through June 15, 1967 through 1976 . . . . . . . . . . 132 xii LIST OF SYMBOLS regression constant in hygrometric formulas area influenced by a wind machine level of significance regression constant in hygrometric formulas coefficient of mass transfer heat capacity per unit horizontal area of a leaf thrust coefficient of a wind machine power coefficient of a wind machine specific heat of the soil soil heat capacity per unit volume constant in soil temperature profile equation chi-square statistic effective leaf diameter diameter of wind machine propeller damping depth vapor pressure vapor pressure of the air vapor pressure of the leaf net outgoing radiation emissivity xiii (Pn) (Fn) G Y max sky surface emissivity of the surface density function for a normal random variable Y thrust of the wind machine latent heat flux density sensible heat flux density convective heat flux required energy to maintain plant at the minimum tolerable temperature net radiation above the leaf net radiation above the surface counter radiation from the atmosphere ratio of longwave sky radiation to black body radiation from surface dry-adiabatic lapse rate (temperature) lapse rate (temperature) at sunset relative humidity derivative of Stefan—Boltzmann equation for radiative flux coefficient of heat transfer von Karman's constant thermal conductivity exchange coefficient constant according to cloud type thermal diffusivity of the soil latent heat of vaporization eddy conductivity wavelength at which the earth emits maximum black-body radiation xiv PW revolutions per minute of wind machine propeller percent water in the soil on a volume basis correlation coefficient total longwave radiation under a couldless sky net radiation net radiation from the soil surface radiation balance of the air specific gas constant for water vapor density of the air bulk density of the soil density of the soil (dry bulk density) soil heat flux flux of terrestrial radiation (n tenths of clouds) flux of terrestrial radiation (clear skies) estimated standard deviation sample variance of the freeze statistics Stefan-Boltzmann constant standard deviation of the normal distribu- tion standard deviation of the minimum temper- ature at Grand Rapids population variance of the freeze statistics time absolute temperature (OK) of a black body XV air temperature at screen height average soil temperature radiating temperature of black COpper plate facing the ground dew point temperature effective sky temperature leaf temperature lake temperature minimum temperature forecast minimum tolerable leaf temperature air temperature at 150 cm surface temperature radiating temperature of black copper plate facing the sky maximum air temperature wet bulb temperature temperature at height 2 Lumley-Panofsky scaling temperature maximum soil temperature for the day at i = 0, 5, 10, 20 and 50 cm minimum soil temperatures for the day at i = 0, 5, 10, 20 and 50 cm potential temperature potential temperature at a chosen reference level mean wind speed friction velocity mean frost date xvi dT/dZ dU/dZ number depending on d variable depending on h 2n/P, where P is the period climatological station minimum temperature agricultural weather station difference between the minimum temperature and the evening dew point sample mean height in the atmosphere temperature profile gradient wind profile gradient xvii INTRODUCTION The grape industry of Michigan is an important segment of the state economy. People who rely upon grapes for all or part of their livelihood include over 1000 farm families, 400 to 500 processor and winery employees, and potentially 2000 to 3000 seasonal part-time employees (Michigan Grape Cooperative). According to the Michigan Agricultural Reporting Service, Michigan grape yields have been highly variable over the past 15 years. Grape production has ranged from 71,500 tons (4.3 tons per acre) in 1965 to 14,500 tons (0.9 tons per acre) in 1976. In the last 10 years, the raw product value of the grape commodities often exceeded 8 million dollars. Appendix A contains data from the Agricultural Reporting Service indicating acreage, yield, uses, and raw product values. Grape production has often been adversely affected by frost and the occurrence of freezes during the spring. Few published accounts of the cold temperature and freeze hazards to the horticulture industry of Michigan exist. The Michigan Freeze Bulletin (1965) describes the cold hazard to fruits, farm crops, and 1 vegetable production in Michigan. This publication contains tables of the probability of selected temper- atures occurring during spring and fall for 85 locations in Michigan. From the probability tables in this work, one may infer the cold hazard to any crop grown provided one is aware of the cold tolerance of the plant or fruit. The statistics that are available from the Michigan Freeze Bulletin (1965) show some degree of freeze and cold temperature hazard to all agricultural areas of the state. The critical threshold temperature varies among plant species and is different for parts of the same plant. Gerber and Hashemi (1965) found that the freezing point of citrus leaves also varied with time of season. Hender— shott (1962) deduced from observations in a portable freeze chamber that the critical temperature for citrus fruit is near 28°F, citrus leaves near 20-220F, and small twigs and branches near 20°F. The air temperatures (in shelters at the 5-foot level) that may be endured for 30 minutes or less by deciduous fruits were reported by Young (1940), and are listed in Table 1. He specified three stages of development: buds closed but showing color, full bloom, and small green fruits. The methods of protecting plants from cold include effective use of natural heat sources. The soil heat flux can be modified by irrigating before the freeze, clean cultivation, and forced harvesting. These passive TABLE 1 AIR TEMPERATURES (SHELTERED THERMOMETERS) ENDURED FOR 30 MINUTES OR LESS BY DECIDUOUS FRUITS IN SELECTED STAGES OF DEVELOPMENT (YOUNG, 1940) STAGE OF DEVELOPMENT FRUIT Buds Closed But Full Small Green Showing Color Bloom Fruits Apples 25°F 28°F 29°F Peaches 25 27 30 Cherries 28 28 30 Pears 25 28 30 Plums 25 28 30 Apricots 25 28 31 Prunes, Italian 23 27 3O Almonds 24 26 30 Grapes 30 31 31 Walnuts, English 30 30 30 SOURCE: Brooks, Physical Microclimatology(195a) practices increase the soil thermal conductivity and heat storage capacity, which increases the heat flux at night and thereby minimizes the rate of cooling. In con— trast, active methods modify the nocturnal microclimate by the use of heat, freezing water, man—made fog, foam, or by employing wind machines to increase the turbulence and enhance the heat flux to the surface. Successful applications of man-made fog for freeze protection is a current development, having only been reported during the last 10 years (approximately). In particular, an atomization method has been found that efficiently produces droplets of 10 to 20 um diameter, and at a high enough rate to saturate the atmosphere and produce a stable fog in the lower 10 m of the atmosphere (MeeamuiBartholic, 1979). The energy requirement for the atomization method is quite noteworthy, in that 100 times less energy is required than if heaters were used to obtain comparable results. BartholhzamuiBrand (1979) have demonstrated that foam insulation for freeze protection may increase low- growing crop temperatures by 100C. Difficulties in applying foam over a large area in a short time span, as well as the cost of the foam agents, have limited its use. Regardless of whether an active or passive cold protection method is chosen, an accurate prediction of minimum air temperature coupled with quantitative know- ledge of the nocturnal temperature inversion will aid the grower in deciding whether or not to employ protective practices. The purpose of this work is to establish the freeze climatology for various agricultural weather stations, report the results of microclimate monitoring in two grape vineyards, and evaluate an empirical minimum tem- perature forecasting scheme for agricultural weather sta- tions in western Michigan. LITERATURE REVIEW 1. Freeze Climatology The purpose of this section is to discuss prob- abilities of occurrence of minimum temperatures computed at selected agricultural weather stations in western Michigan. The probable dates of the last occurrence in the spring and the first occurrence in the fall for the five temperature thresholds of 20, 24, 28, 32, and 36°F are shown in Tables Cl—Cl7 (Appendix C). This allows for computation of the growing season, which is important when determining the adaptability of various cultivars to different climates. Knowledge of the probability of freezes enables the fruit farmer to make management de- cisions concerning frequency of spring freezes and the effect of delaying harvest in the fall. Many other agri- cultural experiment stations have published research of this nature, e. g. Nevada (Sakamoto and Gifford, 1960), Indiana (Schaal et al., 1961), and Iowa (Shaw et al., 1954). Thom and Shaw (1958) discussed at some length their rationale for assuming that the freeze series was random in contrast tx> a linear trend, and normally dis- tributed. A freeze series consists of the sequence of 6 dates of annual occurrence of last spring or first fall freeze dates, with the sensor exposed roughly five feet above the ground. They applied the auto correlation test, and formulated an acceptance region surrounding zero based upon the number of observations in their series. As these coefficients were very small, they assumed that their freeze dates were random when evaluating its fre- quency distribution. Calculating kurtosis and skewness statistics and hypothesizing the existence of an accept- ance region (Geary-Pearson test), they concluded that the freeze data may be represented by a normal distribution. The interpretation of a freeze in meteorology considers that an effect produced by a critical value is also produced by any temperature lower than that value. Thus, a t-degree freeze is the occurrence of a minimum temperature of t degrees or lower. The range of critical temperatures that will cause freezing damage to plants will depend upon the crop and its stage of development. It has been speculated that the young shoots and flower clusters of grapes are more sensitive to freeze than any other commercially grown fruit in Michigan (Michigan Freeze Bulletin, 1965). This is because temperaturescfif300F or lower may cause considerable damage if growth has begun. All growing shoots may be killed at temperatures of 26°F. Neverthe- less, the extent of damage to the plant depends upon the duration of exposure to the critical temperature. A grape 7 bud exhibits apical dominance; that is, a secondary shoot may emerge from the same stem, resulting in a partial crop if the primary bud is killed. Terminology often encountered in freeze studies includes hoar-frost, white frost, and black frost. Hoar- frost is synonymous with frost, referring to the inter- locking matrix of ice crystals that form on exposed objects. A white frost is a particularly heavy coating of hoarfrost that is deposited by sublimation. This is to be distinguished from black frost, in which no ice crystals may be seen, but plant tissues are injured. A white frost, by insulating the plant from further cold and by releasing the latent heat of fusion, may only result in modest damage to the plant. The internal freezing of vegetation that is associated with a black frost is indicative of the dew point being lower than ambient temperature. There is no latent heat of fusion released to offset the drOp in temperature and, therefore, this is the most damaging type of frost. Meteorologists define two distinct types of freezes based upon the physical process involved, the radiation freeze and the advection freeze. The radiation freeze is most often encountered in Michigan, as typified by high pressure systems moving in from the northwest. The clear, dry, and low wind speed conditions are conducive to the formation of temperature inversions near the ground. The advection freeze that occasionally occurs is associated 8 with cold fronts; it is this type of freeze, with the accompanying winds and cloud cover against which a wind machine is useless. If the cold front passes during the day and the skies clear later that evening without the winds subsiding, a "radiation-advection" freeze is said to occur. 2. Freeze Protection with Wind Machines A. Long Wavelength Radiation at Night. Solar radiation will be reflected and scattered by the atmos- phere and absorbed by the earth's surface, which becomes a source of longwave radiation. The total energy radiated by any object above a temperature of absolute zero will be proportional to the fourth power of the temperature of the radiating surface, as stated in the Stefan-Boltzmann law: R = eoT4 (2.1) where T is the abolute temperature in 0K, o is the Stefan- 11 cal cm-2 (0 -4 . -1 Boltzmann constant (7.92 X 10- and s is the emissivity. Assuming that the average tem- perature of the earth's surface is 2870K, the Wien dis- placement law indicates that most of the radiation is emitted in the infrared spectral region with a peak at 10 um: Amax = 2897/T (2.2) Almost all of the sun's radiation is encompassed by short wavelengths from 0.15 um to 4.0 pm, with maximum emission at 0.5 pm. Most of the radiation emitted by the 9 earth's surface is in the infrared region from 4 pm to 50 um. Infrared radiation is emitted during the day as well as the night. During the night, without contributions from the direct solar beam, its diffuse components, or short wave reflected radiation, the long wavelength balance is —RN = 0T4 - G (2.3) where RN is the net radiation, and G is the counter radiation from the atmosphere. Except for thin cirrus, clouds will radiate in the manner of black bodies according to the temperature of their base or top. For example, clouds at 00C will be a source of 0.44 cal cm.2 min.l that is radiated downward towards the earth (Gates, 1965). The clear night sky possesses semi—transparency to longwave infrared radiation, in which the minor atmos- pheric constituents, water vapor, carbon dioxide, and ozone, selectively absorb and emit energy. Absorption spectra for these gases as a function of wavelength also indicate the range in which they will radiate. Water vapor displays a sharp absorption band at 2.7 pm, and broad absorption bands at 6.3 pm, and also beyond 22 um. Carbon dioxide has its only significant absorption bands at 2.8 um, 4.3 um, and 14.9 um, contributing about l/6 of the counter radiation (Geiger, 1965). This gas is uniformly mixed throughout the atmosphere; its flux of radiation would be a nearly constant contribution. Water 10 vapor and carbon dioxide reradiate their captured energy to space and back to earth at a lower temperature than the ground. Beyond about 14 pm, the atmosphere gradually takes on opaque characteristics, tending towards a con- dition where all radiation is absorbed. The spectral range of 8 to 14 pm is often referred to as a "window" in which absorption is approximately 10%, and is of major importance in considering the nocturnal radiation balance. The atmosphere radiates less energy downwards as a result of this phenomenon, accounting for the surface cooling at night as net radiation is negative. Emissivity is the fraction of the total black body radiation intensity emitted or absorbed by a layer or column, and varies according to the specified amount of gas. It usually increases as one descends in the atmos- phere, as a corollary to the rise in the gas concentration. The widthscfifthe absorption bands for water vapor, ozone, and carbon dioxide are directly related to the number of collisions that the gas molecules undergo per unit of time, and will, therefore, be proportional to the total air pressure. To properly synthesize this knowledge with respect to infrared radiation, the "true depth" of a given gas must be substituted for its counterpart, "corrected optical depth." The true depth is the length of a column of pure gas at standard temperature (2880K) and pressure. If this value is multiplied by the ratio of the mean pressure ll of the layer to standard sea level pressure (1013.25 mb), the corrected optical depth for water vapor is obtained. Emissivities as a function of path length and temperature are reported by Sellers (1965). Conceptually, every layer of the atmosphere plays a role in the counter radiation of energy to the earth's surface, which exceeds that to space (except near the poles). A good deal of this counter radiation will orig- inate in the lowest 100 meters of the atmosphere, which is warmer than the upper layers, which serves as the source of the upward flux. A rather unique set of obser- vations as deduced from an early-morning sounding conducted during the 1953 O'Neill, Nebraska micrometeorology exper- iments is reported in Table 2. Approximately 90% of the counter radiation emanates from the lowest 800 to 1600 meters of the atmosphere (Sellers, 1965). B. Energy Budgets of Leaf and Fruit. 1. Radiation and the notion of effective sky temperature. The purpose of this sub-section is to acquire an understanding of the interrelationships between physical processes at the earth-air interface (i. e., radia- tion, convection, and evaporation) and the plant. Factors that determine leaf temperature are summarized at the end in an equation that expresses its energy budget. The leaf temperature may fall below air temperature, and it is imperative to consider this in regard to freeze pro- tection. Characterizing the magnitude of this difference 12 TABLE 2 TOTAL COUNTER RADIATION AT 0635 CST 8/31/53 O'NEILL, NEBRASKA Percent Origiggiing 9.3 0.1 m 15.9 0.4 20.3 0.8 25.8 2.0 35.0 6.0 44°6 20.0 58°9 100.0 74-6 400.0 84-8 1000.0 98-5 4000.0 SOURCE: Physical Climatology, by Sellers (1965) may serve as criteria in determining the amount of energy needed for freeze protection and the suitability of various types of freeze-protection equipment. A model leaf and a sphere to represent its young fruit are shown in Figure 1, with the longwave radiative flux density that it receives from the sky being 0Te4, where Te is the "effective sky temperature," and from the earth's surface esoTs4, where Ts is the surface temperature and as is the emissivity of the surface. The emissivity of water, soil, and natural surfaces varies between .71 and .96 (Brooks, 1959); infrared spectrometer determinations of 13 Amoma .Hmmcfimsm "mousomv .mumnmm m wn 0cm mama HmucoNHuon 6 >3 pm>flmomu pcm pmuqum mmflpflmcmp xsam >mumcm mzu mo cofipmucmmmum oeumEmsom .H musmflm (\W \\ \\V\x\.\\J\W\\\\ NW \\\\k\ \\ \\\\.\.\\k\.\.\\ \\l\ \\.\.\\t\l\\.\.\l\ vaeo mommusm VHBADIHV + vao o HBO e r a. 1. . m e w a 4 E... 11, .@ HobcoNfluom .q ma .1 a. v Bo coHDMHpmu >xm mBo 14 a leaf's emissivity in the 10 um region was .97 (Gates and Trantaporn, 1952). However, assuming that the leaf exhib— its black-body behavior for longwave radiation and main- tains a uniform temperature, it will emit a radiative flux density of 0Tl4 temperature. Simplifying by setting the emissivity of in either direction, Tl being leaf the surface equal to one, the net radiation Fn above the leaf is: 4 4 = 0(Tl -T ) (2.4) (P) e n Sky and 4 (F) = 0(Ts -T 4) (2.5) n surface 1 Businger (1965) aptly describes the effective sky temperature (Te) as the critical variable in the energy budget of the leaf or fruit. This parameter has been correlated with air temperature and/or relative humidity (Brunt, 1939; Goss and Brooks, 1956; Swinbank, 1963). The parameter may be mathematically defined by: 4 4 Te = YTa (2.6) where Ta is the air temperature at screen height, and y is a dimensionless coefficient of the ratio of longwave sky radiation to black-body radiation from the surface. It is occasionally referred to in the literature as "effective emissivity." The downward longwave radiation has been estimated in the past by the construction of Elasser radiation charts for cloudless nights (Brooks, 1952). Researchers who have taken an in-depth look at longwave radiation from clear 15 skies cite two reasons for not using the charts for agri- cultural purposes. They claim that detailed information of both the distribution of water vapor and temperature in the atmosphere is necessary, which cannot be approx- imated with sufficient accuracy from distant radiosonde observations (Gates, 1965; Goss and Brooks, 1956; Swin- bank, 1963). Consequently, many people have endeavored to express the intensity of longwave radiation received at the ground from a clear atmosphere. This was originally postulated as an exponential expression by Angstrom, but Brunt's expression was simpler and gained wide acclaim (Brunt, 1939): R/UT4 = a + b /e (2.7) where R is the total longwave downcoming atmospheric radiation under a cloudless sky, T4 is the outgoing black body radiation, and e is the mean monthly local vapor pressure in millibars. Some reported values of constants in Brunt's nocturnal radiation equation for clear skies appear in Table 3. Many of the correlation coefficients are high, but there is a wide range in the values of a and b. This may be attributed to difficulties with instruments, vari- ations of observational techniques, and the manner of specifying the vapor pressure. The Brunt formulation was later modified by assuming a fixed relationship between vertical optical depth of water vapor, and incorporating 16 TABLE 3 SOME REPORTED VALUES OF CONSTANTS IN BRUNT'S NOCTURNAL RADIATION EQUATION FOR CLEAR SKIES - Correlation Range of Researcher Location Coefficient e (mb) Dines England 0.52 0.065 0.97 7-14 Asklof Sweden 0.43 0.082 0.83 2-4 Angstrom Algeria 0.48 0.058 0.73 5-15 Boutaric France 0.60 0.042 - 3-ll Ramanathan . and Desai Indla 0.47 0.061 0.92 8-18 Brunt England 0.55 0.056 0.95 7-14 Anderson Oklahoma 0.68 0.036 0.92 3-30 Angstrom California 0.50 0.032 0.30 - Eckel Austria 0.47 0.063 0.89 - Goss California 0.66 0.039 0.89 4-22 and Brooks SOURCE: Goss and Brooks, 1956) the pressure dependency of the absorption coefficients of water vapor and observed vapor pressure. Further investigation by Swinbank (1963) revealed that R can be predicted "to a high degree of accuracy" from the low level air temperature alone. He examined the correlation between R and black-body radiation at the corresponding screen temperature Ta' Analyzing two different sets of observations over a range of temper- atures and humidities, a correlation of 0.99 was found. 17 The correlation between R and 0Ta4 was also 0.99, and the regression equation he obtained was: 4 (2.8) R = -17.09 + 1.195 Ta where R is in milliwatts cm'2 and Ta is in OK. An alternative formulation which fits the obser- vations with equivalent accuracy, and is better founded physically, is: R = 5.31 x 10'14 T36 (2.9) Either expression will provide an estimate of R in terms of Ta with an error of less than 0.5 mw cm-Z. The emission of longwave radiation by the atmos- phere is influenced by the 6.3 um water vapor absorption bands. The total area under the black body distribution curve varies as the fourth power of the temperature; however, monochromatic emission varies with a higher power of the temperature for wavelengths shorter than the modal (peak), and with a lower power for wavelengths longer than the modal. The 6.3 um water vapor absorption band is on the short wavelength side of the 3000K black body spectral distribution, whose modal emission is at 10 pm. The strong temperature influence of this band shows that the dependence of the total emission of radiation by the atmosphere upon the sixth power of the temperature is reasonable from a physical standpoint. In conclusion, the excellent correlation showing the dependence of R on T may be explained by the l8 characteristics of the absorption spectra of water and carbon dioxide. Perhaps it is an indication that there is always enough water vapor in the lower troposphere to cause the water vapor bands to emit as black bodies. The com- ponent of R due to carbon dioxide, because of the intense absorption exhibited by the gas at atmospheric concentra- tions, will originate at a level close to the surface at a temperature very nearly equal to Ta. Therefore, the contribution of R from water vapor may be conceived as being a function of Ta’ The depth of the surface layer that is necessary to contain sufficient water vapor to cause full radiation in the relevant wave bands may be shallow enough so as to differ very little from the sur- face temperature Ts' Nevertheless, other observations of Y versus tem- perature seem to show lower correlations. In Figure 2, Y is plotted as a function of temperature for four sets of observations. There_is a large scatter of points, sup- posedly due to variations in both temperature and humidity near the earth's surface. It is important to note that relatively few obser- vations were recorded in the vicinity of 00C. (This was also true for Swinbank's data.) From this data, one may infer that Y would average about 0.7 for a typical freeze night. During most evenings, Y will gradually increase with decreasing temperature. This is also due to the relatively greater downward radiation as a response to the Ammma .Hmmchsm "wousomv .ucmflmc common #6 musumummEmu new mo cofiuocsw 6 mm wusumummamu new CD mcflpcommwuuoo 4Bo GOHDMAUmH hponlxoman wcu ou Amy cofluwflpmu mxm m>m3lmcoH mo oflumm .N mhsmflm 19 mmoeemwmzme cam ATIIxo com com omm chm _ _ p c e _ _ _ _ _ r Too om om S o Aowma .Hmmcflmsmv .cmmz .wwwwmmx n. .l o.o H 58386 o 2365 .nmz .3026 0 Lemma .3003 o $03 .433 £33 4 D $me 4050.055 .83: o D D .0 _U _U .l O. 1. I. my mu .1 h.o A O D D U __ O H D 1.1. D D D 4 D 444 lm.o 4 D rooooazm 44 o 0 O O 4 4 4 o o 4 loi o a.o 20 vertical temperature gradient in the lower atmosphere. 2. Transfer of sensible and latent heat. Some degree of convection will always occur around leaves, regardless of the prevailing wind conditions. The sen- sible heat flux density to the air immediately surrounding the leaf may be expressed by: Fh = ht(Tl-Ta) (2.10) where ht is the coefficient of heat transfer, which depends upon wind speed, size, and shape of the leaf, Ta is the air temperature, and T is the leaf temperature 1 (Businger, 1965). The latent heat flux density may be similarly expressed by: _Le _ Fe ‘ R T (e1 ea) wa (2.11) where L is the latent heat of vaporization, B is the co- efficient of mass transfer, Rw is the specific gas constant for water vapor, e1 and ea are vapor pressures at the leaf surface and of the surrounding air, respectively (Businger, 1965). If the surface of the leaf is wet, the vapor pressure at the surface will be equal to the saturation vapor pressure at the leaf temperature. When this happens, both the coefficient of mass transfer 8 and coefficient of heat transfer h will be a function of wind speed and shape of the leaf. Therefore the ratio B/h will be constant for a range of temperatures and pressures used in the 21 5 cm2 dyne_1C). The psychrometric equation (6.3 x 10- heat transfer coefficient is often incorporated in the dimensionless Nusselt number hd/k, and expressed as a function of Reynolds number vd/u, where d is the effective leaf diameter, k is the thermal conductivity of the air, v is wind speed, and v is the kinematic viscosity of the air. 3. Determination of leaf temperature. The energy balance of a leaf requiring freeze protection can be formu- lated theoretically by considering a single horizontal leaf (Figure 1). The derivation that follows is primarily due to Businger (1965), with additional information from Raschke (1960), Gerber and Harrison (1964), and Gerber and Martsolf (1979). A simple equation for the energy budget of a leaf may be stated by assuming that the temperature of the leaf is uniform, and that the heat capacity per unit horizontal area is C: (F ) (F ) - 2F — 2F = chl (2.12) n sky + n surface h e dt The leaf temperature has a controlling influence over each of the heat-transfer processes. Convection and conduction are proportional to the temperature difference between plant and environment; radiation loss in the infrared varies with temperature raised to the fourth power. The saturation vapor pressure of water is approx- imately an exponential function of temperature. Because of these relationships, the energy balance equation is 22 transcendental; i. e., it cannot be solved as it stands. Raschke (1960) initially solved the energy-balance equation by equating a linear function with a vapor-pressure function (exponential function), and graphically displaying each function in order to find the point of intersection, which gives the temperature of the leaf. Raschke (1960) found a quicker method to obtain the leaf temperature by invoking certain mathematical approximations in considering the temperature difference between the leaf and the air. The key assumption in applying this method is that the curves of the radiation and vapor pressure as a function of temperature (in a small range) can be approximated by their tangents at the Ta' Radiative transfer may be cal— culated by first assuming that the leaf and air tempera- tures are equal, and then incorporating a correction factor to account for the difference in leaf and air temperature. This consists of the product of the tangent of the radiation-temperature curve and the difference in leaf and air temperature. For differences in temperature of less than 5°C, the first term of a Taylor's series may be an adequate approximation to the tangent of the radiation-temperature curve (Gerber and Harrison, 1964): RN = RN(a) - 2(dRN/dT)(Ta-Tl) (2.13) RN 2hr(Ta-Tl) 3 :3‘ m dRN/dT = 4OTa 23 where hr is the derivative of the Stefan-Boltzmann equa- tion for radiative flux, and has the dimensions of a heat- transfer coefficient, and RN(a) is the radiative balance when the leaf temperature equals the air temperature. Equation 2.12 is usually combined with equations 2.4, 2.5, 2.6, 2.10, and 2.11, yielding: 4oTa3(YTa+Ts—2Tl) + 2h(Ta-Tl) + §£%L(ea—el) w a dtl IE? (2.14) = C The surface temperature is not measured very often; it will be a function of soil type, soil cover, heat capacity of the soil, and sky radiation. If the soil cover insulates well, Ts may be a function of the effective sky temperature, soil temperature, and thickness of the in- sulator. 4. Required energy for cold protection. The energy flux density F is the required energy necessary P to maintain the leaf temperature at the minimum tolerable temperature Tm’ which occurs when dTm/dt = 0. This is expressed by equation 2.14 if we substitute em for the vapor pressure at the leaf surface, and Tm for the air temperature Ta' If equation 2.14 is subtracted from such an equation, we obtain: F = 2(hr+h)(Tm-Tl) + 3941(e -e (2.15) ) P RwTa m 1 Assuming that the vapor pressure of the leaf is saturated at air temperature, the difference between the 24 vapor pressure of the leaf and the actual vapor pressure can be adjusted by adding the product of the temperature difference between leaf and air, and the tangent of the saturated vapor pressure-temperature curve at the aver- age temperature. The Clausius-Clapeyron equation ex- presses the difference in vapor pressures between Tm and T1 (in approximate form): __ Le _ em-el - W(Tm T1) (2.16) where e is the average of em and e and Tm may be used 1’ instead of T. Therefore, equation 2.15 becomes: FP = 2(hr+h+he)(Tm-Tl) (2.17) where h = L2§B e R 2T 3 w m In the vicinity of 00C, he is approximately equal to 0.46h, and hr is approximately equal to 1.1 X 10-4 cal cm”2 sec-1, and C = 4.7 x 103 erg cm-2 sec-1C (Businger, 1965). Fuchs and Tanner (1966) describe the method of infrared thermometry for obtaining the leaf temperature. This is one of the most accurate means to measure this parameter, because other methods depend entirely upon contact with the leaf surface. Instruments such as thermocouples, thermistors, and diffusion porometers suffer from the disadvantage that they must make contact 25 with the leaf surface. Because the radiation load on each side of the leaf will be different at different temperatures, you may at best have only an average of the two surfaces, rather than a distinct temperature for the top of the leaf. It is important to note that the factor 2 appears in equation 2.16 because the leaf has two surfaces. In dealing with a fruit bud which is spher- ical, the factor 4 should be used, as the surface of a sphere is four times its cross section (Businger, 1965). Broadly speaking, four processes may be con— sidered to provide the required energy FP: 1. To prevent radiation loss through the use of man-made fog; 2. To utilize the release of the latent heat of fusion by sprinkling; 3. To heat the air surrounding the plants; and 4. To transport the warmer air available above the fruit crOp into the immediate vicinity of the fruit. The remainder of this section will deal with the last process, which is the action of wind machines to prevent damage to fruit crops. C. The Action of Wind Machines in Freeze Protection. Wind machines have been used in Cal— ifornia since the 19205 (Gerber and Busby, 26 1959), but have only been reported in Arizona since 1954 (Hilgeman et al., 1964), and in Florida since about 1960 (Reese and Gerber, 1969). They have also seen limited use in Washington and Idaho orchards (Ballard, 1976), Oregon (Bates, 1972), and British Columbia in Canada (Davis, 1977). To date, no studies of their effectiveness in Michigan have been published, although they have been in use since about 1950. The objective here is to point out the salient features of these studies in order to interpret the results of the experiments at Texas Corners, MI conducted during 1978, 1979, and 1980. The most crucial factor for the successful per- formance of a wind machine is the existence of a suffic- ient temperature inversion in the orchard or vineyard. These values are typically reported in terms of 5—50 foot inversions, or some other comparable range. Wind machines are only effective in the absence of wind (non-advective conditions), and, of course, when the actual temperatures that compose the profile are warm enough to potentially raise the leaf or bud temperatures above critical temper- atures. The primary role of the wind machine in freeze protection is to pull warm air available above the crOp down to its growing level. Turbulence induced by the wind machine is also beneficial as it increases the turbulent transfer coefficient (ht in equation 2.10) for the sensible 27 heat flux towards the leaf or bud (which may be cooled below air temperature during radiative freezes). Although the physiology of freezing damage is beyond the scope of this thesis, it is generally accepted that partially frozen fruit are injured less if they thaw slowly. There- fore, if the wind machine is operated after sunrise, rapid warming that occurs from direct exposure to the sun may be slowed (Crawford, 1965). According to some of the Texas Corners observations, quite often a temperature inversion may exist for at least one-half hour past sunrise. Also, some fruit might not incur freeze damage due to its ability to sub-cool without destructive crystallization. Brooks (1947) speculated that the turbulence would minimize the temperature contrast between the exposed side and the shielded side of the fruit, and that this would enhance the possibility of subcooling without damage. The protection pattern around a wind machine has often been reported to be roughly circular (Gerber and Busby, 1963; Bates, 1972; Crawford and Brooks, 1959; Crawford and Leonard, 1960). However, other protection patterns similar to a torus have also been reported in the literature (Brooks et al., 1951). This pattern was often observed to be elongated on the downdrift side and shortened on the updrift side. Reese and Gerber (1969) utilized the most elaborate instrumentation system of any of the wind-machine trials conducted up until that time to study its protection 28 pattern. They observed that the protected area was apparently kidney-shaped in many instances and not iso— thermal (Figure 3). This hypothesis was also borne out by observations in a Florida citrus grove (Reese and Gerber, 1963) as depicted in Figures 4, 5, and 6. The instrumentation layout in this study was quite unique in that it was designed to simulate the spokes of a wheel, using the machine tower as an axle. Many thermistors were mounted on 28 temperature towers at 5 and 20 feet, and on inversion towers at 5, 20, 35, and 50 feet. Sensitive cup anemometers were used at 5 and 20 feet, and were placed 100, 200, and 300 feet east of the wind machine. Signals from their thermistors were recorded on four Leeds and Northrup 20—point recorders to obtain a complete cover- age of the temperature over the entire area every 80 seconds. The typical air flow pattern was then verified by Reese and Gerber (1969) with the aid of smoke plumes from heaters. They noted an inward air movement immediately prior to the passage of the turning jet, which is where the depression appears in the isotherms. This was accom- panied by an inward flow of air that moves parallel but Opposite to the outward traveling jet. Wind machines act to move warm air downward; in a reciprocal manner, it moves colder air inward from the surface in advance of the jet. As it pushes out a small pocket of air in the lower atmosphere, the air pressure 29 Figure 3. Typical air flow pattern showing direc- tion of air movement around the turning jet based on visual observations and temperature patterns. (Source: Reese and Gerber, 1969) 30 I" \\\ O :7 \ L_\ _J Meteoroloqical Data Sky: Clear Date: January 4, 1963 Wind: NNW 0-2 m. p. h. Time: 2:25 a. m. Inversion: 5-20 ft., 2.10F Square corners indicate 5-50 ft., 9.70F boundaries of 10 acre test plot. Check: 29.50F Trees foliated. Figure 4. Isotherms at the 5-foot level before starting the wind machine. (Source: Reese and Gerber, 1963) 31 _l -—D z-J L. ’ _J Meteorological Data Sky: Clear Date: January 4, 1963 Wind: NNW 0_2 mph Time: 4:20 a. m. 0 Square corners indicate Inversion: 5—20 ft., 3.1 F boundaries of 10 acre test 5-50 ft., 6.9OF plot. Check- 29 GOP Trees defoliated. Dashed line is edge of turning jet. Figure 5. Isotherms at the 5-foot level with the wind machine operating. (Source: Reese and Gerber, 1963) 32 Meteorological Data Sky: Clear Wind: W 0-2.5 mph Date: December 11, 1962 Time: 12:20 a. m. Square corners indicate Inversion: 5—20 ft., 0.50F boundaries of 10 acre 5-50 ft., 5.7OF test plot. Check: 27.50F Trees follated. Dashed line is edge of turning jet. Figure 6. Isotherms at 5-foot level with wind machine operating. (Source: Reese and Gerber, 1963) 33 is lowered surrounding the wind machine. This allows for warmer, less dense air to move into the area. The thrust of the turning jet was seen to maintain this pocket once it was formed by adding energy with each revolution of the wind machine. Early attempts to articulate the adequacy of freeze protection by wind machines were mostly in terms of horsepower per acre. Using the micrometeorological aspects of a dry atmosphere, Ball (1956) showed that 1/4 horsepower per acre would mix a 100-foot layer. This estimate differed from some of the prior field data by nearly two orders of magnitude. The inconsistency of the field data may have occurred because the efficiency of the propeller in transmitting horsepower to the air was not taken into account. For a given thrust, the shaft power is inversely proportional to the propeller diameter (see Appendix B). The most useful characteristic of a wind machine is the thrust. The reach of a wind machine will be de- termined mainly by its thrust and the pressure exerted by the wall of cold air which is trying to flow back into the protected area (Brooks et al., 1952). Crawford (1962) discussed the concepts of power and thrust with respect to wind machines, and derived an equation for the area influenced by a slowly turning wind machine. This derivation involves fluid mechanical theory of the free air jet, and considers it to be geometrically 34 and dynamically similar to an air jet produced by a nozzle. An important assumption in deriving the equation was that the lateral velocity profiles in a turbulent, axially- symmetric jet can be closely approximated by a normal distribution. The air jet must attain some minimum velocity before the turbulent mixing created by the wind machine can be effective, so the average cross sectional velocity was incorporated into the equation: 1 (2.18) 2 71 na 8 J (acres) where A is the area influenced, ua is the minimum value of average cross sectional velocity, and F is the thrust (kg). The constant 25 takes into account the ratio of the average velocity to the centerline velocity of a jet, as well as the decrease of centerline velocity with distance from the nozzle. The average cross-sectional velocity (ua) was defined to be the velocity necessary to cause a temperature rise in the orchard of 10 percent of the temperature inver- sion between five and fifty feet above the ground. Im- plicit in this definition is the frictional decay of the free-air jet by the ground surface and vegetation. Table 4 gives the small amount of data available from field tests of wind machines that include the tem- perature inversion, temperature changes over a given area, and the thrust of a wind machine. Field tests later than 1964 (Reese and Gerber, 1969; Bates, 1972; Davis, 1977) either did not discuss thrust or did not use 35 TABLE 4 AREA OF OCCURRENCE OF A TEMPERATURE RISE OF AT LEAST 10 PERCENT OF THE INVERSION STRENGTH Wind Machine Thrust, Area, Type Orchard Pounds Acres Reference Under tree Peaches 320 3.6 Crawford and Leonard, 1960 Under tree Peaches 320 6.2 Crawford and Leonard, 1960 Under tree Peaches 250 4.4 Crawford and Leonard, 1960 Under tree Peaches 390 12.4 Crawford and Leonard, 1960 Under tree Peaches 470 1.2 Crawford and Leonard, 1960 Tower Prunes 1100 18.8 Goodall et al., 1957 Tower Almonds 1050 19.1 Goodall et al., 1957 Tower Citrus 1050 18.0 Brooks et al., 1952 Tower Citrus 240 7.2 Brooks et al., 1952 Tower Almonds 340 4.6 Rhoades et al., 1955 SOURCE: Crawford, 1964. instrumentation sensitive enough to determine whether adequate mixing was occurring. These data are also summarized in Figure 7. A line of best fit was drawn through the data. Using equation 2.18 and p = 1.29 x 10'3 gm per cubic centimeter, a value of 112.8 centi- meters per second was found for ua from the slope of the line in Figure 7. The amount of temperature rise that a wind machine will provide depends on the strength of the 36 Acres AREA, l l 0 100 200 300 400 500 THRUST, Kilograms Figure 7. Area influenced by wind machines of different thrusts. (Source: Crawford, 1965) 37 inversion. The most comprehensive set of measurements relating the area of protection (resulting in a temper— ature rise of 1 through 40F) that can be expected at various temperature inversions was discussed by Reese and Gerber (1969). These results are summarized in Figures 8 and 9 according to whether or not leaves were present in the orchard. The area of protection was found to be greater with weak inversions when leaves were absent (Figure 8). (The authors do not give any explanation for this result.) The two sets of curves gradually converged as the inversion strength increased. During the occurrence of large temperature inversions (80F or more), the area protected in defoliated citrus trees became less than that found when leaves were present on the trees. The two sets of curves reported by Reese and Gerber (1969) differ because the presence of foliage increases the surface roughness, which in turn creates more eddies in the orchard. Although the jet will penetrate further without foliage, the turbulent mixing and therefore the degree of protection will be less. Although Reese and Gerber (1969) discuss inversion strength as a function of wind speed, they seem to assume calm or very light winds in their figures. Thus, the results of Crawford and Leonard (1960) seem to fit their observations reasonably well, and are summarized in Table 5. Several other studies were reviewed for the purpose of adding data to this table (Crawford and Brooks, 1959; Brooks et al., 1951; Brooks et al., 1952; Brooks 38 H H o N “T_“_—_7 (1) ON N b A._r-—-_r —l_ 11 1 fi—‘ _ - O AREA OF PROTECT ION——Acres PROTECTION--OF Figure 8. The area of protection of l, 2, 3, and 40F that can be expected at the indicated inversion strengths when leaves were not present on trees. (Source: Reese and Gerber, 1969) 39 12' 7 10 AREA OF PROTECTION-Acres PROTECTION--OF Figure 9. The area of protection of 1,2, 3, and 40 F that can be expected at the indicated inversion strengths when leaves were present on trees. (Source: Reese and Gerber, 1969) 40 et al., 1953; Brooks et al., 1954; Rhoades et al., 1955). However, these results were not consonant with Crawford and Leonard's data, either due to the fact that inversions were recorded from 7 to 40 feet, or that the drift was not specified. In Michigan, Van Den Brink (1968) reported obser— vations of temperature inversions from the 5 to 60 foot level in the vicinity of Peach Ridge, near Sparta, Michigan. Table 6 summarizes the types of freeze, fre— quency, and associated temperature characteristics for the spring months 1963 through 1966. The magnitude of the temperature inversions that were encountered during radiative-type frrezes throughout the course of this study usually ranged between 40F and 60F. TABLE 5 RESULTS OF SOME FREEZE PROTECTION TESTS IN CALIFORNIA Inversion Wind Wind Machine Temp Min Areal Date 5'—50' at 50' Thrust Rise Temp Coverage (F) (mph) (lbs) (OF) (OF) (acreS) 3/20/59 7.4 2.0 320 1.0 35 2.7 3/25/59 6.1 2.7 320 1.0 34 3.8 12/8/59 8.6 3.3 250 1.0 23 3.8 1/5/60 5.9 1.7 390 1.0 21. 7.3 SOURCE: Crawford and Leonard, 1960 41 TABLE 6 TYPES OF FREEZES, FREQUENCY, AND ASSOCIATED TEMPERATURE CHARACTERISTICS (SPRING MONTHS, 1963 THROUGH 1966) Type of Freeze Minimum a Temperature Factor . . . Advection- at 5-Foot Level Radlatlon Advectlon. Radiation 32°P or lower A 12 6 5 B 52% 26% 22% (23 cases) c 5.3° 2.0° 4.0° D O 27.9° 29.0° 30.l° E332 F 7.1 6.0 2.6 P 53.4° 52 8° 62.o° 300F or lower A 8 5 3 B 50% o 31% o 19% (16 cases) C 5.4 2.2 3.7 0 26 4° 28.6° 29.2° Eg30°P 6 7 3.9 1.8 P 50 9° 52 8° 63.0° 280F or lower A 7 l 0 B 87% 13% - (8 cases) c 5.4 0.0° - 0 26.1 26.5° - E5280F 4.7 5.0 - F 50.4° 51.0° — 26°P or lower A 3 0 0 B 100% - - (3 cases) C 4.50 - - D 24.7° - - E326OF 4.7 - - P 47.3° - - aFactors: A = Number of cases B = Frequency C = Average maximum inversion (CF), 5-60 ft. D = Average minimum temperature E = Average number of hours, temperature shown F = Average previous day's maximum SOURCE: Van Den Brink, 1968. 42 Gerber and Busby (1962) describe the turbulent mixing of a wind machine as observed by a captive balloon on nylon yarn. The duration of the turbulence will be a fraction of the time required for the machine to make one revolution, and was observed to extend 425 feet downwind and 300 feet upwind (Figure 10). From this data they hypothesize that reduced protection around the edge of a protected area is due to the shorter duration of the turbulence. No other observations of the decay of the turbulence with distance appear in the literature, but speculations abound. For example, Bates (1972) claims that a radius of 320 feet will be the limit at which pro- tection should be expected, but that the turbulence was evident to about 650 feet. In an early study, Moses (1938) says that the effectiveness of a small machine decreases rapidly beyond 300 feet. Recommendations by Brooks et a1. (1952) for spacing of several wind machines in a 40-acre citrus grove were that they should be 600 to 800 feet apart. D. Empirical Minimum Temperature Forecasting Formulas. According to Sutton (1953), Kammerman's rule was the predecessor of many rules for forecasting the minimum temperature. This rule appeals to the principle that the amount of water vapor in the air controls the radiative heat loss. The nocturnal minimum temperature is established by subtracting a constant number of degrees from a previously determined wet-bulb temperature. Height (feet) Time (min) 43 I ' i 1 / . ‘ 0 100 200 I300 400 I ’ Feet from wind machine” up drift 2.5V 5.0 Figure 10. Extent and duration of turbulence down drift created by the wind machine. (Source: Gerber and Busby, 1962) 44 Subsequent investigations revealed that better results were obtained when both the wet-bulb and dry-bulb temperature were taken into account. The physical parameters that are common to the formulation of these empirical relationships are: dry-bulb temperature, wet- bulb temperature, dew point, wind speed, and cloud cover. Bagdonas et a1. (1978) extensively reviewed many empirical and theoretical techniques of minimum temper- ature forecasting. Cold damage to fruit and crOps in the far western regions of the United States sparked interest in developing local temperature forecasting formulas by analyzing data statistically. After the factors to be correlated have been selected, the actual construction of the minimum temperature formulas is similar. A scatter diagram is prepared by plotting one factor against another, and a line of "best fit" is then determined. An average moisture content of the soil surface is usually assumed in the construction of these formulas. An extreme condition in soil moisture is an important factor in minimum temperature forecasting, particularly when a hygrometric formula is applied. The minimum temperature will be lowered or raised, depending on whether an abnormally dry or rain-soaked soil exists. Ellison (1928) discusses empirical formulas which were designed to evaluate the minimum temperature from factors which can be assigned definite values in the early evening. These formulas may be placed into three 45 groups: Group 1: y = f(Y) Group 2: y = f(d) Group 3: y = f(d) + f(h) The following mathematical conventions will be used through- out the remainder Of this discussion: y is the minimum temperature d is the dew point at an afternoon observation n is a number deduced from study of data Vd is a number depending on d Vh is a variable depending on h Formulas in Group 1. The "median-hour" relation- ship uses the midpoint of the daily temperature range to predict the minimum temperature. The temperature at the time of the median is subtracted from the maximum temper— ature, and the remainder is the fall that will occur between the median and the minimum temperature (Beals, 1912). One type of night which often occurs with ideal freeze conditions is when the dew point approaches or reaches the air temperature near the median hour, in which case the median-hour relationship should not be used to predict the minimum temperature. Another rather infrequent case in which this form- ula would not apply is the "advective-radiative" freeze. This situation is defined to be the occurrence of frost at night following the passage of a cold front, which is 46 often preceded by a cloudy afternoon. A rapid drop in air temperature in the early evening is often accompanied by local winds, e. g. mountain and valley winds, and this will cause the tem— perature to fluctuate over short intervals. This formula- tion suffers from the fact that the instantaneous temper- ature at the median hour is affected by local conditions. The time of occurrence of the median hour in many areas of the country is so late that it is not practical to use the formula in the preparation of forecasts. The "post-median hour" relationship consists of recording the difference between the maximum temperature and the lep.nh air temperature, and taking this to be two-thirds of the difference between the maximum and minimum air temperature (Thomas, 1912). This formula is also not practical because of the lateness of the post- median hour. The "pre-median hour" method establishes the tem- perature fall in the early evening. This technique is used by the forecaster to predict the median-hour temperature by extrapolation (Alter, 1920). Although this allows for an earlier approximation of the minimum temperature than by the median-hour method, it is subject to more error. A ”daily temperature range" method was formulated by Smith (1914) in which the mean, greatest, and least daily temperature ranges were compiled for semi-monthly periods. These values are used to forecast the minimum 47 temperature once the maximum temperature is known. Formulas in Group 2. Humphreys (1914) proposed an "evening dew point" relationship in which the temper- ature is assumed not to fall below the coincident dew point. The minimum temperature is predicted to equal the evening dew point. MeteorolOgical records from fruit-frost work show that this relationship will only work consistently for stations that are elevated. The minimum temperature is often 80F to 100F lower than the evening dew point (Ellison, 1928). Keyser (1922) proposed the "wet—bulb minimum tem- perature" method in which the average difference between the wet-bulb temperature at 5 p. m. and the minimum temperature was subtracted from the current 5 p. m. wet- bulb temperature to establish a forecast minimum. Similar- ly, Smith (1920) correlated the difference between the evening temperature and dew point with the difference between the evening dew point and ensuing minimum temper- ature. Nichols (1926) devised the "depression of the dew point below the maximum temperature" method, in which the maximum temperature minus the evening dew point is correlated to the difference between the maximum and minimum temperature. However, Ellison (1928) points out that all of the formulas in the previous paragraph are in error. Under the assumption of constant dew point, the wet-bulb formula 48 implies constant relative humidity. Also, the depression of the evening dew point is a pure number which may cor- respond to widely differing values of absolute humidity or air temperature. Formulas in Group 3. The hygrometric formulas rely upon the concept that the minimum temperature will be greater than or less than the evening dew point by an amount related to the relative humidity. Most of the lit- erature on minimum temperature formulas, especially since 1930, Imus dealt with formulas of this nature. Ellison (1928) reports that the first hygrometric relationship was put forward by Donnel in 1910, while working on Boise, Idaho freeze records: h-a b (2.19) where a and b are constants derived from the data. Smith (1917) used linear regression, and expressed his hygro- metric formula as: Ym-d = a — bh (2.20) where Ym-d is the difference.between the minimum temper- ature and the evening dew point. The first application of a curvilinear form of the hygrometric formula is due to meteorologist Floyd Young (1920), to whom much fruit-freeze forecasting work can be attributed. His equation was: _ _ h-n y — d _7F— + Vd + Vh (2.21) 49 where n = 20, 30, or 40 for clear, partly cloudy, or cloudy skies, respectively. Smith (1920) fit parabolic curves to the hygro- metric data, by suggesting an equation of the form: Y = a + bh + ch2 (2.22) Nichols (1920) felt that it was not necessary to use mathematical curves to fit the hygrometric data, and suggested that: After examining all of the empirical formulas, Ellison (1928) concluded that the hygrometric types were best. This conclusion was more recently borne out by Kangieser (1959), who compared several empirical formulas for clear nights in an arid region. Sutton (1953) remarked that the hygrometric equations worked very well when applied by meteorologists with a good knowledge of local conditions. The Frost Warning Service of the National Weather Service has employed hygrometric formulas very successfully for about 40 years (Bagdonas et al., 1978). One empirical relationship for forecasting the minimum temperature deviates from the hygrometric, median temperature, and maximum-minimum concepts. Georg (1970) devised the "semi—objective radiometer technique," which implicitly establishes a relationship between the nocturnal net radiation and the air temperature at screen height. The radiating temperatures of two black c0pper plates, one facing the sky (Tt) and one facing the ground (Tb), are 50 observed two hours after sunset. A scatter diagram of Tb-Tt vs. Tb-Tm is obtained, and two best-fit lines are computed for nights when T 5,00C and T 3 00C. The t t predictive equations are then used to forecast Tm' It is crucial that instrumental error be minimized to insure the quality of these objective forecasts. The economical net radiometer (Suomi and Kuhn, 1958) was chosen by Georg (1970) because it is shielded from advective heat transport by transparent polyethylene, and is ventilated to prevent dew and frost deposition. Among the assumptions that are made when employing this technique is that cloud cover and wind do not change dramatically throughout the course of the evening, and that the top sensor of the instrument is evaluating the effective radiating temperature of the sky. E. Semi-Empirical and Theoretical Minimum Temper- ature Forecasting Formulas. Consideration of heat-transfer laws has shown that the temperature of the earth's surface at night very closely parallels the air temperature in the boundary layer. This assumption has allowed for the development of several semi-empirical and theoretical techniques for predicting the nocturnal minimum air tem- perature, spanning three decades from 1920 to about 1950. Brunt's (1941) theoretical solution of the noc- turnal cooling of the earth's surface is often quoted in the literature as an approximation of the nocturnal air temperature on clear, calm nights. The equation that he developed, assuming the earth radiates as a black body, 51 is: T 4(l-—a-—b/€) AT = .3. s «t n p C K S S S where: AT is the fall in temperature at the (2.24) ground surface from sunset to sunrise (0K) 0 is the Stefan—Boltzmann constant (7.92 x 10- cal cm-2(0K)‘4 min'l) 11 T is the sunset temperature of the earth's surface (0K) e is the vapor pressure in the atmosphere (mb) t is the time interval in hours and tenths of hours beyond zero on the time scale which is taken as the time of sunset p is the density of the soil (1.6 g 3) cm- 1c>-l C is the specific heat of the soil (0.18ca197 C ) K is the thermal diffusivity of the deg"l cm 1 sec-1) soil (cal a and b are constants derived from the data This equation essentially models the which the heat flux density outward from the face by radiation is constant throughout the is equal to the heat flux density from below situation in earth's sur- night, and the surface. Brunt derived his equation by solving the Fourier heat conduction equation aT/at = KS 82T/82Z with the assumptions: (2.25) l. The initial temperature distribution in the soil is isothermal (T (Z,0) = the sunset temperature of the soil surface). 52 2. The eddy conduction of heat from the air to the earth's surface is equal to zero. 3. The flux of heat to the earth's surface due to condensation processes is equal to zero (assuming no dew or frost). When developing his equation, Brunt assumed one specific conductivity of heat for the surface layers of the earth. Reuter (1951) is credited with extending Brunt's equation to include eddy conductivity in the air, and the variation of temperature with depth in the soil. The semi-empirical method that he developed was: AT — 77 /E (2.26) /KS Os CS + Ca/Ap where: Rn(o) is the net radiation from the soil surface (cal cm‘2 min'l) A is the coefficient of thermal conductivity of the soil (cal deg"1 cm'l sec-1) dT/dZ is the change of temperature with depth in the soil (OK/100 cm) F is the lapse rate of temperature in the air at sunset (OK/100 m) Ae is the coefficient of eddy conductivity in the air (m/sec) Ca is the specific heat capacity of the air (J 9'1 K)”1 P is the dry-adiabatic lapse rate (OK/100 m) and all other symbols are as defined for equation 2.18 53 Several other modifications of the Brunt formula endeavor to create a theoretically more vigorous solution. They have addressed the effect of wind on nocturnal cooling, net radiation as an explicit function of time, and the con- tributions of both the air and soil to the heat radiated from the earth's surface. To include wind in models of nocturnal cooling, eddy transfer coefficients were defined whose magnitude varied with height above the ground. However, it is not a sound practice to establish values of the eddy conduction of heat in an airflow characterized by an unpredictable degree of turbulence. Cooling formulas in which net radiation is not constant do not give sig- nificantly different results for time periods on the order of a night (Georg, 1971). Finally, equations that have included a conductivity parameter involving properties of both air and soil are so complex that they have no practical meaning. The constants in forecasting formulas are affected by local conditions, such as topography, cultural prac— tices, nature of the vegetation, and stage of plant growth. Thus, the constants will vary with respect to time for any location. The theoretical formulas, in addition to the above limitations, are particularly sensitive to the type and condition of the soil. Georg (1971) states: "The soil constants in formulas of the Brunt-Groen type vary both spatially and temporally because of the nature and state of 54 the soil surface layers and changes in the water content of the soil." Assuming average values of the soil constants, i. e., thermal conductivity, is not practical because it will change dramatically with small changes in water content. F. Current Techniques of Minimum Temperature Prediction. Bagdonas et a1. (1978) discuss minimum temper- ature forecasting formulas that are currently being used in 14 nations. References will be cited mainly from this survey to discuss some of the present-day forecasting techniques, according to the following categories: hygro- metric, graphical, Brunt-Reuter, and multiple regression. Hygrometric approach. The Mendoza area in Argentina is an important growing region. The central forecast sta- tion in Buenos Aires uses a hygrometric formula to predict the minimum temperature throughout this region. Linear regression was employed to develop a predictive equation for Tm from Tw, which is the 1800 GMT wet-bulb temperature: Tm = a + bTw (2.27) where a and b are constants derived from the data. A correction factor was developed by segregating data into five different synoptic patterns known to produce frost in the Mendoza area. (An important criterion in distinguishing between the different synoptic patterns is the expected wind speed.) Data were then analyzed sep- arately for each pattern, with the end result being a total correction Cl: 55 c1 = E‘ - oy/i-r2 (2.28) where AT is the difference between the mean value for a given location and the reference forecast point, 0y is the standard deviation of Tm, and r is the correlation co- efficient between Tm at the reference forecast point and the given location. Graphical approach. The Canadian Department Of Transportation (Meteorological Branch, Toronto) has de- veloped a technique to forecast the minimum temperature on clear nights in Hamilton, Ontario, during May. The focal point of this technique is an indirect quantitative measure of the soil heat flux in the nocturnal cooling process. This is accomplished by assuming that the difference between maximum air temperature (TX) and the normal temperature of western Lake Ontario is roughly analogous to the difference between temperatures at the soil surface and several centimeters below. They gathered data to construct a scatter diagram of: (T -T )vs. (T-T x LAKE (2°29) d)l330 EST. Values of AT (maximum minus minimum temperatures) were then marked beside each point and plotted, and best fit isopleths constructed. Predictions from these graphs were then modified by adding a wind correction factor based upon estimated surface wind speed at 0730 EST. Brunt and Reuter's formulas. These formulas have received wide use in the prairie areas of Canada. Eley 56 (cf. Bagdonas, 1978) applied some simplifying assump- tions in Reuter's formula, and gathered historical data to construct nonograms for a graphical solution: ATO = +3; E ft? = F-E/E JCS ps KS + CP/A An empirically derived equation for net—outgoing radiation (E) as a function of surface temperature and vapor pres- sure was found, and Reuter's assumption of A = 65 U, where 6 is the mean wind speed (mph), was applied. The quantity /C;—E;—K; was also determined empirically by observing ATO for radiative nights. This quantity averaged 0.290 cal C_l cm.2 min-%. One nonogram of F-E corresponding to relative humidity and sunset temperature, and another nonogram to obtain ATO from F-E for any date from April through September were constructed. Kagawa (cf. Bagdonas, 1978) rearranged Brunt's formula to make C = /C;—E;_?; the dependent variable, and recorded values for C from field studies. The mode intflmadistribution of C was chosen, since the quantity exhibited a wide range. He followed Reuter's procedure to calculate S(O)n' the flux of terrestrial radiation with n tenths of clouds: 5(0)n = 8(0)O (l-Kn) (2.31) where Kn is a constant according to cloud type: 0.031 for cirrostratus, 0.063 for altostratus, 0.085 for stratus, and 0.099 for nimbostratus. 57 The assumption of constant soil parameters for any locality allowed Kagawa to simplify Brunt's formula: T = C-S(O)O-2.03/E (2.32) Brunt's formula has been used in the Florida penin- sula for at least 10 years. Recently, researchers in this region have sought to improve this method by determining the thermal diffusivity for soils of varying water content. Where this is inconvenient, an approximate thermal diffu- sivity may be determined graphically from soil temperature profiles and the classical heat conduction equation, where K = Ks/pSCS. Multiple-regression equations. Wallis and Georg (cf. Bagdonas et al., 1978) derived multiple—regression equations for 300 fruit-frost temperature survey stations in groves and fields on the Florida peninsula. The pro— cedure was to correlate the minimum temperature at each fruit-frost station with the minimum temperature at three "key" stations, using 40 nights over a three-year period during winter. The minimum temperature for the nights chosen was 2.20C or lower somewhere on the peninsula. A total of 14 "key" stations are maintained by the National Weather Service or Agricultural Experiment Station of Florida. In Canada, Yacowar (cf. Bagdonas et al., 1978) derived a complex set of multiple-regression equations where maximum and minimum temperature were dependent variables, e. g. atmospheric parameters at the surface, 58 850 mb, and 500 mb. This procedure is limited to use at the larger meteorological centers, which would disseminate the information to local forecasters. Jensensius et a1. (1978) of the Techniques Develop- ment Laboratory, National Oceanic and Atmospheric Admin- istration, also derived multiple linear regression equations to forecast maximum and minimum air temperature out to 132 hours, and probability of precipitation amount out to 84 hours for agricultural weather stations in Michigan (see Table 7). Minimum relative humidity and maximum and min- imum soil temperatures 4 inches beneath bare and grassy surfaces were also projected for stations in Indiana. The prediction equations were developed by determining stat— istical relationships (i. e., how much each included parameter reduced the variance) between local weather observations and the output from the six-layer Primitive Equation (PE) model. The predictors in the maximum/minimum air temperature equation are: 1000-850 mb thickness, 1000- 700 mb thickness, 1000-500 mb thickness, 850 mb temperature (the best predictor for minimum air temperature), 500 mb height and temperature, boundary layer and mean relative humidities, number of hours of sunshine, and daily insola- tion at the top of the atmosphere. The mean absolute errors for the resulting minimum temperature forecasts in Michigan are included in Table 8. Soderberg (1969) devised a minimum temperature forecasting scheme for agricultural weather stations in 59 TABLE 7 AGRICULTURAL WEATHER STATIONS IN MICHIGAN USED IN IIHf.AGRICULTURAL FORECAST GUIDANCE Arcadia (Beulah) . Belding . Coldwater . Edmore l 2 3 4 5. Empire 6. Fennville 7. Fremont 8 Glendora 9. Graham 10. Grand Junction 11. Grant 12. Holland 13. Hudsonville 14. Kent City 15. Kewadin 16. Lake City 17. Lake Leelanau 18. Ludington l9. Mapleton 20. Mears 21. Michigan State University Hort. Farm 22. Nunica 23. Onekama (Bear Lake) 24. Paw Paw 25. Peach Ridge 26. Sodus 27. Watervliet SOURCE: Jensensius et al., 1978 *Techniques Development Laboratory, NOAA, U. S. Department of Commerce 6O mumoooHOM noon omlma oousu noon no woman ummoouom poflmaoOE oocouwflmuom o n mmoaoumaaauo oaumaumum usmuso HmoOZM .mo Ca ouo mcofluosvo ousu noHomEou new muouuo onu mo HH< .mchHOE uxo: on» oEflu HmooH .E.o h waouofiwxoummm Hausa coocuoumm ouoa Eoum oflao> oum mcofluosqo ousuouomEou Ham EDEACHE one .Hson mmlma oounu Doom ozu mo uonuo :moE onu co comma ummooHOM ooflwflpoe m paw .hmoHo nomeflao .oocoumflmuom MOM muouuo opsHOmnm cooE onu ohm poGDHOCH Goad "meoz mama ..Hm um msamcwmcmn "momoom .QEoB mv.m 5H.n hn.m mm.m Hm.v nH.n mv.m nm.w oo.v na.n mm.m mm.m Hfl< Susana: .QEoB om.¢ mm.h om.m mv.v ma.m mm.> no.m on.m nm.m. mm.n mm.m va.m Had Essflxoz poo: QEHHO nmuom mmoz poo: oEHHO Qmuom mmoz poo: oEHHO amuom omoz :oflumsvm vmlow omuom wmuma mo omwe A920 oooo Scum musonv cofluoonoum ummoouom oumEHxOHmm¢ Amemfi .mmmoeo0uqumo l3. 14. 15. 16. l7. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. Adrian Allegan Alma Alpena WSO AP Alpena Sewage Ann Arbor Atlanta Bad Axe Baldwin Battle Creek Bay City Benton Harbor Big Rapids Bloomingdale Cadillac Caro Charlotte Chatham Cheboygan Coldwater Detroit City WSO AP Detroit Metro WSO AP East Jordan East Lansing East Tawas Eau Claire Escanaba Fayette Fife Lake Flint WSO Frankfort Gladwin Grand Haven Grand Marais Grand Rapids WSO AP Grayling Greenville Gull Lake Hale Loud Dam Harbor Beach Harrisville Hart Hastings Higgins Lake Hillsdale Holland Houghton 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. Houghton Lake Ionia Iron Mountain Ironwood Ishpeming Jackson FAA AP Kalamazoo St. Hospital Lake City Experiment Farm Lansing WSO AP Lapeer Luddington St. Ignace-Mackinac Bridge Manistee Manistique Marquette WSO Midland Milford GM Proving Ground Mio Hydro Plant Monroe Mount Clemens AF Base Mt. Pleasant University Munising Muskegon WSO AP Newaygo Newberry St. Hospital Onaway State Park Ontonagon Owosso Wastewater Plant Paw Paw Pellston FAA AP Pontiac St. Hospital Port Huron Saginaw FAA AP Saint Johns Sandusky Sault Ste. Marie WSO Seney Nat'l WLR South Haven Exp. Farm Stambaugh Standish Three Rivers Traverse City FAA AP Vanderbilt Watersmeet West Branch Willis 71 .... .....1 . .....,..__ _ .1. Ill'uL A vlirl ._01. caoaA. _ _ ._ “liq“ .|.l.. m mu” l. _100; . 1.1.. AF... 6;. 13¢ :I.I.Ii--_ J....IL . m I...)- _H ._ ...lrln1l .F é. ._.).IwIIIL ." 5 —L1 b Tl.nm_lll.lml.v J ..p..|.|-_tll.& _b . wliu.‘ m o v -C. m _ l.bu_l.li_m. _b. I. .3 .u _ m . .-..-.quin. 1.1: _fl 0.. -_- L. o. ..... Alia. L .1. a . Firth : .11: ... ..... -_ . . - 7!. __ _ but. .Tm.._!.. _ O; , .JU _Ofi ula! LJIC;L_ AnF!mefi. _— ..1iul 9? Lin... 1 o _HIWL Tm..._.lml ._. __ “...-.-n.-..u. ._ .1 .a. m... m. I: . _ . ..|.| Lu ’ Ih.a_ filli¢DlI1_ -. 1 u__ a. _u I e . if c .m (1:! v u. ......_.r _ “.... .— Llplu.ql.m1. \ M .. A _. a a *0 a a c 1 All lib . e .1 a l . . w a. r L .-l—«l-..\ 1 .m w .o. m m .... an. \ o a c (R .u .1 .m .1 t 1 r -. .1 m a M, A o a Figure 11. Locations of stations used in freeze climatology study (1950 through 1979). 72 x = agricultural station 3-30 3-25 Figure 12. 50% probability date of last 20°F in the spring (1950 through 1979» 713 11—2: 11-15 11’): x 11-25 1’ O . u. x = agricultural station - ”a- 3’51... 0.. H t I N N U: D Figure 13. 50% probability date of first 20°F in the fall (1950 through 1979L 74 -15 44-1;‘Qn5r3,-‘ “- _ _ ,._,. 4-3*‘~ Ik LI \‘d\ 5-05 x = agricultural station [Lin-"x“; _-. '41 1 -4_05:_.".::—.-—--— Figure 14. 50% probability date of last 24°F in the spring (1950 through 1979). 75 x = agricultural station ‘—'A...-:s.- -.‘s— 10-25 '10-30 11-05 10-25 Figure 15. 50! probability date of first 24 °F in the fall (1950 through 1979)- 76 5-0 ..L __._ ‘5: ' ' 4-30 -—L.-—-.-.‘- -10 x= agricultural station Figure 16. 5% probability date of last 28°F in the spring (1950 through 1979). 77 9L - . i (Q 7" o— \ ...-I- l X \\I | . ' I x = a ricultural station . t _' . . -l I g ‘7’ 3 - --—-- _ - -- --h 4-20 4—25 4-15 {-30 4-25 4-20 Figure 17. 50% probability date of last 28°F in the spring (1950 through 1979). 78 x= agricultural station Figure 18. 95% probability date of last 28°F in the spring (1950 through 1979). 79 X = agricultural station 9’30 9-30 9-20 9-20 10-10 Figure 19. 5% probability date of first 28°F in the fall (1950 through 1979). 80 7 PC 3 'a—fh404;. \ m-so .2102 412:1 ‘—-.-....---- .- xo’u 73°C.“ :45 U ; i ---r' “1.7:? e-'- "Fl—'1 '-’—- "'1'“ ' 10’1 X’s agricultural station Joe 9 . Figure 20. 50% probability date of first 28°F in the fall (1950 through 1979). 81 11-10 x = agricultural station Figure 21. 95% probability date of first 28°F in the fall (1950 through 1979). 82 160 150 ii: 0 ' 200 19. hi. 2.0 . gs an (: X a ' . . agricultural station -:%~--o- .___- ...- 200 180 170 L 180 190 Figure 22. Length of 28°F growing season, days (1950 through 1979). 83 I 6’16 x'seos _’ X; -.-. V- o o XSPZS ‘ . 4’ ‘r---"' z r x = agricultural station : '-.....-...."_.._..L - 5-10 Figure 23. 5% probability date of last 32°F in the spring (1950 through 1979). 84 x = agricultural station Figure 24. 50% probability date of last 32°F in the spring (1950 through 1979). 85 “'W ‘ fit 7 I’. ‘.i x = agricultural station . .._--_:.:_n.v.:.‘-.--—v .4-20. 6’15 Figure 25. 95% probability date of last 32°F in the spring (1950 through 1979). 86 X = agricultural station; Figure 26. 53 probability date of first 32°F in the fall (1950 through I979). 87 9-30 It)!!!" 'omm I bulk) 2.3m W I ‘4 Q U! 10-10 ’ IO’IO‘C €-.._ 39’255. ...“: | 1047!! \ x = agricultural station ‘ Q’- “ 9-30 10-05 10-20 10-10 Figure 27. 50% probability date of first 32°F in the fall (1950 through 1979). 88 .10-20 x = agricultural station Fi ure 23. 95% probability date of first 32°F in the fall (195 through 1979). 89 It i . 18+.-:_.. .1» ' lt- ' l .--.--.. -.. bg- --. v” . x = agricultural station 4::[55' 170160 Figure 29. Length of 32°F growing season, days (1950 through 1979). 90 most from the climatological network analysis. The ex- planation for this result is that Grand Junction temper— atures are recorded in a low-lying area, where cold soils of low thermal conductivity predominate. The analysis of the freeze dates for the climatological network shows that the two coldest areas in Michigan are the northern Lower Peninsula (Ostego County and inland parts of Antrim, Montmorency, and Cheboygan counties that surround it), and the central western Upper Peninsula (in particular Iron County). The warmest areas are extreme southwestern Michigan (Berrien County) and southeastern Michigan (Monroe, Wayne, Macomb, and St. Clair counties). The length of the 32°F growing season (see Figure 29)varies from 70 to 180 days. The 130 to 140 day growing season in the inland area of the "thumb" (Tuscola and Lapeer counties) 1J5 a bit shorter than many stations located along a lakeshore further to the north, e. g., Manistee County in the northwest Lower Peninsula, Alpena County in the northeast Lower Peninsula, and the region in Marquette County that is part of the northern shore of the Upper Peninsula. The agricultural weather network was estab- lished in 1962, making it necessary to estimate the remaining freeze dates prior to 1962 by linear regression. Table 10 contains a list of the agri- cultural weather stations (Y), the climatological station(s) that it was correlated with (X), the inter- cept, the correlation coefficient (r), the correlation 91 TABLE 10 COMPLETE LISTING OF PREDICTIVE EQUATIONS CALCULATED TO ESTIMATE MINIMUM TEMPERATURES FOR SELECTED AGRICULTURAL WEATHER STATIONS IN MICHIGAN (Y = mx-tb) Y X Slope Intercept r* r2 n** (n0 (b) 1.+ Belding Alma 1.07 -2.46 .95 .90 212 2. Belding Greenville 1.03 - .18 .95 .91 225 3. Edmore Alma 1.02 -2.33 .95 .91 212 4.+ Edmore Greenville .99 - .43 .95 .90 225 5.+ Fremont Newaygo 1.00 5.34 .86 .73 284 6. Glendora Benton Harbor 1.01 -1.60 .84 .70 180 7.+ Glendora Dowagiac .81 7.32 .86 .74 196 8. Glendora Eau Claire .92 2.16 .78 .61 196 9. Glendora South Bend .88 2.39 .79 .63 179 10.1 Graham Grand Rapids 1.06 - .38 .92 .85 227 11. Grand Junction Allegan 1.03 -2.15 .76 .58 227 12 . Grand Junction Benton Harbor 1 . 19 -10 . 47 . 81 . 6 5 180 13 . Grand Junction Bloomingdale . 91 . 4 0 . 82 . 66 236 14.1" Grand Junction South Haven 1.21 -10.41 .83 .70 216 15.+ Holland Holland .95 1.41 .91 .83 223 l6.+ Hudsonville Grand Rapids 1.02 1.19 .90 .81 227 17. Kewadin Frankfort 1.17 -5.47 .86 .74 268 18. Kewadin Mackinaw City 1.01 2.18 .75 .57 311 19.1 Kewadin Traverse City .93 3.85 .88 .78 266 20. Lake Leelanau Frankfort 1.13 -4.87 .82 .67 268 21 . Lake Leelanau Mackinaw City 1. 00 3. 25 . 72 . 52 311 2251’ Lake Leelanau Traverse City .88 4.23 .87 .75 266 23.+ Ludington Ludington .96 3.49 .86 .73 256 24. Mapleton Frankfort 1.13 -4.81 .82 .71 268 25. Mapleton Mackinaw City .98 2.41 .71 .51 311 26.1 Mapleton Traverse City .92 3.25 .89 .79 266 27.1 Mears Hart 1.01 .26 .91 .83 236 28. Paw Paw Kalamazoo .54 14.89 .68 .46 183 29.+ Paw Paw Three Rivers 1.03 - .92 .88 .77 199 30.+ Peach Ridge Grand Rapids 1.00 1.42 .90 .82 227 31. Sodus Eau Claire .94 4.27 .77 .59 196 32.+ Sodus Dowagiac .83 9.17 .82 .67 196 33. Sodus Benton Harbor .95 3.30 .75 .57 180 34. Sodus South Bend .85 6.09 .74 .54 179 35. Watervliet Benton Harbor 1.07 -4.49 .83 .69 180 36.+ Watervliet Dowagiac .90 3.17 .89 .80 196 37. Watervliet Eau Claire .99 - .82 .79 .62 196 38. Watervliet South Bend .95 — .98 .79 .62 179 *correlation coefficient +predictive equations chosen **number of observations 92 coefficient squared (r2), and the number of observations (n). The observations used to develop these relationships cover a 5-year period, 1972-1976, for the months April, May, and June. Only nights when the minimum temperature was less than or equal to 45°F were chosen. The freeze statistics for the selected agricultural weather stations are contained in Appendix C, Tables C1 through C17. The freeze statistics for the 36°F threshold were not mapped. The predictive equations chosen to estimate the minimum temperatures for selected agricultural weather stations were characterized by correlation coefficients that ranged between .86 and .95, except for Sodus and Grand Junction, which were lower. Belding and Edmore each showed correlation coefficients of .95, regardless of whether Greenville or Alma was chosen to construct the regression line. Glendora, Sodus, and Watervliet, which are located in the extreme southwestern area of the state, presented some problems as a set. Eau Claire, Dowagiac, Benton Harbor, and South Bend were all tried as predictors for these stations. Dowagiac was finally chosen because it showed the highest correlation co- efficients for each of these stations. Frankfort, Mackinaw City, and Traverse City were each correlated with the three agricultural network stations in the northwest Lower Peninsula: Kewadin, Lake Leelanau, and Mapleton. Traverse City was subsequently chosen as the predictor for these agricultural network stations. Finally, Grand Junction was the single most difficult 93 station for which to predict, and South Haven was selected over Allegan, Benton Harbor, or Bloomingdale. Table 10 lists the predictive equations for estimating minimum temperatures for selected agricultural weather stations from climatological stations, and their correlation coefficients show a wide range. Belding's correlation of minimum temperatures with Alma, and Grand Junction's correlation of minimum temperatures with South Haven were the best and worst correlations, respectively. The individual sample variance of each of these stations was compared to the sample variance of the climatological station that it was correlated with. The decision rule for testing the equality of the variances (Neter and Wasserman, 1974) conclude where is if F(d/2;n -l,n 2 2 1 2.1) i s1 /s2 :_F(l—d/2,n1-l,n2-l) (3.10) 2 = 022; otherwise conclude C2: 012 # 02: sample variance of the sample variance of the population variance of station population variance of station number of observations station number of observations station agricultural station climatological station the agricultural the climatological at the agricultural at the climatological Choosing the level of significance (a) to be .01, 94 the appropriate F-statistics are F(.005,29,29) = .038, and F(.995,29,29) = 2.63. For spring and fall, 32°F, the variances for all four pairs of stations were found to be equal. The assumption that the variances of the freeze dates were homogeneous was tested by using Bartlett's 2 2 2 2 x test (Bethea et al., 1975). Let sl , $2 , ..., sk be k independent sample variances corresponding to k normal populations with means “i and oiz, i = 1, 2, ..., k. Suppose n1-1, n2-1, ..., nk-1 are the degrees of freedom. 2 k k 2 X = (1n V) 11:1(ni-1) -ifl (ni-l)ln Si /L (3.7) where V = 18m. -l) 5.2/]; (n.-l) (3.8) i=1 1 1 i=1 1 and k L = l + 3 k{-l) jilfig%TI ' k l (3.9) X (n -1) i=1 1 The test statistic (3.7) has an approximate x2 distribution with k-1 degrees of freedom when used as a test statistic for Given k random samples of sizes n1, n2, ..., nk, from k independent normal populations, the statistic x2 can be used to test Ho’ The rejection region for testing H0 is 95 .Eooooum mo moonmoo onu me E can .HIme m : ononz .pomo mm3 Acuma .maumwoumv mamm.m+£vmnmm.o Adlxv x m mHoEu0m onu .ooa A Eooooum mo mooumop mom oaumfiuoum mx onu ouoaooamo 09a ummoom . . . . . . . . . .umeHao am we OH Hm om mm me me mm am em me am om mm as mm mm as a .oauma ooaanaoo oomoom Hm.em we.am mb.ea mm.em Na.ma mm.aa mm.aa mh.mm oo.me mm HooaooHo nemsaao m~.eom He.bma em.eaa ea.ame mm.oaa es.mea ms.mm~ oe.mmm em.maa aoa rowmwm . . . . . . . . . Honou mm om am am am ma as am Ho ma so mm em a mm mm as mm as (Hooauoa ee.~mm we.eaa om.ea ma.mea ms.mm eo.eaa ee.emm mo.~mm om.oma ma Hmoaooao (basaao mm mcaumm om mcaumm om mcflumm om magnum Danna Eooooum Ha Ha HH HH uueum mo pom euro mOON mOvm mOmN mon mx mooumoo lac. u so summom aaoHooaoeaquo oza qamoeaoonoa DMZHmZOU mmB 02¢ .BmmmDm Q¢UHOOAOB mmB m0 MEHmZmUOZOm mmB mom Emma Nx m.BBmQBm 2 X X(k-1),l-a° The x2 statistic was calculated using 3.7 through 3.9 for the 93 climatological stations, the 17 agricultural stations, and the combined set (LU)stationsL at 4 different temperature thresholds for both spring and fall. The indiv— idual variances of the freeze dates were obtained from the computer output of the freeze statistics.If the calculated value for x2 is greater than the tabled value of x2 given in column 1 of Table 11,then the hypothesis of homogeneous var- iances is rejected. For the 17agricu1tural stations,the hy- pothesis of homogeneous variances is accepted for all but one of the 8 data sets (32°F,springL.For both the climatological stations and the combined data set, the hypothesis of ho- mogeneous variances is rejected for six of the 8 data sets. This result supports inclusion of the individual variances in the freeze program. However, by selecting 24 climatolog- ical stations that are in closest proximity to the agricul- tural weather network (referred to as "climatological subset" in Table 11), the hypothesis of homogeneous variances is accepted at all temperature thresholds. Combining the agri- cultural network and the climatological subset, the hypoth- esis of homogeneous variances is accepted at all but two temperature thresholds (32°F and 24°F, spring). The number of agricultural network stations that "fit" the climatological analysis (1. e., the inclusion of this data would not have altered the analysis) was typically between 8 and 10. The agricultural stations that exhibited the largest deviations from the climatological analysis 97 were Grand Junction, Watervliet, Fremont, and Kewadin. Referring to the 5% probability dates of the 28°F in the fall, Grand Junction's date was 3 weeks earlier and Watervliet's date was 2 weeks earlier than the climatolog- ical analysis would otherwise indicate. (Both of these stations are colder in the spring as well as the fall.) The three agricultural stations in Berrien County are all nearly equidistant from Lake Michigan. Perhaps Watervliet's proximity to Paw Paw Lake accounts for it being cooler than Sodus or Glendora. Fremont apparently was warmer in both spring and fall, which may reflect the fact that Newaygo (the station with which it was correlated) is located in a low-lying area, in the vicinity of a reservoir. As an extreme example, the 95% probability date of the first 28°F in the fall is more than 2 weeks later than would be expected in comparison with the climatic analysis. Kewadin is also warmer in both spring and fall. The 5% probability date for the last 32°F in the spring was nearly 3 weeks earlier than the climatological analysis would indicate. It is nearly surrounded by water, with Grand Traverse Bay to the west, Elk Lake and Birch Lake to the south, and Torch Lake to the east. Its proximity to water in conjunction with its elevation (710 feet compared with 580-foot datum at Grand Traverse Bay) that allows for cold- air drainage moderates the temperature decrease during 98 freeze nights. 2. Vineyard Observations A. Temperature Profiles. An important contribu- tion to the grape industry of Michigan in this multi- faceted study is the characterization of the nocturnal microclimate in two vineyards. Results of this three year study are summarized in Table 12, in which the approximate l to 15 meter temperature inversions are reported. To depict the range in the data, the average 1 to 15 meter in- version (Y),the standard deviation (SD), and the number of TABLE 12 DISTRIBUTION OF APPROXIMATE 1 TO 15 METER TEMPERATURE INVERSIONS ACCORDING TO 1 METER TEMPERATURE (1978-1980) (TEXAS CORNERS, MICHIGAN) 185%). Y SD n (iFgefql'lreontcayl) (exciiiifignc’éeor) 24-25 5.5 1.4 4 1 26-27 7.1 3. 3 28-29 10.6 3.3 15 5 30-31 6.0 4.0 26 9 12 32-33 4.4 3.9 12 4 34-35 7.7 3.8 14 5 36-37 4.0 3.3 10 3 38-39 5.6 3.0 41 14 19 40-41 5.8 3.0 23 8 10 42-43 4.2 2.0 32 10 15 44-45 4.8 2.9 30 10 14 .2 46 4.2 2.9 84 28 99 observations in each category (n) are reported. Two visual summaries in the form of cumulative distribution functions (CDF) were then constructed from this table. Figure 30 is the CDF of inversion strength with respect to 1 meter temperature, neglecting the occurrence of in— versions when the 1 meter temperature is above 45°F. Figure 31 is also a CDF which shows the distribution of 1 meter temperatures when inversions of greater than 1 F were occurring. The resolution of the two instrumentation sys- tems, the Leeds and Northrup potentiometer in the 1978— 1979 data (Kellogg vineyard), and the Kaye Instruments digital potentiometer for the 1980 data, were quite different. All 24 channels of the Leeds and Northrup potentiometer were used to record temperatures of six heights: surface, 1.0, 3.7, 8.0, and 15.2 meters. Six sets of four dots that corresponded to the temperature at each height were recorded on a Fahrenheit strip chart every half hour. Based upon the location of these dots, the most—likely temperature to the nearest 0.5°F was noted. The digital instrument, however, was specifically programmed to record temperatures (OF) at the six heights to the nearest o.1°r: 1.0, 2.9, 6.4, 9.8, 12.8, and 17.4 meters once each hour. The inversions that were obtained from this set of data were rounded off to the nearest 0.5°F to be consonant with the resolution of the Leeds and North- rup potentiometer. Figures 32 through 46 are 15 graphs of temperature 100 mOm a W mEoB E H cos: Ahoy numcouum conno>cH .om ousmam Ha 0H m m h m m v m N H . a a 1 a a q a 41 . cm I LQOH (%) Kouenbelg eArieInmna 101 .mcflunsooo ouoB moH M mo mconuo>ca con; E H um Amov ousumuomEoB .Hm ousmflh we «v Nv ow mm mm vm Nm om mm mm a 1) 4 a) q 1 d 4 J 4 d A A). ON 3 n m n T— D. 1 To A ov a J I a b n a m cm .A % om OOH 1023 .QOu um poum0at2w uc>co CDOHU paw .co_uoouflo tcwz .toocm pcfi3 modem: cacao .ccoazofiz .muocuou moxoe um owed .hHIoH Hanna :0 oHLLCLL oncomuoceou cum>ocfi> .mm ouscwm Asuao mess 5 5 5 5 S .D 5 .3 5 5 5 5 5 5 5 5 5 5 1 4 1 4. l 4. 1 A. .1. 4. l 4. 1 4. l 4. l 4 7 6 6 .3 .3 4. 4. 3 3 2 2 l l 0 0 3 3 2 (1 10b 0 0 0 0 D D D 010 0 p D D 2 2 O em 0 AV mm .0 Av mm 0_ Au 0 on “w n_hw n._o no nu nvnu an a .A _u nu no .9 mm o o A. A An a cane 0A0 oaoo too a? .00) 400 (O (0 mm mm (a ) aznqezadmam He we me E NHL. 3 E o.m4 mv E p.mn- we E ciao he ooomusmo me O 1(13 .QOu um powwowpcfl uo>co psofiu cam .cOauoouap pew3 .poomm .muocuoo moxos um ahmfi .e ~.mH.. a .e.aa. e. p.mHu a .o.anv oUMuusmO 0715 DAO Afimqv 05¢? 5 4 6 9 case 0615 5 4. .3 0 C) 5 l .3 0 1.4 E] 0445 10415 C) 46 .Al 0345 E] .A I) 4' E1 (3 .maahfi Haud< :0 oHMLOMQ ousumuoceou 0315 pcfl3 oedema pcwuo pum>o:a> 0245 .11 0215 0145 ElC) 0115 0045 .mm ousowm 0015 2345 2315 2245 mm mm hm mm mm on an mm mm em mm on hm mm mm ow Av me me cc mv .anoaroaz (30) sinusiadmam 101+ .ocu um ooumuflpcd uo>oo psofio tcc .cowuoopdc UCEB .Cccom c:_3 mtwacz Cccuc .cmcwcowz .mpocuou mmxoe um mhoa .mfinmfi HALQ< co QHHCOLQ obsbcuccecu ttm>ocfl> .vm oESOML Aemdv cede .3 .3 .3 3 3 3 .3 .3 5 p3 3 .3 5 .3 '3 3 .3 .3 1a4l4l4l4l414l41414. _/66.334433221100332 000000000000000222 nv O 0000 nvnu Av 00 o oo 0 o O o 0 We. o 0000 D 00 0 DD 00 O D 00 O D D 0 AA 00 D D c A D A A n- . AA .0 A .U a... .0 A O 0 AA E ~.m~.. A A A .A A E o.m_< NU .. I..'_. A £1.40 & o E o.~nv n. _O .. oommusvo O. em mm mm hm mm am on an mm mm em mm on on mm mm 0v av me me we we (50) ainqezadmal 105 .QOu um soumon02. uw>oo vsono Ucc .co.uooL.c 1:.3 .cgcam cc.3 chAQE cccuo .cmc.£0.z .muwcuou mmxmh um mhon .omnm~ Hfiua< co 0H.ucLa ousumuanc» cpm>oc.> .mm wusv.u .Ema. ce.e 55555.355555555555.3 14141414141414.1414 766554433221100332 000000000000000222 nu nu nu.o n.nu nu nu nu nu nu n. nu O nu n. n_.u nu nu n. nu nu nu .0 Au nu 0. 0. n. n. nu O. .u .0 .0 A. A n_.u .u nu A A nu.u .u n. A A n. .u .U nu .0 n. E . .AAAm.0 nu n_nu .U _U m mH0. 0. .0 e32 A. AA“. can 2.25 W0 AA . Au.0 E o .nu .0 campusmo AA am on mm mm mm on mm cm hm mm on ow Hv me me vv me we be we ¢v om (do) aanexadma; 106 .mou um Umumoflccfl um>oo 090.0 was :0.u00u.© 6:.3 .Ucmam ccw3 mv.amz ncmuc .muwcuoo mmxme um whoa .mmumm Hfiuad co wfimuCuQ musumquEcu vum>mcfl> .om muscwu .quu wEnE 5555.3.355555555.3555 414141414141414141 66.3.344332211003322 000000000000002222 O nu 0 Au 0 n. O nu nu.0 nu nuAU.O nu nu o O O O o O 0 000 000 O nu Au nu nu 0. n. D on a E A one 0 Damn. nu A nu nu 0.A A .A A ...A A .A A .0 A .0 .-.0 .v 0. .0 AA 0. A Aflfi .0 0. 0. .0 A AA 0. .0 0. A 0. .0 E ~.mn0 E c.m4 E p.mnu E o.~nu wommusmo ..A em om hm mm on De He me me vv me we 5 v we ¢v om .cmu.:u.2 (do) aznquadma; 107 .mo» um cwumofich uw>ou 630.0 cam .co.u00u.n cad: .cooaw t:_3 mc.acz cccuu .cwvnnu.z .mumcuou mmxwe um ahan .H >mzuom H..Q< co cHMuOua cpsuwucaeou cum>oc.> .bm wpso.m .EMQV weak .3 5 5 .3 .3 5 .3 5 .3 .3 5 .3 .3 5 .3 l 4 1 4 l 4 l 4 l 4 l 4 l 4 l 5 4 4 3 3 2 2 l l O 0 3 3 2 2 0 o 0 O 0 0 0 0 0 0 O 2 2 2 2 O .O O. .O O O O O O _u 0 O nu a m n.” E o O D O O D O A A 0 WM A A D _u 0 . A A A .9 O 0. A rp o o o A A m” .0 .0 nu O n. .0 A 0. E~.mH0 O E o.m 4 ._...mn. o o E o.~nu mommusm O vmmdomwbmeMN—cowmhwmem QQQGVMMMMMMMMMMNNNNNNN (go) aznaezadmam 108 .000 um 00000.00. u0>00 050.0 0:0 ccfluucudt tcdz .Cocam c:.3 mtmgcm 1:000 .cao.;o.z .muocuou mcxwk um whoa .NIH >0: :0 0..»0.0 ousumuvaEcu cum>¢cd> .mm 0.:0.m .suqu 05.9 .3555555555555555 44.141414141414141 66.3.3443322110033 0000000000000022 nunu mm Au 0 cm nunu ow nu aflu 0 a. nu n. .q A E a A© o o 2m . w 0 n A nu nu nunu nu men. @ 00 m a m— 09:) o .0 nu.O nu A “M A 0 @067. 3 A a..A_-v.. 5 me 2...... o 0.000 E o.~..0 . A .0 n. E o m.< E p.mnu E o.Hnu we momwusmo 109 .000 um 00000000. 00>00 0:000 0:0 .:00000000 0:03 .0000m 0:03 m0000z 0:000 .:00.:00: .0000000 mmxwfi 00 0000 .01m >0: :0 000.0000 00000000E00 000>0:.> .0» 000000 .500. 05.9 .35 .3 .3 .3 .3 .3 5 .3 5 .3 .3 .3 5 .3 .3 .3 .3 414141414141414141 66.3.344332211003322 000000000000002222 0 mm nu O O on O nu O can 0 00 .m 0 .O nu.u O 0 AA 0 0000 o 000 an; 00 AD 0 0 .m 0000 0 00000 an AAA .0 m 00000600000 Sn 0 E ) 0 .0 mm 0A 0A 0 00:00Ao 2. E~.m00 me 5.0.20 000 Eo.w¢ . . A we E h mnu E o.an I:- . $0000.50 A we 110 .000 00 0000000:. 00>00 0:000 0:0 .:0.u000.0 0:03 .0100m 0:03 00.000 0:000 .:0o.:0.z .0000000 00x09 um omo. .H >0Zucm H000< :0 0H00000 00000000E00 000>000> .ov 000000 ..mq: 05.0 00000000000 33333333333 5437-1032109 00000022221 0 0 00.. o 0 0m0m oo 0AAOO 0” m o n A D nu MW A A C. A nu 00 00 A 00 0 00A _. C 00 ... .A =.e.>:0 =.m.~a0 E mid E «.00 =.a.~nu 0.0:HO -\\P ..UIIAW mm :0 av me me 00 me 00 be we av om Hm mm mm vm cm hm mm (30) alnqezadmam 111 .QOu um 0ouwufl0cfi u0>00 0:0HU 0:: .cofiuocufi0 0cw3 .00;;m 0cm3 m0wacz 0::uc .cccw£c_z .mumcuou mmxme uw omoa .huw >mz :0 oflfiuOMQ ousumuoaecu cumxmcm> .Hv opscflm E v.5HO. E m.~HO £5 E E E w.m¢ 0.00 m.~nv o.HO Afimqv wefib 0000000000 3333333333 6543210321 0 O 0 O 0 0 0 2, 2 n1 .0 go On. A nu O mu m 000 00:. oo o 0* 1.. 4n: 0* m a f 2 w cm a. Lm cm hm mm mm ow av Ne mv ve mv we be me me om Hm mm mm vm mm mm (30) axnnpxadmal 112 .Qou um kumUWCCM um>ou OSOHU 6:0 .ccmuoouflc v:_3 .cccam ccfl3 mt_mcz cccuo .cmvwzowz .mumcuou mwxcfi um omafi .mtm >cz cc cfifimoga Chaucucceou vuc>ocfl> .mv cusofim Ahmqv weak 00000000000 33333333333 6.3432103210 0000000222 0. 0. Au 0 fig ©o. .0 n— o O . ”a A O. A O O .M O.“ .u. E v.5a.’ E m.NH 0 E3 E E5 E mad Two ado ago .X .\ hm am an on an mm mm «M mm mm hm an an ov av Nv me we we we (30) aznnezadme; 113 .aou um cwumoflccn uw>oo anonu ccm .conuuouwt CCWB .vccam can3 mcwamz vcwuo .muwcuou mmxmfi um ommn .onna >mz co onwmoua upsuwumasmu vum>m2m> .mv auscwh Cains; O O 0 O 0 0 O O 0 0 3 3 3 3 3 3 3 3 3 3 6 5 4. 3 2 l 0 3 2 l O O 0 O O 0 0 2 2 2 O nv O O nu O nu o o. .u nu nu nu o o w a 0 Ha a .m a m, . o .2“ av n. L _O _O “u u. nu .0 . m nu O O A nu O. A EYE. O 0 5920 Eméc O 2'60 E m.~nv E o.n O wm hm mm on ow av Ne mv vv me we hv we av om Hm mm mm vm mm mm .cmofisufl: (do) aanpzadmaL .QOu um vmumonocfl uo>ou csono ccm .ccnuumumc ccnz .cooam Tcd3 mcflacm scape .cccfizofiz .mumcuou mmxwfi um cmwn .vn >cz :0 anamopa musumuoaeou cum>mcm> .vv cuscwk m Asmq. can? 0 O 0 O 0 3 3 3 3 3 6 .3 4 3 2 0 O 0 0 0 © on A 3 o o 6 o o H A 2L 6 m 0. AM A m I. 00 0. 3m 1 © 3 3v A SH 00 3. 2 ..SO a 92 o 2. s 92 e v.5 E a.~0 5 ago 115 .Qou um cmumowch uw>oo cacao can .cofiuowuwc c:_3 .cocam vcflz wcwamm vcwuo .cmvflcuwz .mumcuoo mmxwe um omafi .mHIvH >mz co mHMuODQ musumuoaewu cuc>mcfi> .mv muswflt 2&5 cs; 0 0 0 O 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 6 5 4. 3 2 l O 3 2 l 0 0 0 0 0 0 0 2 2 2 mm m o a o 2” D O O 0 cu I A O 3 fl 0 A D My 0 u A 2 ,w nu n. no a I. J I. 0. .Au we W pm me m a . o 2 ... o o ) O 3 ..w _I h" we 0 3 cm 0 E «.2. S E m.-.. E m.mAd E e60 e a.~0 E o4 O 116 .QOu um vmumoficcd um>oo vsofiu vac .ccfiuuop_t saw: .cozzm ccq3 mcfiacm vacuc .cmmwcufi: .muwcuou mmme as omoa .cfinm— >cz cc ofimucup cgsumuoaeou tum>ocfl> .cv wuscwm AEmQ. wEmF E v.5:0 E m.-. E E E E m.o< e.wD c.90 o.~0 000000000 000000000 6.3432103?— 00000007.2 o 00 O .u o A A w «NA 0 _u _u 0 0A ©o A 0 00D 0 _O A O n. 0 Guam .0 o oufl oo {DO'EJ A r0 f0 «\0 V an ov He mv me vv me me he av av om Hm mm mm em mm cm (50) aznnexadmal 117 versus time for each height during selected evenings. The criteria for selecting the evening were that the minimum temperature at the l-meter level was 45°F or less, and that inversions greater than 1.00F were consistently occurring. As a source of information for the prevailing weather conditions during the chosen evenings, the "Local Climatological Data" for the National Weather Service office at the Kent County Airport at Grand Rapids was consulted. The data available from this publication are listed in Tables 13 and 14, and contain the following information: hour, sky cover (tenths), ceiling (hundreds of feet), tem- perature and dew point (OF), relative humidity (percent), wind direction (tens of degrees from true north) and wind speed (knots). For the time period 10 p. m. through 4 a. m. for 8 of the 15 nights, the cloud cover at Grand Rapids was 3/10 or less. Most of the cloud cover observations during these nights were reported as clear skies. The first four graphs were the consecutive nights April 16 through April 19, 1979, when data were collected during the passage of a particularly strong high pressure system. Calm winds were reported during three of these nights. The night of April 30, 1979 was the coldest recorded at Grand Rapids for the 15 nights in the case study. The 4 a. m. temperature was 24°F (which was also the minimum temperature), and the 15.2 m temperature was 118 TABLE 13 WEATHER CONDITIONS AT GRAND RAPIDS FOR SELECTED NIGHTS DURING THE SPRING OF 1979 Sky Ceiling Rel. . (3)3369?) Hour Cover (1005 of Temp. Pgivrzt Hu- “Sir? Speed (Tenths) ft.) midity ' Ap. 16 10 p.m. O Unlim. 44 36 74 33 8 17 1 a.m. 0 Unlim. 40 34 79 35 9 17 4 a.m. O Unlim. 36 31 82 33 7 17 7 a.m. 0 Unlim. 34 30 85 36 6 Ap. 17 10 p.m. 0 Unlim. 42 28 58 01 6 18 1 a.m. O Unlim. 39 27 62 00 0 18 4 a.m. O Unlim. 34 27 76 28 4 18 7 a.m. 0 Unlim. 35 28 76 35 4 Ap. 18 10 p.m. O Unlim. 43 30 6O 17 5 l9 1 a.m. O Unlim. 41 30 65 00 0 19 4 a.m. O Unlim. 34 30 85 08 4 19 7 a.m. 6 Unlim. 37 3O 76 10 3 Ap. 19 10 p.m. 3 Unlim. 50 34 54 00 0 20 1 a.m. O Unlim. 44 35 71 13 5 20 4 a.m. 2 Unlim. 44 33 65 16 4 20 7 a.m. 0 Unlim. 41 33 73 15 6 Ap. 22 10 p.m. O Unlim. 50 40 69 28 4 23 1 a.m. O Unlim. 46 40 80 15 4 23 4 a.m. O Unlim. 42 39 89 12 3 23 7 a.m. 10 Unlim. 59 40 50 16 5 Ap. 30 10 p.m. O Unlim. 37 30 76 30 7 May 1 1 a.m. 0 Unlim. 32 29 89 05 10 1 4 a.m. 0 Unlim. 29 26 89 21 4 1 7 a.m. 3 Unlim. 31 29 92 00 ()(GF) May 1 10 p.m. 7 Unlim. 44 37 76 11 6 2 l a.m. 10 150 46 35 66 13 9 2 4 a.m. 10 150 46 35 66 12 10 2 7 a.m. 10 120 45 34 65 12 9 May 3 10 p.m. 0 Unlim. 46 33 61 33 5 4 1 a.m. 4 Unlim. 41 33 73 35 6 4 4 a.m. 8 Unlim. 38 33 82 07 4 4 7 a.m. 10 250 38 32 79 05 7 SOURCE: Local Climatological Data for Grand . Rapids, published by the USDC/NOAA/EDIS National Climatic Center 119 TABLE 14 WEATHER CONDITIONS AT GRAND RAPIDS FOR SELECTED NIGHTS DURING THE SPRING OF 1980 Sky Ceiling Rel. Date Dew Wind Hour Cover (1008 of Temp. . Hu- . Speed (1980) (Tenths) ft.) P01nt midity Dlr' Ap. 30 10 p.m. 8 50 50 48 93 27 3 May 1 1 a.m. 6 90 45 45 100 22 3 1 4 a.m. 10 9O 48 48 100 23 5 l 7 a.m. 10 45 49 49 100 25 5 May 6 10 p.m. 3 Unlim. 51 32 48 33 7 7 1 a.m. 2 Unlim. 44 35 71 30 10 7 4 a.m. 7 32 4O 33 76 31 11 7 7 a.m. O Unlim. 41 33 73 29 15 May 7 10 p.m. 2 Unlim. 4O 29 65 28 7 8 1 a.m. 10 100 38 33 82 25 6 8 4 a.m. 10 110 39 34 82 23 5 8 7 a.m. 10 44 4O 33 76 34 8 May 8 10 p.m. 8 60 42 32 68 28 9 9 1 a.m. 6 Unlim. 34 30 85 29 5 9 4 a.m. 10 30 37 33 85 23 4 9 7 a.m. 5 Unlim. 39 34 82 26 4 May 9 10 p.m. 0 Unlim. 44 34 68 11 4 10 1 a.m. 0 Unlim. 41 33 73 16 6 10 4 a.m. O Unlim. 43 33 68 16 7 10 7 a.m. 8 Unlim. 49 34 56 19 9 May 14 10 p.m. O Unlim. 42 37 83 25 5 15 1 a.m. 2 Unlim. 39 36 89 00 0 15 4 a.m. 10 60 43 4O 89 25 5 15 7 a.m. 10 40 45 42 89 35 8 May 15 10 p.m. 0 Unlim. 51 43 74 02 4 16 1 a.m. O Unlim. 45 40 83 06 3 16 4 a.m. O Unlim. 42 38 86 11 4 l6 7 a.m. 0 Unlim. 49 42 77 10 6 SOURCE: Local Climatological Data for Grand Rapids, published by the USDC/NOAA/EDIS National Climatic Center 120 3OOF, indicating a 60F inversion. The 7 a. m. Grand Rapids wind speed was reported as calm. The ceiling values recorded in Tables 13 and 14 were pertinent to the interpretation of vineyard temper- ature profiles. A four-degree inversion was initially recorded in the vineyard while the 10 p. m. Grand Rapids cloud cover was 7/10. Subsequent Grand Rapids observa- tions were overcast skies, accompanied by lower ceilings as middle-level clouds (altostratus) moved in. The inversions after midnight were all very weak. Wind-machine trials were performed on the night of May 3, 1979 and the results of these trials will be dis- cussed in the next section. The Grand Rapids LCD listed 0 and 4/10 cloud cover at 10 p. m. and 1 a. m. respectively. Vineyard temperature inversions were approximately 30F until 2:15 a. m., when the 1.0 m and 15.2 m temperatures coincide. Visual observations in the vineyard confirm that skies became overcast at about this time. The sky condition retrogressed to partly cloudy in the early morning hours, and the temperatures returned to modest inversions. Mostly cloudy conditions prevailed on the night of April 30, 1980, and skies became completely overcast during the following morning. Nevertheless, a 70F temperature inversion was recorded in the vineyard at 11:21 p. m. This coincided with a transition period at Grand Rapids from a 5000-foot ceiling at 10 p. m.(8/10 cloud cover) 121 to a 9000-foot ceiling at l a. m. (6/10 cloud cover). Vineyard inversions oscillated between 30F and 5.50F until 6:30 a. m., when it was less than 10F. The ceiling at Grand Rapids lowered to 4500 feet at 7 a. m. The wind speeds were light throughout the course of the evening, varying between 3 and 6 knots. Unusually brisk northwest winds characterized the night of May 6, 1980. The largest vineyard inversion occurred at 10:30 p. m. when the 1.0 m temperature was 50°F, and the 17.4 m temperature was 550F. The second largest temperature inversion was not observed until 6:30 a. m. the following morning, when the minimum vineyard tempera- ture of 34°F was recorded. The Grand Rapids wind speed at 7 a. m. was 15 knots, which accounts for a relatively low temperature inversion despite clear skies and a near- freezing temperature. No inversions existed after 1:30 a. m. on the morning of May 8, 1980, when temperatures rose in the vineyard and at Grand Rapids during the early-morning hours. The largest temperature inversion of 5.50? was once again recorded at 10:30 p. m. All of the sky cover observations at Grand Rapids for this morning were of overcast skies. Perhaps the most significant vineyard temperature observation occurred during the morning of May 9, 1980. For the hours of 8:30 p. m. through 12:30 a. m., vineyard O I 0 temperature inver31ons were never greater than 2 F. The 122 Grand Rapids 10 p. m. wind speed was 9 knots, accompanied by a 6000-foot ceiling. At 1 a. m. the wind speed diminished to 5 knots and the ceiling became unlimited. Vineyard temperature inversions subsequently increased between 2:30 a. m. and 4:30 a. m. with a temperature inversion of 60F and a 1.0 m temperature of 27.50F. The last three evenings of the case study were characterized by clear skies and unlimited ceiling, with the exception of the latter part of the morning of May 15, 1980. Very strong temperature inversions highlighted the evening of May 9, 1980, with an 80F to 9.50F temper- ature inversion sustained for 6 hours. The minimum vine- yard temperature that morning approached critical levels at 2:30 a. m., when the 1.0 m temperature was 35.50F and the 17.4 m temperature was 45°F. The night of May 14, 1980 was quite unique be- cause the 1 a. m. Grand Rapids observations were 2/10 cloud cover, unlimited ceiling, and calm winds, but at 4 a. m. rain showers were reported. A 90F temperature in- version was recorded at 11:30 p. m., with a 1.0 m reading of 39.50F and an 80F temperature inversion at 2:30 a. m. occurred with a 1.0 m reading of 36.50F. Warm advection was evident after this time, as the 5:30 a. m. 1.0 m tem- perature was 44°F. The final night of the case study was May 15, 1980, 123 and a 40F to 7.50F temperature inversion was sustained for 10 hours under clear skies and an unlimited ceiling. The minimum 1.0 m temperature was 39°F at 5 a. m., while the 17.4 m temperature at this time was 46°F. An examination of the data presented reveals sev- eral occasions when the nocturnal temperature inversions exceed 10°F. During the nights of April 17 and 18, 1979, inversions of 12°F were recorded, and an 11°F inversion was noted during the following night. The largest temper- ature inversion observed (during the course of this study) was 14°F, which occurred on May 22, 1980 at 4:00 a. m. while the 1.0 m temperature was 46°F. A 12.50F inversion had been observed at the previous hour. At 1:00 a. m., May 27, 1980, a 13.50F temperature inversion was recorded, with 10.50F temperature inversions one hour before and one hour after that observation. Table 15 is a comparison of the minimum temper— atures at Grand Rapids, Kalamazoo, and the 1.0 m height in the vineyard for the 15 nights in the case study that have been discussed. Indeed, under the dominating high- pressure system during the nights of April 16 through April 19, 1979, on two occasions the vineyard minimum temperatures at 1.0 m were 90F lower than the Kalamazoo minimum temper- ature. Although the vineyard minimum temperature would be expected to be lower than the minimum temperatures ob- served in the city, part of the temperature differences 124 TABLE 15 COMPARISON OF THE MINIMUM TEMPERATURES AT GRAND RAPIDS, KALAMAZOO, AND THE VINEYARD* FOR NIGHTS WHEN SIGNIFICANT TEMPERATURE INVERSIONS WERE OCCURRING Date Grand Rapids Kalamazoo Vineyard April 17, 1979 34 34 30 April 18 33 35 28 April 19 32 36 27 April 20 39 40 31 April 23 41 45 37 May 1 28 29 24 May 2 45 42 41 May 4 37 37 37 May 1, 1980 44 45' 39 May 7 36 32 34 May 8 36 39 35 May 9 32 34 28 May 10 40 41 36 May 15 38 42 37 May 16 40 44 39 *1.0 m height must be attributed to differences in height of measure (Kalamazoo observations are recorded at roughly 1.5 m). B. Wind-Machine Trials. Wind-machine trials were conducted on the nights of May 3 and May 15, 1979, in the vineyard owned by Peter Dragecivich (maintained with the assistance of Max Miller), located on South Sixth Street, Texas Corners, Michigan. The objective of this experiment was to establish the magnitude of the 125 temperature rise at various locations in the vineyard during the operation of the wind machine. Data that were gathered during this experiment are presented in Table 16, which lists the ambient tem— perature just prior to and during the wind-machine opera- tion. The numbers 1 through 15 correspond to the location of minimum-temperature thermometers throughout the vineyard, which were mounted on posts at a height of 1.5 m. Seven minimum thermometers, corresponding to numbers 1 through 7 in Table 11, were all located along row #49, which is oriented north-south. Station #1 was at the northern end, station #7 was at the southern end, and the wind machine is in the center of the row. Station'#4 was located approximately 1 m north of the wind machine. The other minimum-temperature thermometers along row #49 were placed an equal distance apart (30 m). The eight remaining ther- mometers were placed along an east-west perpendicular, four on each side of the wind machine beginning 12 rows from it (in the center of the vineyard). Stations #8, 9, 10, and 15 were located in rows #61, 67, 73 and 79, respectively. Stations #11, 12, 13, and 14 were located in rows #37, 31, 25, and 19, respectively. There are approx- imately 100 rows in the vineyard, and its approximate dimensions are 650 m by 180 m. The wind machine ran twice on the morning of May 4, the first time for 18 minutes between 3:50 a. m. and 4:08 a. m., and the second time for 15 minutes between 126 TABLE 16 AMBIENT TEMPERATURES OBSERVED BEFORE AND DURING WIND-MACHINE OPERATION AT 15 LOCATIONS (MINIMUM TEMPERATURE THERMOMETBRS AT THE 1% METER LEVEL) IN THE MILLER VINEYARD, SOUTH 6th STREET, NEAR TEXAS CORNERS, MI, THE MORNING OF MAY 4, 1979 (OF) Station Before Wind Machine During Wind Machine Number Operation (5:05 a.m.) Operation (5:15 a.m.) 1 37.0 38.0 2 37.5 37.5 3 36.5 37.0 4 35.5 37.0 5 35.5 37.0 6 36.5 37.5 7 36.0 37.5 8 37.0 37.5 9 36.0 37.0 10 36.5 37.0 11 36.5 37.5 12 36.0 37.0 13 36.5 37.5 14 36.0 37.0 15 36.5 37.0 127 5:15 a. m. and 5:30 a. m. A thermograph was placed beside the instrumentation in the Kellogg vineyard, and it continuously monitored the ambient temperature throughout the course of the evening. The instantaneous 1.0 m tem- perature on the instrumentation tower agreed with the thermograph tracing for this time period. Wind drift was determined prior to the first wind machine trial by a hot-wire anemometer between 1:50 a. m. and 2:45 a. m. A fairly light, steady breeze was observed, whose magnitude was usually from 1 to 2 m/s. The hot- wire anemometer malfunctioned at about this time, so that Table 16 only contains the ambient temperatures at 4:59 a. m. to 5:05 a. m., and the temperatures during the wind- machine operation, which began at 5:15 a. m. and ended at 5:30 a. m. Vine temperatures were periodically monitored at this time, and were consistently 1.50F below the air temperature. The results of the first wind machine trial (data is not shown) showed that temperatures actually decreased during its operation. Although the early-morning hours were characterized by weak inversions (the 3:45 and 4:15 a. m. temperature inversions were 2.50F), substantial wind drift hampered the wind machine's effectiveness. However, the results of the second wind machine trial can at best be described as promising. The wind drift was much less during this time, and was visually observed to be calm or extremely light. Several stations, particularly those 128 closest to the wind machine, recorded a temperature re- sponse of 1.00F to 1.5°P (Table 16). The 1.0 m temper- ature (ambient temperature) at 5:45 a. m. was 37°F, which was a decrease of 1.00F from the 5:15 a. m. observation, and the temperature inversion increased slightly to 2.00F at 5:45 a. m. Some additional observations of wind-machine gusts in a cherry orchard in Mattawan and in the Del Kellogg vine- yard near Texas Corners were recorded on the morning of May 16, 1979. The temperature fluctuations at 7 a. m. in the Kellogg vineyard (% km south of the Miller vineyard on 6th Street) were monitored by a hand-held digital thermometer. The series of temperatures that were the immediate temperature response to a wind-machine passage at several locations over a time period of 10 to 15 sec- onds were noted. The sequence indicated a rapid drop in temperature due to the influx of cold air at the sur- face, followed by a gradual rise. The time of arrival of the wind-machine gust from when the propeller blade was facing perpendicular to the observer, the time required to achieve maximum wind speed, and the end of the temperature cycle were also noted. The maximum wind speed of the gust decreased with distance from the wind machine, as evidenced by the quicker, more dramatic end to the wind-machine gust. Earlier that morning, temper— ature responses to the wind-machine passage were ob- served in Bob Kellogg's cherry orchard in Mattawan. 129 Both of the vineyards are very flat, whereas the cherry orchard contains numerous hollows. The first temperature cycle was recorded in a slight hollow, and, therefore, shows an apparently larger response to the wind machine, despite the fact that it is farther away from the wind machine than where the second observation was taken. That night, Mr. Kellogg observed (with his own minimum temper- ature thermometer at 1% m) a low temperature of 34°F in his deepest hollow, and was able to bring the temperature up to 400F by using the wind machine. 3. Minimum Temperature Forecasting for Selected Agricultural Weather Stations in Western Michigan The 4 p. m. temperature, dew point, and cloud cover at the Kent County Airport, Grand Rapids, during the years 1967 through 1976 were used to evaluate the Soderberg tech- nique. Only nights when the Grand Rapids minimum temper- ature was less than or equal to 45°F for the period April 15 through June 15 were used. The springs<1fl977 and 1978 were chosen to test the method. Figures 47 and 48 provide the forecast temperature for Grand Rapids during non-advective nights under fair skies (0 through 5/10 cloud cover at 4 p. m.), and under cloudy skies (6/10 through 10/10 cloud cover at 4 p. m.), respectively. For nights when the absolute magnitude of the 850 mb temperature advection was anticipated to be greater than 2°C, a correction equation was used to 130 adjust the Grand Rapids forecast. This was obtained by linear regression, in which Y was the correction that must be applied to the Grand Rapids forecast (CF), and X was the corresponding 24 hour 850 mb temperature change (0C). The resulting equation, which was based on the years 1967 through 1976, was: Y = .34x + 3.58 r2 = .76 (4.1) In testing the method, the 850 mb temperature change was already known. However, for Operational purposes, this parameter must be predicted by the forecaster. Table 17 contains the results of taking the average difference between the minimum temperatures at the indicated agricultural station and Grand Rapids. This table is used in conjunction with the Grand Rapids forecast to obtain a forecast for the selected agricul— tural weather station. The frequency distribution of weather conditions at Grand Rapids with respect to minimum temperature is reported in Table 18, where n represents the total number of observations. The term "weather condition" here refers primarily to cloud cover during the course of the evening. Clear skies (possibly with high cirrus) would indicate radiational cooling, and cloudy evenings would be classified according to whether cold or warm advection was occurring. Other criteria which played a role in this categorization were wind speed, wind direction, and the 24 hour 850 mb temperature change. 131 55‘ 45* a b 35 35 (O 4O 4 p. m. Dew POInt N U1 O) O b) U1 15 1 L 1 L 35 45 55 65 75 h 4 p. m. Temperature (0F) Figure 47. Minimum temperature (OF) for non- advection nights when cloud cover at 4 p. m. ranges from 0 through 5/10. Data from April 15 through June 15, 1967 through 1976. 132 55. 40 E: 35 0V 45 _ 4; 30 .,...| ,— O D“ 40 5 Q 35 " 2° 25 - ' 35 0.. V 25 _ 3o 15 ' 25 l L J J J L I I 4_l_ 35 45 55 65 75 4 p. m. Temperature (OF) Figure 48. Minimum temperatures (OF) for non- advection nights when cloud cover at 4 p. m. ranges from 6/10 to 10/10. Data from April 15 through June 15, 1967 through 1976. 133 TABLE 17 AVERAGE DIFFERENCE IN MINIMUM TEMPERATURES BETWEEN THE INDICATED STATION AND GRAND RAPIDS (APRIL 15-JUNE 15, 1967-1976) Station Radiational Cold Warm Cooling Advection Advection 1. Belding —1 l 2 2. Edmore 0 -1 -l 3. Empire -1 -2 -2 4. Fremont 0 l 1 5. Glendora 0 2 2 6. Graham 1 2 2 7. Grand Junction -2 1 0 8. Grant -2 1 1 9. Holland -1 2 2 10. Hudsonville 0 3 3 11. Kent City -1 0 2 12. Kewadin 0 -2 0 13. Lake City -3 -3 -2 14. Lake Leelanau 0 -3 -1 15. Lansing 0 0 0 16. Ludington 1 0 0 l7. Mapleton -1 -3 -l 18. Mears 0 l 19. Muskegon 1 0 20. Nunica -2 1 l 21. Paw Paw 3 4 22. Peach Ridge 2 3 23. Sodus 4 5 24. Traverse City -2 -3 -2 25. Watervliet 2 3 134 TABLE 1 8 FREQUENCY DISTRIBUTION OF WEATHER CONDITIONS AT GRAND RAPIDS, MICHIGAN ACCORDING TO MINIMUM TEMPERATURE (APRIL 15 THROUGH JUNE 15, 1967-1976) Min. . . Cold Warm Advective- Temp. Radiational Advection Advective Radiative 143 36°F 62% (88) 22% (31) 15% (22) 1% (2) 185 38°F 59% (110) 23% (42) 16% (30) 2% (3) 224 40°F 59% (132) 22% (50) 17% (39) 1% (3) 316 45°F 49% (156) 27% (84) 21% (67) 3% (9) The results of the minimum temperature forecast- ing scheme are presented in Table 19, which lists the average absolute error oftflmapredictions, with the standard deviation in parentheses. The most noteworthy result is that the average absolute error of the pre- diction for Grand Rapids, under radiative conditions only, is 2.480F. There are 31 radiative cases, and 18 advective cases. For all observations, the average absolute difference between the minimum temperature predictions using the Soderberg technique and the observed minimum temperatures was 4.100F. Some of the larger errors resulted because agricultural weather stations have been moved during the period that this study covered, or have been located on soils of low thermal conductivity. For example, Empire has been moved 135 TABLE 19 AVERAGE ABSOLUTE DIFFERENCE BETWEEN THE MINIMUM TEMPERATURE PREDICTIONS USING THE SODERBERG TECHNIQUE AND THE OBSERVED MINIMUM TEMPERATURE Station Obsefigjtions Raiiszive Advgfiiive 1. Grand Rapids 3.10 (2.31) 2.48 (1.71) 4.16 (2.83) 2. Belding 3.00 (2.63) 3.08 (2.64) 2.88 (2.70) 3. Edmore 3.66 (2.79) 3.79 (2.58) 3.00 (2.96) 4. Empire 5.31 (3.21) 5.55 (3.37) 4.89 (2.95) 5. Fremont 2.88 (2.17) 2.86 (1.46) 2.93 (3.17) 6. Glendora 3.65 (2.29) 3.64 (2.23) 3.67 (2.50) 7. Graham 2.83 (2.38) 2.65 (2.32) 3.18 (2.53) 8. Grand Junction 4,92 (2.82) 4.97 (2.71) 4.82 (3.09) 9. Grant 4.02 (2.59) 4.10 (2.45) 3.89 (2.87) 10. Holland 5.45 (3.65) 4.84 (2.66) 6.50 (4.82) 11. Hudsonville 3.88 (2.70) 3.42 (2.51) 4.67 (2.89) 12. Kent city 3.00 (2.57) 2.94 (2.70) 3.09 (2.47) 13. Kewadin 3.61 (3.21) 3.39 (3.35) 4.00 (3.01) 14. Lake City 4.57 (3.77) 4.87 (3.86) 4.06 (3.65) 15. Lake Leelanau 5.30 (3.80) 5.39 (4.02) 5.13 (3.42) 16. Lansing 3.51 (2.99) 3.29 (2.37) 3.89 (3.88) 17. Ludington 4.35 (3.31) 4.81 (3.27) 3.56 (3.31) 18. Mapleton 4.88 (3.16) 4.65 (2.90) 5.29 (3.64) 19. Mears 3.59 (3.19) 3.44 (3.15) 3.81 (3.35) 20. Muskegon 3.33 (2.63) 2.90 (2.51) 4.06 (2.73) 21. Nunica 4.37 (2.74) 3.97 (2.26) 5.06 (3.39) 22. Paw Paw 4.77 (3.23) 4.77 (2.42) 4.78 (4.35) 23. Peach Ridge 3.29 (2.44) 3.35 (2.24) 3.17 (2.81) 24. Sodus 5.55 (3.40) 6.39 (3.40) 4.11 (2.97) 25. Traverse City 5.14 (3.77) 5.32 (3.89) 4.83 (3.65) 26. Wavervliet 4.53 (2.99) 4.26 (2.99) 5.00 (3.01) NOTE: tions. Numbers in parentheses are standard devia- 136 several times, and is now located in a relatively colder location approximately 1% miles from Lake Michigan. The Holland and Grand Junction agricultural weather stations are both located on cold soils. Especially on radiative nights, Lake Leelanau will be relatively cold (as compared with Kewadin) due to northerly or northeasterly wind drift off the land. Lake Leelanau is located 2 miles due east of Lake Michigan. Table 20 compares the prediction from the Soderberg method and the 4 p. m. dew point method forecasting the minimum temperature at Grand Rapids. The results are cat- egorized according to whether 850 mb cooling, 850 mb warm- ing, or no temperature change at 850 mb had occurred. Of these cases, 31 were considered to be radiative, and the average absolute error was found to be 6.450F. The frequency distribution of the absolute error of the Soderberg prediction method for Grand Rapids during 1977 and 1978 is presented in Table 21. This table shows that the minimum temperature prediction for Grand Rapids using the Soderberg technique is usually not more than 40F. However, for more than half of the cases when no 850 mb temperature change was observed (i. e., radiative-freeze conditions), the Soderberg prediction was not in error by more than 20F. Table 22 reports the results of comparing the average absolute error of the MOS minimum temperature forecast (Jensensius et al., 1978) to the average 137 TABLE 20 COMPARISON BETWEEN MINIMUM TEMPERATURE FORECASTS USING THE "SODERBERG" PREDICTION METHOD AND THE "4 P. M. DEW POINT" METHOD FOR GRAND RAPIDS (1977 AND 1978) Type of Number * . ** Temperature Change of cases Soderberg Dew P01nt 850 mb cooling 12 3.08 8.58 850 mb warming 16 2.88 5.13 No 850 mb change (total) 21 2.53 7.14 Cloud cover 0 through 5/10 9 2 78 5 44 Cloud cover 6/10 12 2.25 8.42 through 10/10 *Average absolute difference between "Soderberg" prediction and observed minimum temperature **Average absolute difference between "4 p. m. dew point" method and observed minimum temperature absolute error of the Soderberg minimum temperature fore- cast for selected agricultural weather stations in west- ern Michigan, April 15 through June 15, 1978. (The MOS forecasts were not archived during 1977 on a station-by- station basis.) The Soderberg prediction method results in a comparable average absolute error for all observa- tions in the study, being only 0.20F greater than the average absolute error of the MOS minimum temperature forecasts. (It should be noted that MOS forecasts are 138 made 36 hours in advance, and the Soderberg predictions are made 12 hours in advance.) As one may anticipate, it appears to perform better than the MOS forecast in the vicinity of Grand Rapids, i. e., at Hudsonville, Graham, Grand Junction, and Paw Paw. The MOS forecast was better than the Soderberg forecast for slightly more than half of the stations, including Kent City, Lake City, Ludington, Mapleton, Nunica, Peach Ridge, and Sodus. No overall pattern of predicting above or below the observed minimum temperature was discernible in either method. In an attempt to explain the performance of the TABLE 21 FREQUENCY DISTRIBUTION OF THE ABSOLUTE ERROR OF THE SODERBERG PREDICTION METHOD DURING 19T7 AND 1978 FOR GRAND RAPIDS (PERCENTAGES OF TOTAL FOR EACH TYPE OF TEMPERATURE CHANGE ARE GIVEN IN PARENTHESES) . 0 Type of Range of Error in F Temperature Change 0_2 3_4 5-6 7 & over 850 mb cooling 3 (25%) 6 (50%) l (8%) 2 (17%) 850 mb warming 7 (50%) 5 (36%) 0 2 (14%) No 850 mb change (total) 12 (57%) 5 (24%) 4 (19%) 0 C1°“d °°Ver 0 4 (44%) 3 (33%) 2 (23%) 0 through 5/10 Cloud cover 6/10 through 10/10 8 (67%) 2(16-5%) 2(15-5%) 0 139 TABLE 22 COMPARISON BETWEEN THE AVERAGE ABSOLUTE ERROR* USING THE MOS FORECAST AND THE SODERBERG FORECAST FOR SELECTED AGRICULTURAL WEATHER STATIONS IN WESTERN MICHIGAN (APRIL THROUGH JUNE, 1978) Station AAE* from AAE* from Soder— Number .of MOS Forecast berg Forecast. Observations l. Belding 1.95 3.00 20 2. Edmore 3.67 3.79 24 3. Empire 4.24 4.64 25 4. Fremont 3.10 2.55 20 5. Glendora 3.95 3.85 20 6. Graham 3.44 2.96 25 7' 3.322531... 5-29 4-79 24 8. Grant 4.48 4.08 25 Holland 5.08 5.00 25 10. Hudsonville 4-92 4.32 25 11. Kent City 2.56 3.36 25 12. Kewadin 2.96 2.76 25 13. Lake City 3.28 4.28 25 14. Lake Leelanau 4-14 4.32 22 15. Ludington 3.52 4.36 25 16. Mapleton 3.68 4.12 24 17. Mears 3.04 3.64 25 18. Nunica 3.44 4.44 25 19. Paw Paw 4.12 3.88 25 20. Peach Ridge 2.88 3.52 25 21. Sodus 4.60 5.64 25 22. Watervliet 4.88 4.24 25 NOTES: No. of observations (all stations): 529 AAE*--MOS (all stations): 3.80 AAE*--Soderberg (all stations): 4.00 *AAE = Average Absolute Error, tween predicted and observed minimum temperature, F the difference be- 140 Soderberg technique in predicting minimum temperatures, Table 23 shows the results of correlating selected agricultural weather stations with Grand Rapids, Michigan. The correlations were found to be within the range of those reported in Table 10, which lists the equations for predicting minimum temperatures for the agricultural weather network from the climatological network. The six worst and the five best stations (highest and lowest average absolute difference between the Soderberg predic- tion and the observed minimum temperature) were chosen to see whether correlations with Grand Rapids paralleled these results. With the exception of Holland, which was well-correlated with Grand Rapids but not predicted well by the Soderberg method, all stations with average abso- lute errors of at least 50F were poorly correlated with Grand Rapids, and the stations for which lower absolute errors were found were well-correlated with Grand Rapids. This indicates that the success of the Soderberg method is dependent on how well the agricultural weather station is correlated with Grand Rapids. 141 TABLE 23 CORRELATION COEFFICIENT OF THE MINIMUM TEMPERATURES AT SELECTED AGRICULTURAL WEATHER STATIONS IN MICHIGAN AS COMPARED WITH GRAND RAPIDS, MICHIGAN Y X r* r n** l. Belding Grand Rapids .91 .83 198 2. Empire Grand Rapids .78 .61 195 3. Fremont Grand Rapids .88 .78 216 4. Graham Grand Rapids .92 .85 227 5. Holland Grand Rapids .90 .81 203 6. Hudsonville Grand Rapids .90 .81 227 7. Kent City Grand Rapids .89 .80 236 8. Lake Leelanau Grand Rapids .79 .62 214 9. Peach Ridge Grand Rapids .90 .82 227 10. Sodus Grand Rapids .75 .56 184 ll. Traverse City Grand Rapids .79 .62 214 *correlation coefficient **number of observations SUMMARY AND CONCLUSIONS 1. Certain aspects of the occurrence of freezes in Michigan have been addressed. These include the climatology of freezes, vineyard temperature profiles as a parameter to evaluate the wind machine as a freeze— protection device, field trials with a wind machine in a vineyard, and a method to predict the minimum temperature for selected agricultural network stations in western Michigan. Temperature records from selected agricultural weather stations in Michigan have been compared to the climatic stations maintained by the USDC/NOAA/NWS Cooperative Observers Network to determine whether the average freeze dates differ. The last date of occurrence in the spring and the first date of occurrence in the fall were determined for five different temperatures for 17 agricultural weather stations, from the first year that it had been in existence (circa 1962) through 1979. These data were punched onto cards and analyzed by a FORTRAN computer program to determine the freeze stat- istics. The absence of agricultural weather records before 1962 necessitated using the statistical technique of linear regression to construct a 30-year freeze 142 143 climatology for this network. By incorporating agri- cultural weather stations and the USDC/NOAA/NWS Coop- erative Observers Network, a more-refined analysis of the freeze dates was obtained. 2. Graphs of temperature profiles from two vineyards were drawn, as well as graphical and tabular summaries for the three years of observations. The average temperature inversions were obtained between the 1 and 15 meter levels (approximately) for temperatures at the l-meter level that may be critical to grapes. These inversions were of a sufficient magnitude to provide an ample heat source for a wind machine to be potentially effective in the vineyard. This conclusion is based solely upon the Reese and Gerber (1969) graph of area of protection (acres) vs. degree of protection (OF), according to inversion strength. For a GOP inversion (e. 9., when a l-meter temperature of 30°F is occurring), a 20F protection over an area of 3% acres, or a 10F protection over an area 6 acres may be expected. For a 10°F inversion, a 20F protection over 6 acres, or a 10F protection over an area of nearly 10 acres may be antic- ipated. The temperature response to the passage of a wind machine was monitored on May 4, 1979, by 14 minimum temperature thermometers in a Texas Corners vineyard, during which increases of GOP to 1.50F were noted. Tem— perature profiles recorded in a nearby vineyard indicated 144 a small temperature inversion of 2.00F. Although a strong conclusion should not be gleaned from this iso- lated observation, this is nevertheless a positive result as the ambient temperature fell 1.00F during the wind-machine trial. 3. A minimum temperature forecasting scheme developed by Marshall Soderberg of the National Weather Service (NWS) for agricultural weather stations in western Michigan was evaluated. The 4 p. m. temperature, dew point, cloud cover, and anticipated 850 mb temperature trend are used to predict the Grand Rapids minimum temper- ature. This prediction serves as a basis to establish a forecast for 25 agricultural weather stations in south- western Michigan, provided that an average difference between Grand Rapids and the station in question, for different synoptic conditions, has been determined. The average absolute error of 31 predictions under radiative conditions ranged from 2.480F for Grand Rapids to 6.39OF for Sodus. These results are very comparable to those obtained during 1978 from a computer— ized agricultural weather forecast guidance developed by the NWS for Michigan and Indiana (see Table 22). As the NWS guidance was quite complex in its statistical develop- ment and operation, it is concluded that the Soderberg technique is useful as a simple method to forecast nocturnal minimum temperatures at agricultural weather sites in Michigan. RECOMMENDAT IONS 1. The existence of a heat source within the nocturnal temperature profile (i. e., strong inversion) is imperative to the successful Operation of a wind machine. Looking ahead to the time when on-farm computers will prevail, a program to forecast such information would be an invaluable potential tool in aiding the grower to decide when to turn on his wind machine. The objective of a boundary—layer model developed by Georg (1971) is to predict the nocturnal air temperature profile from 1.5 to 24 meters. The input parameters are: the measured net radiation; the ambient temperature at the reference level (TR), and 1.5 m; the wind speeds at 9.0 and 18.0 m; the maximum and minimum soil temperatures for the day at 0, 5, 10, 20, and 50 cm; the percentage of water in the soil on a volume basis; and dew—point temperature. The program will compute a temperature profile up to 24 m with T as a base, and subsequently generate a new value R for T one time-step into the future (see Appendix D). R There is no explicit function within the program to calculate the flux of latent heat due to condensation and sublimation. There is a command within the model that tests for TR 5 Td' which will reduce 145 146 all temperature changes with respect to time by one- half when this condition is encountered. This model differs from the Brunt equation by utilizing assumed air, soil, and wind profiles to cal- culate eddy conductivity, soil heat flux, and convective heat flux within the boundary layer. No other models of this nature have appeared in the literature, and it would be invaluable to merely validate the model as is, let alone improve various aspects of it. 2. Future frost researchers who are cognizant of Businger's dimensionless coefficient may apply this concept to the prediction of minimum temperatures. Observations of downward longwave sky radiation coupled with air temperature at the five-foot level may be used to compute Y over the course of several frost evenings, weather permitting. By measuring Y in the early evening, one may extrapolate to find Y for the early morning, based upon past observations. As downward radiation will remain nearly constant, the minimum temperature may be approximated. Characterizing the effective sky temperature may enable one to know the magnitude of the difference between leaf (or bud) and ambient temperature. Thus, a fruit grower would know whether or not it would be economical to run his wind machine (or other freeze-protection device) when the ambient temperature is above freezing. 147 3. Additional statistical procedures may be incorporated into the Soderberg method. Following the methodology developed for the Mendoza region of Argen- tina (cf. Bagdonas, 1978), a correction factor may be applied to the average difference between Grand Rapids and the agricultural station in question: OY/I:;§, where CY is the standard deviation of the minimum temperatures at Grand Rapids, and r is the correlation coefficient between Grand Rapids and the agricultural station. 4. If resources were available, dew-point hygrometers (or some other suitable means) might be provided at selected agricultural stations. To facilitate the choice of locations, correlations between relatively close agricultural stations might be established. Thus, one or more agricultural station(s) might serve as "key" stations, augmenting Grand Rapids in the role of reference forecasting station. APPENDICES APPENDIX A ACREAGE, YIELD (TONS), USES (TONS), AND RAW PRODUCT VALUES FOR MICHIGAN GRAPES, 1965-1976 Year Acreage fiéfiig . Uses RawVZIE:UCt Juice Wine Fresh (Dollars) 1976 15,800 14,500 10,700 * 1,400 * 1975 15,800 56,000 47,000 5,000 3,000 $6,710,000 1974 15,800 47,500 40,000 5,500 2,000 8,740,000 1973 15,800 23,500 17,800 4,100 1,600 4,630,000 1972 15,800 53,000 45,500 4,700 2,800 8,798,000 1971 15,900 69,000 59,600 6,000 3,400 8,280,000 1970 15,900 62,000 * * 3,600 8,804,000 1969 16,000 38,000 28,200 7,300 2,200 5,510,000 1968 16,100 23,000 16,200 4,600 1,900 2,852,000 1967 16,000 39,000 27,900 7,700 3,100 4,446,000 1966 16,600 49,000 36,400 8,800 3,400 5,145,000 1965 16,600 71,500 54,600 13,200 3,400 7,575,000 *Not available 148 APPENDIX B ESTIMATION OF WIND-MACHINE DESIGN FOR THRUST PER HORSEPOWER The thrust of a wind machine will depend upon the power (P), the diameter of the propeller (dwm), the power coefficient (CP), and the thrust coefficient (CF). Leonard (1953) defined the relation between power, revolutions per minute (N), and diameter of wind-machine propeller: _ 3 5 cP — P/pN dwm (B.l) where p = 1.29 x 10-3 grams per cm3. The thrust co- efficient is the relation between pounds thrust (F), revolutions, and diameter: 4 _ 2 C — F/pN dwm (8.2) F Solving these equations for thrust in terms of power and diameter: _ 3 2 2 2 F — cF pP dwm /cp (B.3) 149 APPENDIX C FREEZE STATISTICS FOR THE AGRICULTURAL WEATHER STATIONS The freeze statistics for the agricultural weather stations are presented in Tables C1 through C17. The following abbreviations have been used: M VAR XBAR SD SD/XBAR THRES number of years of freeze dates that have been read by the computer program number of years of freeze dates for which a complete data set was found variance of the freeze dates mean of the freeze dates standard deviation of the freeze dates coefficient of variation which is the standard deviation of the freeze dates divided by the mean of the freeze dates threshold (followed by temperature, OF) 'Under the column titled "Percent Chance of Season Longer Than Indicated Length (days)," MAX refers to the longest growing season in the data set of the indicated temperature threshold, preceded by the last two digits of the year during which it occurred. 150 TABLE Cl MICHIGAN (1950 THROUGH 1979) FREEZE STATISTICS FOR BELDING, 5? 28 29 20 flRSI FALL ltLElf S'AIISYICS 36 20 (I)? U“! SILIISII 2L LASI SLRING FNELIL 32 JOOONW n-n—omcr Nance O O I 0 ~06: 6nd ‘— OOF‘OON ”0000.3“; (Na-NC O o o 0 (five ON— wu— OFGS‘CC‘ ION-2C5 5") ”fig—- . O O O OFN JG.“ .— 00“)”qu nflCI-fiac ~56.”— O O o O 003‘ eta. C‘C‘uh-\gq "n.s."n °~¢CI O O 0 0 (Thus 3" GOO. as ”no‘kfla NXNO 0 o o o No.— NC." ”I"! ofnc'ficn' gunman-run n—u-o O O I 0 NR— C‘s-o an '.(-'(1'..H_': nmc-;°~fi Gate: 0 0 o O . ~ g a; 3 n f'fixma‘. SLASUH BRO-1N6 SIAIlSIlCS 28 20 2 Sb ocw-mnm rum-nun.) O—C‘JS N o o 0 men NN—n OGN'flF—l It‘s-ofta-ufi 9151019 N 0 O 0 Cal: Nu.- sec; 3% anmCNQ CFO—0 N O o o #83“. NC— :1 (-'u‘~(\3‘ FH'MDWNO cog-Q— ...“ O O . 33¢“ «(you 15]. cl“ 025 .50 .75 .90 .95 FIRSI PPOgADILITICS 0f LLSI SPRING “AVIS LAST @6009 01640039 O'Cnn (0:000 Owe-IN— «1.1-chm d‘dut—fi came-mm 04"”?! Nnd‘ ~10 NuN—C Won‘t. Luv-ICOO.‘ “NC-NF! thinned nwnfio gnu—Nd 6mm. 0 NWFOO: GOG-0",- Q‘D'f-" NNMO t find-tr. '4 ?; € $190.". 4' .flNQiJu‘ finC‘J\\’C‘I ”.4559: 1" 0..-"..IUUI fl' ' L' .8 00' rrrlz ...—O...- 005 0’0 .25 .50 0 .q0 .95 L‘S' PHOPLPILIIIES 0F FIRSI FALL DIIES [IFSI Cumin” «co-06.6 Onto-o pox undo-Oun- a 000'“ «Nan—0° Odd—N Glenn—Id ‘mfnn'. ONO—N C ‘2 flan—o flung—F0 Ifl‘nNF‘ (\f-Nfla O-ugau-o -an—OFI th'o‘“ "(No-(v10 U'U-Co‘o" ”fl" nwoom via-cam: Ira-eon “fl" MIN .95 (DAYS! .75 .90 INDICAYKD LLNOIN LtHIGLR INA!) .05 .10 .25 .50 PCWCTNY CHANCE OF SEASON HL‘ (DU :rem ounce- urn-n... \\\\\ “05¢“: (IO-OFF 119$ 3 .0 c—mhw anon—nun“ 3.30”“ C; {55- - -——~“ ocmwo Influx“— nan—nun“ mrcmo meson. and—N“ (“13.-Dc Intuit-9'1 ""9404“ heft-mm c~ '. 1V: anon—Wm FmQ-d‘ adv-'7"): v-c—o.\'J" \\\\\ NsL‘J ‘4" 1' he Jaw” \L"" J :c.‘ " ‘3. ..‘at‘. ..., .- '-p r l’ o v lo luai‘ ~o '- - ~ - P V TABLE C2 (1950 THROUGH 1979) 5:82) r411 (PLLI:-SIAII.IIC MICHIGAN FREEZE STATISTICS FOR EDMORE, a: (U 2! 3” OJ SIAIISIICS 20 1' H FNLLIF .‘ADI'I‘I I. C- 5 LALI coon—on fins-mac N34:— 0 o o o «Ill—of) on.— dd ac.) nan-3'0 announ— hike-i o o a 0 SN") ‘vwfl I-Io-i 509-0—‘0’ fir)n-3~N war-- 0 C O O :39..- CG— .- oomcea nnccmn Jl‘nfihd O O O 0 fine c-Q‘c-O ('5': ern “.— nnmnmn (50619 O O O I NFC. hh ooon~~ final-3630') n6”: 0 O O Q 3070' cm’a‘cmn. norm-cc»: ..‘IKVNL. o o o o 01?"! hula—l an!” O aemnao N Iona-nah 0113:»: I o o o C‘hh “~- N 8 cannon-o (\J m-IFV‘CJ~ OFIQ 9 o o 0 mar- '00”— an at C300 ”NO C» (DOWFFVU‘O 04;. mu :4 0 0 0 NF- Ni)" an SIAIISIICS ING SLASL f. ROU 32 30 30 .96 067 940 123 6 000. u 8 6 run—- c O'ei‘flm... '3 rang-mu: .7 ‘Lfl-T ._. If‘ a o o v.“ o «act'w LEG.“ .— ,. ‘ X l I \ - c- 2152 .0E .10 .25 .50 .75 .90 .95 FIRSI PROBABILITILS 0F LAST SPRING DAIFS c a LA NQNOU‘ Nan-no COO-1'0 ch—u-n UN‘flN m..nn IFFQQ ONFCN fl???” omntr-U‘ “CNQN nJad‘c'O #CCO' N—m—‘ W¢.¢¢c anflfihj 90.001.— 000W“?! 7‘ ~N¢n Ont-Nd QaDUMtd' J’U'JLfi‘C: H Q—Ic .- éwlfiuofl’ "OJNC «‘5 Mouth—0— ~0g:ufir -D 0‘30: 9 ' “‘DDTC‘.\ \‘J S? v; L’ ’fl ’f‘ ‘&h~\aO—-'-.- FALL HAILS .50 .75 .90 .95 LASI ST 25 .05 .10 O PROBABILIIIFS 0F FIR IIPSI faunas-I cum—1°C Of ‘—N\V duo-add CT 9(- Na. ONONO 6’2—0—65 nun-tuto- {unflhc auto—IN 6.: Acne-n fl-flflfl NIJ‘TOC N-h-nc UO-OO— nun—u cum—c '9 5.00.” 09:00 "Oil" {duhc O—o\\,6~ C‘" Q P_ 0.4 MIN LONGER THAN INDICAICD LCNGIH (DAYS) .05 .10 .25 .50 .75 .50 .95 (LHCFVT CHANCE OF SCASOL M LX “33%)... I; QOnQQ ans-0'"— \\\\\ 10:4: 3.0 OQPNN NOONU‘ O-nCWBQ and—nu ¢~D~D#In O‘NQNO‘ urn-nun G‘N‘Gm‘a C rdbv';; C; curd—ac“; ('5'! KNC N P)~£a‘ .- "duo-ON c-cma‘m ”CF66; «III—«V45 HOCDC {VD-LNG -—~§¥‘\ NQVVBO #6: Ne ~~—u\l-.\ TABLE C3 FREEZE STATISTICS FOR FREMONT, MICHIGAN (1950 THROUGH 1979) 28 29 20 FIRSI fggL FRLEIE SIAIISIICS SIAIISIICS 32 21) 2Q 21 LASI SPRING FRFEZI 56 ocnc¢r~ ”mocha 76346.6 0 o o 0 can Fflfl “d OOO‘NNO Inna-bow own—- .00. 0'70 ~m~ NH one-fine. nn¢nnn unca— o a o 0 9CD!) .30“— OeNr‘H’hD nncnw: 9:3“ 0 o o o in!!!” 0:)— nnhmnm anon-O O O I 0 gen) O 669 O..- N ”#19098 ~f N t). SLASCN SIATISIICS IIIG SW C"! K C: .x'ac .u o o o ”0"? ~~~ conncm “manna; ONNO III 0 O O nP-d NO .- .- cos-6N6 nun—"(um .560.- .n o o 0 4‘0“ {RN ~ camp-n. flnflflffl otVC—o 0‘ o o o hmm no.- Q N 9! VA” If: :«R ”[10 g ‘ I 153 .05 .10 .25 .50 .75 .90 .95 F105! PROHAFILIIICS 0F LASI SPRING DAIFS Last 0000-000 Nann— C‘P‘Inn hhflnfi Own-ON I.) .1" {'0 same 0"- flea-CO mmccc OORQF No-N—t nun??? aroma-cum OLVGNA $34010“ «O‘Cfi can—Nun 0mm. 0 Q emmc; "cc-0G N “00.00 ' Nhn6¢ Alma-04 0 5.11630 Obi-fift- FDV‘HHUN WQ‘HIIUNI, India-tall...“ x :‘t‘ =- 'L .2 LII}: ._.-th ICS 0 .75 .90 .95 LASI DA .5 .05 .10 .25 PROBIBILIIICS 0F FIRSI fALL FIFSI 0'0. 0‘0“ NC mm— Gun—um cult—unu— ‘C FLO!“ non-nu: Gog-IN anus-Ian— o'nflc-s ON—u-n Qua—a0 undo-nu- Fun—ION O—OC-N C3 "‘IIIv-ICI' “and..." «hut-‘0 NCNn—n U‘UOO— tin-Inn NCO—C ”(\Hfilh’o 0 3‘6.)— ans-u- cucum- own—N Oa-mco H" 91:):th I'D—NO \V :6 3".— I_'u can U‘O—flfi‘l‘ 'tx Nc—t :1"? 7 C): ‘H (DAYS) .50 .75 .90 .95 LUI'GLR IMAM INDICAILO LLNGIH SLASOI.‘ .10 .25 PLRCENI ggANCE OF MAX ”FCfisV $19000) alto-III. \\\\\ thflm J0h|fll~ nnoc: outfit» would-CI. #0090” a «ska gun—“N ONNQ“ 5' no: 0'0 «IMO-0C4 33mfifl.c “850‘ N noun—0N C LNG“ 5‘ now Cam ...-0.46.04 memos the—ms qnmmm ohfiuam KN-Mvc ‘QNIHN TABLE C4 FREEZE STATISTICS FOR GLENDORA, (1950 THROUGH 1979) MICHIGAN -m. ICS FIRST FALL fFEiZf SIATISI STATISTICS SP0 I ‘IG fRFCZL LAST 20 2Q 28 32 36 20 29 2M 52 $6 actor) 5" «an NONU‘ ham:- 0 O o O ”4'. O'— Na- ~"°~hc¢» “”5004.- Q1“?!- 0 O O 0 Cum CPO" N.— OOCF CEC- nnc~c~o~ :0 fin LENN— . . O . U‘m-fi Quic- .-u-. (945'? 9.100? 60‘6“ . O C 0 ‘3? dc.- 000‘QQ- In.) DC nu) LJCJ‘U1 ‘oééd O O o 0 “COO F(.— .- ~n-.r~m CF16? 106—6 0 O a o 00'“ 0‘0.— FIN bcwnahc) nr) cc: nr) OC‘ nn 6‘." ”M r: CONT!) NC‘QO 0 O O 0 «run (tan—0 ~‘\V G‘C’C‘U‘ «Ch? ace: 0 O O O O‘Nc' 60‘— NN “Ohn N620]? o O O 0 (new (Nu-o4 NF? (\F’Lf LEON"? “IQ NO 0 O O . In“?! ON-n NF) 10" '11!) an 3- >X TATISTICS I O acne—«a N an: DJ(- 0“: h o o O ...:co cnm c ooccom N nmneh— ...-“1'! .n o o o (no—n 09"“ N canons U.“ nnCOCI‘ SLASIN [HG nan.- .fl 0 O O .51“..- 0‘.“ — 154 .95 FIRST .90 N0 .25 LASI.SPRI 0F .13 PPDbABILITIE' .05 LAST mono.- NONDN ' {Inna n—mN— ONCN" a}: c'fin WOO—(D nun—u"..- ’Dttr-fl Gian—h “neg—N IDLD¢Qn 0.6 #204. nk'HCCHO (Home O O‘O‘Nflfl =N~Od 0.01010? Othhfi ula—ac.- ».Io Jru'fc («NF on C.~——1'§ 09.32”? JNL’TQC .2’1‘\‘\(- '. s b- ..Hu LAST 05 .10 .25 .50 .75 .90 . t PkghABILITILS 0F TIFLT FALL DATLS FILST 9000-6 «1°..an Cato—“AJN ...-0.4.0.. ”ENG—o 13.—Cane CC. "‘6‘ v-~~~~ mfi¢9~ (\C‘ 0.0“ c-OC au- vii—H— ~OF {LN-I a.m.-.0..- O‘U UG— a.m.-0 ”FA—QC“ OflC—N ‘.'.’ O -- :4. "...-I '3‘ vac-nth \~—o(4CJ~ vt‘T'C‘O ‘— OCN.‘ '0'. p'F,\I~.\§N fo'.’N/‘.L-‘ 7‘ Anna-nth 6‘ HI" (OATS) .90 .95 INDICATED LFNGTH .75 .50 LONGER THAN 0 OK .10 PLkCHIT CHANCE OF SILASOI. may ”mu/TEN =0:ch «a.m.-c \\\\\ no.0: N O~m~~r~ 0.00le JK—OCF-O ado-0'16; GOLD—9N can.) ~50- Gnu-n0; msc'mrm a-U" VBU “J anon—cum “10' Ina-u,“ “q 3. and nil—NW 3|Cif~h\\ nwb‘ :u‘fll flH—L-N «QC—Nb (HF-OD m~¢;NN 3‘ ll" so“ in :..-...‘n~ -‘NLVN tho-NJ. Qcmth no“. ‘Jt‘..\c \ \\ \\ ~.mnI-' 1" “nun-5m J)". 3' ’ ‘3 .).’l..“-‘V TABLE C5 FREEZE STATISTICS FOR GRAHAM, MICHIGAN (1950 THROUGH 1979) 29 20 28 FIRST FSEL fRLLZC STATISTICS 36 20 CS 29 STATISTI 32 28 LAST SPRING FRCFZL 3b cenoco nflC‘OIDO Fem—n o o o 0 «OLD O¢n No— OOQONC nnncxcr €5.03 0 O O O GUN 061.. common nnmnco H30.— 0 . O O «rho: can-o o-v-I (30.7596: Panama—um OCEAN-I o O O 4 5‘0“! ¢$~ OQNFn‘ ””0009“ v.23."— . O C . ”COO 61,". ~ C‘th‘bmh ”MOONC 64610.09 0 o O 0 no.” ID~DN IDN €096.06! (070900: :G‘UO o O O 0 "MD." {CW-O 0"“ cognac-c nuannuzn 'Nufl: o o o 0 PM: .— Ina-.- «N OQGOO'C names: 3.0-~00 . o O o can m...- an C‘CMGL" JT ”nee NF, Honnho N nna~nnn Cal-0" 9 O O O 8799 O‘Ifl'fl N O OOFU‘ICN N Inna-ow U- TATISTICS I OOO‘.‘ n o o O QTO‘ no.- 0 0 1 3 2 6 S 2 3 3 q 3 3 5 ING SEASON 1‘. 3.9 7.7 .0 '32." 1 OOO°I~€ trance—n .4?“— fl 0 C O cut—1h con- VA” ‘IHTR SUI!” 155 .05 .10 .25 .50 . .90 .95 FIRST PFOPAMILITILS or 11:! SPRING onyrs 3T LL NLflONN N—‘nC‘JO C C "HON FOWIN‘D N—ONH CCCflN Na¢~r~t o—IONN at cnw aqua-m: CN—oc—t 11".” "Of-“6 -ONC‘“ 31013.“) on NU” .- 5.0flo—fl 010.10.“. C NNlfln'fl ~--‘- g 5.51“} 5" 0N4 c : “flu-cw .05 .10 .25 .50 .75 .90 .95 LAST PROBABILITICS OF FIRST FALL DATES FI"ST (yo-gem «ca—n... Gun—cum cum—ow.— ? X‘U‘Nh "xv—Won GOO-~61 dun-dd ace.“— «aw—Nd Ohm—(M «worm-..— #6 ~00". (no NCN $)C€ Inc-I “NH" 9 2:1).- «Ira—w.- U-C C. 9.- ...-H (N u-c-u- c-UN «Out: '1‘ 0" («On ‘01—. Gmfiyoo nc-oC-a-uv ac~ao' “d" OO-flhfl‘ - p: ~~ v‘\. 900 "dc-fl Oahu 3:. s“~)-‘u-.N ".11 .5 gen 'uuu— I... ‘.-I .IL" A '1. s‘ INDICATED LENGTH ADATSA .5" 075 090 .95 "C .‘ h‘ LONG“? THAN 010 rEKCEuT ggAucc or 5tason 0 MAX marcw O—OOW «dad \\\\\ aoccx woos» n¢m~¢ ONIDFC‘ and—unc- OCH-0‘0 GKHJGO “GHQ-On. ONNIOC NON?- also-Maw NO 0'1 0 nu‘: 1.: "1 wan—cam #6 On.) C K. .7 “an H—¢-\\(\A «0'00 3 €11 "'3?- q—UNCJN 5"“: N»: haw-unit? aura-AN \\\\ \ a‘fiufinu‘ m~n~m~ \n'urfo - " 3(‘D\.~1\V TABLE C6 FREEZE STATISTICS FOR GRAND JUNCTION, MICHIGAN (1950 THROUGH 1979) 2Q 28 FIRST FSEL FREEZE STATISTICS 36 20 C gs ( 28 32 Last SPRING FREEZE STtTISTI QGFRQC.‘ anc¢v~n mph- 0 0 o 0 cut).- n.- och-wen nun-mam... 315(— o o 0 0 one?) U‘Nu. on.- DOONND ””00 cm nun-.1— . o o a 'U'hn ho.- “H back-"fl nncemo 000“ o o . 0 COO curac- OONFCG nuns-nae: 33.-C“ o o o I 11519 “ht-0 “coma-0. nib-.0011? Inwu‘ca o o o I On— cc.- “N GOnOC—O nnmonc ONNO o o o o UNDN '0‘" n0. Gov-63170 nnmno: «one o o o 0 TT” NO.- an .14 \ .1 cat: r?>xmm O N O N ATISTICS 3N I’VIU‘DgflT .‘ACCJ c . o 0 ”\DO C~N N Oc—NCN nuance .— ohm—n h o a o O‘O‘N C"! N oer-mt:- Clfl nncncs a: O 36 30 30 750.53 106.767 CON—t p . . . c-GN WAVN ‘ 27.396 .257 U fink? 30118 156 SPRING DATLS .50 .75 .90 .95 FIRST T .25 .10 PRggAHILITILS 0F [AS CONDO arm-«nu mccnn CONd" GOA—ION “at." Udh‘fl‘. 36.-ON .‘NDCCIG «ta-unn— coo-Nata DID? C C U‘NC-C‘ “NCNO gfimuiCC 3.0:”6 #- (at-3-0.0! OOTDCC N—HFC d-‘NON ~5 anon: “NJ—0‘ mama-0N ~5~Cu3¢u¢ CQNOC' W‘Fj—u-i-O .u-nomm own; .1:- mum“... 6‘. 097-15": k; 0..."...0 a X.'.3 .I'. - -o v- ‘- - - ‘ .05 .10 .25 .50 .75 .90 .95 LIST FRObABILITILS OF FIRST FALL D‘TES T‘TKST I cv-crnm “Oi-ONA e—I—F‘N fidd‘d IONCON GUN ~01“ 66.-no.- donut-«I. v00 cumn 6-0—no OON‘N noun—w... nanmn out“ ...“.- J‘U‘ ‘30“ «can ammo- ONO—O 0‘0 GO.— “G“ «can... NON—N ‘DU‘G‘OO w..- CG-OO’ cut—ac.- JT-a (T‘CIC oi." ' C30?“ T'T'D .‘.-: Ic'a‘o C a. 419:1? 3C: Pun-.m- "! ‘1‘fib'c Av: ““50- In :0. “\IJ“: LONGFR THIN INDICATFD LFNGTN COATS) .25 .50 .75 .90 .95 .10 RCFNT ggAhCE OF SLASOh PE “10) 64.-er QUINN! nun-a. «urn—o FO‘nLJ‘ ~~~ cramp-n Q.-CFC ...-tam FCNC I. ONhoc " ennui—~31 “Ink“?— “0.?an GGF‘NN (VF-«cm 3013‘0-04' n—WNN NmO‘c—I le? .‘I'J‘. ——~§‘.N «‘O‘COJ; 3&6”: ~~N-\'"~l \\\\\ nun—ma! IT'HD‘L'MD .n O. .t c:- a. 93.“. (yr. '1)" 51;: ~) -l_-.ohc TABLE C7 MICHIGAN (1950 THROUGH 1979) FREEZE STATISTICS FOR HOLLAND, 24 20 28 FIRST F§gL FPLEIF STATISTICS 36 20 (0' UN TI 28 LAST SngNb FRLLZL STATIS 36 OOfiOChfi lance-no watc— I O O 0 ”NC ~01. NOI- JOQNQ—Q nnmooc ohm.- o o O 0 C0 3 ”Nu. no. °°¢wmr¢ "nu-“8nd ear-.— 0 o o 0 DVD!" gnu-CI! an.— OOCWMVN «newnnn no¢~ .... .ac¢ con oomc~¢ nnn=—~ ‘9‘— . . . . P51" "a“ OO‘COO“ ”nicotu'. FNNO o o o 0 N05. Oh“ NN OOFOQP‘T ”HOOK.“ O'END o o o 0 was.) ”\UH NS» OCO‘T‘F‘CO' nnhn¢u3 P‘MDNQ o . o o #040 00" Ni") O Gem-awn N ”non—3‘ MINCE; h o o o and than t caoamma— N frames.” 0‘3..— . . o . NIIMO #001 N ATTSTICS UN ST 2R 30 30 76.37 7.667 §.008 .135 on.» I THE SEAS U 2 0 0 3 7 A g y: CG Lth n unnluahc- CPI-fi— g o o 0 0'7"") Inc-0N H l/Xb J IPLR l J u n N var \A 157 .25 .50 .75 .90 .95 FIRST .10 PfiggAPILTTIFS 0F LAST SPRING DATFS #63600- unncu CQF‘W‘HO Ocmcm n—umuo cctnn mama's: ONON—I 0'}.an common “anew mmetr‘ ~0an I'd O.—(\n° DUM'CC 0: Ge— sDth-(IH Ou’unt ‘ cam-no- «co-a.- Odhmnc -um33fl snmmco .°.\\JFI—flv-fl 8: 33.37“!) .05 .10 .25 .50 .75 .90 .95 LAST PROBABILITIFS OF FIRST FALL DATES FIVST CNt‘JuIN '0: ND— O‘HNN dunno—on 0h 6‘). “CV—‘0'! QO-NN div-9'4..— ...-«c: “NC-Una 93.-«n; -"fi-H wnvoa NCAA-)v- OOH—CI! aid—0d Nnmnc "Noflfi‘na U‘O‘HO— M“ roe 5"..- Od\3~n 3‘? 906 _~‘ cw—wua (‘40 com 23:1;3 dc..- MIN .99 .95 INDICAng LENGTH IDAYSI .53 SEASON LHNGCR THAN .25 0F .'5 PFRCFNT CHANCE MAX ”NU ON mb.-nth «...-Ia. \\\\\ 86610 O Qéhfivfi cxuuvo 653F060" outdo-l 6‘5th 3» O¢F° anon—IN Nn-ICF $0.06 .— nFflWN 3.50“— Hth‘ If! unfit-OWN ON #0 5 F'IK. U" N .f ...-0'":ka Qn‘f—‘O‘ (DP-O 8th "u“.VN Nflpcfi IP 3"“... -~~0Uci TABLE C8 FREEZE STATISTICS FOR HUDSONVILLE, MICHIGAN (1950 THROUGH 1979) STATISTICS 28 21 20 FIRST FALL FRLLZI 32 36 20 20 N6 FRFEIL STATISTICS 28 .5 LAST SPR 36 Oath“? nnconm 9051.- . o o o rdfi 6"“ n.— 09.0an nnwnmm www.m— o c o 0 “c. ION— Nod COCONF nnncnn CON— . O O . N‘DG'D nun—I nu- :“Occflhofl finch—v U‘NQ" o o o o On— fih—n ~01 oocnow nflnfiét 0‘: 3 c I o O 0 fun— {~50- ‘sv vac-throw runny—e Ina-3n". I O O O 6km Ina- F003 Canaan-Gin ”Anna—Mn Nun“, ... o . o o (NON Ono-Q 0.!) P’Lfifoulfi finson 3’ nROJlNG SLASLN STATISTICS 20 20 2a 32 36 bOMNQm n-flm‘cwd‘ can“): 3 o O O TNN «to. can-new. 'hPIhfl‘ADO ..‘zwd on . O O moo- ccw N ...‘OOFC"! non—cram 06¢.- r~ o o o J")? 41.0“ 96.:th nnmcns .c—un u. . . . ”‘5'“. v5.61 morwuro nnw‘C-TC.‘ ’"G-‘h w 0 O . twat VON“ SIT/VB 158 .05 .10 .25 .50 .75 .90 .95 FIRST PROBABILITITS OF LAST SPRING DATES IAST “£8390“ (No-«ONO: COP'H'HN «an-mm- N—ONv-O O ccnn -c-FCTr. a—ow— ncrnn c anew nfldcm mttcn d—nNQ N-«V—fl $350030") “nNON IIOAQNG “Tn-Maf. ‘7 'NC acne.— Otnmc 040100” N “...—H c «.10: " ’3‘.‘.\ .V '.?L1.." .51". as... .. ......" s; 14': LAST .05 .10 .25 .50 .75 .90 .95 PROBABILITIFS OF FIRST FALL DATES FIRST 65.-.ch {\O— 3— O-U‘NN and—on... hum GIN «nu an 60— NN ...-nu...— Nofl‘ .1" “Nu-.0“: OO-HN ...-or..." NOT“. 6° OGIO all” CDC-._— ...-Haul. N100 VB: 9-: Cu A's-Q 000 «a. «In-nun... ~mw~L~D "\sflwa FONT-out! "0‘" 3‘ on7‘3\ g'C'. ~\J(\ ETU’ 3“ 9‘ "IN (DAYS) .75 .°0 .95 .50 ASGN ngGLR THAN INOICATFD LENGTH .05 .lo‘ PLRCCNT CHANCE OF S! "A! cargo women “H" \\\\\ nncem QOONQ c-mcrmun an: e ha‘ ...-....— ~¢~Olfl hdrox O '00-an ~DONNF C) mucu‘a. Clio-ICOC'N chunk“: Not! U13 nun-OLVN cue—oh f “.904? H—L‘c‘VcJ once- .nr~.-~La ~a-NNN 1‘5”“? ‘(NC’ \‘ fluCNNsV Jhcnffi nit-0"" ~0-T‘JNf‘. \\\\\ J‘H_A:Cr “Twink-7") JNJ.’C. ‘Iffit‘. 5“ f 1 'l~...l‘ _L I. -_ . ~ .- ....-F'.’ b TABLE C9 FREEZE STATISTICS FOR KEWADIN, MICHIGAN (1950 THROUGH 1979) STATIST 32 28 2A 20 FIRST FALL FREEZE STATISTICS 36 20 28 SPRING FREEZE 32 LAST OOO'ONQ n'nnnmh U‘OO‘O . . . . Qua ch —.-. 090n~0¢u manna-aha" «Inn: . . . . “TON Inn- GOO-Q CCOF‘QID nnnwcw VCCUO o . o o Ins- No.00" a..- 0" (”On an’noc ”Tynan-i . C C . n~.—. No— “I! Owhnhc‘ finnVTO‘O ‘6‘.— O o a o nnn U‘O‘" omncqc nnco~n when 0... U‘CU“ ah N ODFNGO mum-man‘- new“: . . . o nu... ram—o «N n-sncm nnmnon one: C... moo ac.- oonhca nnnahm neon 0.... ave °OQIfi~EN nflTolfiugfl' akin: GROJING SEASON STATISTICS 20 2A 28 32 36 69.-NON nun—ohm Col-‘9 an o o 0 '7.“ an“... canomm FTnCC‘CF O‘BQ Q Q 0 O #003 N:— N OC‘thca nun—aha Gun-0°C .g o o 0 Own? “ht-0 an GC-‘OONU': manna—c 0.09 h o o . ONO Nmo-o .4 9" cums nnnnhc .u“- d C C C 'N’: ”\‘fl - It’d '13.. f7>XA.'»'n l n U!!!) 159 .90 .95 FIRST 75 .50 T SPRING DATES 25 C u 0 ES OF LA 10 PROBABILITI .05 LA .‘B—mho OO-IOJN aunt-an “3?". and—”N 11.00”” 010‘th «cm-ow 1.00000 :0 ommmn (Nu-P dc 09¢“an “INC-nu. GAGA-NH 0...“)Q 0 th9h Ont—fl.- \OIDIDC'O NC (‘0 6 an NON «61:15.00 ccuaon a“; Gnu-Q 1.. 063m.) omaoc 063.3...» LAST .95 .05 .10 .25 .50 .75 .90 PRODABILITIES OF FIRST FALL DATES FIRST "GCNU‘ CDC-QC é‘ «do-AN‘J‘J ...-a.m.: ennmh Woo-.93 Gun—own] nun-qua. GOO-h ”I aflfififll" OO—I—Af‘. alum—nu. O'fiNOQ CANON“ OC‘ ant-I— "dd—Fl «GWNU‘ c—Nc-ui OCH. our. «and. n—dfim «DU-.619 0.0 (JO- ...-C...“ ‘ (NFC..- 0N9“: 3‘09 — v- ‘0‘" :NID—o ‘3 fig \V\-‘ 3‘: a 1 1° dd— 0“: "3 «TU-'1“. -V\“ n&"¥1°1;3 HIN IDATSI .75 .90 .95 INDICATED LENGTH LDNGFR THAN .10 .25 .50 TERCENT ggANCE OF SEASON WAX have: ONIONO non—N \\\\\ 43.-gov. $01061“ NTNCQ crwmao one-GIN CVKON c-mn: "' "duo-N anon-m an. ‘30 .- Guano-N mmmah hunk-0N u-u-Ic-nNN ONm‘vuT CV; INF. anon—(UN ...-«nan. Ohmnc ai—C-ANN I M'- SON LONC‘ "56’ nun—.NCS $00—15 Ub-LC‘O-t ...—‘90:“: \\\\\ rang-c- NNNIOQ 13W 4.4’6; FT'ItVC-IN TABLE C10 MICHIGAN (1950 THROUGH 1979) FREEZE STATISTICS FOR LAKE LEELANAU, FIRST FALL FREEZE STATISTICS TCS SPRING FREEZE STATIST LAST 20 2. 20 32 36 20 A 2 28 52 56 €60!me nyncanh «nuke: 0 O o o IDCO RO— OOMma-o nnnn—c I o o o cure. and OONOQO Inn-non.— ~634- o o o o hhm 0"“! -— COG-ficfi fifltfl‘fi“ mm:— o o o o {INN '0.- an °°M—~ nnnncfi F3-“ 0 O o 0 fixed 1": camnuoo nncanc v? unoo 0 o o 0 I03..- Np— "N COCONNID fln0~g¢¢ Odo—7 o o o 0 can fias— “CV oooccm nncgon NNF‘O o o o 0 man.— Nan-I an at .056— nan—.snn Jim—cc STATISTICS TNG SEASON 0 Oath—.0 N lane; a :4: OG—‘C d‘ o o o Nam NP)" C OOQOG‘O N Inn 36:39 tape a . . . ~cr~ mac-o rt: comm—on m nnnncz 060° C 0 o O 31w" aug— an a r- ‘Dtcnh '0 ””0065: 00“.- ‘fi 0 o o o~- (VI-Ic- 160 .05 .10 .25 .50 .75 .90 .95 FIRST PRORAHILITTES 0F LAST SPRING DATES LAST U‘ONO ONF‘NO 000”” 610—9: “CNN!- umncnn whbfirofl «CNC‘N {IL-'3 3", «1100.1ch N—OCN mum: On nee”: .' Ont: no omncc ctr-~50. Hon-Nun Sumac: WNFNDU‘ HOND— 000i“? .7 mhflgt P; (T LV‘C 3087““?! ON-C'C “fir-AIN Vi.‘)~/TC‘.V‘ u;1.JU'..I.A - 1.; - I If! :1 ...-Ph— .05 .10 .25 .50 .75 .90 .95 LAST PROBABILITIES OF FIRST FALL DATES FIRST ‘6'“, 006166 Gin-RN“ and—u!" No-HDO‘ 0‘ Nun-ONO Got-unfit duo-"non «3.0—Inn “Nu-No GOO-HR; III—Grin. hd‘td 3 o—e—N cad—u— «....an bunny-c1 N—Nfi“ C‘OOCI-n nan—c- finhc C mac-I00! U‘ 09"“ sac-nau— ~¢oc~ ONONO U~G~OOq Clio-Cunt Nc-un-‘N -¢\.~.'C~JL‘ 1", 0°.- ‘fl‘ .06.: .I.‘ e C- " H0 C‘c \\ \‘u s.".')'."'.?h’. luluaht‘oi ['0 4 I‘lr INN v -. .1. In: INDICATED LEAGTH (DAYS) .05 .10 .25 .50 .75 .90 .95 PERCENT CHANCE OF SEASON LONGER THAN HAX mam 01 OMFU‘ “flu" ONIDTAOJI 0"th $0.th «II—"0N IDO-On—O $3.411.— Hon—N Inw'o rmna‘ N «rune-0N finance ~c~con flflmN G‘U'ADSO “‘15". ”H—NN IDNNU‘AD 8": l') {I "flu-N04 tncma who!) D -—‘.U'\. ‘\ \\\\\ in rm: I QONOO O.\IG.'C m .’:...L’Z 3‘5 7" -U-‘Ok -\ --.'..A TABLE C11 MICHIGAN (1950 THROUGH 1979) FREEZE STATISTICS FOR LUDINGTON, 20 24 CC FIRST FggL FREEZE STATISTICS 36 06' an; 20 6° fin C 2 STATISTI 2 GO nr) 28 DO ”"1 LAST SPRING FREEZE 32 C": 56 Dav-Inn— nnonm 3‘ nflnc o o . o d‘hn F0- ‘0'! QOCF—c ”HCCOO Cs‘qnu-n 0 o o 0 “CO No- 28 0 0 8 0 2 3 05—". vino-coha- i-hQ—n O o o o 04-..- NO— Nan 000‘an nncn—h (G‘s-c- . O O O 3205') New. k OQQ 0031' QNQJO O O O O ”‘0 FN \OFGQ 6469‘” tun—c O 0 o o no: €53— "N aha-ND mom: ~Ca‘lfic on 00 ”OF? an @6100 “0'“ {0'6 0 O o O {IN In“ .nn 5“" a C nnmg g c a 66~~m~ N ”7190:!- Inc-0° v o o 0 :‘NF Nun—a N C ao—nnd' N nflnfimd omma 3‘ o o o tho-0* V1 nail-n U N n .— W a— .— ‘ b: Oadhu‘.0 V101 ”NGQNN one— 2 5- o o o O In...— W l’fiN ‘ '— ad (I) Q 7. — IN 0930—!!! On nnnacln z Gad-00'. 0 - O o 0 0‘1)“ OCN all COCOIDU'? ”FILE-0-0 0‘55“” 31 o o o anan {INN R IN” 161 .05 .10 .25 .50 .75 .90 .95 FIRST PROBAEILTTIES OF LAST SPRING DATES LAST hhflfid‘ alto-IN A“: C cnnn Nth‘hn omen"- mccnn smack Shun-In.— ofltGlfifl comm: «cc-«:0. .nu'hrcn \CI’FN—n JG-No-n «uncen thO-Ct QNOHG «cunt: HOOK)? «HORN—n 01910.0 ance-co "CU-No.0 (HOLD. 0 NNWOV) .‘J "N-‘o-I a ‘QU‘IJWC omrso "1 ~15 ..‘N tfllft'b'f'm ... but-c...“- .05 .10 .25 .50 .75 .90 . LAST PROBABILITTFS OF FIRST FALL DATES FIRST «son;— Nut-6N Ono-06.63 a-u-n—u-u-o wahu‘hn «cu-0°C— Dan—GIN dud—tut I00~Nca ...N—an-n OOH-N “..--- tan—n cmomc DOI-u-MV Hun-«nan tofid' Nam—N mac—nu. fluid-I ten—or) «Inc-0O.- ma.°—-—u dun—I n—GFFTT'. Owen: $006.:— "~04 emmmw ndC.—(= ta-O‘C .- woo-a hccu-O t\¢-hd-l urtuv' “- 005 010 .25 050 .75 .90 .95 PERCENT CHANCE OF SEASON LONGER THAN INDICATED LENGTH (OATS) MAR NnNfiN macaw “HO-00" \\\\\ nnacw owner- NNnO‘J‘ adchc undo-n01 Gov-«gm cram:— out-II.“ «metro C'aVMDG N «none-0N "chf. NON—"fl anon—INN H~D~DGO who-mo —~(.~N a‘VQmm GET—C é ~~NN \V 0‘ 53“ Grrmf ~t -—'V‘\ (\ \\\\\ AVG—.....— 0.0ch GAIZ'Q': m-‘H‘J‘C’nl 9'. “N3. .’, :5 Q I .... 1‘4 . 'c‘. \' '.' -.- -O- - bQO-h—p TABLE C12 MICHIGAN (1950 THROUGH 1979) FREEZE STATISTICS FOR MAPLETON, 32 28 2A 20 FIRST FALL FREEZE STATISTICS 36 LV TCS 2A 28 ‘rgguc FREEZE STATIST LAST 36 OOKOOO‘) MHNCHZ ”5105C O O o 0 and“ dPlro- «Inc-a coonme urn-anon: Hcho o o o o 2.9—o nn—o ~— OO—ON— Inc-amoe- 69¢.- 0 o o O emu Out—o a-c-I OOU‘O—d nnmocm Conga O 0 Q 0 d3“. ’ 09—. “H OO-h-IN nnm¢n C oomnq‘! nnxngn Inch: 0 O I O '06 —h" 0“ OGONQO ”'3'th nag”: o o o 0 ~00.— nfl‘c-O RN eemwnao nrnunnra ..‘s. 4 JC‘C t7>xmqh o cacomh 04 non 3°00 C .FF‘oC .n o o 0 than NN—t OO—flmh N ”WP-PTHF ATISTICS O-C oa—cma VIN nnFOuaO ING SEASON GRDU 32 .‘hd G. O o C Jv'avb “Aw—l ... 30 30 83 67 28 1A enh— 0" o o o rmuo N:— nn¢ cum '(pN— O 0 O s. hia- an C. Q X '1 \ ":27 T 7” > x as .11 162 .95 FIRST .90 DF MO I...- TI 0 PROBAPILI .05 LAST chalet» «QC-NO “3830“” CIDO‘F'Q ulna—C‘— InInOOn onemm ~—n—~ In“). On «O‘C'Hn '5—(2 NO minIDCQ #0363“; QNO‘Co‘O 000130; comma “IGNO— 01.4030? cmhmn «ONON GOT-OLD: no~0°o No.- ~4~C. O‘DUTWJI ONIOC‘ ~Hfis\.\l~ .05 .10 .25 .50 .75 .90 .95 LAST PPODABTLTTIES OF FIRST FALL DATES FIRST "C'VDN OONGN an-HNN “dug“ ancfio diva—CG. Gan—awn! flflflflq "$0040 «NON t) Gown-IN nan-on— nun—o ONO NW Dunc-nut Hug—dd Duncan—n N—NF‘N mac—u- cons-Id 'L OWNS“ "Ow-a.- accom— nun-non Hhhcu" FNONO ma‘oc—o nun-u Nun-4a.. ON 3" 0.“ 0‘0 3°; Add JNCCC P)'TG‘IVN :h'fiJAGHn -Tc'b-u (I 5"! J 3 MIN .90 .95 LENGTH (DAYS) ED .75 .10 .25 .50 PERCENT ggANCE 0F SEASON LONGER THAN INDICAT 30006 ONnFO‘ ~~~H Fifi-Dir.“ nan-nan U‘c-ccco dun—1N CIDNOG‘ 0‘ 61,66 undo—N (Whom C’IM‘C‘ a4 don—CON chtfifl‘ ‘C‘CC‘W Dmmhu‘ 01.0750!” "Uh—NO. ”twin? Ch-TI'ILD undo-00461 “CH-t6; Inf—1'90 fl-Nm‘fia \\\\\ «‘Omc’a‘ fihhg‘ nan-nee HPH -mw :7 MGSW'A MICHIGAN (1950 THROUGH 1979) TABLE C13 FREEZE STATISTICS FOR MEARS, 2A 20 28 FIRST FgLL FREEZE STATISTICS ( 36 20 STATISTICS 2A EZE 28 :- L. LAST SPRING FR 32 660 I696 fine-nun NIH-GO o o . . an.— N'— ~— OONI-inn nncnwa 00:30— . o o 0 than mi).- ans-c conngn nnmncn «man- 0 o O 0 I001. Nun" N.— COONn—n nnNQ—sn Cong-fl O o o O 00.0 “Wm—n aOOn-‘N 'OI'ONIHI‘TO 6 mm“ C O O O OWN Gena. ccnnmc nun-ans Q CQJNO o o o o ahc NF— "N accep— flnmfiht ¢nu~a o o o o ”On 00“ "Cd O€.-NO~-fl lflML‘TQc'fi QC‘o-DO O O O 0 N90 £7qu '0'") TNG SEASON STATISTICS O N C N m; 0 oomnnc nnmnvc “Nuc- an o o o '51.“? NNH N OONRO— rnmch‘z ohh: a. o o 0 new Nev-o N ODF)I~CN ”IQCQU‘N .cofl x o o O Nu-H 'QN oo~~mm oowhnm ”MNCUAO~ 1&53 OF EAST SPRING DATES .05 .10 .25 .50 .75 .90 .95 FIRST PRORAhILITIES LAST taunts Nan-Na COO-fin \DF‘QOQN ON—NF‘ IDQC'N") Owe-Ic- «IDOOJC‘N unnecn ‘Ofin‘UC filo-C dc WIT-Mn" 066:". QC‘o-fls'du-I \OQDKICC ONGNQ «Ow-On worm: OFCNDN "\SNDN ~8~8U>'J‘-~l INNFOQ ...—3"“ 00.004): u16'r36' 7"):an .05 .10 .25 .50 . .90 .95 LAST PRUHAOILITIES OF FIRST FALL DATES FIRST "~0th 360166 n—HNN cum—aw..- «new: nae—cc Ono-C461 coo-«Inau- 506.050 «NON: acdfifii Gin—C...- Ina—O‘h Conn-N DOC ~1— aunt-Iran Inna-CU NON—— $000-— non—u wgo—m acme-IO— $050—— Gnu-o— «rm-occu- Nc-uC‘u-nc: I.) O C‘— a... PERCENI'CHANCE or SEASON LGNGIR THAN IOATST .90 INDICATED LENGTH HIN .95 .75 .50 .25 d0 .05 I“): X nachN “1.3th anon—alt \\\ \\ C '—\:L‘A OQ‘OOW ~~¢on manna .Iu-I—ON OCVMDU‘ 3 ACLO ——.‘N (C an ‘0 C'- (‘51:- CI urn-"~04 ONOFH’ CUCNCN ~~~NN ~05. Q30- ” trait-n ”flu-«V‘s VOOnN I" LII-«DVD ——fll\’\‘g\ \\\\\ I Inn: ‘C hhhfio C-‘Ifl‘ff': "'1(..’. IV TABLE C14 FREEZE STATISTICS FOR PAW PAW, MICHIGAN (1950 THROUGH 1979) FIRST FALL FREEZE STATISTICS 29 28 32 36 20 C 2 LAST STRING FREEZE STATIST I S A 28 32 3b DONG?!) FNN“ O O O 0 "~00 on.- N- GONh'pN ”'10" $7.9 Osyflfl O O O 0 3m“; ION-0 on" . 9009.00- nnmono nun-nu. O o o o I‘m—n Nun-n ‘olfl 665‘DmN nnho¢n Ono‘s-o O a o 0 Saw \Do—o GONhOO canon“): Cal‘— 0 a . O '00:... F2: COChgfic-I nnccrc Omno o o o 0 Chan Nh—I 60'0th annex: NOOO o o o 0 0°64 Cd‘— HN comma: nnwncc (NRC o . o o NON ecu-o an aoohxn nnmmnc <3.me O O O O nan Oat—o an 20 2A 28 GRggING SEASON STATISTICS 36 DOC-FRO") nnmgncc 04,36 3‘ o o O GONG: ION—i nonomh nl'OJIO—CD OnQO f. o o 0 70.3.0 NF— ccohnn nun-cam: 0“”..— N o O 0 mnm {‘JN— I « F | ,IA (Lin? w."- in ".‘t M \- 164 .30. .95 FIRST .75 TFS DA .50 .05 .10 .25 PROBABILITIES OF LAST SPRING LAST F0000 NuONO COOP)” c~c¢n~¢ O—OOJ-i nocnn {HG—O ON—ON In???” nd‘c‘h nN-CN Inl'CC I) «named» NCOJo—c Om... akin!— mac-Von .mmncc \Df-nNI ONGO— ommmo -OFQN tun—ON cam“): «Naao ‘ 0“,“) '2‘ amrceo .1 Vlt¥~VOl (”#9331771 win-Gown... 2 2 .1. .‘5 .z I ? TII v—c-o—u-o- .05 II” .25 .50 O .90 .95 L‘S' PRORABILITIES OF FIRST FALL DATES FIRST had‘U‘Q OOONO Oman—am alt-Id".- ~58”th ONQNO ao—c-N nun—nu 361.0 In (No-03°61 {Tutu-0c- Hun—u Noam-fl NCNOC- mac—a. «nu-n.- aznn C flN—(uu O-OOCH ”~— ~O~O~D~D «wen—N U‘O‘OOO “do. enact» 9.00."!- tars: ~DN a: 3 -.- .Arom“e .‘o. LONGER THAN INDICATED LENGTH (OATS) .05 .10 .25 .50 .75 .90 .95 PERCENT CHANCE OF SEASON MAX rfl—h'fl 0‘ mmsna‘ vii-fluid to ”'0 a “ab 3‘ all—Ha!" ”$01156 an! QCK' '— H'IFOCION n—cmn NU‘J‘O‘N nun—ow n MD“) '5 6.1—Ila n-nt‘JN NNONO OFU‘NC "flu-NW 63:64am ‘NLNU‘ ulna-awn“ TABLE C15 MICHIGAN (1950 THROUGH 1979) FREEZE STATISTICS FOR PEACH RIDGE, 32 26 2A 20 FIRST FALL FREEZE STATISTICS 36 20 C 2 TATISTI S c 9 28 LAST SPRING FREEZE 32 56 come-nun finnéan—o ' ‘31-." o o o a thug unc— Na. OOOL‘OC‘. nnOCc—o Nita-u- o O o 0 F300 NN— N— OGQONN nncaao o..fi.c.-n O o o o Odd-i 0'!— ODITOON nncoon N-Jfin—n O o g 0 Swan 59— a... Goa-khm Inn-now!» Uffifl o o o 0 oh.- Na— Qty-"Nob cannon-n QNQO C o o o 5‘0". O‘K— QOnOmfl nnoogn $000: 0 O O O $9.1. ecmw~h:' nP‘H‘JQCO FOOO‘O O O 0 0 NF.— ‘O—n «N ecmnuan unmanag- flfimo o o o 0 tan hon—I an ocsxmna P'H'VJ'UQH') ATISTTCS o emu—nrm- PH':..‘-!)ur.d‘. 000° 10 o o o N~OG¢ no“ N ha OOOFNC 92C» GROWING SEASON moo-emu: n ””660— mtg—u p . . . «wh- “Wu-0 a! CC) acne nna-u—n .fifi— 'fi 0 o o #5.; NN—n an .9 vlrh q -r- S'TT'sxu n 165 .75 .90 5 FIRST TES DA .50 .05 .10 .25 PROBABILITIES DF LAST SPRING LAST 0106an “an EON Ocn‘fiN :n: ‘3: anon-o OCC'IP') Nhnfiw «No-cm “Mitt-f) sen—... 64' Nun :mnccn amt-ck: Nona—co WADE. ~70 mncrwcu ONON—o mmnc Q .0 murmur 0611200 afuh“.y~ not 21mm anus-......» .05 .10 .25 .50 .75 .90 .95 LAST PRORALILITIES OF FIRST FALL DATES FIRST 5‘00!“ a.m.-nu. .2 ado-IN dud—Id O-ND'YHD UGO-Null Can—ION dflflfifl OhNnG “No-Non OO—ww cit—0H?!" IDCFQG (Nu-IN (TN 066 and nuns-:— -DC a: 000‘ «nu-cm.» U‘O‘OUG ant-u- NF‘SQC cue—o. U‘ do: " ~H" Ow‘hmc‘ “N(.'J— SOQ‘OC‘ an: to: "D-Wt‘J'. A. WMLNE‘U) Lad-'h card. ’1; ‘9 I A :IIT? hit—him.— HIN IDNGER THAN INDICATED LENGTH IDATST .05 .10 .25 .50 .75 .90 .95 PERCENT CHANCE OF SEASON TIA! somhm ONOKC‘ dd—Oud Ofann omens: nun—N fir‘lflCh c-IQRU' .— anon—~01 5112313661 NICQO"! «av-«MN G‘NJSG‘Q rafiC‘HC ~~~NN U CS‘ON CFOIOO -"‘NN~ mango mm—nh fl-NNN ¢—=~~ éfiwvnh all-INNN \\\\\ 39.0“: f mhmom (01:96 “fluor‘. EV .7."/“5v1 cu‘Thd “- A. ‘0 -v ! -"-- ‘ ' -‘ hO-IO-O— [v.55 TABLE C16 FREEZE STATISTICS FOR SODUS, LAST SPRING FREEZE STATISTICS (1950 THROUGH 1979) fIRSI FALL rucczr STATISTICS MICHIGAN 20 2A 28 32 36 20 ?4 29 32 coon-run NW"¢'~°° leNOG o o o o 60": ~00— 'fw'CNfi Nun-moo HOF- o o o a hit nan-o o..- GAOHnO—C camN-fio (‘JNNU‘QN 9&1..— . O O . own 0°.- ~— U‘ON'NU‘ wmhnnc wOC—c o o o o 00‘ VOW-“‘0" NNmnflm N000 o o o 0 mar) no... “N U‘U‘Qu-hh omnnmmm OOQO o o a o 0‘6») ION—n NW :‘U‘O‘JMF- «Nut-Jam Fr-NCO u o o o Q—uc hfl‘o-n NW 20 24 TATISTICS 8 936‘! "ASDN S GRDdING 32 36 momma-o NNFMDOIv-Q “‘0‘.- C 0 0 O NWO OWN N G O-Cc-C'c CNN—ink. 00‘9— (‘0 o o o ‘4’.) #0 N 1166 FIRST .90 o 75 SPRING DATES .25 .50 . oID PflggAMILITIES 0F LAST LAST ”00"!“ N09“:— 'CnNN rah—0:0 NONL‘N ecu-mow cummin- ~~CN— Ottnn 0*n0 «cc-ON mint?” sac-CIGU' 8V “V‘s“ u‘nnc C n COC’I'IVD omcmo ammcc C‘mCC‘o-n ONO-Nd m.,—unto N7 cov- a.m.-can“ VOW n00 05:20: 'TI'N‘JHN '1? 2". UNIT {1 005 010 025 050 015 .90 .95 LAST PROBABILITIES OF FIRST FALL DATES FIRST 05m ”N dun-0° an“ Q-«V (5N ulna-III! '10-! cv~ca~v~ ~s~v~°~ Dana-~51 dun-nun “Chg.” c-IGLVO-n cal—own; undue-HI. cmomo N-‘Ifl-ON c \Uc—H ~—~" “'56 It: to Nev-no.4 0' 6.3-nu -—I-OH IDFONO nanom— c O CO.- ...-on NNnNC “NONI: U‘J LDC an and!!! (Sc-60‘s - Writ-(‘3 a-‘racc. ans—"In HIN INDICATED LINGTH (DAYS) .05 .10 .25 .50 .75 .90 ‘095 IENCENT CHANCE OF SEASDA IOPGER THAN HA! «wrath among—o H—H'iN \\\\\ eoaoo ~00~D~D~O mhcmc‘ cine: a-t «cu-«nu dflOCO ncfl'U‘N noun—0Q, «0000‘ 2') (flake-p HdF‘NN “430‘ 3" ”\cc‘ (‘1‘) ans-sumo; 01$an CFC-«t ~L HHsVN“ NON-Gm LDCF'MDN FCC-G'NN $.1—NN If 3 C58 3. “"95““ Tic-Curd) JC‘LON'S v-C. A N“; \\\\\ “’30:?“ .nmmznfi 167 FIRST FALL FREEZE STATISTICS MICHIGAN (1950 THROUGH 1979) TABLE C17 FREEZE STATISTICS FOR WATERVLIET, LAST SPRING FREEZE STATISTICS 6 common N nncnno G-C‘O'a— a... fl”? NF)— Nu- ? OCFNNN N Inn-now.— 0“”.— one. cnn ¢Na ~n thMN memos C oomamc h z «and N nnhawn m ”QQOO‘ .- O-‘QOO _- \\\\\ mggn a mecca m «coma z cocoa 0'00 ~ {Ctnn < an—«N OOFFO n@r u A dunn— «on Non N 506F163? TD C‘IDIDDP‘I In NSC-OD n nnNn—¢ m n—aw— m ~Nn~~ m nnnan ”do-fl 0 cvcnn O 39.-«IN 0‘ flucfia coco ddflnfl 0 mafia who OCH-I ‘3 ‘ m p ( O m—cmb c unnac 3 VB ooh-mm— O oonv~ce 6‘ CON—IN“ 3‘ ONO-IO -0 «.090.— fi nnnnao N nnsczm 0 acvnn o ecu—N 3 JNfiNO cum—O ou‘, (NO I'm—H .: o nap-N 000. not. b mun H€G Q FCC—I (CNN 2 u N U .1 n OOONO m wmhom h «nucw h NflNON om CNGQ” ' m0"” 0 6-0." uh gnu:— nnga h- madam < O OOU‘ON— U C GONG“). N FInC-CNQ VI - N nn—coc oun— u m 0 "05¢ N o I o h- ;J z 0000 «no «a c—mmm ha O$hdfl — omw m {ON cm Nam—C (m mourn a QONNF CFC-I U N . IDIDC’OC O ‘ U‘C-OG—U 2m "CFC“ flN — Q «and q. "mum“ h z 4 I W N .J O- u- 1 £ 0 Geo-0°63 .- O- L 2 N nnCCQ? < m U Owoc pm OC@FCA m flmhuc pm nogmm Q 000. mm nnnooa h“ enema mu “KONG 2m nanéa ¢mn 05”" m0 Omntt a. 0000— CN mam—c am— 2‘. H o O 0 fi '— ”and d o '"F‘C‘N «N O O—h A u m nh— Z d n u u c M O O W 3 cemhcm (fl :1 N ”FIR-€910 40° NdInLT‘F-i ma ”9'3“” In; hxua Q U— «Gama mu o—w—m mo ON¢¢n 000. 2 —0 oomcc no COwOO H thGNm m—n — b h «u go puumm mad 3N ocmhnc h H O n” on nnm¢n¢ J J oatq u n U m h... a m U new < 1 2 N OGFOO— {ON L9 thtd on cmnr— ( n nnhClm a CO HCNON OD NHNON 1m OOOOQ “TN-DO B ' «Immune G 0 $5 398' U0 5'?”an I O o o :L .1. en— 0 ._.—WNW umc h 0“ z NH U U o 0000: h m Lnfihc n nnecoa h fiasco m cN—co u @023; 0 us. c’vNNc 'V".4 L7 Nana—an .z Cal-mm-n a): «HF-7.353. 0 nnnga. out. 4 066mm — mcmvg c \\\\\ acme n=— 4 m d I —Jmfifi one. cum macaw NF: — d“— Nn acute.) 00'1‘5’0 mmxsec Inna-rum INONN‘V flflcuVsu 2 .. fin/141': L’H‘Zlflé’m 51.1.‘H-"f. ’qL x z I .. .-I.-.L'L-a -mu-‘Ls'nl sun--'.".a 'L’f \ L“ \ ':.'.I ' L 1.‘ u t! J‘..’"'.t : «fl»? <25? :211: 2:22: 22.:1 "’>¥'~‘,U‘. )‘(VU‘ bhp—O‘ p—t-u—b-O- bun-h— Rn(0) GI Cl 1' xi ni PW APPENDIX D TEMPERATURE-PROFILE PREDICTION MODEL There are five distinct steps in the model: 1. soil heat flux 2. convective heat flux 3. friction velocity 4. air-temperature profile 5. temperature change with time Input Parameters Input parameters at tO were: an hourly mean value preceding tO (calcmTZHdn-l) ambient air temperature at the reference level, 150 cm (0K) wind speeds at 900 and 1800 cm, respectively maximum soil temperature for the day at i = 0, 5, 10, 20, and 50 cm (0K) minimum soil temperature at same levels (OK) percent water in the soil on a volume basis dew—point temperature (OK) 168 169 Soil Heat Flux The heat flux through the upper boundary of a slab of soil at the earth-air interface during periods of net outgoing radiation is SAT/At)dZ (D.l) Z S(O) = f(pSC 0 Soil layers which exhibit diurnal temperature variation are responsible for the total flux of heat across the earth's surface. Equation D.l is then evaluated as an algebraic sum: 8(0) = (pSCSAT/At)l + (pSCSAT/At)2 + ... + (pSCSAT/At)I (D.2) where the subscripts refer to depths 1 cm, 2 cm, etc., to the depth where AT/At = 0. The soil heat capacity per unit volume (volumet- ric heat capacity) is computed by the formula Cv = DB(CS + PW/lOO) (D.3) A moist, homogeneous soil is assumed, where CE is the bulk density of the soil, 1.6 q cm-3, and C is the specific - S heat of the soil, 0.18 cal g"1 c‘l. Van Wijk (1965) bypassed the need for precise knowledge of the thermal diffusivity of the soil when deriving his equation of the soil temperature profile with respect to time. His equation is: 170 T(Z.t) = TA + ATO e‘(Z/D) sin(wt+CO-Z/D) (D.4) where T is the average soil temperature and is often the same at any level within the depth of diurnal temperature change (OK) AT is the 8mplitude of the soil surface temper- ature ( K/lOO m) D is the damping depth: the depth at which the amplitude of the temperature wave has in- creased to l/e of its value at the surface km” CO is a constant which depends upon the choice of the zero point on the time scale w is 2n/P, where P is the period (sec’l) This equation is actually a solution to the clas- sical Fourier heat conduction equation: aT/at = KSBZT/BZZ which fits the boundary condition T = TO sin wt. This assumption is based upon the observation that, on cloudless days, the diurnal fluctuation of soil temper— ature may be approximated by a sine function of the time. The soil heat flux each hour was computed by use of D.2, D.3, and D.4. Finally, the derivatives of D.4 for each soil level at t0 and at hourly increments after 't were used in a form of D.2 designed to account for the O uneven spacing of maximum soil temperature measurements: 5(0) = 5cV[?ZT7ZETl + YET7KETZ + 2(AT/At)3 + 6(AT7At)é] (D.5) The subscripts refer to descending soil slab numbers, and 171 bars denote averages of the change in temperature with respect to time at the bounding surfaces of each slab. For example, (AT/At)l = [KAT/At)0(fln+ (AT/At)5(nn:D/2 Convective Heat Flux The convective heat flux was solved by FH(0) = Rn(0)-S(O) (D.6) where the horizontal and vertical divergence of heat flux were assumed to be zero, and the net radiation considered to be constant throughout the forecast period. Friction Velocity An approximation to the friction velocity was found from the difference form of Prandtl's logarithmic law, which models the wind velocity in an adiabatic atmosphere: 02 - Ul = [ju*/K)(1nzz/ZO{] - [ju*/K)(1nzl/ZO[] = (U*/K) ln (2221) (0.7) Alternatively, U* = (U2-Ul)k/ln(Z2/Zl) = (Uz-U1)k/ln 2 (D.8) where k is von Karman's constant, 0.40. In the non-adiabatic case, it was necessary to compute a thermal stability index known as the Monin- Obukhov scale length: L = U*30 T/(ngH) (0.9) 172 The scale length is constant with height, making it convenient to express wind and temperature gradients as a function of the dimensionless height ratio Z/L. The non-neutral wind profile is dU/dZ = (U*/kZ)(l+aZ/L) (D.10) where the term (1+aZ/L) represents the first term in the power series expansion of f(Z/L). Integrating D.10: U = (U*/K)[jn(Z/zo)+a(z-zO)/f] (0.11) but 20 is very small, so that the non-adiabatic profile is U = (U*/K) [}n(Z/zo)+aZ/§] (v.12) Air-Temperature Profile The Lumley-Panofsky scaling temperature T* = FH/KU*cp (D.l3) appeared in the temperature profile equation, e-ezo = T*[ln(Z/zo)+aZ/§] (v.14) By neglecting vertical motions in a stable atmosphere, the profile equation was solved in a manner similar to that ] (p.15) Tzl was designated as the reference temperature TR at for obtaining D.7: Z2‘21 ‘“IT" T -Tzl = T*[}n(Z2/Zl)+a 150 cm. Typically L is much greater than 21' so that Zl/L was neglected and the final profile equation was 173 T2 = TR + T* [:ln Z/zR+aZ/L:] (D.16) Temperature Change with Time From the air-temperature profile, dT/dZ at the reference level was computed and then used with FH(O) to find the exchange coefficient: KH = -FH(0)/pcp(dT/dZ) (D.17) This enabled the computation of the eddy conductivity (A): A = K c (D.18) Hp p By considering heat flux across any plane, Brunt (1941) derived an equation for the air-temperature profile valid for the case of constant flux across 2:0, with the boundary condition T This equation was then solved to compute the predicted change in temperature at 150 cm during the next hour, which then establishes the value of the reference temperature for the next iteration of the program: _ 3'5 - 2 _ T(Z,t) — ZFH/A[}KHt/n) exp( Z /4KHt) (Z/2)erfc(Z//4KHt)J (D.19) where erfc is the complimentary error function. The main assumptions in the model were: 1. constant net radiation 2. a homogeneous soil with respect to conduc- tivity and water 3. equality of the exchange coefficients for 174 momentum and heat 4. a neutral wind profile 5. zero advection of heat This model was tested by the Agricultural Weather Service in Florida and presented by J. C. Georg in partial fulfillment of a master's degree from the University of Florida. His results in predicting the nocturnal minimum temperature are very promising: the mean error was -0.16°C, with a standard deviation of 2.4OC. Seventy percent of the errors were within one standard deviation of the mean, and 100% were within two standard deviations. Georg cited the need to improve computation of the friction velocity, both initially and in subsequent time periods. To accomplish this, he suggested obtaining longer time averages of the input wind velocities, and using a log-linear wind profile on nights when the expected wind speed is less than 2.0 m sec-l. He also concluded that omitting a net radiation divergence term distorted some of the temperature profiles. Finally, a means for computing the change in net radiation during the course of the evening would improve the model. BIBLIOGRAPHY BIBLIOGRAPHY Alter, A. G. 1920. Studies of the Frost Problem. Geogr. Ann. 2:20-32. Bagdonas, A.; Georg, J. C.; and Gerber, J. F. 1978. Techniques of Frost Prediction and Methods of Frost and Cold Protection. WMO Technical Note No. 157. Geneva. 160 pp. Ball, F. K. 1954. Energy Changes Involved in Disturbing a Dry Atmosphere. Quart. J. Roy. Meteorol. Soc. Ballard, J. 1976. Wind, Water and Wits. J. Wash. St. Hort. Assn. 81:62ff. (8 pp.) Bartholic, J. F., and Brand, H. J. 1979. Foam Insulation for Freeze Protection,h1Modification of the Aerial Environment of Plants, eds. B. J. Barerld and J. F. GerBer. Vol. 2. St. Joseph, Mich.: ASAE. Bates, E. M. 1972. Temperature Inversion and Freeze Protection by Wind Machine. Agric. Meteorol. 9:335—46. Bethea, R. M.; Duran, B. 5.; and Boullion, T. L. 1975. Statistical Methods :fimr Scientists and Engineers. New York: M. DeEker. 583 pp. Beals, E. A. 1912. Forecasting Frost in the North Pacific States. Bulletin No. 41 (W. B. No. 473). 49 pp. Brooks, F. A. 1947. Action of Wind Machines in Frost Protection. American Fruit Grower 47:15ff. (4 pp.) Brooks, F. A.; Rhoades, D. G.; and Schultz, H. B. 1950. Frost Protection for Citrus. Cal. Ag. 4:13-15. Brooks, F. A.; Kelly, C. F.; Rhoades, D. G.; and Schultz, H. B. 1951. Heat Transfer in Citrus Groves. Cal. _A—g_° 5:14-15. Brooks, F. A.; Kelly, C. F.; Rhoades, D. G.: and Schultz, H. B. 1952. Heat Transfer in Citrus Orchards Using 175 176 Wind Machine in Frost Protection. Cal. Ag. 33(2): 74ff. (10 pp.) _ — Brooks, F. A.; Rhoades, D. G.; and Leonard, A. S. 1952. Wind Machines: 90 and 15 bhp Machines Compared for Frost Protection at Riverside. Cal. Ag. 6:7-8. Brooks, F. A.; Rhoades, D. G.; and Leonard, A. S. 1952. Frost Protection Tests with Wind Machines. Cal. Citrograph 37:14-16. Brooks, F. A. 1952. Heat Transfer in Citrus Orchards Using Wind Machines for Frost Protection. Agr. Eng. 33(3):143—7. Brooks, F. A., Rhoades, D. G., and Leonard, A. S. 1953. Wind Machines: 1953 Report on Frost Protection Tests in California Citrus Groves. Cal. Ag. 7:6-7. Brooks, F. A.; Rhoades, D. G.; and Leonard, A. S. 1954. Wind Machine Tests in Citrus. Cal. Ag. 8:8-10. Brooks, F. A. 1959. An Introduction to Physical Micro- climatology. Davis, Calif.: University of CalIfor- nia. 264 pp. Brunt, David. 1941. Physical and Dynamical Meteorology. New York: Cambridge University Press. 428 pp. Businger, J. A. 1965. Frost Protection with Irrigation. Meteorol. Monog. 6:74—80. (Boston: Amer. Meteorol. Soc.) Crawford, T. V. 1964. Analysis of Area Influenced by Wind Machines in Frost Protection. Trans. ASAE 3:250-2. Crawford, T. V. 1965. Frost Protection with Wind Machines and Heaters. Meteorol. Monog. 6:81-7. (Boston: Amer. Meteorol. Soc.) Crawford, T. V., and Brooks, F. A. 1959. Frost Protec- tion in Peaches. Cal.Ag.13:3-6. Crawford, T. V., and Leonard, A. S. 1960. Wind Machine- Orchard Heater Systems for Frost Protection in Deciduous Orchards. Cal. Ag. 14:10-13. Davis, R. L. 1977. An Evaluation of Frost Protection by a Wind Machine in the Okanogan Valley of British Columbia. Can. J. Plant Sci. 57:71-4. Ellison, E. S. 1928. A Critique on the Construction and Use of Minimum Temperature Formulas. Mon. Wea. Rev. 56:485—91. 177 Fuchs, M., and Tanner, C. B. 1966. Infrared Thermometry of Vegetation. Agronomy J. 46:597-601. Gates, D. M. 1965. Radiant Energy, Its Receipt and Disposal. Meteorol. Monog. 6:1-26. (Boston: Am. Meteorol. Soc.) Gates, D. M., and Tantraporn W. 1952. The Reflectivity of Deciduous Trees and Herbaceous Plants in the Infrared to 25 Microns. Science 115:613-16. Geiger, R. 1957. The Climate Near the Ground. Cambridge, Mass.: Harvard University Press. 494 pp. Georg, J. G. 1970. An Objective Minimum Temperature Forecasting Technique Using the Economical Net Radiometer. J. Appl. Meteorol. 9:711-13. Georg, J. G. 1971. A Numerical Model for Prediction of the Nocturnal Temperature in the Atmospheric Surface Layer. Master's thesis, University of Florida. Gerber, J. F., and Busby, J. N. 1962. Field Trials with a Wind Machine. Fla. State Hort. Soc. 75:13-18. Gerber, J. F., and Harrison, D. S. 1964. Sprinkler Irrigation for Cold Protection of Citrus. Trans. ASAE 7(4):464-8. Gerber, J. F., and Martsolf, J. D. 1979. Sprinkling for Frost and Cold Protection. In Modification of the Aerial Environment of Plants, eds. B. J. Barfield and J. F. Gerber. V01. 2. St. Joseph, Mich.: ASAE. Goss, G. B., and Brooks, F. A. 1956. Some Observations of Longwave Radiation from Clear Skies. Quart. J. Roy. Meteorol. Soc. 82:241-53. Hashemi, F., and Gerber, J. F. 1965. The Freezing Point of Citrus Leaves. Proc. Amer. Soc. Hort. Sci. 86:220-5. Hendershott, C. H. 1961. The Response of Orange Trees and Fruits to Freezing Temperatures. Proc. Amer. Soc. Hort. Sci. 80:247-50. Hilgeman, R. H.; Everling, C. E.; and Dunlap, J. A. 1964. Effect of Wind Machines, Orchard Heaters, and Irrigation Water on Moderating Temperatures in Citrus Grove During Severe Freezes. Am. Soc. Hort. Sci. Proc. 85:232-44. 178 Jensensius, J. 8.; Zurndorfer, E. A.; and Carter, G. M. 1978. Specialized Agricultural Forecast Guidance for Michigan and Indiana. TDL Office Note 78-9. National Weather Service, Systems DeveISpment Office, Techniques Development Laboratory. Kangieser, P. C. 1959. Forecasting Minimum Temperatures on Clear Winter Nights in an Arid Region. Mon. Wea. Rev. 87:19-27. Keyser, E. M. 1922. Calculating Temperature Extremes in Spokane County, Washington. Mon. Wea. Rev. 50: 526-8. Kreyszig, E. 1970. Introductory Mathematical Statistics: Principles and Methods. New York: John Wiley and Sons, Inc. Mee, T. R., and Bartholic, J. F. 1979. Man-Made Fog. In Modification of the Aerial Environment of Plants, eds. B. J. Barfield and J. F. Gerber. Vol. 2. St. Joseph, Mich.: ASAE. pp. 334-52. Mitchell, A.; Eichmeier, A. H.; Johnston, S.; Larson, R. P.; Bell, H. K.; Dexter, S. T.; Downes, J. D.; Kidder, E. H.; Wheaton, R. Z.; and Van Den Brink, C. 1965. Michigan Freeze Bulletin Research Report No. 26. East Lansing: Michigan State University Agricultural Experiment Station. 40 pp. Moses, B. D. 1938. Blowers for Frost Protection. Agric. Eng. 19:307-308. Neter, J., and Wasserman, W. 1974. Applied Linear Statistical Models. Homewood, 111.: Richard D. Irwin, Inc. 842—pp. Nichols, E. S. 1920. Notes on Damage to Fruit by Low Temperatures; Prediction of Minimum Temperatures. Mon. Wea. Rev. 16:37-45. Nichols, E. S. 1926. Notes on Formulas for Use in Forecasting Minimum Temperatures. Mon. Wea. Rev. 54:499-501. Raschke, K. Heat Transfer Between the Plant and the Environment. Ann. Rev. Plant Physiol. 11:111-26. Reese, R. L. and Gerber, J. F. 1963. Field Trials with a Wind Machine in a Citrus Grove. Fla. St. Hort. Soc. 76:81-6. 179 Reese, R. L. and Gerber, J. F. 1969. An Empirical Description of Cold Protection Provided by a Wind Machine. J. Amer. Soc. Hort. Sci. 94(6):697-700. Reuter, H. 1951. Forecasting Minimum Temperatures. Tellus 3:141-7. Rhoades, D. G.; Brooks, F. A.; Leonard, A. S.; and Schultz, H. B. 1955. Frost Protection in Almonds. Cal. Ag. 9(8):3ff. (4 pp.) Sakamoto, A. G. and Gifford, C. S. 1960. The Climate of Nevada. Nev. Agr. Exp. Sta. Bul. 649. Schaal, L. A.; Newman, J. E.; and Emerson, F. H. 1961. Risks of Freezing Temperatures--Spring and Fall in Indiana. Indiana Agr. Exp. Sta. Bul. 721. Sellers, W. D. Physical Climatology. 1965. Chicago:Univer-. sity of Chicago Press. Shaw, R. H.; Thom, H. C. S.; and Barger, G. L. 1954. The Climate of Iowa. Special Report No. 8. Iowa Agr. Exp. Sta. Smith, J. W. 1914. Frost Warnings and Orchard Heating in Ohio. Mon. Wea. Rev. 10:573-9. Smith, J. W. 1920. Predicting Minimum Temperatures from Hygrometric Data. Mon. Wea. Rev. 16:6-19. Soderberg, M. E. 1969. Minimum Temperature Forecasting During Possible Frost Periods at Agricultural Weather Stations in Western Michigan. WBTM CR-28. Kansas City, Mo.: Weather Bureau. 8 pp. Suomi, V. E., and Kuhn, P. M. 1958. An Economical Net Radiometer. Tellus 10:160-3. Sutton, 0. G. 1953. Micrometeorology. New York: McGraw- Hill. 333 pp. Swinbank, W. C. 1963. Longwave Radiation from Clear Skies. Quart. J. Roy. Meteorol. Soc. 89:339-48. Thom, H. C. S. and Shaw, R. H. 1958. Climatological Analysis of Freeze Data for Iowa. Mon. Wea. Rev. 86:251-2. Van Den Brink, C. 1968. Types of Spring Freezes in Michigan and Their Relationship to Protection Equipment. Mich. St. Hort. Soc. 98:102-107. 180 Young, F. D. 1920. Forecasting Minimum Temperatures in Oregon and California. Mon. Wea. Rev. 16: 53-60.