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ZEEB ROAD, A NN ARBO R, Ml 48106 18 BEDFORD ROW, LONDON WC1R 4EJ, EN G LA N D 8013755 Jo n e s , V e r n o n K . RELATIONSHIPS BETWEEN CLIMATE AND CROP YIELDS IN MICHIGAN Michigan State University University Microfilms International Ph.D. 300 N. Zeeb Road, Ann Arbor, MI 48106 1979 18 Bedford Row, London WC1R 4EI, England RELATIONSHIPS BETWEEN CLIMATE AND CROP YIELDS IN MICHIGAN By Vernon K. Jones A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1979 ABSTRACT RELATIONSHIPS BETWEEN CLIMATE AND CROP YIELDS IN MICHIGAN by Vernon K. Jones Multiple regression models were developed for yields of selected field crops in Lenawee, Gratiot, and Gladwin Counties in Lower Michigan. Climatological data were obtained from National Weather Service cooperative observer records. Crops studied were com, oats, soybeans, and dry beans in these counties where yield records were available for the specific crops. Long-term trends were removed by calculating piecewise linear regressions for specific periods. Departures from trend were used as the dependent variable in multiple regression analyses. Predicted yield departures from the regression analyses were added to trend values to obtain predicted annual yields. Two separate analyses were made. The first used monthly climate data for the April through September growing season for 18921977 in Lenawee and Gratiot Counties and 1926-1977 in Gladwin County. Independent variables were temperature; precipitation; soil moisture derived from soil water capacity, precipitation, and potential evapotranspiration; and the squares of each of these. The second Vernon K. Jones analysis used weekly temperatures and precipitation for the growing season of each specific crop. For com, soybeans, and dry beans, the most important climate factors were July and August precipitation. May and June were most important for oats. Temperatures in Use of a soil moisture availability index did little to improve the analysis. Analyses based an weekly data explained a larger portion of the variation in yields (higher R ) than those based on monthly data. A truncated mid- to late-season weekly model may be useful in developing early estimates of yields for the current crop year. Removal of time trends from crop data prior to multiple 2 regression analysis lowers R values. However, this allows the analysis to deal with short-term variations which are largely influenced by growing season weather conditions. ACKfCT^LEDGMENTS It is inpossible to adequately thank or even mention the many people who have given of time, expertise, and concern in helping this research— and researcher— along. The major burden of counsel, advice and discussion was borne by Dr. Dale Linvill with grace, good humor, forebearance, and incredible patience. members were Dr. Georg Borgstran, and Dr. Fred Numberger. Ccmmittee Dr. Charles Cress, Dr. Jay Hannan, Their wisdom, insight, and effective sug­ gestions are much appreciated. Mr. Don Fedewa of the Michigan Agricultural Statistics Service kindly consented to serve as outside examiner. Fellow graduate students played an important role in pro­ viding suggestions, information, and moral support. Various faculty members in Agricultural Engineering but also in Crops and Soils and Agricultural Economics were valuable sources of information and counsel. The involvement and sacrifices of my family over many years are the sine qua non for successful completion of the graduate study process. Most important of all has been the continued support of my wife, Elizabeth. ii TABLE OF CONTENTS Page LIST OF TABLES .......................................... V LIST OF F I G U R E S ..................................... vi Chapter I. INTRODUCTION................................... 1 Objectives of the S t u d y ........................ Setting and Period of the Study................... Rationale for Station and Crop Selection . . . . Geographical Context of Climate Stations . . . . Crop D a t a .................................. Method of S t u d y ................................ 1 1 3 3 4 7 A REVIEW OF CLIMATE AND CROP MODELING............. 9 II. III. Variability and Yields........................... A World View of Climate and Crop Modeling . . . . Research in the United S t a t e s ................... Trends in Michigan and the N a t i o n ............. Technology and Yield T r e n d s ................... Relationships Between Crop Yields and Climate . . Surmary........................................ 9 10 11 12 13 14 28 CLIMATE AND CROP DATA: SELECTION, PREPARATION AND ANALYSIS.................................. 30 Selection of Study Area via Climate Records . . . . Monthly Climate D a t a ........................... Estimation of Missing D a t a ..................... Transformation of Monthly D a t a ................ Analysis of Monthly Climate D a t a................ Weekly Climate D a t a............................. Crop D a t a ..................................... S e l e c t i o n .................................. Analysis of Crop D a t a ........................ 30 31 31 34 39 39 43 43 43 Chapter 17. V. Page ANALYSIS OF CEJMATE-YIELD RELATIONSHIPS........... 55 Analysis Based on Monthly D a t a .................. Results of the Monthly Analysis................ Analysis of Outlying Y i e l d s .................. Analysis Based on Weekly D a t a .................. M e t h o d ..................................... Results of the Weekly Analysis................ Analysis of Outlying Y i e l d s ................... The Phenological Adjustment Approach.......... Weekly vs. Monthly Regressions.................. Intercorrelation of Independent Variables . . . . Limitations.................................. Catastrophic Events.......................... Areal Variability.......................... 55 56 65 71 71 72 84 85 86 88 89 89 90 SUMMARY AND CONCLUSIONS........................ 91 S u n m a r y ..................................... The Study Process .......................... R e s u l t s ..................................... Monthly Analysis............................. Weekly Analysis ................ Conclusions.................................. Relationships ............................. Limitations................................ Monthly vs. Weekly Analyses................... Suggestions for Further Study ................... Secondary Independent Variables................ Removal of Trend .......................... Phenological Stages .......................... Pattern Analysis............................. Caveats..................................... The End and a Beginning........................ 91 91 94 94 95 95 95 96 97 97 98 98 98 99 99 100 LIST OF REFERENCES . 101 A P P E N D I X .......................................... iv 109 LIST OF TABLES Table Page 1. Probability of One Day per Month with Excess Rainfall . 35 2. Day Length Indices for Adrian, Alma, and Gladwin 35 . . 3. Linear Regressions Used for Yield T r e n d s ........... 50 4. Simple Correlations (r) for Yields and Monthly Climate V a r i a b l e s ..................................... 57 5. Multiple Regression Models, Monthly D a t a ........... 58 6. County Climate Variables Selected by Month-Based Multiple Regression Crop M o d e l s ................... 60 7. Statistics from Multiple Regression, Actual and NonExcess Precipitation, Monthly D a t a ................ 66 8. Data for Yield Outliers, Based on Monthly Climate Data . 68 9. Distribution of Climate Variables Selected by WeekBased Regression Models........................... 73 10. Correlations of Deviations frcm Yield Trends and Weekly Climate V a r i a b l e s ........................ 74 11. Full- and Mid-Season Models; Weekly Data; 5% Significance L e v e l ............................. 77 12. Ganna Distribution of Weekly Precipitation, .90 and .95, Adrian and Alma, 1929-77 ..................... 83 13. Yield Regression Statistics, Real-Time vs. Phenologically Adjusted Weekly Climatic Data, Lenawee County, 1943-77 87 v LIST OF FIGURES Figure Page 1. Location of Study Areas in Lover Michigan........... 2 2. Mean Growing Season Temperatures vs. Latitude, Lower Michigan, Apr.-Sept. 1940-69 ..................... 6 3. Decadal Means of Mean Annual Temperatures, Selected Michigan Stations, 1880-1969 ..................... 40 4. Mean Growing Season Tanperatures by Y e a r .............. 41 5. Growing Season Precipitation by Y e a r .................42 6. County Annual Yields, with Segmented Trend Lines . . 44 7. County Acreages of Crops in the S t u d y .................52 8. Actual and Predicted Yields Based on Monthly Climate D a t a ......................................61 9. Signs of Yearly Departures over 10% fran Yield Trend, with Monthly Climate D a t a ........................... 69 10. Actual and Predicted Yields, Weekly Data, 1943-77 plus 1978 vi 79 CHAPTER I nmmjCTiON This study seeks to contribute to our understanding of relationships between weather conditions in the growing season and variations in the yields of major field crops in Michigan. OBJECTIVES OF TOE STUDY 1. To determine long-term relationships between variations in climatic data available from volunteer cooperative observer records and variations in the annual farm yields of specific field crops in Michigan. 2. To determine at what times in the growing season weather variations are related to significant variations in crop yields. 3. To develop a predictive model for estimating annual county crop yields, based on local weather records for the current growing season, both at mid-season and at the end of the season. SETTING AND PERIOD OF THE STUDY Three counties in lower Michigan, identified in Figure 1, were selected for this study. Lenawee County is located in south­ eastern Michigan, along the Ohio border. The weather observations for this study were recorded at Adrian, near the center of the county. 2 LAHt OSCODA ALCONA 06C M AW IOSCO O SC tO LA C L A D t BAT TU SC O U SA N ILA C 6 N A T I0 T OTTAWA S A O tN A W CLINTON OANLANO INSNAAA MACi IIV IN C STN CALNOUN C ASS N IL L S O A ll Nuribers represent stations; see listing in Figure 2 xStations in the crqp-yield study. Figure 1. Location of Study Areas in Lower Michigan. 3 Gratiot County is located in central lower Michigan, lying partly in the Saginaw Valley with its former lake-bottom soils, lhe weather station used is located at Alma, near the center of the county. Gladwin County is located just into the northern half of the lower peninsula, with marginal or near-marginal climatic condi­ tions for warm-season crops. Hie observation station used is near the center of the county, in the town of Gladwin. Hie period of the study includes 1892 through 1977 for Lenawee and Gratiot Counties. 1926. Climatic records began in Gladwin in Yield predictions are made for 1978 for all counties, based on climate data for that year. RATIONALE FOR STATION AND CROP SELECTION GEOGRAPHICAL CONTEXT OF CLIMATE STATIONS An atteirpt was made to obtain records from stations along a south-to-north transect in Lcwer Michigan, as near the center or * eastern center of the peninsula as possible in order to avoid "lake effects" from the nearby Great Lakes. As long a period of record as possible was desired, to provide a long-term data base and to allow maximum repetition of any existing patterns. Inspection of mean growing season temperatures along a latitudinal transect up the peninsula reveals the presence of a climatic transition zone across the Saginaw Bay-Muskegon line in the center of the state (Figure 2). While it somewhat parallels the topographic rise to the higher elevation of northern Lower Michigan, 1 2 3 4 5 6 *Kzo - AA 64- All GUc GLd His 62- Adrian* Allegan Alma* Ann Arbor Atlanta Bad Axe Hst .Aim* *JCk ELan MLfd •MildII MfcP> 7 8 9 10 11 12 13 14 15 16 17 18 Battle Creek Big Rapids Cadillac Caro Charlotte Ctoldwater East Lansing Gladwin* Grayling Greenville Gull Lake Hastings ♦Lpr •Ows Caro 60. 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Higgins Lake Hillsdale Houghton Lake Jackson Kalamazoo Lake City Lapeer Midland Milford Mio Mt. Pleasant Onaway Owosso Vanderbilt West Branch BgRp * Stations in the climate-yield study Htlk Nunfcers refer to Figure 1 58- WBr HgL Vblt Y=96.9-0.80x Y=282.7-5.07x 75 " Y=68.7-0.24x - - - - - - - - - - - - - - - r- - - - 44 45 Latitude in Degrees Figure 2. Mean Growing Season Temperatures vs. Latitude, Lower Michigan, Apr.-Sept. 1940-69 it does not coincide with it. Gladwin and most of Gladwin County, despite being near the northern portion of the tenperature transi­ tion, are at a relatively low elevation on the edge of the Saginaw lake plain. Both Adrian and Alma, south of the transition line, fall close to the trend line. Inspection of climate records and on-site visits indicated that Adrian, Alma, and Gladwin best met the criteria for station selection. Other stations were deficient in length of record or relative historical microclimatic homogeneity; were in locations not representative of county agriculture; or were in counties with low crop acreages and thus insufficient crop records. CROP DATA Records of crop yields for the county containing the selected weather stations were obtained from publications of the Michigan Agricultural Reporting Service and its predecessors. Crops included were com, soybeans, dry beans, and oats. CORN Recent archaeological studies have revealed that c o m (Zea mays) was grown in northern Wisconsin until about 1200 A.D., when the northern limit for c o m growing rapidly shifted to the present border with Illinois during a period of climatic deterioration. The cold, dry period, which drastically changed the Indian cultures, lasted about two hundred years (Bryson, 1975). C o m was found by early European explorers to be canmonly cultivated by the native Indians in Michigan up to the shores of Lake Superior in the 16th 6 and 17th centuries. Types grown in the cooler northern and drier western areas were short, hardy varieties (Weatherwax, 1923). Thus we m y assume that c o m production in Michigan antedates our archival records by a considerable margin, and that adapted genotypes were readily available. C o m is exceeded only by dairy products as a source of cash farm income in Michigan, bringing in nearly $247 million in 1977, or two-and-a-half times as much as dry beans, the next greatest crop income source (Michigan Crop Statistics, 1979). field crop ccmnm to many temperate areas. C o m is a primary It has been widely * studied and serves as a common denominator in climate-yield studies. Long-term records for c o m are available for all three counties studied. SOYBEANS Soybeans are a relatively new crop in Michigan. They have been important enough to appear in the crop reporting records since 1942; thus data from Lenawee and Gratiot Counties are available from that time. Soybeans respond to climate in a manner similar to com. They are less cannon than c o m in areas where climate or soil are marginal. Ihey rank close behind dry beans in market statewide receipts, with $89 million in 1977 (Michigan Department of Agri­ culture, 1979). 7 DRY BEANS Beans, like com, were already being grown in America before the early Europeans arrived. Andersen and Robertson (1978) estimate that commercial dry bean production in Michigan started in the early 1880s. State records of bean production begin in 1895. Dry beans are sensitive to climatic anomalies; in particular to excessive precipitation late in the growing season. They ranked second behind c o m in Michigan cash farm income in 1977, with over $99 million (Michigan Department of Agriculture, 1979). Michigan ranks first in the nation in dry bean production, and provided 94.2% of the nation's navy beans in 1977 (Michigan Department of Agri­ culture, 1978). In the three counties selected, only Gratiot had dry bean acreage sufficient for study. OATS Oats are a cool-season crop, responding to climate in a manner different from c o m or beans. While less important statewide as a source of cash receipts, they are important as a feed grain and as a rotation nurse crop for establishment of hay and grass seedings. Oat records are available since 1892 for all three counties in the study. METHOD OF STUDY In order to analyze short-term or year-to-year variations in yields, most of which may be ascribed to weather, long-term trends representing less than a single oscillation were removed. This was done by fitting linear regressions to segments of the yield data for 8 each crop in each county, then using the annual deviations from these trend lines as the input data for analysis. Multiple regres­ sion analysis was applied for each case, with the above deviations as the dependent variables. Independent variables were temperature and precipitation for periods in the growing season. analyses used monthly and weekly time periods. Separate For the monthly analyses a moisture availability term was derived from a cumulative soil moisture budget, including precipitation and potential evapotranspiration, which was calculated by the Thomthwaite method. After calculation of predicted deviations from trend by the multiple regression models, annual trend values were added back in to provide predicted yields. CHAPTER II A REVIEW OF CLIMATE AND CROP MODELING In a report discussing plans for a specialized National Agricultural Weather Service (Epstein, 1977) the present situation regarding crop-weather relationships is expressed as follcws: Correlations between weather conditions and agricultural output have been made for certain crops at specific locali­ ties within the Nation, but, to date, no general information is available other than the fact that weather can be the most significant variable explaining year-to-year fluctua­ tions in the yield of most ccmmodities. This chapter deals with research which has been done or is in progress with the objective of understanding, explaining, and predicting year-to-year changes in the yields of crops in this study. VARIABILITY AND YIELDS McQuigg (1975) gives three main sources of variability affecting the yield of grain crops over the years: (1) technological change; (2) meteorological variability; and (3) randan "noise." He estimates that total variance about the sample mean is due 75 to 80% to technology, 12-18% to weather, and 5-10% to randan noise. We note that at any given time the available technology is essentially at a given level. Thus the major year-to-year variant is the weather conditions that exist. In any case, McQuigg warns, the weather-technology interaction is still unresolved. We must be 10 aware of the influence which this lack of resolution has on our model estimates. Edey (1977) points out what has also been noted by several other authors: "It is increasingly evident that the greatest threat to food production is still the regional variability and fluctuation and not an overall long-term climatic change." These variations, especially in precipitation, often have a great impact on agri­ cultural production. Edey also noted three shcrtcanings in agroclimatic statis­ tics. First, weather of the next 30 years will not necessarily be the same as that of the past 30. Second, "normal" weather does not exist; we can expect ranges and extremes which can sometimes be disastrous. Third, climatic records of a given station are not necessarily representative of a larger geographic area. Thus the impacts of spatial and temporal variability force us to go beyond normals and averages. A WORLD VIEW OF CLIMATE AND CROP MODELING Different climatic areas may have different limiting factors affecting crop production and yields. Cnop-yield modeling activities in various parts of the world, as reported by Baier (1977a), tend to reflect local conditions. For example, statistical-empirical crop models in Iran and India stress water availability as a variable. In southern Brazil relative humidity in October is an important variable in estimating the yield effects of plant disease stress. Both temperature and precipitation are important variables in wheat 11 models developed for the Anatolian Plateau in Turkey. In lcw- rainfall areas of Israel, annual precipitation figures correlate well with wheat yields. is important in India. Distribution of rainfall as well as amount In Australia a crop-water stress index is important in estimating water available in the root zone through the critical period for wheat. Much of Canada is vulnerable to low temperatures. Baier (1977b), in his sirrmary of the 1977 meeting of the Canada Committee on Agraneteorology, notes estimates that a decrease of 1 degree Celsius (1.8°F) in average simmer temperature would decrease poten­ tial c o m production in Ontario by about 30% and eliminate c o m as a grain crop in most of the remainder of Canada. He concludes that the most probable change in climate is a trend toward more variability, both seasonal and yearly, in climatic factors which will affect agriculture. McKay and Allsop (1977) state that climatic fluctuations, including brief climatic anomalies, are the major cause of varia­ tion in crop yields in Canada. In the prairie provinces, good years may actually be the anomalies. Planning must include an expectation of climatic variations. RESEARCH IN THE UNITED STATES Since this study is concerned with climate-crpp yield relationships in Michigan, it will be most concerned with the portion of the nation which has relatively similar crop weather. 12 TRENDS IN MICHIGAN AND THE NATION Wright (1976a) studied yield trends of specific crops in Michigan for the period 1950-1975, and compared Michigan yields with national trends for those crops. Both state and national yields shewed a sharp increase for the post-World War II period. This was especially spectacular for com, more than doubling the long-term Michigan average of 2016 kg/ha (32 bu/a), as shown by the above reference. Also shown is a lower rate of increase occurring in average yields, starting with winter wheat in 1964 and soybeans in 1968. Dry beans in Michigan are a special case, with peak yields in 1964 and a downward trend since then. In contrast, national bean yields reached a plateau in 1961 and have remained high. While Michigan average yield decreased from 147 kg/ha (1310 lb/a) in 1960-64 to 121 kg/ha (1078 lb/a) in 1970-74, Ontario yields climbed fran 133 kg/ha (1190 lb/a) to 156 kg/ha (1390 lb/a). For the latter period dry beans still followed c o m and wheat in crop market value in Michigan (Wright, 1976b). Clough (1968) quantified yield trends, applying 9-year moving averages to U.S. c o m yields over the period 1916-1965. Fran 1916 to 1935 there was little change in yields. Fran 1935-1951 the average yield moved fran 1640 to 2430 kg/ha (26 to 38 bu/a). Fran 1951 to the time of his study it had almost doubled, fran 2450 to 4500 kg/ha (39 to 71.5 bu/a). He noted that variations in the percentage of average yield were smaller in the latter half of the 13 period. He attributes this reduction to changes in production practices. MoQuigg (1976) found that the technological trend line of wheat yields in Oklahoma actually decreases since 1960. This includes not simply absolute yield, however, but also changing landuse practices, including release of land from government acreage reserves. Katz (1977) found that, although the 1960-1974 linear trend was negative, these data shewed no significant (95% level) evidence that the slope of actual wheat yield was non-zero. Experiment station soybean yields in Iowa, reflecting the state of the art, reached a relatively high level seme years ago. Average farm yields are new approaching this level. However, station yields have not moved upward beyond that plateau, indicating that farm yields must also level off unless unforeseen new techno­ logical breakthroughs are achieved (Thompson, 1975). TECHNOLOGY AND YIELD TRENDS An examination of yield trends in recent years shows the effect of increased fertilizer use, higher-yielding varieties, higher plant populations, and other cultural practices. However, while this technology is still available, farm yields have leveled off and in some years dropped sharply. The years of increasing yields coincided with exceptionally stable and favorable weather which allowed us to carefully tune new practices to give optimum results under a narrow range of favorable weather conditions (Thompson, 1975). 14 Thompson (1969a) concludes that two factors account for most of the variation in wheat yields since 1945. Technology is assumed to be a major factor in the long-term increases in average yields, and weather is assumed to cause the variability around the long-term trend. Thompson (1969b) estimates that the two factors together explain fran 85 to 90% of the yield variability. Dale (1964) studied the effects of moisture stress on c o m in experimental plots at Ames, Iowa fran 1933 through 1962. He held fertility treatments as stable as possible, with most of the change in technology limited to higher-yielding varieties and higher plant populations. He concluded that, although technology is responsible for the steep upward trend during the latter part of the period, benefits fran this technology were possible only because of the low level of moisture stress during that period. An adequately high number of "non-moisture stress days" are necessary to realize the effects of the improved technology. RELATIONSHIPS BETWEEN CROP YIELDS AND CLIMATE A major reason for concern regarding the weather is the inevitable impact weather has on food production. Considerable work is now being done an simulation modeling of crop yields, with climatic conditions as input variables. For such models to be valid, reliable information is needed for both micro-scale crop response and probable climatic conditions. Thompson (1975) reviews the condition of oomplacency and over-confidence in high policy levels of the USDA generated by the 15 unusually favorable and stable weather of the previous two decades. The official view existed that our technological expertise had reduced yield variations in both good and bad weather (Butz, n.d.). Thompson notes that the highly variable weather of 1974 shocked many people into a greater concern over the food supply. Resulting dis­ location in grain markets, the livestock industry, international trade, and the economy as a whole caused serious financial losses as well as boosting inflation. While anyone who has been close to the land has an intuitive understanding that yields are closely related to growing-season weather, intuition is an insufficient basis for scientific analysis. We will look first at techniques which have been useful in studying these relationships, then at seme results obtained fran recent research. SOME TECHNIQUES USED IN STUDYING CROP-CLIMATE RELATIONSHIPS Most crqp-climate studies are of two types, or a ccmbination of these: (1) Simulation studies or physiological models; these attempt to mathematically model the growth process in a given season. (2) Climate-crqp yield or empirical-statistical models; these estimate yield on the basis of statistical relationships fran a series of yield and weather data. with the second type of study. We are concerned primarily While this second approach draws on a large amount of data and shews what happened before, it does not necessarily shew cause and effect. Spurious relationships may occur which have no physical basis in biological reality. 16 Nelson and Dale (1977) state that year-to-year changes in yield over a short period of years should be predicted mostly in weather terms in a multiple regression model, rather than by technological terms. They also note that predictions of the effects of technology on yield depend quite a bit on just what time-weather series is used. tions. This can introduce large errors in yield predic­ They ascribe the larger errors in the 1970s to more highly variable weather. Katz (1977), in a sensitivity analysis of statistical cropweather models by the use of ridge regression techniques, found that a lack of reliability was inherent in coefficients estimated by multiple regression. Sources of errors were: (1) relationships between crop yields and a given climatic variable were non-linear? and (2) climatic variables which were used as predictors possessed seme amount of correlation between them. He states that the multiple regression models in question have been valuable in show­ ing the definite effect of weather variability on yields, but warns that we must be aware of their limitations. Haigh (1977) developed structural models to separate yearto-year variability of crop yields into the effects of weather and those of management, using coefficient of variation analysis for the period 1935-1970. He asked two questions: (1) Has better manage­ ment reduced the effects of bad weather on crop yields; and (2) Has the upward trend in yields leveled off in recent years? His analysis showed that the percent of yield variation explained by management over the period 1928 through 1976 is about 17 two to three times that explained by weather. The interaction of the two accounted for 10 to 20% of the variation in yield. This analysis could be of added value if it were repeated, based on 19651976 technology, rather than on the 1940-1970 period of rapid tech­ nological improvement. Haigh concluded that: (1) there was no evidence found that technology has reduced the sensitivity of grain yields to weather; (2) there is no statistical evidence that increases in grain and soybean yields were leveling off by 1970. RESULTS OF CTOP-CLIMftTE STUDIES CORN Robbins and Domingo (1953) tested the effect of soil moisture depletion to the wilting point at different stages of development. resulted. If moisture were removed before tasseling, low yields Depletion four weeks after tasseling caused significant reduction in yield, but depletion seven weeks after tasseling appeared to cause no significant difference. They concluded that soil moisture was critical only until the c o m reached maturity. Following maturity, soil moisture depletion did not affect yield or moisture content. Yield reductions were therefore related not to total amount of water available but to the duration and timing of moisture deficits. Denmead and Shaw (1960) also studied the effects of soil moisture stress at different stages of grcwth on the yield and development of com. They found that effects on yield of stress 18 at the vegetative stage amounted to about 25%; during silking, about 50%; and at the ear stage, 21%. They further determined that as stress periods recurred, total effect seemed to be less detrimental, as the earlier stresses apparently hardened the plant. Dale (1964, 1965, 1968) showed that rapid increase in Icwa c o m yields, usually credited to improved technology and cultural practices (especially higher plant populations), was possible only due to very favorable weather enjoyed in Iowa for the preceding three years, as well as the 1948-1965 period. Thompson (1969b) used a multiple curvilinear regression on c o m yields in the C o m Belt from 1930 through 1967 to determine the influence of weather. In order to remove the effect of technology, he used one linear trend line for the period 1930-1960 and a second for 1960-67. The main factor affecting yields was July rainfall. Following, with a combined effect less than July rainfall, were (1) the occurrence of average precipitation from September through June; (2) normal June temperature; (3) above-average rainfall in August; and (4) temperature slightly cooler than usual in July and August. Holt and Timmons (1968) found in South Dakota and Minnesota that, as precipitation increased, higher stands, up to a maximum of 54,400 plants per acre, gave higher c o m yields. Precipitation during late July and early August, as the c o m approached silking, affected c o m yield more than that received during early July. Lawlor and Liebhardt (1978) developed a climatic model using a daily water budget. Preliminary results frcm Maryland 19 showed that a July and August moisture deficit is related to lower yields, while a surplus in June shows a positive correlation. Runge and Odell (1958) found, through a multiple correlation study of experimental plots at Urbana, Illinois for 1903 through 1956, that c o m yields were influenced most strongly by precipita­ tion preceding anthesis (beginning of pollination) and by maximun temperature during anthesis. They found that a phenological approach using date of anthesis explained more of the yield variability (67%) than one based on fixed calendar dates with 8-day periods (58%). Including trend by year increased the amount of variation explained by temperatures and rainfall to 75%. Schaal and Blair (1968) found that in c o m production in Tippecanoe County, Indiana, the best c o m yields occurred in years when temperature averaged above normal during the establishment period and belew normal during the grand grewth and reproduction periods. Runge (1968) found that high maximun temperatures of 90 to 100 degrees F (32-38°C) can be beneficial to c o m yield if the plant has adequate available water. He found that maximun temperature and rainfall have a large effect on yield from 25 days before to 15 days after anthesis. At Urbana, this period occurs on the average between June 30 and August 8. Maximun yield effect occurs at approximately one week before anthesis. Actual effect on yield depends on the specific combination of temperatures and precipitation which occurs. This interrelationship could be expected to occur due to the effect of tenperature and available moisture on transpiration. 20 This brings up an inportant source of error in the interpre­ tation of statistical studies. A ccrparison of c o m yield with temperatures suggests that higher-than-normal temperatures are related to decreased yields. Runge's study suggested, however, that the cause of decreased yield under high temperatures is not due to the high temperatures themselves, but rather (1) drier conditions associated with clear, rainless skies, and therefore more insolational heating; and (2) increased moisture stress due to increased evapotranspiration at higher temperatures and levels of radiation. If adequate water is available, higher temperatures may in fact increase rather than decrease yield. Thus interaction between temperature and precipitation variables may exist at high tempera­ tures, but not be reflected in the model developed from long-term data. Runge's statement may be relevant in not only whether or not to irrigate, but also in selecting methods of irrigation. Runge and Benci (1975) used average weekly maximun tempera­ ture and total weekly precipitation data as the growing season progressed, as well as certain soil factors, to project c o m yields for that season. They concluded that with present technology, man- induced or natural climatic change or variation would have a con­ siderable influence on c o m belt production. Dale and others (Dale and Hodges, 1975; Dale, 1977a, b) developed an Energy-Crop Growth (BOG) variable as part of a crop growth simulation model. This was later adapted for use in a climate-yield prediction model for the Tippecanoe County c o m yield study for the period 1957-1975. It includes radiation, a leaf area 21 index (Linvill, 1972), and a ratio of actual to potential evapotranspiration, but excludes a temperature factor. Combined with a nitrogen use index, it explained 67% of the variance in county-com yields. Nitrogen was used as a proxy variable for improvement in technology over time. This appeared to be an improved method of handling the time trend and/or technology component which is a prob­ lem in the Thompson-type multiple regression approach. Dale points out the interaction between weather and manage­ ment which is represented by the N variable. Higher levels of N are related to high yield response when the weather is favorable. During seasons with unfavorable weather, higher levels of N do not produce higher yields. He states that the yield response to one depends on the level of the other. Achutini, Eddy, and LeDuc (1979) studied c o m yields in Icwa and Illinois for the period 1928 to 1973 using a simple multiple regression model. For the years 1949-1973 they concluded that c o m yields in these two states were largely a function of technology, with nitrogen fertilizer accounting for most of the variation. How­ ever, they point out that technology cannot compensate for yield reductions due to weather variability. They also tested models which were truncated after the planting [sic] and silking stages, with sane loss of accuracy. A study of the effects of precipitation alteration in Kansas (Bark, 1978) included statistical crop yield prediction models. This study used the Thanpson approach, including a linear time trend assumed to represent technological improvements over the period of 22 the study. Hie variables for the c o m model in the eastern one- third of Kansas included monthly temperatures for May through August, plus October, and squared terms for each of the above. Palmer "d" values, which include both precipitation and stored soil moisture, were tested as variables to replace monthly precipitation. However, results were inconsistent, so precipitation was used. Also included in the equation was a technological time trend constant C(l) = 1.443 for the years 1946-1975, used as C(l) x (year-1899). The use of all 11 terms plus the trend constant and the regression constant in the equation gave an R 2 =0.91 and a standard error [sic] of 6.71 bushels per acre. Nelson and Dale (1978) used analysis of variance to evaluate the accuracy of four statistical models applied to selected Indiana counties. The traditional multi-variable linear or "Thompson" model used twelve weather and three technology variables. Weather vari­ ables were June, July, and August mean temperatures and precipita­ tion, their squares, and pre-season precipitation from September to June. Technology variables were a linear time trend which was incremented by one year frcm 1941 through 1960, and constant there­ after; a linear term incremented by one each year after an initial value of 1 in 1960; and the square of the latter. The modified Thompson model used the same weather variables but replaced the three technology variables with a single variable representing average annual nitrogen use on c o m land in Indiana. The third model was the 14-term Leeper model (Leeper, Runge and Walker, 1974), using experimental-plot technology adjusted for 23 estimated average state level of technology use. Weather variables were represented for 6 weeks before to 4 weeks after average tasselling date. The 14 terms included linear and quadratic terms for available soil water at planting time, plus 12 complex surmation terms. The surmation terms were based on weekly precipitation and mean daily maximun temperatures. The individual terms and their cross products were weighted by linear and quadratic week numbers 1 to 10. Where appropriate these surmation terms were also multi­ plied by the amount of available stored soil water at planting time. The fourth model replaced all weather variables with a single Energy-Crop Growth (EOG) index. This was a surmation of 84 daily EGG values, frcm 6 weeks before to 6 weeks after 50% silking. Daily ECG values were based on solar radiation, a leaf area index, and on actual and potential evapotranspiration. Where radiation data are not available, BOG may be approximated by using ET. The regression model is composed of the ECG index, nitrogen used for com, and the interaction of the two. Goth the Thompson and modified Thompson models were regressed with full (all variables) and stepwise (critical P value of 2.0) versions. Years tested were 1971 through 1975. Errors of prediction in any single year varied frcm 4 bu/a in the Leeper and ECG models to 37 bu/a in a full Thompson model with 3 technology variables. Lowest yearly average error for the 5 years was 9 bu/a in both the full and modified Thompson models with nitrogen use as the technology vari­ able. Without the anomalous 1974 figures, lowest average error was 7 bu/a for the same two models. 24 The ECG-ET model, Leeper's 14-term model, and the Thompson model with nitrogen use substituted for technology trend variables gave approximately equal levels of prediction accuracy, within about 10 bu/a. The Thatpson model with three technology trend variables proved to be less accurate. Huda and Runge (1978) developed and tested ten c o m yield models for universality, and also tested two other models. They found that the 14-term model developed by Leeper was the best pre­ dictor for ex ante estimation of c o m yield. Niell and Huff (1979) used a technological index plus monthly temperature and precipitation in a crop-leather regression model for 1931-1975 in the midwest c o m belt. A quadratic term for the tech­ nological index plus July precipitation and temperature and the August temperature were the significant variables. Various combina­ tions of pre-season precipitation and interaction terms between the climatic variables were input but were not selected by the regression process. The same basic equation with the same variables was applic­ able to all 45 crop reporting districts in Illinois, Icwa, Indiana, Missouri, and Ohio. SOYBEANS Much less attention has been given to soybeans than to com. Gross and Rust (1972) found by multiple regression methods that, for the period 1956-1965 in Minnesota, the climatic variables most highly correlated with yield were May, June, and July temperatures and the state of soil moisture an the first day of June, July, and August. 25 Non-climatic variables were applied nitrogen, phosphorus, and potash, plant population, and planting date. The soybean model by Bark (1978) used a time trend plus precipitation for July through October and temperature for May 2 through August, plus October. R for this model was 0.92, with a standard error [sic] of 2.05 bu/a. Runge and Odell (1960) found that, for Illinois experiment station yields frcm 1909 through 1957, 68% of the variation lay in precipitation and the maximun daily temperatures. Greater than average rainfall before July 1 decreased yields, but after that date it was beneficial. Yields were reduced by hard rains and cloudiness during the first half of August. Above-average rainfall before June 25 and after September 20 helped, but were detrimental between these dates. Thompson (1962, 193, 1970) studied soybean yields in the C o m Belt for various periods from 1930 through 1968 by multiple regression analysis. He found that the two most important weather variables were above-average July rainfall and below-average August temperatures. August precipitation was relatively more important for soybeans than for com, as their shallower root systems are less able to tap deeper subsoil moisture. He concluded that, while technical inputs to production helped increase yields from 1935 to 1961, a major part of the increase in production was due to the unusually favorable weather in the latter half of the period. Niell and Huff (1979) studied frequency distribution of weather-related deviations frcm technology trends in c o m and 26 soybean yields for 1931-1975. Monthly weather data ware used. Below- normal yields were primarily related to moisture deficits, but also occasionally to excessive precipitation. Above-normal yields tend to occur with normal or above-normal precipitation combined with normal or belcw-normal temperatures in July and August. They also found that negative deviations in yield were consistently larger than positive deviations. They also found that soil characteristics, apparently water-holding capacity, were more strongly related to crop weather sensitivity than were spatial differences of climate. In seasonal soybean-weather simulation model, Pavelo and Decker (1979) found that for the central United States, weather from the flowering stage to maturity has the most influence on yield pre­ diction. Hill, Johnson, and Ryan (1979) also used seasonal simulation of soybeans during four growth stages frcm flowering to maturity. The most moisture-critical period was during the pod-filling stage. DRY BEANS It appears that, despite their susceptibility to direct yield effects and climate-induced disease problems, the question of climateyield relationships in dry beans has not been adequately addressed. A computer search of 800C biological publications for the period 19701978 (BIOSIS) yielded no relevant articles on the subject. Earlier, Robbins and Dcmingo (1956) found yield reductions of about 20% on dry beans in coarse-textured soils in the Columbia Basin under certain moisture-stress conditions. This occurred when 27 visible moisture stress persisted for 15 days prior to blocming; 18 to 22 days during blocming; and about 15 days before the first pods ripened. Stress late in the season hastened ripening of the crop, but bean weight was reduced due to failure to reach maturity. Moisture deficits before blooming retarded development of the plants. Irrigation before the plant showed visible moisture stress at any time in the season appeared to have no advantage. Smucker, Mokma, and Linvill (1978) note that dry bean plants are very susceptible to oxygen deficiency due to flooding. Flooding for more than 24 hours at the preflowering stage reduced yield by 50%, and by 25% when flooded during flowering. ORIS Oats also appear to have received little attention in terms of yield response to weather. If the present cooling trend con­ tinues, they may emerge as a much more important crop in northern areas on the fringe of the C o m Belt, since they grow well in tenperatures cooler than those required for com, soybeans, and dry beans. However, the computer search noted earlier yielded only two references, both of which dealt with yield studies in Florida. Pfahler (1972) found, in a study of 94 oat populations in Florida over a six-year period, a "negative relationship" between yield and environmental variability. Selecting varieties for high yield generally resulted in populations with low environmental variability. 28 McCloud (1977) studied yield trends and variability for eight major Florida field crops. He assumed that the long-term trend was due to technology, and that variability from this trend line was due to weather. Oats and c o m showed increased yield vari­ ability at higher yield levels. He noted that most of the eight crops studied, including com, soybeans, and oats, had apparently reached a yield plateau. SIIWIAKY Awareness of the role of climate in the problem of feeding the world's people is gradually growing. Recent weather-triggered crop disasters have shaken seme of the complacency which resulted frcm technological developments concurrent with an exceptionally long run of favorable weather. The USSR and Canada, due to their vulnerability to cold seasons and cooling trends as well as moisture deficiency, have become very active in bicmeteorological research. Canadian scientists have concluded that climate variability is more threaten­ ing than a cooling trend, and that increased variability is probable in the years ahead (Baier, 1977b). Crop yields in the United States and in Michigan have passed through a period of dramatic increase, but have since leveled off. Until recently, this increase was ascribed to technology; new it appears that at least part of this increase was due to a period of relatively favorable weather. This period of favorable weather may 29 now be over. A problem still exists in separating out technological effects on yield from climatic effects. Most widely-used techniques for evaluating crcp-climate relationships are statistical multiple-regression models. While they may have limited accuracy, they are useful for determining the nature of relationships. One approach is to use time as a proxy variable, assuming that the long-term trend reflects improvement in technology and management. Shorter-term variations around the trend are considered to be due to weather effects. This does, however, fail to clarify either long-term weather trends or shorter-term variations in management. The critical stress period for c o m appears to be during tasselling and silking. Yields are affected most by lack of moisture in late July and early August. rainfall in July. Soybeans are favored by above-average Information was inadequate to provide conclusions in regard to dry beans and oats. A factor repeatedly stressed is that high yields in the 1960s are partially due to an unusually long run of favorable, stable weather. The slowing in the rate of increase in yields with the more variable weather of the 1970s gives ex poste support to this view. We note that most studies and climate-yield models continue the steep upward trend line prevailing over most of the past 20 to 40 years. not the actual case. Recent crop yield trends shew that this is CHAPTER III CLIMATE AND CROP DATA: SELECTION, PREPARATION AND ANALYSIS SETiECTION OF STUDY AREA VIA CLIMATE RECORDS Data for this study were obtained from long-term National Weather Service records taken by volunteer observers. In order to observe the transition from c o m belt to marginal climate and soil conditions, a lengthwise south-to-north transect of the lower peninsula was taken, station sites were restricted to near the center or eastern center of the peninsula in order to minimize lake effects from Lakes Huron, St. Clair, Erie, and especially Lake Michigan. Such "lake effects" may have an influence of several degrees on temperature for many miles inland from the eastern shore of Lake Michigan. Minimum and maximun temperatures are also affected, as are growing season lengths. Cloudiness and precipita­ tion may be affected less sharply, but for equal or greater distances inland (Seeley, 1917). A long period of record was desired, in order to provide a data base as large as possible and to show maximum repetition of any potentially existing patterns. Spatial distribution was also considered. Within these constraints stations were chosen for the best quality of records available. This required a minimum of serious gaps in the record, and no known problems of consistency and 30 31 reliability. The station should be stable with a limited nuriber and distance of moves, either horizontal or vertical. not involve extensive microclimatic changes. Any moves should Station sites should possess no climatic aberrations atypical of the county crop areas. Present sites were visited and past locations traced, to assure that records would not contain excessive variations due to site changes or causes other than actual climatic variation. Another consideration in selection was whether or not the station records have been computerized and processed by the Michigan Department of Agriculture/Michigan Weather Service. This increased the availability and accuracy of the data for a station, and also supplied additional processed data for analysis. Such criteria resulted in the elimination of all but Adrian in Lenawee County, Alma in Gratiot County, and Gladwin in Gladwin County. Each of the three had undergone seme relocation during the period of record used, but present and past sites were judged to be reasonably similar in microclimate. M3NIHLY CLIMATE DATA ESTIMATION OF MISSING DATA Despite the selection of stations with the best possible records, there were times over the years when observations were simply not taken. Adrian data were nonexistent for January through June of 1903, April of 1908, and April through November of 1928. Gladwin data were missing for October-December 1927, March-August 32 and Ocbober-Deceriber 1928, August 1939, and January-May 1941; and incomplete for May and December 1976 and April and October 1977. TEMPERATURE In order to estimate missing temperature data, stations with fairly complete records within a 40-mile radius were used. For Adrian, this included Ann Arbor and Hillsdale, and for Gladwin stations at Mt. Pleasant, Midland, and West Branch were used. Gladwin and adjacent stations showed more variations in records than Adrian due to greater differences in topographic and microclimatic environments. Linear regressions were calculated between each of the check stations (x's) and the subject station (y) for periods which included, when possible, at least 12 months before and 12 months after the missing data. When feasible, specific missing months of the year were also replaced with the nearest same months beyond the above 24 months in order to maintain the annual balance of monthly temperature levels. Discrepancies between Hillsdale-based and Ann Arbor-based estimates for a missing month at Adrian ranged frcm .01 to 2.25°F (.005 to 1.25°C) . All but two of the 16 estimates shewed less than 1°F difference frcm the two sources. Largest discrepancies between Gladwin monthly temperature estimates based on regressions against Mt. Pleasant, Midland, and West Branch ranged frcm 0.28 to 6.64°F (0.15 to 3.7°C). The latter was due to a very low average at Mt. Pleasant for April 1928. 33 Second largest discrepancy was 3.60°F (2.0°C). Of the 19 other estimates, 6 had differences of less than 1°F (0.55°C), 6 were 1 to 1.99°F (0.55 to 1.1°C), and 7 were 2 to 2.99°F (1.1 to 1.7°C). Adrian tenperature estimates were judged to be reliable within 1°F (0.55°C) and Gladwin estimates within 3°F (1.65°C). PRECIPITATION The linear regression technique was tested on precipitation data. Due to relatively large variations in precipitation totals between stations from one month to the next, this method proved to be inaccurate. Isopleth analysis proved to be a more accurate method of providing missing monthly precipitation data than the use of linear regressions. Rather than depending on widely fluctuating relation­ ships between stations for a period of months, the isopleth analysis considered the areal distribution of precipitation for each single month in question. Monthly precipitation totals for all available stations in the Lcwer Peninsula for each specific month which had data missing were posted on a state map at the station location. Isopleths of equal precipitation (isohyets) were sketched at one-inch rainfall intervals. The missing monthly precipitation for the subject sta­ tion was estimated frcm the isohyets and nearby stations. Estimates were judged to be reliable to within one-half inch. The above processes provided data for the years 1892-1977 for Adrian and Alma and 1926-1977 for Gladwin. 34 TRANSFORMATION OF MONTHLY DATA Two new groups of variables were derived frcm the initial observer data. These were (1) non-excess precipitation, and (2) a moisture availability index. NON-EXCESS PRECIPITATION Much of the growing season precipitation occurs in convec­ tive storms. Thus the precipitation record and unadjusted soil measure budget may include precipitation which has beccme unavailable for plant growth due to surface run-off of the excess. To determine the effect of this, two versions of non-excess precipitation were calculated, with precipitation in excess of one and two inches in any calendar day removed. As an indication of the frequency of excess rainfall occurrences, probabilities of one calendar day with over one and over two inches of rainfall within a given growing season month are shewn for each growing season month in Table 1. This probability was determined by dividing the number of days in which excess rain­ fall occurred within that month during the record period by the number of times the month had occurred (i.e., number of years). These figures are based on the years of 1917-1977 for Lenawee and Gratiot Counties and 1926-1977 for Gladwin County. A M3ISTUKE STRESS INDEX A cumulative soil moisture budget or "bank balance" approach was used to estimate the amount of water available for crops during the growing season on a monthly basis. The basic relationship is: 35 Table 1. Probability of One Day per Month with Excess Rainfall Adrian, 1914-1977 Month over 1" over 2" Alma, 1914-1977 over 1" over 2" Gladwin, 1926-1977 over 1" over 2" April .453 .031 .219 .016 .414 .019 May .625 .109 .641 .047 .481 .019 June .719 .063 .672 .031 .654 .096 July .813 .125 .500 .094 .673 .096 August .625 .063 .750 .156 .636 .115 September .672 .063 .735 .078 .636 .058 able 2. Station Day Length Indices for Adrian, Alma, and Gladwin April May June July August September Adrian 1.074 1.190 1.236 1.235 1.138 1.014 Alma 1.078 1.199 1.243 1.240 1.201 1.014 Gladwin 1.083 1.207 1.250 1.246 1.210 1.014 36 MSI(m) = MSI (m-1) + P(m) - PET(m) where MSI = Moisture Stress Index m = a given month P = monthly precipitation in cm PET = potential evapotranspiration in cm The budget is calculated for the growing season, April through September. For the initial month of April, MSI is calculated by: MSI (Apr) = NSC + P(Apr) - PET (Apr) NSC is the net soil capacity, or water available for plant growth. NET SOIL CAPACITY (NSC) The soil profile in Michigan is assumed to be at field capacity (FC) at the start of the growing season. It is also assuned that the plant can continue to extract water frcm the soil until the permanent wilting point (PWP) is reached. Thus NSC = PC - PWP. To obtain the value of NSC, soil types used as cropland in the county were determined frcm Soil Conservation Service county surveys. Percent of each soil type was listed; soil water capacities for each type were determined; and a quantity-weighted average of net soil water capacity was obtained. This calculated average NSC was 37 0.18 inches of water per inch of soil, +0.04 inch, or 2.16 inches 5.49 cm) of water for the one-foot (32 cm) depth for all counties in the study. This quantity was used as a relative, rather than absolute, term; root depth and depth of drying were not used in the analysis. POTENTIAL EVAPOTRANSPIRATION (PET) The PET term in the Moisture Stress Index was computed by the Thomthwaite method. Historical climate data included tempera­ tures but did not include relative humidity, wind, or radiation, which are required by other methods. The Thomthwaite method is not accurate over short periods, or for spring only or fall only measurements (Rosenberg, 1974). It does work well over the span of the entire growing season in the temperate, continental climate of the eastern and midwestem United States where there is a strong correlation between tanperature and radiation (Chang, 1968). The Thomthwaite equation is expressed as follows, with terms defined below: PET = DLI x 1.6 x (10T/I)a "DLI11. A day length index specific for the latitude of the station. It is based on sun path diagrams for 40 and 45 degrees N. latitude (Brown, 1973), interpolated for the latitudes of the observation stations and corrected for day length on the 15th of 38 each month. Day length indices for the months of April through September are shown in Table 2. "T". This is mean monthly temperature for each growing season month each year, in degrees Celcius. "I". "I" is an annual heat index which is constant for a given location. It is the sun of 12 monthly heat indices, "i", where i is a function of monthly normal or long-term mean tempera­ tures. For temperatures belcw 0°C, i is assumed to be zero. The 1 514 value of i is computed by i = (t/5) * where "t" is the mean monthly temperature. Palmer and Havens (1958) have provided a table by which values of "i" may be obtained frcm monthly normal or average temperatures. "a". The exponent "a" in the Thomthwaite equation is constant for a given location. It is calculated frcm I by: a * 6.75 x l(f7I3 - 7.7 x 10"5I2 + 1.792 x 10-2I + 0.49239 M3ISTURE AVAIIABILITE INDEX The Moisture Stress Index was transformed into a Moisture Availability Index. The lowest value of the MSI was -32.97. There­ fore the constant value of 34 was added to all MSI values to obtain positive MAI values. For versions of the regression analysis involving non-excess precipitation, MAI was calculated with the precipitation term replaced by non-excess precipitation. 39 ANALYSIS OF MONTHLY CLIMATE DATA TEMPERATURE Much has been said in recent years about large-scale climatic cooling trends. If a systematic downward trend in temperatures exists it would have duplications for the range and development of agricultural crops, particularly along the climatic margins. Decadal means of mean annual temperatures suggest a cooling trend (Figure 3). However, the temperatures during the growing season would be more important in terms of possible effect on crops. Figure 4 shows mean temperature for the Apri1-September growing season over the period of this study. Inspection of Lenawee County temperatures indicates a downward trend over the approximately last 40 years. Gratiot and Gladwin temperatures do not shew any apparent trend. PRECIPITATION Precipitation for the growing season for Adrian, Alma, and Gladwin is shown in Figure 5. Inspection does not reveal clear patterns over time for any station. .WEEKLY CLIMATE DATA The majority of the Thompson-type statistical crop-weather models reported in the literature use monthly climatic data. Climate data on a monthly scale, while more widely available, tend to dilute the discemable impacts of weather events and conditions on critical stages of plant growth. «r Adrian Alma Alpena 1880 Figure 3. 1890 1900 1910 1920 1930 1950 I960 1970 Decadal Means of Mean Annual Tenperatures, Selected Michigan Stations, 1880-1969 MERN TEMP 41 RPR-SEP 60- Adrian, 1892-1977 1690 1910 1930 I960 1970 I960 1970 MERN TEMP YEAR RPR-SEP 60- Alma, 1892-1977 1890 1910 1930 HERN TEMP YEAR RPR-SEP 60- Gladwin, 1926-1977 1890 1910 1930 YEAR Figure 4. Mean Growing Season Temperatures by Year. 1970 42 40] CJ LJ 01 Q. CO I a. a 01 Adrian, 1892-1977 1890 1903 1916 -41929 4* 1942 1965 1968 1981 1955 1968 1981 1955 1988 1981 YEAR u oi a. a. UJ co i cn 0. a: UJ 20- Ataa, 1892-1977 1903 1942 1918 YEAR 40 CJ UJ 01 0. 0. UJ 20 > CO I 0. cc 01 Gladwin, 1926-1977 1890 1903 1916 1929 1942 YEAR Figure 5. Growing'Season Precipitation by Year. 43 When weekly summary climate data became available for Lenawee and Gratiot Counties, a regression analysis was developed based upon weekly temperature and precipitation. For data purposes the week beginning March 1 was designated as week 1. data end on October 31 at the aid of week 35. Growing season For ending dates of numbered weeks the reader is referred to Table 10. This part of the analysis based on weekly climate data covers the years from 1943 through 1977. CROP DATA SELECTION Crops selected for study were com, oats, soybeans, and dry beans. For the monthly analysis c o m and oats a m studied for 1892- 1977 in Lenawee and Gratiot Counties and 1926-1977 in Gladwin County? soybeans for 1942-1977 in Lenawee and Gratiot Counties; and dry beans for 1895-1977 in Gratiot County. These limitations were caused by the period of climatic record in Gladwin County and by incompleteness of data and length of record for crops in all of the counties. ANALYSIS OF CROP DATA Yearly crop yields for each crop in each county are shewn in Figure 6. These estimates were taken from annual crop reports published by the Michigan Agricultural Reporting Service and its predecessors, in cooperation with the USDA Statistical Reporting Service (Michigan Department of Agriculture, n.d.). Steyaert (1977) reported that these estimates were within 4 to 8% at the state level. 44 Lenawee Com, 1892-1977 bu/a yield 80- 40- 1890 1910 1930 1960 1970 YEAR Gratiot Com, 1892-1977 bu/a yield 80- 40- 1910 1890 1930 1970 YEAR Gladwin Com, 1926-1977 bu/a YIELD 80- 40- 1B90 1910 1930 1960 1970 YEAR Figure 6. County Annual Yields, with Segmented Trend Lines. 45 40i Lenaiwee Soybeans, 1942-1977 yield so­ ns 20 - to- 1090 1910 1930 1950 1970 1950 1970 1950 1970 YERR yield Gratiot Soybeans, 1942-1977 20- 1890 1910 1990 YEAR YIELD Gratiot Dry Beans, 1895-1977 10- 1890 1910 1930 YEAR Figure 6. (continued) 46 Lenawee Oats, 1892-1977 riELD bu/a 60- 40- 20 - 1890 1910 1930 1960 1970 1950 1970 1950 1970 YEAR YIELD bu/a Gratiot Oats, 1892-1977 40- 1890 1910 1930 YEAR Gladwin Oats, 1926-1977 YIELD bu/a 60- 40- 20 - 1910 1930 YEAR Figure 6. (continued) 47 Further adjustments, based on agricultural census data, are used to obtain county yield estimates. In addition to yields, segmented yield trends calculated by piecewise linear regressions are also shewn. YIEUS COHN C o m yields show the greatest increases. These increases began in Lenawee County around 1940, but Gratiot and Gladwin County c o m yields did not begin to increase until nearly 1950. of increase slowed about 1970. The rate This slowing of yield increase is associated with a sharply increased year-to-year variability, in contrast to the relative stability of the previous twenty years. SOYBEANS Soybean yields in Lenawee County increased from 1942 to 1957. Since 1957 the rate of increase has slowed and variation about the trend line has increased. from 1942 to 1948. in the 1959 data. Gratiot County yields increased A definite and permanent jump in yields occurred The reason for this sharp change has not been determined, as the timing of the junp did not coincide with the timing of improved varieties or changes in cultural practices (Erdmann, 1979). County yields. A similar discontinuity did not appear in Lenawee 48 DRY BEANS Gratiot County dry bean yields peaked at an all-time high of 20.3 cwt/a in 1963, and have sham a negative slope since. Yields continued to decrease to a 10.2 cwt/a average for the 1974-77 period. Gladwin yield records are missing fran several years, including 1960-63, but shew a similar but less rapid downward trend since that time in comparison with Gratiot County. 1979 increased to 14.0 cwt/a. State dry bean yields in Lenawee County dry bean records are omitted from the crop reports from 1949 through 1975, due to insuf­ ficient acreage, so no comparison can be made. However, average yields since 1964 have been at a level well above pre-1950 yields. OATS Oat yields are characterized by a much greater year-to-year variability than are c o m yields. southern counties of Michigan. This is particularly true in the A distinct escalation in annual oat yields did not appear until the 1950s. In Gratiot County the increase appeared as an abrupt 20 bushel jump in 1958, dropping 22 bushels in 1959 and remaining at a level averaging 18 bushels higher since 1960. Increases in Gladwin County were more gradual. The increase in Michigan oat yields is probably related to the introduction of later-maturing, higher-yielding varieties. However, at the same time rotation practices were changed, with better crop soils being used for continuous c o m while the decreasing acreage of oats was relegated to poorer soils (Grafius, 1979). 49 LINEAR TRENDS Changes in the level of crop yields over time are apparent. To clarify these trends, segmented linear regressions were fitted to each data set. The regression lines are shewn in the yield diagrams, Figure 6. Judgment was applied in connecting the ends of adjacent pieces, without sacrificing the accuracy of trend values, to avoid excessive dislocation in the relative values of deviations frcm the trend line in adjacent years. exceptions. This was possible with two Gratiot oat yields had a 10-bushel discontinuity between 1958 and 1959, and Gratiot soybeans had a 7-bushel discon­ tinuity between 1948 and 1949. Time periods and coefficients for the linear regression segments are shown in Table 3. Deviations about the regression line represent shorter-term variations within the overall trend. These are considered to be primarily due to year-to-year changes in weather conditions, but are also affected by other uncontrolled variables. The long-term trends as shewn by the regression lines are considered to be due to techno­ logical developments such as increased fertilizer use, inproved varieties, higher plant populations, earlier planting, more effective pest control, and management application of these developments. The deviation frcm long-term trend is obtained by subtracting the annual value of the trend line frcm the actual yield for that year. This residual value is processed as a signed number, positive when the actual yield is above the trend regression line and negative when it lies below. After the predicted annual deviations frcm the trend line are calculated by the multiple regression models, these 50 Table 3. Linear Regressions Used for Yield Trends Lenawee c o m Gratiot c o m Gladwin c o m Lenawee soybeans Gratiot soybeans Years na) a 1892-1940 49 31.60 .107 1938-69 38 31.12 1.714 1969-77 9 86.84 .087 1892-1944 53 34.67 - .007 1942-63 22 29.03 2.036 1962-77 16 74.02 .554 1926-48 23 26.56 .038 1945-77 33 25.72 1.424 1942-57 16 17.27 .507 1957-77 21 25.16 .162 1942-48 7 12.36 .400 29 21.36 .079 54 8.35 - .011 1946-63 18 7.84 .492 1961-77 17 16.44 - .432 1892-1950 59 33.38 .136 1948-69 22 36.99 1.416 1968-77 10 68.35 - .416 1892-1958 67 30.97 .190 1957-77 b) 19 55.08 .398 1926-77 52 20.91 .482 1949-77 b) Gratiot dry beans 1895-1948 Lenawee oats Gratiot oats Gladwin oats b a) n's add to more than total years due to overlapping of regression equations. Lines are connected for best fit without overlap b) discontinuity Regression equation: Y = a + bx x = nth year of record 51 annual residual values are added back into the linear trend value for that year to provide the predicted annual yield. CROP ACREAGES A study of yields cannot be separated fran a consideration of acreages for the crops studied. Average yield may be affected by relative quality and yield potential of land used; by institu­ tional constraints such as government conservation and control programs; and by shifts between different crops. Four questions emerged in regard to crop acreages: (1) What was the pattern of acreage over time in the four crops studied? (2) Did soybeans replace com? (3) Was there a shift between dry beans and soybeans? and (4) What happened to oat acreages, and why? Acreage figures for these crops were available for the years 19421977, and are shown in Figure 7. C o m acreage increased through the 1950s, except for Gladwin County. Government soil bank acreage reserve programs went into operation in the late 1950s. C o m acreage began a downward trend at that time, except for a one-year increase in 1959. This downward trend in c o m continued through the 1960s, followed by an increase in the 1970s. Soybean acreage increased steadily frcm the early 1950s into the 1970s, especially in Lenawee County. Gratiot dry bean acreage lagged yield trends, increasing into the mid-1960s, then dropping off. Oats dropped during the 1950s and 1960s to only one-third to one-tenth of acreages in the late 1940s. 52 o Q X CO UJ 0£ O cr 1000- ><**><><* 1940 leooi 1960 Figure 7a. LuEUP — 1980 4jt>( » it » y » * » » T * ~ K 1970 1980 YEAR Total County Acreages of Crops in the Study. QRCRNfl 0LCRNA O a CO UJ aoo- 0£ a cz 1940 Figure 7b. I960 1980 1970 1980 YEAR C o m Acreage by County, 1942-1977. 800 LEQENO ■B-LNORTR ORORTR X OLOATR o o CO UJ 400- Q£ a GC 1940 Figure 7c. 1950 1960 1970 YEAR Oat Acreage by County, 1942-1977. 1980 53 1200 LEOEND X 100 □ LNSBNR ORSBNR ACRES 600- I960 1960 1970 1980 YEAR Figure 7d. Soybean Acreage, Lenawee and Gratiot Counties, 1942-1977. LEOENO 800- — ORDBNR X 100 ACRES - S - 0R8BNR 400- 194C 1950 I960 1970 1980 YEAR Figure 7e. Dry Bean and Soybean Acreage, Gratiot County, 1942-1977. 54 In Lenawee County, a 40,000 acre decrease in c o m acreage in the 1960s was more than balanced by an increase in soybeans. A 20,000 acre drop in c o m in Gratiot County was not matched by an increase in soybeans, whose acreage was almost constant in the 1960s. In the 1970s a 15,000 acre decline in dry beans grown in Gratiot County was followed, with a two to three year lag, by a similar but not parallel increase in soybeans. Oat acreage declined sharply in the 1950s in Gratiot County and into the mid-1960s in Lenawee County. Lenawee oat acreage dropped frcm 63,000 acres in 1949 to 10,000 acres in 1972, while Gratiot oat acreage dropped from a high of 49,000 acres in 1945 and 1946 to less than 5000 acres in 1977. Gladwin oat acreage decreased from over 10,000 acres in 1952 to 1300 acres in 1967; it has since edged up to 4800 acres in 1977. CHAPTER IV ANALYSIS OF CLIMATE-YIEED RELATIONSHIPS The primary goal of this research is to improve our under* standing of relationships which exist between climate in the growing season and yields obtained frcm field crops. Multiple regression analysis was used to determine seme of these relationships. Separate analyses were made with climatic data on monthly and weekly time scales. ANALYSIS BASED ON M3NTHLY DATA Multiple regressions were m m on each crop studied in each county. The dependent variable in each case was crop yield deviation from the trend line. The independent variables were average monthly tanperatures, total monthly precipitation (or non-excess precipita­ tion) , and a moisture availability index (based an either actual or non-excess precipitation). These three variables were also squared, for three additional variables. For com, soybeans, and dry beans, the growing season months of April through September were included in the regression. The three variables plus three squared terms, for each of six months, resulted in a multiple regression with 36 possible independent variables. Due to the August harvest for oats, the regression for oats included only April through August, or 30 possible variables. 55 56 Each county and each crop was treated separately for actual precipitation and for two versions of non-excess precipitation. The latter excluded any amount in excess of one inch and two inches in a single calendar day. In the latter cases, non-excess precipitation was also used in development of the moisture availability variable. RESULTS OF THE MONTHLY ANALYSIS SIMPLE CORRELATION Simple correlation coefficients (r values) between crop yield deviations from trend and monthly climatic variables are given in Table 4. Caution is urged in the use of these figures. For com, soybeans, and dry beans the critical r value for the 5% significance level is 0.320. Thus for a single crop/county case, it would require that two or more of the 36 variables (6 variables for 6 months) must have r values above 0.32 in order to be statisti­ cally signicant at the 5% level. 0.361. For oats the critical r value is Use of these r values should be combined with an understand­ ing of the physical principles of plant response to the environment. MULTIPLE REGRESSION ANALYSIS The predictor equations for each of the 9 county/crop cases, with variables selected, are shown in Table 5. For com, soybeans, and dry beans there are six possible variables in any of the six months of the growing season, or 36 possible variables out of which the stepwise multiple regression analysis could select the most strongly related. For oats, there are 30 possible variables. The distribution of the variable selection for each crop is shewn in 57 4. Sinple Correlations (r) for Yields and Monthly Climate Variables SOYBEANS DRY SEA OATS COEN Gra Gra .10 & .13 .40 -.17 -.22 .20 .15 .12 -.10 .18 -.01 .02 -.03 .01 -.11 -.01 -.13 .15 -.001 .05 .12 .30 .17 -.03 .05 .18 .01 — — .23 -.16 -.09 -.10 -.04 -.02 .27 .32 .42 .48 .19 .23 -.07 .07 -.03 .23 .29 -.02 -.22 -.05 -.03 -.03 .18 .10 .10 .19 .10 .26 — — .23 -.01 -.01 .11 .32 .34 -.16 -.21 -.12 -.04 .19 .24 -.07 .01 -.01 .11 .24 .22 Gra Gla Len April Temp May n June H July n Aug n Sept .10 -.02 -.08 .06 .01 .20 .06 .14 -.12 .16 .10 -.09 .17 .16 -.08 .12 -.21 .13 .03 -.13 -.42 -.26 -.23 — .17 .27 -.08 .16 -.29 -.35 -.27 -.08 -.04 .08 April Free H May it June H July ii Aug n Sept .02 -.08 -.17 .08 -.18 -.05 .04 .07 .01 .33 .22 .26 .25 .27 .34 .03 -.12 .14 -.31 -.32 -.04 -.05 .13 April MAI (b) May n June •i July n Aug n Sept -.004 -.07 -.14 -.18 -.09 -.04 -.11 -.06 -.01 .14 .03 .04 .23 .12 .16 .11 .19 .18 -.30 -.39 -.26 -.20 -.12 April Temp Sg H H May i i H June •i n July n n Aug n n Sept .18 .27 .03 .11 -.02 -.08 .16 .006 -.13 -.08 .05 .20 .14 .06 -.43 -.30 -.36 -.12 -.26 -.30 -.08 .16 .10 -.09 .08 .15 .17 -.23 -.04 -.09 —— -.20 .12 .13 April Prec Sg ii ii May n n June I I N July II II Aug II II Sept .03 -.07 -.23 .04 -.19 -.11 .04 .05 -.04 .30 .18 .16 .27 .27 .28 -.10 .02 .15 April MAI Sg II •• May II II June II II July H «• Aug I I H Sept -.000 -.18 -.14 -.02 .07 .08 Len Variable (a) Gra -.07 -.15 -.12 -.09 -.09 -.06 -.03 .09 .21 .05 .12 .05 — ■— — Gla __ -.28 -.11 -.01 .04 -.004 -.31 .15 .25 -.11 .01 .02 -.04 .04 .17 .13 — -.29 -.39 -.28 -.25 -.19 .... — — -.21 -.04 -.05 -.04 .08 .18 .18 .08 .23 .09 _ — Len .06 .10 .13 .40 -.17 -.22 .15 .19 .11 -.10 .17 -.004 .02 -.04 .005 -.11 -.01 -.13 .20 -.18 -.08 -.08 -.10 -.06 .22 .28 .40 .42 .19 .23 -.07 .06 -.03 .16 .20 .03 .23 -.17 -.02 -.19 .13 -.04 .09 -.06 .13 .29 .17 .31 -.07 .01 -.P2 .08 .18 .18 Non-excess precipitation far Gratiot soybeans (b) MAI: Moisture Availability Index liable 5# Crop Multiple Regression Models# Monthly Data n R s.e. TtMBMRR A Com 86 .42 6.45 Soybeans 36 .56 2.14 Y= - 48.24 Oats 86 .36 6.81 Y= GRATIOT Com 86 .15 6.96 Y= - 38.06 83 .21 1.87 3.81 + 0.86xADGP + 1.12xJULP - 0.12xJLPQ - .068xAGFQ 36 .35 1.80 Y= - 10.33 + 1.09xADGP + 0.69xJDLP + 0.20xAPRT - .OOllxMXTQ 86 .33 6.28 GLADWIN Com 52 .47 5.23 Y= -135.08 + Oats 52 .39 5.71 Y= -346.49 - .0070xJNTQ Dry Beans (cwt.) Soybeans NXSP Oats Y= - 36.32 + 4.91xftUGP + 4.91xJULP - 0.40xJIPQ - .0092xAQffiQ + 0.40xSPMAI + .0036xSPTQ - 0.44xAGPQ a + 1.07xADGP + 0.79xJUtP + 0.45x3ULT + 0.55xSEPP + 0. 18xAPRT A 85.14 ~ .006xJNTQ - 0.55xM5£MAI - .0036xMXTQ - .0035x3LTQ A + 0.13xftGPQ + 1.17xJULP + 0.53xSEPT A Y— - 18.52 - .0023xJNTQ + 0.85xAPRT - .0082xJLTQ - 1.25xAPRP l.OlxJUNP 0.99xJULP - 0.18xAPPQ + 0.35xAGPQ + 4.47xMM4AI - Il.47xNKMAQ + 0.95xJULT - 2.64XAUGP - 0 55xSEPT A +.0073xAPTQ + 0.67xADGP + 1.34xJUNP + 12.22xMAXT O.lOxMYTQ Note: 1) NXSP=ncn-excess precipitation (excess over l"/day is removed) 2) MAI- Moisture Availability Index 3) Q indicates a squared term 59 Table 6. Also shewn is a combined selection density chart, with variables coded by crop. For com, soybeans, and dry beans, the most significant (selected first by the stepwise regression) and consistent variables were the July and August precipitation. There were three com, two soybean, and one dry bean cases, or six equations. For these six cases a total of 31 variables were selected by the six regression analyses. Of these 31, 17 were July and August precipitation vari­ ables, including the squared terms. The other 14 were scattered over 12 other non-precipitation variables. For the three oat equations with a total of 15 selected variables, the square term for June temperature was selected in all three cases. May and July squared temperatures and June precipita­ tion were selected in two out of the three cases. The other six were scattered, as shewn in Table 6. The moisture availability term appeared to be of little importance, equations. MAI. it did not appear at all in the soybean or dry bean It appeared only once in oats, in Lenawee County as May It appeared also in Gladwin County c o m in May, in both squared and unsquared terms. In total, moisture availability appeared only five times out of a total of 44 variables selected. Correlations with yields are negative in the early part of the season, indicating that planting delays in May due to wet field conditions may tend to decrease yields. Actual and predicted yields, based an monthly climatic data are shewn in Figure 8. Table 6. County Climate Variables Selected by Month-Based Multiple Regression Crop Models com DRY BEANS SOYBEANS In Gr OATS Gr G1 In May In Gr G1 G1 G1 G1 In Gr G1 Jun In In Gr G1 JuL G1 In In Gr G1 G1 Aug In Sep Gr G1 Gr Gr In Gr Gr Gr In Gr In Gr G1 In Gr G1 In In Gr Gl T: Tenperature In: Lenawae County P: Precipitation Gr:' Gratiot County M: Moisture Availability Index Gl: Gladwin County 61 LEBENO YI ELO + YFRED bu/a yielos BP- 4P - 1B90 1910 1930 1950 1970 YEAR YIELDS bu/a a. C o m Yields, Lenawee County, 1892-1977 40' ++ 1SE0 1910 1930 1950 1970 YEAR b. Oat Yields, Lenawee County, 1892-1977. Figure 8. Actual and Predicted Yields Based on Monthly Climate Data. 62 YIELDS 80- + YPRED fti .3 40- 1890 1970 YEAR c. C o m Yields, Gratiot County, 1892-1977 YIELOS LEOEHO YIELD 80+ YPREO 5 40- 1930 1910 1890 d. 1970 YEAR Oat Yields, Gratiot County, 1892-1977 Figure 8. (Continued) 63 LEOENO YIELD YIELDS bu/a 30- 10’ 1890 1910 e. 1930 19S0 1970 YEAR Soybean Yields, Lenawee County, 1942-1977 LEOENO YIELD 4 YPREO YIELOS bu/a 30- 10- 1890 1910 f. 1930 19S0 1970 Y E AR Soybean Yields, Gratiot County, 1942-1977 LEOENO 20- YIEL0 YIELDS bu/a 4 YPREO 10- 1890 1910 g. 1930 1950 1970 YEAR Dry Bean Yields, Gratiot County, 1895-1977. Figure 8. (Continued) 64 YIELDS bu/a 80' 40- 1930 1910 1890 19S0 1970 YEAR h. C o m Yields, Gladwin County, 1926-1977 YIELDS bu/a 60- 40- 1910 1890 1930 I960 1970 YEAR i. Oat Yields, Gladwin County, 1926-1977 Figure 8. (Continued) 65 RESUMS WITH NON-EXCESS PRECIPITATION DATA, Separate multiple regressions were run for all nine county/ crop cases with excess precipitation removed. The first set of runs limited precipitation by removing all precipitation in excess of one inch per calendar day. per day. The second set removed all over two inches The non-excess precipitation term was used in the develop­ ment of the moisture availability variables for these runs. The statistics for all month-based regressions are shewn in Table 7. 2 In most cases, the results in terms of R values obtained under identical restraints differed little frcm the regressions in which 2 actual precipitation was used. Gladwin c o m showed an R drop from .47 with actual precipitation to .20 and .25 for non-excess versions. 2 Gratiot soybeans inproved frcm an R of .23 with actual precipitation to .32 with precipitation over one inch per day removed. Removing 2 two inches returned the R to .26. Ranoval of excess rainfall as tested above appeared to be of little value in the analysis. ANALYSIS OF OUTLYING YIELDS Why do seme years show unusually high or low yields in a specific crop? A qualitative effort was made to determine differ­ ences in weather conditions in these exceptional years. SFITiFmON OF OUTLIERS For each crop/county case, years with extreme yields, i.e., yields farthest from the trend line, were studied. Since using all occurrences outside of one standard deviation was unwieldy and using not in excess of l”/6ay R2 s.e. 6 .40 6.53 6.96 3 .15 .47 5.23 4 5 .56 2.14 Gratiot soybeans 3 .23 Gratiot dry beans 4 Lenawee oats not in excess of 3 Actual Precipitation 3 Statistics from Multiple Regression, Actual and Non-Excess Precipitation, Monthly Data to Table 7. R2 s.e. 6 .41 6.46 6.93 3 .16 6.89 .20 6.15 4 .25 5.97 4 .52 2.21 5 .57 2.12 1.93 3 .32 1.83 3 .26 1.90 .21 1.87 2 .21 1.84 4 .21 1.88 4 .36 6.81 4 .36 6.81 4 .36 6.80 Gratiot oats 5 .33 6.28 5 .31 6.35 5 .33 6.28 Gladwin oats 6 .39 5.66 5 .37 5.71 7 .43 5.56 Crop n vars. R2 s.e. Lenawee c o m 7 .42 6.45 Gratiot c o m 3 .15 Gladwin c o m 8 Lenawee soybeans n vars n vars 67 all outside two s.d.'s provided too few cases, the number of occurrences outlying with approximately 10% of the yields for each case was used. This cut-off point in yield units, number of cases, and percent of total are shewn in Table 8. PLOTS OF OUTLIERS Yield outliers were plotted on a 4-quadrant X-Y plot with the intersection at (0,0). Each of the four crops with all counties combined was plotted for each month of the growing season. Figure 9 shews positve and negative departures from the yield trend lines for each growing season month for all years in the period of record in which the yield of any specific crop is an outlier. Departures of temperature and precipitation from long-term climatic normals are missing in some cases. For com, this includes 1894 and 1928 plus August and September of 1916 and May of 1918 for Lenawee County, and April of 1977 for Gladwin County. and 1936 Gladwin data are missing. For oats, 1904 Gratiot data The X-axis is scaled for temperatures cooler to warmer than the existing climatic normals as given in the official annual climatic sutmaries for Michigan. Y-axis is scaled frcm wetter to drier than normal. cases is the same, as shown in the legend. The Scale in all Sign of the yield departure from trend for the years of yield outliers is plotted at the appropriate X-Y coordinates. Table 8. Data for Yield Outliers, Based on Monthly Climate Data COUNTY Lenawee CROP Corn Gladwin NUMBER % OF TOTAL 13 bu. 8 9.3 5 bu 3 8.3 Oats 14 bu. 8 9.3 Corn 13 bu. 8 9.3 Dry beans 3 cwt 9 10.8 Soybeans 4 bu. 4 11.0 Oats 12 bu. 8 9.3 Corn 11 bu. 5 9.7 Oats 11 bu. 4 7.7 Soybeans Gratiot CUTOFF 69 Com Dry Beans _ + _±___ Ape. Soybeans -+ + + Kay O ats • * -+ «+ - - + 7* + ++- ¥m + Inn + .,+ * + + ♦ + + 4. - + + ■ + +- --- + +-%- Jul. " _ +" ■ty. < + + + _+ - + w " ■=— 5 — ++ + + + + + Aug. + + +J ■' ' *. . - + + + _ — + + 1 _ -*'■ + .. - _+ _ + ► -+ d + iabove trend -ibelcw trend £ G 1 » Signs of Yearly Departures over 10% from Yield Trend, with Monthly Climates. ft O ET ( \ Figure 9. Jt. + Sun. in. C Oj. 0 1 _=i-=a— i+ 6 n + w I i, LEGEND " 1 ~ + ♦- ► +' 70 RESULTS OF OUTLIER ANALYSIS Results appearing in the different plots were qualitatively evaluated by position of the outlying yield cases relative to the cool vs. warm and wet vs. dry axes of the chart. CORN Lower yields were associated with drier July and August weather. Higher yields occurred in wetter Augusts. September showed no consistent pattern. DRY BEANS These shewed no consistent pattern. mostly when July was hot and dry. Lower yields appeared Higher yields appeared only when July was wetter than normal. SOYBEANS These also shewed no definite pattern. appeared when July was dry. All lew yields All outliers, both positive and nega­ tive, appeared in cooler than normal Augusts, with higher yields associated with more moisture. OATS Higher oat yields were associated with wet Aprils, and with warmer temperatures than usual in May, June, and July, with a few exceptions. than usual. Higher yields appeared when Aprils were slightly drier 71 ANALYSIS OF YIELDS CLOSE TO THE TREND LINE To gain perspective on climatic variations with yield, "inliers" were checked for com. These were the 8 to 10% of the years in which yields fell closest to the trend line for those years. Climatic conditions for those years were scattered in much the same manner as outlier years. "Normal" c o m years tended tcward dry and/or warm average weather in August. Septanber weather was scattered in all directions. ANALYSIS BASED ON WEEKLY DATA The majority of the Thompson-type statistical crop-weather models reported in the literature use monthly weather data, as does the preceding part of this study. Climate data on a monthly scale, while more widely available, tend to dilute the discemable impacts of weather events and conditions on critical stages of plant growth. This portion of the study deals with a multiple regression analysis of climate and yields using weekly temperature and precipitation data. METHOD The weekly analysis was applied to data fran Lenawee and Gratiot Counties for the years 1943 through 1977. Weekly data covers the period fran the week ending March 7, designated as week 01, through October 31, ending week 35. the analysis are shown in Table 10. Ending dates of the weeks in 72 'The weekly-based climate-yield analysis uses the same approach of applying multiple regression to de-trended yields as was used in the monthly-based analysis. Independent variables are the mean weekly temperatures and total weekly precipitation. The growing season period fran week 08 through week 32, or April 19 through October 10, was used for com, soybeans, and dry beans. For oats, the period used was week 06 through week 24, or 2 April 5 through August 15. For Gratiot oats, inproved R values were obtained by sunning the temperatures of weeks 16 and 17 into a new variable, 1MP67. While the Michigan Agricultural Reporting Service uses sampling-based objective techniques for mid-season prediction of the current year's yields, a supplemental weather-based predictive model may prove useful. Accordingly, a mid-season regression model was run for each crop/county case. The com, soybean, and dry bean models were truncated at week 24 (August 15), and the oat model at week 17 (June 27). Truncation points were based on the distribution of variables selected by the full-season regression analysis, which is shown in Table 9. RESULTS OF THE WEEKLY ANALYSIS SIMPLE CORRELATION Simple correlation coefficients (r valves) between yield deviations fran trend and weekly temperatures and precipitation for each crop/county case are shown in Table 10. For com, soybeans, and dry beans the critical value for the 5% significance level is ■hWa 9. Distribution of Climate Variables Selected by Week-Based Regression Models WEEK R2 LENAWEE Corn .71 s.e. 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 5.5 T x P Soybeans .58 x 2,0 T x x x x x x x P Oats .82 x 3.6 T P x x x x x x x x GRATIOT Corn .52 6.7 T x P Dry beans.61 Oats .41 x x 1.5 T P Soybeans .71 x x X X 1.3 T x P x 5.2 T P x x X x X x x x x x Table 10- copulations of Deviations fran Yield Trends and m • AX€nas ana Vfeekly Climate Variables Corn Vfeek, Biding Soybeans Len T Gra P T Len P T 06 Apr. 11 07 18 08 25 09 May 10 13 . 22 Aug. .16 -.15 .22 .32 .30 -.09 .18 -.03 .26 .01 .09 .16 .15 -.22 .10 .13 .07 — .16 .14 .13 .-.37 .17 -.27 .03 -.04 .29 .22 -.30 .28 -.10 -.18 -.13 .05 -.03 -.15 -.04 .01 -.19 -.01 -.17 .21 -.38 -.02 .08 -.002 -.10 -.08 .10 -.04 -.05 -.28 -.15 .003 .14 .002 -.04 -.10 .31 .07 .13 -.22 .24 .001 .03 -.'07 .06 .01 .22 .08 .13 -.11 -.03 -.07 -.14 -.07 -.03 .06 .11 .05 -.37 -.16 -.44 .33 -.14 -.19 -.21 -.13 -.31 .15 -.23 .18 .08 -.01 .19 .11 -.24 ,.05 -.13 .06 .39 T*17 -.03 -.20 -.02 -.15 .40 -.08 .11 -.32 -.07 -.41 -.46*'' .08 .07 -.26 .02 -.06 -.04 -.17 .03 -.27 -.13 .08 -.33 .26 -.26 -.38 -.12 .01 .03 .08 -.13 ..03 -.02 .13 -.20 .05 -.05 -.08 .02 .16 -.16 -.07 -.06 -.43 .10 .28 -.03 -.05 -.12 .36 .06 .12 .10 .29 .07 *36 .03 -.25 -.14 -.15 11 -.09 18 .02 .06 1 P -.25 .15 .18 25 T -.11 -.03 .18 1 21 P -.003 .22 in 0. 1 20 T .14 .18 1 19 4 .40 .22 - _Q 200 o o 0 a® 0 Q 0 * 0D00 o 0 a Lenawee Soybeans 50 40 60 70 80 YEAR LEPENP O YIELD O YPRED CO O O a 4 £ Si >- o 0© e 0 □ Q ffi 0 0 * §S®SSBS »■ 000 Q 0 O a0O00 g © ® g a 8 o K 0 s i 0 Lenawee Oats — i------1-40 50 60 70 Y EAR Figure 10. Actual and Predicted Yields, Weekly Data, 1943-1977 plus 1978 80 80 e— LEOSNO O YICLO 80 ■ 0 s ®s YPRED bu/a 8 □ 40- ©m o gg 00 © u ou s V8°§8 m T o ffl© 0°. I 0 1 00 mD< S° 0 © © g0e>00 Gratiot C o m -4SO 40 60 70 80 YEAR LEOENO 20- © YIELO © a 0 CJ YPRED ©® © bu/a © □ lo­ ©0aS rna© mO 3 ©0 3 8 ° o a ®o 0 o 0 © a, ® 0 0 0 m ®© 0 © * © © ° 0 O ®0 P Gratiot Dry Beans 1 1 > 40 50 60 YEAR Figure 10. (Continued) 70 80 81 LEOENP O yielo YIELDS 0 I YPRED 0 ®8o3gfflgS0ffla 20- D mD © O *0B ■ § V 8s® 0 { e 0 o ifi o H ----------------- 1----------------- 1----------------- 1---------- :------ 1----------------- 1----------------- h- 50 40 60 70, 80 YERR LEOENP 0 YIELO 0 YPRED ® o8 V 8a S 8 S' YI ELDS 0 i 0§ 40 ■ m 3 S@ 0 □ 0 0 9 0 _ 0 00 „ 0* » ®a0®g®A 0 000@ o gOa C ® 0 0 40 50 60 YEAR Figure 10. (Continued) 70 80 82 day resulted in a prediction of 83.5 bu/a, while removing all above 2 inches gave a predicted yield of 92.0 bu/a. GAMMA. DISTRIBUTION OF RAINFALL The gaitma distribution for Lenawee and Gratiot weekly precipitation was obtained fran the Michigan Department of Agri­ culture ^Michigan Weather Service {Table 12). Actual precipitation for all predictor weeks which had predictions outside two s.e. 's fran actual yields for the 1943-1977 period of the study plus the 1978 data were checked against the .90 level of the gamna distribu­ tion. This revealed only two cases in addition to the 1978 Lenawee c o m case. For that case, the .90 gartma level (1.65 in.) was substituted for the 23d week actual precipitation (2.78 in.), and the .90 gamna level (2.14 in.) was substituted for the actual (2.15 in.) rainfall for the 29th week. The resulting yield predic­ tion of 88.7 bushels was closer than the uncorrected version to a reasonable figure. The Lenawee soybean model showed an excess of .01 inches in the 29th week for 1978. only .01 bushels. This had an effect on yield prediction of In 1944 the 10th and 17th weeks in the Lenawee oat model had precipitation above the .90 gamma level. This resulted in an adjustment for the oat yield prediction fran 37.5 bushels downward to 31.3 bushels, which was much closer to the 29.2 bushel actual yield. In all other cases prodi tor week precipita­ tion was belcw the .90 gamna level, or adjusting the predictor variables would have resulted in a larger difference between actual and predicted yields. Table 12. Week, ends Gamma distribution of weekly precipitation, .90 and .95, Adrian and Alma, 1929-77 Adrian,Lenawee Co. Aina, Gratiot Co. mean precip mean precip .90 .95 .90 .95 Adrian,Lenawee Co. Week,ends mean precip .90 .95 Alma, Gratiot Co. mean precip .90 .95 1 3/07 .57 1.29 1.69 .57 1.28 1.70 19 7A1 .69 1.53 2.06 .58 1.18 1.54 2 3/14 .55 1.27 1.70 .39 .80 1.03 20 7/18 .82 1.77 2.34 .80 1.70 2.25 3 3/21 .58 1.20 1.51 .46 .97 1.25 21 7/25 .86 1.95 2.62 .51 1.11 1.49 4 3/28 .75 1.62 2.10 .58 1.14 1.44 22 8/01 .65 1.42 1.86 .71 1.52 1.96 5 4/04 .92 1.83 2.31 .62 1.30 1.66 23 8/08 .78 1.65 2.15 1.02 2.17 2.84 6 4/11 .68 1.48 1.90 .59 1.17 1.47 24 8/15 .56 1.15 1.47 .83 1.61 2.06 7 4/18 .80 1.60 2.05 .61 1.34 1.74 25 8/22 .84 1.71 2.19 .88 1.81 2.37 8 4/25 .97 2.09 2.70 .77 1.74 2.33 26 8/29 .77 1.51 2.11 .94 1.93 2.65 9 5/02 .81 1.82 2.39 .89 1.91 2.51 27 9/05 .78 1.67 2.21 .90 2.00 2.69 10 5/09 .76 1.56 1.97 .74 1.66 2.23 28 9/12 .65 1.38 1,81 .84 1.77 2.31 11 5/16 .97 2.16 2.84 .75 1.64 2.15 29 9/19 .96 2.14 2.95 .95 2.04 2.67 12 5/23 .78 1.65 2.15 .62 1.33 1.72 30 9/26 .60 1.35 1.76 .83 1.75 2.24 13 5/30 .70 1.56 2.03 .70 1.61 2.12 31 10/03 .77 1.61 2.13 .71 1.62 2.19 14 6/06 .87 1.74 2.18 .73 1.58 2.04 32 10/10 .80 1.73 2.29 .77 1.54 2.00 15 6/L3 .81 1.76 2.27 .77 1.71 2.26 33 10/17 .73 1.52 2.12 .66 1.35 1.81 16 6/20 .97 2.31 3.11 .77 1.81 2.40 34 ■*r CM \ c r—1 .73 1.63 2.18 .60 1.46 1.98 17 6/27 1.00 2.17 2.85 .85 1.75 2.25 35 10/31 .43 .87 1.14 .53 1.10 1.44 18 7/04 .94 2.05 2.66 .73 1.64 2.17 Data Courtesy of Michigan Weather Service 84 COMPARISON OF RAINFALL LIMITATION METHODS Use of the .90 garrma level as a maxiimm for precipitation in the 1978 Lenawee c o m case gave a yield prediction of 88.7 bu/a, compared with 98.7 bushels for actual precipitation and an actual yield of 76.1 bushels. For the 23d week, net weekly precipitation after removal of rainfall in excess of one inch in any day is equivalent to the .77 gamna level, and for a 2-inch excess, the .94 gamna level. ANALYSIS OF OUTLYING YIELDS Why were predictions farther fran actual yield values in certain years? To determine this, years with weekly-based predic­ tions greater than two standard errors fran actual yields were examined in search of information which might explain the source of difference and thus provide a basis of judgment to apply in future predictions. Lenawee c o m yields in 1974, while predicted to be well belcw trend, were much lower than predicted. year were also lower than predicted. Soybean yields that A very dry mid and later suimer, combined with an early killing frost, was the probable cause. Lenawee soybeans in 1943 fell well below prediction. Normal weather in July and August favored a good crop and a good prediction. However, a cold and wet April and May had delayed planting, and a very cool September limited the maturing process. A moist August 85 of 1977, not included in the predictor variables, boosted soybean yields well above predictions for that year. In 1944, Lenawee oat yields were favored by good weather in the last half of May and most of June? this period contained four of the eight predictor variables as shown in Table 4.7. However, cold, wet weather in April and early May delayed planting, and dry weather from June 23 on may have hampered grain filling. Adjustment of precipitation in the 10th and 17th weeks to the .90 gamma level revised the yield prediction downward fran 37.5 bushels to 31.3 bu/a, which was closer to the actual yield of 29.2 bushels. In 1977, a cool (averaging 4.6°F below normal) and moist June gave oat yields higher than indicated by the predictor variables. This was, however, consistent with negative temperature correlation coeffi­ cients through June. Negative precipitation correlations during May are also consistent with the 1944 case discussed above. Gratiot c o m in 1977 gave yields considerably lower than predicted. While rainfall was more than ample, which increased the yield prediction, cold temperatures late in the season appear to have inhibited the maturation process. August averaged 3.2°F colder than normal, with maximum daily temperatures below 80°F for 18 days of the month, and minima below 50°F for 12 days. THE PHENQDOGICAL ADJUSTMENT APPROACH Plant growth responds not to calendar dates but to actual environmental conditions. Primary control an plant growth is con­ sidered to be accumulated heat units above a specified threshold 86 value. Therefore climatic data were adjusted so that values of weekly independent climatic variables regressed against Lenawee c o m yield deviations from trend were conditions which the plant faced at certain phenological stages based on weekly cunulative 86/50 growing degree days fran the beginning of week 9 (April 26) rather than on elapsed calendar time. Comparison of real-time vs. phenologically adjusted weekly climate data for Lenawee County crops is shown in Table 13. In 2 comparison, R values were higher at each step for real-time data, significance levels were smaller and more variables were allowed into the model at the 5% level, and standard errors of estimate were smaller. These results suggest that this appraoch was not a fruitful direction of inquiry in this particular study. WEEKLY VS. MONTHLY REGRESSIONS As a basis for comparison, Lenawee c o m yields were regressed against monthly weather data in the same way as the weekly analysis, with both constrained to the 5% level of significance for all vari2 ables entering the equation. The R value of the month-based regression was .14, allowing only August precipitation to enter the 2 equation, in contrast to an R of .71 with 6 variables at the weekly level. For comparison, the first variable alone in the week-based 2 analysis gave an R of .30. Standard error for the month-based regression was 8.7 bushels, versus 5.5 at the weekly level. Constraints in the monthly analysis reported in the first part of this chapter were much less rigorous than the 5% 87 liable 13. Yield Regression Statistics, Real-Time vs. Phenologically Mjusted Weekly Climatic Data, Lenawee County, 1943-77 Real-Time Crop Phenologically M justed Weeks Var# Var. R2 Sig. s.d. Var. R2 Sig. s.d. P23 Pll — .18 .27 .011 .062 8.5 8.2 Com 9-30 1 2 3 4 P23 P29 P22 T16 .30 .43 .51 .56 .001 7.9 .012 7.2 .026 6.8 .079 6.5 Soybeans 9-30 1 2 3 4 5 6 P29 T30 T20 T16 P26 .22 .35 .44 .52 .58 .005 .018 .029 .041 .040 1 2 3 4. 5 6 7 8 P09 .22 .005 6.7 T14 .43 .001 5.8 P10 .55 .007 5.2 T15 .64 .015 4.8 T10 .69 .032 4.5 .027 4.2 P21 .74 P17 .79 .025 3.9 P12 .82 .025 3.6 1st 8 only used > Oats 9-24 Note: 2.6 2.4 2.3 2.2 2.0 --- T20 P26 T13 P15 T14 P29 1st .11 7051 .22 .046 .30 .062 .38 .054 .46 .050 .53 .058 6 only used 2.8 2.7 2.5 2.4 2.3 2.2 P12 P09 P10 T14 P21 .22 .36 .47 .54 .60 6.7 6.2 5.7 5.4 5.1 .004 .013 .014 .048 .035 — Last significance level of 5% or less is underlined Variables given by week number; T: temperature P: precipitation Sig.: significance level s.d.: standard deviation *: no variables belcw 5% 88 significance level used in the weekly analysis. In order to attain 2 reasonable R values, variables were allcwed to enter the monthbased predictive equations up to a significance level of nearly .15. 2 Ranges in R values with the weekly analysis were from .41 to .82, compared with .15 to .56 for the monthly analysis. Standard errors of predicted value with the monthly analysis were fran 1.8 to 6.96 bu/a. The full-season weekly model gave standard errors of 1.3 to 6.7 bu/a, while the mid-season models ranged from 1.7 to 7.4 bu/a standard error. INTERCORRELATION OF INDEPENDENT VARIABLES In multiple regression analysis, it is preferable that the relationships among the independent variables are linear and addi­ tive. A small amount of intercorrelation does not cause much diffi­ culty, but with extreme collinearity, in the 0.8 to 1.0 range, the regression coefficients may be less stable in indicating relative importance of the different variables. solutions are: In such a case, two possible (a) create a single new variable fran the highly correlated variables to use in place of than, or (b) use only one of the highly intercorrelated variables (Kim and Kohout, 1975). In the weekly-based analysis using only temperature and precipitation, intercorrelation was not a factor. The highest intercorrelation was +0.62, between 12th week precipitation and 24th week temperature, with no suggestion of causality. were ±.58 or less, with no pattern of occurrence. All others 89 In the monthly-based analysis we find intercorrelations of .93 to .99 between similar unsquared and squared terms, as might be expected. For example, intercorrelation between temperatures and squared temperatures for specific months in Lenawee County ranged fran .95 to .99. Squared terms were included in the multiple regression analysis to determine if relationships between yields and specific climatic variables were linear or quadratic. term was selected by the analysis program. The more dominant Thus the program followed alternative (b) of Kim and Kohout's solution above. Analyses were also run with unsquared terms only and squared terms only. Runs made with both squared and unsquared terms together 2 gave higher R values and lower standard deviations than when run separately. LIMITATIONS CATASTROPHIC EVENTS A yield model which depends on long-term relationships of yields to recorded numerical climatic data often suffers from a basic limitation. Often the specific factor which affects yield is a catastrophic event which does not appear in the data or is diluted by the nunber of observations over a long period. Sane of the events which depress yields may slip through the statistical process undetected. Sane effects which depress yield may be secondary weather-related causes, such as a pest or disease outbreak. Such events may be a particular problem when applying the predictive 90 equation to a particular year, or predicting yield by a technique which does not take into consideration such events. AREAL VARIABILITY Another limitation lies in the areal variability of weather events such as convective precipitation. Nearby fields, whether in the same county or the same township or even the same section, may have different soil moisture regimes due simply to the apparently capricious movement of one or several storms. A 20-year study of precipitation with 22 recording rain gages on two small stream watersheds in south central Lower Michigan demonstrates that one observation station in the center of a county is not necessarily representative of precipitation available for crop growth in the entire county (Eichneier, Wheaton, and Kidder, 1959; Wheaton, Kidder, and Eichneier, 1964; and Mueller, Merva, and Stroimen, 1968). On a larger scale, area variability of crop yields is shown by the following examples. Oat yields in Lenawee County in 1946 were 18.3 bu/aabove the trend line, whilein Gladwin County in the same year theywere 17.4 bu/a below trend. In 1977 Lenawee County c o m yield was 16.3 bu/a above trend, while the Gladwin yield was 13.5 bu/abelow the trend line. On a state-wide scale, climatic carmentaries in monthly and annual climate and/or crop data reports are often contradictory to specific local or county conditions. The local departures fran "normals" may provide more accurate clues than such surmary carments. CHAPTER V SUMMARY AND CONCLUSIONS The purpose of this study is to develop a better understand­ ing of the relationships between specific climatic variables and onfarm yields of major field crops in Lower Michigan. SUMARY THE STUDY PROCESS CLIMATE Climate records were obtained for selected cooperative observer stations. These stations were located along a south-to- north transect up the interior of the peninsula. Reasonably can- plete records were obtained from Adrian in Lenawee County and Alma in Gratiot County for 1892 through 1977 and for 1926-1977 for Gladwin in Gladwin County. Temperature and precipitation were selected as the primary climatic variables. Missing temperature data were estimated by linear regressions against nearby stations. estimated by isopleth analysis. Precipitation was The initial analysis used data on a monthly scale. Secondary climate variables were developed for the monthly analysis. To allow for loss of crop-available water from surface runoff due to intense convection storms, two alternate precipitation 91 92 variables were derived. TVro levels of excess precipitation, or that greater than one inch and two inches in a calendar day, were removed, leaving these non-excess precipitation values as alternate sets of precipitation data. A cumulative moisture variable was derived from a soil bankbalance approach. This began the crop season April 1st with a full soil profile, adding monthly precipitation and subtracting potential evapotranspiration for each month. Potential evapotranspiration was calculated by the Thomthwaite method, based on temperature and daylength index. The Moisture Stress Index developed above was recoded to a Moisture Availability index by adding 34 to each MSI, to make all data values positive. Later in the research porcess the analysis moved to the weekly scale. Records for weekly precipitation and growing degree days were obtained for the Adrian and Alma station for the 1943-47 period. These records covered the 35 weeks from March 1 through October 31. Temperature data were calculated from the total weekly base of 40°F growing degree day data. The final weekly model included only tenperature and precipitation. CROPS Records of c o m and oat yields were obtained for 1892-1977 for Lenawee and Gratiot Counties, and for 1926-1977 for Gladwin County. Dry bean records were available for Gratiot County for 1895 93 through 1977. Soybean data were available for Lenawee and Gratiot Counties for 1942-1977. RELATIONSHIPS Over the period of the study yields have increased markedly, especially from 1940 to 1970. Much of this increase is due to development of improved technology and its application as management practices. Inspection of climatic data does not display the same secular trend which is apparent in yield data. Therefore removal of this long-term trend frcm yield data allows our analysis to con­ centrate on short-term variations. Trend removal is accomplished by fitting appropriate regres­ sion lines to segments of the actual yield data in order to deter­ mine trend, then using the resulting variations about trend as the dependent yield variable in our multiple regression analysis. After analysis the annual values of the trend lines are added back into the predicted departures frcm the lines to provide a predicted yield. A stepwise multiple regression was used, with de-trended crop yield as the dependent variable. Ri*o separate analyses were made, one with monthly-scale climate data and one with weekly data. For both, independent variables included tenperature and precipita­ tion. For the monthly analysis, variables also included a moisture availability index for each of the gncwing season months of April through September, and the squares of each of the three sets of 94 terms. For oats, the September data set was excluded, since the crop is already harvested. RESULTS MONTHLY ANALYSIS The most important variables for com, soybeans, and dry beans in the monthly analysis were July and August precipitation, with a positive relationship. September temperatures were also important for c o m in all three counties. For oats, June tempera­ tures were the most significant variable in all cases, with a nega­ tive relationship. July temperatures entered the equation for Lenawee and Gladwin oats; April and May temperatures for Gratiot and Gladwin oats; and May temperatures for Lenawee oats. June precipitation also appeared for Gratiot and Gladwin oats. The Moisture Availability Index, while appearing in seme cases, was of relatively little importance. Removal of daily rainfall in excess of one inch frcm the analysis did not improve the results, except for Gratiot soybeans. Removal of rainfall over two inches also did not improve the analysis more than marginally. Stepwise multiple regression analysis was constrai ned to a significance level of approximately .15. For the detrended yields, 2 R values for monthly regression models ranged frcm .21 for Gratiot dry beans, with a standard deviation of 1.87 cwt/a (270 kg/ha) to .56 for Lenawee soybeans, with a s.d. of 2.14 bu/a (412 kg/ha). 95 WEEKLY ANALYSIS A multiple regression analysis was applied to detrended crop yields for Lenawee and Gratiot Counties for the years 19431977. Independent variables were mean weekly temperatures and total weekly precipitation. C o m yield was positively related to precipitation in late July and early August. Soybeans appeared to be helped by timely rains in July, August, and September. July and August precipitation showed a positive relation to dry bean yields. Oat yields were negatively related to June temperatures. While restricting the number of variables by requiring a 5% 2 significance level for inclusion, R values were higher than those 2 obtained by the monthly analysis. Weekly-based R values ranged from .41 for Gratiot oats, with a standard deviation of 5.2 bu/a (197 kg/ha), to .82, with a s.d. of 3.6 bu/a (137 kg/ha) for Lenawee oats. CONCLUSIONS RELATIONSHIPS Specific climate factors do explain a significant portion of the variation in yields about a long-term trend line. Adequate pre­ cipitation in July and August is most important for com, soybeans, and dry beans. A cool June is most important for oats. Analysis based on weekly rather than monthly data shows promise; it allows predictive models which provide more accurate estimates of crop yields for the current season. Accuracy in this 96 case means a higher significance level and smaller error of the predicted value. A truncated mid- to late-season weekly model, while in most cases not as accurate as the full-seasan version, may be useful in developing early estimates of yields for the current year. LIMITATIONS CATASTROPHIC EVENTS A yield model which depends on long-term relationships of yields to recorded numerical climatic data suffers fron a primary limitation. Often the specific factor which affects yield is a catastrophic event which does not appear in the data or is diluted by the number of observations over a long period. Other, non- climatic problems may also occur, as well as those indirectly related to climate. An example of the former sometimes occurs in dry beans. A growing season may have optimum conditions for maximizing yields, except for a 3-inch (7.6 cm) thunderstorm on August 21. The latter may be the invasion of southern c o m leaf blight or army worms. AREAL VARIABILITY Another limitation lies in the areal variability of weather events, such as convective precipitation. Nearby fields may have different soil moisture regimes due simply to the apparently capricious behavior of one or several storms. 97 MDNTHLY VS. WEEKLY ANALYSES While monthly climate records are more commonly available, anslysis based on weekly data appears to have advantages. In this study, higher significance levels could be used with a weekly-based analysis, with a larger part of the variability of the dependent variable accounted for and a smaller standard deviation. Correla­ tions between independent variables and the dependent variable, while not statistically acceptable at high levels of significance, may at the weekly level more closely indicate critical stages in plant development if used with caution. Regression models become more sensitive to critical stages of plant growth at the weekly scale than with monthly data. They are also more sensitive to anomalous events in predictor variables, such as excessive precipitation in a predictor week. The use of constraints an the maximum weekly precipitation figure allowed in the predictive equation may help limit this source of error. SUGGESTIONS FOR FURTHER STUDY A researcher would be disappointed if the product of his labors, particularly in a field so closely related to mankind's needs as the production of food, were to gather dust on a shelf. One would hope that those following would find benefit in standing on his shoulders in order to see farther, and more clearly and quickly. 98 SECONDARY INDEPENDENT VARIABLES Use of a specific moisture availability variable was not particularly successful in this study. Formulated in a different manner it could be more useful. Seme studies have used amount of nitrogen applied to c o m as a proxy variable for technological trend. Some caution is needed in this, as between 1970 and 1976 change frcm the previous year in the amount of total nitrogen used in Michigan was opposite in sign to change in state average c o m yields in five years out of six (Michigan Department of Agriculture, 1972-78). While the weekly-based analysis using only tenperature and precipitation variables is an improvement over the more complex monthly analysis, application of carefully developed secondary vari­ ables may improve it. The use of squared terms in this analysis shewed little improvement. REMOVAL OF TREND The use of detrended yields such as in this analysis may prove useful in determining the nature of short-term variations. While the use of piecewise regressions to determine trends appeared preferable to higher-order curve-fitting techniques, it is suggested that the application of cubic splines may give a more accurate means of removing trend. PHENODOGICAL STAGES The growing plant responds to climatic conditions and the existing weather, rather than to the calendar. Yields may be 99 influenced by the weather existing at certain vulnerable stages of development. Thus, where reasonably accurate and reliable phenol- logical and weather information is available, better results may be obtained by relating weather conditions to growth stages rather than to calendar months or weeks. This is especially true under condi­ tions of earlier plantings in recent years, and of increased climatic variability. While the attempts made in this study to adjust weather data to plant development were not successful, it is suggested that this subject should be studied further. PATTERN ANALYSIS Where patterns exist, they may ordinarily be expected to continue and repeat. Determination of the nature of past climatic patterns could therefore be of value in estimating the future environment for plant growth. Fourier analysis and autocovariance techniques were applied to the data in this study in an attempt to determine patterns which exist in climate and/or yield data. Length of record proved to be too short for adequate analysis. CAVEATS One must be constantly aware of variability and inconsistency in the records. For example, the summer may have been dry over the entire state, sharply decreasing state c o m yields, but a part of one county may have had one or two well-timed heavy rains and thus high c o m yields. Narrative statewide summaries in the weather records were often contradictory to local conditions. Also, a given 100 weather observation station may have been moved one or several times, with the various location microclimates affecting the spatial and temporal validity of the record. Correlational and regression studies must be used with ade­ quate levels of knowledge and judgment. As an example, a multiple regression early in this study indicated a strong relationship between Lenawee County oat yields and September temperatures. A moment's reflection reminds us that oats are harvested by the end of August, ruling out any causal relationship. THE END AND A BEGINNING The author sincerely hopes that other researchers will con­ tinue the study of crcp-climate relationships in Michigan. The current state of the art leaves a great opportunity for further development in this field. LIST OF REFERENCES 101 l i s t o f ref er e nc e s Andersen, A. L. and L. S. Robertson, 1978. The Michigan dry edible bean industry - history. In: Dry bean production principles and practice. Extension Bulletin E-1251, Michigan Agricultural Experiment Station, August, 1978. p. 1. Achutuni, Vasuveda R., Amos Eddy, and Sharon K. LeDuc, 1979. Development and testing of technology-weather-phenology related c o m yield models for Iowa and Illinois. 13th Conference on Agriculture and Forest Meteorology, American Meteorological Society, Purdue University, April 4-6, 1977. pp. 70-71. Baier, Wolfgang, 1977a. Crop-weather models and their use in yield assessments. Tech. Note Nr. 151, WM3 Nr. 458, World Meteorological Organization, pp. 22-30. _______ , 1977b. Analysis of present knowledge of climatic variability as related to Canadian agriculture. Climatic variability in relation, to agricultural productivity and practices, 1977 meeting of the Canada Camittee on Agraneteorology, Winnipeg, Manitoba, January 11-12, 1977. Research Branch, Canada Department of Agriculture, Ottawa, January, 1977. p. 7. Bark, L. Dean, 1978. A study of the effects of altering the precipi­ tation pattern on the econary and environment of Kansas. Final report to Kansas Water Resources Board. Department of Physics, Kansas State University, Agricultural Experiment Station, Manhattan, Kansas, October 1, 1978. pp. 39-47, 171-172. Brown, James M. 1973. Tables and conversions for Microclimatology. General Technical Report NC-8. North Central Forest Experi­ ment Station, St. Paul, Minn., USDA, Forest Service, pp. 16-17. Bryson, Reid A., 1975. Shooting at a moving target. Crop Produc­ tivity— Research imperatives. Michigan Agricultural Experiment Station and C. F. Kettering Foundation, pp. 109-132. 102 103 Butz, E., n.d. Report on the influence of weather and climate on U.S. grain production. United States Department of Agriculture, Washington, D.C. Unpublished; quoted in Thompson, 1975. Chang Jen-Hu, 1968. Climate and agriculture; an ecological survey. Aldine Publishing Co., Chicago, pp. 149-150. Clough, M., 1968. Trends and variations in c o m yields over the last fifty years. Feed Situation, Economic Research Service, USDA, Fds-222, February, 1968. pp. 28-32. Dale, Robert F., 1964. Changes in moisture stress days since 1933. Weather and our food supply, CAED Report Nr. 20, Center for Agricultural and Economic Development, Iowa State University, Ames, Iowa. pp. 23-43. _______ , 1965. Weather and technology: a critical analysis of their importance to c o m yields. Agricultural Science Review, v. 3, Nr. 4, 4th Quarter 1965. pp. 25-31. _______ , 1968. The climatology of soil moisture, evaporation, and non-moisture stress days for c o m in Icwa. Agricultural Meteorology, v. 5, March, 1968. pp. 111-128. _______ , 1977a. An energy-crop growth variable for identifying weather effects upon c o m grcwth and yield. 13th Conference on Agriculture and Forest Meteorology, American Meteoro­ logical Society, Purdue University, April 4-6, 1977. pp. 85-86. _______ / 1977b. Final report: correlating c o m grcwth and development with weather. Report under NSF Grant ATM 75-10001 A01, Purdue University, West Lafayette, Indiana, pp. 1-15. Dale, Robert F. and Harry F. Hodges, 1975. Weather and c o m yield study for Tippecanoe County, Indiana. Final Report to Director, Environmental Data Service, National Oceanic and Atmospheric Administration. Denmead, 0. T. and R. M. Shaw, 1960. The effects of soil moisture stress at different stages of grcwth on the development and yield of com. Aqroncmy Journal, v. 52, May-June 1960. pp. 272-274. Edey, S. N., 1977. Freeze probabilities. Climatic variability as related to agricultural productivity and practices, 1977 meeting of the Canada Caimittee an Agraneteorology, Winnipeg, Manitoba, January 11-12, 1977. Research Branch, Canada Department of Agriculture, Ottawa. January, 1977. Sec. 3.5, pp. 1-7. 104 Eichneier, A. H., R. Z. Wheaton, and E. H. Kidder, 1959. Variation in sumertime rainfall in south central Michigan. Quarterly Bulletin of the Mich. Agr. Exp. Sta., Michigan State University, East Lansing, v. 41, Nr. 4, May, 1959. pp. 886-888. Epstein, Edward S., 1977. Federal plan for a National Agricultural Weather Service; a first version, p. 1. Erdmann, Milton H., 1979. Grafius, John E., 1979. Personal discussions, August, 1979. Personal conversation, March 7, 1979. Gross, E. R. and R. H. Rust, 1972. Estimation of c o m and soybean yields using multiple curvilinear regression methods. Proceedings of the Soil Science Society of America, v. 36, March-April, 1972. pp. 316-320. Haigh, Peter H., 1977. Separating the effects of weather and management an crop production. Report on Kettering Founda­ tion Project ST 77-44 through James D. McQuigg, Certified Consulting Meteorologist, Columbia, Mo., November, 1977. 93 pp. Hill, R. W., D. R. Johnson, and K. H. Ryan, 1979. A model for predicting soybean yields frcm climatic data. Agronomy Journal, v. 71, Nr. 2, Marcfr-April, 1979. pp. 251-256. Holt, R. F. and D. R. Tinmans, 1968. Influence of precipitation, soil water, and plant population interactions on c o m grain yields. Agronomy Journal, v. 60, July-August, 1968. pp. 379-381. Huda, A.K. Samsul and E. C. A. Runge, 1978. Developing and testing models for c o m production. Agronomy Abstracts, 70th Annual Meeting, American Society of Agronany, Chicago, December 3-8, 1978. p. 11. Katz, Richard W., 1977. Sensitivity analysis of statistical cropweather models. 13th Conference on Agricultural and Forest Meteorology, American Meteorological Society, Purdue University, April 4-6, 1977. pp. 1-2. Kim, Jae-On and Frank J. Kohout, 1975. Multiple regression analysis, in Nie, Normal et al., Statistical Package for the Social Sciences, 2d Edition, McGraw-Hill, N.Y., 1975. pp. 320-360. 105 Lawlor, D. J. and W. C. Liebhart, 1978. The temporal effect of climatic parameters upon c o m yield in the Delmarva Peninsula. Agronomy Abstracts, 70th Annual Meeting, American Society of Agronomy, Chicago, December 3-8, 1978. p. 11. Linvill, Dale E., 1972. Microclimatic radiation and the grcwth rate of com. Unpublished Ph.D. thesis, Purdue University, West Lafayette, Indiana, December, 1972. McCloud, D. S., 1977. Florida field crop yield trends with a changing climate. Proceedings, Soil and Crop Society of Florida, v. 36. pp. 200-204. Leeper, R. A., E. C. A. Runge, and W. M. Walker, 1974. Effect of plant-available stored soil moisture on c o m yields. II. Variable climatic conditions. Agronomy Journal, v. 66, Nr. 6, November-December, 1974. pp. 798-733. McKay, G. A. and T. Allsqpp, 1977. Climate and climate variability. Climatic variability as related to agricultural productivity and practices, 1977 meeting of the Canada Ccrmittee on Agro­ meteorology, Winnipeg, Manitoba, January 11-12, 1977. Research Branch, Canada Department of Agriculture, Ottawa, January, 1977. Sec. 2.1, pp. 1-10. McQuigg, James D., 1975. Economic impacts of weather variability. Atmospheric Science Department, University of MissouriColimbia. August, 1975. _______ , 1976. Climatic constraints on food grain production. Paper presented to the World Food Conference of 1976, Ames, Icwa, June 27-July 1, 1976. Michigan Department of Agriculture. Michigan Crop Report. USDA cooperating. Continued through various state and federal agencies from prior to 1886 to the present. _______ , 1972 through 1978. Michigan Agricultural Statistics. Michigan Crop Reporting Service, Michigan Department of Agriculture, Annual Reports released in June or July for previous year. _______ , 1979. Michigan Agricultural Statistics. Michigan Agricultural Reporting Service, Michigan Department of Agriculture, July, 1979 and 1979 periodic mail reports. 106 Mueller, Charles C., George E. Merva, and Norton D. Strcmmen, 1968. Seasonal variation of topographical effects on precipitation measurements. Quarterly Bulletin of the Mich. Agr. Exp. Sta., Michigan State University, East Lansing, v. 50, Nr. 4, May, 1968. pp. 599-605. Niell, J. C. and F. A. Huff, 1979. Crop-weather models. 14th Conference on Agricultural and Forest Meteorology, American Meteorological Society, Minneapolis, Minn., April 2-6, 1979. pp. 57-58. Nelson, William L. and Robert F. Dale, 1977. The influence of record period on the estimates of weather and technology effects on c o m yield in multiple regression models. 13th Conference on Agricultural and Forest Meteorology, American Meteorological Society, Purdue university, April 4-6, 1977. pp. 3-4. _______ , 1978. A methodology for testing the accuracy of yield predictions from weather-yield regression models for c o m (Zea mays). Agronomy Journal, v. 70, September-October, 1978. pp. 734-740. Palmer, Wayne C. and A. Vaughn Havens, 1958. A graphical technique for determining evapo-transpiration by the Thomthwaite method. Monthly Weather Review, April, 1958. pp. 123-127. Pfahler, P. L., 1972. Relationship between grain yield and environ­ mental variability in oats. Crop Science, v. 12, MarchApril, 1972. pp. 254-255. Ravelo, Andres C. and Wayne L. Decker, 1979. Soybean-weather analysis model. 14th Conference on Agriculture and Forest Meteorology, American Meteorological Society, Minneapolis, Minn., April 2-6, 1979. pp. 72-73. Robbins, J. S. and C. E. Domingo, 1953. Some effects of severe soil moisture deficits at specific grcwth stages in com. Agronomy Journal, v. 45, December, 1953. pp. 618-621. _______ , 1956. Moisture deficits in relation to the grcwth and development of dry beans. Agronomy Journal, v. 48, Nr. 2, February, 1956. pp. 67-70. Rosenberg, Norman J., 1974. Microclimate: the biological environ­ ment. John Wiley and Sons, New York. Runge, E. C. A., 1968. Effects of rainfall and temperature inter­ actions during the growing season on c o m yield. Agronomy Journal, v. 60, Nr. 5, September-Octdber, 1968. pp. 503-507. 107 _______ , 1960. The relation between precipitation, tenperature, and yield of soybeans on the Agronomy South Farm, Urbana, Illinois. Agronomy Journal, v. 52, Nr. 5, May, 1960. pp. 245-247. Schaal, Lawrence A. and Byron 0. Blair, 1968. The tenperature factor in c o m production in Tippecanoe County, Indiana. Proceedings of the Indiana Academy of Science of 1967, v. 77, 1968. pp. 389-394. Schneider, I. F. and A. E. Erickson, n.d. Water-holding capacity and infiltration rates of soils in Michigan (map). Data from Michigan Agricultural Experiment Station Project 413, Soil Science Department, Michigan State University. Date estimated after 1954. Seeley, Dewey Alsdorf, 1917. The Climate of Michigan and its Relation to Agriculture. Unpublished M.S. thesis, Michigan Agricultural College. Smicker, A. J. M., D. L. Mokma, and D. E. Linvill, 1978. Environ­ mental requirements and stresses. Dry bean production— principles and practices, Ext. Bui. E-1251, Michigan Agricultural Experiment Station, August, 1978. pp. 59-60. Steyaert, L. T., 1977. Quality of United States wheat, com, and soybean crop statistics. University of Missouri, Coluribia. Reported in Nelson and Dale, 1978. Thompson, L. M., 1962. Trends in soybean production and their relation to weather. Soybean Digest, v. 22, Nr. 11, September, 1962. pp. 26-28. _______ , 1963. Weather and technology in the production of c o m and soybeans. CAED Report Nr. 17, Center for Agricultural and Economic Development, Iowa State University, Ames, Icwa. _______ , 1969a. Weather and technology in the production of wheat in the United States. Journal of Soil and Water Conserva­ tion, v. 24,. pp. 219-244. _______ , 1969b. Weather and technology in the production of c o m in the U.S. C o m Belt. Agronomy Journal, v. 61, JanuaryFebruary, 1969. pp. 453-456. _______ , 1970. Weather and technology in the production of soybeans in the central United States. Agronomy journal, v. 62, March-April, 1970. pp. 232-236. 1975. Weather variability, climatic change, and grain production. Science, v. 188, May 9, 1975. pp. 535-541. 108 U.S., National Oceanic and Atmospheric Administration, Environmental Data and Information Service. Climatological Data. U.S. Department of Agriculture, Soil Conservation Service. Soil Survey Maps and Interpretation. Special Advanced Report. USDA-SCS in cooperation with the Michigan Agricultural Experiment Station and the Gratiot County Board of Com­ missioners, 1976. U.S. Department of Agriculture, Soil Conservation Service. Survey, Gladwin County, Michigan, March, 1972. Soil U.S. Department of Agriculture, Soil Conservation Service. Soil Survey, Lenawee County, Michigan, Series 1947, Nr. 10, August, 1961. Weatherwax, Paul, 1923. The Story of the Maize Plant. University of Chicago Press, Chicago, Illinois, p. 12. Wheaton, R. Z., E. H. Kidder, and A. H. Eichmeier, 1964. Variations in summertime rainfall. Transactions of the American Society of Agricultural Engineers, v. 7, Nr. 2, 1964. pp. 114-115. Wright, Karl T., 1976a. 1976-78. Unpublished graphs and personal discussions, _______ , 1976b. Dry edible bean production trends: world, U.S., and Michigan. Staff paper 76-67, Department of Agricultural Economics, Michigan State University. December, 1976. APPENDIX 110 Table A-l. Vxear aav 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 Lenawee County C o m Yields, Actual and Predicted Actual Yield Pred.* Yield Trend Yield 22.2 20.5 18.0 29.0 36.0 32.0 35.0 41.0 44.0 32.0 33.0 37.0 38.0 36.0 39.0 31.0 30.0 36.0 37.0 37.0 38.0 30.0 36.0 33.0 20.0 32.0 19.0 37.0 47.0 43.0 39.0 40.0 29.0 47.0 45.0 40.0 49.0 34.0 26.0 35.0 25.0 31.0 24.0 34.0 31.7 31.8 31.9 32.0 32.1 32.2 32.3 32.5 32.6 32.7 32.8 32.9 33.0 33.1 33.2 33.3 33.4 33.5 33.6 33.7 33.8 34.0 34.1 34.2 34.3 34.4 34.5 34.6 34.7 34.8 34.9 35.0 35.1 35.2 35.3 35.5 35.6 35.7 35.8 35.9 36.0 36.1 36.2 36.3 25.3 23.4 26.1 28.4 37.2 30.5 36.6 35.8 37.9 27.9 31.1 38.7 38.9 33.2 37.5 34.5 33.0 29.7 36.9 39.6 40.5 34.7 32.9 40.9 25.9 35.1 23.2 24.1 42.1 41.7 38.0 29.8 30.0 40.3 37.8 40.3 36.2 27.9 21.7 37.4 36.0 40.5 28.6 36.3 VXcdT Aar 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 Actual Yield Pred.* Pred.# Yield Trend Yield Yield 34.0 31.0 43.0 41.0 34.0 39.0 52.0 35.5 44.5 46.4 42.8 35.8 36.5 58.0 47.6 42.9 51.6 57.4 59.3 62.8 61.1 70.3 78.8 72.0 60.7 88.9 86.7 70.8 70.0 78.1 79.0 78.0 87.9 88.7 93.4 76.0 99.0 96.0 60.0 90.0 78.4 104.0 76.1 36.4 36.5 36.6 36.7 37.8 38.0 39.7 41.4 43.1 44.8 46.6 48.3 50.0 51.7 53.4 55.1 56.8 58.6 60.3 62.0 63.7 65.4 67.1 68.8 70.6 72.3 74.0 75.7 77.4 79.1 80.8 82.6 84.3 86.9 87.0 87.1 87.2 87.3 87.4 87.5 87.5 87.6 87.7 87.8 34.2 31.3 41.6 36.7 34.5 35.6 47.4 34.4 38.4 42.5 40.5 45.4 47.8 46.1 57.9 49.4 55.7 57.7 60.8 62.5 60.2 67.3 75.3 78.7 73.2 79.6 79.1 73.3 83.7 84.5 80.1 82.2 84.7 83.0 84.7 80.5 96.1 87.2 77.9 90.0 80.1 91.7 86.9 37.3 43.4 49.6 40.4 40.3 38.8 62.6 43.4 48.6 42.0 62.3 61.2 58.5 61.5 65.0 80.7 70.4 70.9 86.3 84.4 73.5 71.2 82.5 75.5 77.5 87.8 78.9 89.3 76.8 99.9 92.7 74.3 84.0 79.7 97.8. 88.7® 90.1? ♦Monthly climate data #Weekly climate data a) .90 ganma b) truncated model Ill Table A-3. , Lenawee County Soybean Yields Actual and Predicted VXG6CC a 9V Actual Yield Pred.* Pred.# Yield Trend Yield Yield 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 22.8 16.8 17,8 18.0 17.1 20.2 18.9 23.0 21.3 24.0 23.1 22.3 26.5 23.7 23.7 26.1 28.0 28.9 22.4 17.8 18.3 18.8 19.3 19.8 20.3 20.8 21.3 21.8 22.3 22.9 23.4 23.9 24.4 24.9 25.4 25.5 25.6 25.8 22.7 19.4 16.0 19.3 17.6 18.6 20.2 21!.0 21.8 24.0 22.0 21.3 22.2 25.9 23.2 26.7 28.3 28.7 24.8 22.2 19.9 17.8 20.7 17.7 19.2 21.4 18.9 21.1 23.9 26.7 27.7 26.8 24.2 24.9 24.3 26.7 27.5 iear 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 Actual Yield Pred.* Pred,# Yield Trend Yield Yield 27.8 25.1 21.8 25.9 27.1 27.1 22.5 30.2 26.9 31.0 23.5 32.0 28.5 21.6 29.3 23.7 36.3 27.1 26.0 26.1 26.3 26.5 26.6 26.8 26.9 27.1 27.3 27.4 27.6 27.8 27.9 28.1 28.2 28.4 28.6 28.8 29.0 28.9 25.6 23.4 29.9 28.0 27.0 25.1 28.6 26.2 28.1 22.4 29.6 26.9 25.2 29.6 25.2 31.7 26.1 25.7 23.1 23.7 26.5 24.0 28.3 23.9 28.5 27.9 31.0 24.9 28.8 26.1 27.4 26.2 26.2 29.8a 28. 27.9 Table A-4. Gratiot County Soybean Yields, Actual and Predicted XGoT 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 Actual Yield Pred.* Pred.# Yield Trend Yield Yield 13.9 11.5 13.4 14.2 15.2 14.4 15.1 23.0 21.4 21.8 23.1 20.3 21.6 20.3 21.8 21.5 21.0 21.7 23.4 12.8 13.2 13.6 14.0 14.4 14.8 15.2 21.4 21.5 21.6 21.7 21.8 21.8 21.9 22.0 22.1 22.2 22.2 22.3 13.1 11.5 12.2 13.7 13.2 14.3 14.1 22.0 21.1 21.9 23.0 21.1 19.8 23.4 22.0 21.1 22.2 22.9 22.7 12.2 12.5 14.4 15.2 13.1 16.0 22.2 21.8 19.3 21.5 21.6 21.3 21.9 21.2 21.4 20.8 20.8 24.9 Vmav ICfli 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 Actual Yield Pred.* Pred.# Yield Trend Yield Yield 27.8 22.1 25.2 23.4 18.5 21.4 21.0 21.6 22.0 24.0 16.8 27.6 25.0 23.4 24.7 21.8 26.5 27.4 • 22.4 22.5 22.5 22.6 22.7 22.8 22.9 22.9 23.0 23.1 23.2 23.3 23.3 23.4 23.5 23.6 23.7 23.7 23.8 23.6 22.0 23.3 24.1 21.9 22.5 21.7 21.6 21.9 23.6 22.0 24.5 23.5 24.8 26.7 22.4 26.Q 21.S 25.8 21.5 23.4 22.9 22.5 22.0 22.4 21.6 23.0 25.0 18.5 27.3 23.7 23.9 26.1 20.7 26.5 24.0b 23.5° ^Monthly Climate data #Weekly climate data a) .90 gamna b) truncated model 112 Table A-2. Lenawee County Oat Yields, Actual and Predicted sear Actual Yield Pred.* Yield Trend Yield 1892 29.1 33.5 34.0 33.6 1893 1894 33.8 32.5 1895 33.9 29.6 1896 34.1 33.1 1897 34.2 34.3 1898 32.4 34.3 1899 40.0 34.5 1900 40.0 34.6 1901 34.7 33.0 1902 40.0 34.9 1903 36.0 35.0 1904 43.0 35.1 1905 34.0 35.3 1906 35.4 28.0 1907 23.0 35.6 1908 35.7 30.0 1909 35.8 35.0 1910 36.0 39.0 1911 36.0 36.1 1912 36.2 43.0 1913 36.4 28.0 1914 32.0 36.5 1915 43.0 36.6 1916 34.0 36.8 1917 49 3 36.9 1918 46.0 37.1 1919 37.2 30.9 1920 50.4 37.3 1921 18.0 37.5 1922 34.0 37.6 1923 43.0 37.7 1924 57.0 37.9 1925 38.0 48.0 1926 38.1 40.0 1927 52.0 38.3 1928 41.0 38.4 1929 36.0 38.6 1930 45.0 38.7 1931 40.0 38.8 1932 31.0 39.0 1933 19.0 39.1 1934 39.2 19.0 1935 39.4 42.0 ^Monthly climate data Actual Yield Pred.* Pred.# Vaar X€cuT Yield Trend Yield Yield 25.0 1936 29.3 1937 24.0 1938 35.1 1939 31.2 1940 37.3 1941 36.0 1942 35.2 1943 38.1 1944 36.4 1945 39.9 1946 41.2 1947 42.6 1948 36.2 1949 36.2 1950 40.7 1951 32.4 1952 34.6 1953 36.1 1954 31.3 1955 38.7 1956 31.0 1957 28.2 1958 46.6 1959 40.4 1960 41.4 1961 42.1 1962 26.4 1963 39.9 1964 28.5 1965 30.0 1966 36.1 1967 44.5 1968 41.8 1969 43.2 1970 45.4 1971 43.9 1972 35.9 1973 36.4 1974 37.9 1975 36.8 1976 28.1 1977 31.2 1978 41.1 1979 # Weekly climate data 36.0 28.0 33.0 41.0 64.0 39.0 49.0 19.7 29.2 40.7 59.2 37.6 42.0 45.0 43.5 41.9 37.0 48.4 52.1 52.8 33.2 46.7 54.8 44.2 61.5 50.3 57.7 58.5 68.7 74.4 64.2 58.2 68.5 68.5 69.0 63.0 72.0 60.0 61.1 68.4 61.4 68.7 67.5 39.5 39.6 39.8 39.9 40.1 40.2 40.3 40.5 40.6 40.7 40.9 41.0 41.1 41.3 41.4 42.7 44.1 45.5 46.9 48.3 49.7 51.1 52.6 54.0 55.4 56.8 58.2 59.6 61.1 62.5 63.9 65.3 66.7 68.1 67.1 66.7 66.3 65.9 65.4 65.0 64.6 64.2 63.8 63.4 a) .90 gamna 37.8 35.3 39.4 38.2 38.6 39.1 41.1 24.2 31.2 38.8 42.2 37.2 44.2 35.6 41.4 43.5 39.7 44.9 48.8 49.6 46.4 51.0 60.4 51.1 60.9 53.9 63.8 63.7 63.2 69.1 65.6 67.5 65.2 70.6 68.4 71.3 70.9 65.9 67.7 62.6 69.3 67.4 66.6 20.2 31.3a 41.9 53.3 42.4 39.1 34.5 39.7 40.3 37.6 43.8 53.8 51.6 35.1 47.6 55.8 43.4 59.7 42.8 62.8 53.7 68.7 67.7 69.2 65.0 64.2 63.2 71.7 66.2 71.8 56.2 64.1 70.7 62.1 78.8 68.8 61.9 113 Table A-5. XBcUl 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 Gratiot County C o m Yields, Actual and Predicted Actual Yield Pred.* Yield Trend Yield 31.0 30.0 28.0 36.0 36.0 38.0 37.0 37.0 39.0 42.0 39.0 33.0 32.0 36.0 40.0 36.0 39.0 37.0 32.0 36.0 30.0 39.0 33.0 28.0 23.0 24.0 22.0 48.0 44.0 40.0 40.0 35.0 26.0 39.0 34.0 33.0 34.0 29.0 25.0 34.0 32.0 31.0 18.0 41.0 34.7 34.7 34.6 34.6 34.6 34.6 34.6 34.6 34.6 34.6 34.6 34.6 34.6 34.6 34.6 34.6 34.5 34.5 34.5 34.5 34.5 34.5 34.5 34.5 34.5 34.5 34.5 34.5 34.5 34.5 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.4 34.3 33.5 30.5 31.3 32.8 30.5 36.5 34.1 35.0 38.3 35.3 35.5 39.9 33.1 37.8 38.4 31.6 37.5 30.9 30.7 30.6 39.3 34.4 38.5 34.4 29.6 30.2 27.0 33.9 33.7 39.8 34.4 35.4 33.2 36.1 29.9 33.8 34.1 31.3 31.2 35.5 35.8 33.3 32.4 33.3 Vaar XgO i Actual Yield Pred.* Pred.’ Yield Trend Yield Yield 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 • 1971 1972 1973 1974 1975 1976 1977 1978 1979 *Manthly climate data #Weekly climate data 33.0 37.0 33.0 38.0 30.0 40.0 46.0 34.8 39.2 37.3 32.1 31.9 42.6 56.0 43.5 42.9 56.5 51.6 49.7 48.1 51.1 48.5 54.7 63.2 66.1 76.2 69.0 80.4 78.3 62.8 74.2 73.0 78.6 86.4 86.1 65.1 99.9 95.0 81.0 99.0 68.8 62.1 87.6 34.3 34.3 34.3 34.3 34.3 34.3 34.3 34.3 34.3 35.1 37.2 39.2 41.2 43.3 45.3 47.4 49.4 51.4 53.5 55.5 57.5 59.6 61.6 63.6 65.7 67.7 69.7 71.8 75.7 76.2 76.8 77.3 77.9 78.5 79.0 79.6 80.1 80.7 81.2 81.8 82.3 82.9 83.4 84.0 33.3 33.3 35.5 35.7 33.3 34.9 31.3 31.1 33.5 34.1 35.4 40.2 40.3 44.4 47.7 49.3 52.2 50.8 50.8 57.7 56.8 58.7 61.3 67.7 66.9 71.0 67.0 71.1 79.6 74.2 75.4 75.3 75.6 76.9 79.6 79.1 83.2 81.3 80.4 93.1 80.4 84.7 80.9 29.6 34.2 29.4 33.5 35.0 34.5 55.8 41.9 41.2 60.6 45.5 58.4 46.3 51.0 53.7 56.0 71.3 71.1 74.3 68.9 72.5 80.1 66.7 71.3 82.3 77.0 85.4 79.7 70.1 84.8 88.0 83.4 95.7 77.5 79*1 91.0 72.1 114 Table A-6. XSaJC 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 Gratiot County Dry Bean Yields, Actual and Predicted Actual Yield Pred.* Yield Trend Yield 8.2 9.1 8.6 6.7 9.0 10.8 10.8 8.4 10.2 7.8 11.4 9.6 8.4 10.8 9.0 9.0 7.2 7.2 8.4 6.6 5.4 3.6 6.1 5.4 7.9 10.0 6.0 7.8 8.4 7.8 8.4 7.8 6.0 7.8 5.6 3.0 4.8 9.0 7.2 4.2 9.6 6.0 8.4 8.3 8.3 8.3 8.3 8.3 8.3 8.3 8.3 8.3 8.2 8.2 8.2 8.2 8.2 8.2 8.2 8.2 8.2 8.1 8.1 8.1 8.1 8.1 8.1 8.1 8.1 8.1 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 7.9 7.9 7.9 7.9 7.9 7.9 7.9 7.5 8.3 7.8 8.0 6.9 9.7 8.5 7.9 9.4 8.7 9.7 9.1 7.4 8.8 7.5 7.2 7.2 8.8 9.2 9.0 8.8 5.3 7.7 7.1 7.7 9.1 7.9 7.9 8.9 9.5 9.1 6.8 6.9 9.2 6.1 5.1 6.2 8.9 5.8 6.6 7.8 7.2 8.2 xecu. 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 Actual Yield Pred.* Pred.: Yield Trend Yield Yield 9.6 10.8 7.8 8.4 10.8 9.6 7.8 10.1 8.3 7.7 10.2 12.6 10.7 12.3 13.4 12.1 9.8 9.7 14.6 8.0 12.0 12.0 17.0 17.5 17.0 20.3 13.8 9.9 12.9 11.2 11.1 13.5 11.0 9.3 12.7 11.5 11.0 9.4 10.3 11.0 11.8 7.9 7.9 7.8 7.8 7.8 7.8 7.8 7.8 8.3 8.8 9.3 9.8 10.3 10.8 11.3 11.8 12.3 12.8 13.3 13.7 14.2 14.7 15.2 15.7 16.2 15.2 14.7 14.3 13.9 13.4 13.0 12.6 12.2 11.7 11.3 10.8 10.4 10.0 9.5 9.1 8.7 8.2 Units : cwt/acre *Monthly climate data #Weekly climate data 8.3 7.7 6.8 7.9 7.5 7.3 7,4 8.1 7.0 9.5 8.2 10.4 10.0 11.1 11.5 11.8 10.5 13.2 14.4 13.3 14.8 15.6 15.7 16.6 16.0 15.5 15.3 13.9 14.1 13.0 11.3 11.5 12.6 11.1 12.0 11.2 11.1 10.2 8.8 10.1 8.6 10,1 7.1 9.1 8.0 6.5 11-7 11.1 12.6 12.1 12.9 11.1 10.6 11.3 15.2 9.0 12.8 13.0 15.7 18.1 15.6 18.6 14.0 14.8 13.1 11.5 11.0 10.8 11.1 10.7 12.1 10.2 9.8 9.3 10.9 9.7 10.7 10.3 115 Table A-7. V la ea ar l 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 Gratiot County Oat Yields, Actual and Predicted Actual Yield Pred.* Yield Trend Yield 28.1 28.0 38.9 30.9 36.5 36.2 37.3 39.0 41.0 31.0 42.0 32.0 17.0 36.0 33.0 22.0 33.0 32.0 40.0 31.0 35.0 37.0 31.0 44.0 33.0 44.1 44.0 37.2 39.0 19.0 42.0 32.0 38.0 36.0 40.0 32.0 49.0 23.0 49.0 39.0 32.0 34.0 27.0 35.0 31.2 31.4 31.5 31.7 31.9 32.1 32.3 32.5 32.7 32.9 33.1 33.3 33.5 33.6 33.8 34.0 34.2 34.4 34.6 34.8 35.0 35.2 35.4 35.5 35.7 35.9 36.1 36.3 36.5 36.7 36.9 37.1 37.3 37.4 37.6 37.8 38.0 38.2 38.4 38.5 38.8 39.0 39.2 39.4 36.9 24.9 31.9 35.1 35.8 30.1 30.9 36.3 35.9 27.5 40.5 37.2 30.0 38.5 39.4 10.1 32.4 28.2 37.2 31.2 38.4 37.4 40.8 46.8 36.4 36.2 38.6 34.3 40.2 30.3 38.1 33.0 40.7 38.0 36.5 38.0 42.3 36.5 36.8 35.6 35.3 32.2 31.4 38.6 VI o r Ca Ql 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 .1£62 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ♦Monthly climate data #Weekly climate data Actual Yield Pred.* Pred.' Yield Trend Yield Yield 14.0 37.0 40.0 35.0 55.0 43.0 52.0 27.4 36.6 50.3 53.2 46.8 46.0 39.0 46.6 44.6 37.0 38.9 45.8 46.7 33.0 43.6 61.1 41.7 61.5 52.2 58.6 60.0 61.1 59.7 54.3 63.1 61.9 65.8 68.0 52.9 61.1 60.0 58.0 65.2 56.0 61.0 59.0 39.5 39.7 39.9 40.1 40.3 40.5 40.7 40.9 41.1 41.3 41.4 41.6 41.8 42.0 42.2 42.4 42.6 42.8 43.0 43.2 43.4 43.5 43.7 55.5 55.9 56.3 56.7 57.1 57.5 57.9 58.3 58.7 59.1 59.5 59.9 60.3 60.7 61.1 61.5 61.8 62.2 *2.6 31.4 35.6 41.8 38.1 37.3 44.7 49.5 36.5 35.6 50.5 45.4 42.5 45.5 38.4 37.2 41.0 38.6 35.5 46.0 43.9 41.8 44.4 50.0 52.4 60.9 54.7 59.7 54.8 54.8 57.2 51.3 58.2 64.9 62.5 58.5 58.6 60.6 60.0 65.1 56.4 59.4 67.3 33.0 34.3 51.4 47.7 47.9 42.7 35.3 42.9 43.3 40.0 39.3 41.5 43.2 42.7 41.5 51.2 55.0 58.1 61.8 57.4 54.3 59.9 63.1 57.2 58.1 60.7 66.5 61.4 55.2 65.5 58.2 64.7 59.9 59.8 64.3 68.4 68.0 116 Table A-8. Year 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 Gladwin County C o m Yields, Actual and Predicted Actual '.Yield Yield Trend 27.0 33.0 33.0 12.0 15.0 32.0 31.0 29.0 28.0 28.0 21.0 38.0 27.0 24.0 20.0 26.3 33.0 28.9 31.8 29.3 19.4 23.2 31.4 41.0 37.5 29.9 26.6 26.6 26.7 26.7 26.8 26.8 26.8 26.9 26.9 26.9 27.0 27.0 27.1 27.1 27.1 27.2 27.2 27.2 27.3 27.3 27.4 27.4 31.4 32.8 34.3 35.7 ♦Monthly climate data Units: bushels/acre Pred.* Yield 24.9 25.4 30.3 14.0 23.1 25.7 29.9 25.9 22.6 29.4 24.4 30.2 25.2 27.9 30.0 24.4 28.5 29.7 24.4 23.8 28.9 23.1 27.0 36.6 34.4 36.2 Year 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 Actual Yield Pred.' Yield Trend Yield 42.8 40.8 35.4 44.2 44.1 47.1 38.8 53.2 38.8 48.7 54.6 57.1 56.2 46.5 64.6 61.1 63.2 65.2 67.4 47.9 81.9 66.0 70.0 76.0 65.0 59.2 77.8 37.1 38.5 40.0 41.4 42.8 44.2 45.7 47.1 48.5 49.9 51.4 52.8 54.2 55.6 57.0 58.5 59.9 61.3 62.7 64.2 65.6 67.0 68.4 69.9 71.3 72.7 74.0 75.3 43.2 40.4 36.7 47.2 42.5 49.0 42.5 49.7 47.2 50.0 49.3 55.2 55.5 50.2 57.4 56.9 60.2 67.5 72.2 58.4 77.8 68.0 71.3 77.9 73.3 60.2 66.8 117 Table A-9. Year 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 Gladwin County Oat Yields, Actual and Predicted Actual Yield Pred.* Yield Trend Yield 29.0 16.0 27.0 25.0 32.0 21.0 27.0 17.0 20.0 26.0 14.0 24.0 27.0 35.0 38.7 28.0 40.0 18.7 31.3 36.4 13.6 28.5 40.0 29.0 32.4 39.8 27.8 21.4 21.9 22.4 22.8 23.3 23.8 24.3 24.8 25.3 25.7 26.2 26.7 27.2 27.7 28.1 28.6 29.1 29.6 30.1 30.6 31.0 31.5 32.0 32.5 33.0 33.4 33.9 *Mcnthly climate data Units: bushels/acre 24.9 19.6 27.9 23.5 21.1 20.0 21.8 19.7 18.3 27.0 23.6 25.4 27.8 30.7 26.9 30.0 32.5 26.1 29.5 36.0 30.8 20.3 36.9 30.9 28.5 36.6 32.8 Year 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 Actual Yield Pred.’1 Yield Trend Yield 27.3 33.4 38.6 29.0 37.3 42.8 41.7 40.8 38.6 35.5 46.7 36.2 44.8 26.7 36.9 51.1 51.0 48.8 32.0 44.0 33.8 40.4 52.0 46.8 51.0 53.1 34.4 34.9 35.4 35.9 36.3 36.8 37.3 38.3 38.5 38.7 39.2 39.7 40.2 40.7 41.2 41.6 42.1 42.6 43.1 43.6 44.0 44.5 45.0 45.5 46.0 46.5 47.0 32.8 31.9 41.7 31.1 38.0 41.2 40.1 45.9 35.3 38.9 40.4 38.4 42.2 31.7 36.3 45.3 51.4 42.5 36.2 51.6 41.6 46.7 48.3 44.4 49.3 48.2