FREQUENCY OF MOI$WRE SEFICIENCIES IN THE
LOWER PENINSULA O? MICHIGAN

Thests Ior I'Iw Degree of M. 5.
MICHIGAN STATE UNIVERSITY

Robert J. Moraniec
1959

'I—IESIS

This is to certify that the

thesis entitled

FREQUENCY OF MOISTURE DEFICIENCIES IN
THE LOWER PENINSULA OF MICHIGAN

presented by

Robert J. Moraniec

has been accepted towards fulfillment
of the requirements for

M. S. degree in Agrl. Engineering

   

Major professor

Date January 1959

0-169

FREQUENCY OF MOISTURE DEFICIENCIES IN THE
LOWER PENINSULA OF MICHIGAN

by
Robert J. Moraniec

A THESIS

Submitted to the College of Agriculture of Michigan State
University of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Agricultural Engineering

1959

Approved by W—

ACKNOWLEDGEMFNTS

The author expresses his sincere graditude to
Professor Ernest H. Kidder of the Agricultural Eng-
ineering Department, for his guidance and many help-

ful suggestions during the course of this study.

The author is very grateful to Mr. A. H. Eichmeier,
director of the East Lansing, Office of the United
States Weather Bureau and to Professor W. D. Eaten

for the use of their IBM weather data cards.

The author feels deeply indebted to Dr. A. W.
Farrall, Head of the Agricultural Engineering Department,
for making possible the research funds necessary for

this study.

The author also wishes to thank his wife Leo

Denese, for her inspiration and typing.

I.
II.
III.

IV.

VI.
VII.
VIII.
IX.

XI.
XII.

TABLE OF CONTENTS

Page
INTRODUCTIONOOOOOOOOOOO0.0.0.0000000000000.00.0.00001

REVIEW OF LITERATURE............................. 3
PROCEDURE........................................ 7
A. Calculating Evapotranspiration............... 7
B. Calculation of Moisture Deficient Days...... 10
DISCUSSION OF RESULTS........................... 32
A. Discussion of Moisture Deficient Days

Occurring Once in Ten Years for Each

Moisthre Reservoir.......................... 32
B. Discussion of Moisture Deficient Days

Occurring Five Times in Ten Years for

Each Moisture Reservoir..................... 35
APPLICATION OF RESULTS.......................... 37’
CONCLUSIONS..................................... 39
SUGGESIONS FOR FUTURE STUDIES................... #0
mmmmmms.n.g.u.u.n.. ...... ..u.n.n.u.71
APPENDIX I...................................... 73
APPENDIX 11..................................... 75
APPENDIX III.................................... 76

APPENDIX IV...OOOOOOOOOOOOOOOOOOOOOOOO0.0.0.0... 77

Table
Table

Table

Table

Table

Table

Table

Table

Table

Table

10

LIST OF TABLES

Page
Actual dafly'evapotranspiration..............ll

Example of computation for deter-

mining number of moisture deficient

days for varying soil moisture
reserVOirSOOCOOOOOOOOO0.0...00......0.0.00.013

Moisture deficient days for South
Haven, Michigan for 1, 2, 3, h, 5
and 7-inch soil moisture reservoirs.........16

Moisture deficient days for East
Lansing, Michigan for l, 2, 3, h, 5
and 7—inch soil moisture reservoirs.........l8

Moisture deficient days for Ann
Arbor, Michigan for 1, 2. 3. h. 5,
and 7-inch soil moisture reservoirs.........2O

Moisture deficient days for Big
Rapids, Michigan for 1, 2, 3, A, 5
and 7-inch soil moisture reservoirs.........22

Moisture deficient days for Cold-
water, Michigan for l, 2, 3, h, 5 .
and 7-1n0h 8°11 m018ture reserv01raaooaoaaOQZA

Moisture deficient days for Saginaw,
Michigan for l, 2, 3. h. 5, and 7-
inch soil moisture reservoirs...............26

Moisture deficient days for Traverse
City, Michigan for l, 2, 3, A, 5
and 7-inch soil moisture reservoirs.........28

Moisture deficient days for Roscommon,
Michigan for l, 2, 3, h, 5 and 7-
inch soil moisture reservoirs...............30

Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

Figure

N

10

11

12

13

14

15

16

17

18

LIST OF FIGURES

Page
Location of weather stations used to
determine evapotranspiration............. 12

Location of weather stations used in
calculation of moisture deficient days... 15

Moisture deficient days-in May for
a 1-inch reservoir....................... 41

Moisture deficient days in May for
a 2-inch reservoir....................... 42
Moisture deficient days in May for

a 3-inch reservoir....................... 43
Moisture deficient days in May for

a L'inCh reserVOir,.,..,.,,...,.......... A“
Moisture deficient days in May for

a 6-inch reserVOir.OOOOOOOOCOCCOOOOOOO... [+5
Moisture deficient days in May for

a 8-inCh reserVO1rOOO.OOOOOOCOOOOOOOO.0.. [+6
Moisture deficient days in June for

a 1-inch reservoirOOOOOOOOOOOOOOOOOOOOOOO 1+7
Moisture deficient days in June for

az-inch reservoiFOOOOOOOOOOOO0.0.0.0.... #8
Moisture deficient days in June for
83-inch reservoir.OOOOOOOOOOOOOOOOOOOOOO A9
Moisture deficient days in June for

ah-inch reservoir.OOOOOOOOOOOOOOOOOOOOOO 50
Moisture deficient days in June for
a6-inch reserVOirOOOOOOOOOOOOO0.00.00... 51
Moisture deficient days in June for
88-inch reserVO1r.OOOOOOOOOOOOOOOOOOOOOO 52
Moisture deficient days in July for
a1-1nchreserVOirOOOOOOOOOOOOOOO0.00.0.0 53
Joisture deficient days in July for

a2-1nCh reserVOirOOOOOOOOOO.0.0.0.000... 5h
Moisture deficient days in July for
83-1n0hreserVO1r.OOOOOOOOOOOOOOCOOOOOOO 55
Moisture deficient days in July for

a a-inch reservoir 56

Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

Figure

19

20

21

22

23

24

25

27

28

29

3O

31

32

Page

Moisture deficient days in July for
a 6-inCh reserVOinmaaaaoooaaaaoaooaaoa 57

Moisture deficient days in July for

" 8-lnCh reserVOiranaeaaaaaaaooaaaaaoa 58

Moisture deficient days in August
for a l‘inCh reserVOir.aoaoaaaaaaooooo 59

Moisture deficient days in August
for a Z'inCh reserVOircacao-0000000000060

Moisture deficient days in August
for a 3-inch reserVOir0000000000000... 61

Moisture deficient days in August
for a h-inch reservoir................ 62

Moisture deficient days in August
for a 6-inch reservoir................ 63
Moisture deficient days in August

for a 8-inCh reservoiraaaaoaaoaaoooooo 64
Moisture deficient days in September

for a 1-inch reservoir.................65
Moisture deficient days in September

for a 2-inch reservoir................ 66
Moisture deficient days in September
foraB-ionch reseWOirOOOOOOOOOOOOOOOO 67
Moisture deficient days in September

for a 4-inch reservoir................ 68
Moisture deficient days in September

for a 6-inch reservoir,,,,,,,,,,,,,,,, 69
Moisture deficient days in September

for a 8-inch reservoir

OOOOOOOOOOOOOOIO 7O

INTRODUCTION

Moisture deficiency in the root zone of the soil
during the crop production season, is a major problem
confronting Michigan farmers. With an erratic rainfall
distribution pattern, the amount of moisture available
for the plant may often be less than the amount required
for maximum plant development and yield. The soil is
like a large reservoir where water is added by rainfall,
irrigation, or capillary action, and removed by evapo-
transpiration, deep percolation, or surface runoff.

With good agricultural practices through-out the growing
season on non-irrigated soil the movement of water by
capillary action, deep percolation, and surface runoff
will be negligible. When the balance between rainfall
and evapotranspiration indicates the reservoir is empty,
plant growth is retarded. Evapotranspiration is computed
by finding the amount of water that can be evaporated
with the energy received from the sun. The energy
received from the sun is assumed to be proportional to
the energy used for the evapotranspiration of moisture
from the soil.

The use of supplemental irrigation has been increas-
ing in recent years where rainfall through the growing
season is inadequate. Farmers having irrigation systems
could use an individual bookkeeping system, where the
rainfall is added and evapotranspiration is subtracted

to obtain their soil reserve for each day of the season.
Other farmers contemplating buying irrigation equip-
ment need information on how many times each year, and
the number of years in ten they can expect to use the
equipment.

The objective of this study was to determine
evapotranspiration rates and to compute the frequency of
moisture deficient days through-out the growing season

from the Michigan climatological data.

REVIEW OF LITERATURE

Cahow (3), studied the precipitation in Michigan
and classified a drought as a "period constituting seven
days or more in which leSs than 0.25 inches of precipi-
tation has occurred in 2b hours." He then calculated
the frequency of one, two, three, four, and five week
droughts for the lower peninsula of Michigan.

Van Bavel, (16), developed a method for using
daily precipitation and daily moisture loss to estimate
the supply of available moisture in the soil. This
method assumes that crops have a moisture reservoir in
the soil to the depth of the effective root zone. The
capacity of this reservoir varies directly with the
root depth of the crop and the water holding capacity
of the soil. If the root depth is two feet and the
water holding capacity is one inch per foot then the
crop has a two inch moisture reservoir. In computing
-his daily moisture loss Van Bavel takes into account
the moisture removed by evaporation from the soil and
transpiration from the leaves. This is commonly refered

to as evapotranspiration.

Empirical Formula Based 22,E§perimental Data
Thornthwaite, (12), assumes that the relationship

between temperature and evapotranspiration is exponential.

A

In other words, when temperature and evapotranspiration-
are plotted on log-log paper they form a straight line.

Thornthwaite's (12) assumption is based on exper—
ience with watersheds in central and eastern United States
and is therefore of limited value. Where temperature
and radiation are strongly correlated this method works
well. In southern latitudes or locations where the
land is effected by large bodies of water as in Michigan,
the air temperature lags behind radiation by three to
four weeks giving evapotranspiration values which are
questionable.

Blaney and Griddle (2) developed an empirical for-
mula in which uzt’x xf. '

.UJz monthly evapotranspiration in inches.

t: average monthly temperature in °F.

f a empirical consum tive use factor.

p=. percent of annua daytime hours occuring

that month.

Values of f are obtained by growing various crepe
in large vats or lysimeters that can be weighted with-
out destroying the crop. The daily change in weight is
then given the value of f which is similar for most
crops. The value of f often varies from one location
to another.

The Blaney Criddle formula is based on temperature
and length of day which implies the use of radiation
energy. Good results are obtained where radiation is
closely related to temperature. Estimates of seasonal

requirements are generally better than the shorter

monthly periods.

Theoretical Vapgr Trggsfer Method
Thornthwaite and Holzman (13), developed a vapor

transfer formula in which E = K0 “‘1 ' "ZHW " 31
(Log 152/21)z

E = rate of evaporation.

K =universal constant.

slzheightl.

xl evapor density at height 1.

ulawind speed at height 1.

Formulas of this nature have not been thoroughly

tested and the neccessary data is not available.

Theoretical £22551 Balancg Methgg

This method is based on the fact that the energy
received by the earths surface through radiation must be
equal to the energy used for evaporation plus that used
t0~ heat both the soil and the air. The energy used for
heating the soil and air can be neglected for daily
balances, and if an error of 5 percent is acceptable they
can be neglected on the monthly balances.

Penman (10) first published a method of estimating
the amount of radiative energy gained by the surface
and expressed this in mm of evaporated water. The
method was slightly modified by Van Bavel (18) giving

the following equation for evapotranspiration.
AH+.27 EL

 

ET A+.27
ET = evapotranspiration in mm/day.
23 a slope of t e saturated vapor pressure curve.
at air temperature. (See appendix II, A.)
H = net radiation.
E‘s .35 (e - e )(l+ .0098 u20 min/day.
ea:= saturagion apor pressure at mean air temperature

in mm Hg. (See appendix II, B.)

ed = saturation vapor pressure at mean dew int.
or actual vapor pressure of air in mm g.

also equal to e. 1 (percent relative humidity).

wind speed at 2 meters in miles per day which

is equal to “h x (W)
0%
uhpa wind speed in miles per day at height h in feet.

u2

Van Bavel (18), states that the experimental
evidence so far lends the most support to the Penman

formula for determining evapotranspiration values.

PROCEDURE

Temperature in Michigan lags behind radiation by
approximately four weeks. Any method of calculating
evapotranspiration without using radiation as one of
the variables would give questionable results. Experi-
mental evidence so far show more favorable results with
the Penman formula as a universal method (18). Therefore
the Penman(lO) method was used for calculating evapo-
transpiration. This method indicated the potential
evapotranspiration that can take place on vegetation.
It was then modified by a factor of .75 to obtain
actual evapotranspiration. Tests in the Netherlands

indicate that .75 was the best correction factor for

obtaining actual evapotranspiration from potential

evapotranspiration.

Calculating Evapgtranspiration

Penman's formula is Et :3 A H + .27 E.

Et = potential evapotranspiration in mm/day.

A: a slope of saturated vapor pressure curve.
(see appendix II, A.)

Ht 2 net radiation.

Ea :- auxiliary quantity.

8 := factor denoting influence of diffusion
resistance.

D == factor denoting influence of length

of day.

Net radiatidn values were calculated from:

Ht: Ra (l-r)(0.18 +0.55 n/N) - KT,“

(0.56 - 0.092I‘_ed )(0.10 + 0.90 n/N)
Ra.a mean monthly extraterrestrial radiation.
r =: 0.20 radiation reflection coefficient

for vegetation. .
n/N= ratio actual to possible hours of sgnshine.
¢"= Stefan Boltzman constant 2.01 x 10' mm/day.
Ta = absolute temperature of air 0R.
ed =-saturation vapor pressure at mean dew point.

Values of Ea were calculated from:

Ea== 0.35 (e - e )(l-+ 0.0098 u ) mm/day.

°a1= saturation v por pressure a% mean air
temperature.

u2:= windspeed at two meters.

Values of S were calculated from:

S = La/(La+ 0.16)
La== effective diffusion lenght of air which
is equal to .65 (1 0.0098 uz)

Values of D were calculated from:

11/24 +- 1/r sin N1T/21.
hours from sunrise to sunset.

I'-

The wind speed was given in miles per hour at a

D
N

“ll

height 60 feet in East Lansing, 6h feet in Detroit,
81 feet in Grand Rapids, and 89 feet in Alpena. The
formula Penman (10) uses to convert this to a two meter

'elevation is:

- log 6.6
u2.. uh x ( log h )

’uhfl= wind speed at height h in miles per day.
No further corrections were made to this value because
it was felt that even though'the tower was located in
town on top of a building, the figure obtained for 2

meters would still represent the rural wind speed.

The average air temperatures in cities has been
about 1 to 2% degrees °F higher in the summer time
because of higher night time temperatures brought about
by the slow cooling rate for buildings and roads (5).

East Lansing Temperature

 

 

 

June July Sept.
City Temperature 68.9 72.8 68.8
Rural Temperature 67.0 70.4 67.1
Difference 1.9 °F 2.h °F 1.7 OF

A correction was made on average air temperature by
subtracting 2 oF so that the values would represent aver—
age rural air temperatures.

Average values for relative humidity were about 5
percent lower in cities because the soil is covered

with roads and buildings causing less evapotranspiration (5).

East Lansing Relative Humidity

 

Jmm JMJ Set.
Rural RH‘ 6h 54 6E
City RH 5h 49 50
Difference 10% 5% 11%

To prevent overcorrecting the relative humdity, 5
percent was added to the average city value to give a
representative rural value.

Appendix 1 shows an example of the calculation pro-
cedure for finding evapotranspiration rates. Monthly
calculatings were made for Grand Rapids, Detroit, East

- Lansing, and Alpena with the data listed in Appendix IV.

10

Results of these calculations when modified by multi-
plying by .75 are shown in table 1. Because of the small
difference between the values table 1)for the various
locations through out the state, (figure 1) the value

for Lower Michigan (table I) assumed to represent daily

evapotranspiration for the Lower Peninsula of Michigan.

Calculation of Moisture Deficient Days

In calculating moisture deficient days only the
crop production months, May through September, were
used. The moisture reservoir of the soil was assumed
to be full on the let. of May each year. The reservoir
amounts used were 1, 2, 3, h. 5, and 7-inches, from
which the Lower Michigan daily evapotranspiration values
were subtracted and daily rainfall added, never allowing
the total to go over the individual reservoir amounts
or to go below zero. (See table 2.) By not allowing
the total to go above the reservoir amount, water could
be removed by runoff or deep_percolation. This happened
when heavy rainfall was received in May or June. Later
in the season under good agricultural practices very
little runoff occurs and the soil reservoir will normally
hold all the rainfall.

A moisture deficient day occured each time the
calculated soil moisture was zero as shown in table 2.
The number of moisture deficient days occuring each
month were counted and recorded for the six moisture
reservoirs. This was accomplished by using the IBM
equipment in the tabulating department of Michigan
State University.

11

TABLE 1 -ACTUAL AVERAGE DAILY EVAPOTRANSPIRATION

 

 

Grand Rapids .09 .12 .13 .10 .07
East Lansing .08 .12 .12 .10 .07 ‘
Detroit _ .09 .12 .13 .10 .07
Alpena .08 .11 .12 .10 .06

 

 

Lower Michigan .09 .12 .13 .10 .07

 

 

12

Alpena I e

G and Rapids‘
0' Eas:.Lansing

Detroiv

Figure 1. Location of weather stations used
to determine evapotranspiration.

13

TABLE 2 EXAMPLE OF COMPUTATION FOR DETERMINING
,NUMBER OF MOISTURE DEFICIENT DAYS FOR

VARYING SOIL MOISTURE RESERVOIRS

._- -9. .-_ — - - .___ _

Evapotrans- Precipi-

-.m...- _

 

  

.___.

Moisture Reservoir

  

 

 

 

 

piration tation 1 inch 3 inch 5 inch
Date inches inches inches inches_ inches
Amount from previous months ‘0.33'“fi 0.55 2.75
l. 0.25 0.08 0.30 {2.50
2' 0.25 0.00 0.05 2.25
3 0.25 .0.00 0.00 2.00
.h 0.25 0.75 0.50 0.50 2.50
5 0.25 1.25 1.00 1.50 3.50
6 0.25 .75 1.25 ' 3.25
Total number of
moisture deficient days ,2 l 0

 

 

1h

Weather information for the stations shown in
figure 2 were used for the calculation of moisture
deficient days. This eliminated punching daily rain-
fall on cards. The values calculated for Iowa-Michigan
evapotranspiration given in table 1 were punched in
columns 75 and 76 for all stations except East Lansing,
where columns 73 and 7A were used.

The No. 60A calculating punch did the computing
and a trailer card inserted at the end of each month
was punched with the actual number of moisture deficient
days for the given month. After running the cards
through three times for six moisture reservoirs, the
No. 120 sorter removed the trailer cards. The account-
ing machine printed the information from the trailer
cards and it was compiled in tables 3 through 10. For
easier reading of the tables 3 through 10, all sero's
were omitted. The bottom two lines of tables 3 through
10 give the actual number of moisture deficient days
occuring once in ten years and five times in ten years.
In this paper the probability of .l is refered to as 1
year in 10 and the probability of .5 is refered to as
5 years in 10. This is based on the actual number
occuring over a thirty year period and may change slightly
with a longer period of time.

15

. .
Traverse‘City

O
Roscommon

0
Big Rapids .
Saginaw

 

0
East Lansing

,South Haven
' 0
Ann Arbor

Coldnater
I

Figure 2. (Location of weather stations used
' in calculation of moisture deficient

days.

16

 

 

 

 

 

 

 

 

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m m NN
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21

 

 

 

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25

 

 

 

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m MH 4N 4N N HH M4
m NH M 44
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M NH NN NN NN M MH 4H M MH MM
M MH HN NN M HH m 4M
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29

 

 

 

 

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m OH OH NH NH MH MN MN MN MN OH 3.: H
N MM
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M M M M M OH NH NH NH HM
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M M M MH MH HH N4
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N HH NH H OH M4
N HH M M4
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M H M4
M MH 4 N4
H OH 4H 4H 4H 4 4H ON 4 H4
4 MH 4 _ O4
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N OH OH HH N HH MH NM
M M M M MH MM
MH HN HN HN NN M 4H MN MN | 4 MM
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M NH 4H MH M NH N . MM
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32

DISCUSSION OF RESULTS

A series of maps were made to illustrate the
number of moisture deficient days listed on the bottom
of tables 3 through 10. The number of moisture deficient
days occuring once in ten years were shown on map A
and five times in ten years on map B, of each figure.
One figure was used for each 1, 2, 3, h, 5, and 7-inch
moisture reservoir, or six figures per month for the
months May through September. This gave a total of
30 figures with sixty maps, illustrated in figures 3
through 32.

Discussion of Moisture Deficient Days Occuring
once in Ten Years For Each Moisture Reservoir
l-inch heservoir (Naps A, figures 3, 9, 15, 21. 27)

The number of moisture deficient days for May
ranged from 7 in the south west to 13 in the eastern
part of the state. In June there were lows of 17 in
the south west and 19 in the north central, and a
high of 21 in the eastern part of the state. July
'ranged from 24 in the north to 26 in the Lansing,

Ann Arbor area. August had a low of 23 across the
.central part going to a high of 25 in the north and
29 in the south central part of the state. In Sep-

tember the pattern of moisture deficient days showed

- 33

some decrease of intensity with lows of 12 in the north,
13 in the south and 1h across the center along with

highs of 18 near Ann Arbor and 20 near Roscommon.

2-inch Reservoir (Maps A, figures h, 10, 16, 22, 2 )
The number of moisture deficient days for May was

zero north west of the Goldwater, Lansing, Saginaw area

and 2 in the Ann Arbor area. In June the minimum was

8 at the south edge and the maximum was 19 in the north

eastern part of the state. July went from 20 mois-

ture deficient days in the north central and south

central to 26 in the eastern part of the state. August

had a low of 23 across the central part and highs of

25 in the north and 29 in the south central part of

the state. September had lows of 12 in the north, 13

in the south west and 1h in the”thumfi‘along with highs

of 16 near Ann Arbor and 20 near Roscommon.

3-inch Reservoir (Maps A, figures 5, 11, 17, 23, 29)
There were zero moisture deficient days for May.
In June the minimum was still zero in the south west
and the maximum was 11 in the north east part of the
state. July had lows of 16 near Lansing and 19 near'
Roscommon along with a high of 22 across the central
and into the northern, western and eastern part of the
state. August had a low of 22 in the west central with
a high of 25 in the north and 29 in the Lansing area.
September had lows of 10 in the north and 13 in the

Saginaw, Lansing, Goldwater area increafing to highs

34

of 6 near Roscommon and Detroit.
5-inch Reservoir (Maps A, figures 6, 12, 18, 2h, 30)

. There are zero moisture deficient days for May. In
June the minimum was still zero except for 1 moisture
deficient day near Saginaw. July had a low of 8 near
Lansing increasing to a high of 17 in the north and
northeastern part of the state. August had a low of 20
on the west central edge with a high of 25 in the north-
ern and 30 in the south central part of the state. Sep-
tember had 10 moisture deficient days in the north, 13
near Goldwater, and Lansing with a high of 16 in the
Detroit area.
5-inch Reservoir (Maps A, figures 7, 13, 19, 25, 31)

There were zero moisture defiCient days in May and
June. July had 2 moisture deficient days in the south
central part and 13 in the north east part of the state.
August had a low of 1a near Goldwater and 15 near Ros-
common, increasing to a high of 26 in the Lansing, Ann
Arbor area. September had lows of 8 in the north and 9

near Lansing, along with a high of It in the'thumv'area.

Z-inch Reservoir (Maps A, figure 8, 1t, 20, 26, 32)

There were zero moisture deficient days in May, June
and July. In August there were lows of zero near Cold-
water and the west central area with a high of 22 in the
Ann Arbor area. September had lows of zero in the west
and 2 in the south east along with a high of 7 in the

Lansing area.

35

Discussion of Moisture Deficient Days Occurring
Five Times in Ten Years For Each Moisture Reservoir
1-inch Reservoir (Maps B, figures 3, 8, 15, 21, 27)

The number of moisture deficient days for May
ranged from zero in the south central to A in the
northwest part of the state. Thefintensity of drought
was greater in June with 7 days in the Coldwater area
and 13 inthe northern part of the state. In July there
were lows of 12 at Coldwater and 13 at Roscommon with
a high of 19 in the "thumb" area. August had lows of
12 in the southwest and 13 in the Roscommon area, and
a high of 15 in the Traverse City, Grand Rapids area.
September had a low of 1 in the northern part and a high
of 8 moisture deficient days in the south western part

of the state.

2-inch Reservoir (Maps B, figures 4, 10, 16, 22, 28)
There were zero moisture deficient days for May.

In June the low was zero in the southern part with a

high of 7 in the northern part of the state. July had

a low of 7 near Coldwater and 9 near Roscommon increas-

ing to a high of 15 in the "thumb" area. August had

lows of 12 across the central part and 13 in the northern

part of the state. September had zero moisture deficient

days in Roscommon, Saginaw, Coldwater area increasing

to highs of 3 near Ann Arbor and A near Big Rapids.

36

g-inch Reservoir (Maps B, figures 5, ll, 17, 23, 29)
There were zero moisture deficient days in May and
June. July had a low of zero in the south and another
low of 2 near Roscommon, along with a high of 8 in the
north and northeast. August had a low of zero near
Roscommon and 3 near Coldwater increasing to a high of
12 in the northern and north eastern part of the state.
September had zero moisture deficient days west of the

Saginaw, Coldwater area and 3 days in the Detroit area.

4-inch Reservoir (Maps B, figures 6, 12, 18, 2h, 30)
There were zero moisture deficient days in May and
June. July had zero moisture deficient days over most
of the state except for 2 in the northern part. August
had a low of zero in the southern and north central
part with a high of 5 in the northern and north eastern

part of the state. September had zero moisture deficient

days.

5-inch Reservoir (Maps B, figures 7, 13, 19, 25, 31)
There were zero moisture deficient days in the

months of May, June, July, August and September.

z-inch Reservoir (Maps B, figures 8, 1h, 20, 26, 32)
There were zero moisture deficient days for the

months May, June, July, August and September.

37

APPLICATION OF RESULTS

When irrigation is frequent, the amount of add-
itional water needed each month for a 1, 2, 3, A, 5,
or 7-inch moisture reservoir can be computed for any
location in Lower Michigan by multiplying the number
of moisture deficient days given in figures 3 through
32, by the amount of evapotranspiration per day given
in table 2 for Lower Michigan.

Farmers can compute daily, the average moisture
reserve of their soil reservoir by adding rainfall and
subtracting evapotranspiration. Values of rainfall
can be obtained from the daily weather report or pre-
ferably a rain gage on the farm. The calculated
evapotranspiration rates are given in figure 2. Knowing
the amount of moisture in reserve would be especially
helpful in schedulirig the time of irrigation for
various crops and soils.

Farmers contemplating buying irrigation equipment
can refer to the discussion of moisture deficient days
for the particular soil moisture reservoir in which
they are interested. Then for an illustrated distribution
of moisture deficient days per month, the figures 3

through 32 can be consulted. Each figure has the number

38

of moisture deficient days that can be expected once
in ten years and five times in ten years. The figures
can then be used as an indication of the probable
number of days in which supplemental irrigation water
would be needed on a particular farm throughout Lower

Michigan.

39
CONCLUSIONS

Using the Penman method of calculating potential
evapotran5piration on vegetation and modifying it by
.75 to obtain actual evapotranSpiration, the following
observations are found in the Lower Peninsula of
Michigan.

1. More moisture deficient days occur in the

eastern part of the lower peninsula than in the western

part .

2. More moisture deficient days generally occur
in the northern part of the lower peninsula than in

the southern part.,

3. The smaller soil moisture reservoir has a

greater number of moisture deficient days.

A. In the month of May, water is needed 5 years

out of 10 for a l-inch soil moisture reservoir.

_ 5. In the month of June water is needed 5 years

out of 10 for a l and 2-inch soil moisture reservoir.

6. The months of July and August have the great-

est number of moisture deficient days.

7. The 5 and 7-inch moisture reservoirs do not

need additional water 5 years out of 10.

LO

SUGGESTIONS FOR FUTURE STUDIES

1. A study could be made with weighing Lysimeters
to determine the correction factor which should be
applied to potential evapotranspiration to determine
actual evapotranspiration in Michigan. Possibly .75

will change slightly in Michigan.

2. A study on the frequency of use, of irrigation
equipment, in various part of the state through-out

the growing season on given soil moisture reservoirs.

3. A current soil moisture study could be made by
subtracting present evapotranspiration values and
adding in the rainfall for various soil moisture
reservoirs. Eventually this might be included in a
daily farm weather report that would be helpful in
scheduling irrigation.

L. 0

Figure 3.

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B. Probability of 5 years in 10

 

Figure A. Moisture deficient days in.Mey for
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#3

A. Probability of 1 year in 10

B. Probability of 5 years in 10

 

Figure 5. Moisture deficient days in ugy' for
a 3 - inch reservoir.

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.‘Vt‘hlrt. .6); In, ‘24.?!“ “3%-. I m§9¢§ fins} 10.. an \Pmfltku .. .

 

mm»

 

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._.L

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v
51

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.—

‘3‘

.3
«A
II

n
.‘ n
v'

“cisture
a. l.» in

:‘e 6.

higu

V

#5

A. Probability of 1 year in-lO

B. Probability of.5 years in 10

 

Figure 7. Moisture deficient days in May for
a 5- inch reservoir.

L6

A. Probability of 1 year in 10'

B. Probability of 5 years in 10

 

Figure 8. Moisture deficient days in May for
a 7 - inch reservoir.

I+7.

A. Probability of 1 year in 10

B. Probability of 5 years in 10

 

Figure 9. Moisture deficient days in June for
a J.- inch reservoir.

#8

A. Probability of 1 year in 10

 

B. Probability of 5 years in 10

Figurelo, .Moisture deficient days in June for
. a 2 - inch reservoir.

Figure 11

B.

#9

 

Probability of 5 years in 10

Moisture deficient days in June
a 3 - inch reservoir.

for

‘1

 

 

 

50

A. Probability of 1 year in 10

 

B. Probability of 5 years in 10

Figure 12 Moisture deficient days in June for
a 4 - inch reservoir.

51

A. Probability of 1 year in 10

B. Probability of 5 years in 10

 

Figure 13 Moisture deficient days in June for
a 5 - inch reservoir.

"i-

. film Flt Wfifiaarnttum A."

.n- - .Hu‘- 4-;

. .71... u. .b.<ns...n.x.;nu

 

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.. 41).. 0.....1. Skewers ,\

3......

 

3?

J

. .
sciarr' veer

.- I

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r: .10.‘

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\fl
a'l

'16

Ex

53

A. Probability of 1 year in 10

 

B. Probability of 5 years in 10

 

Figure 15' Moisture deficient days in July'.for
a l - inch reservoir.

54

 

 

A. Probability of 1 year in 10

 

3. Probability of 5 years in 10

 

Figure 16 Moisture deficient days in July for
‘ a 2 - inch reservoir.

55

.A. Probability of 1 year in 10

 

B. Probability of 5 years in 10

 

Figure 1? Moisture deficient days in July for
a 3 - inch reservoir.

56

B. Probability of 5 years in 10

 

Figure 18 Moisture deficient days in July for
a l.- inch reservoir.

 

‘ l
1.,
' 9
C \
Q

A. Probability of 1 year in IO.

 

 

 

 

 

 

 

 

B. Probability of 5 years in 10.

 

fig.1fa Moisture deficient days in July
for a 5 - inch reservoir.

 

 

58

A. Probability of 1 year in 10

B. Probability of 5 years in 10

 

Figure 20 Moisture deficient days in July for
‘ a ‘7- inch reservoir.

 

59

A. Probability of 1 year in 10

 

B. Probability of 5 years in 10

 

Figure 21 Moisture deficient days in Aug. for
a 1-inch reservoir.

60

A. Probability of 1 year in 10

B. Probability of 5 years in 10

 

Figure 22 Moisture deficient days in Aug. for
a 2- inch reservoir.

61

 

A. Probability of 1 year in 10

B. Probability of 5 years in 10

 

Figure 23 Moisture deficient days in Aug. for
a 3 - inch reservoir.

 

 

 

62

A. Probability of 1 year in 10

 

 

B. Probability of 5 years in 10

 

Figure 2!. Moisture deficient days in Aug. for
a h— inch reservoir.

63

 

' A. Probability of 1 year in 10

B. Probability of 5 years in 10-

 

Figure 25 Moisture deficient days in Aug. for
' a .5-inch reservoir.

 

6h

 

A. Probability of 1 year in 10

 

B. Probability of 5 years in 10

Figure 26 Moisture deficient days in AHS- for
a.7 - inch reservoir.

65

A. Probability of 1 year in 10

B. Probability of 5 years in 10

 

Figure 27 Moisture deficient days in Sept. for
a l — inch reservoir.

66

A. Probability of 1 year in 10

B. Probability of 5 years in 10

 

Figure 28 Moisture deficient days in Sept. for
a 2 - inch reservoir.

67

 

u. Probability of 1 year in 100

B. Probability of 5 years in 10

 

yze 29 Moisture deficient days in Sept. for
a 3~ inch reservoir.

68

A. Probability of 1 year in 10

'8. Probability of 5 years in 10

 

Figure 30 Moisture deficient days in Sept. for
a A- inch reservoir.

69

 

A. Probability of l

 

‘v‘. I :‘ J ‘ g
o. rronasiiity of

~il

311‘s?» 7. .Wm macaw wmcmemmfiaam “WW5“ "

‘ ‘3’ m 14mm.mvwxmn.ww I'- "i "‘

W??- -

w -— o—v'rwv

 

Figure3l. Zeeisture deficient days he Sept.ihw‘

a 5.. izifh r‘eservci‘x‘.

7O

 

A. Probability of 1 year inglC

. 8. Probability of 5 years in 10

 

Figure 32 Moisture deficient days in Sept. for
a 7- inch reservoir.

71

REFERENCES

10 ulmd, E 9 Re , ‘nd Re Chen. (1953 ) e EV.1U‘ting
irrigation needs in humid areas. Agricultural Engineering.
Vol. 3‘}. pp. 611-615 a

2. Blaney, H. F., and W. D. Griddle. (1950). Deter-
mining water requirements in irrigated areas from clima-
tolog cal and irrigation data. Soil Cons. Service. Tech.
8‘11. 960 67 pp.

3. Cahow, T. w. (1952). A study of drought frequencies
for the lower peninsula of Michi an. Thesis for M. S.,
Mich. State Co ., East Lansing, Unpublished). A8 pp.

A. Griddle, W. D. (1958). Methods of computing con-
sumptive use of water. Proceeding of the American Society
3f 0. E. Jorr. of the Irrigation Drainage Division. Vol.

6. No. IR .

5. Geiger, a. (1950). The Climate Near the Ground.
Harvard University Press, CambrIage, Mass. ‘ISO pp.

6. Kelley, 0. J. (19k5). Requirement and availability
of soil water. Advances in Agronomy. Vol. 6. pp. 67-94.

7. Knetsch, J. K., and J. Smallshaw. (1958). The
occurrence of drought in the Tennessee Valley. Tenn. Valley
Auth. Report No. T 58-2 AB.

8. Krimgold, D. B. (l95h). Economic feasibility of
gupplimentgl irrigation. Agricultural Engineering. Vol.
50 pp. 2 “'27.

9. Land, w. 3., and J. a. Carreker. (1953). Results of
evapotranspiration and root distribution studies. Agri-
culture Engineering. Vol. 3h. pp. 319-322.

10. Penman, H. L. (19h8). Natural evaporation from open
water, bare soil and grass. Proceedings of Royal Society.
Series A. Vol. 193. pp. 120-1h5.

11. Richards, L. A., and c. H. Wadleigh. (1952). Soil,
water‘ggg Plant Growth. New York Academic Press Inc. 280 pp.

12. Thornethwaite, C. W. (l9h8). An ap roach toward a
rational classification of climate. The a. Rev. Vol. 38.
PP a 5 5‘9“ 0

72

13. Thornthwaite, C. W. and B. Holzman. (1939) The
determination of evaporation from land and water surfaces.
Monthly weather Review, Vol. 67. pp. 36-47.

1h. United States Department of Agriculture, Michigan
Hydrologic Research Station, Normal monthly solar radiation
for East Lansing, Michigan. (19A6-56)

15. United States Department of Commerce, Climatological
Data. 1927-56.

16. Van Bavel, C. H. M. (1953). A drought criterion and
its application on evaluation drought incidence and
hazard. Agronomy Journal. Vol. 45. pp. 167-172.

17. Van Bavel, c. H. M. and M. J. Gilbert. (1954). A
sample field installation for measuring maximum eva trans-
piration. Transactions of the Geophysical Union. 01.

35. PP- 937-9h3.

18. Van Bavel, C. H. M. (1956). Estimati Soil Moisture
Conditions and Time for Irri ation with the Eva otrans-
BIraEIons Method. USDA, - . U. S. Cavernment

r nt ng OffIce. 16 pp.

19. Van Bavel, C. H. M., and F. J. Verlinclan. (1956).
Agriculture drought in North Carolina. N. C. Agr. Expt.
Sta. Tech. Bul. 122. 23 pp.

20. Van Bavel, C. H. M. (1957). Agricultural drought in
Virginia. Va. Agr. Expt. Station. Tech. Bul. 128. 38 pp.

21. Van Bavel, C. H. M., L. A. Forest, and T. C. Peel.
(1957). Agricultural drought in South Carolina. 8. C.
Agr. Expt. Sta. Bul. .hh7. 27 pp.

22. Van Bavel, C. H. M., and J. R. Carreker. (1957).
Agricultural drought in Georgia. Ga. Agr. Expt.
Sta. Tech. Bul. N. S. 15. 41 pp.

23. Van Wijk, W. R., and D. A. de Vries, (1954). Evapo-
transpiration, Netherlands Journal of Agricultural Science.
v01. 20 NO. 20 pp. 105-1190

73

APPENDIX I

:1

AVPOT RANSPIRATION FOR JULY, EAST LANSING

Temp4=7l.l °F - 2°0 correction = 69.1 0F
{Ta =15.0l. (69.1017 Appendix III)
ea =18 .2 (Appendix B, II. )

e .=percent RH (ea): 71 (18.2) = 12.9
IIPi :73 percent
N :15. 1 hr. sunrise to sunset
1‘ =.2 for vegetation
Ra =15. 9 mm/day
==.6A (69.110F 6Agpendix A, II.)
Wind-=12 mph (fig—13.30 mph e 6.6'
log6
Wind =7.2 mph L 60'
L12 -=24 (3.3) = 79 miles per day 6 6.6'
Ht =Ra (l-r)(.18 + .55 n/N)- f'ra‘v
( 856-. 092 ed)( l‘+ .9 n/N
=—l( 1.5 9)(1-.2)(. 18+ .55 x .73)- (15. oz.)
(.6- .0922: 12. 9)(. 1+ .9): .73)
=15 5.9 (. 8H. 18 +.1.02)-15.0A(.56 - 33)
(.1 + .657)
‘7. 38- 262
-=6.76
L8 ='- .65 (1 4'. 0098 L12)
a .65 (l-+. 0098 x 79)
3 1.15
3 = La/La + .16
=1.15/1.15 + .16
-- .879
D = N/2 21.4- 1/11” sin THY/21.
= 15.1/21. + 1/3.1z. sin 15.1(3. ltd/21.
= .63 4 .318 sin 1.96
= .63 + .318 sin 112'
= .63'+ .318 (.92)
=.63 + .292
=.922
E =.35 (1+ .2009811 He? 1--e)
a =-.35 (l + .0098 x W79) d- 12. 9)
= .35 (1 + .(77A) 53
3 35 9AA)
=3.29 nun/day

Et is

76

APPENDIX I CONTINUED:

2 AA. + .ZLEL
Et 4 + .27/SD

E :- .61.(g.76) ’4» 279.29)
t .61. + .27/,879(.922)

 

F g L05 + .85_
”t .61. + .27/.8
E _ 3.91. ._ 3.91.

 

t‘ .6z.+ .338 ’ .978

Et

h.02 mm/day
Et = .158, inches/day
Actual Et:: .158 x .75 .119 inches/day

The data does not warrent .000 accuracy so
rounded off to .00

 

mwca>mMmzwa

0
vs;

0
'31

mwcabmtswzme

75

APPENDIX II

 

 

 

 

 

 

 

 

 

 

 

 

 

 

104 ,

86

68

so //

32 02 oh .6 .8 100 . 102 A 10‘} 1.6

438 , mm Hg/oF
A. Temperature vs. slope of saturated
vapor pressure curve.
(From reference A.)

122

 

.r””l”””fl

 

 

id. . //
.86 , ,/
/

 

68 .x

/

10 20', ‘ 30 #0 50 x 60 70 80
0a) ang

 

 

 

 

 

 

 

 

 

50

 

. B. Temperature vs. saturation vapor pressure.

(From reference A.)

76

APPENDIX III

 

 

100 18.80

 

 

 

Heat of vaporization was assumed to
be constant at 590 cal/gm of H20

(reference A)

77

APPENDIX IV
CLIMATOLOGICAL DATA USED TO SOMPUTE EVAPOTRANSPIRATION

 

 

 

 

 

 

 

 

 

 

 

 

Month m, n/N N r. RH uh Et
mm/ day 73 hr. 0F 76 in/chy
GRAND RAPIDS
flay 15.7 60 14.9 58.2 64 .12
June 16.9 65 15.4 68.5 66 .16
July 15.9 72 15.1 73.6 67 .17
August 14.1 69 14.1 71.6 66 .14
September 11.9 58 12.2 64.1 70 .09
EAST LANSING
May 15.7 62 14.9 ' 56.5 65 .11
June 16.9 67 15.4 67.4 68 .16
July 15.9 73 15.1 71.1 66 .16
August 14.1 69 14.1 69.0 68 .14
September 11.9 58 12.2 61.8 72 .09
DETROIT
May 15.7 58 14.9 57.8 63 .12
June 16.9 65 15.4 68.1 64 .16
July 15.9 69 15.1' 73.1 62 .18
August 14.1 66 14.1 71.3 65 .14
September 11.9 61 12.2- 64.3 68 .10
ALPENA
May 15.7 58 14.9 50.9 68 .11
June 16.9 64 15.4 61.5 70 .15
July 15.9 70 15.1 67.4 68 .16
August 14.0 63 14.1 65.8 7 .14
September 11.6 51 12.2 58.4 75 .08

 

 

 

 

 

 

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