Agricultural Water Management, 18 (1990) 159-171 159 Elsevier Science Publ ishers B.V., Ams te rdam - - Pr in ted in The Nether lands

Crop coefficients of some major crops of the Nigerian semi-arid tropics

Salisu Abdulmumin* and Steven M. Misari Department of Soil Science, Institute for Agricultural Research, Ahmadu Bello University, P.M.B.

1044, Zaria (Nigeria)

(Accepted 3 October 1989 )

ABSTRACT

Abdulmumin, S. and Misari, S.M., 1990. Crop coefficients of some major crops of the Nigerian semi- arid tropics. Agric. Water Manage., 18:159-171.

Crop coefficient (Kc) curves for grain sorghum, cotton, maize, groundnut and millet were devel- oped for the Nigerian semi-arid tropics (8 o to 13 ° N; 5 ° to 15 ° E) based on grass reference ETo deter- mined with the FAO-24 (Penman) procedure and lysimeter measured crop water use data at Samaru, Nigeria ( 11 o 11 'N; 7 ¢ 38'E ). The recommended equation for estimating solar radiation from relative sunshine hours was determined to be Rs = [ 0.28 + 0.46 (n IN)Ra ] using measured solar radiation data. A value of 1.6 was obtained for the ratio of day to night time wind speeds for the growing season ( May to October) using an automatic weather station. A procedure was also developed to estimate daily minimum and maximum relative humidity from daily minimum and maximum temperatures and the usual relative humidity records. The Kc curves developed can be recommended for use in farm water management decisions throughout the semi-arid tropics of West Africa south of the Sahara.

I N T R O D U C T I O N

Dryland, rainfed agriculture accounts for most of the food and fibre pro- duction in the semi-arid tropics of Nigeria (8 ° to 13°N; 5 ° to 15°E). This area supports well over 50 million people. The rainy season is between April and October. Mean annual rainfall ranges between 1200 mm in the south and 500 mm in the north. The major crops include sorghum, millet, maize, groundnut and cotton. Recent droughts and a persistent drying trend over the last two decades point to the need for improved farm water management if crop yields are to be sustained. This may involve supplementary irrigation or breeding drought tolerant varieties. In any case the water requirements of ex- isting crop varieties need to be known.

There have been very few studies on the water use and water requirements of crops in the area. In such studies in the early to mid-1970's (Kowal and

*Present address: ICRISAT, Pa tancheru P.O., A n d h r a Pradesh 502-324, India.

03 78 -3774 /90 /$03 .50 © 1990 Elsevier Science Publ ishers B.V.

160 s. ABDULMUM1N AND S.M. MISARI

Andrews, 1973; Kowal and Kassam, 1973; Kowal and Faulkner, 1975; Kas- sam et al., 1975; Kassam and Kowal, 1976) the water use of several crops was measured using a hydraulic weighing lysimeter at Samaru ( 11 ° 11 'N, 7 ° 38'E). Crop coefficients, referred to as "relative evapotranspiration", were esti- mated as ratios of actual crop water use, measured with the lysimeter, to "po- tential" evaporation estimated with the original Penman (1948) equation. This equation computes evaporation from open water surface, which is not representative of an agricultural surface, especially in the degree of surface roughness (Thorn and Oliver, 1977) and wetness (Monteith, 1985). Thorn and Oliver (1977) pointed to the fact that the Penman (1948) equation un- deremphasises the aerodynamic term in favour of the radiation term. Various modifications have been made to the original Penman equation (Allen, 1986 ). One of these modifications is the concept of reference crop evapotranspira- tion as a standard in place of potential evapotranspiration. The standard ref- erence crops now in use are grass (Doorenbos and Pruitt, 1977 ) and alfalfa (Jensen et al., 1971; Wright, 1982). A quantitative approach to computing the Doorenbos and Pruitt (1977) version of the Penman equation (subse- quently referred to in this paper as FAO-24 (Penman) method was given by Weiss (1983).

The objectives of this work were to determine local input parameters for the FAO-24 (Penman), and use the method, with actual evapotranspiration measured at Samaru, to compute the crop coefficients of grain sorghum, cot- ton, maize, groundnut, and millet for the Nigerian semi-arid tropics.

M A T E R I A L S A N D M E T H O D S

Crop water use over a period of time can be estimated by

ETa ---~ Kc X ETo ( 1 )

where ETa is the actual evapotranspiration, ETo is the grass reference crop eva- potranspiration, and Kc is the crop coefficient.

To establish the values of Kc at various stages of crop growth, ETa and ETo have to be determined.

Measurements O f E T a

The water use of grain sorghum (Kowal and Andrews, 1973), cotton (Ko- wal and Faulkner, 1975), maize (Kowal and Kassam, 1973), groundnut (Kassam et al., 1975) and millet (Kassam and Kowal, 1976) was measured with a hydraulic weighing lysimeter at Samaru in 1970, 1971, 1972, 1973, and 1974, respectively. Details of the design and operation of the lysimeter are given by Kowal and Stockinger (1973). Totals of ET a for 10 day intervals

CROP COEFFICIENTS IN THE NIGERIAN SEMI-ARID TROPICS 16 !

(decades) of the growth period of each crop obtained from results of these studies were used to compute K~ for the respective crop.

As the lysimeter was not irrigated, a water balance analysis was conducted to determine if there was adequate moisture supply to the crops as required by the definition of ETa (Doorenbos and Pruitt, 1977 ). The analysis was made for each year with the following simple water balance equation:

A A w = P - ETa --DP (2)

where A AW is the change in available soil moisture, P is the amount of rain- fall, and DP is the drainage at the bottom of the lysimeter.

The lysimeter design allowed no horizontal runoff. Total AW was about 140 mm for the 1.2 m deep lysimeter (Kowal, 1968). Before the first rain it was assumed that AW = 0.0. Water loss before planting was estimated with eq. ( 1 ) assuming Kc=0.35. These were similar to assumptions made by Kowal and Faulkner ( 1975 ) while computing the lysimeter water balance for cotton. EX0 before planting was estimated with the FAO-24 (Penman) method as will be explained later. After planting, ET a values were obtained from the lysimeter water use data. For the first 40 days the effective root zone was assumed to be the top 60 cm. Starting with an estimated AW at planting, the water balance components were computed for each 10 day period. DP was assumed to occur when AW reaches 140 mm.

Figure 1 shows plots of (P-ETa) and percent AW for each of the crops. The results for cotton were similar to those obtained by Kowal and Faulkner ( 1975 ). Assuming that crops maintained at about 50% of maximum AW would suffer no detrimental water stress, maize, groundnut and millet were clearly well watered up to maturity. The maize variety matures at 120 days. The sorghum and cotton varieties were long-season crops usually planted so that their harvests coincide with a dry period. Sorghum reaches maturity at 135 days (Goldsworthy, 1970). For the remaining period the crop dries to har- vest, and does not require high soil moisture after the 13th decade. This means that a Kc curve up to the 13th decade is sufficient to determine the potential seasonal water requirements of the crop. On the other hand, the cotton vari- ety had indeterminate growth, the growth period being determined by mois- ture availability (Kowal and Faulkner, 1975). In other words, the crop fits its growth period to the length of the rains. Even if irrigation is possible, water has to be withheld at a certain point to enable the crop to dry for harvest. Therefore, a scaled Kc curve from a season of average length is sufficient to determine the water requirements of the crop.

From this water balance analysis it was assumed that although the lysime- ter was not irrigated in any of the years, sufficient rainfall was received to make the crop water use data valid for the determination of Kc curves. Ten day periods may, of course, at times be too long for water balance analysis of

] 62 S. ABDULMUMIN AND S.M. MISARI

P-ETa (ram/10 days) and AW (%) P-ETa (ram/10 days) and AW (%)

14o SORGHUM (1970) 14o- COTTON (1971) 120 120 -

100 ~ I 100 -

8 0 80 1

eo 6 0

40 40

20 20

- 2 0 - - 2 0 -

- 4 0 ~ ~ / . - , . / . - . . . / / , / ~ ~ / ~ / / 40 i ,/ / / / / " ~ m ~O

2 3 4 6 6 :, e o ~ o . 1 2 . , 4 , 6 w l T . w I ~ a 4 e • 7" e , ~ o . ~ = ~ , ~ 1 7 . 1 ~

Decades (xlO days) Decade8 (xl0 days)

P-ETa (ram/10 days) and AW (%) P-ETa (ram/10 days) and AW (%) r

140

1 2 0

1oo lO0 •

80 80

8 O ~ ~ 01

40 40 "

2 0 - - - 2 0 "

o_ o

/ / / " , × / / / , / / / / " / / ." - 4 0 - " 4 0 1

.eo---~ ~ - ~ , -eo "i /: 4 /~ / I ' " ' , ' ,~ /~ 4 /', /, /~ "i "': d ' / I ,'l /~'~" 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 16 t7" 1~ I 2 3 4 6 (I 7 8 9 tO 11 112 13 t4 16 l g 17" 18

Decades (xl0 days) Decades (xl0 days)

[ ] ( P - E T a ) • R a i n f a l l - C r o p ET P-ETa (mm/10 days) and AW (%) [ ] AW • Available water (%)

t 2 0

t O 0

8O

6O

4 0 "

- 2 0

- 4 0 - / / " 7 / / / /

-eo ~ - ~ l / I ,/q / I /~ /p / I / t / I / ( / I /', /' /: /', ": / 2 3 4 6 0 7" 8 9 10 11 12 13 14 16 16 17 18

Decades (xlO days)

Fig. 1. Lysimeter water balance components .

CROP COEFFICIENTS IN THE NIGERIAN SEMI-ARID TROPICS [ 63

this nature as the crop can suffer long periods of water stress if rainfall is not well distributed.

Determination Of ETo

ETo for each decade of crop growth period was determined with a quanti- fied form of the FAO-24 (Penman) method, expressed by Weiss ( 1983 ) as

( A ~ +J-~f(U)(es-ea)) (3) EXo = C Rn d + 7

where A is the slope of the vapour pressure versus temperature curve (mbar); 7 is the psychrometric constant (mbar ° C - I ) ; Rn is the net radiation (mm d a y - ~ ) ; f ( U ) is the wind function (mm m b a r - l d a y - l ) ; es is the satu- ration vapour pressure at mean air temperature (mbar); ea is the actual vapor pressure derived from mean relative humidity and es (mbar); and c is a factor to adjust EXo to local climatic conditions.

Parameters A and es were determined from mean daily air temperature ac- cording to the procedure of Lowe ( 1977 ). The psychrometric constant 7 was determined by

CpP (4) 7- Le where Cp is the specific heat of dry air ( 1004.1 J ° C- ~ kg- l ); p is the atmos- pheric pressure (mbar); e is the ratio of the mass of water vapour to dry air (0.622); and L is the latent heat of vaporization (2.45 × l0 -6 J kg-l ). Cp and L were assumed to be constant. P was assumed equal to 938 mbar for the elevation of Samaru of 686 m above sea level.

The saturation vapour pressure ea was determined by (Lowe, 1977)

ea =es (RH/100) (5)

where RH is the mean relative humidity (%). The net radiation Rn was determined as the sum of net incoming solar and

outgoing longwave radiation:

Rn=Rr, s +Rnl (6)

where Rn~ is the net shortwave radiation (MJ m -2 day -~ ) and Rnl is the net longwave radiation ( MJ m - 2 day- 1 ).

Rns is given by

Rn~ = (1- -a )Rs (7)

where R~ is the total incoming shortwave radiation (MJ m - 2 day- ~ ) and a is the surface albedo.

Mean crop albedo was assumed to be a=0 .25 in agreement with FAO-

164 S. ABDULMUMIN AND S.M. MISARI

0.8 r = 0.84

o.e [] ~ 0 ~

0.4 ~

0 0.2 0.4 0.6 0.8

n/N

Fig. 2. Plot of Rs/Ra versus n/N.

24(Penman) . Rs was measured simultaneously with ETa in 1972, 1973 and 1974 using a Kipp solarimeter connected to an integrator. No Rs measure- ments were made in 1970 and 1971 for grain sorghum and cotton, respec- tively. For these crops, therefore, Rs was estimated with

R~= a+b Ra (8)

where n is the number of observed hours of sunshine; N is the number of max imum possible hours of sunshine for the latitude; Ra is the extraterrestrial radiation for the latitude (MJ m -2 day-~ ); and a, b are constants.

Constants a and b were determined using the R~ data of 1972, 1973 and 1974 and relative hours of sunshine recorded at the location during these pe- riods. N and Ra were estimated for the latitude of Samaru from tables given by Doorenbos and Pruitt (1977). The correlation curve is given in Fig. 2. Values of a = 0.28 and b= 0.46 were obtained using a least squares curve fit- ting procedure.

The net longwave radiation Rnl was estimated by

R,I =o 'T 4 (0 .34 -0 .044 ~ ) (0.1 +0.9n/N) (9)

where ty is the Boltzman constant ( 4.9 X 10 - 3 j m - 2 day- ~ K - 4 ) and T is the mean air temperature (K).

Equation (9) is equivalent to multiplying f ( T ) , f(ed) and f (n /N) of the FAO-24 (Penman) method.

CROP COEFFICIENTS IN THE NIGERIAN SEMI-ARID TROPICS | 65

The wind function corresponding to the grass reference of FAO- 24 (Penman) was used to determine f (U) . This is given as

f (U) =0.27 ( l . 0 + 1~00) (10)

where U24 is the 24 hour wind run (km day -~ ). The correction factor c (eq. 3) was computed using the subroutine in Ap-

pendix III of Doorenbos and Pruitt (1977). The subroutine requires esti- mates of Rs, mean day-time wind speed Uo (m s- l ), the ratio (Ur) of Ud to mean night-time wind speed Un (m s- 1 ), and the maximum relative humid- ity for the day RHmax. Uo and Un were determined with an automatic weather station (Campbell Scientific Inc., Utah, U.S.A.) at the location during the 1987 rainy season (Fig. 3). Mean Ur was determined to be 1.6. Uo was then estimated from the 24 hour windrun using this value of Ur.

Relative humidity is normally recorded in a weather station at the location at 10.00 and 16.00 hours local time. Analysis of the automatic weather station data of 1987 shows that minimum relative humidity for the day (RHmin) oc- curs, on average, at about 15.50 h, very close to 16.00 h. Figure 4 shows the correlation between RHmin and relative humidity at 16.00 hours (RHj6) de- rived from the data. Least squares fitting gave the following equation:

RHmin = 3.25 + 0.886 ( R H I 6 ) . ( 11 )

4

Day ~ Night

3

q)

2

~

q~ 1

O I I I [ I I I

2 4 0 245 2 5 0 255 2 6 0 265 270 275 280

J u l i a n day

Fig. 3. T rendso fmean day and night t ime wind speedsa tSamarudur ing pan of thera inyseason in 1987.

166 S. ABDULMUMIN AND S.M. MISARI

6 0

r = 0 . 9 2 [ ] [ ]

5s

[ ] [3 ° 50 O ~ 0

40 , , , 40 45 50 55 BO

RH16 (~)

Fig. 4. Plot of daily minimum relative humidity (RHmi.) versus relative humidity at 16.00 hour (RHI6).

0.9

r = 0 .81

0.8 []

~ o.7 y ~ O.6

[]

0 . 5 J []

0.4 t L I I - -

0.4 0.5 0.6 0.7 0 .8 o.g

T m i n / T m a x

Fig. 5. Plot of the ratios RHI6/RHma x and Trnin/Tnaax.

On the other hand, RHma x Occurs, on average, at 05.20 h. Least squares curve fitting (Fig. 5 ) showed that RHmax can be estimated by

RHI6 ( 1 2 ) RHmax -- T m i n / Tma x

CROP COEFFICIENTS IN THE NIGERIAN SEMI-ARID TROPICS 167

where Trnin is the daily m in im um temperature (°C) and Tmax is the daily maximum temperature ( °C) . The mean daily relative humidi ty (RH in eq. 5 ) was estimated as the average of Rnmi n and RHma x.

A microcomputer program was written in BASIC, using the methodology outlined above, and incorporating the subroutine for computing the correc- tion factor c from Appendix III of Doorenbos and Pruitt ( 1977 ), to compute mean decade ET0. The required data of mean daily Tmax, Train, RHI6 and 1_7_,4 for each decade were determined from weather records of the location. Aver- age Kc for each decade was then computed with:

Kc = ETa/ET0- (13)

RESULTS AND DISCUSSION

Crop coefficient (Kc) curves for the five crops are given in Fig. 6. The x- axis is expressed as percentage time to maturity assuming days to maturity of 140, 100, 120, 120 and 90 for sorghum, cotton, maize, groundnut and millet, respectively. The fitted curves were drawn by hand, keeping in mind the typ- ical shape of such curves (e.g. Doorenbos and Pruitt, 1977; Fereres et al., 1980; Abdulmumin, 1988 ). Major deviations of the estimated Kc points from the curves may be due to short wet and dry spells as the lysimeter was not irrigated. However, as the results of the water balance analysis showed no significant stress periods, the scatter of points around the curve can be as- sumed to be normal for an experimental data.

Ideally, EXo of the reference crop should be experimentally measured with a lysimeter. However, when ETa of the various crops reported here were mea- sured the concept of a reference crop was not in widespread use, and no such measurements were made. Repeating the experiment in the desired manner will involve constructing several costly lysimeters. The alternative procedure used here is to determine grass ETo from climatic data using the FAO- 24 (Penman) in a manner similar to that o fAbdu lmumin ( 1988 ). The FAO- 24 (Penman) was developed by Doorenbos and Pruitt ( 1977 ) with data from different climates around the world, and is adjustable to local climatic con- ditions through the correction factor c. They estimated the accuracy of the method to within 10% when used over 10 to 30 day periods. We assumed that FAO-24 (Penman) can be used to model EXo for a location without having to grow grass, once the necessary variables specific to the location are deter- mined. Kc curves can then be developed with measured ETa. The fact that ETa was measured locally makes the Kc values locally calibrated. Although the values may not be exactly the same as would be obtained with measured ET0, they should be accurate enough for the purpose of estimating crop water re- quirements in the climatic region.

| 6 8 S. A B D U L M U M I N A N D S.M. MISARI

,.= ~ p coeffl~nt ,.=~p c~fficient I SORGHUM COTTON

0 . 8 ~ o 0 .8

I o.e~ o.e

0.4 0 ,4

0 . 2 - 0 . 2 ~ I

01 i i L 0 i b J J t

o o.= e4 o.a o.a ~ t= o o.= 0.4 o.6 o.8 ~ 1.= Percentage time ~ mat~lty (x 0.01) Percentage t i n to maturity (x 0.01)

Crop coefficient ~a Crop coefficient

1.= D MAIZE t / ~ ~ ~ O U N D N U T

0 .8 0 .8

o . , o °, F / ° - \

0 .2 0 .2 ~ I

0,2 0.4 0.• 0.8 1 1.2 0 0.2 0.4 O,e 0.8 1 1.2

Percentage time to maturity (x 0.01) Percentage time to maturity (x 0.01)

Crop coefficient 1.2 / MILLET

0 0.2 0,4 0.6 0.8 1 1.2

Percentage time to maturity (x 0.01)

Fig. 6. Kc curves for five crops of the Nigerian semi-arid tropics.

The FAO-24 (Penman) requires estimates of RHma x as one of the variables required to estimate the correction factor c. The problem is that RHma x and RHmi n are not routinely recorded in weather stations. Development of empir- ical methods for estimating RHma x with automatic weather station data helps to overcome this problem. While eqs. ( 11 ) and ( 12 ) are probably useful only

CROP COEFFICIENTS IN THE NIGERIAN SEMI-ARID TROPICS 169

in the climatic region for which they were developed, the same procedure can be used elsewhere to obtain the required estimates.

Several people have questioned the accuracy of estimating mean daily va- pour pressure from mean daily relative humidi ty (eq. 5 ) as is done in FAO- 24(Penman) . It was argued that one should average actual estimates of ea obtained from the two daily observations of RH. Figure 7 shows a compari- son of 10 day mean ea estimated with the two methods, using data of the five seasons at Samaru. The slope is essentially unity, with a correlation coeffi- cient of 1.0. It does seem, at least from these results, that the two methods would give the same results. This may be explained by the conservative na- ture of ea, which does not change much during the day.

The coefficients for determining Rs in eq. (8) are site-specific. The values a=0 .28 and b--0.46, although similar to a=0 .25 and b=0.50 of FAO- 24 (Penman) , are nevertheless different. The locally determined coefficients may have improved the estimates ofETo. FAO-24 (Penman) also relies heav- ily on the use of tables. It is difficult to get exact values of variables, say es from mean temperatures, from tables. The quantitative procedure of Weiss ( 1983 ), however, enables variables to be determined from the original phys- ical or empirical relationships. Further, the procedure is easier to computer- ise. It should be noted, however, that Weiss ( 1983 ) modified the actual FAO- 24 (Penman) to estimate alfalfa reference evapotranspiration. He used an al- falfa wind function, a different method for estimating the net longwave radia- tion term, and used mean daily R H instead of RHmax to determine the correc-

3 o

r = 1.0

26

20

> I0

5-

0 I I I I I

0 5 10 15 20 25 30

%(mbar) from mean RH

Fig. 7. Comparison between ea calculated with mean daily relative humidity (eq. 5) and ea estimated from relative humidity and air temperature at 10.00 and 16.00 hours and averaged (ea values are means over 10 day periods).

170 S. ABDULMUMIN AND S.M. MISARI

tion factor c. With these modifications the method gave estimates that were within 13% of measured alfalfa evapotranspiration. In our analysis no such changes were made to the actual FAO-24 (Penman) as our interest was grass reference evapotranspiration. Although no measured grass evapotranspira- tion data were available, the results of Weiss ( 1983 ) may give an indication of the possible accuracy of the procedure.

CONCLUSIONS

Crop coefficient (Kc) curves for grain sorghum, cotton, maize, groundnut and millet were developed using grass reference EWo derived from a modified version of the FAO-24 (Penman) procedure and actual water use of the crops experimentally measured at Samaru, Nigeria. As Samaru lies at about the centre of the semi-arid tropical zones of Nigeria, the Kc curves should apply to the whole zone, and by extrapolation, to the whole semi-arid tropical re- gion of West Africa. This means that the curves can be used in water manage- ment decisions, such as the determinat ion of crop water requirements, and supplementary irrigation scheduling. However, certain modifications will be necessary before the curves can be used to moni tor crop water use under strictly rainfed conditions. During long dry spells when available soil mois- ture falls below 50%, crops may not be using water to the levels suggested by the curves. Water use may also be higher during very wet conditions. Sugges- tions on how these modifications can be achieved are available from the lit- erature (e.g., Doorenbos and Pruitt, 1977; Burman et al., 1980).

ACKNOWLEDGEMENTS

We wish to thank the Director of the Institute for Agricultural Research ( IAR), Ahmadu Bello University, Zaria, Nigeria, for permission to publish this work. IAR is supported by the Ministry of Science and Technology of the Federal Republic of Nigeria. We also acknowledge the suggestions of Dr. J.L. Montei th and other anonymous reviewers of this paper.

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CROP COEFFICIENTS IN THE NIGERIAN SEMI-ARID TROPICS 171

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