Agronomy Journal 94:1204-1211 (2002)
© 2002 American Society of Agronomy
SOIL WATER DYNAMICS
Profile Water Balance Model under Irrigated and Rainfed Systems
Uttam Kumar Mandal*,a,
K. S. Sundara Sarmab,
U. S. Victora and
N. H. Raoc
a Div. of Resour. Manage., Cent. Res. Inst. for Dryland Agric., Santoshnagar, P.O.-Saidabad, Hyderabad-500059, India
b Div. of Agric. Physics, Indian Agric. Res. Inst., Pusa, New Delhi-110012, India
c Natl. Acad. of Agric. Res. and Manage., Rajendranagar, Hyderabad-500030, India
* Corresponding author (uttamkm{at}crida.ap.nic.in)
Received for publication November 20, 2000.
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ABSTRACT
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A profile moisture model has been developed to evaluate the seasonal soil moisture fluctuation with respect to soil characteristics and land use pattern under irrigated and rainfed conditions in an area of agricultural fields. Daily rainfall and irrigation were used as model inputs. Instantaneous uniform redistribution of soil moisture in the effective root zone and negligible contribution of soil water through upward flux were assumed. An empirical model was used to determine the root depth. Runoff was estimated from rainfall data using the curve number technique of the Soil Conservation Service adapted for conditions in India and combined with a soil moisture–accounting procedure. The modified Penman method was used to calculate the reference evapotranspiration. To calculate the crop coefficient (Kc), regression equations were developed taking Kc as the dependent variable on normalized difference vegetation index. This model was very easy to parameterize and required a minimum soil data set of field capacity and permanent wilting point. To evaluate model performance, observed values of soil water were taken for wheat (Triticum aestivum L.) in the Mehrauli (sandy loam to loam texture) and Daryapur (loamy texture) soil series under irrigated conditions and for gram (Cicer arietinum L.) in the Jagat (clay loam texture) and Holambi (loam texture) soil series under rainfed conditions in Delhi. The r2 and D index between observed and predicted soil water values varied between 0.67 and 0.77 and 0.83 and 0.93, respectively.
Abbreviations: AMC, antecedent moisture conditions • CN, curve number • DAS, days after sowing • ET, evapotranspiration • FC, field capacity • NDVI, normalized difference vegetation index • PET, potential evapotranspiration • PWP, permanent wilting point
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INTRODUCTION
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AN UNDERSTANDING of the principles of water movement in the soil profile and a continuous evaluation of the storage and balance of soil water are important for efficient soil and water management, irrigation scheduling, and runoff prediction. But physical measurement of soil moisture in every field presents practical difficulties. The assessment of soil moisture by gravimetric methods is very difficult without disturbing soil and plant roots. In situ methods like the neutron probe need calibration for each soil type and set of circumstances in which they are to be used (Hillel, 1998). Precise determinations of soil water content by time domain reflectometry require specific calibrations at water contents above 0.15 m3 m-3 in soils with high clay content, salt, or both (Topp et al., 2000). The sample requirement to represent large areas will also be high. Microwave remote sensing usually provides a measure of surface moisture over a large area, but this technique has a fundamental limitation of sensing the moisture content in a layer only 2 to 5 cm thick at the surface (Schmugge et al., 1980) rather than the root zone. Hence, a necessity arises to develop a method to determine soil profile moisture over a large area, at least an agricultural field, that is quick, easy to determine, and reliable. Application of mathematical modeling techniques to the various hydrological processes taking place in the soil profile might provide such estimates of soil profile moisture.
Simulation of the root zone moisture profile can be done by either empirical or physical models, which operate by solving the soil water balance equation. There are essentially two types of soil water balance models: models based on simple bookkeeping procedures (Rao, 1987; Campbell and Diaz, 1988) and dynamic simulation models based on the physics of unsaturated flow in soil (Feddes et al., 1988). The former requires data of soil water storage properties, namely the field capacity (FC) and permanent wilting point (PWP). Despite some limitations of FC and PWP (Hillel, 1980), they are acceptable for practical soil water simulations. But physics-based models need data of soil water storage as well as transmission characteristics (e.g., soil hydraulic conductivity vs. moisture content relationship). The simple water balance models are therefore preferred in field applications and large-area studies (Rao, 1998). Examples of applications include prediction of irrigation demands, crop water stress effects, irrigation schedules, and crop yields (Raes et al., 1988; Rao et al., 1990; Penning de Vries et al., 1989); prediction of runoff (Pathak et al., 1989); and prediction of ground water recharge (Rushton, 1988). More recently, soil water balance models have been used as central components of watershed conservation and management models such as CREAMS, EPIC, ANSWERS, etc. But all of these models require a large data set of soil and crop parameters.
Therefore, a field investigation has been undertaken with the objectives of developing and field testing a profile water balance model, which requires relatively less information of soil and crop parameters to estimate soil water over a large area having similar soil characteristics and land use pattern.
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MATERIALS AND METHODS
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Development of the Profile Water Balance Model
The soil water balance includes runoff, infiltration of rainfall or irrigation into soil, redistribution of infiltrated water within the root zone, evapotranspiration (ET), and percolation below the root zone. The soil reservoir is divided into two layers: (i) an active layer of depth in which roots are present at any given time and from which both moisture extraction and drainage would occur and (ii) a passive layer of depth [maximum root depth - root depth attained any day after sowing (DAS)] from which only drainage would occur. The two layers are distinct in the initial phase of crop growth, and their relative depths are governed by the rate of root growth. But once the maximum root depth is attained, the entire root zone becomes only one layer. The soil water balance in the upper layer is governed by daily values of rainfall, runoff, irrigation, ET, and drainage to the second layer. Drainage into it from the upper layer and drainage out of the layer as deep percolation govern the soil water balance in the lower layer.
It is assumed that effective rainfall (rainfall - runoff) and the applied irrigation on any day are redistributed instantaneously (without any time lag) and uniformly over the root zone. The rainfall and applied irrigation in excess of FC percolate to the lower passive zone and are instantaneously redistributed in that zone. The remaining water in excess of FC of the passive zone moves out of it as deep percolation. If the updated water balance is less than or equal to water content at permanent wilting point (PWP), then the updated water balance is limited to PWP (lower limit). The contribution to soil moisture from upward flux is not considered in this model.
For Layer 1 (the active root zone), the soil moisture content (MC1, m3 m-3) at the end of any day (i) can be estimated by the daily soil water balance equation for this layer given by:
 | [1] |
for i = 1, 2,...N, where
The daily increase in DRD is:
 | [2] |
and Pi is given by:
 | [3] |
if Pi < 0, then Pi = 0.
For the passive root zone,
 | [4] |
if Pi = 0 Otherwise,
 | [5] |
and
 | [6] |
if DPi < 0, then DPi = 0 where RDM is maximum root depth (mm) and DP is drainage out of the passive root zone layer as deep percolation.
The data of daily rainfall (R, mm) for the growing season of each crop for the period under consideration are used as input. Daily runoff (Q, mm) is estimated from daily rainfall data using the curve number (CN) technique of the Soil Conservation Service (USDA, 1972) adapted for conditions in India (Ministry of Agric., 1972; Sahu, 1990) and combined with the soil moisture–accounting procedure suggested by Sharpley and Williams (1990). Details of runoff estimation are presented in the appendix.
Root depth of the crop increases with time. The Borg and Grimes (1986) root growth model is used to determine the root depth:
 | [7] |
where DTM = DAS to maximum root depth. The minimum value of RD was set equal to 150 mm according to the assumption that soil evaporation would take place from the top 150 mm of the profile.
In the model, ET occurs at a maximum rate called potential ET (PET, mm d-1) as long as the moisture content in the root zone is more than a minimum threshold value. When water content falls below the threshold value, the value of ET becomes a decreasing function of water content and PET (Doorenbos and Kassam, 1979). The value of PET is a function of crop type, crop growth stage, and climatic parameters. To obtain PET, the reference ET (ET0) is multiplied by the corresponding value of the crop coefficient (Kc) for the day.
 | [8] |
Reference ET (mm d-1) was determined using the modified Penman method with locally obtained meteorological data by applying the procedures given by Doorenbos and Pruitt (1977). The meteorological data were daily maximum and minimum temperature, relative humidity, wind speed, and sunshine hours. Solar radiation was calculated from sunshine hours using the Angstrom equation applied in the Delhi region (Gangopadhayay et al., 1970).
The Kc was estimated from spectral reflectance. The spectral reflectance of crops was measured using a portable spectroradiometer (model LI-1800 with input optics 1800-06 telescope receptor with 15° field of view attached to the fiber optic cable, LI-COR, Lincoln, NE) in a field where there was no water limitation. Canopy reflectance was monitored every other day throughout the crop growing season within the range of 300 to 1100 nm during the observation period of 1130 to 1230 h. The reflectance spectrum was calculated as the ratio between the reflected and incident spectra on the canopy where the incident spectrum was periodically obtained from the light reflected by a BaSO4 reference panel. Percentage reflectance values were calculated by dividing the canopy reflectance by the standard. Reflectance values within the range of 600- to 700-nm (Rr) and 800- to 900-nm range (IRr) were used to calculate the normalized difference vegetation index (NDVI) (Deering et al., 1975):
 | [9] |
The Kc values were collected from available references (Table 1) for the entire crop growth periods. The Kc for each value of DAS of crop were converted into values for each day by interpolation (Fig. 1)
. A regression equation was developed taking the Kc as the dependent variable on NDVI using the CURVEFIT software package. The Kc values were calculated each day using NDVI values for the specific crop.
A computer program was written in FORTRAN 77 language to calculate the profile water content using the above-mentioned criteria.
Field Experiment
The soil water balance model was tested at the experimental farm of the Indian Agricultural Research Institute (IARI), New Delhi, during 1997–1998. The farm is situated at latitudes 28°37' N to 28°39' N and longitudes 77°9' E to 77°11' E, and elevation ranges from 217 to 241 m above mean sea level. The climate of Delhi is subtropical semiarid with hot, dry summers and cool winters (Sehgal et al., 1992). The mean maximum temperature during summer months (May, June, and July) varies from 43.9 to 45°C. From November, mean maximum temperature shows a decreasing trend and drops to a minimum of 5°C in the month of January. The period from December to February is the winter season. The mean annual temperature is 25.5°C, and the mean summer and mean winter temperatures are 33 and 17.3°C, respectively. The mean annual rainfall is 710 mm (average of past 30 yr), of which as much as 75% is received during the monsoon months (July to September).
The soil of the experimental fields belongs to the major group of Indo–Gangetic Alluvium (Typic Ustochrept). The relief is nearly level with almost uniform slope ranging from 1 to 3%. The profile water balance model was tested by comparing with field observations of soil moisture made in the study area during 1997 to 1998.
The data used to run the model were:
- Daily weather data of rainfall, maximum and minimum temperature, relative humidity, wind speed, and sunshine hours recorded in the observatory (0.5–2 km away from experimental fields) of the Division of Agricultural Physics at IARI in New Delhi from November to April 1997 to 1998
- Soil properties of different soil series and crop information as given in Tables 2 and 3, respectively
- Daily Kc values calculated from the best-fit equation of NDVI vs. Kc
- Times and amounts of irrigation in the case of wheat.
Wheat variety HD 2285 was sown with the help of a bullock-drawn plow, keeping row-to-row distance of 20 cm, and seeds were placed at 4- to 5-cm soil depth. A row spacing of 30 cm was kept for gram variety RS-10. It was grown as a rainfed crop, so irrigation was not applied. Seventy-five millimeters of water was applied during each irrigation (check basin method with each plot size of 6 by 15 m) of the wheat crop. Soil moisture, measured at weekly intervals from the beginning of crop growth until harvest, was used to evaluate the model performance. Soil samples were collected with a soil auger at 15-cm depth intervals down to 105 cm. Wet soil was oven-dried to constant weight at 100 to 110°C for 24 h. The mass wetness, also called gravimetric wetness (W), is the ratio of the weight loss in drying to the dry weight of the sample measure:
 | [10] |
The mass-basis water content was converted to volume basis (m3 m-3) by multiplying it with bulk density. For each soil series, four locations were sampled within a block of agricultural field for each moisture content observation. The size of each block varied between 1 and 2 ha. Bulk density and soil texture were measured by the core method (Blake and Hartge, 1986) and bouyoucos hydrometer method (Gee and Bauder, 1986), respectively. Soil water retention at PWP and FC were measured in pressure plate apparatus at 1.5 MPa and 0.033 MPa (Cassel and Nielsen, 1986). Four replications were used for measuring bulk density, soil texture, and soil water retention.
The values of ET and soil moisture content in the root zone at the end of each day were modeled for the entire growing season (December to April) of the 1997 to 1998. The predicted values of daily soil moisture content in the root zone were compared with the observed field moisture data. In the beginning of the crop growth, observed soil water data were considered up to the root depth calculated by the empirical root growth model. When the root growth was more than 105 cm, the observed values were considered up to 105-cm depth. The final soil water content output of the model at the end of each day was with respect to the PWP. The PWP values for different soil series were added to final soil water content to get the absolute value of final soil water content.
For testing of the model, r2 and standard error were calculated using observed value (O) and predicted model value (P) of soil water content. Willmott (1982) proposed an "index of agreement" (D) to evaluate model performance. The value of D is calculated as follows:
 | [11] |
where 
= mean of observed values.
Willmott (1982) also suggested the use of both systematic (MSEs) and unsystematic (MSEu, random) error terms. The mean square error (MSE) is made up of the systematic and the unsystematic portion that is MSEs and MSEu, respectively:
 | [12] |
 | [13] |
 | [14] |
where Pr = a + bO; n is the number of observations; and a and b are regression coefficients of the intercept and slope, respectively. Systematic error is related to the model performance, and random error is related to observations or measurements.
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RESULTS AND DISCUSSION
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The temporal changes of NDVI during the growth period for all crops showed that these values generally increased gradually at the beginning of the growth period, showed a maximum, and then decreased during senescence (Fig. 2)
. In the case of wheat, NDVI followed the usual bell-shaped curve with a peak (0.8) at 75 DAS. For gram, NDVI increased as the crop growth progressed and attained a maximum (0.57) at 57 DAS, followed by a gradual decrease as the crop attained physiological maturity. Quick senescence in the harvesting stage might be the cause of the decrease of NDVI below 0.25.
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Fig. 2. Normalized difference vegetation index (NDVI) of wheat and gram (error bars are ± one standard deviation).
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The best-fit equation of Kc vs. NDVI (Fig. 3)
for wheat was
 | [15] |
where number of points = 59, r2 = 0.98, and root mean squared error = 0.048. For gram, the best-fit equation of Kc vs. NDVI (Fig. 3) was
 | [16] |
where number of points = 53, r2 = 0.97, and root mean squared error = 0.075. High r2 values for regressing Kc on NDVI indicated similarities between the Kc curve and the vegetation index and showed the potential for modeling a vegetation index into a crop coefficient (Bausch and Neale, 1987).
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Fig. 3. Relationship between crop coefficient (Kc) and normalized difference vegetation index (NDVI) for wheat and gram.
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The model underestimated soil water content under wheat in 1997 to 1998 for both the Mehrauli and Daryapur soil series, except in three observations (Fig. 4 and 5)
. Like observed values, model values also showed that the Daryapur series had larger soil water contents than the Mehrauli series. Model predictions varied from observed values within ±6.3 and ±10.2% for the Daryapur and Mehrauli series, respectively. For the Mehrauli soil series, wheat ET for 2 d (108 DAS and 110 DAS) was less than PET, and on all other days, it was equal to the potential rate. In the Daryapur soil series, ET was equal to PET throughout the growth period. Runoff and percolation below the root zone were 40 and 234 mm, respectively, for the Daryapur series and 9 and 176 mm, respectively, for the Mehrauli series. A considerable amount of irrigation water percolated below the root zone during the crop growth. In some cases, predicted percolation was more than 85% of irrigation water.
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Fig. 4. Observed and predicted values of soil water content during the growth period of wheat in the Mehrauli soil series (error bars are ± one standard deviation).
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Fig. 5. Observed and predicted values of soil water content during the growth period of wheat in the Daryapur soil series (error bars are ± one standard deviation).
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Here, CN techniques were used on a daily time step to predict daily runoff for a specific precipitation event on a daily basis. The SWRRB (Arnold et al., 1990) and SWAT (Arnold et al., 1996) models also used the CN techniques to estimate daily runoff from daily rainfall data. Rao (1995) also predicted the runoff at Indore, Akola, Patancheru (ICRISAT), Bellary, and Delhi watersheds of India, using the same procedure, which was comparable to observed runoff.
The soil water contents under gram in initial stages of crop growth were higher in all of the layers and decreased gradually as the crops reached maturity. Like observed values, the predicted values of soil water content on the Jagat series were more than on the Holambi series. The overall deviation of model estimation from observed values varied within ±7.4 and ±8.7% for the Jagat and Holambi series, respectively (Fig. 6 and 7)
. The runoff was much less (1 mm) in both cases. There was no predicted deep percolation. In the beginning of the crop season, rainfall and initial soil water storage were moderate, and ET was equal to PET up to 37 and 46 DAS in the Holambi and Jagat series, respectively. After that, ET decreased gradually because of dry spells. For gram, there was no irrigation. Rainfall was also only 78 mm during the growing season. To meet the ET demand, the soil water content gradually decreased with the advancement of crop growth. Evapotranspiration became equal to PET whenever there was rain and was strongly related to the soil moisture content in the root zone (Mani, 1989).
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Fig. 6. Observed and predicted values of soil water content during the growth period of gram in the Jagat soil series (error bars are ± one standard deviation).
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Fig. 7. Observed and predicted values of soil water content during the growth period of gram in the Holambi soil series (error bars are ± one standard deviation).
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The r2 and D index values and low values of the error component indicated good agreement between modeled and observed values for the estimation of root zone soil moisture (Table 4). The assumption of instantaneous, uniform redistribution of soil water over the effective root zone is no doubt a limiting assumption on a microscale. However, the scale of the problem, both in terms of the large size of the cropped area (space) and the convenient time intervals for operating irrigation systems, as well as operational constraints in the irrigation system provide a justification for use of this simple model. The assumption of instantaneous redistribution of soil moisture is justified in view of the slow rate of ET and large intervals of irrigation operation. In most cases, model underpredictions of soil water content might be due to keeping FC as the upper limit of soil moisture. Still, the model was effective (a maximum of ±10% deviation from observed values) in predicting average soil moisture conditions at the end of each day. Also, this model has a scope of using remote sensing throughout the growing season for estimating the Kc on an operational basis and can be linked with geographic information systems (GIS) over a region having similar soil characteristics and land use patterns.
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APPENDIX
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Runoff Estimation Using Curve Number Techniques
The CN method defines a retention parameter S (mm), which varies with time because of changes in soil moisture content. The parameter S is related to CN by the relationship:
 | [A1] |
The values of the CN vary with antecedent moisture conditions (AMC). In the original procedure of USDA and its Indian adaptation, three such conditions are defined as AMCI, AMCII, and AMCIII, corresponding to dry, average, and wet catchment conditions, respectively. These conditions are identified empirically based on the cumulative rainfall in the 5 d preceding the current rainfall event for the growing season. Two limiting values of the cumulative rainfall of the previous 5 d are defined for identifying the AMC. If this rainfall is <36.6 mm, then AMCI applies; if it is more than 53.3 mm, AMCIII applies; and if it is in between, AMCII applies.
The values of the CN for average AMC (CN for AMCII or CN = CN2) are tabulated for various soil, land use, and management conditions by the Ministry of Agriculture (1972). The corresponding values of CN for dry CN1 and wet CN3 catchment conditions are given by:
 | [A2] |
and
 | [A3] |
For Indian conditions, Ministry of Agriculture (1972), the Government of India, and Sahu (1990) reported the following modification for runoff estimation with respect to the soil type:
 | [A4] |
for soil regions of India except for the black soil region with AMCII and AMCIII condition and
 | [A5] |
for black soil regions with AMCII and AMCIII conditions. However, in real situations, the AMC value is not restricted to the three discrete conditions identified empirically for the cumulative rainfall but can vary over a continuous range, and the value of S can be directly related to the soil moisture content in the active layer by the equations of Sharpley and Williams (1990):
 | [A6] |
where S1 is the value of S associated with CN1 (S2 for CN2 and S3 for CN3), FFC is the fraction of FC, and w1 and w2 are called shape parameters. The value of FFC is given by:
 | [A7] |
The shape parameters are defined as
 | [A8] |
 | [A9] |
The average condition CN (CN2) was decided on the basis of hydrologic soil group and land use pattern. The CN1 and CN3 were calculated from Eq. [A2] and [A3], respectively. Corresponding S1, S2, and S3 values were calculated from Eq. [A1] using the CN1, CN2, and CN3 values. The shape parameters w1 and w2 were calculated using Eq. [A8] and [A9]. The retention parameter S was calculated from Eq. [A6] using the fraction of FC (Eq. [A7]) value, which depended on soil type and w1 and w2 values. Daily runoff was calculated using S and daily rainfall data from Eq. [A4] as the soil of the region is alluvial, not a black soil.
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ACKNOWLEDGMENTS
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The first author is grateful to Indian Agricultural Research Institute, New Delhi, India, for providing all the facilities to run this experiment during his Ph.D. program. Both authors are grateful to the associate editor (Dr. Steven R. Evett) and the reviewers for their valuable suggestions in improving the manuscript and to Dr. Calvin H. Pearson for his assistance in the publication of this paper.
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TOP
ABSTRACT
INTRODUCTION
