New Approaches in Water Balance Computations (Proceedings of the Hamburg Workshop, August 1983). IAHS Publ. no. 148.

Soil water hydrology: simulation for water balance computations

KEITH E. SAXTON USDA-ARS, Agricultural Engineering Department, Washington State University, Pullman, Washington 99164, USA

ABSTRACT Soil moisture occurs as the result of the climatic, crop, and soil processes which impact water on a vegetated landscape. This complex and highly dynamic water supply provides the water upon which the vast majority of the world food supply depends. Most importantly, it is as variable within and between years and location as the variables which determine its occurrence. The physical processes which determine the dynamic state of soil water have been mathematically described and combined into several simulation models in recent years for agricultural and hydrological objectives. These vary in complexity, inputs, and products according to their objective and developers. Several of these models have been applied to the simulation of daily estimates throughout the crop year. The SPAW model developed by the author has been applied to a variety of situations and objectives. This model will be briefly described followed by a discussion of several recent trial applications. These results and those of other similar models suggest that we now can use simulation models to integrate existing knowledge with current observation to provide dynamic soil water estimates useful for several important agricultural and hydrological assessment and prediction needs.

Hydrologie de 1'humidité du sol: simulation pour les calculs du bilan hydrologique RESUME La teneur en humidité du sol résulte des processus climatiques, du type de culture et des processus du sol qui ont une influence sur un paysage couvert de végétation. Cette humidité du sol, à la fois complexe et dynamique, est à la base des apports en eau dont dépend la majorité des approvisionnements en vivres de la planète. D'une importance prépondérante est le fait que sa variabilité entre les années et à l'intérieur de chaque année et entre les différents sites est aussi grande que pour les variables qui déterminent sa présence. Ces dernières années, les processus physiques qui déterminent l'état dynamique de l'humidité du sol ont été décrits mathématiquement et combinés dans plusieurs modèles de simulation pour des objectifs hydrologiques et agricoles. Il y a de notables différences quant à la complexité, les données d'entrée et les résultats suivant l'objectif et la

47

48 Keith E.Saxton

personalité de ceux qui les ont mis au point. Plusieurs de ces modèles ont été utilisés pour la simulation des estimations journalières tout au long d'une culture. Le modèle SPAW, mis au point par l'auteur, a été appliqué dans plusieurs situations et pour des objectifs différents. Le modèle sera brièvement décrit puis on discutera de plusieurs essais récents. Les résultats, ainsi que ceux d'autres modèles similaires, suggèrent que nous pouvons maintenant utiliser les modèles de simulation pour intégrer les connaissances existantes avec les données d'observation afin de réaliser des estimations dynamiques de l'humidité du sol que l'on peut utiliser pour plusieurs besoins importants d'estimation et dans le domaine de l'agriculture et de l'hydrologie.

INTRODUCTION

The occurrence and distribution of soil water is a complex and integral part of any hydrological water balance. Whether the emphasis is on surface runoff, streamflow, évapotranspiration, or groundwater, soil water plays a dominant role. Every water balance scheme or hydrological model makes some attempt to predict the occurrence and impact of soil water. The magnitude and time-depth distribution of water in the upper 1-2 m of the earth's mantle readily identify why soil water is of significant importance. Within the hydrological cycle, the storage and release of soil water is second in magnitude only to the precipitation source itself. In climates with less than 400 mm precipitation, virtually all of the precipitation enters the shallow soil layers to be transferred back to the atmosphere by évapotranspiration (ET). In progressively wetter climates, the soil mantle is more likely to reach a state of high wettness or saturation resulting in more surface runoff and throughflow to deeper layers and groundwater.

The importance of soil water is readily apparent when reviewing a description of almost any hydrologie or agricultural system. The infiltration and évapotranspiration processes, in particular, are strongly related to the time-depth status of the soil-water profile. Most groundwater recharge occurs only after the soil profile becomes significantly wetted. Crop production is highly dependent on having adequate available soil water throughout the growing season. Any attempt to estimate crop yields must include soil-water effects.

The objective of this paper is to briefly review recent advances in the simulation of soil water with particular emphasis on those aspects pertinent to soil-water balance computations for hydrologie and agricultural applications. Mathematical representations of the major processes will be described and simulation models reviewed which integrate these into predictive systems.

RECENT ADVANCES

Numerous developments have occurred in recent years that have significantly enhanced the knowledge and predictability of soil water occurrence. Most of these have been incorporated into computer

Soil water hydrology 49

simulation methods, which in themselves have provided insight and predictive capability. While too numerous to describe fully, several advancements merit review and referencing.

Soil water occurs as a result of several processes that operate within the time line either sporadically or more continuously. Very simply, precipitation is the principle resupply, soil porosity is the storage medium, and évapotranspiration accounts for the majority of depletion. The variables and process equations involved within this total system are numerous and complex. The ability to assemble these equations into computer simulation methods has been the most important advance in recent years.

The inputs and descriptions for these soil water simulations can be categorized into those related to climate, soils, and plants. Climate includes both precipitation and those variables related to the ET potential.

Daily precipitation is the most common input to soil water balance models. Measured values are most often used if available near the study site. But recent efforts for long-term studies or locations away from measurement locations have caused the development of improved stochastic methods. Richardson (1981) and Woolhiser & Roldan (1982) report good success with a spatially distributed parameter model which maintains the statistical characteristics of the regional precipitation pattern while providing random-based sequences. Orsborn et al. (1982) provide a useful summary to several methods and considerations for precipitation inputs to water budget simulât ions.

Most évapotranspiration methods begin with a climatically deter­mined potential ET rate for each day (Saxton et al., 1974a). The inputs vary from only air temperature or pan evaporation to a full complement of radiation and aerodynamic descriptions. It is often necessary to estimate these inputs; and, again, recent progress has been made. The methods of Richardson (1981) in particular provided good statistical methods based on limited data. Intercorrelations among precipitation, solar radiation, and air temperatures were considered in their techniques.

Vegetation plays a significant role in the ET process; thus to simulate soil water requires an adequate description of the growth state and water-related functions. This is especially important where agricultural crops are involved because they rapidly change over the course of a growing season. Descriptions of this biological phase of water balance computations are some of the most difficult. The above-ground growth is often described by time distributions of crop canopy or leaf-area index (Saxton & McGuiness, 1982) and include crop residues. The phenologic development may be a part of crop coefficients (Jensen, 1973; Wright, 1982) or described separately (Saxton et al., 1974b).

Root effects are perhaps the least understood. They have been described by some as a time-varying rooting depth with a density distribution (Ritchie, 1972), or an effective water uptake time-depth distribution (Saxton et al., 1974b). Taylor & Klepper (1973) provide a detailed description for corn, but much actual detail as to how to mathematically represent the root effectiveness is still lacking.

Plant water stress is another area difficult to represent mathem­atically. Leaf-water potentials and resistances through the leaves,

50 Keith E.Saxton

stems, and roots have been described and measured (Salisbury & Ross, 1978; Gates, 1980). Some have incorporated this approach even though definitive numbers are yet very empirical. The work of Denmead & Shaw (1962) provides a summary of empirical relationships which incorporate the plant response in relation to atmospheric demand and available soil water.

Methods to describe the soil characteristics for holding and transmitting water have received considerable recent advancement. While the concepts of soil tensions and conductivities in relation to soil features have been described for decades, recent mathematical and statistical analyses of voluminous data have provided significant predictive advancements for hydrologie purposes. Rawls et al. (1982) analysed over 5000 tension curves to develop predictive equations based on soil texture, bulk density, and organic matter. Brakensiek et al. (1981) extended these analyses to determine within-texture variation. Arya & Paris (1981) provided a tension equation based on pore-size distribution which is potentially useful, and Campbell (1974) described predictive equations for tension and conductivity. These and other results will all contribute considerably toward much improved soil relationships for hydrological soil water balance computations.

SOIL WATER BALANCE MODELS

There have been several models developed in recent years that incorporate some or most of the modern process representations just discussed. These have a very wide range of detail and complexity depending upon the data available, the system being represented, crops to be considered, and relative emphasis among the several system processes. A few of these methods will be reviewed to provide a perspective from the simple to more complex. Experience has generally shown that the accuracy of the results is somewhat in proportion to the complexity, thus each user must select an appropriate method according to the study needs.

A simple daily water budget based on an equation of the type

ARl± = (ARI^j + n±_1) K (1)

where ARI = antecedent retention index for day i, R = daily retention (infiltration), and K = a seasonally varied coefficient less than 1.0, was adopted from an exponential antecedent precipitation index (Saxton & Lenz, 1967). Daily estimates of actual ET provided reasonable estimates of antecedent soil moisture as compared with observed soil moisture data. Guidelines for estimating K coeffic­ients were provided.

Haan (1972) simulated daily ET in a model written to estimate monthly streamflow from daily precipitation by the relationship

E = Ep(M/C) (2)

where E = actual ET (mm day - 1), E p = potential ET by the Thornthwaite method (mm day- ), M = available soil moisture (mm), and C = maximum available soil moisture (mm). Twenty-five millimetres of soil

Soil water hydrology 51

moisture were made readily available and the ratio M/C was set to 1.0 until that was depleted. On days with rainfall, E p was divided by 2 to account for cloudy conditions. Such a simplified scheme will only work well where monthly or seasonal results are being analysed and only then with calibration for crop and soil conditions.

A similar single equation approach was applied by Holtan et al. (1975) and England (1975). Their equation is

ET = (GI) k E [<S - SA)/S]X (3)

where ET = actual ET (mm day - 1), GI = growth index of crop (%), k = ratio of ET to pan evaporation for full canopy, EP = pan evaporation (mm day - 1), S = total soil porosity (%), SA = available soil porosity (%), and x = exponent estimated to be 0.10. The GI values reflect crop growth and harvest and are time dependent. The soil storage values S and SA for the root zone approximate water stress although a more precise representation which includes root development and crop stress would significantly improve this aspect. Betson (1976) used a modification of this approach for monthly ET estimates.

Soil moisture depletions (actual ET) for irrigation scheduling have been estimated by Jensen et al. (1971) by the relationship

ET = Kc E t p (4)

where ET = actual ET (mm day - 1), E t = potential ET (mm day - 1), and Kc = a coefficient representing the combined effects of the resistance of water movement from the soil to the various evaporating surfaces, the resistance to the diffusion of water vapour from the surfaces to the atmosphere, and the relative amount of radiant energy available as compared with the reference crop. This inclusive coefficient was estimated as

Kc = Kco Ka + Ks <5)

where Kco = mean crop coefficient based on experimental data (soil moisture not limiting), Ka = In (AW + l)/ln 101, AW = remaining available soil moisture (in), and Kg = the increase when the soil surface is wetted and equals (0.9 Kc) times 0.8, 0.5, and 0.3 for day 1, 2, and 3 after wetting. This method has worked successfully for irrigated conditions where soil water seldom limits transpiration and considerable calibration of the several coefficients has been conducted.

Morton (1975, 1976) presented a method based on regional climatic data and showed its application to many large basins in the USA and Canada. Hanson (1976) and Aase et al. (1973) have developed ET prediction equations for native rangeland of the western USA. Grigel & Hubbard (1971) describe an empirical ET model, SOGGY.

Other methods have restricted their data inputs to readily available climatological data which often makes them more practical than more sophisticated methods. Eagleman (1967) described a method based on air temperature and humidity. Brun et al. (1972), Kanemasu et al. (1976), and Rosenthal et al. (1977) described methods using air temperature, Rn, and LAI. Jensen et al. (1971) discussed a similar practical approach for irrigation scheduling, but the

52 Keith E.Saxton

technique can be modified and applied to hydrological needs. Several methods have been developed which describe the ET

processes within the soil-plant-atmosphere system. The soil-plant-atmosphere model (SPAM) described by Lemon et al. (1973) and Shaw-croft et al. (1974) treats the ET and plant growth characteristics in detail. A similar model reported by Hanks et al. (1969) and Nimah and Hanks (1973a, b) concentrates more on the soil moisture and its plant interaction. A model by Goldstein & Mankin (1972), PROSPER, represents the same system with emphasis on forested basins.

Even more sophisticated models are being developed as new

POTENTIAL ET

\ I INTERCEPTION

\

SOIL EVAPORATION •

I POTt \ \

T M ST, 0-6m

I ACTUAL SOIL EVAPORATION

\ TiME of YEAR

UNUSED ENERGY

% TRANSFER to CANOPY

/ OTHER

ENERGY SINKS

TRANSPIRATION

POTENTIAL

TRANSPIRATION

ACTUAL

TRA NSPIRA TION

\ PHENOLOGICAL STATE

% of CANOPY TRANSPIRING

TIME of YEAR

I ROOT DISTRIBUTION, %

SOIL DEPTH,

tee!

TiME of YEAR

ACTUAL ET

• ACTUAL ET

WITHDRAWAL

FROM SOIL

MOISTURE

SOIL MOISTURE REDISTRIBUTION

zW

!»»»«* ̂ ' ,»\«v ̂ ' A \ * ' ̂ ,*«*

INFILTRATION

«^ ,\«* ̂l •

SOIL MOIST.,%

q = (k) a i ^ i - (Af )

I FIG.l Schematic computational sequence of the SPAW model (Saxton et ai., 1974b; Sudar et al., 1981).

Soil water hydrology 53

capability in computing capacity and ease of programming is available. Kristensen & Jensen (1975) applied a detailed ET model to the crops of barley, sugar beet and grass over a 4-year period with reported accuracy of 10%. Van Bavel & Ahmed (1976) described a model of the soil moisture flow and root uptake programmed in CSMP. Hansen (1975) reported a more general model of the soil-plant-atmosphere system programmed in DYNAMO II. Lambert & Penning deVries (1973) presented a model of the ET system called TROIKA. Van Keulen (1975) presented a model programmed in CSMP with all details well described, and Makkink & van Heemst (1974) showed the application results of a similar model.

A comprehensive model to compute daily actual ET from small basins was developed and reported by Saxton et al. (1974b) and revised as shown by Sudar et al. (1981). This model, shown schematically in Flg.l, separates the major climatic, crop, and soil effects into a calculation procedure with emphasis on graphical representation of principle relationships. Calculated amounts of interception evaporation, soil water evaporation, and plant transpiration are combined to provide daily actual ET estimates.

Beginning at the top of Fig.l, intercepted water at the plant and soil surfaces is considered to have first use of the potential ET energy, and no resistances are imposed. Remaining potential ET is divided between soil water evaporation or plant transpiration according to the plant canopy present described by soil shading or leaf-area index. Actual soil evaporation is the potential limited by soil water content at the surface, except in the very wet range, thus represents the traditional two-stage drying sequence. For dry soil with a plant canopy, a percentage of the unused soil water evaporation potential is returned to the plant transpiration potential to account for re-radiated energy from the heated soil and air. Actual transpiration is computed through sequential considerat­ion of plant phenology to describe the transpirabillty of the existing canopy, a root distribution to reflect where in the soil profile the plant is attempting to obtain water, and a water stress relationship which is applied to each soil layer and is a function of the plant-available water of the soil layer and the atmospheric demand on the plant. The soil water is adjusted by abstracting the daily actual ET from each rooting layer, adding daily infiltration computed from daily precipitation minus measured or estimated runoff, and estimating soil water redistribution and percolation by a Darcy-type unsaturated flow computation.

EXAMPLE SOIL WATER SIMULATIONS

Results using the SPAW model just described readily illustrate the computations which can now be obtained for water balance simulations of the soil water. This model utilizes minimal input data and moderately complex computations to provide quite reasonable computation costs of 1-2 cents per computation day on IBM-Amdahl large-scale computers. The accuracy is accordingly not as precise as that expected from more complex models, but accurate enough for most hydrological water balances.

Figure 2 shows the time distribution of soil water for several

54 Keith E.Saxton

I 2 - ! 8 m

' MAR rTpR~+"l^A7~"VjÏÏN~n JUL ' AUG l ^ s I F 1 O c T i N o F

FIG.2 Observed soil water in soil layers vs. that simulated by the SPAW model for Iowa corn field during 1970 (Saxton et al., 1974b).

layers of a silt loam soil during the growing season of corn. The simulated results provide a reasonably accurate representation of the observed data which were obtained with the neutron scatter technique at three sites within a 32-ha field. The dynamics of the soil water in the upper layers are quite apparent and resulted from the 780 mm of precipitation during the April-October growing season.

The simulations in Fig.3 demonstrate a significant contrast to those Fig.2, where the data are for a growing season of winter wheat where nearly all precipitation occurs during the winter months. With appropriate climatic data and crop and soil parameters, the SPAW model was used to provide good water budget simulations. The silt loam soils are fallowed for one year prior to the winter wheat crop year because annual precipitation averages only 300 mm in this location.

Soil water hydrology 55

The data of Table 1 further illustrate the effectiveness of simulating soil water hydrology. These values were computed using measured climatic data, soil characteristics from soil series descriptions, and mean growth characteristics for corn (maize) for 11 selected sites along a transect which had annual average precipit­ation ranging from 450 to 1050 mm and lake evaporation (potential ET) ranging from 1040 to 1890 mm during the 10 years of continuous

3 0 - 0-20 err

10-

30^ 20-45 cm C A L C U L A T E D

O B S E R V E D

90 -150 cm 10-

2 0 - , , —

1 0 J

150-200 cm 20-1.--- ' "

J F M A M J J A S 0 N D

FIG.3 Observed soil water in soil layers vs. that simulated by the SPAW model for eastern Washington wheat during 1980.

simulation for each site. The columns of Table 1 represent the USWB station numbers in Kansas and Missouri (USA) and average annual values of potential ET, actual ET, soil water evaporation,

TABLE 1 Mean annual water simulated by the SPAW model

budget for 10 years (1967-1976) as

Station ID

(nun)

1699 58 52 4857 8259 6333 6014 3300 6563 4978 5671 6633

KS

KS

KS

KS

KS

KS

MO

MO

MO

MO

MO

Pot. ET (mm)

1887 1689 1438 1313 1321 1280 1224 1102 1062 1044 1016

Act. ET

(mm)

391

497

586

571 584

584

683

665 653

645 652

Soil evap. (mm)

132 218

226

84

91

91

152

157

168

145

160

Plant trans. (mm)

137

142

208

335

330

338

35 3 325

305

312

302

Inter. evap. (mm)

122

137

152

152

163

155

178

183

180 188

191

Prec.

(mm)

457

5 8 9 704

861

892

919

871

871

937

1054 1006

Run­off

(mm)

61

81

113

185

180 206

135

122

218

292

274

Deep perc. (mm)

3

3

0 94

114

122

64

89 71

104 86

Plant stress

41 .6 33. 7 28.7 16.2 16.4 14.0

9.8

5.8

5.9

6.3

5.0

Yield red.

8.4

7 . 5

6.6

3.4

3.7

3.0

2.0 1.3

1.5

1.1 1.2

56 Keith E.Saxton

transpiration, intercepted water evaporation, precipitation, runoff, deep percolation, plant stress (accumulative index), and crop grain yield reduction (accumulative index). Only precipitation and potential ET (reduced pan evaporation) are measured values.

The average values in Table 1 show the general rainfall disposition into and out of the soil profile. More detailed outputs, which are readily available, show the dynamic changes that occur day-to-day (like those of Figs 1 and 2) and result in many important inter­actions in relation to hydrology and crop production. The consistent trends and relative magnitudes of the Table 1 values show the adaptability and utility of simulation models such as SPAW even without voluminous verification data. However, as in this case, some data are nearly always necessary for original model calibrations.

RESEARCH NEEDED

While there have been significant advances in nearly all aspects of soil water simulations, there are many facets that yet need to be further defined. Always the accuracy of the simulation method must be considered with respect to the study objectives. For broad-scale, longer-term water budgets, several existing models may be adequate. For more defined conditions where crop, soil, or climatic conditions may result in subtle, yet very meaningful differences, the degree of accuracy is severely limiting.

Essentially every relationship in every simulation method could command further refinement. But obviously some are more important depending on study objectives, thus sensitivity analyses should be applied to suggest the relative importance and accuracy. In general, it appears at this time that the plant physiology descriptions are the least well known. The root distribution and soil-root inter­actions, within plant reactions, and the leaf-atmosphere boundary layer, all play a dominant role in coupling the soil water to the evaporative demand. Good simulation descriptions for this system have yet to be developed.

The physics of soil water storage and conductivity have been diligently studied for many years, yet the description of soil-water characteristic relationships over a landscape is possible only in a general way because of spatial variation and complex changes with the biological and physical soil development processes. Methods to adequately represent the soil-water relationships for applied simulation need considerable further study. Each simulation method, data, and internal representation needs careful evaluation to define the research for additional applied knowledge.

CONCLUSIONS

Soil water hydrology is an important portion of the overall hydrological regime of any landscape and merits detailed study and evaluation just as has surface water hydrology and groundwater hydrology. While soil water hydrology is quite dependent on climatic inputs, soil characteristics, and the vegetation being grown, there have been significant recent advancements which describe these

Soil water hydrology 57

physical processes as they interact with soil water and each other such that several simulation models have been developed that provide good results and insights for hydrological water balances. Simulations by the SPAW model for corn and wheat in significantly different climates demonstrate this capability.

Simulation models of soil water have a broad range of detail and complexities. The amount of input required and accuracy of results are closely related to this spectrum. This simulation capability will continue to enhance our understanding of the soil water hydrological system plus provide representations for broad-scale hydrological simulation models which incorporate the soil water system. Further research with emphasis on plant and soil processes is necessary to develop a level of accuracy and flexibility for good results over a broad range of hydrological situations and objectives.

ACKNOWLEDGEMENTS Contribution from the Agricultural Service, US Department of Agriculture, in cooperation with the College of Agriculture Research Center, Washington State University, Pullman, Washington 99164, USA. Scientific Paper no. 6620.

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58 Keith E.Saxton

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Soil water hydrology 59

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