Soil Water Balance in the Sudano-SaheUan Zone (Proceedings of the Niamey Workshop, February 1991). IAHS Publ. no. 199,1991.

Review of models for predicting soil water balance

R. J. LASCANO Texas Agricultural Experiment Station, Route 3, Box 219, Lubbock, Texas 79401-9757, USA

Abstract In this paper the application of models to study the soil water balance is reviewed. The difficulty in measuring components of the soil water balance has prompted the use of simulation models to investigate the processes involved. Simulation models integrate levels of knowledge about separate parts of a system and they can be used as exploratory tools to investigate solutions to problems that in agriculture are normally site-specific. Models are simplified representations of the real system and must be used with precaution. It is imperative that proposed algorithms used in the models be tested by comparing simulated results with independently obtained real data. This review is structured in four sections. First, modelling and simulation terms are defined, strategy of model building and verification are presented, and types of models are outlined. Second, the concept of soil water balance is given. Third, examples of types of soil water balance models are delineated, and fourth, an energy-water balance model is applied to simulate water use by a sorghum crop.

INTRODUCnON

In recent years population growth worldwide has resulted in increased intensification of land and water use in an effort to increase agricultural production. This is a global problem and it is most acute in Africa, where the combination of record population growth and widespread land degradation is reducing grain production per person. It is not surprising that the WorldWatch Institute in their 1990 State of the World Report notes that "The world's farmers are finding it more difficult to keep up with growth in population" (Brown, 1990). For example, in Africa a drop of 20% in grain production from the peak in 1967 has converted the continent into a grain importer. To increase agricultural production it will be necessary to apply technological innovations to enhance the efficiency of soil and water management. Exploratory work can be done with models to investigate possible solutions to problems that are usually site-specific. There is much knowledge about separate parts of a system, but it is difficult to connect these pieces of information (Ferrari, 1978). It is in this context that the role of models and simulation techniques can be used to address specific areas of agricultural research.

This paper is organized in four sections. First, modelling and simulation

443

R. J. Lascano AAA

terms are defined and types of models are discussed; second, the concept of soil-water balance is reviewed; third, examples of soil-water models are outlined; and fourth, an energy-water balance model (Lascano et al, 1987) is used to simulate the water use of a sorghum crop in a semiarid environment.

SYSTEMS, MODELS AND SIMULATION

The aim of this section is to present basic definitions of terms used in modelling and simulation. Also, a brief review of the strategy of model-building and model verification, and types of models is presented.

Definitions

Definitions of system, models and simulation are given by de Wit (1982). A system is a limited part of reality that contains interrelated elements, a model is a simplified representation of a system and simulation is the art of building mathematical models and the study of their properties in reference to those of the systems. A mathematical model is simply an equation or set of equations which represents the behaviour of a system (France & Thornley, 1984).

In recent years the terms artificial intelligence and expert systems have been used to describe a wide array of computer applications. Artificial intelligence is that branch of computer science that deals with ways of representing knowledge using symbols rather than numbers and with rules-of-thumb, or heuristic, methods for processing information (Mishkoff, 1985). Expert system is a computer program which contains both declarative knowledge (facts about objects, events and situations) and procedural knowledge (information about courses of action) to emulate the reasoning processes of human experts in a particular domain. There are two types of expert systems: rule-based and model-based. The components of an expert system are a knowledge base, an inference engine, and a user interface (Mishkoff, 1985). The inference engine controls the operation of the expert system by selecting the rules to use, accessing and executing the rules, and determining when a solution has been found. The user interface allows bi-directional communication between the expert system and the user, e.g. natural language processing.

Hardware versus software

In computer terminology hardware refers to machinery that makes up a computer system and software to the instructions for the computer to execute. Examples of hardware include a disk-drive, modem, printer, microprocessor, etc., and examples of software include programming languages such as,

445 Review of models for predicting soil water balance

Fortran, Pascal, LISP, CSMP and Basic, and operating systems such as, MS-DOS, UNIX, Wylbur, and OS/2.

In the past, execution of complex agricultural models was restricted to large main-frame computers which are normally operated by universities or large corporations. However, with the miniaturization of processors and increase in speed, it is now possible to execute complex operations and instructions at the personal computer level. For example, a computer with an Intel 80486 processor operating at 33 MHz clock speed is truly a "number cruncher" that can execute up to 107 instructions per second. In addition, the added power of modular programming languages, e.g. Pascal and C, have made the coding of simulation models easier to write and more importantly easier to understand.

Type of models

According to France & Thornley (1984) agricultural models can be divided as follows. An empirical model is based on observed qualitative relationships and sets out principally to describe; whereas, a mechanistic model is based on known principles and attempts to give a description of the system with understanding. A static model is a model that does not contain time as a variable and a dynamic model contains the time variable explicitly. A deterministic model does not have random variables and makes definite predictions, and a stochastic model contains some random elements or probability distributions. In reality most agricultural models are a combination of the several types of models.

Models can be solved by either analytical or numerical techniques. Analytical models are ones in which all relationships are expressed in closed form so that the equations can be solved by the classical methods of analytical mathematics. Numerical models are ones in which the governing equations are solved by means of step-by-step numerical calculations. Most agricultural models include equations that require both types of solution.

Strategy of model-building

The strategy of model-building is to distinguish the various levels of knowledge that conform the system. Each level of knowledge is characterized by the level of organization within the systems or by the relaxation times of phenomena, i.e. the time necessary for the recovery from small disturbances (Boulding, 1956; de Wit, 1970). Each level has its own principles and each level is an integration of items from lower levels. To build a model is to join two levels of knowledge. The level with the short relaxation times is the level which provides the explanation (explanatory level) and one with the long relaxation times, the level which is to be explained (explainable level).

The construction of a simulation model is still as much an art as a science. There is no systematic nor objective way of building a simulation

R. J. Lascano 446

model. Nevertheless, Hillel (1977) identified 14 distinct and sequential phases in the construction and operation of a simulation model. These phases in the form of a flow chart are shown in Eg. 1. The 14 phases are self-explanatory; however, an important one is the verification of the model by comparing simulated results with independently obtained real data.

EXAMINE SYSTEM'S BEHAVIOR

DEFINE PROBLEM REQUIRING SIMULATION

31 FORM CONCEPTUAL MODEL

\ -FORMULATE MATHEMATICAL MODEL

X DEVELOP ALGORITHMS

CHECK ALGORITHMS REJECT

ACCEPT

CODE COMPUTER MODEL

ESTIMATE PARAMETERS

REJECT

CONDUCT SIMULATION EXPERIMENTS

REJECT MODEL -<f «^ CHECK RESULTS

ACCEPT MODEL

^ REJECT SIMULATION COMPARE PREDICTIONS ^ ^ , y

VS FACTS - ' "

ACCEPT SIMULATION

APPLY SIMULATION TO SOLVE PROBLEM

Fig. 1 Phases in the construction and operation of a simulation model (from Hillel, 1977).

447 Review of models for predicting soil water balance

Verification of models

Scientific theory cannot advance without experimentation and the same holds true for simulation models. Concepts and processes that are used to simulate the behaviour of the system must be verified by doing experiments with the model and the actual system, both, on the explainable level (Penning de Vries, 1977). For instance, the simulated output of crop growth must be compared to measured values obtained from a field experiment. In many cases results obtained with the model and the actual system will not agree and the user may be tempted to "adjust" model parameters and equations to produce a better fit. However, as pointed by de Wit (1970) "it is a disastrous way of working because the model degenerates then from an explanatory model into a demonstrative model ... the technique reduces into the most cumbersome and subjective technique of curve fitting that can be imagined."

Testing and evaluation of a model is a continuous process. Testing refers to the correctness of the model, i.e. the mathematical equations must correctly represent the stated assumptions. Evaluation is concerned with aspects such as, plausibility, goodness-of-fit, elegance, simplicity, and utility (France & Thornley, 1984).

SOIL-WATER BALANCE

The water balance is simply a statement of the law of conservation of matter, i.e. matter can neither be created nor destroyed but can only change from one state or location to another. The water content of a given soil volume cannot increase without addition from the outside, nor it can diminish unless transported to the atmosphere by evaporation or to deeper zones by drainage (Hillel, 1971).

In its simplest form, the water balance equation states that, changes in volumetric water content of soil over a period of time are equal to the difference between the amount of water added Wm and the amount of water withdrawn Wout during the same period:

tjy = W- - W , (1) m out K±J

AW will be positive if gains exceed losses; and conversely, AW will be negative when losses exceed gains. The terms of the water balance are normally expressed in units of volume per unit area, e.g. mm.

For a given soil volume, gains and losses of water can be itemized as follows. The amount of water added Win may be precipitation, RF or irrigation Ir, or both:

Wia = RF + IT (2)

and the losses of water WQUt may be due to the processes of runoff ROFF, drainage D and soil evaporation, E and crop transpiration, T:

R. J. Lascano 448

WQUt = ROFF + D + E + T (3)

In the above equation ROFF is normally a loss of water, but it may also be a gain if water enters the field from an adjacent one. Drainage D refers to the the water draining out of the root zone and may also be positive depending on whether the flow is upward or downward.

The integral form of the water balance equation is given by:

AW = RF + IT - ROFF -D-QE + T) (4)

with the various components summed over a time period. This equation can also be written in differential form, by expressing the time-rates of the simultaneous fluxes. In either case, integral or differential form, the equation must obey the mass-conservation law.

Measurements of the components of the water balance equation are essential to maintain a water budget. However, lysimetry is the only hydrological method in which the experimenter has a complete knowledge of each of the terms of the water balance equation. Because of this difficulty the modelling of the soil-water balance equation has been a favourite subject of many scientists. This is the topic of the next section of this paper.

SOIL-WATER BALANCE MODELS

In this review soil-water simulation models are grouped into three categories based upon the hierarchy or degree of complexity of the system modelled. First, starting with the simplest case models that simulate water infiltration in a bare soil are reviewed. Second, models that also include the process of evaporation and thus the energy balance at the bare soil surface are presented. Third, simulation models that include plants and thus the process of transpiration are outlined.

Infiltration

Mechanistic approach In these types of models the soil-water balance is simply AW = (RF + IT) - ROFF -D. Evaporation at the soil surface is set to zero and the quantity of water entering the soil (RF + / ) is described by the process of infiltration. Drainage, D, is usually assumed to be zero at a depth well below the root zone and ROFF is calculated as the difference between the RF and the infiltration rate subject to conditions of soil surface sealing, ponding, etc. However, to simulate the changes of water content with respect to time in the vertical dimension we must use Darcy's law, the basic equation describing isothermal water flow through a porous media:

/w = -£(e)8Y/8Z (5)

where / is water flux density in m s"1, K(e) is the unsaturated hydraulic

449 Review of models for predicting soil water balance

conductivity in m s"1, a function of the volumetric water content (9), and 6Y/6Z is the hydraulic head gradient, Y is the sum of pressure and gravitational potential, and Z is the vertical soil depth, both expressed in m. To obtain the general flow equation and account for transient, as well as steady, flow processes, we must introduce the continuity (conservation of mass) equation:

se/Sr = -SJJSZ (6)

where t is time in seconds. Combination of the Darcy and continuity equations results in what is commonly referred to as the Richards equation (Richards, 1931):

88/8f = 5/6Z [K{Q)WI§Z\ (7)

This second order nonlinear partial differential equation cannot be solved analytically and thus changes in water content (6) with time (t) and depth (Z) must be solved by numerical methods with appropriate boundary conditions (e.g. Hanks & Bowers, 1962; Van Keulen & Van Beek, 1971; de Wit & Van Keulen, 1972; Lascano & Van Bavel, 1983; Lafolie et ai, 1989). To obtain analytical solutions to the Richards equation it must be transformed to a diffusion form for which ready solutions are available (e.g. Carslaw & Jaeger, 1959). The treatment of this subject is beyond the scope of this review.

Infiltration rate can be described by either solving the Richards equation or by considering a relationship between cumulative infiltration and time expressed as a function of some empirical or physical infiltration parameters. Examples of procedures to calculate infiltration into soils are given by Green & Ampt (1911), and Philip (1957), and more recently by Baumhardt et al. (1990) and Haverkamp et al. (1990).

Empirical approach An example of an empirical calculation of the soil-water balance is the one used in the EPIC model (Williams et al, 1984; Steiner et al, 1987). In EPIC a different notation is used and this is reproduced here for consistency. Runoff (Q) is calculated with:

Q = (R - Q.2s)2/R + 0.8s (8)

where R is the daily rainfall in mm and 5 is a retention parameter, whose value is calculated by:

s = smx{l - 8/[9 + exp (Wl - W2&)]} (9)

where smx is the upper limit of s, 9 is the volumetric water content, Wl and Wl are shape parameters.

The rate of water movement through a layer i (Oi in mm day"1) is calculated when the water content (SW^ exceeds the upper limit of available soil water (UL). Water in excess of ULi is divided into 4 mm increments for

R. J. Lascano 450

routing through the soil profile to allow for a reduced K(&) as 0 decreases. The storage is based on the equation:

°i = SWoi t1 " tlTÏ\ (10)

where SWoi is the water content of layer i at the beginning of the day in mm, t is the time interval (24 h) and TT is the travel time through layer / in hours. TT is calculated as:

TT = (SWi - UL)lq (11)

where q is the saturated hydraulic conductivity in mm h"1. In this model water that is held in a soil layer above the ILt drains during subsequent days. Also, water is not allowed to flow from layer i if the layer below is saturated.

Infiltration and evaporation from a bare soil

Mechanistic approach The water balance for this system is given by (AW = (RF + Jr) - ROFF - D - E.) The fate of (RF + Jr), ROFF and D are treated as explained in the previous section. To mechanistically simulate E we must take into account the major factors that determine the evaporative flux, i.e. the energy balance of the soil surface. Such a procedure was first given by Penman (1948) and is called the combination method because it combines the surface energy balance with the simultaneous transport of heat and water above the surface. The energy balance at the soil surface is given by:

Rn+LE+A+S = 0 (12)

where Rn is the net irradiance in W m"2, LE is the product of the latent heat of water L in J kg"1 and the evaporation rate E in kg m"2 s"1, A is the sensible heat flux to the air in W m"2, and S is the soil heat flux in W m"2. In this equation fluxes towards the surface have a positive sign. During the daytime Rn is positive, LE is negative, and A and S are generally negative.

The value of RR is found as:

Rn = (1 - «)i?g + /?, - €o(Ts + 273.16)4 (13)

where a is the soil albedo, a function of the water content of the superficial layer, R is the incoming shortwave irradiance in W m"2, R{ is longwave sky irradiance in W m"2, 6 is the surface emissivity a function of the superficial water content, a is the Stefan-Boltzmann constant (5.67 x 10"8 W m"2 K"4), and Ts is the surface temperature in °C.

The term Rl can be calculated from a number of different functions that relate i?, to air temperature (Ta) and humidity (Ha) (e.g. Brunt, 1939; Kimball et al, 1982;). Van Bavel & Hillel (1976) used the following equation to calculate R,:

451 Review of models for predicting soil water balance

Rt = 0(Ta + 273.16)4 [0.605 + 0.048(1370//a)^ (14)

where Ta is the air temperature (°C) at screen height, and H& is absolute humidity of air at the reference level of 2 m above the surface in kg m"3.

Functions that relate a and e to the surface water content are given by ten Berge (1986).

The value of E is calculated from:

E = (Hs - Ha)/Rc (15)

where Hs is absolute humidity of the air at the soil surface in kg m"3 and depends not only upon the surface temperature Ts, but also on the surface water content (Van Bavel & Hillel, 1976):

Hs = H0 exp['P1/46.97(rs + 273.16)] (16)

where HQ is the saturation humidity at 2", Yj is the pressure potential associated with the 9j of the surface layer. This approach is approximate in that it assumes that the water content of the surface layer is equal to that at the very surface. In numerical models the surface layer should be 0.005 m thick or less; otherwise, serious errors are introduced in the calculation of E (Lascano & Van Bavel, 1986). Rc is the reciprocal of the turbulent transfer coefficient, the aerodynamic resistance between the soil surface and the reference elevation in s m"1 and is given by:

Rc = Ra St (17)

where Ra is the adiabatic or neutral value of Rc and St is the stability correction. For a more detailed review of this subject the reader is referred to Monteith (1973) and Pruitt et al. (1973). As an example Rc under stable condition (St = 1) can be calculated by:

Rc=Ra = [ln(2.0/Zo)]2/0.16£/a (18)

where ZQ is the surface roughness length in m and Ua is the wind speed in m s"1.

The sensible heat flux A is calculated from:

A = (Ts - Ta)C/Rc (19)

where Ts is the soil surface temperature and T& the air temperature at screen height, both in °C and C is the volumetric specific heat of air in J m"3.

The remaining term in the energy balance, the soil heat flux S, is calculated from (de Vries, 1966):

S = 2{TX - Ts) Kl/Dl (20)

where T, is the soil temperature at the centre of the surface layer in °C, K^ is

R. J. Lascano 452

the thermal conductivity in W m"1 s"1 and D, is the soil layer thickness in m. The time rate of the change in water content (de/dr) of the top layer is

found using equation (7) and must equal the flux at the surface E minus by the flux of water across the bottom.

Analytical solutions of the energy balance equation can only be achieved by introducing simplifying assumptions limiting their use and application. Examples of analytical solutions to the energy balance are given by Pratt et al. (1980) and Milly (1984). These types of models are mainly coupled with remote sensing observations. Examples of numerical solutions of the energy balance are given by Sasamori (1970), Van Keulen (1975), Van Bavel & Hillel (1976), Lascano & Van Bavel (1983), Camillo et al. (1983) and ten Berge (1986) among others.

Empirical approach An empirical approach to calculate E is given by Ritchie (1972) where E from a bare soil is calculated on a daily basis. The calculation of E is based on the premise that soil evaporation takes place in two stages. First, the constant rate stage and second, the falling rate stage. During the constant rate stage E occurs at the potential rate until the upper limit (UL) of stage one is reached. This UL is a function of soil texture and varies between 5 mm in sands to 14 mm of water in clay loams. The falling stage rate is more dependent on the hydraulic properties of the soil and less dependent on the available energy at the soil surface. Cumulative evaporation in stage two from an initially wet soil is given by:

IE = ktVl (21)

where k is an empirical constant determined from cumulative evaporation data for a single drying cycle on a given soil. Measurements of k consistently result in values of about 3.5 mm day"̂ 2 (Ritchie & Johnson, 1990). This approach is also used in the EPIC model (Williams et al., 1984) and CERES-type models (Jones et al., 1986).

Energy and water balance of a soil-plant system

To mechanistically describe soil and crop evaporation the water and energy balance for both the soil surface and the crop canopy must be considered separately. Examples of these type of models are given by Norman & Campbell (1983), Chen (1984), Shuttleworth & Wallace (1985), Lascano et al. (1987), and Dierckx et al. (1988).

The distinguishing characteristic of the models of Shuttleworth & Wallace (1985) and Lascano et al. (1987) is the use of a "soil resistance" term to calculate latent and sensible heat fluxes from the soil surface into the boundary layer above as suggested by Monteith (1981). For further discussion of the soil resistance term the reader is referred to Shuttleworth & Wallace (1985) and Choudhury & Monteith (1988).

A schematic diagram of the mass and energy flow below and above the soil surface, and above the plant canopy as modelled by Lascano et al. (1987)

453 Review of models for predicting soil water balance

is given in Fig. 2. The objective of this model, hereafter referred to as ENWATBAL, is to calculate the soil and crop evaporation. At each time step, ENWATBAL calculates and updates values of soil water content (e.) and temperature (T.) for each soil layer. From these values the interlayer fluxes of water and heat below the soil surface are calculated. At the soil surface, the fluxes LE, A, Rn, and S are calculated from an energy balance solution. Similarly, for the single-layer plant canopy the latent heat (LE ), net radiation (Rnc), and sensible heat (A) fluxes are also calculated. In ENWATBAL the disposition of radiant energy by the plant canopy and the soil surface, as a function of leaf area index (LAI), were calculated from the Chen (1984) model.

| S ( 1 ) 111 I

'S(2)

! I Jw(i)

PLANT CANOPY

SOIL SURFACE

LAYER (1)

LAYER (2)

Fig. 2 Schematic diagram of the energy and mass fluxes below and above the soil surface and above the plant canopy. Variables with units are given in the text (from Lascano et al, 1987).

Inputs to ENWATBAL are the intial soil water and temperature profiles, soil moisture retention curve and unsaturated hydraulic conductivity for each soil horizon. Plant input parameters are the LAI as a function of time and the root distribution as a function of soil depth and time. Weather inputs are daily total irradiance, daily maximum and minimum air and dewpoint temperatures, daily wind speed, and the quantity of rain or irrigation.

The ENWATBAL model was tested by comparing measured and calculated values of soil and crop evaporation, and soil surface and crop canopy temperatures over the growing period of a dryland cotton crop in the High Plains of Texas (Lascano et al., 1987; Lascano, 1989). From these comparisons it was concluded that simulated values of soil and crop

R. J. Lascano 454

> < - I 3 S O Q LU LT

05 < LU 2

E E

LU

5 oc

s CE O D. < > LU J

5

5 0 0 -

4 0 0 -

300 -

2 0 0 -

1 0 0 -

Oi

y = 0.988 x + 4.78 / SE slope = 0.015 V *

(a)

0 100 200 300 400 500 600

SIMULATED CUMULATIVE (E+T) in mm

(b)

215 216 217 218 219

DO Y, 1988

Fig. 3 (a) measured cumulative (E + T) of sorghum as a function of simulated cumulative (E + T) and (b) measured and simulated daily values of soil evaporation as a function of day of year (DOY), Lubbock, Texas, 1988. Values plotted correspond to the well watered sorghum crop + 80 kg N ha.

evaporation, and soil surface and crop canopy temperatures were within one standard deviation of the measured values.

SOIL AND CROP EVAPORATION FROM A SORGHUM CROP

In a field situation it is difficult to measure daily values of soil (E) and crop (T) evaporation over the entire growing season. One way of complementing field measurements of E and T is to use simulated values obtained with a mechanistic model. As an example, ENWATBAL was used to evaluate the

455 Review of models for predicting soil water balance

m > <

3 O Q W H < _l 3

600

400

200-

100-

180 200 220 240 260 280 3 0 0

DOY, 1988

Fig. 4 Simulated values of cumulative (E + T) of sorghum as a function of nitrogen applied and day of year (DOY), Lubbock, Texas, 1988. Values plotted correspond to the well watered sorghum crop (100% ET).

LU > I -

<

ÏI O c û h

CO

>T, N=80

*-T, N =0

> E, N=0

> E, N=80

180 220 240 260

DOY, 1988

280 300

Fig. 5 Simulated values of cumulative soil (E) and crop (T) evaporation from sorghum as a function of nitrogen applied and day of year (DOY), Lubbock, Texas, 1988. Values plotted correspond to the well watered sorghum crop (100% E + T).

effect of two water and two nitrogen treatments on the daily and seasonal partition of E and T. Sorghum (Sorghum bicolor, L. var. MB9) was planted 26 May 1988 on three 100 by 100 m plots located on the Texas Agricultural Experiment Station, near Lubbock, Texas (Mabry, personal communication). Irrigation treatments consisted of two water levels that weekly replaced 50 and 100% of potential evaporation (E + T). Nitrogen treatments were two

R. J. Lascano

E E c

y -

Q

z < LU

> < a a LU I -< _J 5)

DOY, 1988

.Fig. 6 Simulated daily values of soil (E) and crop (T) evaporation of sorghum as a function of day of year (DOY), Lubbock, Texas, 1988. Values plotted correspond to the well watered sorghum crop (100% E + T) + 80kgN ha'1.

levels of 0 and 80 kg ha"1. Root distribution, LAI, and water use were measured weekly throughout the growing season. Soil E was measured daily for five days twice during the growing season. Daily weather parameters were recorded using a nearby weather station.

Comparison of simulated versus measured values of cumulative (E + T) and daily E are given in Fig. 3(a) and 3(b), respectively. From this comparison it can be concluded that ENWATBAL, at least statistically, adequately simulated cumulative (E + T) and daily E. Simulated values of cumulative (E + T), and the components E and T as a function of time for the well watered sorghum at two nitrogen levels are shown in Figs 4 and 5 respectively. These results show that for the well watered sorghum (100% E + T), cumulative (E + T) over time was not greatly affected by nitrogen level (Fig. 4). The impact of nitrogen fertilizer was on the partition of E and T. For instance, nitrogen fertilizer reduced cumulative E at the end of the growing season by 30% and increased cumulative T by 26% (Fig. 5). In other words, the water saved by reducing E was effectively transpired (T) by the sorghum crop.

Simulated daily values of E and T for the growing season are given in Fig. 6. These results illustrate the manner in which E and T are controlled by a set of interacting factors that cannot be expressed by a simple rale or formula. Rather, it is necessary to maintain a continuously updated, calculated water balance, that accounts for the unfolding pattern of weather events, the growth of the crop, and the hydraulic properties of the soil in the root zone.

CONCLUDING REMARKS

It is tempting for agricultural modellers to ignore the "field experiments" that

456

457 Review of models for predicting soil water balance

are necessary to validate proposed algorithms. We must remember that models are simplified representations of the real system and there is no such thing as a totally mechanistic model. Simulation models must be used with precaution and judgement and their original capabilities should not be overstated and their limitations recognized. It is appropriate to end with Zymurg's First Law of evolving system dynamics: "Once you open a can of worms, the only way to recan them is to use a larger can."

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