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A microcomputer scheduling program for supplementary irrigation

T. Hess, Department of Water Management, Silsoe College, Bedford, UK


A real-time irrigation scheduling computer package for use on farms is described. The package comprises four models: a reference crop evapotranspiration model, an actual evapotranspiration model, a soil water balance model and an irrigation forecast model. The models used have been shown to produce reliable estimates of the soil water balance. However, the predictions are sensitive to the accuracy of the input data measured on the farm. This paper summarizes the experience of applying such a program to supplementary irrigation in the United Kingdom.

The Irrigation Management Services (IMS) scheduling program (Hess, 1994) was produced by Silsoe College from an original program by Siddig (1982). Between 1984 and 1989, it was used to provide an irrigation scheduling service to farmers and growers in eastern England in conjunction with in situ monitoring of soil water and crop cover (Hess and Mathieson, 1988). The service provided weekly advice for the forthcoming ten days on which fields to irrigate, when and how much. There are several such 'bureau' services using water balance methods that are (or have been) available in the United Kingdom to assist with irrigation scheduling (Bailey and Spackman, 1988; Paulson, 1988; Turvill, 1988; Parkes, 1994). In each case, the bureau collects weather data for the region, whilst the farmer reports rainfall and irrigation recorded at the farm, usually on a weekly basis. The irrigation requirement forecasts are then sent to the farmer by post or fax.

Since 1990 many more farmers have access to microcomputers and there has been a demand for scheduling packages for use on-farm. The IMS program (Hess, 1994) has therefore been supplied to farmers, research stations and agricultural colleges for real-time irrigation scheduling. The requirements for a scheduling model must be viewed in the context of irrigation in the United Kingdom. The main irrigated crops are potatoes, sugar beet and vegetables that are grown between April and September on light soils. Rainfall during this period is typically erratic, unreliable and spatially variable, such that the seasonal irrigation requirement may range from less than 100 to 300 mm. Water is usually applied by mobile hose-reel rain-guns or sprinklers in doses of 15 to 30 mm. Increasingly, the concern of the grower is for maintaining high quality produce, thus irrigation water is applied at relatively small soil water deficits (20 - 50 mm). In such situations, the problems facing the grower are deciding when the crop will need water and how much to apply, in order to meet crop requirements, minimize drainage and runoff, make efficient use of labour, water and power, and to complete the application before other crops on the farm require irrigation.


There are four main components to the model (Figure 1):

1. calculation of a daily reference crop evapotranspiration from local meteorological data,

2. adjustment of the reference crop evapotranspiration to an actual evapotranspiration, taking account of crop cover and soil water content,

3. calculation of a soil water deficit, and

4. extrapolation of the water balance to predict the timing of the next irrigation.

Each of these components is described briefly below.

FIGURE 1 - The IMS irrigation scheduling model

Reference crop evapotranspiration model

Reference crop evapotranspiration (ETo) is calculated on a daily basis and stored in a file for use in the calculation of actual evapotranspiration. The IMS program allows four methods to calculate, or estimate, the daily ETo.

1. Long-term average rates of ETo can be used according to the month.

2. Daily ETo may be entered directly if it is available from an external source (e.g., modified pan evaporation or subscription to a weather data service).

3. ETo is calculated on a daily basis using meteorological data from a nearby meteorological station using the Penman (1963) combination equation as modified by Thom and Oliver (1977) for rural lowland areas. For most of the meteorological stations used, neither net nor shortwave radiation are measured. Maximum daylight hours and extra-terrestrial radiation are calculated as a function of latitude and date, and received shortwave radiation is then estimated from the sunshine duration. The vapour pressure deficit in the bulk aerodynamic term is calculated from 0900 GMT readings from a wet and dry bulb psychrometer or mean relative humidity and the saturated vapour pressure at the mean air temperature.

4. ETo may be imported from an automatic weather station using the program AWSET (Hess, 1994) to pre-process the weather data and calculate daily ETo by either the Penman-Monteith (as presented by Smith, 1991), Penman (Penman, 1963), or FAO Modified Penman (Doorenbos and Pruitt, 1977) method.

Actual evapotranspiration model

Actual evapotranspiration, ETa, is calculated from the reference crop evapotranspiration using a largely empirical, one-dimensional model, making adjustments for the crop type, stage of growth and restrictions due to limiting soil water deficits. The surface area is separated into two components: a cropped part and a bare soil part, and the evaporation from each is modelled separately. Finally, a weighted average is calculated according to the degree of crop cover.

Three parameters must be calculated each day as inputs to the actual evapotranspiration model: available water capacity (AWC) of the root zone, crop cover fraction, and soil water deficit. Reference crop evapotranspiration is read from the file for the appropriate meteorological station.

If the crop is well watered and the water content of the root zone is not allowed to reach a stage where transpiration is reduced, then the estimate of ETa is insensitive to the assumptions made about rooting depth and available water capacity. These only become important if the crop is stressed and actual water use falls below potential rates. The easily, and total, available water capacities of the root zone are calculated each day from the root depth and water holding characteristics of the sub- and topsoil with a modification for the topography of the surface layer using the method of Siddig (1982).

Three zones are identified; the upper cultivated layer (assumed to be within the topsoil), the topsoil and the subsoil. The AWC of the soil on each day is the sum of the AWC of each layer down to the depth of the roots. Prior to emergence all evaporation is from bare soil and the root depth does not influence ETa. Between emergence and the time of reaching maximum rooting depth, the depth of roots on any day is estimated from a sigmoidal curve of root development (Borg and Grimes, 1986).

Water use from the cropped portion of the ground, ETc, is calculated as a function of reference crop evapotranspiration for the day.

ETc = ETo × Kc × Ks, (1)


ETc = water use from the cropped portion of the ground (mm d-1)
Kc = crop factor (dimensionless)
Ks = fraction of the available water capacity that is readily available (dimensionless)

It is important to note that the definition of the crop factor, Kc, is different from that used by Doorenbos and Pruitt (1977). Here it refers to the relative transpiration from the crop at that stage of development, compared to the reference crop, and assumes that the crop covers 100% of the surface. During the period from emergence to 85% crop cover, for most crops, Kc = 1. After 85% cover, Kc is increased by 10 - 20%, depending on the crop type.

The soil water availability factor, Ks, is an adjustment to the potential crop water use to account for limiting deficits. The readily available water (RAW) of the root zone is calculated from:

RAW = AWC × rd × Ks, (2)


AWC = available water capacity (mm m-1)
rd = root depth (m)
Ks = fraction of the available water capacity that is readily available (dimensionless)

If the soil water deficit is less than the readily available water of the root zone, then Ks = 1, otherwise, it is reduced linearly between RAW and permanent wilting point (PWP).

The evaporation from bare soil is calculated independently. Whilst the profile is at field capacity, bare soil evaporation is assumed to occur at the same rate as ETo. Initially evaporation from wet soil will occur at the potential rate. As the soil dries the ratio of actual to potential evaporation will vary from one at field capacity to almost zero at some limiting deficit. The rate of fall follows a linear decline when expressed against relative soil water deficit. Thus,

Es = ETo (1 - SWD/SWDmax), (3)


Es = soil evaporation (mm d-1)
SWD = soil water deficit (mm)
SWDmax = maximum soil water deficit under bare soil (mm)

The only parameter required to describe the drying characteristics of the soil is an upper limit to the soil water deficit under bare soil. Experience has shown this to be about 15mm for light soils.

It is clear from the above that both Es and ETc on any day will depend upon the soil water deficit, whilst the soil water deficit itself will depend upon the actual evapotranspiration. For small time steps, such as one day, it is acceptable to use the soil water deficit from the previous day to estimate today's actual evapotranspiration.

The actual evapotranspiration is calculated from:

ETa = (ETc x CC) + (Es × (1 - CC)), (4)


ETa = actual evapotranspiration (mm d-1)
CC = crop cover fraction

Es and ETc calculated above may fall below their potential rates under dry soil conditions. However, a limitation of single layer water balance models is that it is difficult to account for rain, or irrigation, falling on an otherwise limiting dry soil. The IMS model accounts for this by directing 50% of the rainfall or irrigation to a store of water which is available at the potential rate, regardless of the soil water status. This store of water is used first. Therefore, if irrigation were applied on a dry soil, 50% of that water could be used at the potential rate, the remainder would be distributed throughout the root zone and may only be available at the restricted rate given by equation 1.

Soil water balance model

The actual evapotranspiration calculated above forms one of the inputs to the daily water balance model. A simple, single layered, water balance model is used, based upon the following assumptions:

1. The soil has a high hydraulic conductivity and no drainage impediment.

2. There is no temporary storage of water in excess of field capacity beyond one day.

3. The water table is deep and there is no significant contribution from groundwater to the root zone.

4. At the end of each day, the water content of the root zone is uniformly distributed.

5. Soil below the root zone is at field capacity.

6. Rainfall and irrigation systems do not apply water at such high application rates as to exceed the infiltration capacity of the soil.

Initially, as all rainfall and irrigation is assumed to be effective, no losses are assumed due to runoff or interception. However, if the sum of rainfall plus irrigation exceeds the soil water deficit, then any excess water is assumed to be lost to runoff or drainage, D, within the day, such that by the end of the day, SWD is equal to zero (that is, the soil is at field capacity).

Thus, the soil water deficit on each day can be calculated from:

SWDi = SWDi-1 + ETai + Di - (Ri + Ii), (5)


SWDi = soil water deficit on day i (mm)
ETai = actual evapotranspiration on day i (mm)
Di = runoff or drainage on day i (mm)
Ri = rainfall on day i (mm)
Ii = irrigation on day i (mm)

Irrigation scheduling model

The timing of irrigation is determined according to a maximum allowable soil water deficit. It may be kept constant through the season in line with equipment capabilities, or it may be adjusted to account for variations in crop susceptibility. The choice of maximum allowable deficit is left to the operator, although the readily available water of the root zone each day is calculated by the program as a guide.

If the maximum allowable deficit has been exceeded, the program will advise that an irrigation is required. Otherwise it will produce a forecast water balance for the next ten days. Whereas for the historical water balance, ETo may be calculated from measured meteorological data, for the irrigation forecast it must be estimated. The forecast ETo for each day is based upon a combination of the ETo from the previous day and the long-term average ETo for the time of year (as used by Buchleiter et al., 1988). This assumes that the ETo tomorrow is most likely to be similar to the ETo today but that by the end of the forecast period, it is most likely to be equal to the long term average for the time of year.

Given the forecast ETo, ETa is calculated in the same manner as above. This is then used in the water balance to predict the soil water deficit for each of the forthcoming ten days. Rainfall and irrigation are both set to zero, thus, the forecast date of irrigation is a worst case. If rain falls before the next irrigation, it is assumed that the grower will delay application. The depth of rainfall to permit a one day delay is calculated from the forecast ETa.

FIGURE 2 - Observed and predicted soil water deficits from seven sites in 1986

FIGURE 3 - Example of model and probe comparison for one season showing rainfall and irrigation (columns), predicted soil water deficit (line) and observed soil water deficits (points)


Model validation

For six years the program was used in conjunction with fortnightly neutron probe readings of soil water content and in situ measurements of rainfall and irrigation amount. Although this data was not collected under experimental conditions, it provided a large data set against which to validate the model.

It was found that the model performed well (e.g., Figure 2), especially prior to the irrigation season. Figure 3 shows the relationship between the soil water deficits predicted by the model and the mean of three soil water deficits measured by the neutron probe from seven sites in one season. Although the scatter appears large, in many cases this reflects a large variance of the three observed values on a single day. Prior to the start of irrigation the mean variance was 1.45 mm; however, this increased to 12.5 mm after the start of irrigation. Therefore, although the model may show a considerable deviation between the predicted value and the mean of the three neutron probe values, it was often within the range of the observed values.

Discrepancies during the irrigation season were largely explained by differences between the rainfall and irrigation amounts reported by the farmer and those recorded in the field (see below).

Sources of error

Experience with the program has shown that the main source of error is in the measurement (or estimation?) of input data, and in particular irrigation and precipitation amounts. Farmers frequently use a single rain gauge to schedule irrigation for the whole farm, often sited close to the farm buildings for convenience. Summer rainfall in the United Kingdom can be extremely variable spatially. An example has been cited where rainfall recorded over one week differed by 16 mm over a distance of 300 m. Thus the rainfall amount entered into the model may be significantly different from that actually falling in the field. Similarly, farmers' estimates of irrigation applications are usually subject to wide margins of error and are rarely measured in the field. Mackenzie (1987) showed that in over 80% of cases, discrepancies between the model estimates of soil water deficit and actual deficit measured in the field during the irrigation season could be explained by errors in the estimation of rainfall and irrigation amounts.

The second source of error is human error in data entry. People always make mistakes and often the person running the computer program is not the person reading the met data or the person applying the irrigation. Thus there may be confusions in communication ('..his 7 looked like a 9..', or ' forgot to record that irrigation on the 17th') as well as direct data entry errors which may not be trappable or immediately apparent. For example, during the 1994 season, one farmer using the IMS program alongside the 'Irriguide' bureau service (Bailey and Spackman, 1988) noticed a discrepancy between the scheduling advice from the two systems. Closer inspection revealed that over a two-month period, the rainfall reported to 'Irriguide' was 20 mm less than that entered into the IMS program. This was equivalent to one irrigation. In some cases rainfall amounts differed on the same day, and in other cases the date of rainfall was different.

A particular problem of water balance models is that any error in the input data will be carried forward and errors will accumulate. For example, if the actual irrigation application were 5 mm less than assumed, after four irrigations this would be equivalent to an extra irrigation (of 20 mm) that would have been missed. This cumulative error is only removed when the soil is fully wetted by heavy rainfall or irrigation and the soil water deficit is returned to zero.


Data requirement

A model designed to be operated by farmers and growers, at a reasonable cost, must be constrained by the availability of site specific information. In general the only data available regarding the site are: location; crop type and variety; planting date; equipment available; and soil textural class (topsoil and subsoil).

Other soil and crop parameters (such as available water capacity, crop coefficients, rooting depths) can be estimated from a database of default information appropriate to the region with the option of overriding with site specific data if available. Daily weather data may be obtained from nearby meteorological stations but rainfall and irrigation applications have to be recorded at the farm by the grower.

Ease of use

The user interface of the program must be easy to use and consistent. This is simple to program with visual programming tools that are now available. In addition, wherever possible, there should be range-checking on input data to check, for example, that the minimum temperature is less than the maximum, wet bulb temperatures are less than dry bulb, and so on. Any data entered in excess of reasonable limits should be queried.

Updating the model predictions

The IMS water balance model has been written as a 'real time' irrigation scheduling model with the advantage of updates of actual measurements from the field. For example, crop cover development is modelled upon the basis of linear interpolation between estimated dates of emergence, 20% cover and full cover. However, the modelled values can be updated by observed values from the field on any day and cover and are recalculated upon the basis of the observed values. The past soil water deficits are also recalculated. For the purposes of the scheduling forecast, the cover is estimated from the average cover development rates.

Similarly, soil water deficits can be updated if actual observations (e.g., from neutron probe) are available, or for some reason (see below) the model predictions do not agree with what can be seen in the field.

Output requirements

The output should be clear and simple to interpret. It should indicate when the next irrigation is due and how much water should be applied. It should also indicate what to do if it rains before the irrigation date. The default output should only contain that information needed to schedule the irrigation. However, full details of the simulated water balance should be available in case there is a query on the advice. One criticism of bureau services is that generally it is not possible to see how the advice was derived and whether there had been any errors or inappropriate assumptions in the model use.


Although the model used in the program is based upon a number of simplifying assumptions, experience has shown that the predicted soil water deficits compare well with deficits measured in the field especially where little irrigation has been applied. This is largely due to the circumstances in which the program is being used, namely flat land, with light soils under supplementary irrigation. As with all water balance models however, the program is sensitive to errors and uncertainties in the input data which far outweigh simplifications or inadequacies in the underlying model.

A major limitation of the IMS program as it stands is that it considers each field (or irrigated unit) independently. The problem facing many farmers and growers in the United Kingdom is often 'which field should I irrigate next', rather than 'does this field need irrigation'. This is particularly true where water, equipment or labour are insufficient to meet the full crop water requirement. The IMS program has been incorporated within a mixed linear program for whole farm scheduling (Upcraft et al., 1989) to produce optimum irrigation schedules, within the constraints imposed by equipment, labour and water availability. It is hoped to develop this into a format suitable for use on farm in the near future.


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