Model Theory

The ACRU manual (Schulze, 1995) has detailed information on the ACRU Modelling system However, a summary is given in this Section.

The ACRU model has the following properties:

1. It is a physical conceptual model, i.e. it is conceptual in that it conceives of a system in which important processes and couplings are idealised, and physical to the degree that physical processes (Figure 3.6) are represented explicitly. See Annex A for a commentary on Figure 3.6.

2. ACRU is not a parameter fitting or optimising model and variables (rather than optimised parameters) are estimated from physical characteristics of the catchment.

Figure 3.6 ACRU Agro-hydrological Model showing processes (from Schulze, 1995)

3. The model uses daily time steps and thus daily rainfall input, thereby making optimal use of available data. Certain more cyclic, conservative and less sensitive variables (e.g. temperature, reference potential evaporation), for which values may have to be input at monthly level (if daily values are not available), are transformed internally in ACRU to daily values by Fourier Analysis without any calibration. The appropriateness of these Fourier analysis and synthetic disaggregation methods with regard to tropical conditions are yet to be determined.

4. The ACRU model revolves around daily multi-layer soil water budgeting. It has been structured to be highly sensitive to climate and to land cover/use changes on the soil water and runoff regimes, and its water budget is responsive to supplementary watering by irrigation, to changes in tillage practices or to the onset and degree of plant stress.

Figure 3.7 The options of ACRU model (from Schulze, 1995).

5. ACRU has been designed as a multi-level model, with either multiple options (Figure 3.7) or alternative pathways (or a hierarchy of pathways) available in many of its routines, depending on the level of available input data available or the detail of output required. Thus, for example, reference potential evaporation, interception losses, values of soil water retention constants, maximum (i.e. "potential") and total evaporation ("actual evapotranspiration"), leaf area index, components of the peak discharge

estimation, hydrograph routing, reservoir storage : area relationships or the length of phenological periods in crop growth, all may be estimated by various methods according to the level of input data at hand or the relative accuracy of simulation required.

6. ACRU can operate as a field or as a lumped small (30km²) catchment model. However, for large (4000km²) catchments or in areas of complex land uses and soils ACRU can operate as a semi-distributed cell-type model. In semi-distributed mode, individual sub catchments (ideally not exceeding 30 km²) are identified, discretized and flows can take place from

"exterior" through "interior" cells according to a predetermined scheme, with each sub catchment able to generate individually requested outputs which may be different to those of other sub catchments or with different levels of input/information.

7. The model includes a dynamic input option to facilitate modelling the hydrological response to climate or land use or management changes in a time series, be they long term/gradual changes (e.g. forest growth, urbanisation, expansion of irrigation project or climate trends), or abrupt changes (e.g. clear felling, fire impacts, construction of a dam, development of an irrigation project, or introduction of new land management strategies such as tillage practices), or changes of an intra-annual nature (e.g. crops with non-annual cycles, such as sugarcane). A dynamic input file is then accessed each year with the new variable inputs to be used from that year onwards, e.g. crop coefficients, root mass distributions, planting dates or soils properties (for new tillage practices).

8. ACRU operates in conjunction with the interactive ACRU Utilities, which are a suite of software tools to aid in the preparation of input information (e.g.

the ACRU Menubuilder) and output information (e.g. the ACRU Outputbuilder). The ACRU Menubuilder prompts the user with unambiguous questions, leading the user into inputting, for example, complex distributed catchment information easily. The Menubuilder contains alternative decision paths with pre-programmed Decision Support Systems. Furthermore, the

Menubuilder includes a help facility, built-in default values as well as warning and error messages.

9. ACRU operates on a daily time step and since rainfall is the driving input variable of the model, the minimum daily data requirement should include a period of daily rainfall data. In addition, the model requires some compulsory and other optional information (Figure 3.8).

Figure. 3.8 Data requirements for the ACRU model (from Schulze, 1995) 3.4.2.1 Canopy Storage

Important to hydrological modelling is the canopy storage or interception loss, i.e. the portion of the precipitation which, after interception, does not reach the ground because it is retained by the aerial portion of the vegetation, to be either absorbed by it or returned to the atmosphere by evaporation. Interception loss may be viewed as the difference between gross and net precipitation (Schulze, 1995). On a day with rainfall, the net precipitation available for subsequent

addition to the soil water budget or for eventual stormflow (the water which is generated on or near the surface of a (sub) catchment from a rainfall event, to contribute to flow in the streams within that (sub) catchment) generation, is calculated from the difference between gross precipitation and the canopy interception losses for the day. On a day following a day with rainfall, the remaining potential evaporation, after the wet canopy evaporation has been completed, is then available for the transpiration process from the dry canopy and soil water evaporation.

The Von Hoyningen-Huene (1983) approach is employed as the estimator of canopy or interception loss in ACRU (Shulze, 1995).

3.4.2.2 Infiltration

Infiltration is the process whereby rainfall or irrigated water enters the soil profile. Redistribution is the process which occurs once infiltration has terminated and may be defined as the process whereby water moves through the unsaturated soil profile, either towards the surface by soil water evaporation and/or transpiration induced capillary action, or downwards by gravity toward the groundwater store. The Green and Ampt method calculates infiltration (sub daily) as a function of the redistribution rates for different soil horizons only if curve number (CN) method is not used.

3.4.2.3 Evapotranspiration

The combination of two separate processes whereby water is lost on the one hand from the soil surface by evaporation and on the other hand from the crop by transpiration is referred to as evapotranspiration. ACRU is described as a multi-layer soil water budgeting model and that most rainfall is transformed into evaporation either through the soil or through the plant (evapotranspiration). In ACRU evaporation takes place from previously intercepted water as well as simultaneously from the various soil horizons, in which case it is either split into separate components of soil water evaporation (from the topsoil horizon only) and plant transpiration (from all horizons in the root zone), or combined, as

total evaporation. Evaporative demand on the plant is estimated, inter alia, according to atmospheric demand (through a reference potential evaporation) and the plant's stage of growth. The roots absorb soil water in proportion to the distributions of root mass density of the respective horizons, except when conditions of low soil water content prevail, in which case the relatively wetter horizons provide higher proportions of soil water to the plant in order to obviate plant stress as long as possible. In ACRU the reference potential evaporation is the evaporation from the United States evaporation class Apan i.e. Eapan

During hydrological modelling in ACRU, vegetation (natural vegetative cover) and land use (implying anthropogenic influence through building roads, cropping, including plantations, as well as agricultural practices such as irrigation and/or tillage operations) processes may be grouped functionally into

1. above-ground factors, implying - canopy interception losses

- consumptive water use by plants and - shading of the soil, into

- evaporation of water from the soil surface and

- evaporation of water from plant tissue (transpiration) 2. surface factors, which focus on

- protection by the plant/litter cover against erosion, and 3. below-ground factors, concerned with

- plant root distribution - root water uptake and - the onset of plant stress.

To estimate vegetation water use the concepts of crop coefficient, maximum evaporation and reference potential evaporation are used and leaf area index (LAI) where available is also employed. This LAI approach uses the Von Hoyningen-Huene (1983) method in Shulze (1995) to account for the basic physical processes of evaporation and empirically derived crop coefficients to account for specific vegetation conditions.

Total evaporation, E, may equal or be less than the maximum evaporation, Em, also termed "potential evapotranspiration". On a given day, E can be reduced to less than Em either when soil water has been depleted below a critical threshold value (when plant stress sets in) or when there is an excess of water in the soil profile. Actual soil water evaporation, Es, is computed from the topsoil horizon. Es for the day can either be occurring at maximum (or "stage one") rate (Esm) if a minimum threshold of soil water resides in the topsoil horizon, or below the maximum rate once soil water content has dried to a

"stage two" level, in which case Es declines very rapidly with time.

Actual plant transpiration (Et) is calculated next, initially for the topsoil horizon, then from the subsoil horizon where transpiration is determined based on whether there is soil water deficiency or soil water excess. More details on the various Et processes, which include soil water stress being induced either from a soil water deficiency or excess, are given in Chapter 7 of ACRU Theory Manual (Shulze, 1995).

3.4.2.4 Surface runoff

In the ACRU model, runoff is generated as stormflow dependent upon the magnitude of daily rainfall in relation to dynamic soil water budgeting. The generated streamflow in a (sub) catchment comprises baseflow and stormflow, with the stormflow component consisting of quickflow response, i.e. stormflow released into the stream on the day of the rainfall event, and a delayed stormflow response, i.e. in essence a surrogate for post-storm interflow. The generation of stormflow in ACRU is based on the premise that, after initial abstractions (through interception, depression storage and infiltration before runoff commences), the runoff produced is a function of the magnitude of the rainfall and the soil water deficit from a critical response depth of the soil. The soil water deficit antecedent to a rainfall event is simulated by ACRU's multi-layer soil water budgeting routines on a daily basis. A modified United States SCS curve number method is used for computing the daily stormflow where the

potential maximum retention of the curve number is replaced by a soil water deficit.

The ACRU model utilises the United States Department of Agriculture's Soil Conservation Service (SCS) unit hydrograph concepts in order to compute the peak discharge from the generated daily stormflow volume. For realistic total storm hydrographs, standard unit hydrograph convolution procedures should be used to superimpose the single unit hydrographs in specified time steps according to the temporal distribution of effective rainfall within a day. However, when using a daily model and in the assumed absence of recording rainfall data or, alternatively, in the absence of a realistic synthetic rainfall distribution over time for a particular event, a uniform rainfall distribution is assumed. In ACRU, when the hydrograph routing option is not invoked, a single rather than an incremental unit hydrograph is used for peak discharge computation.

3.4.2.5 Baseflow

Baseflow consists of water from previous rainfall events that has percolated through the soil horizons into the intermediate and groundwater zones and then contributes as a delayed flow to the streams within a (sub) catchment. ACRU applies two response coefficients to baseflow generation. The first relates the drainage rate of water out of the bottom subsoil horizon store, when its soil water content exceeds the drained upper limit, into the intermediate/groundwater store. This response rate is slower for heavy textured than for light textured soil.

The second response coefficient concerns baseflow release of water from the intermediate/groundwater store into the stream. This coefficient depends intrinsically on factors such as geology, catchment area and slope. If, on a given day, no contribution is made to the baseflow store by drainage, then baseflow releases are calculated as the product of the previous day’s groundwater store and a user specified coefficient of baseflow (second response coefficient). The baseflow store’s magnitude is then reset.

3.4.2.6 River Runoff Routing

In ACRU, the assumption that stormflow generated on a particular day passes to the catchment outlet on the same day is considered valid for small (30km²) catchments, but not necessarily true of larger catchments When the ACRU model is applied in the semi distributed mode on larger catchments, the option to invoke the hydrograph routing options in order to reflect the translation and attenuation of the hydrograph taking place through river reaches and reservoirs encountered en route to the catchment outlet is available. Three methods used for routing in ACRU model are the Storage indication method, the Muskingum method and the Muskingum Cunge methods.

3.4.2.6 Next Step

Having reveiewed models to find an appropriate one to use for the PhD, the ACRU model was found to be the most appropriate when the models were judged against a set of selection criteria. With the relevant processes of the ACRU model already described the next step is to identify the appropriate data required for a successful hydrological modelling. In the next chapter the data availability, analysis and the model setup required are presented.