Description of the Core Rainfall/Runoff Model

In rainfall/runoff modelling rainfall intensities play an essential role. Therefore, data recorded at short intervals have to be processed. Daily observations, which were available in sufficient number, were assumed as sufficient for our purpose.

The mathematical concept for splitting rainfall into soil retention, direct runoff and deep infiltration is based on the CN-method of the US Soil Conservation Service (US-SCS). It uses the following rainfall/runoff relation:

with    Q = direct runoff

P = precipitation

I_a = initial retention of rainfall in the soil

S = maximum retained humidity up to saturation limit

all units in mm.

This non-linear approach leads to near zero runoff values for low precipitation. Larger values are obtained for increasing rainfall volumes, and thus reveals a phenomenon observed in real world.

As generally the required information about soil characteristics is not available, it is often assumed

Furthermore, in order to facilitate the use of nomograms, the following substitution has been introduced:

with S expressed in inches (25.4 mm).

This has led to the term "CN-method".

CN-values are tabulated for four different soil types (from deep well drained sands to poorly permeable soils with high clay content or with high groundwater level / or impermeable layer) and a considerable number of various combinations of land use and vegetation cover. However, these tabulated values can only serve as an approximation. Particularly for large-scale investigations they have to be adjusted by calibration.

Furthermore, according to the vegetation period and the accumulated rainfall height of the preceding five days, three different antecedent moisture conditions (AMC) are distinguished. The SCS handbook contains tables permitting the transformation of the CN-values tabulated for AMC II (medium moisture) into values valid for AMC I (dry) or AMC III (wet). However, for computer aided application the transformation with mathematical functions is more appropriate.

As a novelty, the approach of the CN-method has not only been used for determination of the direct runoff, but also for assessment of deep infiltration. For this purpose, the amount of daily rainfall was reduced by the portion of direct runoff.

The modelling consisted of the stages model preparation (manually) and model calculation (automated and in daily steps).

For model preparation, first a grid map "hydrological soil classification" has been created. It is based on the map "surface geology" which had been prepared earlier for the purpose of groundwater modelling. Influences due to urbanisation and land use have been considered through correction factors. In order to facilitate calibration, the assignment of standardised CN-values for direct runoff and deep infiltration can be easily modified.

For each day, the actual model calculation consists of the following steps:

1. Monitoring values from the rainfall station, together with their co-ordinates, are read in and used for calculation of a precipitation grid. Existing data gaps are automatically compensated.
   
2. The rainfall total of the preceding 5 days is calculated (not for the individual stations but for the continuous raster).
   
3. The current CN-value for the surface process is calculated from pre-rain index and CN-value for each grid cell.
   
4. The potential direct runoff, and, in a further step, the moisture retention in the soil are calculated from the current CN-value (for the surface process) for each grid cell .
   
5. Deep infiltration (=shallow groundwater recharge) from soil moisture retention and CN-value (for the infiltration process) for each grid cell is calculated. For future refinement of the model, it is also envisaged to include potential evapotranspiration, in order to consider seasonal variations more accurately.