Modifications

For the purpose of this study some modifications to the model illustrated above are made, which are listed in the following:

(a) Güntner et al. (2001) introduced a weighting for the calculation of the generator prob- abilities of a generator. When averaging over the scale-invariant levels, the higher reso- lution levels contribute a larger amount of boxes to the statistics. Therefore they should have greater influence on the resulting properties of a generator to increase the accuracy of the estimated P values. The actual implementation considers this concept by calcu- lating a weighting factor for each level in dependency of its number of wet boxes. When the properties of a generator are calculated, the statistics of each level are multiplied with

the factor. This results in weighted probabilitiesP(1/0), P(0/1), P(x/x) and weighted

9°E 10°E 11°E 12°E 13°E 47°N 48°N 49°N 50°N Rain gauges Catchment Low mountain ranges Forelands Alps

Fig. 4.21: Spatial pattern of precipitation regimes

Furthermore the definition of Olsson (1998) forWx/x-distributions leads to symmetrical

distributions. Güntner et al. (2001) defines the distribution asW2= 1−W1, allowing to

reproduce internal event asymmetries. This way e.g. storm events may be represented better, as asymmetrical distributions can redistribute large parts of the volume to the be- ginning of the event.

(b) The boundary between the volume classes was set by Olsson (1998) to the mean vol- ume of all boxes in a level. Güntner et al. (2001) compared various values (upper and lower quartile, median and mean) to distinguish between small and large volumes. They found, that the mean suits best for the generation of the parameters of their model. But for application within this study, which focuses on heavy precipitation events, it seems to be reasonable to introduce a more significant threshold. The mean value does not con- tain information about the event structure, it just divides absolute values. It has long been recognised, that absolute rainfall amount not necessarily influences runoff and erosion, but its intensity and temporal distribution (see e.g. Dikau, 1986). Heavy precipitation events lead to destruction of the soil aggregates at the surface, causing splash erosion as well as reduction of infiltration rates by soil sealing. Advective persistent precipitation may also have high volumes, but over longer time intervals, which induces surface runoff and erosion by overflow of the soil water storage. Therefore a separation of advective

and convective events is considered important. Assuming that convective precipitation has higher dynamics and variability than the usually more static advective events, rainfall intensity can be used to define a threshold for the generator. The gradient of the rainfall intensity between two consecutive boxes quantifies the relative dynamics of the precip- itation event, irrespective of the absolute amount. Seasonal differences in precipitation patterns are governed either by convective processes, i.e. higher dynamics in summer, or advective processes in winter. However advective precipitation may also occur in sum- mer, thus the generator must be capable of recognising these. In order to separate the events, the 90th percentiles are used instead of the mean, to differentiate more clearly between the rainfall characteristics. The evaluation of the generators properties in Sec-

tion 5.1.3 shows, that probabilities andWx/x-distributions of all regions are very similar,

and thus regionalisation of the generator shall be achieved by fitting the volume threshold to the regions. Additionally the volume thresholds are calculated for each position class, as the latter contains implicit information about the dynamics in the event structure of the different regions.

(c) To determinate the number of histogram intervalskfornvalues, Olsson (1998) suggests

the formula k = 1 + 3.3 logn. A problem of this definition is, that for higher cascade

levels too few valuesn exist, resulting in too few classes and thus a coarse probability

distribution. If otherwise too many classes are formed, the number of members assigned to each class becomes very small. Therefore the number of classes is fixed in this study to seven, resulting in clear patterns of the histogram.

(d) As the desired temporal resolution in AtmoStations is 1h, a re-aggregation of the disag-

gregated boxes has to be made. The input resolution of precipitation data is 10, respec- tively 7 hours, which results after disaggregation over 7 levels in an output resolution of

9.375 min, respectively 6.5625min. As a re-aggregation to 60 min does not result in

integer numbers, the excess boxes are added to the re-aggregated volumes in a regular pattern.

Note: As described in Section 4.2, the land surface modelPROMET consists of a number of sub-models, which all have to be parameterised, and therefore need a huge amount of input data. It is beyond the scope of this work, to describe the exact parameterisation of the sub- models used within this study. Thus, merely the model parameters, which are most important for the results of the erosion module, are briefly addressed in appendix C.

5.1. Calibration of the Cascade Model

This section covers not only the calibration and configuration of the cascade model. Because the study area is a very heterogeneous region, some preliminary testing has to be executed, in order to verify the applicability of the cascade model for the different geographic regions. Also the correct setup of the cascade configuration must be found and evaluated.