APPLICATION: FLOOD FORECASTING MODEL FOR KLODZKO CATCHMENT (POLAND) - Modelling Uncertainty in Flood Forecasting Systems - page 88

Collier (1991) and Moore (2002), among others. The impact of the forecasted
precipitation on the forecasted flood is particularly influential in quick-response basins.
The uncertainty in the forecasted precipitation results from the uncertainty in (1) the quantity,
(2) the temporal distribution over the forecast period, and (3) the spatial distribution
over the catchment. When a forecast is based on a probabilistic quantitative precipitation
forecast, sampling methods such as the Monte Carlo technique are commonly used
for the propagation of uncertainty through a forecasting model. In the availability of
probabilistic forecasts of precipitations, the Bayesian theory based approach recently
reported by Kelly and Krzysztofowicz (2000) and Krzysztofowicz (1999) may also be
used. However it is not always possible to provide a reliable probabilistic assessment
of the uncertainty in the precipitation, in which case alternative methods must be used.
The methodology presented in Chapter 4 of this thesis can be used in the framework of
Monte Carlo (MC) simulation as well as the fuzzy Extension Principle (EP). The
application of the methodology in both MC and EP frameworks is presented by Maskey
and Price (2004). This method explicitly takes into account the uncertainty due to the
unknown temporal structure of the precipitation. It is particularly important when the
frequency of the available precipitation measurement is not sufficiently small. This
methodology is independent of the structure of the forecasting model. That is, the
methodology can be used with any rainfall-runoff-routing type deterministic model.
5.2 Implementation of the methodology for uncertainty assessment
due to precipitation
This section presents the implementation of the methodology of uncertainty assessment
presented in Section 4.1 to propagate the uncertainty due to the precipitation in the flood
forecasting model (rainfall-runoff type) of the Klodzko catchment. Subsection 5.2.1 describes
the reconstruction of precipitation by disaggregation and Subsection 5.2.2 describes the
construction of a MF to represent the uncertainty in the magnitude of the precipitation.
The propagation of the reconstructed precipitation using the fuzzy Extension
Principle by the &-cut method is presented in Subsections 5.2.3, and the simplification
applied to the methodology for the present application is presented in Subsection 5.2.4.
5.2.1 Precipitation time series reconstruction using temporal disaggregation
for uncertainty assessment
Uncertainty in flood forecasting related to the uncertainty in time series inputs like pre-
cipitation is discussed in Section 4.1. The principle of the disaggregation of time series
inputs for the treatment of uncertainty is also outlined in Subsection 4.1.1. The idea here
is to divide the given temporal period into a fixed number of subperiods and to randomly
disaggregate the given accumulated sum into as many subperiods, which aggregate up to
the given accumulated sum. The disaggregated precipitations distributed over the
subperiods (as a reconstructed time series) are then used in the rainfall-runoff
model as inputs. Let an accumulated sum of the precipitation for a subbasin i ( i =1,…, m )