A linear catchment model for real time flood forecasting.

Abstract

A linear reservoir cell model is presented which is proposed as a good candidate for real

time flood forecasting applications. The model is designed to be computationally efficient

since it should be able to run on a P.C and must operate online in real time. The model

parameters and forecasts can be easily updated in order to allow for a more accurate

forecast based on real time observations of streamflow and rainfall.

The final model, once calibrated, should be able to operate effectively without requiring

highly skilled and knowledgeable operators. Thus it is hoped to provide a tool which can be

incorporated into an early warning system for mitigation of flood damage, giving water

resources managers the extra lead-time to implement any contingency plans which may be

neccssary to ensure the safety of people and prevent damage to property.

The use of linear models for describing hydrological systems is not new, however the

model presented in this thesis departs from previous implementations. A particular

departure is the novel method used in the conversion of observed to effective rainlfall. The

physical processes that result in the rainfall to runoff conversion are non-linear in nature.

Most of the significant non-linearity results from rainfall losses, which occur largely due to

evaporation and human extraction. The remaining rainfall is converted to runoff. These

losses are particularly significant in the South African climate and in some regions may be

as much as 70-90 % of the total observed rainfall. Loss parameters are an integral part of

the model formulation and allow for losses to be dealt with directly. Thus, input to the

model is observed rainfall and not the "effective" rainfall normally associated with

conceptual catchment models.

The model is formulated in Finite Difference form similar to an Auto Regressive Moving

Average (ARMA) model; it is this formulation which provides the required computational

efficiency. The ARMA equation is a discretely coincident form of the State-Space

equations that govern the response of an arrangement of linear reservoirs. This results in a

functional relationship between the reservoir response constants and the ARMA

coefficients, which guarantees stationarity of the ARMA model.