Kieran M. O'Connor

A non-linear combination of the forecasts of rainfall-runoff models by the first-order Takagi–Sugeno fuzzy system

Abstract With a plethora of watershed rainfall-runoff models available for flood forecasting and more than adequate computing power to operate a number of such models simultaneously, we can now combine the simulation results from the different models to produce the combination forecasts. In this paper, the first-order Takagi–Sugeno fuzzy system is introduced and explained as the fourth combination method (besides other three combination methods tested earlier, i.e. the simple average method (SAM), the weighted average method (WAM), and the neural network method (NNM)) to combine together the simulation results of five different conceptual rainfall-runoff models in a flood forecasting study on eleven catchments. The comparison of the forecast simulation efficiency of the first-order Takagi–Sugeno combination method with the other three combination methods demonstrates that the first-order Takagi–Sugeno method is just as efficient as both the WAM and the NNM in enhancing the flood forecasting accuracy. Considering its simplicity and efficiency, the first-order Takagi–Sugeno method is recommended for use as the combination system for flood forecasting.

Methods for combining the outputs of different rainfall–runoff models

Abstract The present paper promotes the concept of combining the estimated output of different rainfall–runoff models to produce an overall combined estimated output to be used as an alternative to that obtained from a single individual rainfall–runoff model. Three methods of combining model outputs are considered, namely the simple average method (SAM), the weighted average method (WAM) and the neural network method (NNM). The estimated discharges of five rainfall–runoff models for 11 catchments are used to test the performance of these three combination methods. The results confirm that better discharge estimates can be obtained by combining the model outputs of different models.

Comparison of four updating models for real-time river flow forecasting

Abstract Four different error-forecast updating models are investigated in terms of their capability of providing real-time river flow forecast accuracy superior to that of rainfall-runoff models applied in the simulation (nonupdating) mode. The first and most widely used is the single autoregressive (AR) model, the second being an elaboration of that model, namely the autoregressive-threshold (AR-TS) updating model. A fuzzy autoregressive-threshold (FU-AR-TS) updating model is proposed as the third form of model, the fourth and final error-forecast updating model applied being the artificial neural network (ANN) model. In the application of these four updating models, the lumped soil moisture accounting and routing (SMAR) conceptual model has been selected to simulate the observed discharge series on 11 selected test catchments. As expected, it is found that all of these four updating models are very successful in improving the flow forecast accuracy, when operating in real-time forecasting mode. A less expected, but nonetheless welcome, result is that the three updating models having the most parameters, i.e. AR-TS, FU-AR-TS, and ANN, do not show any considerable advantages in improving the real-time flow forecast efficiency over that of the simple standard AR model. Thus it is recommended that, in the context of real-time river flow forecasting based on error-forecast updating, modellers should continue to use the AR model.

A real-time combination method for the outputs of different rainfall-runoff models

Abstract Application of the concept of combining the estimated forecast output of different rainfall-runoff models to yield an overall combined estimated output in the context of real-time river flow forecasting is explored. A Real-Time Model Output Combination Method (RTMOCM) is developed, based on the structure of the Linear Transfer Function Model (LTFM) and utilizing the concept of the Weighted Average Method (WAM) for model output combination. A multiple-input single-output form of the LTFM is utilized in the RTMOCM. This form of the LTFM model uses synchronously the daily simulation-mode model-estimated discharge time series of the rainfall-runoff models selected for combination, its inherent updating structure being used for providing updated combined discharge forecasts. The RTMOCM is applied to the daily data of five catchments, using the simulation-mode estimated discharges of three selected rainfall-runoff models, comprising one conceptual model (Soil Moisture Accounting and Routing Procedure—S...

A simple non-linear rainfall-runoff model with a variable gain factor

Abstract A simple non-linear rainfall-runoff model, incorporating a variable gain factor dependent on the prevailing soil moisture state of the catchment, is developed. The simulation mode output of an auxilliary simple linear model is used as an index of the soil moisture state and simple and realistic functional relationships between the gain factor and the prevailing catchment wetness index are assumed. The resulting model, referred to as the variable gain factor model (VGFM), is tested on the data of five catchments, assuming two different functional forms of gain factor variation with the catchment wetness index. The results indicate significant improvement over the performance of the simple linear model for the test catchments. The operation of the model is shown to be equivalent to a special form of the non-linear Volterra model.

Indices for assessing the prediction bounds of hydrological models and application by generalised likelihood uncertainty estimation

Abstract To reflect the uncertainties of a hydrological model in simulating and forecasting observed discharges according to rainfall inputs, the estimated result for each time step should not be just a point estimate (a single numerical value), but should be expressed as a prediction interval, i.e. a band defined by the prediction bounds of a particular confidence level α. How best to assess the quality of the prediction bounds thus becomes very important for understanding the modelling uncertainty in a comprehensive and objective way. This paper focuses on seven indices for characterizing the prediction bounds from different perspectives. For the three case-study catchments presented, these indices are calculated for the prediction bounds generated by the generalized likelihood uncertainty estimation (GLUE) method for various threshold values. In addition, the relationships among these indices are investigated, particularly that of the containing ratio (CR) to the other indices. In this context, three main findings are obtained for the prediction bounds estimated by GLUE. Firstly, both the average band-width and the average relative band-width are seen to have very strong linear correlations with the CR index. Secondly, a high CR value, a narrow band-width, and a high degree of symmetry with respect to the observed hydrograph, all of which are clearly desirable properties of the prediction bounds estimated by the uncertainty assessment methods, cannot all be achieved simultaneously. Thirdly, for the prediction bounds considered, the higher CR values and the higher degrees of symmetry with respect to the observed hydrograph are found to be associated with both the larger band-widths and the larger deviation amplitudes. It is recommended that a set of different indices, such as those considered in this study, be employed for assessing and comparing the prediction bounds in a more comprehensive and objective way.

Application of an empirical infiltration equation in the SMAR conceptual model

An empirical equation, which relates the infiltration rate to the actual soil moisture content, is proposed and incorporated in the Soil Moisture Accounting and Routing (SMAR) model to demonstrate one application of that equation. A modified SMAR model (SMARY) is developed and tested on four catchments with different climatic conditions. The results show that the SMARY model performs better than the SMAR model in terms of R2, mean square error and relative error. The modified model provides a more rational interpretation of the physical process of infiltration and also provides a tool for determining the actual infiltration rate under specific soil moisture conditions.

A nearest neighbour linear perturbation model for river flow forecasting

Abstract The non-parametric nearest neighbour method (NNM) for river flow forecasting is explored and developed further as the nearest neighbour linear perturbation model (NNLPM), which combines the nearest neighbour concept with the concept of perturbations from a mean value, as used in the linear perturbation model (LPM). The NNLPM model is tested on six catchments and its results are compared with those of the simple linear model (SLM) and the linear perturbation model (LPM). The results indicate that the NNLPM is a more reliable indicator of the discharge forecast than either the SLM or the LPM in the case of non-seasonal catchments.

A discrete linear cascade model for hydrology

Abstract The discrete analogies of the classical Muskingum and the equal-reservoir cascade models are compared with the ARMA-type models used in the generation of synthetic time series. Applying the cascade concept to the ARMA-type difference equation and including a pure translation parameter, a family of discrete linear parametric models is developed. Expressions are derived for the direct estimation of model parameters by cumulants for the general input-output case and for the special case of a white-noise input. The family of models can be applied in unit-hydrograph analysis, in flood routing, and in the generation of synthetic time series.

A Comparative Study of Three Neural Network Forecast Combination Methods for simulated river flows of different Rainfall-runoff models

Abstract The performances of three artificial neural network (NN) methods for combining simulated river flows, based on three different neural network structures, are compared. These network structures are: the simple neural network (SNN), the radial basis function neural network (RBFNN) and the multi-layer perceptron neural network (MLPNN). Daily data of eight catchments, located in different parts of the world, and having different hydrological and climatic conditions, are used to enable comparisons of the performances of these three methods to be made. In the case of each catchment, each neural network combination method synchronously uses the simulated river flows of four rainfall—runoff models operating in design non-updating mode to produce the combined river flows. Two of these four models are black-box, the other two being conceptual models. The results of the study show that the performances of all three combination methods are, on average, better than that of the best individual rainfall—runoff model utilized in the combination, i.e. that the combination concept works. In terms of the Nash-Sutcliffe model efficiency index, the MLPNN combination method generally performs better than the other two combination methods tested. For most of the catchments, the differences in the efficiency index values of the SNN and the RBFNN combination methods are not significant but, on average, the SNN form performs marginally better than the more complex RBFNN alternative. Based on the results obtained for the three NN combination methods, the use of the multi-layer perceptron neural network (MLPNN) is recommended as the appropriate NN form for use in the context of combining simulated river flows.