Non-linear Rainfall-runoff Model Research Articles

Effective Optimization Technique for a Nonlinear Rainfall-Runoff Model

AbstractThe purpose of this paper is to propose an effective optimization technique that can overcome the local minimum problem resulting from the nonlinear construction of the rainfall-runoff model. First, this technique attempts to approximate the nonlinear function by using a finite number of terms of linear functions, referred to as the linearization process. Then, these linear functions would be optimized by the sum of squared errors (MSSE). Finally, the optimized parameters of a nonlinear function using the step-iterative algorithm were obtained. Its features and capabilities are demonstrated by means of a binary function and a conceptual rainfall-runoff model (Xinanjiang model). To optimize the model parameters, 10 years of historical data in the Changzhao basin are applied, whereas the most recent three years are utilized to verify these parameters. With reference to the binary function, the proposed linearlized search technique (LST) converge quickly from any starting point. With regard to the hy...

A Non-Linear Rainfall-Runoff Model with a Sigmoid Gain Factor to Simulate Flow Frequency Distribution Curves for Amazon Catchments

A Non-Linear Rainfall-Runoff Model with a Sigmoid Gain Factor to Simulate Flow Frequency Distribution Curves for Amazon Catchments The objective of this paper is to simulate flow frequency distribution curves for Amazon catchments with the aim of scaling power generation from small hydroelectric power plants. Thus, a simple nonlinear rainfall-runoff model was developed with sigmoid-variable gain factor due to the moisture status of the catchment, which depends on infiltration, and is considered a factor responsible for the nonlinearity of the rainfall-runoff process. Data for a catchment in the Amazon was used to calibrate and validate the model. The performance criteria adopted were the Nash-Sutcliffe coefficient (R2), the RMS, the Q95% frequencyc flow percentage error, and the mean percentage errors ranging from Q5% to Q95%.. Calibration and validation showed that the model satisfactorily simulates the flow frequency distribution curves. In order to find the shortest period of rainfall-runoff data, which is required for applying the model, a sensitivity analysis was performed whereby rainfall and runoff data was successively reduced by 1 year until a 1.5-year model application minimum period was found. This corresponds to one hydrological year plus the 6-month long "memory". This analysis evaluates field work in the ungauged sites of the region.

A non-linear rainfall-runoff model applied to Amazon small catchments with limited data to simulate the flow duration curves

In Amazon, hydroelectric power production excludes ungauged small catchments. Thus, the main objective of this paper is the implementation of a non-linear rainfall-runoff model on small catchments in the Amazon region to simulate flow duration curves for the hydropower production. Because the rainfall-runoff process is non-linear, modification is applied to a simple linear model based on the residuals relationship between the simulated and observed discharges. For calibration and sensitivity analysis of the model, seven years to one year of rainfall and flow data were used; and for validation, seven-year data from a small source catchment were used. The sensitivity analysis determined that the minimum length of data is 18 months. Thus, the model was applied in an experimental catchment with 1.5 year of data. The good results of the model application showed that it could be applied in other small catchments with limited data in the Amazon region to simulate flow duration curves.

A nonlinear rainfall–runoff model embedded with an automated calibration method – Part 1: The model

Summary The purpose of this paper is to propose a nonlinear rainfall–runoff model that can overcome two problems of the ANN (artificial neural networks) based rainfall–runoff models. These two problems both result from the construction of the memory of the rainfall–runoff process. First, the two problems are explained. Then, the nonlinear computational unit (NCU), which is the building block of the proposed model, is introduced. The proposed model is established by cascading several NCUs and hence is called the nonlinear computational units cascaded (NCUC) model. The instructions to model the rainfall–runoff process using the NCUC model are given in this paper. Two actual storm events are simulated using a well-calibrated NCUC model. The modeling results are evaluated using five common performance criteria. The performance of the NCUC model is compared with that of three conventional and two ANN based rainfall–runoff models. The comparison shows that the NCUC model outperforms the conventional models and performs as well as the ANN based models. However, unlike the ANN based models, the memory of the rainfall–runoff process is involved implicitly in the NCUC model. Therefore, the capability of the NCUC model is more comprehensive than that of the ANN based models. It can be concluded that the NCUC model can solve the problems encountered by the ANN based rainfall–runoff models.

A nonlinear rainfall-runoff model using neural network technique: example in fractured porous media

One of the more advanced approaches for simulating groundwater flow in karstic and fractured porous media is the combination of a linear and a nonlinear model. The paper presents an attempt to determine outflow influencing parameters in order to simulate aquifer outflow. Our approach in this study is to create a productive interaction system between expert, mathematical model, MERO, and artificial neural networks (ANNs). The proposed method is especially suitable for the problem of large-scale and long-term simulation. In the present project, the first objective is to determine aquifer outflow influencing parameters by the use of MERO model, which gave a good results in a fissured and chalky media, and then introduce these parameters in neural network (NN). To determine outflow influencing parameters, we propose to test the NN under fourth different external input scenarios. The second objective is to investigate the effect of temporal information by taking current and past data sets. The good found results reveal the merit of ANNs-MERO combination and specifically multilayer perceptron (MLP) models. This methodology provided that the network with lower, lag and number hidden layer, consistently produced better performance.

A non-linear rainfall–runoff model using an artificial neural network

A rainfall–runoff model that can be successfully calibrated (i.e., yielding sufficiently accurate results) using relatively short lengths of data, is desirable for any basin in general, and the basins of developing countries like India, in particular, for which scarcity of data is a major problem. An artificial neural network paradigm, known as the temporal back propagation neural network (TBP-NN), is successfully demonstrated as a monthly rainfall–runoff model. The performance of this model in a “scarce data” scenario (i.e., the effects of using reduced calibration periods on the performance) is compared with Volterra-type Functional Series Models (FSM), utilising the data of the River Lee (in the UK) and the Thuthapuzha River (in Kerala, India). The results confirm the TBP-NN model as being the most efficient of the black-box models tested for calibration periods as short as six years.

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

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.

Parameter Uncertainty Propagation Analysis for Urban Rainfall Runoff Modelling

The paper proposes a strategy for model uncertainty propagation analysis. As an example, parameter uncertainty propagation analysis in the runoff block of the HYSTEM-EXTRAN model is carried out. The model is a modification of the well-known SWMM (Storm Water Management Model). Uncertainty propagation methods such as first-order analysis, sensitivity analysis, statistical linearization and Monte-Carlo analysis are discussed and applied. A pathway of parameter uncertainty propagation analysis is given based on validity, simplicity, and computational requirements. The pathway starts with sensitivity analysis which may help to reduce the dimensions of a multidimensional model by discarding insensitive parameters. This is to obtain a mathematically tractable uncertainty propagation problem for a complicated model. Then, the nonlinearity of the model must be quantified to check the validity of first-order analysis. If first-order analysis is not valid, and if components of model output uncertainty need to be known, the application of statistical linearization is the only analytical alternative. Monte-carlo analysis can always be applied and taken as a reference as long as the components of the model output uncertainty are not of interest. The parameter sensitivity is characterized by its sensitivity coefficient which is defined as the ratio of the coefficient of variance of a model output to the coefficient of variance of the model parameter itself. A nonlinear rainfall runoff model usually results in a variable parameter sensitivity. Hence, recommendations about parameter sensitivity cannot be generalized for a given rainfall-runoff model, but depend on the type and the range of the model output variable. It is shown that the type of probability density function describing the parameter uncertainty with known mean and variance has only a small effect on the results of the model output uncertainty.

Improvement of Nonlinear Rainfall-Runoff Model

Water resources engineers have long been aware that the linear assumption of unit hydrograph models produces poor results in some basins. The Amorocho-Branstetter nonlinear model is an alternative to unit hydrograph models in these instances, but has not been as popular, perhaps because the user had to determine the parameters by trial-and-error, thereby needing to understand more of the mathematical background of the model than desirable. Moreover, in many instances, the trial-and-error procedure was expensive and tedious. This paper presents a way to efficiently calculate the three main model parameters, memory, U, order, IORD, and truncation, M1 and M2. These calculations are programmed into the model so the user need not supply them.

A non-linear rainfall-runoff model, providing for variable lag time

The cascading reservoir analogue of the rainfall-runoff process is extended, by the introduction of an additional parameter, to permit application to catchments exhibiting variable lag times. A semi-empirical relationship between lag time and storage is incorporated, and the total-runoff hydrograph provided for. The resulting non-linear model leads to improved representation of the observed events against which it has been assessed.