Rainfall-Runoff Modelling Using Artificial Neural Networks (ANNs)

Over the last decades or so, artificial neural networks (ANNs) have become one of the most promising tools for modelling hydrological processes such as rainfall-runoff processes. In most studies, ANNs have been demonstrated to show superior result compared to the traditional modelling approaches. They are able to map underlying relationships between input and output data without detailed knowledge of the processes under investigation, by finding an optimum set of network parameters through the learning or training process. This thesis considers two types of ANNs, namely, self-organizing map (SOM) and feed-forward multilayer perceptron (MLP). The thesis starts with the issue of understanding of a trained ANN model by using neural interpretation diagram (NID), Garson's algorithm and a randomization approach. Then the applicability of the SOM algorithm within water resources applications is reviewed and compared to the well-known feed-forward MLP. Moreover, the thesis deals with the problem of missing values in the context of a monthly precipitation database. This part deals with the problem of missing values by using SOM and feed-forward MLP models along with inclusion of regionalization properties obtained from the SOM. The problem of filling in of missing data in a daily precipitation-runoff database is also considered. This study deals with the filling in of missing values using SOM and feed-forward MLP along with multivariate nearest neighbour (MNN), regularized expectation-maximization algorithm (REGEM) and multiple imputation (MI). Finally, once a complete database was obtained, SOM and feed-forward MLP models were developed in order to forecast one-month ahead runoff. Some issues such as the applicability of the SOM algorithm for modularization and the effect of the number of modules in modelling performance were investigated. It was found that it is indeed possible to make an ANN reveal some information about the mechanisms governing rainfall-runoff processes. The literature review showed that SOMs are becoming increasingly popular but that there are hardly any reviews of SOM applications. In the case of imputation of missing values in the monthly precipitation, the results indicated the importance of the inclusion of regionalization properties of SOM prior to the application of SOM and feed-forward MLP models. In the case of gap-filling of the daily precipitation-runoff database, the results showed that most of the methods yield similar results. However, the SOM and MNN tended to give the most robust results. REGEM and MI hold the assumption of multivariate normality, which does not seem to fit the data at hand. The feed-forward MLP is sensitive to the location of missing values in the database and did not perform very well. Based on the one-month ahead forecasting, it was found that although the idea of modularization based on SOM is highly persuasive, the results indicated a need for more principled procedures to modularize the processes. Moreover, the modelling results indicated that a supervised SOM model can be considered as a viable alternative approach to the well-known feed-forward MLP model

Imputation of missing values in a precipitation-runoff process database

Hydrologists are often faced with the problem of missing values in a precipitation-runoff process database to construct runoff prediction models. They tend to use simple and naive methods to deal with the problem of missing data. Thus far, the common practice has been to discard observations with missing values. In this paper, we present some statistically principled methods for gap filling and discuss the pros and cons of these methods. We employ and discuss imputations of missing values by means of self-organizing map (SOM), multilayer perceptron (MLP), multivariate nearest-neighbor (MNN), regularized expectation-maximization algorithm (REGEM) and multiple imputation (MI) in the context of a precipitation-runoff process database in northern Iran in order to construct a serially complete database for analyses such as runoff prediction. In our case, the SOM and MNN tend to give similar and robust results. REGEM and MI build on the assumption of multivariate normal data, which we don't seem to have in one of our cases. MLP tends to produce inferior results because it fragments the data into 68 different models. Therefore, we conclude that it makes most sense to use either the computationally simple MNN method or the more demanding SOM

Interpolating monthly precipitation by self-organizing map (SOM) and multilayer perceptron (MLP)

There are needs to find better and more efficient methods to interpolate precipitation data in space and time. Interpolation of precipitation is explored using a self-organizing map (SOM) in a region with large complexity of precipitation mechanisms (northern Iran). The technique is used both for regionalization and for interpolating monthly precipitation for stations with missing data for 1-, 2-, 5- and 10-year periods using a jack-knife procedure to obtain objective results. The SOM is able both to find regions with similar precipitation mechanisms and to interpolate with accuracy. The results show that precipitation interpolation can be improved considerably by taking into account the regionalization properties in the SOM modelling. The SOM results are compared with those from a well-defined multilayer perceptron (MLP). The findings suggest that, without regionalization, MLP modelling is generally better than SOM. However, when regionalization is included, SOM performs better than MLP. Il est nécessaire de trouver des méthodes meilleures et plus efficaces pour interpoler des données de précipitation dans l'espace et le temps. L'utilisation d'une carte auto-organisée (SOM) pour l'interpolation des précipitations est explorée dans une région aux mécanismes de précipitation très complexes (nord de l'Iran). La technique est utilisée pour la régionalisation et pour l'interpolation des précipitations mensuelles de stations qui présentent des lacunes pour des périodes de 1, 2, 5 et 10 ans, à l'aide d'une procédure jack-knife pour obtenir des résultats objectifs. La SOM est capable d'identifier les régions dont les mécanismes de précipitation sont similaires et d'interpoler avec précision. Les résultats montrent que l'interpolation des précipitations peut être considérablement améliorée en tenant compte des propriétés de régionalisation dans la modélisation SOM. Les résultats de SOM sont comparés avec ceux d'un perceptron multi-couches (PMC) bien défini. Les résultats suggèrent que, sans régionalisation, la modélisation par PMC est généralement meilleure que par SOM. Cependant, lorsque la régionalisation est introduite, la SOM donne de meilleurs résultats que le PMC

Review of the self-organizing map (SOM) approach in water resources: Analysis, modelling and application

The use of artificial neural networks (ANNs) in problems related to water resources has received steadily increasing interest over the last decade or so. The related method of the self-organizing map (SOM) is an unsupervised learning method to analyze, cluster, and model various types of large databases. There is, however, still a notable lack of comprehensive literature review for SOM along with training and data handling procedures, and potential applicability. Consequently, the present paper aims firstly to explain the algorithm and secondly, to review published applications with main emphasis on water resources problems in order to assess how well SOM can be used to solve a particular problem. It is concluded that SOM is a promising technique suitable to investigate, model, and control many types of water resources processes and systems. Unsupervised learning methods have not yet been tested fully in a comprehensive way within, for example water resources engineering. However, over the years, SOM has displayed a steady increase in the number of applications in water resources due to the robustness of the method

Estimation of Fagus orientalis Lipsky height using nonlinear models in Hyrcanian forests, Iran

Tree height is one of the most important variables in describing forest stand structure. However, due to difficulty in height measurement, especially in dense and mountainous forests, the common approach is to invoke the height-diameter (H-D) models. The oriental beech (Fagus orientalis Lipsky) is one of the most important species of Hyrcanian forests, over the mid to high-altitudes (400-1 800 m a.s.l.), in northern Iran. In this study, the H-D relationship of beech trees was investigated separately for mid-altitude and high-altitude in Shafaroud forests of Guilan using 14 nonlinear H-D models and an artificial neural network model (ANN). To collect data, a systematic random sampling method within a 100 × 100 m regular randomized grid was applied. In total, 3 243 individual trees in 255 circular plots with 0.1 ha were measured. For comparing the results, performance criteria including root mean square error (RMSE), R2adj, Akaike's information criterion (AIC), and mean absolute error (MAE) were used. In high and mid altitudes, Meyer (1940) and Bates and Watts (1980) models had the best performance, while Watts (1983) model and Burkhart-Strub (1974) model had the worst performance in high-altitude and in mid-altitude, respectively. On the other hand, the ANN model had the best accuracy and performance in both sites. Since the performance of the ANN model is superior and consistent compared to the common nonlinear models, here it is preferred for both regions