Monthly Rainfall Prediction using Artificial Neural Networks and M5 Model Tree (Case study: Station of AHAR)

Introduction
Rainfall is considered as one of the most important factures in water cycle. Prediction of monthly rainfall is important for many purposes such as estimating torrent, drought, run-off, sediment, irrigation programming and also management of drainage basins. Rainfall prediction in each area is mediated by punctual data measured as humidity, temperature, wind speed and etc. As Iran is located in a hot and arid region and also for lack of water sources, and water supply and protection it is important to study rainfall characteristics in this area. The limitations such as unavailability of adequate data about rainfall measure in different temporal and spatial scales and also complicated boundaries among meteorology factures related to rainfall caused inexact and non- trustable examinations. According to recent improvements especially in the field of computer processing and new data mining methods such as artificial neural network, decision trees, genetic algorithms and Support vector machines, so many efforts have been taken to solve complicated and high dimension issues in different kinds of engineering fields.
Material and Methods
In this study, we have used different kinds of meteorology parameters on month scale in AHAR region. It is located in East Azarbayjan Province, IRAN. Different concepts of combination of these meteorology parameters have been entered to artificial neural network and M5 model tree as our chosen data mining methods. The idea of artificial neural networks is based on structure of human brain. These structures include three layers that named as input layer, hidden layer and output layer. To achieve the best structure of this network we must try different combination of parameters and change the type of transfer function and other factures. M5 model tree is a data mining approach that divides the data space into smaller subspaces by divide-and-conquer method. This technique splits the parameter space into areas (subspaces) and builds in each of them by a linear regression model. The M5 model tree approach, (Quinlan, 1992), based on the principle of information theory, makes it possible to split the multidimensional parameter of space and generate the models automatically according to the overall quality criterion. It also allows the number of models. The splitting in this approach follows the idea of a decision tree, but instead of the class labels, it has linear regression functions at the leaves, which can predict continuous numerical attributes. Thus, they are analogous to piece-wise linear functions. Computational requirements for model trees grow rapidly with increase in dimensionality of the data set. Model trees learn efficiently and can tackle tasks with very high dimensionality. The major advantage of the model trees relative to regression trees is that model trees are much smaller than regression trees, the decision strength is clear, and regression functions do not normally involve many variables. Finally, after making these models, we evaluate these models with statistics such as RMSE and R coefficient.
 
Results and discussion
In this paper, we have tried various combinations of different meteorology parameters. Then we choose the best model according to these facts. At first, that model has high amount of R coefficient and lesser amount of RMSE and it is also made by less meteorology parameters. We achieve, respectively, the amount of 0.84 and 12.14 for R and RMSE statistics in artificial neural network method and amount of 0.87 and 11.45 for R and RMSE statistics in M5 model tree approaches. We achieve our best results in M5 model tree method, with using the combination of maximum and minimum amount of monthly temperature, maximum and minimum amount of monthly relative humidity and maximum and minimum amount of monthly pressure at station. We also achieve our the best result in artificial neural network method by using  the combination of maximum and minimum amount of monthly temperature, maximum and minimum amount of monthly relative humidity, and maximum and minimum amount of monthly pressure at station. The results indicate that, both of artificial neural networks and M5 model tree methods present the comparatively exact result for rainfall prediction in the region. However, due to having simple and understandable equations provided with M5 model tree method, this method could be considerate as an efficient application and as substitute for rainfall measurement.
Conclusion
Both of artificial neural networks and M5 model tree have good performance in predicting monthly rainfall. The results shows that both of these methods have almost equal performance in this case but due to providing simple and explicit equations with M5 model tree method, this method could be considerate as an efficient and practical application and substitutes for rainfall measurement.