Hierarchical Fuzzy Systems Integrated with Particle Swarm Optimization for Daily Reference Evapotranspiration Prediction: A Novel Approach

Reference evapotranspiration (ET0) is a crucial element for deriving a meaningful scheduling of irrigation for major crops. Thus, precise projection of future ET0 is essential for better management of scarce water resources in many parts of the globe. This study evaluates the potential of a Hierarchical Fuzzy System (HFS) optimized by Particle Swarm Optimization (PSO) algorithm (PSO-HFS) to predict daily ET0. The meteorological variables and estimated ET0 were employed as inputs and outputs, respectively, for the PSO-HFS model. The FAO 56 PM method to ET0 computation was implemented to obtain ET0 values using the climatic variables obtained from two weather stations located in Gazipur Sadar and Ishurdi, Bangladesh. Prediction accuracy of PSO-HFS was compared with that of a FIS, M5 Model Tree, and a Regression Tree (RT) model. Several statistical performance evaluation indices were used to evaluate the performances of the PSO-HFS, FIS, M5 Model Tree, and RT in estimating daily ET0. Ranking of the models was performed using the concept of Shannon’s Entropy that accounts for a set of performance evaluation indices. Results revealed that the PSO-HFS model performed better than the tree-based models. Generalization capabilities of the preposed models were evaluated using the dataset from a test station (Ishurdi station). Results revealed that the models performed equally well with the unseen test dataset, and that the PSO-HFS model provided superior performance over other tree based models. The overall results imply that PSO-HFS model could effectively be utilized to model ET0 values quite efficiently and accurately.

Application of M5 Model Tree in Passive Remote Sensing of Thin Ice Cloud Microphysical Properties in Terahertz Region

This article presents a new method for retrieving the Ice Water Path (IWP), the median volume equivalent sphere diameter (Dme) of thin ice clouds (IWP < 100 g/m2, Dme < 80 μm) in the Terahertz band. The upwelling brightness temperature depressions caused by the ice clouds at 325.15, 448.0, 664.0 and 874.0 GHz channels are simulated by the Atmospheric Radiative Transfer Simulator (ARTS). The simulated forward radiative transfer models are taken as historical data for the M5 model tree algorithm to construct a set of piecewise functions which represent the relation of simulated brightness temperature depressions and IWP. The inversion results are optimized by an empirical relation of the IWP and the Dme for thin ice clouds which is summarized by previous studies. We inverse IWP and Dme with the simulated brightness temperature and analyze the inversion performance of selected channels. The 874.4 ± 6.0 GHz channel provides the most accurate results, because of the strong brightness temperature response to the change of IWP in the forward radiative transfer model. In order to improve the thin ice clouds IWP and Dme retrieval accuracy at the middle-high frequency channels in Terahertz band, a dual-channel inversion method was proposed that combines the 448.0 ± 3.0 GHz and 664.0 ± 4.2 GHz channel. The error analysis shows that the results of the 874.4 ± 6.0 GHz channel and the dual-channel inversion are reliable, and the IWP inversion results meet the error requirement range proposed by previous studies.

Evaluating the Performance of Different Artificial Intelligence Techniques for Forecasting: Rainfall and Runoff Prospective

The forecasting plays key role for the water resources planning. Most suitable technique is Artificial intelligence techniques (AITs) for different parameters of weather forecasting and generated runoff. The study compared AITs (RBF-SVM and M5 model tree) to understand the rainfall runoff process in Jhelum River Basin, Pakistan. The rainfall and runoff of Jhelum river used from 1981 to 2012. The Different rainfall and runoff dataset combinations were used to train and test AITs. The data record for the period 1981–2001 used for training and then testing. After training and testing, modeled runoff and observed data was evaluated using R2, NRMSE, COE and MSE. During the training, the dataset C2 and C3 were found to be 0.71 for both datasets using M5 model. Similar results were found for dataset of C3 using RBF-SVM. Over all, C3 and C7 were performed best among all the dataset. The M5 model tree was performed better than other applied techniques. GEP has also exhibited good results to understand rainfall runoff process. The RBF-SVM performed less accurate as compare to other applied techniques. Flow duration curve (FDCs) were used to compare the modeled and observed dataset of Jhelum River basin. For High flow and medium high flows, GEP exhibited well. M5 model tree displayed the better results for medium low and low percentile flows. RBF-SVM exhibited better for low percentile flows. GEP were found the accurate and highly efficient DDM among the AITs applied techniques. This study will help understand the complex rainfall runoff process, which is stochastic process. Weather forecasting play key role in water resources management and planning.

Pipe Break Rate Assessment While Considering Physical and Operational Factors: A Methodology Based on Global Positioning System and Data Driven Techniques

Deterioration of urban Water Distribution Networks (WDNs) is one of the primary cases of water supply losses, leading to the huge expenditures on the replacement and rehabilitation of elements WDNs. An accurate prediction of pipes failure rate play a substantial role in the management of WDNs. In this study, a field study was conducted to register pipes break and relevant causes in the WDN of Yazd City, Iran. In this way, 851 water pipes were incepted and localized by the Global Positioning System (GPS) apparatus. Then, 1033 failure cases were reported in the eight zones of under study WDN during March-December 2014. Pipes break rate (BRP) was calculated using the depth of pipe installation (hP), number of failure (NP), pressure of water pipes in operation (P), and age of pipe (AP). After completing a pipe break database, robust Artificial Intelligence models, namely Multivariate Adaptive Regression Spline (MARS), Gene-Expression Programming (GEP), and M5 Model Tree were employed to extract precise formulation for the pipes break rate estimation. Results of the proposed relationships demonstrated that MARS model with Coefficient of Correlation (R) of 0.981 and Root Mean Square Error (RMSE) of 0.544 provided more satisfying efficiency than M5 model (R = 0.888 and RMSE = 1.096). Furthermore, statistical results indicated that MARS and GEP models had comparatively at the same accuracy level. Explicit equations by AI models were satisfactorily comparable with those obtained by literature review in terms of various conditions: physical, operational, and environmental factors and complexity of AI models. Through a probabilistic framework for the pipes break rate, the results of first-order reliability analysis that MARS technique had highly satisfying performance when MARS-extracted-equation was assigned as a limit state function.

Modelling Reference Evapotranspiration using a Novel Regression-based Method: Radial basis M5 Model Tree

In the current study, an ability of a novel regression-based method is evaluated in modelling daily reference evapotranspiration (ET0), which is an important issue in water resources management plans and helps farmers in irrigation planning. The method was developed by hybridizing radial basis function and M5 model tree and called as radial basis M5 model tree (RM5Tree). The radial-based kernel function was used to control the input variables in modelling process of M5 model tree. The new model results were compared with traditional M5 model tree (M5Tree), response surface method (RSM) and two neural networks (multi-layer perceptron neural networks, MLPNN & radial basis function neural network, RBFNN) with respect to several statistical indices. Daily climatic data (relative humidity, RH, solar radiation, SR, wind speed, air temperature, T) recorded at three stations in Turkey, Mediterranean Region, were used. The effect of each weather data on ET0 was also investigated by utilizing three different input scenarios with various combinations of input variables. On the whole, the RM5Tree provided the best results (NSE > 0.997) followed by the MLPNN (NSE > 0.990), and M5Tree (NSE > 0.945) in modelling daily ET0. The SR was observed as the most effective input parameter on ET0 which was followed by the T and RH. However, the findings of the third modelling scenario revealed that taking into account of all variables would considerably increase models’ accuracies for the three stations.