Daily Rainfall Prediction Research Articles

Maximizing daily rainfall prediction accuracy with maximum overlap discrete wavelet transform‐based machine learning models

AbstractRainfall is an important phenomenon for various aspects of human life and the environment. Accurate prediction of rainfall is crucial for a wide range of sectors, including agriculture, water resources management, energy production, disaster management and many more. The ability to predict rainfall in an accurate fashion enables stakeholders to make informed decisions and take necessary actions to mitigate the impacts of natural disasters, water scarcity and other issues related to rainfall. In addition, advances in rainfall prediction technologies have the potential to contribute to sustainable water management and the preservation of water resources by providing the necessary information for decision‐makers to plan and implement effective water management strategies. Hence, it is important to continuously improve the accuracy of rainfall prediction. In this paper, the integration of the maximum overlap discrete wavelet transform (MODWT) and machine learning algorithms for daily rainfall prediction is proposed. The main objective of this study is to investigate the potential of combining MODWT with various machine‐learning algorithms to increase the accuracy of rainfall prediction and extend the forecast time horizon to 3 days. In addition, the performances of the proposed hybrid models are contrasted with the models hybridized with commonly used discrete wavelet transform (DWT) algorithms in the literature. For this, daily rainfall raw data from three rainfall observation stations located in Turkey are used. The results show that the proposed hybrid MODWT models can effectively improve the accuracy of precipitation forecasting, based on model evaluation measures such as mean square error (MSE) and Nash‐Sutcliffe coefficient of efficiency (CE). Accordingly, it can be concluded that the integration of MODWT and machine learning algorithms have the potential to revolutionize the field of daily rainfall prediction.

Hybrid artificial intelligence models based on adaptive neuro fuzzy inference system and metaheuristic optimization algorithms for prediction of daily rainfall

In this study, our primary objective is the accurate prediction of daily rainfall through the application of various hybrid Artificial Intelligence (AI) methods. These methods are grounded in the Adaptive Neuro Fuzzy Inference System (ANFIS) and employ metaheuristic optimization algorithms, specifically the Artificial Bee Colony (ABC), Genetic Algorithm (GA), and Simulated Annealing (SA). The meteorological data utilized for modeling rainfall prediction is sourced from Hoa Binh province in Vietnam. To enhance the datasets, we employed the Savitzky-Golay filtering as a preprocessing noise reduction technique. The performance of the models was assessed using well-established statistical error criteria, including the Correlation Coefficient (R), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and other contingency scores. Our findings indicate that the ANFIS-ABC hybrid model outperforms other models, such as ANFIS-SA and ANFIS-GA, in predicting daily rainfall, achieving an R value of 0.82 with raw data and 0.9 with preprocessed data. Notably, the results underscore the positive impact of employing noise reduction through data preprocessing, enhancing the predictive quality of the hybrid models. This study holds significance in the realm of water resource and land management, offering valuable insights for the accurate prediction of daily rainfall.

Enhanced rainfall prediction performance via hybrid empirical-singular-wavelet-fuzzy approaches

Rainfall is a vital process in the hydrological cycle of the globe. Accessing reliable and accurate rainfall data is crucial for water resources operation, flood control, drought warning, irrigation, and drainage. In the present study, the main objective is to develop a predictive model to enhance daily rainfall prediction accuracy with an extended time horizon. In the literature, various methods for the prediction of daily rainfall data for short lead times are presented. However, due to the complex and random nature of rainfall, in general, they yield inaccurate prediction results. Generically, rainfall predictive models require many physical meteorological variables and consist of challenging mathematical processes that require high computational power. Furthermore, due to the nonlinear and chaotic nature of rainfall, observed raw data typically has to be decomposed into its trend cycle, seasonality, and stochastic components before being fed into the predictive model. The present study proposes a novel singular spectrum analysis (SSA)-based approach for decomposing observed raw data into its hierarchically energetic pertinent features. To this end, in addition to the stand-alone fuzzy logic model, preprocessing methods SSA, empirical mode decomposition (EMD), and commonly used discrete wavelet transform (DWT) are incorporated into the fuzzy models which are named as hybrid SSA-fuzzy, EMD-fuzzy, W-fuzzy models, respectively. In this study, fuzzy, hybrid SSA-fuzzy, EMD-fuzzy, and W-fuzzy models are developed to enhance the daily rainfall prediction accuracy and improve the prediction time span up to 3 days via three (3) stations' data in Turkey. The proposed SSA-fuzzy model is compared with fuzzy, hybrid EMD-fuzzy, and widely used hybrid W-fuzzy models in predicting daily rainfall in three distinctive locations up to a 3-day time horizon. Improved accuracy in predicting daily rainfall is provided by the SSA-fuzzy, W-fuzzy, and EMD-fuzzy models compared to the stand-alone fuzzy model based on mean square error (MSE) and the Nash-Sutcliffe coefficient of efficiency (CE) model assessment metrics. Specifically, the advocated SSA-fuzzy model is found to be superior in accuracy to hybrid EMD-fuzzy and W-fuzzy models in predicting daily rainfall for all time spans. The results reveal that, with its easy-to-use features, the advocated SSA-fuzzy modeling tool in this study is a promising principled method for its possible future implementations not only in hydrological studies but in water resources and hydraulics engineering and all scientific disciplines where future state space prediction of a vague nature and stochastic dynamical system is important.

Assessment of Accuracy of Indian Almanac for Daily Rainfall Prediction

Background/Objectives: Modern science is able to predict various aspects of weather including rainfall, but it still does not provide high accuracy when we consider longer duration predictions in the future, which are very important for Agriculture. In countries like India, Ancient knowledge-based rainfall predictions are being made till this day. This research paper is an attempt to predict daily rainfall based on a limited implementation of rules from various Panchangs, and assessment of accuracy of these predictions in an unbiased manner. Methods: These predictions have been compared against the revalidated and actual daily rainfall data for accuracy calculation. We have assessed accuracy for overall 30 versions/test scenarios, which contain 7 versions of Traditional Maharashtrian Panchang, 8 versions of Telugu Panchang, 1 version of Saptanadi. This is followed by 4 scenarios of comparison with actual data and 4 with Hourly predictions vs data. Findings: We achieved a respectable accuracy of 81%(For Traditional Maharashtrian Panchang) and 79% (Telugu Panchang) when tested with 40 years of revalidated daily rainfall data between 1st Jan 1980 to 31st Aug 2020 across the world in India and other continents. Novelty: The comparison is based on daily rainfall accuracy which has not been seen before. Also, for the first time, we are able to prove the global applicability of the Panchang rules for precipitation prediction. This study is not intended to comment on the overall accuracy of any of the Panchangs, makes best possible combination useful to Indian farmer. We intend to make these predictions available as a website and an API to make this research directly usable. Keywords: Panchang; Conjunctions; Nakshatras; Ecliptic Longitude; Right Ascension; Rainfall Prediction; Weather Prediction

Predictive Modelling of Statistical Downscaling Based on Hybrid Machine Learning Model for Daily Rainfall in East-Coast Peninsular Malaysia

In recent years, climate change has demonstrated the volatility of unexpected events such as typhoons, flooding, and tsunamis that affect people, ecosystems and economies. As a result, the importance of predicting future climate has become even direr. The statistical downscaling approach was introduced as a solution to provide high-resolution climate projections. An effective statistical downscaling scheme aimed to be developed in this study is a two-phase machine learning technique for daily rainfall projection in the east coast of Peninsular Malaysia. The proposed approaches will counter the emerging issues. First, Principal Component Analysis (PCA) based on a symmetric correlation matrix is applied in order to rectify the issue of selecting predictors for a two-phase supervised model and help reduce the dimension of the supervised model. Secondly, two-phase machine learning techniques are introduced with a predictor selection mechanism. The first phase is a classification using Support Vector Classification (SVC) that determines dry and wet days. Subsequently, regression estimates the amount of rainfall based on the frequency of wet days using Support Vector Regression (SVR), Artificial Neural Networks (ANNs) and Relevant Vector Machines (RVMs). The comparison between hybridization models’ outcomes reveals that the hybrid of SVC and RVM reproduces the most reasonable daily rainfall prediction and considers high-precipitation extremes. The hybridization model indicates an improvement in predicting climate change predictions by establishing a relationship between the predictand and predictors.

Deep learning model for daily rainfall prediction: case study of Jimma, Ethiopia

Abstract Rainfall prediction is a critical task because many people rely on it, particularly in the agricultural sector. Rainfall forecasting is difficult due to the ever-changing nature of weather conditions. In this study, we carry out a rainfall predictive model for Jimma, a region located in southwestern Oromia, Ethiopia. We propose a Long Short-Term Memory (LSTM)-based prediction model capable of forecasting Jimma's daily rainfall. Experiments were conducted to evaluate the proposed models using various metrics such as Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), Nash–Sutcliffe model efficiency (NSE), and R2, and the results were 0.01, 0.4786, 0.81 and 0.9972, respectively. We also compared the proposed model with existing machine-learning regressions like Multilayer Perceptron (MLP), k-Nearest Neighbors (KNN), Support Vector Machine (SVM), and Decision Tree (DT). The RMSE of MLP was the lowest of the four existing learning models i.e., 0.03. The proposed LSTM model outperforms the existing models, with an RMSE of 0.01. The experimental results show that the proposed model has a lower RMSE and a higher R2.

Evaluation of several cumulus parameterization schemes for daily rainfall predictions over Palembang City

The daily rainfall prediction calculated from four Cumulus schemes i.e.: Kain-Fritsch (KF), New Tiedtke (NT), Grell 3D ensemble (G3D), and Betts-Miller-Janjic (BMJ) had been tested for compliance with daily observation data for 90 days (1 Dec 2018 to 28 Feb 2019) from three observer stations in Palembang city: BMKG-Kenten (Kenten), BMKG-SMB2 (SMB2) and Unsri Bukit Besar (UBB). The test results show that the BMJ cumulus scheme provides better suitability for 19 out of 45 unique indicators for rainfall event indicator (REI) groups and for as many as 13 out of 27 unique indicators for rainfall intensity indicator (RII) groups. The four schemes are able to provide the good performance for each on different indicators and stations, however, in general the BMJ scheme gives the best performance in predicting daily rainfall over Palembang city.

Bayesian Regularized Neural Network Model Development for Predicting Daily Rainfall from Sea Level Pressure Data: Investigation on Solving Complex Hydrology Problem

Prediction of daily rainfall is important for flood forecasting, reservoir operation, and many other hydrological applications. The artificial intelligence (AI) algorithm is generally used for stochastic forecasting rainfall which is not capable to simulate unseen extreme rainfall events which become common due to climate change. A new model is developed in this study for prediction of daily rainfall for different lead times based on sea level pressure (SLP) which is physically related to rainfall on land and thus able to predict unseen rainfall events. Daily rainfall of east coast of Peninsular Malaysia (PM) was predicted using SLP data over the climate domain. Five advanced AI algorithms such as extreme learning machine (ELM), Bayesian regularized neural networks (BRNNs), Bayesian additive regression trees (BART), extreme gradient boosting (xgBoost), and hybrid neural fuzzy inference system (HNFIS) were used considering the complex relationship of rainfall with sea level pressure. Principle components of SLP domain correlated with daily rainfall were used as predictors. The results revealed that the efficacy of AI models is predicting daily rainfall one day before. The relative performance of the models revealed the higher performance of BRNN with normalized root mean square error (NRMSE) of 0.678 compared with HNFIS (NRMSE = 0.708), BART (NRMSE = 0.784), xgBoost (NRMSE = 0.803), and ELM (NRMSE = 0.915). Visual inspection of predicted rainfall during model validation using density‐scatter plot and other novel ways of visual comparison revealed the ability of BRNN to predict daily rainfall one day before reliably.

Long-term rainfall prediction using atmospheric synoptic patterns in semi-arid climates with statistical and machine learning methods

In this paper, we evaluate the performance of 8 statistical and machine learning methods, driven by atmospheric synoptic patterns, for long-term daily rainfall prediction in a semi-arid climate (Tenerife, Spain). Cross-validation is used to reconstruct 36 years of daily rainfall data at 17 gauges. Prediction is independent for each gauge. The reconstructed series are compared with the observed records in order to select the optimal hyperparameters within each family of models. The predictive performance of the models is evaluated using several metrics and statistics related with rainfall intensity and occurrence at daily, monthly and annual aggregation scales. Multivariate and univariate analysis of variance are used to evaluate the differences among models.The results of our work demonstrate that the performance of most machine learning models is very sensitive to the selected hyperparameters. Neural networks are found to perform best to predict rainfall occurrence and intensity. All methods underestimate the variance of the observed series at daily time scales. Generalized linear models using gamma-distributed errors perform best for predicting rainfall extremes, however, their performance limits its practical applications. Results improve significatively at larger temporal aggregations (monthly or annual) making statistical and machine learning methods more valuable for water resources studies.

Development of advanced artificial intelligence models for daily rainfall prediction

Abstract In this study, the main objective is to develop and compare several advanced Artificial Intelligent (AI) models namely Adaptive Network based Fuzzy Inference System optimized with Particle Swarm Optimization (PSOANFIS), Artificial Neural Networks (ANN) and Support Vector Machines (SVM) for the prediction of daily rainfall in Hoa Binh province, Vietnam. For this, meteorological variable parameters such as maximum temperature, minimum temperature, wind speed, relative humidity and solar radiation were collected and used as input parameters and daily rainfall as an output parameter in the models. Validation of the developed models was achieved using various quality assessment criteria such as correlation coefficient (R) and Mean Absolute Error (MAE), Skill Score (SS), Probability of Detection (POD), Critical Success Index (CSI), and False Alarm Ratio (FAR). The results showed that all the AI models provided reasonable predictions of daily rainfall but the SVM was found to be the best method for predicting rainfall. This method was also found to be the most robust and efficient prediction model while taking into account of input variability using the Monte Carlo approach. This AI based study would be helpful in quick and accurate prediction of daily rainfall.

Hybrid Deep Learning Approach for Multi-Step-Ahead Daily Rainfall Prediction Using GCM Simulations

Deep Learning (DL) is an effective technique for dealing with complex systems. This study proposes a hybrid DL approach, a combination of one-dimensional Convolutional Neural Network (Conv1D) and Multi-Layer Perceptron (MLP) (hereinafter referred to as hybrid Conv1D-MLP model), for multi-step-ahead (1-day to 5-day in advance) daily rainfall prediction. Nine meteorological variables, closely associated with daily rainfall variation, are used as inputs to the hybrid model. The causal variables are obtained from a General Circulation Model (GCM). In general, simulation of meteorological variables from GCM is much better than rainfall estimate and observed records of meteorological variables is sparsely available, if not completely unavailable at many locations. Thus, proposed scheme helps to establish the effectiveness of the DL approach in augmenting the quality of rainfall prediction, exploiting the potential of GCM in simulating meteorological variables. The developed hybrid model is applied to twelve different locations in different climatic regimes in terms of daily precipitation characteristics. The proposed hybrid approach is compared with a DL approach namely, Multi-Layered Perceptron (deep MLP) and another machine learning approach namely, Support Vector Regression (SVR). It is also found that the performance of the model gradually decreases as the prediction lead time (in days) increases. Overall, this study establishes the fact that the hybrid Conv1D-MLP model is more effective in capturing the complex relationship between the causal variables and daily variation of rainfall. The benefit is due to the unification of potentials of individual approaches for extracting the hidden features of hydrometeorological association.

Potential of Hybrid Data-Intelligence Algorithms for Multi-Station Modelling of Rainfall

One of the most challenging tasks in rainfall prediction is designing a reliable computational methodology owing the random and stochastic characteristics of time-series. In this study, the potential of five different data-driven models including Multilayer Perceptron (MLP), Least Square Support Vector Machine (LSSVM), Neuro-fuzzy, Hammerstein-Weiner (HW) and Autoregressive Integrated Moving Average (ARIMA) were employed for multi-station (Hien, Thank My, Hoi Khanh, Ai Nghia and Cai Lau) prediction of daily rainfall in the Vu Gia-Thu Bon River basin in Central Vietnam. Subsequently, hybrid ARIMA-MLP, ARIMA-LSSVM, ARIMA-NF and ARIMA-HW models were also utilized to predict the daily rainfall at these stations. The results were evaluated in terms of widely used performance criteria, viz.: determination coefficient (R2), root mean square error (RMSE), mean absolute error (MAE) and correlation coefficient (CC). Besides, the Taylor diagram is also used to examine and compare the similarity between the observed and predicted rainfall. The quantitative analysis indicated that the HW model increased the prediction accuracy by 5%, 3% and 2% at Hien, Ai Nghia and Cau Lau stations, respectively, compared to the other models. Likewise, the NF model increased the prediction accuracy at Thanh My and Hoi Khanh stations in contrast to the other models in terms of the mean absolute error. Also, the results of hybrid ARIMA-NF and ARIMA-HW models showed the best performance in terms of predictive skills and verified to increase the prediction accuracy in comparison to the single models.

Prediction of daily reservoir inflow using atmospheric predictors

Reservoir systems need the forecast of rainfall and inflow on daily time scale for planning of water allocation to different users. Prediction of daily rainfall or daily reservoir inflow is a challenging task in water resource management. This study aims at forecasting the daily reservoir inflow using the projections of atmospheric variables extracted from the global climatic models as input. Daily rainfall series for the future period is simulated using a calibrated weather generator based on generalized linear models. The simulated daily rainfall series are compared with the monthly predictions obtained from local polynomial regression model, and the best correlated daily rainfall simulation is transformed into stream flow using a calibrated and validated soil and water assessment tool to generate the daily inflow series. The modelling procedure was applied to a typical reservoir catchment in India. Diagnostic checks carried out to assess the performance of the rainfall simulations revealed that the simulated series are having the same statistical characteristics as that of the observed series. The simulated inflow was found to be acceptable with respect to the performance indicators evaluated in the study. The methodology adopted is data driven, flexible and easy to implement.

Performance comparison of artificial neural network models for daily rainfall prediction

With an aim to predict rainfall one-day in advance, this paper adopted different neural network models such as feed forward back propagation neural network (BPN), cascade-forward back propagation neural network (CBPN), distributed time delay neural network (DTDNN) and nonlinear autoregressive exogenous network (NARX), and compared their forecasting capabilities. The study deals with two data sets, one containing daily rainfall, temperature and humidity data of Nilgiris and the other containing only daily rainfall data from 14 rain gauge stations located in and around Coonoor (a taluk of Nilgiris). Based on the performance analysis, NARX network outperformed all the other networks. Though there is no major difference in the performances of BPN, CBPN and DTDNN, yet BPN performed considerably well confirming its prediction capabilities. Levenberg Marquardt proved to be the most effective weight updating technique when compared to different gradient descent approaches. Sensitivity analysis was instrumental in identifying the key predictors.

Organization of vertical shear of wind and daily variability of monsoon rainfall

Very little is known about the mechanisms that govern the day to day variability of the Indian summer monsoon (ISM) rainfall; in the current dominant view, the daily rainfall is essentially a result of chaotic dynamics. Most studies in the past have thus considered monsoon in terms of its seasonal (June–September) or monthly rainfall. We show here that the daily rainfall in June is associated with vertical shear of horizontal winds at specific scales. While vertical shear had been used in the past to investigate interannual variability of seasonal rainfall, rarely any effort has been made to examine daily rainfall. Our work shows that, at least during June, the daily rainfall variability of ISM rainfall is associated with a large scale dynamical coherence in the sense that the vertical shear averaged over large spatial extents are significantly correlated with area-averaged daily rainfall. An important finding from our work is the existence of a clearly delineated monsoon shear domain (MSD) with strong coherence between area-averaged shear and area-averaged daily rainfall in June; this association of daily rainfall is not significant with shear over only MSD. Another important feature is that the association between daily rainfall and vertical shear is present only during the month of June. Thus while ISM (June–September) is a single seasonal system, it is important to consider the dynamics and variation of June independently of the seasonal ISM rainfall. The association between large-scale organization of circulation and daily rainfall is suggested as a basis for attempting prediction of daily rainfall by ensuring accurate simulation of wind shear.

Prediction of daily rainfall by a hybrid wavelet-season-neuro technique

Accurate daily rainfall prediction is required for accurate streamflow prediction, flooding risk analysis, constructing a reliable flood control and early warning system. However, because of its nonlinearity, prediction of daily rainfall with high accuracy and long prediction lead time is difficult. There are many daily rainfall prediction methods in the literature, but they are known to yield inaccurate predictions with short lead time, require many physical parameters and involve complicated mathematical equations with huge computational burden. Recently, artificial neural network has been used for predicting rainfall with the objective of addressing the above mentioned problems. But still, the accuracy has not been satisfactory and predictions are with short lead time. In this study, two methods called combined season-multilayer perceptron (SAS-MP) and hybrid wavelet-season-multilayer perceptron (W-SAS-MP) were developed to enhance prediction accuracy and extend prediction lead time of daily rainfall up to 5 days by using data from two stations in Turkey. These two models were compared with the stand-alone multilayer perceptron and another most commonly used method called combined wavelet-multilayer perceptron (W-MP). The performances of the models were evaluated by using coefficient of determination, coefficient of efficiency and root mean squared error. The SAS-MP model was found to be better than W-MP in most cases, except lead time day 1, where W-MP performed better. Throughout all the lead times, however, the hybrid W-SAS-MP model performed best with CE values of 0.911 and 0.909, respectively, for prediction lead time of 1 day and 0.588 and 0.570, respectively, for prediction lead time of 5 days at Stations 17836 and 17837, respectively, at the model testing (validation) phase. Therefore, W-SAS-MP can be an appropriate tool for enhancing daily rainfall prediction accuracy and extend prediction lead time.

Estimation and prediction of maximum daily rainfall at Sagar Island using best fit probability models

Sagar Island, setting on the continental shelf of Bay of Bengal, is one of the most vulnerable deltas to the occurrence of extreme rainfall-driven climatic hazards. Information on probability of occurrence of maximum daily rainfall will be useful in devising risk management for sustaining rainfed agrarian economy vis-a-vis food and livelihood security. Using six probability distribution models and long-term (1982–2010) daily rainfall data, we studied the probability of occurrence of annual, seasonal and monthly maximum daily rainfall (MDR) in the island. To select the best fit distribution models for annual, seasonal and monthly time series based on maximum rank with minimum value of test statistics, three statistical goodness of fit tests, viz. Kolmogorove–Smirnov test (K-S), Anderson Darling test (A 2 ) and Chi-Square test (X 2) were employed. The fourth probability distribution was identified from the highest overall score obtained from the three goodness of fit tests. Results revealed that normal probability distribution was best fitted for annual, post-monsoon and summer seasons MDR, while Lognormal, Weibull and Pearson 5 were best fitted for pre-monsoon, monsoon and winter seasons, respectively. The estimated annual MDR were 50, 69, 86, 106 and 114 mm for return periods of 2, 5, 10, 20 and 25 years, respectively. The probability of getting an annual MDR of >50, >100, >150, >200 and >250 mm were estimated as 99, 85, 40, 12 and 03 % level of exceedance, respectively. The monsoon, summer and winter seasons exhibited comparatively higher probabilities (78 to 85 %) for MDR of >100 mm and moderate probabilities (37 to 46 %) for >150 mm. For different recurrence intervals, the percent probability of MDR varied widely across intra- and inter-annual periods. In the island, rainfall anomaly can pose a climatic threat to the sustainability of agricultural production and thus needs adequate adaptation and mitigation measures.

Hybrid Wavelet-Postfix-GP Model for Rainfall Prediction of Anand Region of India

An accurate prediction of rainfall is crucial for national economy and management of water resources. The variability of rainfall in both time and space makes the rainfall prediction a challenging task. The present work investigates the applicability of a hybrid wavelet-postfix-GP model for daily rainfall prediction of Anand region using meteorological variables. The wavelet analysis is used as a data preprocessing technique to remove the stochastic (noise) component from the original time series of each meteorological variable. The Postfix-GP, a GP variant, and ANN are then employed to develop models for rainfall using newly generated subseries of meteorological variables. The developed models are then used for rainfall prediction. The out-of-sample prediction performance of Postfix-GP and ANN models is compared using statistical measures. The results are comparable and suggest that Postfix-GP could be explored as an alternative tool for rainfall prediction.

Design of Neural Network models for Daily Rainfall Prediction

Rainfall is a random process and prediction of rainfall requires consistent as well as relevant information of meteorological and environmental data. In this paper, two different artificial neural networks models are proposed for consecutive daily rainfall prediction on the basis of the preceding events of rainfall data. Model designed for rainfall forecast is based on the pattern recognition methodology. In this method relevant spatial and temporal feature of rainfall series in past are extracted. These features are then utilized to predict the rainfall in future. Time lag delay neural network has capability to learn from the past event and predict the next value. Rainfall prediction is done on basis of rainfall on previous day to rainfall for the preceding six days. The proposed network is capable of forecasting daily rainfall one day in advance with accuracy of R2 = 0.96 and NMSE = 0.0005.

Multivariate nonlinear ensemble prediction of daily chaotic rainfall with climate inputs

The basic characteristic of a chaotic system is its sensitivity to the infinitesimal changes in its initial conditions. A limit to predictability in chaotic system arises mainly due to this sensitivity and also due to the ineffectiveness of the model to reveal the underlying dynamics of the system. In the present study, an attempt is made to quantify these uncertainties involved and thereby improve the predictability by adopting a multivariate nonlinear ensemble prediction. Daily rainfall data of Malaprabha basin, India for the period 1955-2000 is used for the study. It is found to exhibit a low dimensional chaotic nature with the dimension varying from 5 to 7. A multivariate phase space is generated, considering a climate data set of 16 variables. The chaotic nature of each of these variables is confirmed using false nearest neighbor method. The redundancy, if any, of this atmospheric data set is further removed by employing principal component analysis (PCA) method and thereby reducing it to eight principal components (PCs). This multivariate series (rainfall along with eight PCs) is found to exhibit a low dimensional chaotic nature with dimension 10. Nonlinear prediction employing local approximation method is done using univariate series (rainfall alone) and multivariate series for different combinations of embedding dimensions and delay times. The uncertainty in initial conditions is thus addressed by reconstructing the phase space using different combinations of parameters. The ensembles generated from multivariate predictions are found to be better than those from univariate predictions. The uncertainty in predictions is decreased or in other words predictability is increased by adopting multivariate nonlinear ensemble prediction. The restriction on predictability of a chaotic series can thus be altered by quantifying the uncertainty in the initial conditions and also by including other possible variables, which may influence the system. (C) 2011 Elsevier B.V. All rights reserved.