Rakesh Khosa

Comparative study of different wavelets for hydrologic forecasting

Use of wavelets in the areas of hydrologic forecasting is increasing in appeal on account of its multi resolution capabilities in addition to its ability to deal with non-stationarities. For successful implementation of wavelets based forecasting methodology, selection of the appropriate mother wavelet form and number of decomposition levels plays an important role. Wavelets based forecasting methodologies have been discussed extensively in published literature but discussion on some key issues of concern such as selection of mother wavelets is rather meager. Appropriately, therefore, this paper presents a comparative evaluation of different wavelet forms when employed for forecasting future states of various kinds of time series. The results suggest that those wavelet forms that have a compact support, for example the Haar wavelet, have a better time localization property and show improved performance in the case of time series that have a short memory with short duration transient features. In contrast, wavelets with wider support, for example db2 and spline wavelets, yielded better forecasting efficiencies in the case of those time series that have long term features. Results further suggest that db2 wavelets perform marginally better as compared to the spline wavelets. It is hoped that this study would enable a reasoned selection of mother wavelets for future forecasting applications.

Long term forecasting of groundwater levels with evidence of non-stationary and nonlinear characteristics

Groundwater systems are in general characterised by non-stationary and nonlinear features. Modelling of these systems and forecasting their future states requires identification and capture of these underlying features that seem to drive these processes. Recently, wavelets have been used extensively in the area of hydrologic and environmental time series forecasting owing to its ability to unravel these aforementioned component features. In this paper, dynamic wavelet based nonlinear model (Wavelet Volterra coupled model) is tested for its ability to yield reliable long term forecasts of groundwater levels at two sites in Canada. The model results are compared with the results from other recent techniques like wavelet neural network (WA-ANN), Wavelet linear regression (WLR), Artificial neural network and dynamic auto regressive (DAR) Models. The results of the study show the potential of wavelet Volterra coupled models in forecasting groundwater levels in addition to being more versatile and simpler to use when compared with other competing models.

Wavelet‐based multiscale performance analysis: An approach to assess and improve hydrological models

The temporal dynamics of hydrological processes are spread across different time scales and, as such, the performance of hydrological models cannot be estimated reliably from global performance measures that assign a single number to the fit of a simulated time series to an observed reference series. Accordingly, it is important to analyze model performance at different time scales. Wavelets have been used extensively in the area of hydrological modeling for multiscale analysis, and have been shown to be very reliable and useful in understanding dynamics across time scales and as these evolve in time. In this paper, a wavelet-based multiscale performance measure for hydrological models is proposed and tested (i.e., Multiscale Nash-Sutcliffe Criteria and Multiscale Normalized Root Mean Square Error). The main advantage of this method is that it provides a quantitative measure of model performance across different time scales. In the proposed approach, model and observed time series are decomposed using the Discrete Wavelet Transform (known as the a trous wavelet transform), and performance measures of the model are obtained at each time scale. The applicability of the proposed method was explored using various case studies––both real as well as synthetic. The synthetic case studies included various kinds of errors (e.g., timing error, under and over prediction of high and low flows) in outputs from a hydrologic model. The real time case studies investigated in this study included simulation results of both the process-based Soil Water Assessment Tool (SWAT) model, as well as statistical models, namely the Coupled Wavelet-Volterra (WVC), Artificial Neural Network (ANN), and Auto Regressive Moving Average (ARMA) methods. For the SWAT model, data from Wainganga and Sind Basin (India) were used, while for the Wavelet Volterra, ANN and ARMA models, data from the Cauvery River Basin (India) and Fraser River (Canada) were used. The study also explored the effect of the choice of the wavelets in multiscale model evaluation. It was found that the proposed wavelet-based performance measures, namely the MNSC (Multiscale Nash-Sutcliffe Criteria) and MNRMSE (Multiscale Normalized Root Mean Square Error), are a more reliable measure than traditional performance measures such as the Nash-Sutcliffe Criteria (NSC), Root Mean Square Error (RMSE), and Normalized Root Mean Square Error (NRMSE). Further, the proposed methodology can be used to: i) compare different hydrological models (both physical and statistical models), and ii) help in model calibration.

Wavelet Spectrum and Self-Organizing Maps-Based Approach for Hydrologic Regionalization -a Case Study in the Western United States

Hydrologic regionalization deals with the investigation of homogeneity in watersheds and provides a classification of watersheds for regional analysis. The classification thus obtained can be used as a basis for mapping data from gauged to ungauged sites and can improve extreme event prediction. This paper proposes a wavelet power spectrum (WPS) coupled with the self-organizing map method for clustering hydrologic catchments. The application of this technique is implemented for gauged catchments. As a test case study, monthly streamflow records observed at 117 selected catchments throughout the western United States from 1951 through 2002. Further, based on WPS of each station, catchments are classified into homogeneous clusters, which provides a representative WPS pattern for the streamflow stations in each cluster.

Wavelet Volterra Coupled Models for forecasting of nonlinear and non-stationary time series

This paper provides a simple forecasting framework for nonlinear and non-stationary time series using Wavelet based nonlinear models. The proposed method exploits the ability of wavelets to detect non-stationarities that may be present in a given time series in combination with higher order nonlinear Volterra Models. The utility of the proposed model is verified using two examples: the first based on a synthetically generated times series with nonlinear and non stationary features; the second case study examined in the paper pertains to forecasting of number of pilgrims visiting the well known religious shrine at Katra in the state of Jammu and Kashmir in India. Further, the proposed model was applied to 3 time series from M3 competition. The results show that the proposed models perform better when compared with the performance of some well known benchmark models. The long term predictive capability of the wavelet based nonlinear models has also been studied separately. Developed Wavelet based model for nonlinear and non-stationary time series.Tested using the tourism time series and other well known time series.Wavelet based model performs better than other benchmark models.

A non-linear and non-stationary perspective for downscaling mean monthly temperature: a wavelet coupled second order Volterra model

This study presents a multiscale framework for downscaling of the General Circulation Model (GCM) outputs to the mean monthly temperature at regional scale using a wavelet based Second order Voltera (SoV) model. The models are developed using the reanalysis climatic data from the National Centers for Environmental Prediction (NCEP) and are validated using the simulated climatic dataset from the Can CM4 GCM for five locations in the Krishna river basin, India. K-means clustering, based on the multiscale wavelet entropy of the predictors, is used for obtaining the clusters of the input climatic variables. Principal component analysis (PCA) is used to obtain the representative variables from each cluster. These input variables are then used to develop a wavelet based multiscale model using Second order Volterra approach to simulate observed mean monthly temperature for the selected locations in the basin. These models are called W-P-SoV models in this paper. For the purpose of comparison, linear multi-resolution models are developed using Multiple Linear regression (MLR) and are called W-P MLR models. The performance of the models is further compared with other Wavelet-PCA based models coupled with Multiple linear regression models (P-MLR) and Artificial Neural Networks (P-ANN), and, stand-alone MLR and ANN to establish the superiority of the proposed approach. The results indicate that the performance of the wavelet based models is superior in terms of downscaling accuracy when compared with the other models used.

Multi resolution genetic programming approach for stream flow forecasting

Genetic Programming (GP) is increasingly used as an alternative for Artificial Neural Networks (ANN) in many applications viz. forecasting, classification etc. However, GP models are limited in scope as their application is restricted to stationary systems. This study proposes use of Multi Resolution Genetic Programming (MRGP) based approach as an alternative modelling strategy to treat non-stationaries. The proposed approach is a synthesis of Wavelets based Multi-Resolution Decomposition and Genetic Programming. Wavelet transform is used to decompose the time series at different scales of resolution so that the underlying temporal structures of the original time series become more tractable. Further, Genetic Programming is then applied to capture the underlying process through evolutionary algorithms. In the case study investigated, the MRGP is applied for forecasting one month ahead stream flow in Fraser River, Canada, and its performance compared with the conventional, but scale insensitive, GP model. The results show the MRGP as a promising approach for flow forecasting.

Wavelet-based model for long-term forecasting of CO 2 levels in atmosphere

The CO2 levels in the atmosphere serve as an indicator for global warming. The forecasts of CO2 levels that may be expected in the foreseeable future would help in formulating credible policies as well as plans towards a sustainable future. The objective of this paper is to analyse the time series of CO2 levels observed at Mauna Loa (Hawaii) using wavelet analysis and to develop a recursive forecasting model based on wavelet decomposition. Wavelet analysis enables a decomposition of a given time series into a multi resolution series providing, in the process, an insight into the likely causative influences that operate at various scales. The main advantage of wavelet analysis is that it yields simultaneous time-frequency description of the given time series while isolating features that are localized in time as well as those occurring over a longer term time horizon. Additionally, multi resolution capability of wavelet decomposition can also reveal changes or perturbations that may be masked at a single scale. The wavelet analysis of the observed CO2 levels reveals that the trend underlying the CO2 levels is time varying and there are significant changes in the slope of the trend around 1992. In order to incorporate these changes, recursive forecasting wavelet models were developed for long term forecasting and the results reveal their superior performance over traditional models like SARIMA.

What Constitutes a Fair and Equitable Water Apportionment

Water has been a source of conflict since time immemorial. Numerous mechanisms have been proposed for solving such conflicts but multiplicity of water uses and users along with self-serving definition of equitable, makes dispute resolution challenging. Doctrines advocating water appropriation based on the notion of equity and fairness are intuitively appealing. However, subjectivity of this concept impedes their translation to universal principles for water allocation as fairness quotient of any mechanism is determined unitedly by gamut of diverse factors. Thus, the present study critically reviews the connotations of equity and equality to arrive at a procedurally and distributionally just apportionment policy for real-world water conflicts. It seeks an equal opportunity paradigm for deservedness-based resource distribution that could be unanimously amenable to all stakeholders. The study is very apposite as there is a lurking fear of heightened water conflicts that could have bitter socio-political ramifications.

Impact of Anthropogenic Interventions on the Vembanad Lake System

Estuarine and coastal zone processes have always been topic of research due to their being prime centers of rich resources like diverse habitat and natural beauty. Other than ecological reasons these aquatic bodies act as important economic centers, tourist places, serve in navigational purposes, and fishing. One of the India’s most valued natural sites is the Vembanad Lake and estuarine system that lies on the western coast in the state of Kerala. This natural system, which comprises the lake, the Kuttanad wetland region and the Cochin estuary, is included in the Ramsar list of important wetland sites. Six major rivers, namely, Periyar, Muvattupuzha, Pamba, Manimala, Meenachil, and Achenkovil contribute to the system. The whole system has been vastly modified throughout the last couple of centuries owing to sedimentation and human-driven factors. On the other hand, there has been constant reclamation of the low-lying areas on the periphery of the lake and the wetlands, leading to reduction in the spread area. The special characteristics of these lands that lie to the east of the lake is that the ground level is lower than the lake water level. Therefore, the lake water easily serves for irrigational purpose in these adjacent lands. According to tentative proposals in the recent years it was intended to make further developments in the catchment areas for various purposes. The present paper takes a modeling approach to find out what would be the possible impact on the lake water profile as well as salinity/solute concentration if these proposals are implemented. The study has been carried out using the two-dimensional hydrodynamic modeling software MIKE 21 with HD and AD modules. The results from the hydrodynamic model of the lake, although not fully representative, show that the lake water levels and salinity might face quantitatively relevant changes which can pose a threat to the natural environment.