Determining the amplitude and timing of streamflow discontinuities: A cross wavelet analysis approach

Records of natural processes, such as gradual streamflow fluctuations, are commonly interrupted by long or short disruptions from natural non‐linear responses to gradual changes, such as from river‐ice break‐ups, freezing as a result of annual solar cycles, or human causes, such as flow blocking by dams and other means, instrument calibrations and failure. The resulting abrupt or gradual shifts and missing data are considered to be discontinuities with respect to the normal signal. They differ from random noise as they do not follow any fixed distribution over time and, hence, cannot be eliminated by filtering. The multi‐scale resolution features of continuous wavelet analysis and cross wavelet analysis were used in this study to determine the amplitude and timing of such streamflow discontinuities for specific wavebands. The cross wavelet based method was able to detect the strength and timing of abrupt shifts to new streamflow levels, gaps in data records longer than the waveband of interest and a sinusoidal discontinuity curve following an underlying modeled annual signal at ±0.5 year uncertainty. Parameter testing of the time‐frequency resolution demonstrated that high temporal resolution using narrow analysis windows is favorable to high‐frequency resolution for detection of waveband‐related discontinuities. Discontinuity analysis on observed daily streamflow records from Canadian rivers showed the following: (i) that there is at least one discontinuity/year related to the annual spring flood in each record studied, and (ii) neighboring streamflows have similar discontinuity patterns. In addition, the discontinuity density of the Canadian streamflows studied in this paper exhibit 11‐year cycles that are inversely correlated with the solar intensity cycle. This suggests that more streamflow discontinuities, such as through fast freezing, snowmelt, or ice break‐up, may occur during years with slightly lowered solar insolation. Copyright © 2013 John Wiley & Sons, Ltd.     

Multivariate hydrologic time series analysis

The objective of this study is to establish a multivariate watershed hydrologic system model involving meteorological data as the input and river flow as the output of the system. Monthly hydrological time series of runoff, temperature and precipitation were selected for analysis. A first-order autoregressive-moving average (ARMA) transfer function model was found adequate to describe the multivariate watershed hydrologic system for the monthly runoff and meteorological time series. The results also indicated that the coordinated use of the meteorological and hydrometric data would enhance the accuracy of estimation of runoff characteristics.     

Spectral density of a river flow time series

This paper presents the application of a periodogram approach to estimate the spectral density of a stochastic component of a daily river flow time series. The application of a goodness-of-fit test allows comparisons of spectra, and suggests criteria for the length of records for spectral analysis.     

Stochastic Modeling of Groundwater Fluoride Contamination: Introducing Lazy Learners

While it remains the primary source of safe drinking and irrigation water in northwest Iran's Maku Plain, the region's groundwater is prone to fluoride contamination. Accordingly, modeling techniques to accurately predict groundwater fluoride concentration are required. The current paper advances several novel data mining algorithms including Lazy learners [instance-based K-nearest neighbors (IBK); locally weighted learning (LWL); and KStar], a tree-based algorithm (M5P), and a meta classifier algorithm [regression by discretization (RBD)] to predict groundwater fluoride concentration. Drawing on several groundwater quality variables (e.g., concentrations), measured in each of 143 samples collected between 2004 and 2008, several models predicting groundwater fluoride concentrations were developed. The full dataset was divided into two subsets: 70% for model training (calibration) and 30% for model evaluation (validation). Models were validated using several statistical evaluation criteria and three visual evaluation approaches (i.e., scatter plots, Taylor and Violin diagrams). Although Na⁺ and Ca²⁺ showed the greatest positive and negative correlations with fluoride (r = 0.59 and −0.39, respectively), they were insufficient to reliably predict fluoride levels; therefore, other water quality variables, including those weakly correlated with fluoride, should be considered as inputs for fluoride prediction. The IBK model outperformed other models in fluoride contamination prediction, followed by KStar, RBD, M5P, and LWL. The RBD and M5P models were the least accurate in terms of predicting peaks in fluoride concentration values. Results of the current study can be used to support practical and sustainable management of water and groundwater resources.     

Modification of the DRASTIC Framework for Mapping Groundwater Vulnerability Zones

The DRASTIC technique is commonly used to assess groundwater vulnerability. The main disadvantage of the DRASTIC method is the difficulty associated with identifying appropriate ratings and weight assignments for each parameter. To mitigate this issue, ratings and weights can be approximated using different methods appropriate to the conditions of the study area. In this study, different linear (i.e., Wilcoxon test and statistical approaches) and nonlinear (Genetic algorithm [GA]) modifications for calibration of the DRASTIC framework using nitrate (NO₃) concentrations were compared through the preparation of groundwater vulnerability maps of the Meshqin-Shahr plain, Iran. Twenty-two groundwater samples were collected from wells in the study area, and their respective NO₃ concentrations were used to modify the ratings and weights of the DRASTIC parameters. The areas found to have the highest vulnerability were in the eastern, central, and western regions of the plain. Results showed that the modified DRASTIC frameworks performed well, compared to the unmodified DRASTIC. When measured NO₃ concentrations were correlated with the vulnerability indices produced by each method, the unmodified DRASTIC method performed most poorly, and the Wilcoxon–GA–DRASTIC method proved optimal. Compared to the unmodified DRASTIC method with an R² of 0.22, the Wilcoxon–GA–DRASTIC obtained a maximum R² value of 0.78. Modification of DRASTIC parameter ratings was found to be more efficient than the modification of the weights in establishing an accurately calibrated DRASTIC framework. However, modification of parameter ratings and weights together increased the R² value to the highest degree.     

Forecasting effective drought index using a wavelet extreme learning machine (W-ELM) model

A drought forecasting model is a practical tool for drought-risk management. Drought models are used to forecast drought indices (DIs) that quantify drought by its onset, termination, and subsequent properties such as the severity, duration, and peak intensity in order to monitor and evaluate the impacts of future drought. In this study, a wavelet-based drought model using the extreme learning machine (W-ELM) algorithm where the input data are first screened through the wavelet pre-processing technique for better accuracy is developed to forecast the monthly effective DI (EDI). The EDI is an intensive index that considers water accumulation with a weighting function applied to rainfall data with the passage of time in order to analyze the drought-risk. Determined by the autocorrelation function (ACF) and partial ACFs, the lagged EDI signals for the current and past months are used as significant inputs for 1 month lead-time EDI forecasting. For drought model development, 97 years of data for three hydrological stations (Bathurst Agricultural, Wilsons Promontory and Merredin in Australia) are partitioned in approximately 90:5:5 ratios for training, cross-validation and test purposes, respectively. The discrete wavelet transformation (DWT) is applied to the predictor datasets to decompose inputs into their time–frequency components that capture important information on periodicities. DWT sub-series are used to develop new EDI sub-series as inputs for the W-ELM model. The forecasting capability of W-ELM is benchmarked with ELM, artificial neural network (ANN), least squares support vector regression (LSSVR) and their wavelet-equivalent (W-ANN, W-LSSVR) models. Statistical metrics based on agreement between the forecasted and observed EDI, including the coefficient of determination, Willmott’s index, Nash–Sutcliffe coefficient, percentage peak deviation, root-mean-square error, mean absolute error, and model execution time are used to assess the effectiveness of the models. The results demonstrate enhanced forecast skill of the drought models that use wavelet pre-processing of the predictor dataset. Based on statistical measures, W-ELM outperformed traditional ELM, LSSVR, ANN and their wavelet-equivalent counterparts (W-ANN, W-LSSVR). It is found that the W-ELM model is computationally efficient as shown by a faster running time with the majority of forecasting errors in lower frequency bands. The results demonstrate the usefulness of W-ELM over W-ANN and W-LSSVR models and the benefits of wavelet transformation of input data to improve the performance of drought forecasting models.     

Comparison of machine learning models for predicting fluoride contamination in groundwater

Groundwater is an especially important freshwater source for water supplies in the Maku area of northwest Iran. The groundwater of the area contains high concentrations of fluoride and is, therefore, important in predicting the fluoride contamination of the groundwater for the purpose of planning and management. The present study aims to evaluate the ability of the extreme learning machine (ELM) model to predict the level of fluoride contamination in the groundwater in comparison to multilayer perceptron (MLP) and support vector machine (SVM) models. For this purpose, 143 water samples were collected in a five-year period, 2004–2008. The samples were measured and analyzed for electrical conductivity, pH, major chemical ions and fluoride. To develop the models, the data set—including Na⁺, K⁺, Ca²⁺ and HCO₃ ^? concentrations as the inputs and fluoride concentration as the output—was divided into two subsets; training/validation (80% of data) and testing (20% of data), based on a cross-validation technique. The radial basis-based ELM model resulted in an R ² of 0.921, an NSC of 0.9071, an RMSE of 0.5638 (mg/L) and an MABE of 0.4635 (mg/L) for the testing data. The results showed that the ELM models performed better than MLP and SVM models for prediction of fluoride contamination. It was observed that ELM models learned faster than the other models during model development trials and the SVM models had the highest computation time.     

Development of a short-term river flood forecasting method for snowmelt driven floods based on wavelet and cross-wavelet analysis

In this study, a new method of stand-alone short-term spring snowmelt river flood forecasting was developed based on wavelet and cross-wavelet analysis. Wavelet and cross-wavelet analysis were used to decompose flow and meteorological time series data and to develop wavelet based constituent components which were then used to forecast floods 1, 2, and 6 days ahead. The newly developed wavelet forecasting method (WT) was compared to multiple linear regression analysis (MLR), autoregressive integrated moving average analysis (ARIMA), and artificial neural network analysis (ANN) for forecasting daily stream flows with lead-times equal to 1, 2, and 6 days. This comparison was done using data from the Rideau River watershed in Ontario, Canada. Numerical analysis was performed on daily maximum stream flow data from the Rideau River station and on meteorological data (rainfall, snowfall, and snow on ground) from the Ottawa Airport weather station. Data from 1970 to 1997 were used to train the models while data from 1998 to 2001 were used to test the models. The most significant finding of this research was that it was demonstrated that the proposed wavelet based forecasting method can be used with great accuracy as a stand-alone forecasting method for 1 and 2 days lead-time river flood forecasting, assuming that there are no significant trends in the amplitude for the same Julian day year-to-year, and that there is a relatively stable phase shift between the flow and meteorological time series. The best forecasting model for 1 day lead-time was a wavelet analysis model. In testing, it had the lowest RMSE value (13.8229), the highest R² value (0.9753), and the highest EI value (0.9744). The best forecasting model for 2 days lead-time was also a wavelet analysis model. In testing, it had the lowest RMSE value (31.7985), the highest R² value (0.8461), and the second highest EI value (0.8410). It was also shown that the proposed wavelet based forecasting method is not particularly accurate for longer lead-time forecasting such as 6 days, with the ANN method providing more accurate results. The best forecasting model for 6 days lead-time was an ANN model, with the wavelet model not performing as well. In testing, the wavelet model had an RMSE of 57.6917, an R² of 0.4835, and an EI of 0.4366.