K. Srinivasan

Investigation and comparison of sampling properties of L-moments and conventional moments

Abstract The first part of this article deals with fitting of regression equations for the sampling properties, variance of L-standard deviation ( l 2 ), and bias and variance of L-skewness ( t 3 ), based on Monte-Carlo simulation results, for generalised Normal (Lognormal-3) and Pearson-3 distributions. These fitted equations will be useful in formulating goodness-of-fit test statistics in regional frequency analysis. The second part presents a comparison of the sampling properties between L-moments and conventional product moments for generalised Normal, generalised Extreme Value, generalised Pareto and Pearson-3 distributions, in a relative form . The comparison reveals that the bias in L-skewness is found to be insignificant up to a skewness of about 1.0, even for small samples. In case of higher skewness, for a reasonable sample size of 30, L-skewness is found to be nearly unbiased. However, the conventional skewness is found to be significantly biased, even for a low skewness of 0.5 and a reasonable sample size of 30. The overall performance evaluation in terms of “Relative-RMSE in third moment ratio” reveals that conventional moments are preferable at lower skewness, particularly for smaller samples, while L-moments are preferable at higher skewness, for all sample sizes . This point is illustrated through an application that seeks to obtain an appropriate regional flood frequency distribution for the 98 catchment areas located in the central region of India, spread over six hydrometeorologic subzones.

Performance‐based optimal design and rehabilitation of water distribution networks using life cycle costing

[1]xa0A new multiobjective formulation is proposed for the optimal design and rehabilitation of a water distribution network, with minimization of life cycle cost and maximization of performance as objectives. The life cycle cost is considered to comprise the initial cost of pipes, the cost of replacing old pipes with new ones, the cost of cleaning and lining existing pipes, the expected repair cost for pipe breaks, and the salvage value of the pipes that are replaced. The performance measure proposed in this study is a modification to the resilience index to suit application to water distribution networks with multiple sources. A new heuristic method is proposed to obtain the solution for the design and rehabilitation problem. This heuristic method involves selection of various design and rehabilitation alternatives in an iterative manner on the basis of the improvement in the network performance as compared to the change in the life cycle cost on implementation of the alternatives. The solutions obtained from the heuristic method are used as part of the initial population set of the multiobjective, nondominated sorting genetic algorithm (NSGA-II) in order to improve the search process. Using a sample water distribution network, the modified resilience index proposed is shown to be a good indicator of the uncertainty handling ability of the network.

Post-blackening approach for modeling dependent annual streamflows

The post-blackening (PB) approach is introduced for modeling annual streamflows that exhibit significant dependence. This is a hybrid approach that blends a simple low-order, linear parametric model with the moving block resampling scheme. Empirical simulations performed using known hypothetical nonlinear parametric models, show that the hybrid model gains significantly by utilizing the merits of both the parametric model and the moving block resampling scheme (nonparametric). Following this, the performance of the PB model is tested with four annual streamflow records with complex dependence, drawn from different parts of the world. The results from these examples show that the PB approach exhibits a better performance in terms of preservation of summary statistics, dependence structure, marginal distribution, and drought characteristics of historical streamflows, compared to low-order linear parametric models and model based resampling schemes (nonparametric model). Furthermore, it offers flexibility to the modeler and is also simple to implement on a personal computer. This hybrid approach seems to offer considerable scope for improvement in hydrologic time series modeling and its applications to water resources planning.

Evaluation and selection of hedging policies using stochastic reservoir simulation

A hedging policy is characterized by three parameters, namely, starting water availability (SWA), ending water availability (EWA) and hedging factor (HF). The effects of these three parameters on the reservoir performance indicators have been evaluated and discussed for a southwest monsoon-dependent within-year reservoir system in southern India. For the performance evaluation, synthetically generated periodic inflow sequences from a periodic autoregressive model have been used. Quite a number of the 1800 hedging policies considered for the reservoir system, yield a better overall performance compared to the standard operating policy (SOP). Reliability, Resilience and vulnerability are found to increase with SWA for a specified EWA. On the other hand, all these performance indicators are found to decrease with EWA for a specified SWA. Hence, it is desirable to start the hedging at reasonably high SWA. All performance indicators remain practically constant at higher ranges of EWA for a given SWA. If hedging is started when there is enough water in storage, reliability, resilience and average deficit increase with degree of hedging, whereas vulnerability decreases significantly up to a hedging factor of 0.3. An interactive computer program has been developed for the selection of compromising hedging policies, and its usefulness has been discussed.

Post-blackening approach for modeling periodic streamflows

Abstract The post-blackening (PB) approach introduced by the authors for modeling annual streamflows in an earlier work is extended to model periodic streamflows. This is basically a semi-parametric approach that blends a simple low-order, linear periodic parametric model with the moving block resampling scheme. The first part of the paper demonstrates the hybrid character of the PB model through Monte-Carlo simulations performed on hypothetical data sets drawn from a known population. Following this, the PB model is used for stochastic simulation of periodic streamflows of Beaver and Weber rivers in the US. The results show that the PB model is more consistent in reproducing a wide variety of statistics of periodic streamflows, compared to low-order linear periodic parametric models (Box–Jenkins type) and the periodic k -nearest-neighbor bootstrap (nonparametric) method. In addition, the PB model is able to preserve cross-year serial correlations as well as the month-to-year cross-correlations. This hybrid approach seems to offer considerable scope for improvement in hydrologic time series modeling.

A hybrid stochastic model for multiseason streamflow simulation

A hybrid model is presented for stochastic simulation of multiseason streamflows. This involves partial prewhitening of the streamflows using a parsimonious linear periodic parametric model, followed by resampling the resulting residuals using moving block bootstrap to obtain innovations and subsequently postblackening these innovations to generate synthetic replicates. This model is simple and is efficient in reproducing both linear and nonlinear dependence inherent in the observed streamflows. The first part of this paper demonstrates the hybrid character of the model through stochastic simulations performed using monthly streamflows of Weber River (Utah) that exhibit a complex dependence structure. In the latter part of the paper the hybrid model is shown to be efficient in simulating multiseason streamflows, through an example of the San Juan River (New Mexico). This model ensures annual-to-monthly consistency without the need for any adjustment procedures. Furthermore, the hybrid model is able to preserve both within-year and cross-year monthly serial correlations for multiple lags. Also, it is seen to be consistent in predicting the reservoir storage (validation) statistic at low as well as high demand levels.

Improved higher lead time river flow forecasts using sequential neural network with error updating

Abstract This paper presents a novel framework to use artificial neural network (ANN) for accurate forecasting of river flows at higher lead times. The proposed model, termed as sequential ANN (SANN), is based on the heuristic that a mechanism that provides an accurate representation of physical condition of the basin at the time of forecast, in terms of input information to ANNs at higher lead time, helps improve the forecast accuracy. In SANN, a series of ANNs are connected sequentially to extend the lead time of forecast, each of them taking a forecast value from an immediate preceding network as input. The output of each network is modified by adding an expected value of error so that the residual variance of the forecast series is minimized. The applicability of SANN in hydrological forecasting is illustrated through three case examples: a hypothetical time series, daily river flow forecasting of Kentucky River, USA and hourly river flow forecasting of Kolar River, India. The results demonstrate that SANN is capable of providing accurate forecasts up to 8 steps ahead. A very close fit (>94% efficiency) was obtained between computed and observed flows up to 1 hour in advance for all the cases, and the deterioration in fit was not significant as the forecast lead time increased (92% at 8 steps ahead). The results show that SANN performs much better than traditional ANN models in extending the forecast lead time, suggesting that it can be effectively employed in developing flood management measures.

Multi-Objective Simulation-Optimization Model for Long-term Reservoir Operation using Piecewise Linear Hedging Rule

An efficiently parameterized and appropriately structured piecewise linear hedging rule is formulated and included within a multi-objective simulation-optimization (S-O) framework that seeks to obtain Pareto-optimal solutions for the long-term hedged operation of a single water supply reservoir. Two conflicting objectives, namely, “minimize the total shortage ratio” and “minimize the maximum shortage” are considered in the S-O framework, while explicit specification of constraints is avoided in the optimization module. Evolutionary search based non-dominated sorting genetic algorithm is used as the driver, which is linked to the simulation engine that invokes the piecewise linear hedging rule within the S-O framework. Preconditioning of the multi-objective stochastic search of the time-varying piecewise linear hedging model is effected by feeding initial feasible solutions sampled from the Pareto-optimal front of a simple constant hedging parameter model, which has resulted in significant improvement of the Pareto-optimality and the computational efficiency.

Analysis of Spatio-temporal Characteristics and Regional Frequency of Droughts in the Southern Peninsula of India

A detailed regional drought study is carried out in the southern peninsula of India to characterize the spatio-temporal nature of droughts and to predict the drought magnitudes for various probabilities in the homogeneous drought regions. The method of several random initializations of the cluster centres of the K-means algorithm is suggested for the identification of the initial regions in the context of drought regionalization, which is shown to perform better than the initialization from the Ward’s algorithm and the Ward’s algorithm itself. The peninsula is classified into seven spatially well-separated homogeneous drought regions. The robust L-moment framework is used for the regional frequency analysis of drought magnitudes computed using the standardized precipitation index. The Pearson type III is found to be appropriate for regional drought frequency analysis in six of the regions, while the robust Wakeby distribution is suggested for one region. Low magnitude droughts are frequent and dominant in the northern part of west coast, the north-eastern coast and its adjoining inland region, while high magnitude droughts are less in number and are experienced in semi-arid central part, southern part of western coast, south-eastern part and north-western inland region. The spatial maps of drought magnitudes indicate that at higher return periods (100 and 200xa0years) the south-eastern part of the peninsula is likely to encounter high magnitude droughts, while the central region is likely to experience the same at lower return periods (10 and 50xa0years). Hence these regions need to be given special importance in the drought mitigation planning activities.