P. P. Mujumdar

OPTIMAL RESERVOIR OPERATION FOR IRRIGATION OF MULTIPLE CROPS

A model for the optimal operating policy of a reservoir for irrigation under a multiple crops scenario using stochastic dynamic programming (SDP) is developed. Tntraseasonal periods smaller than the crop growth durations form the decision intervals of the model to facilitate irrigation decisions in real situations. Reservoir storage, inflow to the reservoir, and the soil moisture in the irrigated area are treated as state variables. An optimal allocation process is incorporated in the model to determine the allocation of individual crops when a competition for water exists among them. The model also serves as an irrigation scheduling model in that at any given intraseason period it specifies whether irrigation is neede and if it is, the amount of irrigation to be applied to each crop. The impact on crop yield due to water deficit and the effect of soil moisture dynamics on crop water requirements are taken into account. A linear root growth of the crop is assumed until the end of the vegetative stage, beyond which the root depth is assumed to be constant. The applicability of the model is demonstrated through a case study of an existing reservoir in India.

Nonparametric methods for modeling GCM and scenario uncertainty in drought assessment

Hydrologic implications of global climate change are usually assessed by downscaling appropriate predictors simulated by general circulation models (GCMs). Results from GCM simulations are subjected to a number of uncertainties due to incomplete knowledge about the underlying geophysical processes of global change (GCM uncertainties) and due to uncertain future scenarios (scenario uncertainties). With a relatively small number of GCMs available and a finite number of scenarios simulated by them, uncertainties in the hydrologic impacts at a smaller spatial scale become particularly pronounced. In this paper, a methodology is developed to address such uncertainties for a specific problem of drought impact assessment with results from GCM simulations. Samples of a drought indicator are generated with downscaled precipitation from available GCMs and scenarios. Since it is very unlikely that such small samples resulting from GCM scenarios fit a known parametric distribution, nonparametric methods such as kernel density estimation and orthonormal series methods are used to determine the probability distribution function (PDF) of the drought indicator. Principal component analysis, fuzzy clustering, and statistical regression are used for downscaling the mean sea level pressure (MSLP) output from the GCMs to precipitation at a smaller spatial scale. Reanalysis data from the National Center for Environmental Prediction (NCEP) are used in relating precipitation with MSLP. The information generated through the PDF of the drought indicator in a future year may be used in long-term planning decisions. The methodology is demonstrated with a case study of the drought-prone Orissa meteorological subdivision in India.

Modeling GCM and scenario uncertainty using a possibilistic approach: Application to the Mahanadi River, India

Climate change impact assessment on water resources with downscaled General Circulation Model (GCM) simulation output is characterized by uncertainty due to incomplete knowledge about the underlying geophysical processes of global change (GCM uncertainties) and due to uncertain future scenarios (scenario uncertainties).Disagreement between different GCMs and scenarios in regional climate change impact studies indicates that overreliance on a single GCM with a scenario could lead to inappropriate planning and adaptation responses. This paper focuses on modeling GCM and scenario uncertainty using possibility theory in projecting streamflow of Mahanadi river, at Hirakud, India. A downscaling method based on fuzzy clustering and Relevance Vector Machine (RVM) is applied to project monsoon streamflow from three GCMs with two green house emission scenarios. Possibilities are assigned to all the GCMs with scenarios based on their performance in modeling the streamflow of the recent past (1991–2005), when there are signals of climate forcing. The possibilities associated with different GCMs and scenarios are used as weights in computing the possibilistic mean of the CDFs projected for three standard time slices 2020s, 2050s, and 2080s. The result shows that the value of streamflow at which the CDF reaches 1 reduces with time, which shows the reduction in probability of occurrence of extreme high flow events in future. Historic record of monsoon streamflow of Mahanadi river also shows similar decreasing trend, which may be due to the effect of high surface warming. Reduction in Mahandai streamflow is likely to pose a major challenge for water resources engineers in meeting water demands in future.

Real-time reservoir operation for irrigation

A short-term real-time reservoir operation model is developed for irrigation of multiple crops. Two major features of the model distinguish it from the earlier models which address the problem of reservoir operation for irrigation: its capability to consider interdependence of crop water allocations across time periods and its ability to provide an adaptive release policy. Integration of reservoir operation with on-farm utilization of water by crops is achieved through the use of two models: An operating policy model, which optimizes reservoir releases across time periods in a year, and an allocation model, which optimizes irrigation allocations across crops within a time period. The model is applied to a case study of an existing reservoir in India.

Climate change impact assessment: Uncertainty modeling with imprecise probability

Hydrologic impacts of climate change are usually assessed by downscaling the General Circulation Model (GCM) output of large-scale climate variables to local-scale hydrologic variables. Such an assessment is characterized by uncertainty resulting from the ensembles of projections generated with multiple GCMs, which is known as intermodel or GCM uncertainty. Ensemble averaging with the assignment of weights to GCMs based on model evaluation is one of the methods to address such uncertainty and is used in the present study for regional-scale impact assessment. GCM outputs of large-scale climate variables are downscaled to subdivisional-scale monsoon rainfall. Weights are assigned to the GCMs on the basis of model performance and model convergence, which are evaluated with the Cumulative Distribution Functions (CDFs) generated from the downscaled GCM output (for both 20th Century [20C3M] and future scenarios) and observed data. Ensemble averaging approach, with the assignment of weights to GCMs, is characterized by the uncertainty caused by partial ignorance, which stems from nonavailability of the outputs of some of the GCMs for a few scenarios (in Intergovernmental Panel on Climate Change [IPCC] data distribution center for Assessment Report 4 [AR4]). This uncertainty is modeled with imprecise probability, i.e., the probability being represented as an interval gray number. Furthermore, the CDF generated with one GCM is entirely different from that with another and therefore the use of multiple GCMs results in a band of CDFs. Representing this band of CDFs with a single valued weighted mean CDF may be misleading. Such a band of CDFs can only be represented with an envelope that contains all the CDFs generated with a number of GCMs. Imprecise CDF represents such an envelope, which not only contains the CDFs generated with all the available GCMs but also to an extent accounts for the uncertainty resulting from the missing GCM output. This concept of imprecise probability is also validated in the present study. The imprecise CDFs of monsoon rainfall are derived for three 30-year time slices, 2020s, 2050s and 2080s, with A1B, A2 and B1 scenarios. The model is demonstrated with the prediction of monsoon rainfall in Orissa meteorological subdivision, which shows a possible decreasing trend in the future.

A conditional random field-based downscaling method for assessment of climate change impact on multisite daily precipitation in the Mahanadi basin

Downscaling to station-scale hydrologic variables from large-scale atmospheric variables simulated by general circulation models (GCMs) is usually necessary to assess the hydrologic impact of climate change. This work presents CRF-downscaling, a new probabilistic downscaling method that represents the daily precipitation sequence as a conditional random field (CRF). The conditional distribution of the precipitation sequence at a site, given the daily atmospheric (large-scale) variable sequence, is modeled as a linear chain CRF. CRFs do not make assumptions on independence of observations, which gives them flexibility in using high-dimensional feature vectors. Maximum likelihood parameter estimation for the model is performed using limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization. Maximum a posteriori estimation is used to determine the most likely precipitation sequence for a given set of atmospheric input variables using the Viterbi algorithm. Direct classification of dry/wet days as well as precipitation amount is achieved within a single modeling framework. The model is used to project the future cumulative distribution function of precipitation. Uncertainty in precipitation prediction is addressed through a modified Viterbi algorithm that predicts the n most likely sequences. The model is applied for downscaling monsoon (June-September) daily precipitation at eight sites in the Mahanadi basin in Orissa, India, using the MIROC3.2 medium-resolution GCM. The predicted distributions at all sites show an increase in the number of wet days, and also an increase in wet day precipitation amounts. A comparison of current and future predicted probability density functions for daily precipitation shows a change in shape of the density function with decreasing probability of lower precipitation and increasing probability of higher precipitation.

An imprecise fuzzy risk approach for water quality management of a river system.

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA) problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max-min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga-Bhadra river system in India.

Application of fuzzy probability in water quality management of a river system

Water quality management of a river system is addressed in a fuzzy and probabilistic framework. Two types of uncertainty, namely randomness and vagueness, are treated simultaneously in the management problem. A fuzzy-set-based definition that is a more general case of the existing crisp-set-based definition of low water quality is introduced. The event of low water quality at a check-point in the river system is considered as a fuzzy event. The risk of low water quality is then defined as the probability of the fuzzy event of low water quality. Instead of constraining the risk of violation of water quality standard by a finite value of risk through a chance constraint, a fuzzy set of low risk that considers a range of risk levels with appropriate membership values is introduced. Different goals associated with the management problem are expressed as fuzzy sets. The resulting management problem is formulated as a fuzzy multiobjective optimization problem.

A stochastic dynamic programming model for stream water quality management

This paper deals with development of a seasonal fraction-removal policy model for waste load allocation in streams addressing uncertainties due to randomness and fuzziness. A stochastic dynamic programming (SDP) model is developed to arrive at the steady-state seasonal fraction-removal policy. A fuzzy decision model (FDM) developed by us in an earlier study is used to compute the system performance measure required in the SDP model. The state of the system in a season is defined by streamflows at the headwaters during the season and the initial DO deficit at some pre-specified checkpoints. The random variation of streamflows is included in the SDP model through seasonal transitional probabilities. The decision vector consists of seasonal fraction-removal levels for the effluent dischargers. Uncertainty due to imprecision (fuzziness) associated with water quality goals is addressed using the concept of fuzzy decision. Responses of pollution control agencies to the resulting end-of-season DO deficit vector and that of dischargers to the fraction-removal levels are treated as fuzzy, and modelled with appropriate membership functions. Application of the model is illustrated with a case study of the Tungabhadra river in India.

Stochastic models of streamflow: some case studies

Abstract Ten candidate models of the Auto-Regressive Moving Average (ARMA) family are investigated for representing and forecasting monthly and ten-day streamflow in three Indian rivers. The best models for forecasting and representation of data are selected by using the criteria of Minimum Mean Square Error (MMSE) and Maximum Likelihood (ML) respectively. The selected models are validated for significance of the residual mean, significance of the periodicities in the residuals and significance of the correlation in the residuals. The models selected, based on the ML criterion for the synthetic generation of the three monthly series of the Rivers Cauvery, Hemavathy and Malaprabha, are respectively AR(4), ARMA(2,1) and ARMA(3,1). For the ten-day series of the Malaprabha River, the AR(4) model is selected. The AR(1) model resulted in the minimum mean square error in all the cases studied and is recommended for use in forecasting flows one time step ahead.