Multiobjective Analysis of Irrigation Planning in River Basin Development

A river basin that is extensively developed in the downstream reaches and that has a high potential for development in the upper reaches is considered for irrigation planning. A four-reservoir system is modeled on a monthly basis by using a mathematical programing (LP) formulation to find optimum cropping patterns, subject to land, water, and downstream release constraints. The model is applied to a fiver basin in India. Two objectives, maximizing net economic benefits and maximizing irrigated cropped area, considered in the model are analyzed in the context of multiobjective planning, and the tradeoffs are discussed.

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.

Strong motion compatible source geometry

Strong motion array records are analyzed in this paper to identify and map the source zone of four past earthquakes. The source is represented as a sequence of double couples evolving as ramp functions, triggering at different instants, distributed in a region yet to be mapped. The known surface level ground motion time histories are treated as responses to the unknown double couples on the fault surface. The location, orientation, magnitude, and risetime of the double couples are found by minimizing the mean square error between analytical solution and instrumental data. Numerical results are presented for Chi-Chi, Imperial Valley, San Fernando, and Uttarakashi earthquakes. Results obtained are in good agreement with field investigations and those obtained from conventional finite fault source inversions.

Constraining uncertainty in regional hydrologic impacts of climate change: Nonstationarity in downscaling

Regional impacts of climate change remain subject to large uncertainties accumulating from various sources, including those due to choice of general circulation models (GCMs), scenarios, and downscaling methods. Objective constraints to reduce the uncertainty in regional predictions have proven elusive. In most studies to date the nature of the downscaling relationship (DSR) used for such regional predictions has been assumed to remain unchanged in a future climate. However,studies have shown that climate change may manifest in terms of changes in frequencies of occurrence of the leading modes of variability, and hence, stationarity of DSRs is not really a valid assumption in regional climate impact assessment. This work presents an uncertainty modeling framework where, in addition to GCM and scenario uncertainty, uncertainty in the nature of the DSR is explored by linking downscaling with changes in frequencies of such modes of natural variability. Future projections of the regional hydrologic variable obtained by training a conditional random field (CRF) model on each natural cluster are combined using the weighted Dempster-Shafer (D-S) theory of evidence combination. Each projection is weighted with the future projected frequency of occurrence of that cluster (''cluster linking'') and scaled by the GCM performance with respect to the associated cluster for the present period (''frequency scaling''). The D-S theory was chosen for its ability to express beliefs in some hypotheses, describe uncertainty and ignorance in the system, and give a quantitative measurement of belief and plausibility in results. The methodology is tested for predicting monsoon streamflow of the Mahanadi River at Hirakud Reservoir in Orissa, India. The results show an increasing probability of extreme, severe, and moderate droughts due to limate change. Significantly improved agreement between GCM predictions owing to cluster linking and frequency scaling is seen, suggesting that by linking regional impacts to natural regime frequencies, uncertainty in regional predictions can be realistically quantified. Additionally, by using a measure of GCM performance in simulating natural regimes, this uncertainty can be effectively constrained.

A heuristic clustering algorithm using union of overlapping pattern-cells

Relative geometric arrangements of the sample points, with reference to the structure of the imbedding space, produce clusters. Hence, if each sample point is imagined to acquire a volume of a small M-cube (called pattern-cell), depending on the ranges of its (M) features and number (N) of samples; then overlapping pattern-cells would indicate naturally closer sample-points. A chain or blob of such overlapping cells would mean a cluster and separate clusters would not share a common pattern-cell between them. The conditions and an analytic method to find such an overlap are developed. A simple, intuitive, nonparametric clustering procedure, based on such overlapping pattern-cells is presented. It may be classified as an agglomerative, hierarchical, linkage-type clustering procedure. The algorithm is fast, requires low storage and can identify irregular clusters. Two extensions of the algorithm, to separate overlapping clusters and to estimate the nature of pattern distributions in the sample space, are also indicated.

An integrated model for optimal reservoir operation for irrigation of multiple crops

An integrated model is developed, based on seasonal inputs of reservoir inflow and rainfall in the irrigated area, to determine the optimal reservoir release policies and irrigation allocations to multiple crops. The model is conceptually made up of two modules, Module 1 is an intraseasonal allocation model to maximize the sum of relative yields of all crops, for a given state of the system, using linear programming (LP). The module takes into account reservoir storage continuity, soil moisture balance, and crop root growth with time. Module 2 is a seasonal allocation model to derive the steady state reservoir operating policy using stochastic dynamic programming (SDP). Reservoir storage, seasonal inflow, and seasonal rainfall are the state variables in the SDP. The objective in SDP is to maximize the expected sum of relative yields of all crops in a year. The results of module 1 and the transition probabilities of seasonal inflow and rainfall form the input for module 2. The use of seasonal inputs coupled with the LP-SDP solution strategy in the present formulation facilitates in relaxing the limitations of an earlier study, while affecting additional improvements. The model is applied to an existing reservoir in Karnataka State, India.

Local polynomial convexity of the union of two totally-real surfaces at their intersection

We consider the following question: Let S (1) and S (2) be two smooth, totally-real surfaces in C-2 that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is S-1 boolean OR S-2 locally polynomially convex at the origin? If T (0) S (1) a (c) T (0) S (2) = {0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dim(R)(T0S1 boolean AND T0S2) = 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.

Predictive uncertainty of chaotic daily streamflow using ensemble wavelet networks approach

Perfect or even mediocre weather predictions over a long period are almost impossible because of the ultimate growth of a small initial error into a significant one. Even though the sensitivity of initial conditions limits the predictability in chaotic systems, an ensemble of prediction from different possible initial conditions and also a prediction algorithm capable of resolving the fine structure of the chaotic attractor can reduce the prediction uncertainty to some extent. All of the traditional chaotic prediction methods in hydrology are based on single optimum initial condition local models which can model the sudden divergence of the trajectories with different local functions. Conceptually, global models are ineffective in modeling the highly unstable structure of the chaotic attractor. This paper focuses on an ensemble prediction approach by reconstructing the phase space using different combinations of chaotic parameters, i.e., embedding dimension and delay time to quantify the uncertainty in initial conditions. The ensemble approach is implemented through a local learning wavelet network model with a global feed-forward neural network structure for the phase space prediction of chaotic streamflow series. Quantification of uncertainties in future predictions are done by creating an ensemble of predictions with wavelet network using a range of plausible embedding dimensions and delay times. The ensemble approach is proved to be 50% more efficient than the single prediction for both local approximation and wavelet network approaches. The wavelet network approach has proved to be 30%-50% more superior to the local approximation approach. Compared to the traditional local approximation approach with single initial condition, the total predictive uncertainty in the streamflow is reduced when modeled with ensemble wavelet networks for different lead times. Localization property of wavelets, utilizing different dilation and translation parameters, helps in capturing most of the statistical properties of the observed data. The need for taking into account all plausible initial conditions and also bringing together the characteristics of both local and global approaches to model the unstable yet ordered chaotic attractor of a hydrologic series is clearly demonstrated.

On the basin-scale detection and attribution of human-induced climate change in monsoon precipitation and streamflow

Detecting and quantifying the presence of human-induced climate change in regional hydrology is important for studying the impacts of such changes on the water resources systems as well as for reliable future projections and policy making for adaptation. In this article a formal fingerprint-based detection and attribution analysis has been attempted to study the changes in the observed monsoon precipitation and streamflow in the rain-fed Mahanadi River Basin in India, considering the variability across different climate models. This is achieved through the use of observations, several climate model runs, a principal component analysis and regression based statistical downscaling technique, and a Genetic Programming based rainfall-runoff model. It is found that the decreases in observed hydrological variables across the second half of the 20th century lie outside the range that is expected from natural internal variability of climate alone at 95% statistical confidence level, for most of the climate models considered. For several climate models, such changes are consistent with those expected from anthropogenic emissions of greenhouse gases. However, unequivocal attribution to human-induced climate change cannot be claimed across all the climate models and uncertainties in our detection procedure, arising out of various sources including the use of models, cannot be ruled out. Changes in solar irradiance and volcanic activities are considered as other plausible natural external causes of climate change. Time evolution of the anthropogenic climate change ``signal'' in the hydrological observations, above the natural internal climate variability ``noise'' shows that the detection of the signal is achieved earlier in streamflow as compared to precipitation for most of the climate models, suggesting larger impacts of human-induced climate change on streamflow than precipitation at the river basin scale.

Ganga-Brahmaputra river discharge from Jason-2 radar altimetry: An update to the long-term satellite-derived estimates of continental freshwater forcing flux into the Bay of Bengal

This paper discusses the use of Jason-2 radar altimeter measurements to estimate the Ganga-Brahmaputra surface freshwater flux into the Bay of Bengal for the period mid-2008 to December 2011. A previous estimate was generated for 1993-2008 using TOPEX-Poseidon, ERS-2 and ENVISAT, and is now extended using Jason-2. To take full advantages of the new availability of in situ rating curves, the processing scheme is adapted and the adjustments of the methodology are discussed here. First, using a large sample of in situ river height measurements, we estimate the standard error of Jason-2-derived water levels over the Ganga and the Brahmaputra to be respectively of 0.28 m and 0.19 m, or less than similar to 4% of the annual peak-to-peak variations of these two rivers. Using the in situ rating curves between water levels and river discharges, we show that Jason-2 accurately infers Ganga and Brahmaputra instantaneous discharges for 2008-2011 with mean errors ranging from similar to 2180 m(3)/s (6.5%) over the Brahmaputra to similar to 1458 m(3)/s (13%) over the Ganga. The combined Ganga-Brahmaputra monthly discharges meet the requirements of acceptable accuracy (15-20%) with a mean error of similar to 16% for 2009-2011 and similar to 17% for 1993-2011. The Ganga-Brahmaputra monthly discharge at the river mouths is then presented, showing a marked interannual variability with a standard deviation of similar to 12500 m(3)/s, much larger than the data set uncertainty. Finally, using in situ sea surface salinity observations, we illustrate the possible impact of extreme continental freshwater discharge event on the northern Bay of Bengal as observed in 2008.

Computing Reeb Graphs as a Union of Contour Trees

The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. This paper describes a fast algorithm to compute the Reeb graph of a piecewise-linear (PL) function defined over manifolds and non-manifolds. The key idea in the proposed approach is to maximally leverage the efficient contour tree algorithm to compute the Reeb graph. The algorithm proceeds by dividing the input into a set of subvolumes that have loop-free Reeb graphs using the join tree of the scalar function and computes the Reeb graph by combining the contour trees of all the subvolumes. Since the key ingredient of this method is a series of union-find operations, the algorithm is fast in practice. Experimental results demonstrate that it outperforms current generic algorithms by a factor of up to two orders of magnitude, and has a performance on par with algorithms that are catered to restricted classes of input. The algorithm also extends to handle large data that do not fit in memory.