Deepak Kashyap

Estimation of unconfined aquifer parameters by genetic algorithms

Abstract Unconfined aquifer parameters, viz. transmissivity, storage coefficient, specific yield and delay index from a pumping test are estimated using the genetic algorithm optimization (GA) technique. The parameter estimation problem is formulated as a least-squares optimization, in which the parameters are optimized by minimizing the deviations between the field-observed and the model-predicted time–drawdown data. Boultons convolution integral for the determination of drawdown is coupled with the GA optimization technique. The bias induced by three different objective functions: (a) the sum of squares of absolute deviations between the observed and computed drawdown; (b) the sum of squares of normalized deviations with respect to the observed drawdown; and (c) the sum of squares of normalized deviations with respect to the computed drawdown, is statistically analysed. It is observed that, when the time–drawdown data contain no errors, the objective functions do not induce any bias in the parameter estimates and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the case considered, defining the objective function as the sum of the squares of absolute deviations between the observed and simulated drawdowns resulted in the best possible estimates. A comparison of the GA technique with the curve-matching procedure and a conventional optimization technique, such as the sequential unconstrained minimization technique (SUMT), is made in estimating the aquifer parameters from a reported field pumping test in an unconfined aquifer. For the case considered, the GA technique performed better than the other two techniques in parameter estimation, with the sum-of-squares errors obtained from the GA about one fourth of those obtained by the curve matching procedure, and about half of those obtained by SUMT. Citation Rajesh, M., Kashyap, D. & Hari Prasad, K. S. (2010) Estimation of unconfined aquifer parameters by genetic algorithms. Hydrol. Sci. J. 55(3), 403–413.

Stochastic design of beams on reinforced random earth beds in deterministic mode

One of the main soil parameters in analysis and design of foundations is modulus of subgrade reaction (MSR) which is a stochastic process. However, design engineers prefer a deterministic approach invoking mean of MSR and rather empirical factors of safety to account for the uncertainty. The present study includes the stochasticity in the deterministic designs by linking the factors of safety (in respect of maximum deflection and bending moment) to the allowable risk of failure through a Monte Carlo simulation on a lumped parameter deterministic model. A parametric study reveals that for a given risk level, the factors of safety are strongly dependent upon the coefficient of variation of MSR, and only mildly upon other geometric parameters of foundation system. This facilitates development of closed form equations for the upper bounds on factors of safety exclusively in terms of allowable risk of failure and the coefficient of variation of MSR.

Rationalization of factors of safety in analysis of beams on geosynthetic reinforced random earth beds by Monte Carlo simulation

Abstract The paper presents an approach for rationalizing the factors of safety in the analysis and design of foundations, wherein a single lumped value is assigned to an uncertain soil parameter on the basis of multiple field testing. A soil-foundation system, comprising a geosynthetic layer (idealized as a beam) placed over a random poor soil and overlain by a compacted sand layer and the foundation beam, has been modeled in a lumped parameter mode. The model parameters comprise among other, the relative stiffness of the random poor soil that has been treated as a lognormally distributed random variable. Monte Carlo simulation has been performed on the model at various levels of the coefficient of variation (COV) of the uncertain/random parameter to arrive at the probability distribution functions (PDF) of the state variables viz., the normalized mid-span deflection and bending moment in the foundation beam. These PDFs have been subsequently invoked to correlate the factors of safety to the COV and the risk of failure. It has been suggested that factors of safety should be introduced in the foundation design by considering COV of the uncertain soil parameters and the allowable risk.

Kernel Function Model for Planning of Agricultural Groundwater Development

AbstractA linked kernel-optimization model for the planning of optimal groundwater development for irrigation is presented. The planning ensures optimization of zonal crop patterns subject to the constraints on the maximum water table depth and the stream-aquifer interflow at the dynamic equilibrium. The model is computationally inexpensive as compared to the traditional linked simulation-optimization models. Its use is demonstrated by applying it to a canal command area in India. Five kernel models are developed relating the maximum water table depth and four critical stream-aquifer interflow rates to the crop areas. The necessary data base is generated by using a physically based precalibrated simulation model of groundwater flow. The kernel models are linked to a genetic algorithm-based optimizer for arriving at the optimal cropping pattern and the associated pumping pattern. The near-optimal solution so obtained is further fine-tuned through an inexpensive application of the linked simulation-optimiza...

DEVELOPMENT OF A SITE-SPECIFIC ZHD MODEL USING RADIOSONDE DATA

Estimation of precipitable water vapor (PWV) in the atmosphere using ground based GPS (Global Positioning System) data requires an appropriate model for computation of zenith hydrostatic delay (ZHD). Presented herein is a site-specific ZHD model (SSM) for a station at New Delhi, India. The model has been developed by regressing one-year atmospheric vertical profile data collected through radiosonde. The model based on surface atmospheric pressure at the station, has been validated invoking data of three more years. The ZHD values estimated through the model disagree at the 0.3 mm level with ZHD values obtained from raytracing of radiosonde data. Further, Saastamoinen ZHD model provides an error about 0.23 mm rms while about 0.19 mm by the developed model (SSM). Thus, developed SSM can be used for precise estimation of PWV.

Stochastic analysis of beams on reinforced earth beds

The present study comprises Monte-Carlo simulation assisted analysis of foundations resting on reinforced earth beds using the concept of beams on an elastic foundation, treating the modulus of subgrade reaction (MSR) as a stationary stochastic field characterised by mean, variance, autocorrelation function (ACF) and the autocorrelation distance (ACD). Realisations of the MSR, generated by solving a stochastic differential equation, are fed to a deterministic distributed parameter model to generate realisations of two dependent stochastic fields, namely deflection and bending moment in the foundation beam, and two random variables, namely the location of occurrence of maximum deflection and the bending moment. Subsequently these realisations are analysed to evolve probability distribution functions, variance and ACF of the dependent stochastic fields and the random variables. It is revealed that the ACF of these fields is independent of the ACF of the MSR. Further, variance of deflection is found to increase as the ACD of the MSR increases, implying requirement of a larger factor of safety when random soils display low frequency (macro level) variations. On the other hand, variance of the bending moment is larger at smaller ACDs of the MSR, indicating that for bending moments a larger factor of safety is required when the random soils display high frequency (micro level) variations.

New Model of Variogram of Groundwater Hydraulic Heads

Kriging is a powerful tool for interpolation and network design. A necessary prerequisite for a kriging application is the variogram that describes the variation of the semivariance with distance. Variograms are routinely derived from the measurements of the concerned variable. Presented herein is a model of the variogram of groundwater hydraulic heads that permits the estimation of the semivariance corresponding to any distance in terms of the transmissivity (T) and standard deviation ( σW ) of the flux. The model thus evolves the variogram from the aquifer attributes rather than from the measured heads. Treating the flux as a normally distributed random variable, with zero mean and an assigned standard deviation, synthetic discrete steady-state stationary head fields are generated by the Monte Carlo simulation. The fields so generated are employed to evolve experimental variograms, and hence to estimate the parameters of the Gaussian model for various values of T and σW . Closed form functional relation...

A nonlinear optimisation method for aquifer parameter estimation

Abstract A numerical scheme is developed to estimate quantitatively parameters related to geohydrological and hydrological characteristics of groundwater aquifers, employing historic data of hydraulic head, rainfall, pumpages, etc. The scheme is based upon the constrained minimisation of the sum of the squares of the residues in the Boussinesq equation. Derivatives of hydraulic head are estimated by the least-squares polynomial approximation.

Effect of Spatial Extent of Atmospheric Variables on Development of Statistical Downscaling Model for Monthly Precipitation in Yamuna-Hindon Interbasin, India

AbstractAtmospheric variables (being predictors) play a crucial role in statistical downscaling (SD) studies, which subsequently are used to assess the hydrological impacts of climate change on water resources development and management. The spatial extent of these variables has an utmost importance in development of the SD model and for projecting the precipitation series. In this paper, an attempt is made to identify the spatial extent of atmospheric variables in terms of National Center for Environmental Prediction (NCEP) grid points that result in development of an efficient SD model for precipitation. A case study of the Yamuna-Hindon interbasin is considered to illustrate the applicability of the methodology proposed for capturing the effect of spatial domain of atmospheric variables on development of the SD model. The precipitation in the area is likely to be influenced by surrounding climate, topography, atmospheric circulation, thermodynamic processes, etc. Various cases of spatial extent, which ...

Modeling of Variably Saturated Flow in Response to Pumping from an Unconfined Aquifer: Numerical Evidence of Gravity-Delayed Drainage and Its Parameterization

AbstractA numerical model of variably saturated axis-symmetric radial flow is employed to simulate and parameterize the gravity-delayed drainage, viewing it as the vertical accretion over falling water table. Numerical experiments are conducted to simulate the head fields at advancing discrete times as pumping is sustained at the assigned well. The head fields are invoked to generate the corresponding time series of water table elevation and the accretion rate over it. Employing these time series, the optimal structure/parameters of gravity-delayed drainage equation are estimated by the least-squares approach under a variety of hydrogeologic/geometric conditions. It is revealed that generally, a two-parameter gravity-delayed drainage equation reproduces parsimoniously the accretion time series.