Water table fluctuation with a random initial condition

The nonlinear Boussinesq equation is used to understand water table fluctuations in various ditch drainage problems. An approximate solution of this equation with a random initial condition and deterministic boundary conditions, recharge rate and aquifer parameters has been developed to predict a transient water table in a ditch-drainage system. The effects of uncertainty in the initial condition on the water table are illustrated with the help of a synthetic example. These results would find applications in ditch-drainage design.Notation A / tanh t - a lower value of the random variable representing the initial water table height at the mid point - a+b Upper value of the random variable representing the initial water table height at the midpoint - B tanh t - C 4/ - h variable water table height - h mean of the variable water table height - h _m variable water table height at the mid point - h _m mean of the variable water table height at the mid point - K hydraulic conductivity - L half spacing between the ditches - m ₀ initial water table height at the mid point - N Uniform rate of recharge - S specific yield - t time of observation - x distance measured from the ditch boundary - (4/SL)(NK)^1/2 - (L/4)(N/K)^1/2 - dummy integral variable     

Determining Hydraulic Characteristics of Production Wells using Genetic Algorithm

Proper well management requires the determination of characteristic hydraulic parameters of production wells such as well loss coefficient (C) and aquifer loss coefficient (B), which are conventionally determined by the graphical analysis ofstep-drawdowntest data. However, in the present study, the efficacy of a non-conventional optimization technique called Genetic Algorithm (GA), which ensures near-optimal or optimal solutions, is assessedin determining well parameters from step-drawdown test data. Computer programs were developed to optimize the well parametersby GA technique for two cases: (i) optimization of B and C only, and (ii) optimization of B, C and p (exponent) as well as to evaluate the well condition. The reliability and robustness of the developed computer programs were tested usingnine sets of published and unpublished step-drawdown data from varying hydrogeologic conditions. The well parameters obtained by the GA technique were compared with those obtained by the conventional graphical method in terms of root mean square error(RMSE) and visual inspection. It was revealed that the GA technique yielded more reliable well parameters with significantlylow values of RMSE for almost all the datasets, especially in caseof three-variable optimization. The optimal values of the parametersB, C and p for the nine datasets were found to range from 0.382 to 2.292 min m^-2, 0.091 to 3.262, and 1.8 to 3.6, respectively. Because of a wide variation of p, the GA techniqueresulted in considerably different but dependable and robust well parameters as well as well specific capacity and well efficiency compared to the graphical method. The condition of three wells was found to be good, one well bad and that of the remaining five wells satisfactory. The performance evaluation of the developed GA code indicated that a proper selection of generation number and population size is essential to ensure efficient optimization. Furthermore,a sensitivity analysis of the obtained optimal parameters demonstrated that the GA technique resulted in a unique set ofthe parameters for all the nine datasets. It is concluded thatthe GA technique is an effective and reliable numerical tool for determining the characteristic hydraulic parameters of production wells.     

Forecast model of water consumption for Naples

The data refer to the monthly water consumption in the Neapolitan area over more than a 30 year period. The model proposed makes it possible to separate the trend in the water consumption time series from the seasonal fluctuation characterized by monthly peak coefficients with residual component. An ARMA (1,1) model has been used to fit the residual component process. Furthermore, the availability of daily water consumption data for a three-year period allows the calculation of the daily peak coefficients for each month, and makes it possible to determine future water demand on the day of peak water consumption.Notation j numerical order of the month in the year - i numerical order of the year in the time series - t numerical order of the month in the time series - h numerical order of the month in the sequence of measured and predicted consumption values after the final stage t of the observation period - Z _ji effective monthly water consumption in the month j in the year i (expressed as m³/day) - T _ji predicted monthly water consumption in the month j in the year i minus the seasonal and stochastic component (expressed as m³/day) - C _ji monthly peak coefficient - E _ji stochastic component of the monthly water consumption in the month of j in the year i - Z _i water consumption in the year i (expressed as m³/year) - Z _j (t) water consumption in the month j during the observation period (expressed as m³/day) - evaluation of the correlation coefficient - Z _j (t) water consumption in the month j during the observation period minus the trend - Y _t transformed stochastic component from E _t : Y _t =ln Et - Y _t+h measured value of stochastic component for t+h period after the final stage t of the observation period - Y _t (h) predicted value of stochastic component for t+h period after the final stage t of the observation period - _j transformation coefficients from the ARMA process (m, n) to the MA () process     

Water Drainage in Layered Soils. Laboratory Experiments and Numerical Simulation

Experimental results during first and second drainage in a vertical column of saturated layered soil were compared to those predicted from simulation. The sample was composed of a sandyloam soil overlying a fine sand. The soil water content was measured by using -ray absorption method (²⁴¹Am) and the water pressure through tensiometers, arranged vertically along the column and connected to pressure transducers. From the evaluation of moisture and pressure versus time, the characteristic curves () of the layers were obtained and approximated by van Genuchten's analytical equation. The relationship K() between hydraulic conductivity and moisture was estimated by van Genuchten's prediction model. () and K() equations were used as inputs in the numerical model. The drainage of water was simulated by Richard's partial differential equation, which was solved with the finite differences computational scheme type Laasonen. The upper and lower boundary conditions were zero flux and a periodically changing head respectively. Numerical results show a good agreement with experimental data, with small deviations for certain hours.     

Time-dependent soil-water distribution under a circular trickle source

Soil-water distribution in homogeneous soil profiles of Yolo clay loam and Yolo sand (Typic xerorthents) irrigated from a circular source of water, was measured several times after the initiation of irrigation. The effect of trickle discharge rates and soil type on the locations of the wetting front and soil-water distribution was considered. Soil-water tension and hydraulic conductivity, as functions of soil-water content, were also measured. The theories of time-dependent, linearized infiltration from a circular source and a finite-element solution of the two-dimensional transient soil-water equation were compared with the experimental results. In general, for both soils the computer horizontal and vertical advances of the wetting front were closely related to those observed. With both theories, a better prediction of the wetting front position for the clay loam soil than for the sandy soil is shown. The calculated and measured horizontal vertical advances did not agree over long periods of time. With the linearized solution, overestimated and underestimated vertical advances for the clay and sandy soils, respectively, were shown. The finite-element model approximate in a better way the vertical advances than the linearized solution, while an opposite tendency for the horizontal advances indicated, especially in sandy soil.Notation k constant (dK/d) - K hydraulic conductivity - K ₀ saturated hydraulic conductivity - J ₀,J ₁ Bessel functions of the first kind - h soil water tension - q Q/r ₀ ² - Q discharge rate - r cylindrical coordinate; also horizontal distance in soil surface - R dimensionless quantity forr - r ₀ constant pond radius - R ₀ dimensionless quantity forr ₀ - t time - T dimensionless quantity fort - x, y Cartesian coordinates - z vertical coordinate; also vertical distance along thez axis chosen positively downward - Z dimensionless quantity forz - empirical soil characteristic constant - dummy variable of integration - volumetric soil water content - matrix flux potential - dimensionless quantity for      

A real-time flood forecasting model based on maximum-entropy spectral analysis: II. Application

The MESA-based model, developed in the first paper, for real-time flood forecasting was verified on five watersheds from different regions of the world. The sampling time interval and forecast lead time varied from several minutes to one day. The model was found to be superior to a state-space model for all events where it was difficult to obtain prior information about model parameters. The mathematical form of the model was found to be similar to a bivariate autoregressive (AR) model, and under certain conditions, these two models became equivalent.Notation A _k parameter matrix of the bivariate AR model - B backshift operator in time series analysis - eT forecast error (vector) at timet = T - _t uncorrelated random series (white noise) - F _k forward extension matrix of the entropy model forkth lag - I identity matrix - m order of the entropy model - N number of observations - P order of the AR model - Q _p peak of the direct runoff hydrograph - R correlation matrix - t _p time to peak of the direct runoff hydrograph - ₁ coefficient of variation - ₂ ratio of absolute error to the mean - forecasted runoff - x _i observed runoff - mean of the observed runoff - X ^–1 inverse ofX matrix - X* transpose of theX matrix Abbreviations AIC Akaike information criterion - AR autoregressive (model) - AR(p) autoregressive process of thepth order - ARIMA autoregressive integrated moving average (model) - acf autocorrelation function - ccf cross-correlation function - FLT forecast lead time - MESA maximum entropy spectral analysis - MSE mean square error - STI sampling time interval     

Optimization-simulation models for the design of an Irrigation project

Optimization-simulation models were used for the systems analysis of a water resources system. The Karjan Irrigation reservoir project in India was taken as the system. Two types of optimization models, i.e., linear programming, and dynamic programming (continuous and discontinuous) were used for preliminary design purposes. The simulation technique was used for further screening. The linear programming model is most suitable for finding reservoir capacity. Dynamic programming (continuous and discontinuous models) may be used for further refining the output targets and finding the possible reservoir carry-over storages, respectively. The simulation should then be used to obtain the near optimum values of the design variables.Notations a ₁ Unit irrigation benefit [Rs.10⁵ L^–3] - B ₁ Gross annual irrigation benefit [Rs.10⁵] - B _1,t Gross irrigation benefit in periodt [Rs.10⁵] - C ₁ Annual capital cost of irrigation [Rs.10⁵] - C ₁ Annual capital cost function for irrigation [Rs.10⁵ L^–3] - C _1,t Fraction of annual capital cost for irrigation in periodt [Rs.10⁵] - C ₂ Annual capital cost of reservoir [Rs.10⁵] - C ₂ Annual capital cost function for reservoir [Rs.10⁵ L^–3] - C _2,t Fraction of annual capital cost for reservoir in periodt [Rs.10⁵] - El _t Reservoir evaporation in timet [L³] - f _t Optimal return from staget [Rs.10⁵] - g _t The return function for periodt [Rs.10⁵] - I _t Catchment inflow into the reservoir in periodt [L³] - I _t Water that joins the main stem just above the irrigation diversion canal in timet [L³] - _t Local inflow to the reservoir from the surrounding area in timet [L³] - Ir Annual irrigation target [L³] - K _t Proportion of annual irrigation targetIr to be diverted for irrigation in timet - K _t Amount by whichK _t exceeds unity is the fraction of the end storage which is assigned to reservoir evaporation losses - L Loss in irrigation benefits per unit deficit in the supply [Rs.10⁵ L^–3] - L ₁ Lower bound on annual irrigation target,Ir [L³] - L ₂ Lower bound on reservoir capacity,Y [L³] - N Number of time periods in the planning horizon - O _t Total water release from the reservoir in periodt [L³] - O _t ^* The optimal total water release from the reservoir in timet [L³] - _t Secondary water release from the reservoir in timet [L³] - O _t Reservoir release to the natural channel in timet [L³] - Od _t Irrigation demand in timet [L³] - Om ₁ Annual OM cost of irrigation [Rs.10⁵] - Om ₁ Annual OM cost function for irrigation [Rs.10⁵ L^–3] - Om _1,t Fraction of annual OM cost for irrigation in periodt [Rs.10⁵] - Om ₂ Annual OM cost of reservoir [Rs.10⁵] - Om ₂ Annual OM cost function for reservoir [Rs.10⁵ L^–3] - Om _2,t Fraction of annual OM cost for reservoir in periodt [L³] - Omin_t Lower bound onO _t in timet [L³] - Omax_t Upper bound onO _t in timet [L³] - P _t Precipitation directly upon reservoir in timet [L³] - S _t Gross/live reservoir storage at the end of timet (gross storage in the linear program and live storage in the dynamic program) [L³] - S _t–1 Gross/live reservoir storage at the beginning of timet [L³] - t Any time period - Tr_t Transformation function - U ₁ Upper bound onIr [L³] - U ₂ Upper bound onY [L³] - Y Total capacity of reservoir at maximum pool level [L³] - Ya Fixed active (live) capacity of the reservoir (Y-Yd) [L³] - Ya _t Active (live) capacity (Ymax_t –Ymin_t) of the reservoir in timet [L³] - Yd Dead storage of the reservoir [L³] - Ymax_t Capacity up to the normal pool level of the reservoir in timet [L³] - Ymax_t Live capacity up to the normal pool level of the reservoir in timet [L³] - Ymin_t Capacity up to the minimum pool level of the reservoir in timet [L³] - Ymin_t Live capacity up to the minimum pool level of the reservoir in timet [L³]     

Dam-Break flood forecasting in Piemonte region,northwest Italy

Six major reservoirs in Piemonte region, northwest Italy, have been examined in order to assess the possible flood damages to the downstream area. In this paper, some results of the hydraulic study are presented. The floods are simulated by computer models with the input data which describe the imagined dam-break events as well as other facts. Some important practical aspects of the work are extensively discussed, i.e. the problems concerning determination of the dam-breaches, the influence of the breach parameters, and estimation of the hydraulic resistance factors.Notation A = cross sectional area of water flow - C = Chezy roughness coefficient - C = discharge coefficient - g = acceleration due to gravity - H = height of dam-breach - H = height of dam - h = water surface level above the datum plane - L = width of dam - Q = flow discharge - Q_e, Q_u = inflow and outflow discharges respectively - q = lateral inflow discharge - R_* = hydraulic radius - T = formation time of dam-breach - t = time - V = volume of reservoir storage - W = width of dam-breach - X = downstream distance from a dam along the river - = velocity distribution factor     

Use of parameter estimation in determining soil hydraulic properties from unsaturated transient flow

This paper proposes a model for determining the parameters given by the closed-form equations of van Genuchten. An objective function is made by the observed data from vertical drainage, and the solutions of optimization show that less computation and more accurate estimates are made as head profiles are taken into account rather than cumulative drainage. Sensitivity analysis of the error vector to parameters interprets this reason. The convergence and stability of solutions are evaluated with different magnitudes of measured errors in the head, and the results show good estimates will be obtained if a sufficient pressure head at the soil bottom is applied. A variable _k is introduced to avoid the estimations of and n being affected by the uncertainties of Ks and _s .     

Efficient steam turbines produced by the “Ural Turbine Plant” company

Design features and efficiency of some steam turbines produced at present by a plant formed as a result of division of the Turbine Motor Plant Company into several enterprises are presented.Translated from Élektricheskie Stantsii, No. 11, November 2004, pp. 27 – 32.     

Spectral Reflectance,Growth and Chlorophyll Relationships for Rice Crop in a Semi-Arid Region of India

Relations among spectral reflectance, chlorophyll a, and growth of rice plants grown on irrigated light textured soil in a semi arid region are presented here. There was a linear relation between spectral reflectance and rice plant height (r = 0.97), for band 1 (0.45–0.52 m) reflectance values. On the other hand, in bands 2 (0.52–0.60 m) and 3 (0.63–0.69 m), reflectance values decreased until 70 days after planting (DAP) and then increased during the reproductive phase of the crop. The near infrared band 4 (0.76–0.90 m) showed a maximum reflectance at 59 DAP (panicle initiation stage) and a decline in reflectance thereafter through maturity. The peak value of IR/R ratio was 16.39 at 62 DAP during the early reproductive phase; thereafter, it declines gradually with the maturity of the crop. Chlorophyll a concentration was high during early growth (vegetative and early reproductive stages) and decreased during the flowering and maturity stages. The rice plant canopy show a high chlorophyll a concentration at 64 and 59 DAP for sites A and B, respectively. Chlorophyll a concentration is higher in site A plant canopies than it is in site B during the entire crop cycle. A good inverse correlation (r = 0.91) has been found between chlorophyll a and band 1, while the IR/R ratio and the normalised difference vegetation index (NDVI) showed a relationship (r = 0.78) with the chlorophyll a concentration during the crop cycle. Band 2, 3 and 4 radiance values show a biphasic linear relationship with chlorophyll a concentrations, negative for early growth and positive for flowering and maturity stages. Results indicate that the period between 66 to 70 DAP is most suitable for the assessment of rice crop yield, based on chlorophyll a concentration.     

A real-time flood forecasting model based on maximum-entropy spectral analysis: I. Development

This paper, the first of two, develops a real-time flood forecasting model using Burg's maximum-entropy spectral analysis (MESA). Fundamental to MESA is the extension of autocovariance and cross-covariance matrices describing the correlations within and between rainfall and runoff series. These matrices are used to derive the model forecasting equations (with and without feedback). The model may be potentially applicable to any pair of correlated hydrologic processes.Notation a _k extension coefficient of the model atkth step - B _k backward extension matrix forkth step - B _ijk element of the matrixB _k (i,j=1, 2) - c _k coefficient of the entropy model atkth step in the LB algorithm - e _k (e _x ,e _y )k = forecast error vector atkth step - E _k error matrix atkth step - E _ijk element of theE _k (i,j=1, 2) - f frequency - F _k forward extension matrix atkth step - F _ijk element of theF _k matrix (i,j=1, 2) - H(f) entropy expressed in terms of frequency - H _X entropy of the rainfall process (X) - H _Y entropy of the runoff process (Y) - H _XY entropy of the rainfall-runoff process - I identity matrix - forecast lead time - m model order, number of autocorrelations - R correlation matrix - S _x standard deviation of the rainfall data - S _y standard deviation of the runoff data - t time - T ₁ rainfall record - T ₂ runoff record - T rainfall-runoff record (T=T ₁ T ₂) - x _t rainfall data (depth) - X X() = rainfall process - mean of the rainfall data - y _t direct runoff data (discharge) - Y Y() = runoff process - mean of the runoff data - (x, y) _t rainfall-runoff data (att T) - (x, y, z) _t rainfall-runoff-sediment yield data (att T) - z complex number (in spectral analysis) - _k coefficient of the LB algorithm atkth step - _nj Lagrange multiplier atjth location in the _n matrix - _{n n} = matrix of the Lagrange multiplier atkth step - _X (k), _Y (k) autocorrelation function of rainfall and runoff processes atkth lag - _XY (k) cross-correlation function of rainfall and runoff processes atkth lag - W ₁(f) power spectrum of rainfall or runoff - W ₂(f) cross-spectrum of rainfall or runoff Abbreviations acf autocorrelation function - ARMA autoregressive moving average (model) - ARMAX ARMA with exogenous input - ccf cross-correlation function - det() determinant of the (...) matrix - E[...] expectation of [...] - FLT forecast lead time - KF Kalman filter - LB Levinson-Burg (algorithm) - MESA maximum entropy spectral analysis - MSE mean square error - SS state-space (model) - STI sampling time interval - forecast ofx - forecast ofx -step ahead - x _F feedback ofx-value (real value) - |x| module (absolute value) ofx - X ^–1 inverse of the matrixX - X* transpose of the matrixX     

Optimization of the water chemistry of the primary coolant at nuclear power plants with VVÉR

Results of the use of automatic hydrogen-content meter for controlling the parameter of hydrogen in the primary coolant circuit of the Kola nuclear power plant are presented. It is shown that the correlation between the hydrogen parameter in the coolant and the hydrazine parameter in the makeup water can be used for controlling the water chemistry of the primary coolant system, which should make it possible to optimize the water chemistry at different power levelsTranslated from Élektricheskie Stantsii, No. 12, December 2004, pp. 31 – 33.     

Two-step dynamic programming approach for optimal irrigation water allocation

A two-step (deterministic and stochastic) dynamic programming approach has been introduced in this study to solve the complex problem of optimal water allocation in a run-of-the-river-type irrigation project. The complexity of a real-world situation is represented by incorporating in the optimization model the stochasticity of water supply and the nonlinearity of crop production functions. A nonlinear, dated, and multiplicative production function is transformed into a sequentially additive type to replace the usual method of creating an additional state of the plant variable which only increases the dimension of the problem. As compared to the explicit stochastic dynamic programming which necessitates, along with its use, an enormous computational complexity due to the so-called curse of dimensionality, the present model can approximate the theoretical global optimum, at least for the present case study, with a dramatic reduction in computer processing time. It also eliminates the rigidity of the policy derived by the explicit approach, since it provides irrigation planners with alternative decision policies which incorporate intangibles and other nonengineering factors. The traditional method of fixing the cropping pattern based on deterministic estimates of a dependable water supply can likewise be evaluated by the use of the present model. The results of the model's application appear to be practically acceptable.     

Errors of kinematic-wave and diffusion-wave approximations for time-independent flows

Time-independent (or steady-state) cases of planar (overland) flow were treated. Errors of the kinematic-wave and diffusion-wave approximations were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth-gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with error in the range of 1–2% for values ofKF ₀ ² (7.5). Even for small values ofKF ₂ ⁰ (e.g.,KF ₂ ⁰ =0.75), the errors were typically in the range of 11–15%. The accuracy of the diffusion wave approximation was greatly influenced by the downstream boundary condition. The error of the kinematic wave approximation was found to vary from 7 to 13% in the regions 0.05x0.95 forKF ₀ ² =0.75 and was greater than 30% forKF ₀ ² =0.75.     

Protection of Overhead Conductors at the Inlet to a Connector

A method that enables determination of maximum amplitudes of standing vibration waves, off-horizontal angles of the conductors, moments of resistance, and cutting forces in any cross section of any type of conductor and connector with the help of SVT-connector software is described. Comparative values of the mentioned parameters at the outlet of the conductor from rigid dress and at the inlet to the connector are presented.     

A new analytical model to predict the hydraulic conductivity of unsaturated soils

A new analytical model is presented for the prediction of hydraulic conductivity. The new model is based on the Brutsaert characteristic curve () and the Mualem integral relation. It is presented by a series expansion of the effective saturation () power and given in a simple algebraic relation. For checking the new model, twelve soils were selected from the available literature and a comparison was made between the new model, the experimental curve and the van Genuchten model as well. The suggested model is very close to the van Genuchten model in all cases except one and it exhibits hysteresis, due to the different values of the parameter b of Brutsaert equation for the wetting and drainage curves. Also a second model is presented, based on the Burdine integral relation.     

Pre-posterior analysis as a tool for data evaluation: Application to aquifer contamination

This paper deals with the frequently encountered problem of pre-posterior data evaluation, i.e., assessment of the value of data before they become available. The role of data is to reduced the risk associated with decisions taken under conditions of uncertainty. However, while the inclusion of relevant data reduces risk, data acquisition involves cost, and there is thus an optimal level beyond which any addition of data has a negative net benefit. The Bayesian approach is applied to construct a method for updating decisions and evaluating the anticipated reduction in risk following consideration of additional data. The methodology is demonstrated on a problem of management of an aquifer under threat of contamination.Notation L matrix of losses for all combinations of states and decisions - l, m, h possible salinity levels from the proposed borehole - N, M, F possible decisions - P(·) vector of prior probabilities of states - P(.|l), P(.|m), P(.|h) conditional (updated) probability vectors of the different states given the salinity levels - P(.|), P(.|), P(.|) probability vectors of the different salinity levels given the true states (likelihood function) - P(l), P(m), P(h) probabilities of the salinity levels, irrespective of the true state - R(.|l), R(.|m), R(.|h) posterior risk vectors of the different decisions given the salinity levels - R(N), R(M), R(F) prior risk associated with different decisions - , , possible true states     

Runoff changes simulated using a rainfall-runoff model

The Sacramento rainfall-runoff model has been used in experiments with 60 year daily series for the Czech part of the Labe River basin; simulations with decreased and/or increased inputs (precipitations, air temperature, evapotranspiration) provide results that could be used to appraise the runoff changes due to climatic warming.Simulations with the modified parameters are used for evaluation of runoff changes caused by landuse changes. For both purposes, the long-term data sets appear to be desirable; it is then possible to take into account accidental influences. The simulations also provide, as an output, the water contents in different zones of soil moisture; the relationships among evapotranspiration, soil moisture, and baseflow clearly appear in these results.     

Possibility of predicting earthquakes using measuring systems of the dam at the Chirkeiskaya hydrolectric power plant

The main group of earthquake precursors represent deformations and slants of the earth surface, which are registered in the course of geodetic monitoring in the nearest active fractures.Translated from Gidrotekhnicheskoe Stroitelstvo, No. 9, September 2004, pp. 61–66.