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.     

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     

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 .     

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.     

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.     

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.     

Determination of optimal unit hydrographs by linear programming

A unit hydrograph (UH) obtained from past storms can be used to predict a direct runoff hydrograph (DRH) based on the effective rainfall hyetograph (ERH) of a new storm. The objective functions in commonly used linear programming (LP) formulations for obtaining an optimal UH are (1) minimizing the sum of absolute deviations (MSAD) and (2) minimizing the largest absolute deviation (MLAD). This paper proposes two alternative LP formulations for obtaining an optimal UH, namely, (1) minimizing the weighted sum of absolute deviations (MWSAD) and (2) minimizing the range of deviations (MRNG). In this paper the predicted DRHs as well as the regenerated DRHs by using the UHs obtained from different LP formulations were compared using a statistical cross-validation technique. The golden section search method was used to determine the optimal weights for the model of MWSAD. The numerical results show that the UH by MRNG is better than that by MLAD in regenerating and predicting DRHs. It is also found that the model MWSAD with a properly selected weighing function would produce a UH that is better in predicting the DRHs than the commonly used MSAD.Notations M number of effective rainfall increments - N number of direct runoff hydrograph ordinates - R number of storms - MSAD minimize sum of absolute deviation - MWSAD minimize weighted sum of absolute deviation - MLAD minimize the largest absolute deviation - MRNG minimize the range of deviation - RMSE root mean square error - P _m effective rainfall in time interval [(m–1)t,mt] - Q _n direct runoff at discrete timent - U _k unit hydrograph ordinate at discrete timekt - W _n weight assigned to error associated with estimatingQ _n - _n ⁺ error associated with over-estimation ofQ _n - _n ^– error associated with under-estimation ofQ _n - _max ⁺ maximum positive error in fitting direct runoff hydrograph - _max ^– maximum negative error in fitting direct runoff hydrograph - _max largest absolute error in fitting obtained direct runoff - E _r,1 thelth error criterion measuring the fit between the observed DRHs and the predicted (or reproduced) DRHs for therth storm - E ₁ averaged value of error criterion overR storms     

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     

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     

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     

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.     

Optimal flood control in multireservoir cascade systems with deterministic inflow forecasts

This article presents the formal analysis of a problem of the optimal flood control in systems of serially connected multiple water reservoirs. It is assumed, that the basic goal is minimization of the peak flow measured at a point (cross-section) located downstream from all reservoirs and that inflows to the system are deterministic. A theorem expressing sufficient conditions of optimality for combinations of releases from the reservoirs is presented together with the relevant proof. The main features of the optimal combinations of controls are thoroughly explained. Afterwards, two methods of determining the optimal releases are presented. Finally, the results of the application of the proposed methodology to a small, four reservoir system are presented.Notations c _i contribution of theith,i=1, ...,m, reservoir to the total storage capacity of the multireservoir system - d _i (t) one of the uncontrolled inflows to the cascade at timet (fori=1 main inflow to the cascade, fori=2, ...,m, side inflow to theith reservoir, fori=m+1 side inflow at pointP) - total inflow to theith reservoir,i=2, ...,m, at timet (i.e., inflowd _i augmented with properly delayed releaser _i–1 from the previous reservoir) (used only in figures) - d(t),d _S (t) (the first term is used in text, the second one in figures) aggregated inflow to the cascade (natural flow at pointP) at timet - time derivative of the aggregated inflow at timet - i reservoir index - m number of reservoirs in cascade - P control point, flood damage center - minimal peak of the flow at pointP (cutting level) - Q _p (t) flow measured at pointP at timet - flow measured at pointP at timet, corresponding to the optimal control of the cascade - r _i (t) release from theith reservoir at timet, i=1, ...,m - optimal release from theith reservoir at timet, i=1, ...,m - r ₁ ^* (t) a certain release from theith reservoir at timet, different than ,i=1, ...,m, (used only in the proof of Theorem 1) - a piece of the optimal release from themth reservoir outside period at timet - assumed storage of theith reservoir at time (used only in the proof of Theorem 1) - s _i (t) storage of theith reservoir at timet, i=1, ...,m - time derivative of the storage of theith reservoir at timet, i=1, ...,m - storage capacity of theith reservoir,i=1, ...,m - (the first term is used in text, the second one in figures) total storage capacity of the cascade of reservoirs - S* sum of storages, caused by implementingr _i ^* ,i=1, ...,m, of all reservoirs measured at (used only in the proof of Theorem 1) - t time variable (continuous) - t ₀ initial time of the control horizon - t _a initial time of the period of constant flow equal at pointP - initial time of the period of the essential filling of theith reservoir,i=1, ...,m (used only in the proof of Theorem 1) - t _b final time of the period of constant flow equal at pointP - final time of the period of the essential filling of theith reservoir,i=1, ...,m (used only in the proof of Theorem 1) - time of filling up of theith reservoir while applying method with switching of the active reservoir - t _f final time of the control horizon - fori=1, ...,m–1, time lag betweenith andi+1th reservoir; fori=m time lag between the lowest reservoir of the cascade and the control pointP     

Field Applicability of the SCS-CN-Based Mishra–Singh General Model and its Variants

The general soil conservation service curve number (SCS-CN)-based Mishra and Singh (Mishra and Singh, 1999, J. Hydrologic. Eng. ASCE, 4(3), 257–264) model and its eight variants were investigated for their field applicability using a large set of rainfall-runoff events, derived from a number of U.S. watersheds varying in size from 0.3 to 30351.5 ha, grouped into five classes based on the rainfall magnitude. The analysis based on the goodness of fit criteria of root mean square error (RMSE) and error in computed and observed mean runoff revealed that the performance of the existing version of the SCS-CN method was significantly poorer than that of all the model variants on all the five data sets with rainfall 38.1 mm. The existing version showed a consistently improved performance on the data with increasing rainfall amount, but greater than 38.1 mm. The one-parameter modified SCS-CN method (a = 0.5 and = a median value) performed significantly better than the existing one on all the data sets, but far better on rainfall data less than 2 inches. Finally, the former with = 0 was recommended for routine field applications to any data set.     

Intangible Flood Damage Quantification

Flooding is a natural disaster that may cause tremendous tangibleand intangible damage to the national economy. The tangible damage assessment, i.e. the monetary value of all direct and indirect physical damages, has already been studied, whileintangible damages have not yet been taken into account. Thisarticle, therefore, is the first systematic attempt to assess bothtangible and intangible damages. The new proposed Anxiety-Productivity and Income Interrelationgship Approach (API) has been developed to quantify the intangible damage in monetary terms. The Bangkok area has been selected as the research area because several severe flood events have occurredthere over the last two decades. The 1983 Bangkok flood caused 6600 million baht in damage, according to estimates by the National Statistical Office (NSO). This article examines the totalflood damage (including the intangible damage) at different flood magnitudes. Case studies with and without flood mitigation projects are studied and compared. Furthermore, thisarticle also discusses the improvements over the conventional approach offered by the new API methodology.     

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     

An Aquifer Management Case Study – The Chalk of the English South Downs

The Chalk aquifer of the English South Downs is very heavily utilised. The groundwater resources have enjoyed a formal programme of management which started in the 1950s, although a number of actions had been taken earlier in order to deal with saline intrusion and potential risk to groundwater quality from urbanisation. In the late 1950s the policy of leakage/storage boreholes was first adopted, whereby the leakage boreholes along the coast were pumped in winter to intercept fresh water discharge to the sea and to maximise the recharge potential inland, and inland storage boreholes were used, as much as possible, in the summer months only. A comprehensive monitoring programme supported by aquifer modelling has enabled a gradual increase in overall abstraction to take place without increasing groundwater degradation due to saline intrusion. There have been various pollution prevention strategies over the years, and these have been effective in protecting the groundwater despite the high population density and widespread agricultural activity within the South Downs. The management of the aquifer has clearly been successful; there are many lessons from this experience that can be applied to other regions and other aquifers.     

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.     

On the predictability of the water-table variation in a ditch-drainage system

The irrigation in regions of brackish groundwater in many parts of the world results in the rise of the water-table very close to the groundsurface. The salinity of the productive soils is therefore increased. A proper layout of the ditch-drainage system and the prediction of the spatio-temporal variation of the water table under such conditions are of crucial importance in order to control the undesirable growth of the water-table. In this paper, an approximate solution of the nonlinear Boussinesq equation has been derived to describe the water-table variations in a ditch-drainage system with a random initial condition and transient recharge. The applications of the solution is discussed with the help of a synthetic example.Notations a lower value of the random variable representing the initial water-table height at the groundwater divide - a+b upper value of the random variable representing the initial water-table height at the groundwater divide - h variable water-table height measured from the base of the aquifer - K hydraulic conductivity - L half width between ditches - m ₀ initial water-table height at the groundwater divide - N(t) rate of transient recharge at time t - N ₀ initial rate of transient recharge - P N ₀/K - S Specific yield - t time of observation - t ₀ logarithmic decrement of the recharge function - T Kt/SL - x distance measured from the ditch boundary - X x/L - Y h/L - Y mean of Y - Y Variance of Y