Genetic Algorithm Based Parameter Estimation of Nash Model

Unit hydrograph method is usually used to resolve surface runoff concentration process. Empirical unit hydrograph is sometimes jagged and not smooth because of estimation errors. Owing to the randomicity of correction method, there is some localization in its application. The application of instantaneous unit hydrograph is relatively wider. Generally, moment method is used to estimate the parameters of instantaneous unit hydrograph. However, the error is obvious between the observed flood process and the predicted flood process with moment method, especially near the flood peak. The genetic algorithm toolbox of matlab software is used to optimize the parameters of instantaneous unit hydrograph. The statistical function gamcdf(x, α, β) in matlab toolbox is used to calculate S(t) curve, which can avoid the errors caused by approximate formula method. The case study indicates that the weighted sum of absolute error applying the method in this paper is 25, the result applying moment method is 63, and the result of approximate formula method is 49. The results show that the method in this paper is more effectual than the other two methods.     

On the parametric approach to unit hydrograph identification

Unit hydrograph identification by the parametric approach is based on the assumption of a proper analytical form for its shape, using a limited number of parameters. This paper presents various suitable analytical forms for the instantaneous unit hydrograph, originated from known probability density functions or transformations of them. Analytical expressions for the moments of area of these form versus their definition parameters are theoretically derived. The relation between moments and specific shape characteristics are also examined. Two different methods of parameter estimation are studied, the first being the well-known method of moments, while the second is based on the minimization of the integral error between derived and recorded flood hydrographs. The above tasks are illustrated with application examples originated from case studies of catchments in Greece.Notations A catchment area - a,b,c definition parameters (generallya is a scale parameter, whileb andc are shape parameters) - C _v coefficient of variation - C _s skewness coefficient - D net rainfall duration - f( ) probability density function (PDF) - F( ) cumulative (probability) distribution function (CDF) - g( ) objective function - H net rainfall depth - H ₀ unit (net) rainfall depth (=10 mm) - I(t) net hyetograph - i(t) standardized net hyetograph (SNH) - I _n n ^th central moment of the standardized net hyetograph - Q(t) surface runoff hydrograph - q(t) standardized surface runoff hyrograph (SSRH) - Q _n n ^th central moment of the standardized surface runoff hydrograph - S _D (t) S-curve derived from a unit hydrograph of durationD - s(t) standardizedS-curve (SSC) - t time - T _D flood duration of the unit hydrographU _D (t) - T ₀ flood duration of the instantaneous unit hydrographU ₀(t) (= right bound of the functionU ₀(t)) - t _U IUH lag time (defined as the time from the origin to the center of area of IUH or SIUH) - t _I time from the origin to the center of the area of the net hyetograph - t _Q time from the origin to the center of the area of the surface runoff hydrograph - t _p time from the origin to the peak of IUH (or SIUH) - U _D (t) unit hydrograph for rainfall of durationD (DUH) - U _o (t) instantaneous unit hydrograph (IUH) - u(t) standardized instantaneous unit hydrograph (SIUH) - U _n nth central moment of area of IUH - U _n nth moment of IUH about the origin - U _n nth moment of IUH about the right bound (when exists) - V surface runoff volume - V ₀ volume corresponding to the unit hydrograph     

Development and Integration of Sub-hourly Rainfall–Runoff Modeling Capability Within a Watershed Model

Increasing urbanization changes runoff patterns to be flashy and instantaneous with decreased base flow. A model with the ability to simulate sub-daily rainfall–runoff processes and continuous simulation capability is required to realistically capture the long-term flow and water quality trends in watersheds that are experiencing urbanization. Soil and Water Assessment Tool (SWAT) has been widely used in hydrologic and nonpoint sources modeling. However, its subdaily modeling capability is limited to hourly flow simulation. This paper presents the development and testing of a sub-hourly rainfall–runoff model in SWAT. SWAT algorithms for infiltration, surface runoff, flow routing, impoundments, and lagging of surface runoff have been modified to allow flow simulations with a sub-hourly time interval as small as one minute. Evapotranspiration, soil water contents, base flow, and lateral flow are estimated on a daily basis and distributed equally for each time step. The sub-hourly routines were tested on a 1.9 km² watershed (70% undeveloped) near Lost Creek in Austin Texas USA. Sensitivity analysis shows that channel flow parameters are more sensitive in sub-hourly simulations (Δt = 15 min) while base flow parameters are more important in daily simulations (Δt = 1 day). A case study shows that the sub-hourly SWAT model reasonably reproduces stream flow hydrograph under multiple storm events. Calibrated stream flow for 1 year period with 15 min simulation (R ² = 0.93) shows better performance compared to daily simulation for the same period (R ² = 0.72). A statistical analysis shows that the improvement in the model performance with sub-hourly time interval is mostly due to the improvement in predicting high flows. The sub-hourly version of SWAT is a promising tool for hydrology and non-point source pollution assessment studies, although more development on water quality modeling is still needed.     

The Influence of Conceptual Flow Simulation Model Parameters on Model Solution

This article investigates the influence of conceptual flow simulation model parameters (i.e coefficients and constants that need to be estimated in calibration) on model solution (surface runoff) to understand the characteristics of the model. A new conceptual watershed yield model (WYM) was employed. There are four physical parameters, two fitting coefficients and two initial estimates of the surface water and groundwater storagesthat control the functioning of the model. The conceptual model was applied on Ling River near Kahuta and detailed sensitivity analysis was performed to explore the most sensitive model parameters. The most sensitive model parameters worked out were C _g (a fitting coefficient, which reflects the rate at whichgroundwater runoff occurs), w _r (watershed retention is the initial rainfall losses before runoff begins), p _gr (inputparameter that reflects the discharge capacity of the groundwateraquifer). The model parameters like i _c (infiltration coefficient), g _wsm (input parameter that depends on the subsurface storage available in the watershed) and e _p (input parameter) have negligible effect on model solution. It was observed that w _r (watershed retention) is the only surface runoff controlling parameter and p _gr and C _g are the groundwater runoff controlling parameters.     

Another Look at Z-transform Technique for Deriving Unit Impulse Response Function

This paper presents a technique to derive the unit impulse response functions (UIRF) used for determination of unit hydrograph by employing the Z-transform technique to the response function derived from the Auto Regressive Moving Average (ARMA) process of order (p, q). The proposed approach was applied to reproduce direct surface runoff for single storm event data registered over four watersheds of area ranging from 0.42 to 295 km². It is observed that the UIRF based on ARMA (1, 2) and ARMA (2, 2) provides a better representation of the watershed response. Further, to test the superiority of the developed impulse response function form ARMA process, the direct runoff hydrographs were computed using the simple ARMA process and optimized Nash’s two parameter model and compared with the results obtained from UIRF’s of ARMA model. The performance of the models based on the graphical presentation as well as from the test statistics viz. RMSE and MAPE indicates that UIRF-ARMA (p, q) performs better than optimized Nash Model and mostly similar to simple ARMA (p,q) model. Further more, the ARMA process of order p ≤ 2 and q ≤ 2 is generally sufficient and less cumbersome than the Argand diagram based approach for UIRF derivation.     

Generation of Runoff Components from Exponential Expressions of Serial Reservoirs

Taiwan frequently experiences heavy rainfall events during the summer. The rainfall–runoff regeneration is an important job in specific areas where excessive rainfall causes serious flooding. The primary goal of this study is to generate and understand runoff components of the watershed outlet by using a conceptual model of three linear cascade reservoirs. The conceptual model is needless to determine direct runoff and excess rainfall in advance. Every linear cascade reservoir has an independent response function with an exponential expression. The outflows of the linear reservoirs represent streamflow components of a watershed outlet during rainfall–runoff processes, in which surface runoff is considered as quick runoff, whereas subsurface and groundwater runoffs are slow runoffs. In the simulation process, mean rainfall as model inputs were estimated using the block Kriging method. Available recordings of 68 rainfall–runoff events during 1966–2002 were used as the study sample. Fifty-four events were calibrated to determine the best hydrograph parameters and were used to compare simulation precision resulting from the model with those based on the Nash with NLP. The efficacy of the proposed model was verified using the remaining 14 observed rainfall–runoff data from an actual basin. The seven averaged parameters, which were applied for verification, show that the IUH shape of quick flow is more sharp-pointed with the peak shifted forward than that of slow flow. In rainfall–runoff processes, peak discharge of quick runoff is far larger than that of slow runoff, the time it takes for the peak discharge for a quick flow is earlier than that for a slow runoff, and the base time of a slow flow is longer than that of a quick flow. Furthermore, this study also found: (1) the base time of a slow runoff hydrograph is the same as that of a total runoff hydrograph; (2) the base time of a quick runoff hydrograph is contrariwise to the value of the soil antecedent moisture; (3) an amount of quick runoff is directly proportional to that of total runoff. These analytical results reveal that the model used in this study is suitable to evaluate hydrological conditions in this and other watersheds and can be further applied to watershed management in Taiwan.     

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     

Estimation of Clark’s Instantaneous Unit Hydrograph Parameters and Development of Direct Surface Runoff Hydrograph

We present a method to estimate Time of Concentration (T _c) and Storage Coefficient (R) to develop Clark’s Instantaneous Unit Hydrograph (CIUH). T _c is estimated from Time Area Diagram of the catchment and R is determined using optimization approach based on Downhill Simplex technique (code written in FORTRAN). Four different objective functions are used in optimization to determine R. The sum of least squares objective function is used in a novel way by relating it to slope of a linear regression best fit line drawn between observed and simulated peak discharge values to find R. Physical parameters (delineation, land slope, stream lengths and associated drainage areas) of the catchment are derived from SPOT satellite imageries of the basin using ERDAS: Arc GIS is used for geographic data processing. Ten randomly selected rainfall–runoff events are used for calibration and five for validation. Using CIUH, a Direct surface runoff hydrograph (DSRH) is developed. Kaha catchment (5,598 km²), part of Indus river system, located in semi-arid region of Pakistan and dominated by hill torrent flows is used to demonstrate the applicability of proposed approach. Model results during validation are very good with model efficiency of more than 95% and root mean square error of less than 6%. Impact of variation in model parameters T _c and R on DSRH is investigated. It is identified that DSRH is more sensitive to R compared to T _c. Relatively equal values of R and T _c reveal that shape of DSRH for a large catchment depends on both runoff diffusion and translation flow effects. The runoff diffusion effect is found to be dominant.     

Aggregated runoff from small watersheds based on stochastic representation of storm events

This paper is concerned with the estimation of aggregated direct runoff from small watersheds during a time interval (0,t), homogeneous with respect to rainfall characteristics. The storm events are simulated by a Poisson process, whereas direct runoff is estimated by the SCS method or a linear regression model. The probability of the occurrence of direct runoff is incorporated in the proposed method by examining the possibility of each storm exceeding the watershed losses index. A closed form solution is derived for the expected total direct runoff in the interval (0,t). Finally, the proposed method is applied to a particular set of conditions.Notation Q direct runoff - P rainfall depth - S index of watershed storage - CN Curve Number of SCS method - t time - T _i time interval between successive storm events (i andi+1) - X _i storm depth of theith event (case a) excess storm depth of theith event (case b) - Y(t) total direct runoff in (0,t) - N(t) number of storm events in (0,t) - F(t) distribution function of the time between storm events - G(x) distribution function of the storm depth - F _n(t),F _n+1(t) n-fold and (n+1)-fold convolution ofF(t), respectively - G _n(x),G _n+1(x) n-fold and (n+1)-fold convolution ofG(x), respectively - E[X] expected mean value - p probability of exceeding the thresholde,p+q=1 - * convolution operation     

基于Nash 瞬时单位线法的渗透坡面汇流模拟

基于Nash瞬时单位线法,结合Horton土壤入渗经验模型,并考虑植被对降雨的截流作用,建立了渗透坡面汇流计算的数学模型。以矩形坡面为研究对象,基于其汇流时间-面积特性,结合等流时线法,推导建立了Nash瞬时单位线参数n、K的确定方法。其中,参数n的值为1.0,K的值与坡面汇流时间相等,相当于单一线性水库。应用本文建立的模型,对林地渗透坡面降雨径流进行计算,并与实测值进行比较。结果表明,计算值与实测值的变化趋势基本吻合,初步验证了本文方法的合理性。     

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     

A variable sorptivity infiltration equation

Horizontal and vertical one-dimensional infiltration are compared when they both occur in a homogeneous isotropic porous body initially at a uniform low water content _n under constant concentration (₀) or constant pressure head (H ₀) conditions. From a consideration of the physics governing infiltration under such conditions, the conclusion is reached that the magnitude of the pressure head gradient atx=0, wherex=0 denotes the infiltration surface in the horizontal case, must be larger than the magnitude of the pressure head gradient atz=0, wherez=0 denotes the infiltration surface in the vertical case, for all finitet>0, so that for the hydraulic head gradient atz=0 to be greater than (1/2K ₀)S _x t ^–1/2 but smaller than [(1/2K ₀)S _x t ^–1/2+1],K ₀ being the hydraulic conductivity at ₀ andS _x the sorptivity during horizontal infiltration. On these grounds, it is further argued that if the sorptivityS _z is introduced for the case of vertical infiltration, then it must be equal toS _x fort=0 only and that it must decrease with time. Results obtained by solving soil-water flow equations for the infiltration conditions defined above, and from experiment, support the above conclusions. An equation for the relationship between cumulative infiltration and time during vertical infiltration is developed after assuming thatS _z decreases with time in an exponential manner. Cumulative infiltration versus time relationships given by this equation are compared with those obtained from the numerical solution of the soil-water flow equation and from experiment.     

Impact of Flood Spreading on Infiltration Rate and Soil Properties in an Arid Environment

Flood spreading (FS) is one of the suitable methods for flood management and water harvesting that increases the groundwater recharge, makes soil more fertile and increases nutrients in soil. It is also a method for reusing sediment, which is usually wasted. The purpose of this paper is to investigate the impact of flood spreading on physical and chemical soil properties (soil texture, infiltration rate, pH, EC, Na, P, K, Ca, Mg, Cl, HCO₃, and SO₄). It is examined that the soil properties change in the flood spreading projection area (FSP). The physico-chemical properties of soil and infiltration rate were measured in different soil depths at both flood spreading and control area. For the 20 cm of top soil, the amount of clay increased after the flood spreading implementation especially in the first and second dikes. Increasing clay was accompanied by decreasing soil infiltration and sand percentage. The mean differences of the clay, sand and infiltration rate between FSP and the control area were statistically significant (P < 0.01). A significant difference was not observed in 20–30 cm of the depth. Soil pH, Mg, HCO₃, Cl and SO₄ in different soil layers did not show any significant difference between the control and FSP. Soil EC in 0–20 cm depth of FSP and control area was showed a significant difference (P < 0.05) but no significant differences were found in deeper layers (P < 0.05). K, Na and Ca were remarkably different between 0 and 10 cm depths (P < 0.05) whereas no significant differences were found in deeper layers (P < 0.05). Comparison of the physico-chemical properties and infiltration rates between the dikes in the FSP shows that there are the significant differences between the medians of dike 1 with dikes 2, 3, 4 and 5, but the differences were not observed between dikes 3, 4 and 5. Our results show that the flood spreading operation can be influenced by the area that is under this operation. This study allowed us to investigate the mechanisms that regulate the infiltration rate and chemical soil properties throughout a seasonally flooded area.     

Efficacy of Nakagami-<Emphasis Type="Italic">m</Emphasis> Distribution Function for Deriving Unit Hydrograph

This paper applies the Nakagami-m distribution for the derivation of unit hydrograph (UH). The applicability of this distribution was verified using the data from 13 watersheds and results were compared with other distributions, viz., Gamma (GM), Beta, normal (NL), log-normal (LN), Weibull (WB), logistic (LG), generalized logistic (GLG) and Pearson type 3 (PT3). Based on visual comparison as well as statistical measures, such as root mean square error (RMSE), coefficient of efficiency (CE), mean absolute percentage error (MAPE), and application efficiency (η _dist.), it was found that the Nakagami-m distribution yielded satisfactory UHs and direct runoff hydrographs for watersheds of various sizes.     

叶尔羌河径流演变规律与变异特征

科学认识气候变化与人类活动影响下,以径流为主要指征的水循环过程及其变化,是合理利用水资源的前提,对于认识水文机理,应对径流变化具有重要价值。选取干旱区内陆河流叶尔羌河卡群断面1957-2015年长系列实测月径流系列、1962-2015年长系列实测月气温与降水系列,采用年内分配完全调节系数Cr、年内分配不均匀系数Cn、相对变化幅度Cm、集中度Cd、集中期D、年际径流均值、最大流量及出现时间、最小流量及出现时间、年际极值比等多指标,运用Mann-Kendall法、累积距平法、R/S法、排列熵法等多方法,揭示叶尔羌河径流演变规律与变异特征,并进行归因分析。结果表明:近60年来,叶尔羌河流域径流量年内分配趋均匀化、年际变化呈显著增多趋势且为正持续性,其中1957-1961年和1993-2015年为显著径流增加时段;Mann-Kendall法与排列熵法均证实了1997年为该径流序列的突变点也为变异点;气温,特别是夏季7-8月平均气温(相关系数为0.81)为叶尔羌河径流量变化的主要影响因素。     

Overland Flow on a Pervious Surface

ABSTRACT

This article presents the analytical solutions for overland runoff hydrographs produced by a uniform rainfall with decay soil infiltration rates. It was found that the kinematic wave travel time through a catchment under such a nonuniform rainfall excess is not a constant, but varies between the time of concentration and the time of equilibrium according to the soil moisture condition. The analytical solutions reveal that kinematic wave travel times are part of the hydrograph convolution process and can hardly be measured from observed hydrographs. The findings of this article suggest that the time of concentration of a small catchment shall be estimated by velocity-based methods rather than those empirical formulas developed for and calibrated by the time difference between the center of mass of the rainfall excess and the inflection point on recession of the observed runoff hydrograph.     

Climate Variability Influences on Hydrological Responses of a Large Himalayan Basin

The hydrological cycle, a fundamental component of climate is likely to be altered in important ways due to climate change. In this study, the historical daily runoff has been simulated for the Chenab River basin up to Salal gauging site using a simple conceptual snowmelt model (SNOWMOD). The model has been used to study the impact of plausible hypothetical scenarios of temperature and rainfall on the melt characteristics and daily runoff of the Chenab River basin. The average value of increase in snowmelt runoff for T + 1°C, T + 2°C and T + 3°C scenarios are obtained to be 10, 28 and 43%, respectively. Whereas, the average value of increase in total streamflow runoff for T + 1°C, T + 2°C and T + 3°C are obtained to be 7, 19 and 28%, respectively. Changes in rainfall by −10 and + 10% vary the average annual snowmelt runoff over the T + 2°C scenario by −1% and + 1% only. The result shows that melt is much more sensitive to increase in temperature than to rainfall.     

Karst Spring Discharges Analysis in Relation to Drought Periods,Using the SPI

Based on the long hydrological time series, the correlation between karst spring discharge series and rainfall has been analysed, using the Standard Precipitation Index (SPI). Analysis has been focused on the drought periods. Data come from a large karst system (Campania, Southern Italy), in an area characterised by a distribution of the precipitation prevalently during autumn-winter period. Insufficient recharge due to poor rainfall results in flat spring hydrographs (with no peak during spring season) that indicate a continuously decreasing discharge. Specifically, it has been found that 12 months cumulative rainfall, expressed by SPI₁₂, and spring discharge have similar trend. When SPI₁₂ will be equal or less that − 1, springs reduce the discharge, and a flat spring hydrograph will be produced when SPI reaches value less than − 1.5. In these cases, the prolonged shortage of accumulated rainfall causes a reduction in spring discharge also during the following year as well, pointing out a memory effect of the karst aquifer, and more complex rainfall–discharge relationship is observed.     

An application of linear programming to determine optimal systems for rainwater management: An economic view

Two decision models, one for determining optimal systems for rainwater management and the other for allocating additional water supplies from managed rainfall in conjunction with irrigation water, are formulated. The application of a rainwater management model to the command and to a watercourse, decides the minimum cost activities to manage rainwater. The output from the first model is used as the input in the second model which optimally allocates water to competing crops. It has been shown that 80% of rainwater could be managed economically in rice fields and in storage underground through artificial recharge. Optimal allocation of managed rainwater in conjunction with irrigation water increases the income of the project area to the extent of 14%.List of symbols AER Total available energy kWh - B _max Maximized value of the objective function, Rs - C _W Cost of canal water, Rs/10³ m³ - C _i Cost of managing rainwater through activityi, Rs/10³/m³ - C _min Minimized cost of managing surplus rainwater, Rs - C _RF Average cost of managed rainwater through activityi, Rs/10³ m³ - E _i Energy consumption in rainwater management activityi, kWh/10³ m³ (only energy required for pumping water is considered) - FLS Available capacity for fallow land storage, 10³ m³ - FPS Total storage in lined and unlined farm ponds, 10³ m³ - GWR Runoff diversion for artificial recharge through inverted tubewells, 10³ m³ - i A suffix for management activities having values 1,2,3,..., - j Crop index having values 1,2,3,..., - k Index for crop season, 1=kharif (summer) and 2=rabi(winter) - MRF Maximum rainfall surplus (runoff) available for management. (Runoff value at a 5-year return period was adopted) - P _j Income from crop activityj, Rs/ha - RFL Storage in fallow alkali land, 10³ m³ - RFS Storage in rice fields up to various depths, 10³ m³ - RWM _i Volume of rainwater managed through activityi, 10³ m³ - VCW Volume of canal water, 10³ m³ - VGW Volume of ground water, 10³ m³ - X _j Area under cropj, ha.     

Comparative Evaluation of Analytic Solutions in Predicting Soil Moisture Profiles in Vertical One-Dimensional Infiltration under Ponded and Constant Flux Boundary Conditions

The problem of vertical one-dimensional infiltration for both ponded and constant flux boundary conditions was studied through the use of existing analytic solutions. Main objective was to compare the soil moisture profile developed under constant flux boundary condition at the time of ponding , with that moisture profile developed under ponded conditions at an earlier time . Time t _C denotes the time when the decreasing infiltration rate for the ponded conditions becomes equal to the constant flux _q , applied for the constant flux case. One might state that the analytical solutions, for both cases do not give identical profiles. An approximate coincidence might be brought about through a modification in the diffusivity which, in many respects, seems justified. Practical outcome of the above analysis is the determination of the time of ponding T, after which surface runoff starts, for the constant flux case. This is of practical significance either under natural conditions of rainfall or under conditions of sprinkle-irrigation, since surface runoff is directly related with soil erosion and waste of irrigation water. Therefore any attempt to determine the time of ponding T is well merited.