Using Optimized Deep Learning to Predict Daily Streamflow: A Comparison to Common Machine Learning Algorithms

From a watershed management perspective, streamflow need to be predicted accurately using simple, reliable, and cost-effective tools. Present study demonstrates the first applications of a novel optimized deep-learning algorithm of a convolutional neural network (CNN) using BAT metaheuristic algorithm (i.e., CNN-BAT). Using the prediction powers of 4 well-known algorithms as benchmarks – multilayer perceptron (MLP-BAT), adaptive neuro-fuzzy inference system (ANFIS-BAT), support vector regression (SVR-BAT) and random forest (RF-BAT), the CNN-BAT model is tested for daily streamflow (Q_t) prediction in the Korkorsar catchment in northern Iran. Fifteen years of daily rainfall (R_t) and streamflow data from 1997 to 2012 were collected and used for model development and evaluation. The dataset was divided into two groups for building and testing models. The correlation coefficient (r) between rainfall and streamflow with and without antecedent events (i.e., R_t-1, R_t-2, etc.) (as the input variables) and Q_t (as the output variable) served as the basis for constructing different input scenarios. Several quantitative and visually-based evaluation metrics were used to validate and compare the model’s performance. The results indicate that R_t was the most effective input variable on Q_t prediction and the integration of R_t, R_t-1, and Q_t-1 was the optimal input combination. The evaluation metrics show that the CNN-BAT algorithm outperforms the other algorithms. The Friedman and Wilcoxon signed-rank test indicates that the prediction power of CNN-BAT algorithm is significantly/statistically different from the other developed algorithms.

     

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     

Optimal allocation of water resources in large river basins: I. Theory

The major purpose of this paper is to present the useful techniques in the optimal allocation of water resources (OAWR) and to demonstrate using water resources applications how these methods can be conveniently employed in practice for systematically studying both simple and complex water resources problems. Formal modelling techniques in multiobjective decision-making provide many benefits to professionals working in water resources and elsewhere. A new Large-system Hierarchical Dynamic Programming (LHDP) method to solve the model can be carried out to ascertain the consequences of meaningful parameter changes upon the optimal or compromise solution.As a case study, the techniques and methods are applied to the OAWR of the Yellow River Basin (YRB) of China. The next paper shares with the reader recent research results on the OAWRYRB.Notation L _i inflows from the trunk stream in the subregioni. - S _i run-off volume of the river sectioni. - Q _i net inflows of intervals in the subregioni. - W _i volumes of water drawn the trunk stream ofi into subdistricti. - H _i volumes of water returning to the trunk stream in the subdistricti. - B _i(W _i) the maximum net benefits (in hundred million yuan) from the annual-water consumption ofW _iin subregioni. - W _ik the annual-water consumption (in hundred million m³) of sectorK in subregioni, k = 1, 2, 3, 4. - B _ik(W _ik the maximum net benefits (in hundred million yuan) from the annual consumptionW _ikof sectork in subregioni. - BS _i(S _i) the maximum net benefits (in hundred million yuan) obtained from the optimal allocation of the run-off volumeS _iof river trunki among different sectors within the months of a year.     

Spectral‐ALS data fusion for different roughness parameterizations of forested floodplains

Natural river floodplains and adjacent wetlands grow typically a diverse and heterogeneous combination of herbs, shrubs and trees, which play an essential role in determining the total flow resistance. Hydrodynamic effects of trees in forested floodplains can provide the majority of flow resistance during flood events. Nevertheless, ground‐based techniques to acquire vegetation parameters are expensive and difficult to apply over long reaches. This paper presents a novel method of automated roughness parameterization of riparian woody vegetation by fusion of Quickbird multi‐spectral image with airborne laser scanning (ALS) data. The data fusion approach includes: individual tree detection and estimation of vegetation metrics from light detection and ranging (LiDAR) data, assessment of predictive models for the vegetation parameters and spatial mapping of the vegetation parameters for the forest plants in the riparian corridor. The proposed method focuses on estimation of plant density (d), crown diameters (D_C), tree height (h), stem diameter (D_S), crown base height (cbh) and leaf area index (LAI). The procedure is tested along a 14‐km reach of the Sieve River (Tuscany, Italy) characterized by high woody plant density. Due to the complex study area, the data fusion approach explains with variable reliability the local vegetation properties (R²(D_C) = 0.14, R²(h) = 0.84, R²(D_S) = 0.25, R²(cbh) = 0.66). The generated structural parameter maps represent spatially explicit data layers that can be used as inputs to hydrodynamic models used to analyse flow resistance effects in different submergence conditions of vegetation. A simple flow resistance model was applied over a test area comparing the results of the proposed method and a traditional ground‐based approach. The modelling results showed that the new method is able to provide accurate output data to describe the interaction between water levels and bio‐mechanical characteristics of vegetation. The proposed methodology provides a fast, repeatable and accurate way of obtaining floodplain roughness, which enables regular updating of vegetation characteristics. Copyright © 2010 John Wiley & Sons, Ltd.     

Bi-site Analysis of Meteorological Drought Duration: Theoretical Modeling and Application

Droughts are regional incidents that threat the environment and limit most of the socio-economic activities. Given the dry and wet state sequences for two sites, X_t^{( 1 )}X_t^{\left( 1 \right)} and X_t^{( 2 )}X_t^{\left( 2 \right)} , this paper presents a procedure to reduce the two sequences X_t^{( 1 )}X_t^{\left( 1 \right)} and X_t^{( 2 )}X_t^{\left( 2 \right)} to one sequence Z _t for the purpose of simplifying the analysis of drought duration at two sites jointly. Theoretical models to evaluate the expected value and the variance of the process Z _t and the occurrence probability of the dry state at two sites jointly are presented and verified using simulation experiments. Historical data for the period 1939–2005 and generated rainy season precipitation data for two gauging sites in Central Jordan, namely Amman Airport and Madaba, is used in the present study to investigate the occurrence of droughts. The joint analysis of drought duration obtained using the historical precipitation at the two sites appears to be inconsistent especially for droughts of duration longer than 3 years. On the other hand, the joint analysis of drought duration obtained theoretically by employing the characteristics of the process Z _t are found to match well with the more reliable drought statistics obtained empirically by analyzing the long generated precipitation. Considering 25 years planning horizon, droughts of 1, 2, and 3 years duration are the most frequent droughts in the region of Central Jordan. The return period of such regional droughts ranges from 8–30 years.     

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     

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     

三峡水库消落带斜坡岩体劣化过程地质强度指标研究

三峡库区消落带岩体劣化研究多针对室内岩样,难以应用到现场岸坡稳定性分析评价中。本文开展了水库实际运行状态下原位跨孔声波测试和井下电视,获取了不同深度下岩体物理力学参数,改进了GSI系统对岸坡劣化带岩体的描述,拓展了广义Hoek-Brown(H-B)准则在劣化带岩体强度动态评价中的应用,得出主要结论如下:广义H-B准则可以评估、描述原位岸坡岩体强度,结合水位循环消落原位跨孔声波测速,改进并构建了GSI量化取值方法;GSI结合广义H-B准则得到的特征深度强度包线表明,三轴受压应力状态可以提高岩体强度,且可明显抑制岩体劣化;脆-延转换线σ1=4σ3计算的H-B准则适用范围表明GSI系统对岩体劣化评价有宽泛的适用性,且随着GSI下降适用范围下降;通过指数回归构建了考虑劣化过程的GSI(t)、Erm(t)时效曲线,并基于GSI(t)解得不同深度结构面处二、三维强度劣化包线。强度劣化包线显示表层结构面的劣化敏感性高于深层,且表层受劣化影响H-B准则适用范围下降最明显;结合多层面GSI(t)曲线可得三维结构面GSI(t,h)时空函数。这种基于消落带原位跨孔声波的GSI(t)时效函数以及二、三维结构面...     

关于坝体混凝土的强度分级、结构抗力标准值及其分项系数

坝体混凝土的强度分级、结构抗力标准值及其分项系数等参数是混凝土坝设计规范中的重要参数,针对目前各有关规范之间对这些参数存在诸多与国家标准《水利水电工程结构可靠性设计统一标准》不相一致之处,本文指出:在对坝工混凝土强度分级中,由标号R(kg/cm2)改为以等级C(N/mm2)表示后,最近的重力坝和拱坝设计规范中又采用按Cd(N/mm2)和C90(MPa)分级,显然有违与国际标准保持一致及与其它有关规范相协调的初衷;对修编中的拱坝设计规范中,不能以坝体混凝土湿筛试件替代承载能力极限状态方程中的结构抗力的材料性能标准值;在从单一安全系数套改分项系数时,不能改变结构抗力的分项系数γm和结构系数γd的内涵,并将两者混淆。最后,为使这些参数与与国家标准《水利水电工程结构可靠性设计统一标准》相协调,提出了相应修改建议。     

Suitability of ANN-Based Daily Streamflow Extension Models: a Case Study of Gaoping River Basin,Taiwan

It is well known that sufficiently long and continuous streamflow data are required for accurate estimations and informed decisions in water-resources planning, design, and management. Although streamflow data are measured and available at most river basins, streamflow records often suffer from insufficient length or missing data. In this work, artificial neural networks (ANNs) are applied to extend daily streamflow records at Lilin station located in Gaoping River basin, southern Taiwan. Two ANNs, including feed forward back propagation (FFBP) and radial basis function (RBF) networks, associated with various time-lagged streamflow and rainfall inputs of nearby long-record stations are employed to extend short daily streamflow records. Performances of ANNs are evaluated by root-mean-square error (RMSE), coefficient of efficiency (CE), and histogram-matching dissimilarity (HMD). Inconsistency among these evaluation measures is solved by the technique for order performance by similarity to ideal solution (TOPSIS), a widely used multi-criteria decision-making approach, to find an optimal model. The results indicate that RBF-E1 (entire-year data training with Q _t and Q _t?1 inputs) has the minimum RMSE of 104.4 m³/s, second highest CE of 0.956, and third lowest HMD of 0.0096, which outperforms other ANNs and provide the most accurate reconstruction of daily streamflow records at Lilin station.     

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     

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     

黄河流域1961—2012年蒸散发时空变化特征及影响因素分析

基于黄河流域1 500个0.25°×0.25°网格,应用可变下渗能力模型VIC-3L计算1961—2012年黄河流域水文过程,获得日尺度的实际蒸散发量和潜在蒸散发量数据。运用Mann-Kendall趋势检验方法和Budyko水分能量平衡公式,分析了实际蒸散发量、潜在蒸散发量、蒸散发率和干燥指数的时空变化趋势及蒸散发受水分能量供应条件限制情况。结果表明:总体上实际蒸散发量和潜在蒸散发量呈减小趋势,其中潜在蒸散发量减小趋势显著,但在流域不同区域的增减趋势不同;蒸散发率和干燥指数的变化不明显;黄河流域上游蒸散发主要受能量供应条件限制影响,而中下游受水量供应条件限制影响较大。     

Design of Sprinkler Irrigation Subunit of Minimum Cost with Proper Operation. Application at Corn Crop in Spain

MATLAB^? software named PRESUD (Pressurized Subunit Design) was developed to identify the optimum solid set sprinkler irrigation subunit design with a criterion of minimizing the annual water application cost (C_T). This C_T is defined as the cost per cubic meter of water applied to the soil for crop use. In this study, only rectangular subunits are considered, using an iterative method for calculating the lateral and manifold pipelines. The results indicate that water cost (C_w)_, which includes the investment and operation costs for pumping water from the source to the subunit inlet, makes up 75 % of C_T. Another important factor is energy cost, which comprises 14 % of C_T. The remaining variables, such as sprinkler spacing and layout, or application rate (AR_a), have a lower impact on C_T. In cases of use groundwater, the proportion of energy cost in C_W can reach 40 %; thus, energy is an important part of C_T. Results shows that the criterion of limiting the maximum difference in pressure heads in the irrigation subunit (Δh?T, and the use of tools such as PRESUD can help obtain better solutions.     

Predicting Drought Magnitudes: A Parsimonious Model for Canadian Hydrological Droughts

A multiplicative relationship, drought magnitude (M) = drought intensity (I) × drought duration or length (L) is used as a basis for predicting the largest expected value of hydrological drought magnitude, E(M _T ) over a period of T-year (or month). The prediction of E(M _T ) is carried out in terms of the SHI (standardized hydrological index, tantamount to standard normal variate) sequences of the annual and monthly streamflow time series. The probability distribution function (pdf) of I (drought intensity) was assumed to follow a truncated normal. The drought length (L _c ) was taken as some characteristic duration of the drought period, which is expressible as a linear combination of the expected longest (extreme) duration, E(L _T ) and the mean duration, L _m of droughts and is estimated involving a parameter ø (range 0 to 1). The drought magnitude (deficit-sum, M) has been assumed to follow a gamma pdf, in view of the observed behavior of M. The model M = I × L has been invoked via two approximations, viz. Type-1 involves only mean of I and Type-2 involves both mean and variance of I through the theorem of extremes of random numbers of random variables. The E(L _T ) were obtained using the Markov chain (MC) model of an appropriate order, which turned out to be zero order Markov chain (MC-0) at the annual time scale. At the monthly time scale, the E(L _T ) was best represented by MC-0 for SHI sequences with low value of lag-1 autocorrelation (ρ?<?0.3) and first order Markov chain (MC-1) for SHI sequences with ρ?>?0.3. At low cutoff levels (q?≤?0.2), the trivial relationship E(M _T ) = E(I) × E(L _T ) i.e. without considerations of the extreme number theorem and the pdf of M yielded satisfactory results.     

长期恒荷载作用下混凝土时变断裂试验研究

服役中的大体积混凝土结构处在长期荷载作用下,与服役时间相关的时变断裂问题直接关系到结构的安全。采用标准三点弯曲梁试件,分别施加约0.7Pmax、0.75Pmax、0.8Pmax、0.85Pmax、0.95Pmax的恒定荷载进行长期加载,试验测得在不同恒荷载水平下的时变裂缝口张开位移CMOD(t)。试验结果表明,CMOD(t)在持载阶段不断增大,CMOD(t)-t曲线呈现出三个阶段特征:第一阶段,CMOD(t)快速增大而裂缝口张开速率CMOR(t)逐渐减小;第二阶段,CMOD(t)增大而CMOR(t)几乎不变;第三阶段,CMOD(t)和CMOR(t)都快速增大直至试件断裂破坏。与不考虑时间相关性的单调加载静态断裂试验相比,时变断裂试验的临界裂缝口张开位移CMOD(tc)偏大;随着恒荷载水平的增大,时变断裂临界裂缝口张开位移CMOD(tc)减小且接近单调加载静态断裂的临界裂缝口张开位移。对于不同恒荷载水平的试件,其时变断裂寿命tcr随着长期恒荷载水平的增大而减小,且时变断裂寿命与荷载比P/Pmax成指数关系。     

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]     

A Simplified Model for Predicting Drought Magnitudes: a Case of Streamflow Droughts in Canadian Prairies

The model for prediction of drought magnitudes is based on the multiplicative relationship: drought magnitude (M) = drought intensity (I) × drought duration (L), where I, L, and M are presumed to obey respectively the truncated normal probability distribution function (pdf), the geometric pdf, and the normal pdf. The multiplicative relationship is applied in the standardized domain of the streamflows, named as SHI (standardized hydrological index) sequences, which are treated equivalent to standard normal variates. The expected drought magnitude E(M _T ), i.e. the largest value of M over a sampling period of T-time units (T-year, T-month, and T-week) is predicted for hydrological droughts using streamflow data from Canadian prairies. By suitably amalgamating E(L _T ) with mean and variance of I in the extreme number theorem based relationship, the E(M _T ) is evaluated. Using Markov chain (MC), the E(L _T ) is estimated involving the geometric pdf of L. The Markov chains up to order one (MC-1) were found to be adequate in the proposed model for the annual to weekly time scales. For a given level of drought probability (q) and a sampling period T-time units; the evaluation of E(M _T ) requires only 3 parameters viz. lag-1 autocorrelation (ρ ₁ ), first order conditional probability (q _q , present instant being a drought given past instant was a drought) in SHI sequences and a parameter ø (value 0 to 1), which were estimated from historical data of streamflows. A major strength of the proposed model lies in the use of simple and widely familiar normal and geometric pdfs as its basic building blocks for the estimation of drought magnitudes.     

基于熵权-TOPSIS的滴灌春玉米灌水定额研究

为准确得到适宜于北疆地区滴灌春玉米的灌水定额,设置了W₁(225 m³/hm²)、W₂(300 m³/hm²)、W₃(375 m³/hm²)、W₄(450 m³/hm²)、W₅(525 m³/hm²)、W₆(600 m³/hm²) 6个水平的灌水定额,研究灌水定额对春玉米生长发育和产量的影响。选取部分生长指标、产量指标、节水指标作为评价指标,结合耗水规律和指标显著性进行分析,并采用熵权-TOPSIS综合评价法,优选适宜于北疆地区滴灌春玉米的灌水定额。结果表明：滴灌春玉米的关键生育期为抽雄散粉期,该生育期最优灌水定额为525 m³/hm²;耗水量和耗水强度...     

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