Spatio‐temporal variability in underwater light climate in a turbid river‐floodplain system: Driving factors and estimation using Secchi disc

The underwater light climate has important effects on primary producers. The aim of this research was to evaluate its variability in a turbid river‐floodplain system. Photosynthetically active radiation (PAR) was measured in the Middle Paraná River during different hydrological phases to (a) analyse the photosynthetically active radiation attenuation coefficient (k) and euphotic depth (Z_eu) as well as their associations with optically active components and (b) develop and evaluate indices and regression models based on Secchi disc (SD) measurements to estimate k and Z_eu. Values of k were higher in the fluvial system than in the floodplain and during low‐water stage than high‐water stage. Particulate components controlled the light climate variability. Chromophoric dissolved organic matter and chlorophyll‐a had significant effects during floods. The estimation of k and Z_eu was sensitive to temporal but not to spatial variations. The highest prediction accuracy was observed when using specific non‐linear regressions for each hydrological phase, especially for Z_eu estimation (low stage: k = 1.76 × SD^?0.80, Z_eu = 2.62 × 1/SD^?0.80; high stage: k = 2.04 × SD^?0.53, Z_eu = 2.26 × 1/SD^?0.53). The indices k × SD and Z_eu/SD were significantly different from those proposed for clear water environments. It is concluded that temporal variations should be considered when estimating k and Z_eu in turbid river‐floodplain systems because of the temporal heterogeneity in optically active components. Considering that ecological implication of the light climate depends on Z_eu:depth ratio, we propose to estimate Z_eu instead of k. Finally, indices proposed for clear water environments are not recommended to be applied to turbid environments.     

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     

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     

水文干旱与气象干旱临界转变条件的判定及响应关系

水文干旱与气象干旱的响应关系对于建立健全干旱监测预报系统具有重要意义。基于区域水文干旱指数(SHI)与标准化降水指数(SPI),结合游程理论和非线性关系模型分析喀什河流域水文干旱与气象干旱的特征、响应关系及驱动因素。结果表明:水文干旱的年平均干旱历时和干旱烈度大于气象干旱,且随着SPI和SHI时间尺度的增加,识别出的干旱历时和干旱烈度也有所增加。基于三参数(log 3 P1)对数函数(Logarithm)模型可以更好地表征两者的响应关系。在3个月尺度下,气象干旱历时至少为1. 10个月且干旱的烈度至少为0. 83时,将诱发水文干旱;在6个月尺度下,气象干旱历时至少为1. 60个月且干旱的烈度至少为0. 91时,易发生水文干旱。     

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     

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.     

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     

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.     

Extreme dry weather intervals of the growing season in Bačka,Yugoslavia

A method of describing and analyzing the stochastic process of droughts, which are defined here as the upper extremes of intervals of no rainfall, is recommended. All important components of extreme dry weather intervals such as their duration, time of occurrence, their total number in a given time interval [0, t], the longest drought duration in a given time interval [0, t], and time T(t) of occurrence of the longest drought are taken into consideration. Application of the method is performed using the records of nine meteorological stations in Baka, Yugoslavia and a good agreement is found between the theoretical and empirical distribution functions for all analyzed components of the process. On the basis of the performed computations, a set of maps showing the contours of extreme dry weather intervals, having return periods from 2, 5... up to 100 years, related to the growing season (1 April –30 September), for the region of Baka in Yugoslavia is obtained. If the period of exploitation of an irrigation system is 60 years, then it could be expected to appear as 20 dry weather intervals having 3 year return periods. The duration of dry weather intervals is given on the set of maps. The obtained results give a prognosis of an average state of droughts during long time intervals (60, 100, 200... years).     

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     

Diagnosing anomalous characteristics of atmospheric water cycle structure during seasonal-scale drought events: A case study in middle and lower reaches of Yangtze River

Anomalous characteristics of the atmospheric water cycle structure are highly significant to the mechanisms of seasonal-scale meteorological droughts. They also play an important role in the identification of indicative predictors of droughts. To better understand the causes of seasonal meteorological droughts in the middle and lower reaches of the Yangtze River (MLRYR), characteristics of the atmospheric water cycle structure at different drought stages were determined using standardized anomalies. The results showed that the total column water vapor (TCWV) was anomalously low during drought occurrence periods. In contrast, there were no anomalous signals at the drought persistence and recovery stages in the MLRYR. Moreover, there was no significant temporal correlation between the TCWV anomaly and seasonal-scale drought index (the 3-month standardized precipitation index (SPI₃)). During drought events, water vapor that mainly originated from the Bay of Bengal was transported southwest of the MLRYR. Meanwhile, the anomalous signal of water vapor transport was negative at the drought appearance stage. At the drought persistence stage, the negative anomalous signal was the most significant. Water vapor flux divergence in the MLRYR showed significant positive anomalous signals during drought events, and the signal intensity shifted from an increasing to a decreasing trend at different drought stages. In addition, a significant positive correlation existed between the anomaly of water vapor flux divergence and regional SPI₃. Overall, water vapor flux divergence is more predictive of droughts in the MLRYR.     

Recent Climate Trends and Drought Behavioral Assessment Based on Precipitation and Temperature Data Series in the Songhua River Basin of China

Precise analysis of spatiotemporal trends of temperature, precipitation and meteorological droughts plays a key role in the sustainable management of water resources in the given region. This study first aims to detect the long-term climate (monthly/seasonally and annually) trends from the historical temperature and precipitation data series by applying Spearmen’s Rho and Mann-Kendall test at 5 % significant level. The measurements of both climate variables for a total period of 49 years (1965–2013) were collected from the 11 different meteorological stations located in the Songhua River basin of China. Secondly, the two well-known meteorological drought indices including the Standardized Precipitation Index (SPI) and Reconnaissance Drought Index (RDI) were applied on normalize data to detect the drought hazards at 3, 6, 9 and 12 month time scale in the study area. The analysis of monthly precipitation showed significant (p < 0.05) increasing trends during the winter (November and December months) season. Similarly, the results of seasonal and annual air temperature showed a significant increase from 1 °C to 1.5 °C for the past 49 years in the basin. According to the Sen’s slope estimator, the rate of increment in seasonal temperature slope (0.26 °C/season) and precipitation (9.02 mm/season) were greater than annual air temperature (0.04 °C/year) and precipitation (1.36 mm/year). By comparing the results of SPI and RDI indices showed good performance at 9 (r = 0.96, p < 0.01) and 12 (r = 0.99, p < 0.01) month drought analysis. However, the yearly drought analysis at over all stations indicated that a 20 years were under dry conditions in entire study area during 49 years. We found the extreme dry and wet conditions in the study region were prevailing during the years of 2001 and 2007, and 1994 and 2013, respectively. Overall, the analysis and quantifications of this study provides a mechanism for the policy makers to mitigate the impact of extreme climate and drought conditions in order to improve local water resources management in the region.

     

An analytical solution for water-table fluctuation in a finite aquifer due to transient recharge from a strip basin

Two cases of water-table fluctuation in a finite aquifer in response to transient recharge from a strip basin are investigated. In the first case the aquifer is bounded by open water-bodies, whereas in second one the aquifer is bounded by impermeable boundaries on both sides. Analytical solutions are presented to predict the transient position of the water-table. The solutions are obtained by using finite Fourier sine and cosine transforms.Notations A width of the aquifer [L] - e specific yield - h variable water-table height [L] - h ₀ initial water-table height [L] - weighted mean of the depth of saturation [L] - K hydraulic conductivity [LT^–1] - m,n integers - P ₁ +P ₀ initial rate of transient recharge [LT^–1] - P ₁ final rate of transient recharge [LT^–1] - P constant rate of recharge [LT^–1] - x ₁ distance of left boundary of the strip basin [L] - x ₂ distance of right boundary of the strip basin [L] - t time of observation [T] - decay constant [T^–1]     

Utilization of Time-Based Meteorological Droughts to Investigate Occurrence of Streamflow Droughts

Complexities of streamflow drought analyses motivate utilization of simple, alternative methods, which can provide timely information for effective water resources management. For this purpose time-based meteorological drought characteristics, identified by SPI _{3 − month} , SPI _{6 − month} and SPI _Anuual are investigated. A boxplot approach is used to exclude non-rainy months from the analysis. Streamflow drought characteristics are described by drought intensities, and are calculated by the threshold level method. The non-parametric Wilcoxon–Mann–Whitney test is used to investigate relations between streamflow drought intensities and SPI _{3 − month} , SPI _{6 − month} and SPI _Anuual . The study area is the Doroodzan Watershed and Reservoir in southwestern Iran, with four rain gauge and two hydrometric stations. According to the results, most of time-based SPI values show significant relations (at 5% level of significance) with streamflow drought intensities. However, the most significant relation is between SPI _Anuual of Jamalbeik rain gauge station (centrally located in the study area) and drought intensities of Chamriz hydrometric station (located at the reservoir inlet). Comparison of study results with available records of documented droughts, confirms applicability of the proposed procedures. The SPI _Anuual is based on one-year-ahead moving average rainfalls. Then, SPI _Anuual of Jamalbeik station can be used to investigate occurrence of streamflow drought in Chamriz hydrometric station.     

Population dynamics and exploitation patterns of Oreochromis niloticus in Lake Tana,northwest Ethiopia

Oreochromis niloticus is the dominant commercial fish in the Lake Tana region. However, its fishery is progressively declining over time. Little or no updated information exists on the population dynamics and exploitation patterns of the species, which is crucial to guide its sustainable management. Accordingly, the purpose of the present study was to generate essential biological parameters on the growth, mortality and stock status of O. niloticus, using length‐frequency data collected monthly from the commercial fish catches of 1 year (2014–2015). The total mortality coefficient (Z) was derived from the length‐converted catch curve. Biological reference points were predicted from relative yield‐ and biomass‐per‐recruit analyses. The estimated values of the von Bertalanffy growth parameters were L_∞ = 44.1 cm, K = 0.44/year, and t₀ = ?0.34/year, and the growth performance index (Φ′) was 2.93. The total mortality (Z), natural (M) and fishing mortality (F) rates were 2.37, 0.98 and 1.39 per year, respectively. The current fishery exploitation rate of 0.59 exceeds the estimated biological reference points of E_max (0.52), confirming the stock of O. niloticus in the lake is being overexploited above optimum levels. Size indicators of the catches further illustrate 31% of the landed fish are harvested before reaching sexual maturity, with mega‐spawners comprising only 15%. This indicates the stock is suffering from both growth and recruitment overfishing. The logistic selection model indicated 50% of the fish vulnerable to capture was at 18.14 cm TL. The fish exhibited a year‐round recruitment pattern, with a major peak during May and June. Sustainably managing the fishery, therefore, requires increasing the fish size at first capture (L_c) towards L_opt.     

Streamflow Drought Severity Analysis of Betwa River System (India)

Streamflow appraisal in time and space particularly in semi arid and dry sub humid regions has vital importance in the formulation of round the year plan of water uses comprising domestic & industrial water supply, irrigation scheduling, reservoir operation, in-stream flow maintenance etc. Drought severity analysis including the estimation of flow availability, drought duration, and deficit volume etc. was carried out using the 20–42 years (1960–2001) 10-daily streamflow data of five sites on the Betwa River system and. independent streamflow drought events were described by pooling the data, and severity of an independent drought event classified using a new drought severity index (DSIe) defined as a function of (1) the ratio of deficit flow volume to corresponding volume at the truncation level and (2) the ratio of duration of deficit flow to the maximum possible duration of the independent streamflow drought event. The study found that the upper reaches of river course were more prone to severe droughts than were the lower reaches. The drought events starting during August−November were more likely to be severe drought events than those in the other months.     

Wavelet Transform Method for Synthetic Generation of Daily Streamflow

Synthetic generation of daily streamflow sequences is one of the most critical issues in stochastic hydrology. In this study, a new wavelet transform method is developed for synthetic generation of daily streamflow sequences. Firstly, daily streamflow sequences with different frequency components are decomposed into the series of wavelet coefficients W ₁(t), W ₂(t),...,W _P (t) and scale coefficients (the residual) C _P (t) at a resolution level P using wavelet decomposition algorithm. Secondly, the series of W ₁(t), W ₂(t),...,W _P (t) and C _P (t) are divided into a number of sub-series based on a yearly period. Thirdly, random sampling is performed from sub-series of W ₁(t), W ₂(t),...,W _P (t) and C _P (t), respectively. Based on these sampled sub-series, a large number of synthetic daily streamflow sequences are obtained using wavelet reconstruction algorithm. The advantages of this newly developed method include: (1) it is a nonparametric approach; (2) it is able to avoid assumptions of probability distribution types (Normal or Pearson Type III) and of dependence structure (linear or nonlinear); (3) it is not sensitive to the original data length and suitable for any hydrological sequences; and (4) the generated sequences from this method could capture the dependence structure and statistical properties presented in the data. Finally, a case study in Jinsha River, China, indicates that the new method is valid and efficient in generating daily streamflow sequences based on historical data.     

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]     

Risk Assessment of Droughts in Gujarat Using Bivariate Copulas

This study presents risk assessment of hydrologic extreme events droughts in Saurashtra and Kutch region of Gujarat state, India. Drought is a recurrent phenomenon and risk assessment of droughts can play an important role in proper planning and management of water resources in the study region. In the study, drought events are characterized by severity and duration, and drought occurrences are modeled by Standardized Precipitation Index (SPI) computed on mean areal precipitation, aggregated at a time scale of 6?months for the period 1900?C2008. After evaluating several distribution functions, drought variable??severity is best described by non-parametric kernel density, whereas duration is best fitted by exponential distribution. Considering the extreme nature of drought variables, the upper tail dependence copula families including two Archimedean??Gumbel-Hougaard, BB1 and one elliptical??Student??s t copulas are evaluated for modeling joint distribution of drought variables. On evaluating their performance using various goodness-of-fit measures, Gumbel-Hougaard copula is found to be the best performing copula in modeling the joint dependence structure of drought variables. Also, while comparing with traditional bivariate distributions, the copula based distributions are resulted in better performance as compared to bivariate log-normal and the logistic model for bivariate extreme value distributions. Then joint and conditional return periods of drought characteristics are derived, which can be helpful for risk based planning and management of water resources systems in the study region.