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]     

Analytical solutions of unsteady drainage problems for soils subjected to variable recharge from a semi-confined aquifer

In drainage of agricultural lands, the upward vertical recharge from a semi-confined aquifer depends on the difference of the piezometric heads on the two sides of the semi-impermeable layer through which this recharge takes place. This means that the recharge through the semi-impermeable base depends on the unknown height of the unsteady water table. In the nonhomogeneous Boussinesq equation, which describes the drainage problems, the downward uniform rate of the recharge from rain or irrigation and the recharge from the semiconfined aquifer are expressed by two terms. By solving the Boussinesq equation expressions for the nondimensional height of the water table and the nondimensional discharge of the drains per unit drained area are obtained for three different initial conditions. Some known solutions are shown as special cases of the present solutions. Variation of nondimensional water table heights at half distance of the drain spacing and the nondimensional discharge of the drains with nondimensional time have been graphically illustrated with the help of synthetic examples.Notation B _s thickness of the semi-impervious layer [L] - c hydraulic resistance of the semi-impervious layer [T] - D depth of the drains from the base [L] - d _e equivalent depth [L] - h=h(x, t) height of the water table [L] - h ₀ initial height of the water table [L] - h _t water table height at mid-distance of drains att [L] - h _j ,h _k water table height at mid-distance of drains at timej andfk, respectively [L] - H ₀ piezometric head in the semi-confined aquifer [L] - K hydraulic conductivity of the soil [LT^–1] - K _s hydraulic conductivity of the semi-impervious layer [LT^–1] - k ₀,k ₁,k ₂ nondimensional constants - L distance between the drains [L] - q ₀ upward recharge per unit surface area through the semi-impervious layer [LT^–1] - q _t discharge per unit drainable area of drains at timet [LT^–1] - R,R ₀ recharge per unit surface area from rain or irrigation during the unsteady and steady-state, respectively, [LT^–1] - S specific yield of the soil - t time of observation [T] - x distance measured from the drain [L] - leakage factor [L] - nondimensional distance - nondimensional time     

Water table fluctuation in response to transient recharge from a rectangular basin

A problem of water-table fluctuation in a finite two-dimensional aquifer system in response to transient recharge from an overlying rectangular area is studied. An analytical solution is obtained by using the method of finite Fourier transform to predict the transient position of the water-table. The solution for constant rate of recharge is shown as a special case of the present solution. Effects of variation in the rate of recharge on the growth of two-dimensional groundwater mound is illustrated with the help of a numerical example.Notation A half width of the aquifer [L] - B half length of the aquifer [L] - D half width of the recharge basin [L] - e specific yield - h varying water-table height [L] - h ₀ initial water-table height [L] - h weighted mean of the depth of saturation [L] - K hydraulic conductivity [LT^–1] - L half length of the recharge basin [L] - P(t) time varying rate of recharge [LT^–1] - P ₁ +P ₀ initial rate of time varying recharge [LT^–1] - P ₁ final rate of time varying recharge [LT^–1] - t time of observation [T] - x, y coordinate axes - decay constant [T^–1]     

On the prediction of groundwater mound formation due to transient recharge from a rectangular area

Recharge to the aquifer leads to the growth of a groundwater mound. Therefore, for the proper management of an aquifer system, an accurate prediction of the spatio-temporal variation of the water table is very essential. In this paper, a problem of groundwater mound formation in response to a transient recharge from a rectangular area is investigated. An approximate analytical solution has been developed to predict the transient evolution of the water table. Application of the solution and its sensitivity to the variation of the recharge rate have been illustrated with the help of a numerical example.Notations a = Kh/e [L²/T] - A = aquifer's extent in the x-direction [L] - B = aquifer's extent in the y-direction [L] - e = effective porosity - h = variable water table height [L] - h ₀= initial water table height [L] - h = weighted mean of the depth of saturation [L] - K = hydraulic conductivity [L] - m, n = integers - P = constant rate of recharge [L/T] - P ₁+P₀= initial rate of transient recharge [L/T] - P ₁= final rate of transient recharge [L/T] - s = h ²–h ₀ ² [L²] - t = time of observation [T] - x,y = space coordinates - x ₂–x₁= length of recharge area in x-direction [L] - y ₂–y₁= width of recharge area in y-direction [L] - z = decay constant [T^-1]     

Forecast model of water consumption for Naples

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

Water table fluctuation with a random initial condition

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

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     

Water table fluctuation due to transient recharge in a 2-D aquifer system with inclined base

Recharging of aquifers due to irrigation, seepage from canal beds and other sources leads to the growth of water table near to the ground surface causing problems like water logging and increase of salinity in top soils in many regions of the world. This problem can be alleviated if proper knowledge of the spatio — temporal variation of the water table is available. In this paper an analytical solution for the water table fluctuation is presented for a 2-D aquifer system having inclined impervious base with a small slope in one — direction and receiving time varying vertical recharge. Application of the solution in estimation of water table fluctuation is demonstrated with the help of an example problem.Notations A length of the aquifer [L] - B width of the aquifer [L] - D mean depth of saturation [L] - e specific yields - h variable water table height [L] - K hydraulic conductivity [LT ^–1] - P(t) transient recharge rate [LT ^–1] - P ₁+P _o initial rate of transient recharge [LT ^–1] - P ₁ final rate of transient recharge [LT ^–1] - q slope of the aquifer base in percentage - r decay constant [T ^–1] - t time of observation [T] - x, y coordinate axes - x ₂–x ₁ length of the recharge basin [L] - y ₂–y ₁ width of the recharge basin [L]     

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     

Deoxygenation potential of the Richmond River Estuary floodplain,northern NSW,Australia

Periodic deoxygenation events (DO < 1 mg/L) occur in the Richmond River Estuary on the east coast of Australia following flooding and these events may be accompanied by total fish mortality. This study describes the deoxygenation potential of different types of floodplain vegetation in the lower Richmond River catchment and provides a catchment scale estimate of the relative contribution of floodplain vegetation decomposition to deoxygenation of floodwaters. Of the major vegetation types on the floodplain slashed pasture was initially (first 5 to 7 h) the most oxygen demanding vegetation type after inundation (268 ± mg O₂ m^?2 h^?1), followed by dropped tea tree cuttings (195 ± 18 mg O₂ m^?2 h^?1) and harvested cane trash (110 ± 8 mg O₂ m^?2 h^?1). However, 10 h after inundation the oxygen consumption rates of slashed pasture (105 ± 5 mg O₂ m^?2 h^?1) and tea tree cuttings (59 ± 7 mg O₂ m^?2 h^?1) had decreased to a rate less than the harvested cane trash (110 ± 8 mg O₂ m^?2 h^?1). The oxygen demands of the different floodplain vegetation types when inundated were highly correlated with their nitrogen content (r² = 0.77) and molar C:N ratio (r² = 0.82) reflecting the dependence of oxygen demand of vegetation types on their labile carbon content. The floodplain of the lower Richmond River (as flooded in February 2001) has the potential to deoxygenate about 12.5 × 10³ mL of saturated freshwater at 25°C per day which is sufficient to completely deoxygenate floodwater stored on the floodplain with 3 to 4 days. In addition, oxidation of Fe²⁺ mobilized during the decomposition of floodplain vegetation via iron reduction and discharged from groundwater and surface runoff in acid sulfate soil environments could account for about 10% of the deoxygenation of floodwater stored on the floodplain. Management options to reduce floodplain deoxygenation include removing cuttings from slashed pasture and transporting off‐site, reducing slashed pasture windrow loads by using comb‐type mowers, returning areas of the floodplain to wetlands to allow the establishment of inundation tolerant vegetation and retaining deoxygenated floodwaters in low lying areas of the floodplain to allow oxygen consumption process to be completed before releasing this water back to the estuary. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Nitrogen processing by biofilms along a lowland river continuum

While numerous studies have examined N dynamics along a river continuum, few have specifically examined the role of biofilms. Nitrogen dynamics and microbial community structure were determined on biofilms at six sites along a 120 km stretch of the lowland Ovens River, South Eastern Australia using artificial substrates. Terminal restriction fragment length polymorphism (T‐RFLP), chlorophyll a and protein analyses were used to assess biofilm microbial community composition. N dynamics was determined on the biofilms using the acetylene (C₂H₂) block technique and assessing changes in NH, NO_x and N₂O. Unlike microbial community structure, N dynamics were spatially heterogeneous. Nitrification, determined from the difference in accumulation of NH before and after addition of C₂H₂, occurred mostly in the upper sites with rates up to 1.4 × 10^?5 mol m^?2 h^?1. The highest rates of denitrification occurred in the mid‐reaches of the river (with rates up to 1 × 10^?5 mol m^?2 h^?1) but denitrification was not detected in the lower reaches. At the very most, only 50% of the observed uptake of NO_x by the biofilms following addition of C₂H₂ could be accounted for by denitrification. Copyright © 2005 John Wiley & Sons, Ltd.     

First estimation of the diffusive methane flux and concentrations from Lake Winnipeg,a large,shallow and eutrophic lake

Freshwater lakes are increasingly recognized as significant sources of atmospheric methane (CH₄), potentially offsetting the terrestrial carbon sink. We present the first study of dissolved CH₄ distributions and lake-air flux from Lake Winnipeg, based on two-years of observations collected during all seasons. Methane concentrations across two years had a median of value of 24.6 nmol L^-1 (mean: 41.6 ± 68.2 nmol L^-1) and ranged between 5.0 and 733.8 nmol L^-1, with a 2018 annual median of 24.4 nmol L^-1 (mean: 46.8 ± 99.3 nmol L^-1) and 25.1 nmol L^-1 (mean: 38.8 ± 45.2 nmol L^-1) in 2019. The median lake-air flux was 1.1 µmol m^?2 h^?1 (range: 0.46–70.1 µmol m^?2h^?1, mean: 2.9 ± 10.2 µmol m^?2 h^?1) in 2018, and 5.5 µmol m^?2h^?1 (range: 0.0–78.4 µmol m^?2 h^?1, mean: 2.7 ± 8.5 µmol m^?2 h^?1) in 2019, for a total diffusive emission of 0.001 Tg of CH₄-C yr^?1. We found evidence of consistent spatial variability, with higher concentrations near river inflows. Significant seasonal trends in CH₄ concentrations were not observed, though fluxes were highest during the fall season due to strong winds. Our findings suggest Lake Winnipeg is a CH₄ source of similar mean magnitude to Lake Erie, with lower concentrations and fluxes per unit area than smaller mid- to high-latitude lakes. Additional work is needed to understand the factors underlying observed spatial variability in dissolved gas concentration, including estimations of production and consumption rates in the water column and sediments.     

A water policy intercomparison model for a region with three seasons

A water policy model is proposed as a solution to the problem of obtaining maximum net benefit from providing irrigation and urban water in regions where the major source of supply is groundwater. In essence, the model introduces an innovative scheme based on two types of penalties. These intervene when either watertable elevation falls below a critical value during the operation of a system of wells or a remote source is used to partially cover the needed amount of water expected from the basic groundwater source. Another specific idea of the model is the consideration, for southern regions, of a three-season division in the climatic character of a year. The algorithm is illustrated by a numerical example in which five possible alternatives are compared. The conclusion of the study (although a function of regional economics, natural conditions, as well as specific zonal water policy constraints) reveals a compromise between limiting the amount provided from remote sources and confining the aquifer operation to critical values of the water-table elevation.Notation B benefits from water use, 10³ US$ - C sum of total costs, 10³ US$ - CMR total maintenance-repair cost, 10³ US$ - CO total cost of operation, 10³ US$ - C _HO unit cost of operation per hour, US$ hr^–1 - C _y unit average cost of a repaired pump, US$/(year × well) - d screen diameter for each well, m - H _G average groundwater elevation, m - H _{W cr} critical water elevation value in wells, m - H _{W dj} hydraulic head deficit in wells (belowH _{W cr} ), m - H _{W j} seasonal water elevation in each well, m - j current season - K average hydraulic conductivity of the aquifer, m s^–1 - NB net benefit, 10³ US$ - Ns maximum number of seasons - N _HO number of hours of operation per well and month - N _{W j} number of wells in operation over a seasonj - n _j number of months over each seasonj - P sum of total penalties, 10³ US$ - PH total penalty for pumping whenH _{W dj} >0, 10³ US$ - PQ total penalty for remote source use, 10³ US$ - P _RSj unit penalty for remote source use, 10³ US$ month^–1 - P _{W dj} unit penalty for pumping whenH _{W dj} >0, 10³ US$ month^–1 - pRM percentage of repaired and maintained pumps yearly, % - Q _iRj discharge needed for irrigation use, m³ s^–1 - Q _Nj total discharge needed by users, m³ s^–1 - Q _Pj total seasonal yield capacity of the battery, m³ s^–1 - Q _RSj discharge covered from remote sources, m³ s^–1 - Q _UWj discharge needed for urban water use, m³ s^–1 - Q _j seasonal operated pumping rate in each well, m³ s^–1 - Q _waj weighted average of pumping rate at timet _j , m³ s^–1 - S _Y average specific yield of the aquifer - S _cr critical drawdown value in wells, m - S _j seasonal drawdown in each well - T average transmissivity of the aquifer, m² s^–1 - t _OPj current duration of system operation - t _j –t _j–1 duration of each seasonj     

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

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

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

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

Impact of an urban centre on the nitrogen cycle processes of epilithic biofilms during a summer low‐water period *

Nitrogen transformations in epilithic biofilms of a large gravel bed river, the Garonne, France, has been studied upstream (one site) and downstream (four sites) of a large urban centre (Toulouse, 740 000 inhabitants). High biomass, up to 49 g AFDM m^?2 (ashes free dry matter) and 300 mg chlorophyll a m^?2 (Chl. a), were recorded at 6 and 12 km downstream from the main wastewater treatment plant outlet. The lowest records upstream and larger downstream (less than 16 g AFDM m^?2 or 120 mg Chl. a m^?2) could be explained by recent water fall (early summer low‐water period). Measurements of nitrogen exchange at the biofilm–overlying water interface were performed in incubation chambers under light and dark conditions. The addition of acetylene at the mid‐incubation time allowed evaluation of both nitrification (variation in NH₄⁺ flux after the ammonium monooxygenase inhibition) and denitrification (N₂O accumulation related to the inhibition of N₂O reduction). Denitrification (D_w) and nitrification rates were maximum at sites close to the city discharges in dark conditions (up to 9.1 and 5.6 mg N m^?2 h^?1, respectively). Unexpected denitrification activities in light conditions (up to 1.4 mg N m^?2 h^?1) at these sites provided evidence for enhanced nitrogen self‐purification downstream. As confirmed by most probable number (MPN) counts, high nitrification rates in biofilm close downstream were related to enhanced (more than almost 3 log) nitrifying bacteria densities (up to 7.6×10⁹ MPN m^?2). Downstream of an urban centre, nitrogen transformations in the biofilm appeared to be influenced by the occurrence of an adapted microflora which is inoculated or stimulated by anthropic pollution. Copyright © 2002 John Wiley & Sons, Ltd.     

Instream flows for recreation are closely correlated with mean discharge for rivers of western North America

Effective river regulation requires consideration for environmental and economic aspects and also for social aspects including recreation. Our study investigated relationships between river hydrology and recreational flows (RF) for canoes, kayaks, rafts and other non‐motorized boats, for 27 river reaches in the Red Deer and Bow river basins of southern Alberta, Canada. A subjective RF method involved regression analyses of data from River Trip Report Cards, volunteer postcard‐style surveys rating flow sufficiency. A total of 958 trip reports were submitted for the rivers between 1983 and 1997 and about 30 reports permitted confident regression analysis for a river reach. Values from these analyses were very consistent with values from the ‘depth discharge method’, a hydraulic modelling approach that used stage–discharge ratings to determine flows that would produce typical depths of 60 and 75 cm for minimal and preferred flows, respectively. Values were also consistent with expert opinions from river guidebooks and maps and aggregate values were calculated from the combined RF methods. These were very closely correlated with mean discharge (Q_m) across the rivers (r² = 0.94 for minimal and 0.96 for preferred flows). The relationship best fitted a power function (straight plot on log versus log scales) with a consistent slope but vertical offset for minimal versus preferred flows. Close relationships between guidebook estimates of RF and Q_m were also observed for rivers in the American Rocky Mountain states of Idaho (r² = 0.55 and 0.74), Montana (r² = 0.34 and 0.80) and Colorado (r² = 0.43 and 0.51), but the association was weaker for the Pacific Northwest state of Oregon (r² = 0.35 and 0.26). These analyses indicate that RF can be confidently determined through a combination of subjective and hydraulic methods and reveal that RF values represent a systematic function of discharge for a broad range of alluvial and constrained river reaches. From these analyses we provide the ‘Alberta equation’: minimal recreational flow = 3 × Q_m^0.59 (Q_m in m³/s), and preferred flows would typically be 1.5 times higher. For other river regions the exponent ‘0.59’ may be relatively constant but adjustments to the coefficient ‘3’ could be applicable. Copyright © 2005 John Wiley & Sons, Ltd.     

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     

Anthropogenic and seasonal influences on the dynamics of selected heavy metals in Lake Naivasha, Kenya

Lake Naivasha is a freshwater lake in the Eastern Rift Valley of Kenya (0°45′S and 36°20′E). It has no surface outlet and is perceived to be under anthropogenic stress. Being situated at the basin of the rift valley, the lake acts as a sink for wastes from the town of Naivasha and the surrounding horticultural industry. Flux experiments were conducted to investigate the dynamics of heavy metals between the sediment–water interface in Lake Naivasha. In situ benthic flux experiments were conducted at two sites, one near the municipal wastewater inflow to the lake (site SS), and one at the papyrus field near the horticultural farms (site SH). Sediment samples from the exposed riparian land were collected during the dry season after the lake has receded, and the fluxes of selected metals were determined in the laboratory under simulated conditions. Aluminium in situ benthic flux at site SS averaged 7 mmol m^?2 h^?1, and was correlated positively with pH (Pearson correlation coefficient (r) = 0.89). While the in situ benthic flux of aluminium at site SH averaged 1 mmol m^?2 h^?1. In situ benthic fluxes of copper and manganese were predominantly positive at site SS, but not at site SH. The papyrus field at site SH played an important role in buffering of the lake in regard to the selected metals investigated in this study. Redox‐sensitive metals were precipitated in the benthic flux experiment for this site.