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1.
A time domain boundary element in a cylindrical coordinate system is developed for the analysis of wave propagation in a half space. The integral formulation is based on Graffi's dynamic reciprocal theorem and Stokes' fundamental solutions. The field quantities (displacements and tractions) are expressed as products of Fourier series in the tangential direction and linear polynomials in the other spatial directions. Gaussian integration is used to integrate the non-singular parts of the integral equations, whereas the integration of the singular components, which are either of order 1/r or 1/r2, is handled by special numerical schemes. In the time marching aspect, the field quantities are assumed to vary linearly in the temporal direction as well. Examples for wave propagation due to various forms of surface excitations are reported to demonstrate the accuracy of the method.  相似文献   

2.
Abstract

It is shown that magnetic fields generated by flows v r,(r,t)er+vT where vT is an arbitrary toroidal component (er˙vT≡V≡vT≡0), cannot be maintained indefinitely against ohmic dissipation. The poloidal field variable max |r 2 B r| is shown to decay strictly monotonically with an undetermined decay rate. A bound on the growth of the toroidal field norm ∥T∥1 is established solely dependent on the rate of conversion of poloidal to toroidal field, so that when the poloidal field is negligible then ∥T∥1 decays strictly monotonically. The main application of these results is to models of stellar evolution based on axisymmetric differential rotation and spherically symmetric contraction. This symmetric velocity theorem overlaps with two already known theorems, namely the toroidal velocity theorem where v r≡0 and the radial velocity theorem where vT≡0. The new theorem does not entirely include the already established ones, principal differences being in the rates of decay and the field variables for which the decay is proven (see Table 1).  相似文献   

3.
《水文科学杂志》2013,58(4):700-712
Abstract

The groundwater flow equation governing the elevation (h) of the steady-state phreatic surface in a sloping aquifer fed by constant recharge over a bi-circular sector is rhh′ ? r 2 Bh′ + Pr 2 ? PR 2 = 0, where r is the radial coordinate, P is a constant involving recharge and aquifer properties, and B is the slope of the aquifer—bedrock boundary. The derived flow equation describes radially convergent flow through a sloping aquifer that discharges to a water body of fixed head. One important simplification is that in which the width of the bi-circular sector is constant, and the draining land becomes a rectangular aquifer. The bi-circular sector and rectangular-strip groundwater flow problems are solved in terms of implicit equations. The solutions for the steady-state phreatic surfaces depend on the ratio of recharge to hydraulic conductivity, the slope of the aquifer-bedrock, and the downstream constant-head boundary. Computational examples illustrate the application of the solutions.  相似文献   

4.
The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small but finite inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,?v,?t), x and v being the particle position and velocity, respectively. For arbitrary inertia, position and velocity variables are coupled, with the result that p(x,?v,?t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small (but nevertheless finite) inertia, (x,?v)-variables decouple and the determination of p(x,?v,?t) is reduced to solve a system of two standard forced advection–diffusion equations in the space variables x. The latter equations are derived here from first principles, i.e., from the well-known Lagrangian evolution equations for position and particle velocity.  相似文献   

5.
Abstract

The process-based Soil and Water Assessment Tool (SWAT) model and the data-driven radial basis neural network (RBNN) model were evaluated for simulating sediment load for the Nagwa watershed in Jharkhand, India, where soil erosion is a severe problem. The SWAT model calibration and uncertainty analysis were performed with the Sequential Uncertainty Fitting algorithm version 2 and the bootstrap technique was applied on the RBNN model to analyse uncertainty in model output. The percentage of data bracketed by the 95% prediction uncertainty (95PPU) and the r factor were the two measures used to assess the goodness of calibration. Comparison of the results of the two models shows that the value of r factor (r = 0.41) in the RBNN model is less than that of SWAT model (r = 0.79), which means there is a wider prediction interval for the SWAT model results. More values of observed sediment yield were bracketed by the 95PPU in the RBNN model. Thus, the RBNN model estimates the sediment yield values more accurately and with less uncertainty.

Editor D. Koutsoyiannis; Associate editor H. Aksoy

Citation Singh, A., Imtiyaz, M., Isaac, R.K., and Denis, D.M., 2014. Assessing the performance and uncertainty analysis of the SWAT and RBNN models for simulation of sediment yield in the Nagwa watershed, India. Hydrological Sciences Journal, 59 (2), 351–364.  相似文献   

6.
Abstract

Bayly (1993) introduced and investigated the equation (? t + v·▽-η ▽2)S = RS as a scalar analogue of the magnetic induction equation. Here, S(r, t) is a scalar function and the flow field v(r, t) and “stretching” function R(r, t) are given independently. This equation is much easier to handle than the corresponding vector equation and, although not of much relevance to the (vector) kinematic dynamo problem, it helps to study some features of the fast dynamo problem. In this note the scalar equation is considered for linear flow and a harmonic potential as stretching function. The steady equation separates into one-dimensional equations, which can be completely solved and therefore allow one to monitor the behaviour of the spectrum in the limit of vanishing diffusivity. For more general homogeneous flows a scaling argument is given which ensures fast dynamo action for certain powers of the harmonic potential. Our results stress the singular behaviour of eigenfunctions in the limit of vanishing diffusivity and the importance of stagnation points in the flow for fast dynamo action.  相似文献   

7.
Asim Biswas  Bing Cheng Si 《水文研究》2012,26(24):3669-3677
There are various factors governing the spatial and temporal variability of soil water storage including soil properties, topography and vegetation. Some factors act locally, whereas others act nonlocally, which means that a factor measured at one location has effect on soil water storage at another location. The objective of this study was to examine the effects of local and nonlocal controls of soil water storage in a hummocky landscape using cyclical correlation analysis. Soil water storage, soil properties and terrain indices were measured along a 128‐point transect of 576 m long from the semiarid, hummocky, prairie pothole region of North America. There are large coefficients of determination (r2) between soil water storage and sand content (r2 = 0.32–0.53), organic carbon content (r2 = 0.22–0.56), depth to carbonate layer (r2 = 0.13–0.63), wetness index (r2 = 0.25–0.45) and other variables at the measurement scale at different times, indicating strong local effects from these variables. The correlation coefficients were also calculated by physically shifting the spatial series of soil water storage with respect to that of controlling factors. The shifting improves the correlation between the spatial series, and the length of shifting indicated the difference in the response of soil water to its controlling factors. For example, the value of r2 increased more than eightfold (r2 = 0.47–0.64) after shifting the spatial series of soil water storage by 54 m, almost equal to the average length of existing slope, compared with the very weak correlation (r2 = 0.02–0.08) at the measurement scale. This indicated the nonlocal effect from the relative elevation. The identification of nonlocal effects from factors improves the prediction of soil water storage. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

8.
《水文科学杂志》2012,57(1):87-101
ABSTRACT

The coefficient of determination R2 and Pearson correlation coefficient ρ = R are standard metrics in hydrology for the evaluation of the goodness of fit between model simulations and observations, and as measures of the degree of dependence of one variable upon another. We show that the standard product moment estimator of ρ, termed r, while well-behaved for bivariate normal data, is upward biased and highly variable for bivariate non-normal data. We introduce three alternative estimators of ρ which are nearly unbiased and exhibit much less variability than r for non-normal data. We also document remarkable upward bias and tremendous increases in variability associated with r using both synthetic data and daily streamflow simulations from 905 calibrated rainfall–runoff models. We show that estimators of ρ = R accounting for skewness are needed for daily streamflow series because they exhibit high variability and skewness compared to, for example, monthly/annual series, where r should perform well.  相似文献   

9.
In this study, the KLME approach, a moment-equation approach based on the Karhunen–Loeve decomposition developed by Zhang and Lu (Comput Phys 194(2):773–794, 2004), is applied to unconfined flow with multiple random inputs. The log-transformed hydraulic conductivity F, the recharge R, the Dirichlet boundary condition H, and the Neumann boundary condition Q are assumed to be Gaussian random fields with known means and covariance functions. The F, R, H and Q are first decomposed into finite series in terms of Gaussian standard random variables by the Karhunen–Loeve expansion. The hydraulic head h is then represented by a perturbation expansion, and each term in the perturbation expansion is written as the products of unknown coefficients and Gaussian standard random variables obtained from the Karhunen–Loeve expansions. A series of deterministic partial differential equations are derived from the stochastic partial differential equations. The resulting equations for uncorrelated and perfectly correlated cases are developed. The equations can be solved sequentially from low to high order by the finite element method. We examine the accuracy of the KLME approach for the groundwater flow subject to uncorrelated or perfectly correlated random inputs and study the capability of the KLME method for predicting the head variance in the presence of various spatially variable parameters. It is shown that the proposed numerical model gives accurate results at a much smaller computational cost than the Monte Carlo simulation.  相似文献   

10.
We consider the second-order differential equations ofP-SV motion in an isotropic elastic medium with spherical coordinates. We assume that in the medium Lamé's parameters , r p and compressional and shear-wave velocities , r, wherer is radial distance. With this regular heterogeneity both the radial functions appearing in displacement components satisfy a fourth-order differential equation which provides solutions in terms of exponential functions. We then consider a layered spherical earth in which each layer has heterogeneity as specified above. The dispersion equation of the Rayleigh wave is obtained using the Thomson-Haskel method. Due to exponential function solutions in each layer, the dispersion equation has similar simplicity, as in a flat-layered earth. The dispersion equation is further simplified, whenp=–2. We obtain numerical results which agree with results obtained by other methods.  相似文献   

11.
Abstract

The generation of eddies by a large-scale flow over mesoscale topography is studied with the help of two- and three-layer nonlinear quasi-geostrophic models of the open ocean. The equations are integrated forward in time with no eddies present initially. For a given time, the displacement of the interface between layers two and three (ζ) tends to a well-defined limit (function of the horizontal spatial coordinates) as ρ 3 - ρ 2 → 0 (ρr is the density of layer r). Even for values of α[= (ρ 3 - ρ 2)/(ρ 2 - ρ 1)] as small as 0.01 the potential energy due to ζ is not negligible and it can reach, in some cases, a considerable fraction of the total eddy energy.  相似文献   

12.
Abstract

Abstract Base flows make up the flows of most rivers in Zimbabwe during the dry season. Prediction of base flows from basin characteristics is necessary for water resources planning of ungauged basins. Linear regression and artificial neural networks were used to predict the base flow index (BFI) from basin characteristics for 52 basins in Zimbabwe. Base flow index was positively related to mean annual precipitation (r = 0.71), basin slope (r = 0.76), and drainage density (r = 0.29), and negatively related to mean annual evapotranspiration (r = –0.74), and proportion of a basin with grasslands and wooded grasslands (r = –0.53). Differences in lithology did not significantly affect BFI. Linear regression and artificial neural networks were both suitable for predicting BFI values. The predicted BFI was used in turn to derive flow duration curves of the 52 basins and with R 2 being 0.89–0.99.  相似文献   

13.
Abstract

A new method is presented to generate stationary multi-site hydrological time series. The proposed method can handle flexible time-step length, and it can be applied to both continuous and intermittent input series. The algorithm is a departure from standard decomposition models and the Box-Jenkins approach. It relies instead on the recent advances in statistical science that deal with generation of correlated random variables with arbitrary statistical distribution functions. The proposed method has been tested on 11 historic weekly input series, of which the first seven contain flow data and the last four have precipitation data. The article contains an extensive review of the results.

Editor D. Koutsoyiannis

Citation Ilich, N., 2014. An effective three-step algorithm for multi-site generation of stochastic weekly hydrological time series. Hydrological Sciences Journal, 59 (1), 85–98.  相似文献   

14.
Abstract

A simple mean-field model of a nonlinear stellar dynamo is considered, in which dynamo action is supposed to occur in a spherical shell, and where the only nonlinearity retained is the influence of the Lorentz forces on the zonal flow field. The equations are simplified by truncating in the radial direction, while full latitudinal dependence is retained. The resulting nonlinear p.d.e.'s in latitude and time are solved numerically, and it is found that while regular dynamo wave type solutions are stable when the dynamo number D is sufficiently close to its critical value, there is a wide variety of stable solutions at larger values of D. Furthermore, two different types of dynamo can coexist at the same parameter values. Implications for fields in late-type stars are discussed.  相似文献   

15.
Abstract

The need for specifying water availability in terms of its time sequence and distribution, rather than in terms of lumped quantities or flow duration, has given rise to data asquisition programs which use shorter sampling intervals. Shorter time intervals, in turn, has resulted in serially correlated observations. In order to determine the reliability of design variables derived from these observations, it is necessary to reduce these data to an equivalent series of independent observations, or find the effective lenght of the series.

A general parametric formula is developed for the effective number of observations for the second order autoregressive process, which has been found to apply to the series of mean daily river flows. Different values of the parameters were programmed in a digital computer to obtain tables for data reduction.  相似文献   

16.
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17.
Abstract

Some unique coupled wind–water erosion processes exist in the desert-loess transitional zone in the middle Yellow River basin. Based on data from 40 stations on 29 rivers, a study was made on the influence of such processes on suspended sediment grain-size characteristics of the tributaries of the Yellow River. Results show that the percentage of >0.05-mm grain size decreases with the increased annual mean precipitation, but increases with the increase in the annual mean number of sand-dust storm days. The percentage of <0.01-mm grain size increases with the increase in the annual mean precipitation, but decreases with the increase in the annual number of sand-dust storm days. Based on annual mean data from 40 stations, multiple regression equations were established between the percentages of >0.05-mm grain size (r >0.05) and <0.01-mm grain size (r <0.01), annual mean precipitation (P m) and annual mean number of sand-dust storm days (D ss). On this basis, the relative contributions of the variations in D ss and P m to the variation in r >0.05 and r <0.01 were estimated. The results indicate that the variation in sand-dust storm frequency exerts greater influences on the variation in grain-size characteristics of suspended load than does the variation in annual mean precipitation. With the increase in the coupled wind–water processes index, expressed by P m/D ss, the percentage of >0.05-mm grain size in suspended sediment decreases and the percentage of <0.01-mm grain size increases. With the variation in P m/D ss, different combinations of r >0.05 with r <0.01 appear, which have some influence on the formation of hyperconcentrated flows. There exist some optimal ratios of coarse to fine fractions in suspended sediment that make sediment concentrations of hyperconcentrated flows the highest. The optimal r >0.05/r <0.01 value is related to some range of the index P m/D ss. When the P m/D ss index falls in this range, the optimum combination of relative coarse with fine sediments in the suspended load appears, and thus results in the peak values of sediment concentration.  相似文献   

18.
Abstract

We consider the growth of disturbances to large-scale zonally-asymmetric steady states in a truncated spectral model for forced and dissipated barotropic flow. A variant of the energy method is developed to optimize the instantaneous disturbance energy growth rate. The method involves solving a matrix eigenvalue problem amenable to standard numerical techniques. Two applications are discussed. (1) The global stability of a family of steady states is assessed in terms of the Ekman damping coefficient r. It is shown that monotonic global stability (i.e., every disturbances energy monotonically decays to zero) prevails when r≥rc . (2) Initially fastest-growing disturbances are constructed in the r<rc regime. Particular attention is paid to a subregion of the r<rc regime where initially-growing disturbances exist despite stability with respect to normal modes. Nonlinear time-dependent simulations are performed in order to appraise the time evolution of various disturbances.  相似文献   

19.
This study examined the hysteresis exhibited in concentration–discharge (C–Q) relationships in the runoff from four hydrologically separated fields (catchments) at an intensively managed grassland. The objectives were to examine C–Q relationships constructed from high-resolution time series of flow, temperature, pH, conductivity, nitrate and turbidity, and their implications for hydrological processes. High-resolution datasets from the quality assured records of the Rothamsted Research North Wyke Farm Platform in the UK were examined using a graphical method and cross-correlation statistics. The study found that storm events based C–Q hysteresis reflects the cross-correlation that is generally hidden in time series analysis of large datasets, and that although Q and water quality variables can be effectively influenced by catchment size, the C–Q relationship is less significantly influenced. The dominant C–Q relationships of the water variables in the study area reflect that saturated overland flow was prevalent during the study period in the catchments, while the CCF results indicate coupled transfer of sediments and solute in the area at lag ≥ 0.
EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR M. D. Fidelibus  相似文献   

20.
This paper examines a model for estimating canopy resistance rc and reference evapotranspiration ETo on an hourly basis. The experimental data refer to grass at two sites in Spain with semiarid and windy conditions in a typical Mediterranean climate. Measured hourly ETo values were obtained over grass during a 4 year period between 1997 and 2000 using a weighing lysimeter (Zaragoza, northeastern Spain) and an eddy covariance system (Córdoba, southern Spain). The present model is based on the Penman–Monteith (PM) approach, but incorporates a variable canopy resistance rc as an empirical function of the square root of a climatic resistance r* that depends on climatic variables. Values for the variable rc were also computed according to two other approaches: with the rc variable as a straight‐line function of r* (Katerji and Perrier, 1983, Agronomie 3 (6): 513–521) and as a mechanistic function of weather variables as proposed by Todorovic (1999, Journal of Irrigation and Drainage Engineering, ASCE 125 (5): 235–245). In the proposed model, the results show that rc/ra (where ra is the aerodynamic resistance) presents a dependence on the square root of r*/ra, as the best approach with empirically derived global parameters. When estimating hourly ETo values, we compared the performance of the PM equation using those estimated variable rc values with the PM equation as proposed by the Food and Agriculture Organization, with a constant rc = 70 s m?1. The results confirmed the relative robustness of the PM method with constant rc, but also revealed a tendency to underestimate the measured values when ETo is high. Under the semiarid conditions of the two experimental sites, slightly better estimates of ETo were obtained when an estimated variable rc was used. Although the improvement was limited, the best estimates were provided by the Todorovic and the proposed methods. The proposed approach for rc as a function of the square root of r* may be considered as an alternative for modelling rc, since the results suggest that the global coefficients of this locally calibrated relationship might be generalized to other climatic regions. It may also be useful to incorporate the effects of variable canopy resistances into other climatic and hydrological models. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

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