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1.
Vegetation in arid and semi-arid regions is affected by intermittent water availability. We discuss a simple stochastic model describing the coupled dynamics of soil moisture and vegetation, and study the effects of rainfall intermittency. Soil moisture dynamics is described by a ecohydrological box model, while vegetation is represented by site occupancy dynamics in a spatially-implicit model. We show that temporal rainfall intermittency allows for vegetation persistence at low values of annual rainfall volume, whereas it would go extinct if rainfall were constant. Rainfall intermittency also generates long-term fluctuations in vegetation cover, even in the absence of significant inter-annual variations in the statistical properties of precipitation.  相似文献   

2.
An important question regarding the study of mean field dynamo models is how to make precise the nature of their underlying dynamics. This is difficult both because relatively little is known about the dynamical behaviour of infinite dimensional systems and also due to the numerical cost of studying the related partial differential equations. As a first step towards their understanding, it is useful to consider the corresponding truncated models. Here we summarise some recent results of the study of a class of truncated axisymmetric mean field dynamo models. We find conclusive evidence in these models for various types of intermittency as well as multiple attractors and final state sensitivity. We also find that the understanding of the underlying dynamics of such dynamo models requires the study of a new class of dynamical systems, referred to as the non-normal systems. Current work demonstrates that these types of systems are capable of a novel type of intermittency and also of relevance for the understanding of the full axisymmetric PDE dynamo models.  相似文献   

3.
This study examines the role of rainfall variability on the spatial scaling structure of peak flows using the Whitewater River basin in Kansas as an illustration. Specifically, we investigate the effect of rainfall on the scatter, the scale break and the power law (peak flows vs. upstream areas) regression exponent. We illustrate why considering individual hydrographs at the outlet of a basin can lead to misleading interpretations of the effects of rainfall variability. We begin with the simple scenario of a basin receiving spatially uniform rainfall of varying intensities and durations and subsequently investigate the role of storm advection velocity, storm variability characterized by variance, spatial correlation and intermittency. Finally, we use a realistic space–time rainfall field obtained from a popular rainfall model that combines the aforementioned features. For each of these scenarios, we employ a recent formulation of flow velocity for a network of channels, assume idealized conditions of runoff generation and flow dynamics and calculate peak flow scaling exponents, which are then compared to the scaling exponent of the width function maxima. Our results show that the peak flow scaling exponent is always larger than the width function scaling exponent. The simulation scenarios are used to identify the smaller scale basins, whose response is dominated by the rainfall variability and the larger scale basins, which are driven by rainfall volume, river network aggregation and flow dynamics. The rainfall variability has a greater impact on peak flows at smaller scales. The effect of rainfall variability is reduced for larger scale basins as the river network aggregates and smoothes out the storm variability. The results obtained from simple scenarios are used to make rigorous interpretations of the peak flow scaling structure that is obtained from rainfall generated with the space–time rainfall model and realistic rainfall fields derived from NEXRAD radar data.  相似文献   

4.
Near-surface soil CO2 gas-phase concentration (C) and concomitant incident rainfall (Pi) and through-fall (Pt) depths were collected at different locations in a temperate pine forest every 30 min during the 2005 and 2006 growing seasons (and then averaged to the daily timescale). At the daily scale, C temporal variations were well described by a sequence of monotonically decreasing functions interrupted by large positive jumps induced by rainfall events. A stochastic model was developed to link rainfall statistics responsible for these jumps to near-surface C dynamics. The model accounted for the effect of daily rainfall variability, both in terms of timing and amount of water, and permitted an analytical derivation of the C probability density function (pdf) using the parameters of the rainfall pdf. Given the observed positive correlation between daily C and soil CO2 fluxes to the atmosphere (Fs), the effects of various rainfall regimes on the statistics of Fs can be deduced from the behavior of C under different climatic conditions. The predictions from this analytical model are consistent with flux measurements reported in manipulative experiments that varied rainfall amount and frequency.  相似文献   

5.
Many recent studies have been devoted to the investigation of the nonlinear dynamics of rainfall or streamflow series based on methods of dynamical systems theory. Although finding evidence for the existence of a low-dimensional deterministic component in rainfall or streamflow is of much interest, not much attention has been given to the nonlinear dependencies of the two and especially on how the spatio-temporal distribution of rainfall affects the nonlinear dynamics of streamflow at flood time scales. In this paper, a methodology is presented which simultaneously considers streamflow series, spatio-temporal structure of precipitation and catchment geomorphology into a nonlinear analysis of streamflow dynamics. The proposed framework is based on “hydrologically-relevant” rainfall-runoff phase-space reconstruction acknowledging the fact that rainfall-runoff is a stochastic spatially extended system rather than a deterministic multivariate one. The methodology is applied to two basins in Central North America using 6-hour streamflow data and radar images for a period of 5 years. The proposed methodology is used to: (a) quantify the nonlinear dependencies between streamflow dynamics and the spatio-temporal dynamics of precipitation; (b) study how streamflow predictability is affected by the trade-offs between the level of detail necessary to explain the spatial variability of rainfall and the reduction of complexity due to the smoothing effect of the basin; and (c) explore the possibility of incorporating process-specific information (in terms of catchment geomorphology and an a priori chosen uncertainty model) into nonlinear prediction. Preliminary results are encouraging and indicate the potential of using the proposed methodology to understand via nonlinear analysis of observations (i.e., not based on a particular rainfall-runoff model) streamflow predictability and limits to prediction as a function of the complexity of spatio-temporal forcing relative to basin geomorphology.  相似文献   

6.
ABSTRACT

The objective of this paper is to understand how the natural dynamics of a time-varying catchment, i.e. the rainfall pattern, transforms the random component of rainfall and how this transformation influences the river discharge. To this end, this paper develops a rainfall–runoff modelling approach that aims to capture the multiple sources and types of uncertainty in a single framework. The main assumption is that hydrological systems are nonlinear dynamical systems which can be described by stochastic differential equations (SDE). The dynamics of the system is based on the least action principle (LAP) as derived from Noether’s theorem. The inflow process is considered as a sum of deterministic and random components. Using data from the Ouémé River basin (Benin, West Africa), the basic properties for the random component are considered and the triple relationship between the structure of the inflowing rainfall, the corresponding SDE that describes the river basin and the associated Fokker-Planck equations (FPE) is analysed.
EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR D. Gerten  相似文献   

7.
A theoretical solution framework to the nonlinear stochastic partial differential equations (SPDE) of the kinematic wave and diffusion wave models of overland flows under stochastic inflows/outflows, stochastic surface roughness field and stochastic state of flows was obtained. This development was realized by means of an eigenfunction representation of the time-space overland flow depths, and by transforming the problem into the phase space. By using Van Kampen's lemma and the cumulant expansion theory of Kubo-Van Kampen-Fox, the deterministic partial differential equation (PDE) for the evolutionary probability density function (pdf) of overland flow depths was finally obtained. Once this deterministic PDE is solved for the time-varying pdf of overland flow depths, then the time-space varying pdf of overland flow depths can be obtained by a transformation given in the text. In this solution framework it is possible to incorporate the stochastic dynamic behavior of the parameters and of the forcing functions of the overland flow process. For example, not only the individual rainfall duration and fluctuating rain intensity characteristics but also the sequential behavior of rainfall patterns is incorporated into the evolutionary probability density function of overland flow depths.  相似文献   

8.
A theoretical solution framework to the nonlinear stochastic partial differential equations (SPDE) of the kinematic wave and diffusion wave models of overland flows under stochastic inflows/outflows, stochastic surface roughness field and stochastic state of flows was obtained. This development was realized by means of an eigenfunction representation of the time-space overland flow depths, and by transforming the problem into the phase space. By using Van Kampen's lemma and the cumulant expansion theory of Kubo-Van Kampen-Fox, the deterministic partial differential equation (PDE) for the evolutionary probability density function (pdf) of overland flow depths was finally obtained. Once this deterministic PDE is solved for the time-varying pdf of overland flow depths, then the time-space varying pdf of overland flow depths can be obtained by a transformation given in the text. In this solution framework it is possible to incorporate the stochastic dynamic behavior of the parameters and of the forcing functions of the overland flow process. For example, not only the individual rainfall duration and fluctuating rain intensity characteristics but also the sequential behavior of rainfall patterns is incorporated into the evolutionary probability density function of overland flow depths.  相似文献   

9.
Simulation of quick runoff components such as surface runoff and associated soil erosion requires temporal high‐resolution rainfall intensities. However, these data are often not available because such measurements are costly and time consuming. Current rainfall disaggregation methods have shortcomings, especially in generating the distribution of storm events. The objectives of this study were to improve point rainfall disaggregation using a new magnitude category rainfall disaggregation approach. The procedure is introduced using a coupled disaggregation approach (Hyetos and cascade) for multisite rainfall disaggregation. The new procedure was tested with ten long‐term precipitation data sets of central Germany using summer and winter precipitation to determine seasonal variability. Results showed that dividing the rainfall amount into four daily rainfall magnitude categories (1–10, 11–25, 26–50, >50 mm) improves the simulation of high rainfall intensity (convective rainfall). The Hyetos model category approach (HyetosCat) with seasonal variation performs representative to observed hourly rainfall compared with without categories on each month. The mean absolute percentage accuracy of standard deviation for hourly rainfall is 89.7% in winter and 95.6% in summer. The proposed magnitude category method applied with the coupled HyetosCat–cascade approach reproduces successfully the statistical behaviour of local 10‐min rainfall intensities in terms of intermittency as well as variability. The root mean square error performance statistics for disaggregated 10‐min rainfall depth ranges from 0.20 to 2.38 mm for summer and from 0.12 to 2.82 mm for the winter season in all categories. The coupled stochastic approach preserves the statistical self‐similarity and intermittency at each magnitude category with a relatively low computational burden. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

10.
We explore the impact of uncertainties in the spatial–temporal distribution of rainfall on the prediction of peak discharge in a typical mountain basin. To this end, we use a stochastic generator previously developed for rainfall downscaling, and we estimate the basin response by adopting a semi-distributed hydrological model. The results of the analysis provide information on the minimum rainfall resolution needed for operational flood forecasting, and confirm the sensitivity of peak discharge estimates to errors in the determination of the power spectrum of the precipitation field.  相似文献   

11.
《水文科学杂志》2013,58(6):1065-1091
Abstract

In the last two decades, several researchers have claimed to have discovered low-dimensional determinism in hydrological processes, such as rainfall and runoff, using methods of chaotic analysis. However, such results have been criticized by others. In an attempt to offer additional insights into this discussion, it is shown here that, in some cases, merely the careful application of concepts of dynamical systems, without doing any calculation, provides strong indications that hydrological processes cannot be (low-dimensional) deterministic chaoti. Furthermore, it is shown that specific peculiarities of hydrological processes on fine time scales, such as asymmetric, J-shaped distribution functions, intermittency, and high autocorrelations, are synergistic factors that can lead to misleading conclusions regarding the presence of (low-dimensional) deterministic chaos. In addition, the recovery of a hypothetical attractor from a time series is put as a statistical estimation problem whose study allows, among others, quantification of the required sample size; this appears to be so huge that it prohibits any accurate estimation, even with the largest available hydrological records. All these arguments are demonstrated using appropriately synthesized theoretical examples. Finally, in light of the theoretical analyses and arguments, typical real-world hydrometeorological time series, such as relative humidity, rainfall, and runoff, are explored and none of them is found to indicate the presence of chaos.  相似文献   

12.
We present a derivation of a stochastic model of Navier Stokes equations that relies on a decomposition of the velocity fields into a differentiable drift component and a time uncorrelated uncertainty random term. This type of decomposition is reminiscent in spirit to the classical Reynolds decomposition. However, the random velocity fluctuations considered here are not differentiable with respect to time, and they must be handled through stochastic calculus. The dynamics associated with the differentiable drift component is derived from a stochastic version of the Reynolds transport theorem. It includes in its general form an uncertainty dependent subgrid bulk formula that cannot be immediately related to the usual Boussinesq eddy viscosity assumption constructed from thermal molecular agitation analogy. This formulation, emerging from uncertainties on the fluid parcels location, explains with another viewpoint some subgrid eddy diffusion models currently used in computational fluid dynamics or in geophysical sciences and paves the way for new large-scales flow modeling. We finally describe an applications of our formalism to the derivation of stochastic versions of the Shallow water equations or to the definition of reduced order dynamical systems.  相似文献   

13.
Groundwater age and life expectancy probability density functions (pdf) have been defined, and solved in a general three-dimensional context by means of forward and backward advection–dispersion equations [Cornaton F, Perrochet P. Groundwater age, life expectancy and transit time distributions in advective–dispersive systems; 1. Generalized reservoir theory. Adv Water Res (xxxx)]. The discharge and recharge zones transit time pdfs were then derived by applying the reservoir theory (RT) to the global system, thus considering as ensemble the union of all inlet boundaries on one hand, and the union of all outlet boundaries on the other hand. The main advantages in using the RT to calculate the transit time pdf is that the outlet boundary geometry does not represent a computational limiting factor (e.g. outlets of small sizes), since the methodology is based on the integration over the entire domain of each age, or life expectancy, occurrence. In the present paper, we extend the applicability of the RT to sub-drainage basins of groundwater reservoirs by treating the reservoir flow systems as compartments which transfer the water fluxes to a particular discharge zone, and inside which mixing and dispersion processes can take place. Drainage basins are defined by the field of probability of exit at outlet. In this way, we make the RT applicable to each sub-drainage system of an aquifer of arbitrary complexity and configuration. The case of the well-head protection problem is taken as illustrative example, and sensitivity analysis of the effect of pore velocity variations on the simulated ages is carried out.  相似文献   

14.
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15.
Analysis of structural fuzzy random seismic response   总被引：2，自引：0，他引：2  
Ａｎａｌｙｓｉｓｏｆｓｔｒｕｃｔｕｒａｌｆｕｚｚｙｒａｎｄｏｍｓｅｉｓｍｉｃｒｅｓｐｏｎｓｅ张跃，王光远ＹｕｅＺＨＡＮＧａｎｄＧｕａｎｇ－ＹｕａｎＷＡＮＧ１）（ＤｅｐａｒｔｍｅｎｔｏｆＣｉｖｉｌＥｎｇｉｎｅｅｒｉｎｇＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔ...  相似文献   

16.
In this paper, stochastic dynamic responses of dam–reservoir–foundation systems subjected to spatially varying earthquake ground motions are investigated using the displacement-based fluid finite elements. For this purpose, variable-number-node two-dimensional (2D) fluid finite elements based on the Lagrangian approach is programmed in FORTRAN language and incorporated into a computer program SVEM, which is used for stochastic dynamic analysis of solid systems subjected to spatially varying earthquake ground motion. The spatially varying earthquake ground motion model includes incoherence, wave-passage and site-response effects. The incoherence effect is examined by considering the Harichandran and Vanmarcke coherency model. The effect of the wave passage is investigated by using various wave velocities. Homogeneous medium and firm soil types are selected for considering the site-response effect where the foundation supports are constructed. The Sar?yar concrete gravity dam, constructed in Turkey is selected for numerical example. The ground motion is described by filtered white noise and applied to each support point of the 2D finite element model of the dam–reservoir–foundation system. The record of Kocaeli earthquake in 1999 is used in the analyses. Displacements, stresses and hydrodynamic pressures occurring on the upstream face of the dam are calculated for four cases. It is concluded that spatially varying earthquake ground motions have important effects on the stochastic dynamic response of dam–reservoir–foundation systems.  相似文献   

17.
Space–time variability of precipitation plays a key role as driver of many environmental processes. The objective of this study is to evaluate a spatiotemporal (STG) Neyman–Scott Rectangular Pulses (NSRP) generator over orographically complex terrain for statistical downscaling of climate models. Data from 145 rain gauges over a 5760-km2 area of Cyprus for 1980–2010 were used for this study. The STG was evaluated for its capacity to reproduce basic rainfall statistical properties, spatial intermittency, and extremes. The results were compared with a multi-single site NRSP generator (MSG). The STG performed well in terms of average annual rainfall (+1.5 % in comparison with the 1980–2010 observations), but does not capture spatial intermittency over the study area and extremes well. Daily events above 50 mm were underestimated by 61 %. The MSG produced a similar error (+1.1 %) in terms of average annual rainfall, while the daily extremes (>50-mm) were underestimated by 11 %. A gridding scheme based on scaling coefficients was used to interpolate the MSG data. Projections of three Regional Climate Models, downscaled by MSG, indicate a 1.5–12 % decrease in the mean annual rainfall over Cyprus for 2020–2050. Furthermore, the number of extremes (>50-mm) for the 145 stations is projected to change between ?24 and +2 % for the three models. The MSG modelling approach maintained the daily rainfall statistics at all grid cells, but cannot create spatially consistent daily precipitation maps, limiting its application to spatially disconnected applications. Further research is needed for the development of spatial non-stationary NRSP models.  相似文献   

18.
Nonlinear ensemble prediction of chaotic daily rainfall   总被引：3，自引：0，他引：3  
The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. Many of these approaches aim at only analyzing the chaotic nature and not its prediction. In the present study, an attempt is made to identify chaos using various techniques and prediction is also done by generating ensembles in order to quantify the uncertainty involved. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha, Mahanadi and All-India for the period 1955–2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series. Correlation dimension method is done on the phase randomized and first derivative of the data series to check whether the saturation of the dimension is due to the inherent linear correlation structure or due to low dimensional dynamics. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996–2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are done from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature.  相似文献   

19.
We conducted hydrographic observations in 2002 to investigate the anticyclonic eddy that emerges every summer in Funka Bay, Hokkaido, Japan, and elucidate dynamical structure and wind-driven upwelling within the eddy. The anticyclonic eddy has a vertical scale of 32 m and is characterized by a strong baroclinic flow and a sharp pycnocline with a concave isopycnal structure. The sharp pycnocline occurs below a warm and relatively low-salinity water termed summer Funka Bay water (FS), which is formed by heating from solar radiation and dilution from river discharge in summertime Funka Bay. Flow of the anticyclonic eddy rotates as a rigid body at each layer, and the horizontal scale and rotation period of the eddy in the surface layer are about 15 km and 2.2 days, respectively. The dynamical balance of the anticyclonic eddy is well explained by the gradient flow balance. The contribution of centrifugal force to the gradient flow balance is about 27%. Therefore, the effect of the nonlinear term associated with centrifugal force cannot be neglected in considering the dynamics of the anticyclonic eddy in summertime Funka Bay. In addition, upwelling of subsurface water was observed in the surface layer of the central part of the eddy. The formation mechanism of this upwelling is consistent with interaction between horizontal uniform wind and the eddy. This upwelling is driven by upward Ekman pumping velocity related to the horizontal divergence of Ekman transport. In summertime Funka Bay, there are two wind effects that affect the anticyclonic eddy: a decay effect of the upwelling of subsurface water resulting from horizontal uniform wind (mainly northwesterly wind), and a maintenance or spin-up effect of horizontal non-uniform wind (mainly southerly–southeasterly seasonal wind) with negative wind stress curl.  相似文献   

20.
The authors present a statistical procedure to estimate the probability distributions of storm characteristics. The approach uses recent advances in stochastic hydrological modeling. The temporal dynamics of rainfall are modeled via a reward alternating renewal process that describes wet and dry phases of storms. In particular, the wet phase is modeled as a rectangular pulse process with dependent random duration and intensity; the global dependence structure is described using multidimensional copulas. The marginal distributions are described by Generalized Pareto laws. The authors derive both the storm volume statistics and the rainfall volume distribution within a fixed temporal window preceding a storm. Based on these results, they calculate the antecedent moisture conditions. The paper includes a thorough discussion of the validity of the assumptions and approximations introduced, and an application to actual rainfall data. The models presented here have important implications for improved design procedures of water resources and hydrologic systems.  相似文献   

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