Geophysical flows under location uncertainty,Part II Quasi-geostrophy and efficient ensemble spreading     

V. Resseguier  E. Mémin  B. Chapron 《地球物理与天体物理流体动力学》2017,111(3):177-208

Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. In this paper, simplified geophysical dynamics are derived from a Boussinesq model under location uncertainty. Invoking usual scaling approximations and a moderate influence of the subgrid terms, stochastic formulations are obtained for the stratified Quasi-Geostrophy and the Surface Quasi-Geostrophy models. Based on numerical simulations, benefits of the proposed stochastic formalism are demonstrated. A single realization of models under location uncertainty can restore small-scale structures. An ensemble of realizations further helps to assess model error prediction and outperforms perturbed deterministic models by one order of magnitude. Such a high uncertainty quantification skill is of primary interests for assimilation ensemble methods. MATLAB^® code examples are available online.  相似文献   

Issues and Options in the Delineation of Well Capture Zones under Uncertainty          下载免费PDF全文

Emil O. Frind  John W. Molson 《Ground water》2018,56(3):366-376

The delineation of wellhead protection areas (WHPAs) under uncertainty is still a challenge for heterogeneous porous media. For granular media, one option is to combine particle tracking (PT) with the Monte Carlo approach (PT‐MC) to account for geologic uncertainties. Fractured porous media, however, require certain restrictive assumptions under this approach. An alternative for all types of media is the capture probability (CP) approach, which is based on the solution of the standard advection‐dispersion equation in a backward mode, making use of the analogy between forward and backward transport processes. Within this context, we review the current controversy about the correct form of the conceptual model for transport, finding that the advection‐diffusion model, which represents the diffusive interchange between streamtubes with differing velocities, is more physically realistic than the conventional advection‐dispersion model. For mildly to moderately heterogeneous materials, stochastic theories and simulation experiments show that this process converges at the field scale to an effective advection‐dispersion process that can be simulated with conventional transport models using appropriate macrodispersivity values. For highly heterogeneous materials, stochastic theories do not yet exist but there is no reason why the process should not converge naturally as well. Macrodispersivities appear to be formation‐specific. The advection‐dispersion model can be used for capture zone delineation in heterogeneous granular media. For fractured porous systems, hybrid equivalent porous medium and discrete fracture network or CP‐based approaches may have potential. In general, capture zones delineated by PT without MC will always be too small and should not be used as a basis for land‐use decisions.  相似文献   

Probabilistic estimation of irrigation requirement under climate uncertainty using dichotomous and marked renewal processes     

《Advances in water resources》2013

This study addresses estimation of net irrigation requirement over a growing season under climate uncertainty. An ecohydrological model, building upon the stochastic differential equation of soil moisture dynamics, is employed as a basis to derive new analytical expressions for estimating seasonal net irrigation requirement probabilistically. Two distinct irrigation technologies are considered. For micro irrigation technology, probability density function of seasonal net irrigation depth (SNID) is derived assessing transient behavior of a stochastic process which is time integral of dichotomous Markov process. Probability mass function of SNID which is a discrete random variable for traditional irrigation technology is also presented using a marked renewal process with quasi-exponentially-distributed time intervals. Comparing the results obtained from the presented models with those resulted from a Monte Carlo approach verified the significance of the probabilistic expressions derived and assumptions made.  相似文献   

Fluid flow dynamics under location uncertainty     

Etienne Mémin 《地球物理与天体物理流体动力学》2014,108(2):119-146

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   

Uncertainty in hydrograph separations based on geochemical mixing models     

《Journal of Hydrology》2002,255(1-4):90-106

A detailed uncertainty analysis of three-component mixing models based on the Haute–Mentue watershed (Switzerland) is presented. Two types of uncertainty are distinguished: the ‘model uncertainty’, which is affected by model assumptions, and the ‘statistical uncertainty’, which is due to temporal and spatial variability of chemical tracer concentrations of components. The statistical uncertainty is studied using a Monte Carlo procedure. The model uncertainty is investigated by the comparison of four different mixing models all based on the same tracers but considering for each component alternative hypotheses about their concentration and their spatio-temporal variability. This analysis indicates that despite the uncertainty, the flow sources, which generate the stream flow are clearly identified at the catchments scale by the application of the mixing model. However, the precision and the coherence of hydrograph separations can be improved by taking into account any available information about the temporal and spatial variability of component chemical concentrations.  相似文献   

A Hierarchical Bayesian Model Averaging Framework for Groundwater Prediction under Uncertainty          下载免费PDF全文

Nima Chitsazan  Frank T.‐C. Tsai 《Ground water》2015,53(2):305-316

Groundwater prediction models are subjected to various sources of uncertainty. This study introduces a hierarchical Bayesian model averaging (HBMA) method to segregate and prioritize sources of uncertainty in a hierarchical structure and conduct BMA for concentration prediction. A BMA tree of models is developed to understand the impact of individual sources of uncertainty and uncertainty propagation to model predictions. HBMA evaluates the relative importance of different modeling propositions at each level in the BMA tree of model weights. The HBMA method is applied to chloride concentration prediction for the “1,500‐foot” sand of the Baton Rouge area, Louisiana from 2005 to 2029. The groundwater head data from 1990 to 2004 is used for model calibration. Four sources of uncertainty are considered and resulted in 180 flow and transport models for concentration prediction. The results show that prediction variances of concentration from uncertain model elements are much higher than the prediction variance from uncertain model parameters. The HBMA method is able to quantify the contributions of individual sources of uncertainty to the total uncertainty.  相似文献   

Parameter Estimation for Groundwater Models under Uncertain Irrigation Data   总被引：1，自引：0，他引：1       下载免费PDF全文

Yonas Demissie  Albert Valocchi  Ximing Cai  Nicholas Brozovic  Gabriel Senay  Mekonnen Gebremichael 《Ground water》2015,53(4):614-625

The success of modeling groundwater is strongly influenced by the accuracy of the model parameters that are used to characterize the subsurface system. However, the presence of uncertainty and possibly bias in groundwater model source/sink terms may lead to biased estimates of model parameters and model predictions when the standard regression‐based inverse modeling techniques are used. This study first quantifies the levels of bias in groundwater model parameters and predictions due to the presence of errors in irrigation data. Then, a new inverse modeling technique called input uncertainty weighted least‐squares (IUWLS) is presented for unbiased estimation of the parameters when pumping and other source/sink data are uncertain. The approach uses the concept of generalized least‐squares method with the weight of the objective function depending on the level of pumping uncertainty and iteratively adjusted during the parameter optimization process. We have conducted both analytical and numerical experiments, using irrigation pumping data from the Republican River Basin in Nebraska, to evaluate the performance of ordinary least‐squares (OLS) and IUWLS calibration methods under different levels of uncertainty of irrigation data and calibration conditions. The result from the OLS method shows the presence of statistically significant (p < 0.05) bias in estimated parameters and model predictions that persist despite calibrating the models to different calibration data and sample sizes. However, by directly accounting for the irrigation pumping uncertainties during the calibration procedures, the proposed IUWLS is able to minimize the bias effectively without adding significant computational burden to the calibration processes.  相似文献   

A simulation-based fuzzy chance-constrained programming model for optimal groundwater remediation under uncertainty   总被引：3，自引：0，他引：3  

L. He  G.H. Huang  H.W. Lu 《Advances in water resources》2008,31(12):1622-1635

In this study a simulation-based fuzzy chance-constrained programming (SFCCP) model is developed based on possibility theory. The model is solved through an indirect search approach which integrates fuzzy simulation, artificial neural network and simulated annealing techniques. This approach has the advantages of: (1) handling simulation and optimization problems under uncertainty associated with fuzzy parameters, (2) providing additional information (i.e. possibility of constraint satisfaction) indicating that how likely one can believe the decision results, (3) alleviating computational burdens in the optimization process, and (4) reducing the chances of being trapped in local optima. The model is applied to a petroleum-contaminated aquifer located in western Canada for supporting the optimal design of groundwater remediation systems. The model solutions provide optimal groundwater pumping rates for the 3, 5 and 10 years of pumping schemes. It is observed that the uncertainty significantly affects the remediation strategies. To mitigate such impacts, additional cost is required either for increased pumping rate or for reinforced site characterization.  相似文献   

Quantifying the effect of thermospheric parameterization in a global model     

David J. Pawlowski  Aaron J. Ridley 《Journal of Atmospheric and Solar》2009,71(17-18):2017-2026

Global climate models have become useful tools for studying the important physical processes that affect the Earth's upper atmosphere. However, the results produced by all models contain uncertainty that stems for the manner in which the model is driven, as well as in the treatment of the internal physics and numerics. In order to fully understand the scientific value of the model results then, it is necessary to have a quantitative understanding of the uncertainty in the model. In this study, the global ionosphere–thermosphere model is used to investigate how uncertainty in the use of parameters in a large scale model can affect the model results. Eight parameters are studied that ultimately have an effect on the thermospheric temperature equation. It is found that among these, uncertainty in the thermal conductivity, NO cooling, and NO binary diffusion coefficients most strongly translate to uncertainty in the temperature and density results. In addition, variations in the eddy diffusion coefficient are shown to result in significant uncertainty in the thermospheric composition, and ultimately the electron density.  相似文献   

Impacts of uncertain river flow data on rainfall‐runoff model calibration and discharge predictions     

Hilary McMillan  Jim Freer  Florian Pappenberger  Tobias Krueger  Martyn Clark 《水文研究》2010,24(10):1270-1284

In order to quantify total error affecting hydrological models and predictions, we must explicitly recognize errors in input data, model structure, model parameters and validation data. This paper tackles the last of these: errors in discharge measurements used to calibrate a rainfall‐runoff model, caused by stage–discharge rating‐curve uncertainty. This uncertainty may be due to several combined sources, including errors in stage and velocity measurements during individual gaugings, assumptions regarding a particular form of stage–discharge relationship, extrapolation of the stage–discharge relationship beyond the maximum gauging, and cross‐section change due to vegetation growth and/or bed movement. A methodology is presented to systematically assess and quantify the uncertainty in discharge measurements due to all of these sources. For a given stage measurement, a complete PDF of true discharge is estimated. Consequently, new model calibration techniques can be introduced to explicitly account for the discharge error distribution. The method is demonstrated for a gravel‐bed river in New Zealand, where all the above uncertainty sources can be identified, including significant uncertainty in cross‐section form due to scour and re‐deposition of sediment. Results show that rigorous consideration of uncertainty in flow data results in significant improvement of the model's ability to predict the observed flow. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

Two-stage decision-making under uncertainty and stochasticity: Bayesian Programming     

Kenneth W. Harrison 《Advances in water resources》2007

This paper develops a new method for decision-making under uncertainty. The method, Bayesian Programming (BP), addresses a class of two-stage decision problems with features that are common in environmental and water resources. BP is applicable to two-stage combinatorial problems characterized by uncertainty in unobservable parameters, only some of which is resolved upon observation of the outcome of the first-stage decision. The framework also naturally accommodates stochastic behavior, which has the effect of impeding uncertainty resolution. With the incorporation of systematic methods for decision search and Monte Carlo methods for Bayesian analysis, BP addresses limitations of other decision-analytic approaches for this class of problems, including conventional decision tree analysis and stochastic programming. The methodology is demonstrated with an illustrative problem of water quality pollution control. Its effectiveness for this problem is compared to alternative approaches, including a single-stage model in which expected costs are minimized and a deterministic model in which uncertain parameters are replaced by their mean values. A new term, the expected value of including uncertainty resolution, or EVIUR, is introduced and evaluated for the illustrative problem. It is a measure of the worth of incorporating the experimental value of decisions into an optimal decision-making framework. For the illustrative problem, the two-stage adaptive management framework extracted up to approximately 50% of the gains of perfect information. The strength and limitations of the method are discussed and conclusions are presented.  相似文献   

Alternate decision rules,the flexibility premium,and land development over time and under uncertainty     

A. A.?BatabyalEmail author 《Stochastic Environmental Research and Risk Assessment (SERRA)》2004,18(2):141-146

The Arrow–Fisher–Henry (AFH) analysis of land development under uncertainty has been conducted in a two period model. Recently, Capozza and Helsley (1990), Batabyal (1996, 1997, 2000), and others have analyzed the question of land development under uncertainty in a multi-period setting. We extend this literature by examining the role that time independent and time dependent decision rules play in the decision to develop land over time and under uncertainty. We first construct a dynamic and stochastic model of decision making in the context of land development. Next, we use this model to analyze the expected profit of a landowner when this landowner uses, respectively, time independent and time dependent decision rules. Finally, we compare and contrast the properties of time independent and time dependent decision rules and we discuss the magnitude of the premium stemming from the maintenance of temporal flexibility in decision making.  相似文献   

The inverse problem and ground water management     

H. A. Loaiciga  M. A. Marino 《Stochastic Environmental Research and Risk Assessment (SERRA)》1987,1(3):161-168

The response of groundwater basins to natural and anthropogenic inputs depends on many interrelated factors such as the values of groundwater flow and mass transport parameters. This work presents a theoretical analysis of the impact of parameter uncertainty on groundwater management decisions. It is shown that under classical, Bayesian, and deterministic assumptions about the parameter structure, the resulting management decisions could be very different. This underscores the importance of adopting the proper parameter structure and the need for using consistent methods to solve the inverse problem.  相似文献   

龙岗金龙顶子火山空降碎屑物数值模拟及概率性灾害评估   总被引：1，自引：0，他引：1  

于红梅  许建东  吴建平  栾鹏  赵波 《震灾防御技术》2013,8(1):62-71

空降碎屑物为爆炸式火山喷发产生的一种重要的灾害类型,数值模拟已成为一个快速有效地确定火山灰扩散和沉积范围的方法。本文根据改进的Suzuki(1983)二维扩散模型,编写了基于Windows环境下的火山灰扩散程序。通过对前人资料的分析,模拟了龙岗火山群中最新火山喷发——金龙顶子火山喷发产生的空降碎屑物扩散范围,与实测结果具有很好的一致性,证实了模型的可靠性和参数的合理性。根据该区10年的风参数,模拟了7021次不同风参数时金龙顶子火山灰的扩散范围,以此制作了火山灰沉积厚度超过1cm和0.5cm时的概率性空降碎屑灾害区划图。本文的研究可为龙岗火山区火山危险性分析和灾害预警与对策提供重要的科学依据。  相似文献   

过坝下泄水流中温室气体排放速率的数值模拟     

黄菊萍  欧洋铭  李然  冯镜洁  李哲 《湖泊科学》2022,34(2):664-674

当水流通过泄洪建筑物下泄时,水体中所溶解的温室气体(二氧化碳(CO2)、甲烷(CH4)等)会因为所受压力的瞬间改变而导致溶解度降低,从而造成气液之间传质的发生及水中温室气体的排放.然而,目前对于泄流条件下水中温室气体排放的研究还较为缺乏.鉴于原型观测与模型试验的局限性,本文建立了大坝泄流条件下温室气体排放速率的数学模型...  相似文献   

Facets of uncertainty: epistemic uncertainty,non-stationarity,likelihood, hypothesis testing,and communication   总被引：1，自引：1，他引：0  

Keith Beven 《水文科学杂志》2016,61(9):1652-1665

ABSTRACT

This paper presents a discussion of some of the issues associated with the multiple sources of uncertainty and non-stationarity in the analysis and modelling of hydrological systems. Different forms of aleatory, epistemic, semantic, and ontological uncertainty are defined. The potential for epistemic uncertainties to induce disinformation in calibration data and arbitrary non-stationarities in model error characteristics, and surprises in predicting the future, are discussed in the context of other forms of non-stationarity. It is suggested that a condition tree is used to be explicit about the assumptions that underlie any assessment of uncertainty. This also provides an audit trail for providing evidence to decision makers.