scholarly journals Subgrid-Scale Parameterization with Conditional Markov Chains

2008 ◽  
Vol 65 (8) ◽  
pp. 2661-2675 ◽  
Author(s):  
Daan Crommelin ◽  
Eric Vanden-Eijnden
Keyword(s):  
Markov Chain ◽  
Correlation Functions ◽  
Probability Distributions ◽  
Model Performance ◽  
Subgrid Scale ◽  
Oceanic Circulation ◽  
Ensemble Forecasts ◽  
New Approach ◽  
Lorenz 96 ◽  
Wave Properties

Abstract A new approach is proposed for stochastic parameterization of subgrid-scale processes in models of atmospheric or oceanic circulation. The new approach relies on two key ingredients: first, the unresolved processes are represented by a Markov chain whose properties depend on the state of the resolved model variables; second, the properties of this conditional Markov chain are inferred from data. The parameterization approach is tested by implementing it in the framework of the Lorenz ’96 model. Performance of the parameterization scheme is assessed by inspecting probability distributions, correlation functions, and wave properties, and by carrying out ensemble forecasts. For the Lorenz ’96 model, the parameterization algorithm is shown to give good results with a Markov chain with a few states only and to outperform several other parameterization schemes.

scholarly journals Data-based stochastic subgrid-scale parametrization: an approach using cluster-weighted modelling

2012 ◽  
Vol 370 (1962) ◽  
pp. 1061-1086 ◽  
Author(s):  
Frank Kwasniok
Keyword(s):  
Clustering Algorithm ◽  
Prediction Models ◽  
Statistical Modelling ◽  
Scale Model ◽  
Ensemble Prediction ◽  
Subgrid Scale ◽  
New Approach ◽  
Lorenz 96 ◽  
The Impact

A new approach for data-based stochastic parametrization of unresolved scales and processes in numerical weather and climate prediction models is introduced. The subgrid-scale model is conditional on the state of the resolved scales, consisting of a collection of local models. A clustering algorithm in the space of the resolved variables is combined with statistical modelling of the impact of the unresolved variables. The clusters and the parameters of the associated subgrid models are estimated simultaneously from data. The method is implemented and explored in the framework of the Lorenz '96 model using discrete Markov processes as local statistical models. Performance of the cluster-weighted Markov chain scheme is investigated for long-term simulations as well as ensemble prediction. It clearly outperforms simple parametrization schemes and compares favourably with another recently proposed subgrid modelling scheme also based on conditional Markov chains.

scholarly journals A possibilistic interpretation of ensemble forecasts: experiments on the imperfect Lorenz 96 system

2020 ◽  
Vol 17 ◽  
pp. 39-45 ◽  
Author(s):  
Noémie Le Carrer ◽  
Peter L. Green
Keyword(s):  
Performance Metrics ◽  
Initial Conditions ◽  
Probability Distributions ◽  
Weather Prediction ◽  
High Sensitivity ◽  
Ensemble Forecasting ◽  
Dynamical Equations ◽  
Ensemble Forecasts ◽  
Novel Approach ◽  
Lorenz 96

Abstract. Ensemble forecasting has gained popularity in the field of numerical medium-range weather prediction as a means of handling the limitations inherent to predicting the behaviour of high dimensional, nonlinear systems, that have high sensitivity to initial conditions. Through small strategical perturbations of the initial conditions, and in some cases, stochastic parameterization schemes of the atmosphere-ocean dynamical equations, ensemble forecasting allows one to sample possible future scenarii in a Monte-Carlo like approximation. Results are generally interpreted in a probabilistic way by building a predictive density function from the ensemble of weather forecasts. However, such a probabilistic interpretation is regularly criticized for not being reliable, because of the chaotic nature of the dynamics of the atmospheric system as well as the fact that the ensembles of forecasts are not, in reality, produced in a probabilistic manner. To address these limitations, we propose a novel approach: a possibilistic interpretation of ensemble predictions, taking inspiration from fuzzy and possibility theories. Our approach is tested on an imperfect version of the Lorenz 96 model and results are compared against those given by a standard probabilistic ensemble dressing. The possibilistic framework reproduces (ROC curve, resolution) or improves (ignorance, sharpness, reliability) the performance metrics of a standard univariate probabilistic framework. This work provides a first step to answer the question whether probability distributions are the right tool to interpret ensembles predictions.

scholarly journals Post processing rainfall forecasts from numerical weather prediction models for short term streamflow forecasting

2013 ◽  
Vol 10 (5) ◽  
pp. 6765-6806 ◽  
Author(s):  
D. E. Robertson ◽  
D. L. Shrestha ◽  
Q. J. Wang
Keyword(s):  
Numerical Weather Prediction ◽  
Prediction Models ◽  
Probability Distributions ◽  
Weather Prediction ◽  
Streamflow Forecasting ◽  
Post Processing ◽  
Short Term ◽  
Ensemble Forecasts ◽  
New Approach ◽  
Numerical Weather

Abstract. Sub-daily ensemble rainfall forecasts that are bias free and reliably quantify forecast uncertainty are critical for flood and short-term ensemble streamflow forecasting. Post processing of rainfall predictions from numerical weather prediction models is typically required to provide rainfall forecasts with these properties. In this paper, a new approach to generate ensemble rainfall forecasts by post processing raw NWP rainfall predictions is introduced. The approach uses a simplified version of the Bayesian joint probability modelling approach to produce forecast probability distributions for individual locations and forecast periods. Ensemble forecasts with appropriate spatial and temporal correlations are then generated by linking samples from the forecast probability distributions using the Schaake shuffle. The new approach is evaluated by applying it to post process predictions from the ACCESS-R numerical weather prediction model at rain gauge locations in the Ovens catchment in southern Australia. The joint distribution of NWP predicted and observed rainfall is shown to be well described by the assumed log-sinh transformed multivariate normal distribution. Ensemble forecasts produced using the approach are shown to be more skilful than the raw NWP predictions both for individual forecast periods and for cumulative totals throughout the forecast periods. Skill increases result from the correction of not only the mean bias, but also biases conditional on the magnitude of the NWP rainfall prediction. The post processed forecast ensembles are demonstrated to successfully discriminate between events and non-events for both small and large rainfall occurrences, and reliably quantify the forecast uncertainty. Future work will assess the efficacy of the post processing method for a wider range of climatic conditions and also investigate the benefits of using post processed rainfall forecast for flood and short term streamflow forecasting.

RESTRICTED SOLID-ON-SOLID MODEL: FROM LOCAL MORPHOLOGY TO CORRELATION FUNCTIONS AND SCALING EXPONENTS

2004 ◽  
Vol 18 (06) ◽  
pp. 827-840
Author(s):  
CHIH-CHUN CHIEN ◽  
NING-NING PANG ◽  
WEN-JER TZENG
Keyword(s):  
Computer Simulation ◽  
Probability Distribution ◽  
Correlation Functions ◽  
Master Equations ◽  
Interfacial Phenomena ◽  
Solid Model ◽  
Direct Simulation ◽  
Kpz Equation ◽  
Scaling Exponents ◽  
New Approach

We study the restricted solid-on-solid (RSOS) model by grouping consecutive sites into local configurations and obtain the master equations of the probability distribution of these local configurations in closed forms. The obtained solutions to these equations fit very well with those from direct computer simulation of the RSOS model. To demonstrate the effectiveness of this new approach for studying interfacial phenomena, we then calculate the correlation functions and even scaling exponents based on this obtained probability distribution of local configurations. The results are also consistent very well with those obtained from the KPZ equation or direct simulation of the RSOS model.

scholarly journals The Sum and Difference of Two Lognormal Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Stochastic Process ◽  
Probability Distributions ◽  
Operator Splitting ◽  
Splitting Method ◽  
Unified Approach ◽  
New Approach ◽  
Numerical Examples ◽  
Operator Splitting Method ◽  
Approximate Probability ◽  
Analytical Series

We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1) the algebraic sum ofNlognormals, and (2) the sum and difference of other correlated stochastic processes, for example, two correlated CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion.

scholarly journals Inundation mapping based on reach-scale effective geometry

2018 ◽  
Vol 22 (11) ◽  
pp. 5967-5985 ◽  
Author(s):  
Cédric Rebolho ◽  
Vazken Andréassian ◽  
Nicolas Le Moine
Keyword(s):  
Model Performance ◽  
Model Complexity ◽  
Hydraulic Geometry ◽  
Future Event ◽  
New Approach ◽  
Flow Equations ◽  
Geometrical Properties ◽  
Inundation Maps ◽  
Extreme Flood ◽  
Inundation Mapping

Abstract. The production of spatially accurate representations of potential inundation is often limited by the lack of available data as well as model complexity. We present in this paper a new approach for rapid inundation mapping, MHYST, which is well adapted for data-scarce areas; it combines hydraulic geometry concepts for channels and DEM data for floodplains. Its originality lies in the fact that it does not work at the cross section scale but computes effective geometrical properties to describe the reach scale. Combining reach-scale geometrical properties with 1-D steady-state flow equations, MHYST computes a topographically coherent relation between the “height above nearest drainage” and streamflow. This relation can then be used on a past or future event to produce inundation maps. The MHYST approach is tested here on an extreme flood event that occurred in France in May–June 2016. The results indicate that it has a tendency to slightly underestimate inundation extents, although efficiency criteria values are clearly encouraging. The spatial distribution of model performance is discussed and it shows that the model can perform very well on most reaches, but has difficulties modelling the more complex, urbanised reaches. MHYST should not be seen as a rival to detailed inundation studies, but as a first approximation able to rapidly provide inundation maps in data-scarce areas.

Analysis of an M/G/1 queue with two types of impatient units

1995 ◽  
Vol 27 (03) ◽  
pp. 840-861 ◽  
Author(s):  
M. Martin ◽  
J. R. Artalejo
Keyword(s):  
Markov Chain ◽  
Performance Measures ◽  
Mathematical Analysis ◽  
Service System ◽  
Probability Distributions ◽  
Embedded Markov Chain ◽  
Renewal Processes ◽  
Stationary Probability ◽  
Markov Renewal Processes ◽  
Specific Performance

This paper deals with a service system in which the processor must serve two types of impatient units. In the case of blocking, the first type units leave the system whereas the second type units enter a pool and wait to be processed later. We develop an exhaustive analysis of the system including embedded Markov chain, fundamental period and various classical stationary probability distributions. More specific performance measures, such as the number of lost customers and other quantities, are also considered. The mathematical analysis of the model is based on the theory of Markov renewal processes, in Markov chains of M/G/l type and in expressions of ‘Takács' equation' type.

scholarly journals An explicit algebraic model for the subgrid-scale passive scalar flux

2013 ◽  
Vol 721 ◽  
pp. 541-577 ◽  
Author(s):  
Amin Rasam ◽  
Geert Brethouwer ◽  
Arne V. Johansson
Keyword(s):  
Channel Flow ◽  
Rotation Rate ◽  
Model Performance ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Subgrid Scale ◽  
Scalar Flux ◽  
Algebraic Form ◽  
New Model ◽  
Flux Model

AbstractIn Marstorpet al. (J. Fluid Mech., vol. 639, 2009, pp. 403–432), an explicit algebraic subgrid stress model (EASSM) for large-eddy simulation (LES) was proposed, which was shown to considerably improve LES predictions of rotating and non-rotating turbulent channel flow. In this paper, we extend that work and present a new explicit algebraic subgrid scalar flux model (EASSFM) for LES, based on the modelled transport equation of the subgrid-scale (SGS) scalar flux. The new model is derived using the same kind of methodology that leads to the explicit algebraic scalar flux model of Wikströmet al. (Phys. Fluids, vol. 12, 2000, pp. 688–702). The algebraic form is based on a weak equilibrium assumption and leads to a model that depends on the resolved strain-rate and rotation-rate tensors, the resolved scalar-gradient vector and, importantly, the SGS stress tensor. An accurate prediction of the SGS scalar flux is consequently strongly dependent on an accurate description of the SGS stresses. The new EASSFM is therefore primarily used in connection with the EASSM, since this model can accurately predict SGS stresses. The resulting SGS scalar flux is not necessarily aligned with the resolved scalar gradient, and the inherent dependence on the resolved rotation-rate tensor makes the model suitable for LES of rotating flow applications. The new EASSFM (together with the EASSM) is validated for the case of passive scalar transport in a fully developed turbulent channel flow with and without system rotation. LES results with the new model show good agreement with direct numerical simulation data for both cases. The new model predictions are also compared to those of the dynamic eddy diffusivity model (DEDM) and improvements are observed in the prediction of the resolved and SGS scalar quantities. In the non-rotating case, the model performance is studied at all relevant resolutions, showing that its predictions of the Nusselt number are much less dependent on the grid resolution and are more accurate. In channel flow with wall-normal rotation, where all the SGS stresses and fluxes are non-zero, the new model shows significant improvements over the DEDM predictions of the resolved and SGS quantities.

Hydrological modelling and anthropogenic water use

2021 ◽  
Author(s):  
Ponnambalam Rameshwaran ◽  
Ali Rudd ◽  
Vicky Bell ◽  
Matt Brown ◽  
Helen Davies ◽  
...  
Keyword(s):  
Climate Change ◽  
Water Use ◽  
Hydrological Model ◽  
Model Performance ◽  
River Flows ◽  
Discharge Data ◽  
New Approach ◽  
Water Demands ◽  
The Impact ◽  
Grid Based

<p>Despite Britain’s often-rainy maritime climate, anthropogenic water demands have a significant impact on river flows, particularly during dry summers. In future years, projected population growth and climate change are likely to increase the demand for water and lead to greater pressures on available freshwater resources.</p><p>Across England, abstraction (from groundwater, surface water or tidal sources) and discharge data along with ‘Hands off Flow’ conditions are available for thousands of individual locations; each with a licence for use, an amount, an indication of when abstraction can take place, and the actual amount of water abstracted (generally less than the licence amount). Here we demonstrate how these data can be used in combination to incorporate anthropogenic artificial influences into a grid-based hydrological model. Model simulations of both high and low river flows are generally improved when abstractions and discharges are included, though for some catchments model performance decreases. The new approach provides a methodological baseline for further work investigating the impact of anthropogenic water use and projected climate change on future river flows.</p>

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