scholarly journals Rotating shallow water flow under location uncertainty with a structure-preserving discretization

2021 ◽  
Author(s):  
Rüdiger Brecht ◽  
Long Li ◽  
Werner Bauer ◽  
Etienne Mémin
Keyword(s):  
Total Energy ◽  
Shallow Water ◽  
Large Scale ◽  
Climate Models ◽  
Deterministic Model ◽  
Weather Prediction ◽  
Random Model ◽  
Small Scale ◽  
Structure Preserving ◽  
Rotating Shallow Water

<p>We introduce a new representation of the rotating shallow water equations based on a stochastic transport principle. The derivation relies on a decomposition of the fluid flow into a large-scale component and a noise term that models the unresolved small-scale flow. The total energy of such a random model is demonstrated to be preserved along time for any realization. Thus, we propose to combine a structure-preserving discretization of the underlying deterministic model with the discrete stochastic terms. This way, our method can directly be used in existing dynamical cores of global numerical weather prediction and climate models. For an inviscid test case on the f-plane we use a homogenous noise and illustrate that the spatial part of the stochastic scheme preserves the total energy of the system. Finally, using an inhomogenous noise, we show  that the proposed random model better captures the structure of a large-scale flow than a comparable deterministic model for a barotropically unstable jet on the sphere.</p>

scholarly journals The MJO in a Coarse-Resolution GCM with a Stochastic Multicloud Parameterization

2015 ◽  
Vol 72 (1) ◽  
pp. 55-74 ◽  
Author(s):  
Qiang Deng ◽  
Boualem Khouider ◽  
Andrew J. Majda
Keyword(s):  
General Circulation ◽  
Large Scale ◽  
Deterministic Model ◽  
Weather Prediction ◽  
General Circulation Models ◽  
Radar Data ◽  
Equation Model ◽  
Death Process ◽  
Relevant Parameter ◽  
Convective Systems

Abstract The representation of the Madden–Julian oscillation (MJO) is still a challenge for numerical weather prediction and general circulation models (GCMs) because of the inadequate treatment of convection and the associated interactions across scales by the underlying cumulus parameterizations. One new promising direction is the use of the stochastic multicloud model (SMCM) that has been designed specifically to capture the missing variability due to unresolved processes of convection and their impact on the large-scale flow. The SMCM specifically models the area fractions of the three cloud types (congestus, deep, and stratiform) that characterize organized convective systems on all scales. The SMCM captures the stochastic behavior of these three cloud types via a judiciously constructed Markov birth–death process using a particle interacting lattice model. The SMCM has been successfully applied for convectively coupled waves in a simplified primitive equation model and validated against radar data of tropical precipitation. In this work, the authors use for the first time the SMCM in a GCM. The authors build on previous work of coupling the High-Order Methods Modeling Environment (HOMME) NCAR GCM to a simple multicloud model. The authors tested the new SMCM-HOMME model in the parameter regime considered previously and found that the stochastic model drastically improves the results of the deterministic model. Clear MJO-like structures with many realistic features from nature are reproduced by SMCM-HOMME in the physically relevant parameter regime including wave trains of MJOs that organize intermittently in time. Also one of the caveats of the deterministic simulation of requiring a doubling of the moisture background is not required anymore.

scholarly journals Improved moist-convective rotating shallow water model and its application to instabilities of hurricane-like vortices

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Tropical Cyclone ◽  
Shallow Water ◽  
Water Vapour ◽  
Large Scale ◽  
Precipitable Water ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Atmospheric Motions ◽  
Rotating Shallow Water

We show how the two-layer moist-convective rotating shallow water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection on large-scale atmospheric motions, can be improved by including, in addition to the water vapour, precipitable water, and the effects of vaporisation, entrainment, and precipitation. Thus improved mcRSW becomes cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

scholarly journals Variational data assimilation with superparameterization

2015 ◽  
Vol 2 (2) ◽  
pp. 513-536 ◽  
Author(s):  
I. Grooms ◽  
Y. Lee
Keyword(s):  
Data Assimilation ◽  
Large Scale ◽  
Climate Models ◽  
Low Cost ◽  
Ocean Model ◽  
Variational Data Assimilation ◽  
Scale Model ◽  
Small Scale ◽  
New Applications ◽  
Lorenz 96

Abstract. Superparameterization (SP) is a multiscale computational approach wherein a large scale atmosphere or ocean model is coupled to an array of simulations of small scale dynamics on periodic domains embedded into the computational grid of the large scale model. SP has been successfully developed in global atmosphere and climate models, and is a promising approach for new applications. The authors develop a 3D-Var variational data assimilation framework for use with SP; the relatively low cost and simplicity of 3D-Var in comparison with ensemble approaches makes it a natural fit for relatively expensive multiscale SP models. To demonstrate the assimilation framework in a simple model, the authors develop a new system of ordinary differential equations similar to the two-scale Lorenz-'96 model. The system has one set of variables denoted {Yi}, with large and small scale parts, and the SP approximation to the system is straightforward. With the new assimilation framework the SP model approximates the large scale dynamics of the true system accurately.

scholarly journals Generalized Z-Grid Model for Numerical Weather Prediction

Atmosphere ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 179 ◽  
Author(s):  
Yuanfu Xie
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Numerical Models ◽  
Weather Prediction ◽  
Shallow Water Equation ◽  
Computing Time ◽  
Time Integration ◽  
Grid Model ◽  
Rotating Shallow Water ◽  
Volume Models

Z-grid finite volume models conserve all-scalar quantities as well as energy and potential enstrophy and yield better dispersion relations for shallow water equations than other finite volume models, such as C-grid and C-D grid models; however, they are more expensive to implement. During each time integration, a Z-grid model must solve Poisson equations to convert its vorticity and divergence to a stream function and velocity potential, respectively. To optimally utilize these conversions, we propose a model in which the stability and possibly accuracy on the sphere are improved by introducing more stencils, such that a generalized Z-grid model can utilize longer time-integration steps and reduce computing time. Further, we analyzed the proposed model’s dispersion relation and compared it to that of the original Z-grid model for a linearly rotating shallow water equation, an important property for numerical models solving primitive equations. The analysis results suggest a means of balancing stability and dispersion. Our numerical results also show that the proposed Z-grid model for a shallow water equation is more stable and efficient than the original Z-grid model, increasing the time steps by more than 1.4 times.

scholarly journals New Statistical Model for Variability of Aerosol Optical Thickness: Theory and Application to MODIS Data over Ocean*

2016 ◽  
Vol 73 (2) ◽  
pp. 821-837 ◽  
Author(s):  
Mikhail D. Alexandrov ◽  
Igor V. Geogdzhayev ◽  
Kostas Tsigaridis ◽  
Alexander Marshak ◽  
Robert Levy ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Optical Thickness ◽  
Large Scale ◽  
Climate Models ◽  
Marine Boundary Layer ◽  
Structure Functions ◽  
Aerosol Optical Thickness ◽  
Small Scale ◽  
Scale Invariant ◽  
Modis Data

Abstract A novel model for the variability in aerosol optical thickness (AOT) is presented. This model is based on the consideration of AOT fields as realizations of a stochastic process that is the exponent of an underlying Gaussian process with a specific autocorrelation function. In this approach, AOT fields have lognormal PDFs and structure functions with the correct asymptotic behavior at large scales. The latter is an advantage compared with fractal (scale invariant) approaches. The simple analytical form of the structure function in the proposed model facilitates its use for the parameterization of AOT statistics derived from remote sensing data. The new approach is illustrated using a 1-yr-long global MODIS AOT dataset (over ocean) with 10-km resolution. It was used to compute AOT statistics for sample cells forming a grid with 5° spacing. The observed shapes of the structure functions indicated that, in a large number of cases, the AOT variability is split into two regimes that exhibit different patterns of behavior: small-scale stationary processes and trends reflecting variations at larger scales. The small-scale patterns are suggested to be generated by local aerosols within the marine boundary layer, while the large-scale trends are indicative of elevated aerosols transported from remote continental sources. This assumption is evaluated by comparison of the geographical distributions of these patterns derived from MODIS data with those obtained from the GISS GCM. This study shows considerable potential to enhance comparisons between remote sensing datasets and climate models beyond regional mean AOTs.

scholarly journals The Interaction between Atmospheric Gravity Waves and Large-Scale Flows: An Efficient Description beyond the Nonacceleration Paradigm

2016 ◽  
Vol 73 (12) ◽  
pp. 4833-4852 ◽  
Author(s):  
Gergely Bölöni ◽  
Bruno Ribstein ◽  
Jewgenija Muraschko ◽  
Christine Sgoff ◽  
Junhong Wei ◽  
...  
Keyword(s):  
Steady State ◽  
Wave Breaking ◽  
Large Scale ◽  
Climate Models ◽  
Weather Prediction ◽  
Simple Wave ◽  
Mean Flow ◽  
Action Density ◽  
Total Energy Balance ◽  
Flow Interactions

Abstract With the aim of contributing to the improvement of subgrid-scale gravity wave (GW) parameterizations in numerical weather prediction and climate models, the comparative relevance in GW drag of direct GW–mean flow interactions and turbulent wave breakdown are investigated. Of equal interest is how well Wentzel–Kramer–Brillouin (WKB) theory can capture direct wave–mean flow interactions that are excluded by applying the steady-state approximation. WKB is implemented in a very efficient Lagrangian ray-tracing approach that considers wave-action density in phase space, thereby avoiding numerical instabilities due to caustics. It is supplemented by a simple wave-breaking scheme based on a static-instability saturation criterion. Idealized test cases of horizontally homogeneous GW packets are considered where wave-resolving large-eddy simulations (LESs) provide the reference. In all of these cases, the WKB simulations including direct GW–mean flow interactions already reproduce the LES data to a good accuracy without a wave-breaking scheme. The latter scheme provides a next-order correction that is useful for fully capturing the total energy balance between wave and mean flow. Moreover, a steady-state WKB implementation as used in present GW parameterizations where turbulence provides by the noninteraction paradigm, the only possibility to affect the mean flow, is much less able to yield reliable results. The GW energy is damped too strongly and induces an oversimplified mean flow. This argues for WKB approaches to GW parameterization that take wave transience into account.

scholarly journals Selective decay for the rotating shallow-water equations with a structure-preserving discretization

2021 ◽  
Vol 33 (11) ◽  
pp. 116604
Author(s):  
Rüdiger Brecht ◽  
Werner Bauer ◽  
Alexander Bihlo ◽  
François Gay-Balmaz ◽  
Scott MacLachlan
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Structure Preserving ◽  
Rotating Shallow Water ◽  
Selective Decay ◽  
Rotating Shallow Water Equations

scholarly journals Influence of condensation and latent heat release upon barotropic and baroclinic instabilities of vortices in rotating shallow water f -plane model

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Heat Release ◽  
Shallow Water ◽  
Latent Heat ◽  
Large Scale ◽  
Lower Layer ◽  
Passive Scalar ◽  
Water Model ◽  
Moist Convection ◽  
Latent Heat Release ◽  
Rotating Shallow Water

Analysis of the influence of condensation and related latent heat release upon developing barotropic and baroclinic instabilities of large-scale low Rossby-number shielded vortices on the f - plane is performed within the moist-convective rotating shallow water model, in its barotropic (one-layer) and baroclinic (two-layer) versions. Numerical simulations with a high-resolution well-balanced finite-volume code, using a relaxation parameterisation for condensation, are made. Evolution of the instability in four different environments, with humidity (i) behaving as passive scalar, (ii) subject to condensation beyond a saturation threshold, (iii) sub-ject to condensation and evaporation, with two different parameterisations of the latter, are inter-ompared.The simulations are initialised with unstable modes determined from the detailed linear stability analysis in the “dry” version of the model. In a configuration corresponding to low-level mid-latitude atmospheric vortices, it is shown that the known scenario of evolution of barotropically unstable vortices, consisting information of a pair of dipoles (“dipolar breakdown”) is substantially modified by condensation and related moist convection, especially in the presence of surface evaporation. No enhancement of the instability due to precipitation was detected in this case. Cyclone-anticyclone asymmetry with respect to sensitivity tothe moist effects is evidenced. It is shown that inertia-gravity wave emission during the vortex evolution is enhanced by the moist effects. In the baroclinic configuration corresponding to idealised cut-off lows in the atmosphere, it is shown that the azimuthal structure of the leading unstable mode is sensitive to the details of stratification. Scenarios of evolution are completely different for different azimuthal structures, one leading to dipolar breaking, and another to tripole formation. The effects of moisture considerably enhance the perturbations in the lower layer, especially in the tripole formation scenario.

Introduction

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Rotating Shallow Water

A brief introduction to the main philosophy of the book is given, explaining how the shallowness of large-scale motions in the atmosphere and ocean can be exploited in modelling, thus justifying the rotating shallow-water approach adopted throughout the book.

Sign in / Sign up

Export Citation Format

Share Document