Validating weather and climate models at small Rossby numbers: including a boundary layer

Beare, Robert J.; Cullen, Michael J.

doi:10.1002/qj.2852

Cited by 7 publications

(11 citation statements)

References 25 publications

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“…Equation (9) is only accurate to O( ) in the boundary layer, assuming h/H is independent of . As discussed in [26], it is more typical for h/H to decrease with ; that paper suggests h/H 0.7 . The SGT approximation to Equation (1) consists of Equations (8), (9) and…”

Section: The Sg Approximation To the Um Equationsmentioning

confidence: 93%

“…H is a typical boundary layer depth. This scaling is discussed in [26]. Since the aim is to apply the diagnostic procedure directly to model data, the subtraction of a basic state as in Equation (4) is not used.…”

Section: The Sg Approximation To the Um Equationsmentioning

confidence: 99%

“…Solving Equation (11) then involves inverting a N × N penta-diagonal matrix at each horizontal gridpoint, where N is the number of model levels and K m is nonzero. Next, use (u e , v e ) to evaluate the components of P 2 , Equation (26). Central differencing has to be used because the upwind direction is not known in advance.…”

Section: Computational Aspectsmentioning

confidence: 99%

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The Use of Semigeostrophic Theory to Diagnose the Behaviour of an Atmospheric GCM

Cullen

2018

Fluids

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A diagnostic method is presented for analysing the large-scale behaviour of the Met Office Unified Model, which is a comprehensive atmospheric model used for weather and climate prediction. Outside the boundary layer, on scales larger than the radius of deformation, semi-geostrophic theory will give an accurate approximation to the model evolution. In particular, the ageostrophic circulation required to maintain geostrophic and hydrostatic balance against prescribed forcing and a rate of change of the geostrophic pressure can be calculated. In the tropics, the balance condition degenerates to the weak temperature gradient approximation. Within the boundary layer, the semi-geotriptic approximation has to be used because friction and rotation are equally important. Assuming the calculated pressure tendency and ageotriptic circulation match the observed model behaviour, the influence of the large-scale state and the nature of the forcing on the model response can be deduced in a straightforward way. The capabilities of the diagnostic are illustrated by comparing predictions of the ageotriptic circulation from the theory and the model. It is then used to show that the effects of latent heat release can be included by modifying the static stability, and to show the effect of an idealised tropical heat source on the subtropical jet. Finally, the response of the ageotriptic flow to boundary layer heating in the tropics is demonstrated. These illustrations show that the model behaviour on large scales conforms with theoretical expectations, so that the results of the diagnostic can be used to aid the development of further improvements to the model, in particular investigating systematic errors and understanding the large-scale atmospheric response to forcing.

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Section: The Sg Approximation To the Um Equationsmentioning

confidence: 93%

Section: The Sg Approximation To the Um Equationsmentioning

confidence: 99%

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The Use of Semigeostrophic Theory to Diagnose the Behaviour of an Atmospheric GCM

Cullen

2018

Fluids

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“…These equations can be solved for u e , given that u e 5 u g at the top of the boundary layer and is zero at the ground. Beare and Cullen (2013) derive equations analogous to Eq. (A1) for the circulation required to maintain Ekman balance in time in the presence of dynamical and physical forcing.…”

Section: B Interaction Of the Boundary Layer With Balanced Dynamicsmentioning

confidence: 99%

Physics–Dynamics Coupling in Weather, Climate, and Earth System Models: Challenges and Recent Progress

Groß

Wan

Rasch

et al. 2018

Monthly Weather Review

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Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and microphysical processes. Typically, each component is developed, at least initially, independently. Once development is mature, the components are coupled to deliver a model of the required complexity. The implementation of the coupling can have a significant impact on the model. As the error associated with each component decreases, the errors introduced by the coupling will eventually dominate. Hence, any improvement in one of the components is unlikely to improve the performance of the overall system. The challenges associated with combining the components to create a coherent model are here termed physics–dynamics coupling. The issue goes beyond the coupling between the parameterizations and the resolved fluid dynamics. This paper highlights recent progress and some of the current challenges. It focuses on three objectives: to illustrate the phenomenology of the coupling problem with references to examples in the literature, to show how the problem can be analyzed, and to create awareness of the issue across the disciplines and specializations. The topics addressed are different ways of advancing full models in time, approaches to understanding the role of the coupling and evaluation of approaches, coupling ocean and atmosphere models, thermodynamic compatibility between model components, and emerging issues such as those that arise as model resolutions increase and/or models use variable resolutions.

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“…Example 1. In [2] the authors consider a system of equations modelling the behaviour of the atmospheric boundary layer, which served as our original motivation for the present study. In that model, n " 1, m " 3, Ω " p0, 1q, and the function K, referred to as a stability function, is defined as follows:…”

Section: Introductionmentioning

confidence: 99%

Numerical approximation of young-measure solutions to parabolic systems of forward-backward type

Caddick

Süli

2019

APPL ANAL DISCRETE M

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Dedicated to Academician Professor Gradimir Milovanović on the occasion of his 70th birthday. Miles Caddick and Endre SüliT his paper is concerned with the proof of existence and numerical approximation of large-data global-in-time Young measure solutions to initial-boundaryvalue problems for multidimensional nonlinear parabolic systems of forwardbackward type of the form Btu´divpapDuqq`Bu " F , where B P R mˆm , Bv¨v ě 0 for all v P R m , F is an m-component vector-function defined on a bounded open Lipschitz domain Ω Ă R n , and a is a locally Lipschitz mapping of the form apAq " KpAqA, where K : R mˆn Ñ R. The function a may have unequal lower and upper growth rates; it is not assumed to be monotone, nor is it assumed to be the gradient of a potential. We construct a numerical method for the approximate solution of problems in this class, and we prove its convergence to a Young measure solution of the system.

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Validating weather and climate models at small Rossby numbers: including a boundary layer

Cited by 7 publications

References 25 publications

The Use of Semigeostrophic Theory to Diagnose the Behaviour of an Atmospheric GCM

The Use of Semigeostrophic Theory to Diagnose the Behaviour of an Atmospheric GCM

Physics–Dynamics Coupling in Weather, Climate, and Earth System Models: Challenges and Recent Progress

Numerical approximation of young-measure solutions to parabolic systems of forward-backward type

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