Atmospheric Transport Schemes: Desirable Properties and a Semi-Lagrangian View on Finite-Volume Discretizations

Lauritzen, Peter H.; Ullrich, Paul A.; Nair, Ramachandran D.

doi:10.1007/978-3-642-11640-7_8

Cited by 50 publications

(61 citation statements)

References 83 publications

(61 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, we must be cautious with their application to the turbulent convective-scale regime (cf. Lauritzen et al 2011). Although some successful turbulent applications may be found in the literature, semiLagrangian schemes work most efficiently for a relatively laminar flow.…”

Section: Data Assimilationmentioning

confidence: 99%

Scientific Challenges of Convective-Scale Numerical Weather Prediction

Yano

Ziemiański²,

Cullen

et al. 2018

Bulletin of the American Meteorological Society

View full text Add to dashboard Buy / Rent full text

After extensive efforts over the course of a decade, convective-scale weather forecasts with horizontal grid spacings of 1–5 km are now operational at national weather services around the world, accompanied by ensemble prediction systems (EPSs). However, though already operational, the capacity of forecasts for this scale is still to be fully exploited by overcoming the fundamental difficulty in prediction: the fully three-dimensional and turbulent nature of the atmosphere. The prediction of this scale is totally different from that of the synoptic scale (103 km), with slowly evolving semigeostrophic dynamics and relatively long predictability on the order of a few days. Even theoretically, very little is understood about the convective scale compared to our extensive knowledge of the synoptic-scale weather regime as a partial differential equation system, as well as in terms of the fluid mechanics, predictability, uncertainties, and stochasticity. Furthermore, there is a requirement for a drastic modification of data assimilation methodologies, physics (e.g., microphysics), and parameterizations, as well as the numerics for use at the convective scale. We need to focus on more fundamental theoretical issues—the Liouville principle and Bayesian probability for probabilistic forecasts—and more fundamental turbulence research to provide robust numerics for the full variety of turbulent flows. The present essay reviews those basic theoretical challenges as comprehensibly as possible. The breadth of the problems that we face is a challenge in itself: an attempt to reduce these into a single critical agenda should be avoided.

show abstract

Section: Data Assimilationmentioning

confidence: 99%

Scientific Challenges of Convective-Scale Numerical Weather Prediction

Yano

Ziemiański²,

Cullen

et al. 2018

Bulletin of the American Meteorological Society

View full text Add to dashboard Buy / Rent full text

show abstract

“…A number of desirable properties for numerical schemes solving the continuity and other prognostic equations have been identified (e.g., Rasch and Williamson, 1990;Schär and Smolarkiewicz, 1996;Lin and Rood, 1996;Jöckel et al, 2001;Lauritzen et al, 2011). These deal with 1.…”

Section: Desirable Propertiesmentioning

confidence: 99%

A hybrid Eulerian–Lagrangian numerical scheme for solving prognostic equations in fluid dynamics

Kaas

Sørensen

Lauritzen³

et al. 2013

Geosci. Model Dev.

View full text Add to dashboard Buy / Rent full text

Abstract.A new hybrid Eulerian-Lagrangian numerical scheme (HEL) for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables.The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow.The time stepping in Eulerian representation is achieved in two steps: first a mass-conserving Eulerian or semiLagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space.The HEL scheme has been designed to be accurate, multitracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place; i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely.The properties of HEL are here verified in twodimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.

show abstract

“…Horizontal tracer mass fluxes are derived using the horizontal wind field. The vertical velocity ω FFSL used in the FFSL tracer transport is derived from the continuity equation for the tracer from the horizontal tracer mass fluxes for individual model grid boxes (Lin, 2004;Lauritzen et al, 2011). This vertical velocity ω FFSL differs from the vertical velocity ω spec deduced from the wind field, since different advection schemes are used for the air-mass density and for trace gases: the spectral advection is used for air-mass density, whereas the grid-pointbased FFSL transport is used for the tracers.…”

Section: Kinematic Vertical Velocitymentioning

confidence: 99%

“…The internal grid in the FFSL transport module differs from the η-grid in ECHAM5: it is variable in the vertical dimension and fixed in the horizontal dimensions. This concept is denoted as "vertically Lagrangian" (Lin, 2004) or "floating Lagrangian vertical coordinate" (Lauritzen et al, 2011). In each advection time step, horizontal mass fluxes through the lateral boundaries are calculated for each grid box.…”

Section: Kinematic Vertical Velocitymentioning

confidence: 99%

Kinematic and diabatic vertical velocity climatologies from a chemistry climate model

et al. 2016

View full text Add to dashboard Buy / Rent full text

Abstract. The representation of vertical velocity in chemistry climate models is a key element for the representation of the large-scale Brewer-Dobson circulation in the stratosphere. Here, we diagnose and compare the kinematic and diabatic vertical velocities in the ECHAM/Modular Earth Submodel System (MESSy) Atmospheric Chemistry (EMAC) model. The calculation of kinematic vertical velocity is based on the continuity equation, whereas diabatic vertical velocity is computed using diabatic heating rates. Annual and monthly zonal mean climatologies of vertical velocity from a 10-year simulation are provided for both kinematic and diabatic vertical velocity representations. In general, both vertical velocity patterns show the main features of the stratospheric circulation, namely, upwelling at low latitudes and downwelling at high latitudes. The main difference in the vertical velocity pattern is a more uniform structure for diabatic and a noisier structure for kinematic vertical velocity. Diabatic vertical velocities show higher absolute values both in the upwelling branch in the inner tropics and in the downwelling regions in the polar vortices. Further, there is a latitudinal shift of the tropical upwelling branch in boreal summer between the two vertical velocity representations with the tropical upwelling region in the diabatic representation shifted southward compared to the kinematic case. Furthermore, we present mean age of air climatologies from two transport schemes in EMAC using these different vertical velocities and analyze the impact of residual circulation and mixing processes on the age of air. The age of air distributions show a hemispheric difference pattern in the stratosphere with younger air in the Southern Hemisphere and older air in the Northern Hemisphere using the transport scheme with diabatic vertical velocities. Further, the age of air climatology from the transport scheme using diabatic vertical velocities shows a younger mean age of air in the inner tropical upwelling branch and an older mean age in the extratropical tropopause region.

show abstract

Atmospheric Transport Schemes: Desirable Properties and a Semi-Lagrangian View on Finite-Volume Discretizations

Cited by 50 publications

References 83 publications

Scientific Challenges of Convective-Scale Numerical Weather Prediction

Scientific Challenges of Convective-Scale Numerical Weather Prediction

A hybrid Eulerian–Lagrangian numerical scheme for solving prognostic equations in fluid dynamics

Kinematic and diabatic vertical velocity climatologies from a chemistry climate model

Contact Info

Product

Resources

About