• Behrens, J., 1996: An adaptive semi-Lagrangian advection scheme and its parallelization. Mon. Wea. Rev.,124, 2386–2395.

  • ——, 1998: Atmospheric and ocean modeling with an adaptive finite element solver for the shallow-water equations. Appl. Numer. Math.,26, 217–226.

  • Bregman, A., and Coauthors, 1995: Aircraft measurements of O3, HNO3, and N2O in the winter arctic lower stratosphere during the Stratosphere–Troposphere Experiment by Aircraft Measurements (STREAM) 1. J. Geophys. Res.,100, 11 245–11 260.

  • Dethloff, K., A. Rinke, R. Lehmann, J. H. Christensen, M. Botzet, and B. Machenhauer, 1996: Regional climate model of the Arctic atmosphere. J. Geophys. Res.,101, 23 401–23 422.

  • Dritschel, D. G., and M. H. P. Ambaum, 1997: A contour-advection semi-Lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields. Quart. J. Roy. Meteor. Soc.,123, 1097–1130.

  • Edouard, S., B. Legras, F. Lefèvre, and R. Eymard, 1996: The effect of small-scale inhomogeneities on ozone depletion in the Arctic. Nature,384, 444–447.

  • Haynes, P., and J. Anglade, 1997: The vertical-scale cascade in atmospheric tracers due to large-scale differential advection. J. Atmos. Sci.,54, 1121–1136.

  • Machenhauer, B. and M. Olk, 1997: The implementation of the semi-implicit scheme in cell-integrated semi-Lagrangian models. Numerical Methods in Atmospheric and Oceanic Modelling—The Andre J. Robert Memorial Volume, C. Lin, R. Laprise, and H. Ritchie, Eds., CMOS/NRC Research Press, 103–126.

  • Orsolini, Y., P. Simon, and D. Cariolle, 1995: Filamentation and layering of an idealized tracer by observed winds in the lower stratosphere. Geophys. Res. Lett.,22, 839–842.

  • Plumb, R. A., and Coauthors, 1994: Intrusions into the lower stratospheric Arctic vortex during the winter of 1991–1992. J. Geophys. Res.,99, 1089–1105.

  • Rinke, A., K. Dethloff, and J. H. Christensen, 1999: Arctic winter climate and its interannual variation simulated by a regional climate model. J. Geophys. Res.,104, 19 027–19 038.

  • Searle, K. R., M. P. Chipperfield, S. Bekki, and J. A. Pyle, 1998: The impact of spatial averaging on calculated polar ozone loss: 1. Model experiments. J. Geophys. Res.,103, 25 397–25 408.

  • Staniforth, A., and J. Côté, 1991: Semi-Lagrangian integration schemes for atmospheric models—A review. Mon. Wea. Rev.,119, 2206–2223.

  • Verfürth, R., 1993: A posteriori error estimators and adaptive mesh-refinement techniques for the Navier–Stokes equations. Incompressible Computational Fluid Dynamics Trends and Advances, M. D. Gunzenburger and R. A. Nicolaides, Eds., Cambridge University Press, 447–475.

  • Waugh, D. W., and R. A. Plumb, 1994: Contour advection with surgery: A technique for investigating finescale structure in tracer transport. J. Atmos. Sci.,51, 530–540.

  • ——, and Coauthors, 1994: Transport out of the lower stratospheric arctic vortex by Rossby wave breaking. J. Geophys. Res.,99, 1071–1088.

  • View in gallery

    Jan monthly mean geopotential (m) for the Arctic, simulated in HIRHAM for 1990.

  • View in gallery

    Adaptively refined grid, corresponding to the situation in Fig. 7.

  • View in gallery

    Initial configuration for the model problem with a circular wind field.

  • View in gallery

    Result of the advection with the model problem after some hours of model time. With high (local) resolution, fine structures are visible (left) while numerical dissipation has led to heavy erosion with coarse (global) grid resolution (right). Note that the total mass of the tracer is conserved in both cases.

  • View in gallery

    Initial tracer distribution for the experiments.

  • View in gallery

    Tracer concentration after 288 h of model time, using highly resolved wind data on a grid of 110 × 100 grid points (left), vs low-resolution 22 × 20 grid points (right).

  • View in gallery

    Tracer concentration after 288 h of model time, calculated on a uniform grid with approx 55-km resolution (top, left), and calculated on an adaptive grid with approx 20 km (top, right), 10-km (bottom, left), and 5-km (bottom, right) resolution, respectively.

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Evolution of Small-Scale Filaments in an Adaptive Advection Model for Idealized Tracer Transport

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  • 1 Center of Mathematical Sciences, Munich University of Technology, Munich, Germany,
  • | 2 Alfred Wegener Institute for Polar and Marine Research, Potsdam, Germany
  • | 3 Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany
  • | 4 Alfred Wegener Institute for Polar and Marine Research, Potsdam, Germany
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Abstract

The formation of small-scale filaments in a novel two-dimensional adaptive tracer transport model is investigated. The numerical model is based on a semi-Lagrangian advection scheme, and an adaptively and locally refined triangular mesh. The adaptive modeling approach allows very high local resolution, showing fine-grained filamentation under the influence of gradients in the wind field. Wind data for the tracer transport experiment are taken from the high-resolution regional climate model for the Arctic atmosphere, HIRHAM. The influence of horizontal advection model resolution and varying wind data resolution has been investigated.

Corresponding author address: Dr. Jorn Behrens, Munich University of Technology, D-80290 Munich, Germany.

Email: behrens@mathematik.tu-muenchen.de

Abstract

The formation of small-scale filaments in a novel two-dimensional adaptive tracer transport model is investigated. The numerical model is based on a semi-Lagrangian advection scheme, and an adaptively and locally refined triangular mesh. The adaptive modeling approach allows very high local resolution, showing fine-grained filamentation under the influence of gradients in the wind field. Wind data for the tracer transport experiment are taken from the high-resolution regional climate model for the Arctic atmosphere, HIRHAM. The influence of horizontal advection model resolution and varying wind data resolution has been investigated.

Corresponding author address: Dr. Jorn Behrens, Munich University of Technology, D-80290 Munich, Germany.

Email: behrens@mathematik.tu-muenchen.de

1. Introduction

The perturbed chemistry within the polar stratospheric vortex has generated great interest in the respective dynamics. The atmospheric distribution of trace constituents in the lower stratosphere not only depends on chemical sources and sinks but also on the redistribution as a result of transport, induced by various dynamical processes (Waugh et al. 1994).

The quasi-horizontal dispersion of a passive tracer on synoptic timescales is likely to occur through the formation of tracer filaments in the presence of a background wind shear. Plumb et al. (1994) showed that fine structures seen in aircraft data coincide with filamentary structures produced by a contour advection model. Edouard et al. (1996) claim that the ozone depletion depends on the resolution of the model, as small-scale structures influence the local depletion rate. These results have been questioned in (Searle et al. 1998). We do not take sides in this dispute, because we do not study the total reduction of ozone concentration. However, even in the latter study one can observe from the figures (e.g., Fig. 1) that higher horizontal resolution causes great differences in the local distribution of constituents. The scale cascade of tracers under the influence of shear and strain has also been investigated in detail by Haynes and Anglade (1997).

Bregman et al. (1995) carried out in situ measurements of the trace gases O3, HNO3, and N2O in the Arctic lower stratosphere during February 1993 on board a Cessna Citation aircraft during the first Stratosphere–Troposphere Experiment by Aircraft measurements campaign. Strong variations in the concentrations and distributions of these trace gases were found. The time series with a resolution of minutes showed pronounced small-scale variations and large horizontal variations in the range of some dozen kilometers, indicating that the aircraft flew through air masses with different origins. Unfortunately these data do not allow the identification of horizontal scales below some dozen kilometers.

The horizontal resolution required for the reproduction of filaments cannot be achieved by general circulation models to date. Most approaches, therefore, use offline chemistry transport models with high local resolution. However, even these offline models often do not reach down to horizontal scales, sufficient for the resolution of fine filaments. When attempting to model filamental structures, most other investigators use contour advection models (see Dritschel and Ambaum 1997 for a description).

In this study, we adopt an adaptive modeling technique, developed in Behrens (1996 1998), in order to achieve very high local resolution. More precisely, the offline tracer transport model can be refined to an arbitrarily high local resolution (we go as far as approx 5 km here). This is done automatically by the adaptive algorithm at locations where finescale structures are observed.

We consider the horizontal transport of a conserved passive tracer in the lower polar stratosphere in an idealised configuration, using the wind components from a high-resolution regional climate model (HIRHAM). HIRHAM is a sophisticated climate model, which resolves the Arctic region with a horizontal resolution of 0.5°. It is forced at the lateral and lower boundaries by European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data. We state that wind data, taken for the tracer transport, are at least state of the art, regarding resolution, subgrid-scale parametrization, and quality (Dethloff et al. 1996; Rinke et al. 1999). Other studies used driving wind data of far lower resolution. Orsolini et al. (1995) used a global model with horizontal resolution in the advecting winds of about 1.125° while Edouard et al. (1996) used data with a resolution of about 2.8°

Three main aspects are investigated. First, we examine the influence of varying resolution of wind data. While this has been studied extensively in Waugh and Plumb (1994), we give some experience of our experiments. Moreover, we try to illustrate the applicability of very high resolution advection to coarse-resolution wind data, by a simple model problem. Finally, the influence of varying horizontal resolution of the transport model on the formation of small-scale filamental structures is studied.

This study is of methodological character. We do not claim that our simulated results represent measured realistic situations. This is not possible yet, because a passive conserved tracer without chemistry is simulated. An artificial initial concentration distribution is used, which by no means has anything to do with reality. However, the components of our investigation are chosen to be the best possible: wind data are highly accurate, representing the dynamical system of the Arctic atmosphere, and a locally refined conservative model for the tracer transport simulation is used. So we have good reason to believe that in a future investigation, including measured initial tracer distributions and chemical reaction models, realistic high-resolution results can be produced.

The next section describes briefly the HIRHAM model and experiment. The adaptive model is described in section 3. Section 4 treats the experiments and the corresponding results in detail. Finally we draw some conclusions.

2. High-resolution model of the arctic atmosphere

In this section the model delivering the driving wind data for our very high resolution tracer transport simulations is described. Global circulation models (GCMs) cannot capture mesoscale features caused for example by coastlines, ice sheets, and mountains, due to limitations to the horizontal resolution. However, the horizontal resolution can be increased up to the mesoscale over a limited area of interest by nesting a regional model into either a global model or data analyses.

This is the philosophy of the regional climate model HIRHAM. HIRHAM applies the primitive equations. Prognostic variables are the horizontal wind components, temperature, specific humidity, surface pressure, and liquid water content. The integration domain covers the whole Arctic north of approximately 65°N with a horizontal resolution of 0.5° × 0.5°. It has been formulated in hybrid vertical coordinates, which reduce to terrain-following sigma coordinates near the surface and pressure coordinates at the top of the atmosphere. The vertical resolution of the model uses 19 levels with 5 levels in the lower stratosphere and the upper level at 10 hPa. Centered second-order-accurate finite differences and a semi-implicit time step of 300 s have been used. The lateral boundaries are supplied by ECMWF analyses updated every 6 h at 1.5° × 1.5° horizontal resolution and 19 vertical levels. A linear fourth-order horizontal diffusion scheme on model levels has been applied. The model closely reproduces the observed monthly mean circulation patterns in the tropopause and the lower stratosphere, as shown in Dethloff et al. (1996) and Rinke et al. (1999). The simulated geopotential structure at 73.4 hPa (we call this the 70-hPa layer) during January 1990, with a cold low, is presented in Fig. 1, well known as Polar Vortex with in our situation two centers, one north of Greenland the other southeast of Novaya Zemlya. We performed some experiments with wind data representing other years and found no principal differences from the results presented here. However we omit the discussion of other situations, because we want to focus on the methodological properties of the adaptive scheme.

In section 4 the transport of a passive tracer at 73.4 hPa in the vortex is analyzed. This corresponds to an altitude of 18 km and a potential temperature of 420 K and represents the center of layer 4 of HIRHAM. The wind field reproduces the situation in January 1990. Because stratospheric motion is thought to be constrained largely within horizontal layers, down to scales of 1–10 km where three-dimensional motion is expected to dominate, we use a two-dimensional horizontal transport scheme here. Wind data represent the (u, υ) values in the mentioned layer of the three-dimensional HIRHAM model. We believe these are “best possible” choices among the available wind fields for the lower stratosphere of the Arctic.

3. Adaptive tracer transport model

For the experiments, described in section 4, we use an adaptive tracer transport model. While a detailed description of the basic model ideas can be found in Behrens (1996), we give a brief overview here. The model solves the advection equation in two dimensions:
i1520-0493-128-8-2976-EQ1
The wind u = u(x, y, t) is given by the HIRHAM data (cf. section 2). Here, R = R(x, y, t) is the right-hand side of (1), which can contain additional forces but is set to zero in our case (i.e., we simulate the advection of an idealized passive tracer without diffusion and without other sources and sinks). In addition, C = C(x, y, t) denotes the (scalar) concentration of the tracer, while (x, y, t) is the space–time coordinate.

The time-dependent part of the equations is discretized by the semi-Lagrangian method, which has been reviewed in Staniforth and Côté (1991). Spatial discretization is implemented by means of a finite-element-like representation of the scalar functions.

An adaptive grid generator refines the triangular grid down to a lower bound, where the gradient of the tracer concentration C is large. On the other hand, in regions where C is small, the grid is coarsened up to an upper bound. To formulate it mathematically, for each grid element Ti we calculate the local gradient C|Ti of the concentration. Let max = maxi(C|Ti) denote the maximum of these local gradients. Then, a grid element is refined (one level unless it has reached the preset finest level), if C|Ti > θrefmax, where θref (0 ⩽ θref ⩽ 1) is a given tolerance. The obvious analogous algorithm is applied for the coarsening with a tolerance θcrs. We set θref = 0.2 and θcrs = 0.1. Table 1 gives the level of refinement and the corresponding horizonal grid resolution used in the experiments. In all cases, the coarsest level is set to 4.

One should keep in mind that this error indicator is very simple and should not be used in cases where more complex phemomena are to be modeled. A good introduction to error estimation can be found in, for example, Verfürth (1993). With this mechanism, we achieve very high local resolution without exhausting limited computing resources. An example of an adaptively refined grid is given in Fig. 2.

The model uses a cell-integrated semi-Lagrangian interpolation scheme, originally introduced in Machenhauer and Olk (1997). It is adapted to triangular unstructured grids. Upstream values are not only interpolated at grid points, but the integral of the upstream valued function is promoted to the downstream grid. This results in a better representation of accumulation or dispersion of tracer mass in convergent or divergent flow fields, respectively, compared to standard semi-Lagrangian interpolation schemes.

4. Experiments and results

In this section we try to answer three main questions. The first one is of rather philosophical character, as we ask: why can we see small-scale filaments in the tracer advection when these structures are not present (due to coarse resolution) in the driving wind data?1 There are other more in-depth investigations of this question (Plumb et al. 1994; Haynes and Anglade 1997); however we decided to take this example into consideration because of its simple and instructive character. The more practical aspects of our investigation will analyze the influence of resolution of wind data and model resolution to the formation of small-scale structures.

a. Influence of wind gradient

In order to explore the first question, let us think of a simplified example: let u in (1) be a constant circular wind with decreasing velocity toward the boundary, acting in a closed box: u(x, y) = [u(x, y), υ(x, y)] ≡ [−y · d, x · d], where d ≡ 4 · ‖(xcenter, ycenter) − |(x, y)|‖2. Let the initial concentration distribution be given by a rectangle with concentration 1 and 0 everywhere else (see Fig. 3). After advecting this configuration for some time, one will observe the formation of small-scale stirring in the transport model, while obviously no dynamical features are present in the underlying data. These small-scale structures are caused by the presence of a gradient in the wind field acting orthogonally to the gradient of the concentration. In general, whenever a gradient in the wind field is nontangential to the gradient of the concentration, stirring will occur. If this process can be resolved fine enough by the transport scheme, we will see small-scale filamentation. On the other hand, if resolution is too coarse, filaments will not be visible due to numerical dissipation (see Fig. 4).

It is therefore reasonable to use a very high resolution tracer transport scheme with high-resolution data. The wind data contain subgrid-scale information, due to parameterized phenomena. The shape of the wind field is influenced by these parameterizations, resulting in filamentation by the above-mentioned interaction of gradients.

b. Influence of wind data resolution

In order to determine the influence of data resolution (i.e., the resolution of the given wind field) to the formation of small-scale filaments, wind data are given on grids of 110 × 100, 55 × 50, and 22 × 20 grid points, respectively. This corresponds to a mesh size of approximately 50, 100, and 250 km, respectively (or approx 0.5° × 0.5°, 1° × 1°, and 2.5° × 2.5° respectively). Minimal mesh size of the transport model is set to approximately 10 km. Here and in all the following experiments, the tracer concentration is initialized as shown in Fig. 5. This position corresponds to the left “eye” of the Arctic polar vortex in January 1990.

Compared to the reference case (110 × 100 data points), the 55 × 50 gridpoint case shows no significant changes. However, reducing the data field to only 22 × 20 points results in a different behavior. On the one hand, wind structure is slightly different, resulting in a displaced path of the transport. On the other hand, a more interesting behavior, namely the formation of small-scale filaments, is deteriorated. When comparing both plots in Fig. 6, one observes that fine mixing structures are present only in the high-resolution case.

Note that interpolation of the wind dataset to the computational grid of the very high resolution transport model is a problem in itself. We tried bilinear and biquadratic interpolation and found no significant difference. The experiments shown in this study use bilinear interpolation for efficiency and shape-preserving reasons. This is in accordance with the choice in the contour advection simulations in Waugh and Plumb (1994).

c. Influence of model resolution

The next series of experiments aims at determining a necessary calculation grid resolution for the formation of small-scale filaments. Wind data are taken from the high-resolution dataset (i.e., 110 × 100 data points). The first case uses a uniformly refined grid with a resolution of approximately 55 km. This is almost the resolution of the given dataset. Three additional model configurations are probed with local resolutions of approximately 20, 10, and 5 km, respectively. Note that all of these high-resolution tracer advection simulations can be calculated on a standard workstation due to the adaptive refinement strategy.

As one would expect, finer resolution causes finer structures in the tracer concentration function. Figure 7 shows the tracer concentration for the different resolutions. While there are more and more second-order filamentations visible, the main path and structure of the tracer field remain unchanged when increasing the resolution.

5. Conclusions

The main result of our study is that adaptive modeling is a very powerful means for high-resolution tracer transport simulations. We were able to calculate the tracer transport with 5-km local resolution for 1 month of model time on a 100 Mflop s−1 capable workstation with 196 MB of main memory within approximately 8 h. At this high resolution small-scale filaments are visible, which up to now could not be resolved by models based on uniform grids, due to the limited computational resources.

Although the formation of small-scale filaments depends only on the presence of gradients in the wind field (which can be embodied in coarsely resolved wind data) we recommend taking the best (i.e., highest resolution) data available for future experiments. A too coarse resolution in the wind data can deteriorate the formation of small structures.

This study only gives some hints on possible real-life phenomena. In order to simulate real tracer transport over the Arctic within the framework of HIRHAM data, it would be desirable to perform the offline transport modeling with a 3D adaptive model. It is intended to develop a 3D model in the near future. Additionally, for realistic simulations a chemical module and measured initial concentration distribution is required.

Acknowledgments

The authors thank the anonymous reviewers for their helpful hints and suggestions.

REFERENCES

  • Behrens, J., 1996: An adaptive semi-Lagrangian advection scheme and its parallelization. Mon. Wea. Rev.,124, 2386–2395.

  • ——, 1998: Atmospheric and ocean modeling with an adaptive finite element solver for the shallow-water equations. Appl. Numer. Math.,26, 217–226.

  • Bregman, A., and Coauthors, 1995: Aircraft measurements of O3, HNO3, and N2O in the winter arctic lower stratosphere during the Stratosphere–Troposphere Experiment by Aircraft Measurements (STREAM) 1. J. Geophys. Res.,100, 11 245–11 260.

  • Dethloff, K., A. Rinke, R. Lehmann, J. H. Christensen, M. Botzet, and B. Machenhauer, 1996: Regional climate model of the Arctic atmosphere. J. Geophys. Res.,101, 23 401–23 422.

  • Dritschel, D. G., and M. H. P. Ambaum, 1997: A contour-advection semi-Lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields. Quart. J. Roy. Meteor. Soc.,123, 1097–1130.

  • Edouard, S., B. Legras, F. Lefèvre, and R. Eymard, 1996: The effect of small-scale inhomogeneities on ozone depletion in the Arctic. Nature,384, 444–447.

  • Haynes, P., and J. Anglade, 1997: The vertical-scale cascade in atmospheric tracers due to large-scale differential advection. J. Atmos. Sci.,54, 1121–1136.

  • Machenhauer, B. and M. Olk, 1997: The implementation of the semi-implicit scheme in cell-integrated semi-Lagrangian models. Numerical Methods in Atmospheric and Oceanic Modelling—The Andre J. Robert Memorial Volume, C. Lin, R. Laprise, and H. Ritchie, Eds., CMOS/NRC Research Press, 103–126.

  • Orsolini, Y., P. Simon, and D. Cariolle, 1995: Filamentation and layering of an idealized tracer by observed winds in the lower stratosphere. Geophys. Res. Lett.,22, 839–842.

  • Plumb, R. A., and Coauthors, 1994: Intrusions into the lower stratospheric Arctic vortex during the winter of 1991–1992. J. Geophys. Res.,99, 1089–1105.

  • Rinke, A., K. Dethloff, and J. H. Christensen, 1999: Arctic winter climate and its interannual variation simulated by a regional climate model. J. Geophys. Res.,104, 19 027–19 038.

  • Searle, K. R., M. P. Chipperfield, S. Bekki, and J. A. Pyle, 1998: The impact of spatial averaging on calculated polar ozone loss: 1. Model experiments. J. Geophys. Res.,103, 25 397–25 408.

  • Staniforth, A., and J. Côté, 1991: Semi-Lagrangian integration schemes for atmospheric models—A review. Mon. Wea. Rev.,119, 2206–2223.

  • Verfürth, R., 1993: A posteriori error estimators and adaptive mesh-refinement techniques for the Navier–Stokes equations. Incompressible Computational Fluid Dynamics Trends and Advances, M. D. Gunzenburger and R. A. Nicolaides, Eds., Cambridge University Press, 447–475.

  • Waugh, D. W., and R. A. Plumb, 1994: Contour advection with surgery: A technique for investigating finescale structure in tracer transport. J. Atmos. Sci.,51, 530–540.

  • ——, and Coauthors, 1994: Transport out of the lower stratospheric arctic vortex by Rossby wave breaking. J. Geophys. Res.,99, 1071–1088.

Fig. 1.
Fig. 1.

Jan monthly mean geopotential (m) for the Arctic, simulated in HIRHAM for 1990.

Citation: Monthly Weather Review 128, 8; 10.1175/1520-0493(2000)128<2976:EOSSFI>2.0.CO;2

Fig. 2.
Fig. 2.

Adaptively refined grid, corresponding to the situation in Fig. 7.

Citation: Monthly Weather Review 128, 8; 10.1175/1520-0493(2000)128<2976:EOSSFI>2.0.CO;2

Fig. 3.
Fig. 3.

Initial configuration for the model problem with a circular wind field.

Citation: Monthly Weather Review 128, 8; 10.1175/1520-0493(2000)128<2976:EOSSFI>2.0.CO;2

Fig. 4.
Fig. 4.

Result of the advection with the model problem after some hours of model time. With high (local) resolution, fine structures are visible (left) while numerical dissipation has led to heavy erosion with coarse (global) grid resolution (right). Note that the total mass of the tracer is conserved in both cases.

Citation: Monthly Weather Review 128, 8; 10.1175/1520-0493(2000)128<2976:EOSSFI>2.0.CO;2

Fig. 5.
Fig. 5.

Initial tracer distribution for the experiments.

Citation: Monthly Weather Review 128, 8; 10.1175/1520-0493(2000)128<2976:EOSSFI>2.0.CO;2

Fig. 6.
Fig. 6.

Tracer concentration after 288 h of model time, using highly resolved wind data on a grid of 110 × 100 grid points (left), vs low-resolution 22 × 20 grid points (right).

Citation: Monthly Weather Review 128, 8; 10.1175/1520-0493(2000)128<2976:EOSSFI>2.0.CO;2

Fig. 7.
Fig. 7.

Tracer concentration after 288 h of model time, calculated on a uniform grid with approx 55-km resolution (top, left), and calculated on an adaptive grid with approx 20 km (top, right), 10-km (bottom, left), and 5-km (bottom, right) resolution, respectively.

Citation: Monthly Weather Review 128, 8; 10.1175/1520-0493(2000)128<2976:EOSSFI>2.0.CO;2

Table 1.

Highest local grid resolution and corresponding refinement level for the adaptive simulation.

Table 1.

1

In fact, subgrid features are present in the wind data as they are parameterized in the underlying model and thus contribute to the shape of the wind field!

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