• Grell, G. A., 1993: Prognostic evaluation of assumptions used by cumulus parameterizations. Mon. Wea. Rev, 121 , 764787.

  • Grell, G. A., , J. Dudhia, , and D. R. Stauffer, 1995: A description of the fifth-generation Penn State/NCAR Mesoscale Model (MM5). NCAR Tech. Note NCAR/TN-398 + STR, 122 pp.

    • Search Google Scholar
    • Export Citation
  • Guo, Y-R., , and S. Chen, 1994: Terrain and land use for the fifth-generation Penn State/NCAR mesoscale modeling system (MM5): Program TERRAIN. NCAR Tech. Note NCAR/TN-397 + IA, 114 pp.

    • Search Google Scholar
    • Export Citation
  • Hoinka, K. P., , E. Richard, , G. Poberaj, , R. Busen, , J. L. Caccia, , A. Fix, , and H. Mannstein, 2003: Analysis of a potential vorticity streamer crossing the Alps during MAP IOP-15 on November 1999. Quart. J. Roy. Meteor. Soc, 129 , 609632.

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    • Export Citation
  • Klemp, J. B., , and D. R. Durran, 1983: An upper boundary condition permitting internal gravity wave radiation in numerical mesoscale models. Mon. Wea. Rev, 111 , 430444.

    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J., , S. J. Taubman, , P. D. Brown, , M. J. Iacono, , and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmosphere: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res, 102 , 1666316682.

    • Search Google Scholar
    • Export Citation
  • Reisner, J., , R. M. Rasmussen, , and R. T. Bruintjes, 1998: Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Quart. J. Roy. Meteor. Soc, 124 , 10711107.

    • Search Google Scholar
    • Export Citation
  • Schär, C., , D. Leuenberger, , O. Fuhrer, , D. Lüthi, , and C. Girard, 2002: A new terrain-following vertical coordinate formulation for atmospheric prediction models. Mon. Wea. Rev, 130 , 24592480.

    • Search Google Scholar
    • Export Citation
  • Shafran, P. C., , N. L. Seaman, , and G. A. Gayno, 2000: Evaluation of numerical predictions of boundary layer structure during the Lake Michigan Ozone Study (LMOS). J. Appl. Meteor, 39 , 412426.

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    • Export Citation
  • Zängl, G., 2002a: Stratified flow over a mountain with a gap: Linear theory and numerical simulations. Quart. J. Roy. Meteor. Soc, 128 , 927949.

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  • Zängl, G., 2002b: An improved method for computing horizontal diffusion in a sigma-coordinate model and its application to simulations over mountainous topography. Mon. Wea. Rev, 130 , 14231432.

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    • Export Citation
  • Zängl, G., 2003: A generalized sigma coordinate system for the MM5. Mon. Wea. Rev, 131 , 28752884.

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    MM5 results at a pressure level of 250 hPa valid at 1500 UTC 6 Nov 1999: (left) Results of the VC1 run, using the original vertical coordinate, and (right) results of the VC2 run, using the modified vertical coordinate. (a), (b) PV (contour interval is 2 PVU); (c), (d) potential temperature (contour interval is 2 K); and (e), (f) relative vorticity (contour interval is 5 × 10−5 s−1). The shaded area indicates the Alps for heights larger than 800 m. In (c) and (d) the model topography is also contoured with an increment of 400 m

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    MM5-simulated PV (contour interval is 2 PVU) at various pressure levels at 1500 UTC 6 Nov 1999, applying (a), (c), (e) the standard terrain-following coordinate system VC1 and (b), (d), (f) the modified system VC2. The shaded area indicates the Alps for heights larger than 800 m

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    MM5-simulated water vapor mixing ratio (contour interval is 50 ppmv) and horizontal wind at 325 hPa at 1400 UTC 6 Nov 1999, performed with (a) the standard terrain-following coordinate system VC1 and (b) the modified system VC2. The shaded area indicates mixing ratios below 150 ppmv

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    MM5-simulated vertical wind (contour interval is 0.5 m s−1) at 250 hPa at 1500 UTC 6 Nov 1999 applying (a) the standard terrain-following coordinate system VC1 and (b) the modified system VC2. Shaded areas indicate negative vertical velocities. The dashed line in (a) shows the baseline of the cross section given in Fig. 5

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    MM5-simulated θ (contour interval is 2 K) and w (contour interval is 0.25 m s−1) at 1500 UTC 6 Nov 1999 for (a) the standard terrain-following system VC1 and (c) the modified system VC2; isolines show θ; the shaded area indicates negative vertical velocity. The difference fields VC1 − VC2 are given for (b) θ (contour interval is 1 K) and (d) w (contour interval is 0.25 m s−1). (e) The orography; the baseline of the cross section is indicated in Fig. 4a

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    (a) Vertical velocity measured by the aircraft along the flight track at 45°N between 1440 and 1600 UTC (full line) 6 Nov 1999 after applying a running mean of 50 s or 10 km to the original data. The bold dotted line indicates the simulated vertical velocity using the standard terrain-following system (VC1), and the bold full line shows the result using the modified system (VC2). (b) The orography; the baseline of the track is given in Fig. 4a

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The Influence of the Vertical Coordinate on Simulations of a PV Streamer Crossing the Alps

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  • 1 Institut für Physik der Atmosphäre, DLR, Wessling, Germany
  • | 2 Meteorologisches Institut, Universität München, Munich, Germany
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Abstract

In this note the impact of the vertical coordinate system on upper-tropospheric and lower-stratospheric structures is studied using the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5). Two different simulations are compared. One uses the original sigma coordinate, and the second one uses a modified coordinate system having smoother coordinate surfaces in the free atmosphere. Fields of atmospheric variables, such as wind and temperature, show only a weak signal related to the vertical coordinate system. However, diagnostic quantities involving horizontal and vertical derivatives react very sensitively to the vertical coordinate. The results indicate that, in the presence of steep topography, a meaningful computation of the potential vorticity (PV) field in the tropopause region is possible with the modified coordinate system only. This is mainly because disturbances in the horizontal wind field that appear at first sight unimportant induce large errors in the relative vorticity field with the original coordinate system. In addition, the simulation with the original coordinate indicates a spurious moisture transport across the tropopause above the orography. On the other hand, the impact of the coordinate system on the structure and the amplitude of orographic gravity waves turns out to be quite small.

Corresponding author address: K. P. Hoinka, Institut für Physik der Atmosphäre, DLR, Postfach 1116, D-82230 Wessling, Germany. Email: klaus.hoinka@dlr.de

Abstract

In this note the impact of the vertical coordinate system on upper-tropospheric and lower-stratospheric structures is studied using the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5). Two different simulations are compared. One uses the original sigma coordinate, and the second one uses a modified coordinate system having smoother coordinate surfaces in the free atmosphere. Fields of atmospheric variables, such as wind and temperature, show only a weak signal related to the vertical coordinate system. However, diagnostic quantities involving horizontal and vertical derivatives react very sensitively to the vertical coordinate. The results indicate that, in the presence of steep topography, a meaningful computation of the potential vorticity (PV) field in the tropopause region is possible with the modified coordinate system only. This is mainly because disturbances in the horizontal wind field that appear at first sight unimportant induce large errors in the relative vorticity field with the original coordinate system. In addition, the simulation with the original coordinate indicates a spurious moisture transport across the tropopause above the orography. On the other hand, the impact of the coordinate system on the structure and the amplitude of orographic gravity waves turns out to be quite small.

Corresponding author address: K. P. Hoinka, Institut für Physik der Atmosphäre, DLR, Postfach 1116, D-82230 Wessling, Germany. Email: klaus.hoinka@dlr.de

1. Introduction

Most numerical models employ some kind of terrain-following vertical coordinate system. The classical sigma formulation yields a very rough grid above mountainous terrain where individual terrain features such as mountain peaks are well visible in the coordinate surfaces, even at tropopause level. The use of hybrid coordinates reduces the amplitude of these features, but their structure remains unchanged below a certain height or pressure level that typically lies in the lower stratosphere. Therefore, Schär et al. (2002) recently introduced a modified terrain-following system in which small-scale topographic structures in the coordinate surfaces decay rapidly with height. The implementation of the modified coordinate system involves a splitting of the terrain field into a heavily smoothed component and a small-scale deviation, which allows for a very rapid decay of small-scale features without violating the invertibility of the coordinate transformation. Zängl (2003) presented an adaptation of this method to the pressure-based sigma-coordinate system of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (Penn State–NCAR) Mesoscale Model (MM5).

Schär et al. (2002) and Zängl (2003) both demonstrate that the accuracy of advection over mountainous terrain greatly benefits from the modified coordinate definition. This is partly because computing horizontal advection in the presence of steeply sloping coordinate surfaces involves large contributions of the metric terms arising from the coordinate transformation, giving rise to substantial discretization errors. Moreover, Zängl (2003) showed that discretization errors related to steep coordinate surfaces can generate unphysical vertical motions, which can further enhance the advection errors. Most of the model tests presented by Schär et al. (2002) and Zängl (2003) were highly idealized, but Schär et al. (2002) also performed a real case simulation of an event observed during the field phase of the Mesoscale Alpine Programme (MAP). Using the standard sigma system, strong small-scale disturbances were obtained above the Alps, particularly in the middle to upper troposphere. Both the isentropes and the humidity field appear very noisy with the original coordinate, but most of the disturbances disappear with the smoothed vertical coordinate.

An even stronger coordinate effect can be expected for derived quantities involving horizontal and/or vertical derivatives of the fields predicted by the model. An important example for such a quantity is the potential vorticity (PV), which is very useful for interpreting model results because of its conservation properties. In particular, the understanding of synoptic evolutions in the tropopause region, such as PV streamers and tropopause folds, and of the related exchange processes between the stratosphere and the troposphere relies strongly on the potential vorticity. A recent study of a PV streamer observed on 6 November 1999 during the field phase of MAP focused on the impact of the Alps on this streamer (Hoinka et al. 2003). This study shows that significant gravity waves were excited as the eastern flank of the PV streamer approached the Alps, reaching up to the lower stratosphere because the directional wind shear was weak between the surface and the lower stratosphere. Moreover, the interactions of the airflow with the Alps were found to be conducive for the formation of a cutoff low over the Mediterranean Sea. Yet, in the tropopause region, the numerical simulations conducted in this study exhibit a fairly noisy structure in the PV field above the Alps, the interpretation of which remains uncertain.

One of the goals of the present note is to investigate whether the coordinate system used in the numerical model could have played a role in the occurrence of this noise. To this end, we present additional numerical simulations of the 6 November 1999 case, demonstrating that the coordinate system indeed plays an important role. In addition, we analyze to what extent the structure of the orographically induced gravity waves depends on the coordinate system, and we consider the impact of the coordinate formulation on the structure of upper-tropospheric humidity.

2. Setup of the simulations

The simulations presented in the following have been performed with the MM5 (Grell et al. 1995). The simulations employ two interactively nested domains with a horizontal mesh size of 15 and 5 km, respectively. The numbers of grid points are 180 × 180 and 211 × 130, respectively, so that the outer domain covers almost all of Europe. The extent of the second domain can be inferred from Fig. 1. The model orography has been interpolated from United States Geological Survey (USGS) terrain data of 5′ and 30″ resolution for the first and second domain, respectively. It is filtered by a two-pass smoother–desmoother in order to remove two-grid-interval waves (Guo and Chen 1994). In the vertical, there are 59 model levels, and the upper boundary is located at 100 hPa in the simulations presented here. A test with a significantly higher upper boundary (50 hPa) confirmed that the model results are insensitive to this choice. The upper-boundary condition used in the simulation is an improved version of the ZKlemp and Durran (1983) radiative condition (see Zängl 2002a). The PV, relative vorticity ζ, and potential temperature θ fields shown in the following are computed on the model surfaces and then linearly interpolated to pressure surfaces.

To allow for a realistic simulation of the PV streamer, a full suite of physics parameterizations is used. Boundary layer processes are treated with the Gayno–Seaman scheme (Shafran et al. 2000), cloud microphysics are parameterized with the so-called Reisner2 scheme (Reisner et al. 1998), and the radiation scheme accounts for the interactions with atmospheric moisture and clouds (Mlawer et al. 1997). In both model domains, the Grell (1993) cumulus parameterization is used in order to account for subgrid-scale convection. Moreover, the modified diffusion scheme described in Zängl (2002b) is used for temperature and for the mixing ratios of water vapor and cloud water. This scheme has been found to reduce numerical errors above steep topography regardless of the vertical coordinate used.

In the following, two different simulations are presented, differing in the specification of the vertical coordinate. The first one (VC1) uses the original sigma coordinate, and the second one (VC2) uses the modified coordinate system described in Zängl (2003). Both simulations are started at 0000 UTC 6 November 1999 and are run for 22 h. The initial and boundary conditions are taken from the operational European Centre for Medium-Range Weather Forecasts (ECMWF) analyses, which are available every 6 h.

3. Results

One aim of the MAP field experiment was to perform measurements within a PV streamer crossing the Alps in order to investigate the impact of the orography on the streamer's development. Data were collected in situ and remotely sensed using the DLR aircraft Falcon on 6 November 1999 when a streamer passed over the Alps (Hoinka et al. 2003).

In the following discussion, results are shown for the afternoon of 6 November 1999. At this time, aircraft measurements that can be used for intercomparison were performed. We first analyze the behavior of PV, potential temperature (θ), and relative vorticity (ζ) at tropopause level. Then, we consider the evolution of upper-tropospheric and lower-stratospheric dry air that is transported around the streamer toward the Alps. Finally, we investigate the structure of mountain-generated gravity waves that propagate upward into the stratosphere.

a. Parameter at tropopause level

Within the tropopause region there is a strong change with height in the static stability as well as in other meteorological parameters. Therefore, in this region meteorological parameters might react particularly sensitively to the vertical coordinate system used. Let us first consider the behavior of PV at the 250-hPa level, which crosses the tropopause in the Alpine region (Figs. 1a and 1b).

The PV field obtained from the VC1 simulation (Fig. 1a) exhibits a highly noisy pattern above the central and eastern Alps, with amplitudes exceeding 10 PVU at some places [1 potential vorticity unit (PVU) ≡ 10−6 K m2 kg−1 s−1]. Adjacent extrema of the noise pattern typically have a distance of 3 to 5 times the grid distance (Δx), corresponding to a wavelength of 6Δx − 10Δx. In the VC2 run, however, there are almost no indications of small-scale noise (Fig. 1b). Instead, meridionally oriented bandlike structures form above the central Alps and are advected northward by the ambient flow. Above the western Alps, the disturbances are generally much weaker, but there is still a significant difference between the VC1 and VC2 runs.

To get more insight into the origin of the PV noise in the VC1 run, we separately considered the fields that enter into the computation of the PV. The θ fields, displayed in Figs. 1c and 1d, do not appear to be responsible. Though the isentropes above the Alps are somewhat smoother in VC2 than in VC1, the differences between the two runs are quite small. Analyzing the difference field (not shown) reveals that the differences do not exceed 1 K except for a small region above the western Alps where there is pronounced gravity wave activity. The differences also remain weak when calculating the vertical derivative of θ, which is the quantity that enters into the computation of PV (not shown).

On the other hand, the relative vorticity ζ exhibits the same noise structures as the PV (Figs. 1e and 1f), although the differences in the wind field (see Fig. 3 later) also appear to be small. The typical amplitude of the ζ noise exceeds the planetary vorticity (≈10−4 s−1). A closer analysis revealed that small disturbances in the wind field that are barely noticeable when looking at the wind field itself are responsible for the noise. This behavior can be explained by the fact that a shearlike disturbance of 1 m s−1 (10 km)−1, which is indeed inconspicuous in the presence of ambient winds of more than 30 m s−1, already corresponds to a relative vorticity of 10−4 s−1. We also verified that the noise appearing in the vorticity field does not depend significantly on the method of computation. Calculating ζ on the model surfaces followed by a vertical interpolation to pressure surfaces yields essentially the same result as calculating ζ from a wind field that has previously been interpolated to pressure surfaces. The peak amplitude of the noise tends to be 5%–10% smaller with the latter method, but the structure is the same in both cases. We thus conclude that the errors leading to the noise in the vorticity field are already present in the wind field (though not readily evident) and not related to a particular differencing method.

It remains to be discussed why the noise in the PV and ζ fields is much stronger over the central and eastern Alps than over the western Alps although the latter exhibit the steepest orographic slopes. Our analysis of the model output indicates that this difference is related to the vertical wind shear, which is much stronger over the central and eastern Alps, where the tropopause is close to the 250-hPa level, than over the western Alps, where 250 hPa is well above the tropopause. To understand the relevance of the vertical shear for generating small-scale wind disturbances, recall that horizontal momentum advection is computed along the terrain-following coordinate surfaces. The ensuing metric terms involve the vertical wind shear and are zero in a shear-free environment. Consequently, differencing errors related to sloping coordinate surfaces strongly depend on the presence of vertical shear.

To corroborate that the noise signal in the PV field related to the underlying mountains is strongest where the vertical wind shear is large—namely, in the tropopause region—PV fields at various pressure levels are given in Fig. 2. During the afternoon of 6 November 1999, the center of the meridionally elongated PV streamer was located at the western edge of the Alps (Hoinka et al. 2003). Correspondingly, the area with the noisiest PV field at 500 hPa is found west of the Alps (Fig. 2a). Since the tropopause forms the bottom layer of the streamer, the tropopause is found at successively higher levels (lower pressure) toward the east. Consequently, the “noisy area” is shifted toward the east with decreasing pressure, lying above the western Alps at 400 hPa (Fig. 2c) and above the northwestern Alps at 300 hPa (Fig. 2e). Finally, at 250 hPa the area with disturbed PV is located above the central Alps (Fig. 1a).

The corresponding PV fields resulting from the VC2 simulations exhibit the expected smooth streamer configuration, with a broad extension at 250 hPa (Fig. 1b) as shown by the curved 3–7 PVU isolines extending south. At 300 hPa the streamer is narrower, and at 400 hPa the southern rim of the streamer touches the northwestern edge of the Alps.

To summarize, our results demonstrate that the basic meteorological variables, such as wind and θ, show only a weak signal related to the vertical coordinate system. However, diagnosed quantities involving horizontal and vertical derivatives react very sensitively to the vertical coordinate system. This is particularly evident in the tropopause region where there is a large vertical wind shear. Under such circumstances, the computation of horizontal momentum advection is subject to substantial discretization errors in the presence of steeply sloping coordinate surfaces. Though not readily evident in the wind field proper, the resulting wind disturbances can induce spurious vorticity well exceeding the planetary vorticity. As a consequence, a meaningful computation of the potential vorticity field over steep topography is possible with the modified coordinate system only.

b. Upper-tropospheric moisture

Schär et al. (2002) and Zängl (2003) pointed out that the accuracy of horizontal advection can depend significantly on the chosen vertical coordinate. As an example, we consider the water vapor mixing ratio of the present case. In general, there are very weak differences in the humidity fields between both simulations for pressure levels larger than 350 hPa and smaller than 250 hPa. However, the humidity within the layer between 350 and 250 hPa shows pronounced differences above the Alps. As an example, Fig. 3 shows the water vapor mixing ratio at 325 hPa using both coordinate systems. Above the western Alps and farther to the west there are virtually no differences in humidity. The same is valid for the area east of the central Alps. Above and north of the central Alps, however, the differences are fairly substantial.

As evident from the VC2 run with the modified coordinate system, dry air is transported southward in the western part of the streamer and back toward the north in the eastern part (Fig. 3b). The latter path crosses the Alpine crest in a region where the 325-hPa level is close to the tropopause (see Fig. 2b). The corresponding result of the VC1 run (Fig. 3a) also exhibits a southward transport of dry air in the western part of the streamer. However, it appears that most of the dry air advected northward over the Alpine crest does not reach the northern side of the Alps. This effect is strongest where the 325-hPa level is closest to the tropopause (between x = 600 km and x = 800 km) and can be explained by the fact that the numerical errors related to the sloping coordinate surfaces tend to smooth out vertical gradients in the advected variables. As a consequence, the layers immediately above (below) the tropopause are moistened (dried), which becomes most evident above the tropopause because of the exponential decrease with height of the mixing ratio. North of the Alps between x = 600 km and x = 800 km, the mixing ratio at 325 hPa is at least 50% larger in VC1 than in VC2. At 310 hPa, the peak difference even exceeds 100% (not shown). Since this numerical mixing constitutes an artificial mass exchange between the stratosphere and the troposphere, we conclude that the modified vertical coordinate will be of large importance for future high-resolution studies of stratosphere–troposphere exchange over mountainous topography.

c. Mountain waves

Zängl (2003) demonstrated that steep coordinate surfaces can generate unphysical vertical motions that have a structure similar to orographic gravity waves. Figures 1 and 2 indicate that gravity waves occurred above the southwestern part and above the northern part of the Alps. These waves were generated by the Alps and propagated to the upper troposphere and lower stratosphere because there was little directional wind shear in the case considered. We now check to what extent these waves are influenced by errors related to the vertical coordinate.

Figure 4 displays horizontal fields of the vertical velocity at 250 hPa as simulated using both vertical coordinate systems. In agreement with the θ fields (Figs. 1c and 1d), there are wave signals above the southwestern Alps that differ only weakly between the two simulations. In the area where strongly disturbed PV was encountered in the VC1 run (see Fig. 1a), the vertical wind field exhibits smaller-scale structures in VC1 than in VC2, but their amplitude is well below that of the gravity waves over the southwestern Alps. This suggests that the orographic gravity waves are not severely affected by the numerical errors related to the coordinate system. We can corroborate this finding by reconsidering the above-mentioned result of Zängl (2003). The setting investigated there had a maximum topographic slope of about 65% and a wind profile with zero winds up to 1.5 times the mountain height (so as to exclude orographic gravity waves) increasing up to 10 m s−1 higher above. The magnitude of the spurious vertical wind obtained for this setting is about 0.2 m s−1. In case of a homogeneous ambient flow of 10 m s−1, however, one would obtain vertical wind maxima in excess of 5 m s−1.

To consider the vertical structure of the waves, Fig. 5 depicts a zonal cross section of vertical velocity above the baseline indicated in Fig. 4a. Strong wave response can be clearly seen above the French Massif Central located between 100 and 300 km from the west and above the southwestern Alps, which are located between 300 and 500 km. There is even a weak gap of intensity between both orographic barriers. The wave activity is strongest in the upper troposphere and in the lower stratosphere. The θ difference field in Fig. 5b shows a positive difference in the middle to upper troposphere above the mountains, whereas there is a predominantly negative difference over the Po Valley to the east of the Alpine arc. The amplitude is generally smaller than 2 K. The w difference field in Fig. 5d also exhibits weak differences over the Alps, reaching more than 0.25 m s−1 in the upper troposphere. The largest deviation is found in the middle troposphere to the east of the Alps, amounting to more than 0.5 m s−1. This feature is related to a major convective cell that happens to be at a slightly different location in the two runs.

It is recommendable and useful to compare simulated data to real atmospheric data. Therefore, similar to Hoinka et al. (2003), we compare the waves simulated by the MM5 with those measured in situ with the DLR aircraft Falcon. The aircraft flew at an altitude between 11.2 and 11.8 km. Hoinka et al. (2003) used the French mesoscale model Meso-NH, applying a mesh size of 8 km, in order to investigate the wave structure above the same cross section. At flight level, the resulting simulated structure differed strongly in amplitude and phase from the observed one (see Fig. 11 of Hoinka et al. 2003). Figure 6 shows the MM5-simulated vertical velocities using a 5-km mesh size. In general, the higher resolution of the MM5 simulations allows for a better representation of the wave structure than the previous Meso-NH simulation. The extended region of notable up- and downdrafts is the same for the observation and simulations. There is a reasonably good agreement between measurement and simulation up to 350 km from the west, whereas farther to the east, both datasets get out of phase. Even so, the amplitudes of the simulated waves are of similar strength as the observed ones, while the amplitudes were strongly underestimated in the Meso-NH simulation. An additional MM5 run with an 8-km grid confirmed that the improvements in the representation of the gravity waves are mainly due to the higher resolution of the present simulations.

Comparing the VC1 run with the VC2 run, one notices that the wave amplitudes tend to be slightly larger in VC1 (dotted line) than in VC2 (bold solid line), but the differences are small compared to the differences between model and observation. Moreover, the phase error of the simulation does not seem to depend on the vertical coordinate. This further confirms that wave-related vertical winds are much stronger than the numerical errors produced by the original coordinate system.

4. Concluding remarks

We investigated the impact of the modified vertical coordinate introduced by Schär et al. (2002) and Zängl (2003) on simulations of upper-tropospheric features over mountainous topography. Specifically, we conducted high-resolution (5 km) MM5 simulations of a PV streamer that passed over the Alps on 6 November 1999. The major findings are as follows.

The wind and temperature fields show only a weak signal related to the vertical coordinate system. However, diagnostic quantities involving horizontal and vertical derivatives, such as the potential vorticity, react very sensitively to the vertical coordinate. The difference is particularly pronounced in the tropopause region where the PV field obtained with the original coordinate is contaminated with excessive noise, while there is a smooth PV distribution when using the modified coordinate. Our analysis revealed that the noise occurring with the original coordinate is primarily due to small-scale disturbances in the wind field that are at first sight hardly noticeable. These disturbances are most likely related to advection errors occurring over steep topography in the presence of large vertical wind shear. They are associated with spurious relative vorticity well exceeding the planetary vorticity, implying that a meaningful diagnosis of the potential vorticity field is possible with the modified vertical coordinate only.

The simulation with the original terrain-following coordinate system indicates a spurious moisture transport across the tropopause above parts of the Alps. This is related to the fact that the advection errors related to steeply sloping coordinate surfaces act similar to a strong vertical diffusion. In the region affected most strongly by this error, the mixing ratio is more than 50% larger with the original coordinate system than with the modified one. On the other hand, the impact of the coordinate system on the structure and amplitude of orographic gravity waves turned out to be quite small. This is in agreement with the success of a large number of previous studies in simulating orographic gravity waves with standard sigma-coordinate models.

Acknowledgments

The authors are indebted to Christoph Schär (ETH, Zürich) and another anonymous referee for useful comments.

REFERENCES

  • Grell, G. A., 1993: Prognostic evaluation of assumptions used by cumulus parameterizations. Mon. Wea. Rev, 121 , 764787.

  • Grell, G. A., , J. Dudhia, , and D. R. Stauffer, 1995: A description of the fifth-generation Penn State/NCAR Mesoscale Model (MM5). NCAR Tech. Note NCAR/TN-398 + STR, 122 pp.

    • Search Google Scholar
    • Export Citation
  • Guo, Y-R., , and S. Chen, 1994: Terrain and land use for the fifth-generation Penn State/NCAR mesoscale modeling system (MM5): Program TERRAIN. NCAR Tech. Note NCAR/TN-397 + IA, 114 pp.

    • Search Google Scholar
    • Export Citation
  • Hoinka, K. P., , E. Richard, , G. Poberaj, , R. Busen, , J. L. Caccia, , A. Fix, , and H. Mannstein, 2003: Analysis of a potential vorticity streamer crossing the Alps during MAP IOP-15 on November 1999. Quart. J. Roy. Meteor. Soc, 129 , 609632.

    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., , and D. R. Durran, 1983: An upper boundary condition permitting internal gravity wave radiation in numerical mesoscale models. Mon. Wea. Rev, 111 , 430444.

    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J., , S. J. Taubman, , P. D. Brown, , M. J. Iacono, , and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmosphere: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res, 102 , 1666316682.

    • Search Google Scholar
    • Export Citation
  • Reisner, J., , R. M. Rasmussen, , and R. T. Bruintjes, 1998: Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Quart. J. Roy. Meteor. Soc, 124 , 10711107.

    • Search Google Scholar
    • Export Citation
  • Schär, C., , D. Leuenberger, , O. Fuhrer, , D. Lüthi, , and C. Girard, 2002: A new terrain-following vertical coordinate formulation for atmospheric prediction models. Mon. Wea. Rev, 130 , 24592480.

    • Search Google Scholar
    • Export Citation
  • Shafran, P. C., , N. L. Seaman, , and G. A. Gayno, 2000: Evaluation of numerical predictions of boundary layer structure during the Lake Michigan Ozone Study (LMOS). J. Appl. Meteor, 39 , 412426.

    • Search Google Scholar
    • Export Citation
  • Zängl, G., 2002a: Stratified flow over a mountain with a gap: Linear theory and numerical simulations. Quart. J. Roy. Meteor. Soc, 128 , 927949.

    • Search Google Scholar
    • Export Citation
  • Zängl, G., 2002b: An improved method for computing horizontal diffusion in a sigma-coordinate model and its application to simulations over mountainous topography. Mon. Wea. Rev, 130 , 14231432.

    • Search Google Scholar
    • Export Citation
  • Zängl, G., 2003: A generalized sigma coordinate system for the MM5. Mon. Wea. Rev, 131 , 28752884.

Fig. 1.
Fig. 1.

MM5 results at a pressure level of 250 hPa valid at 1500 UTC 6 Nov 1999: (left) Results of the VC1 run, using the original vertical coordinate, and (right) results of the VC2 run, using the modified vertical coordinate. (a), (b) PV (contour interval is 2 PVU); (c), (d) potential temperature (contour interval is 2 K); and (e), (f) relative vorticity (contour interval is 5 × 10−5 s−1). The shaded area indicates the Alps for heights larger than 800 m. In (c) and (d) the model topography is also contoured with an increment of 400 m

Citation: Monthly Weather Review 132, 7; 10.1175/1520-0493(2004)132<1860:TIOTVC>2.0.CO;2

Fig. 2.
Fig. 2.

MM5-simulated PV (contour interval is 2 PVU) at various pressure levels at 1500 UTC 6 Nov 1999, applying (a), (c), (e) the standard terrain-following coordinate system VC1 and (b), (d), (f) the modified system VC2. The shaded area indicates the Alps for heights larger than 800 m

Citation: Monthly Weather Review 132, 7; 10.1175/1520-0493(2004)132<1860:TIOTVC>2.0.CO;2

Fig. 3.
Fig. 3.

MM5-simulated water vapor mixing ratio (contour interval is 50 ppmv) and horizontal wind at 325 hPa at 1400 UTC 6 Nov 1999, performed with (a) the standard terrain-following coordinate system VC1 and (b) the modified system VC2. The shaded area indicates mixing ratios below 150 ppmv

Citation: Monthly Weather Review 132, 7; 10.1175/1520-0493(2004)132<1860:TIOTVC>2.0.CO;2

Fig. 4.
Fig. 4.

MM5-simulated vertical wind (contour interval is 0.5 m s−1) at 250 hPa at 1500 UTC 6 Nov 1999 applying (a) the standard terrain-following coordinate system VC1 and (b) the modified system VC2. Shaded areas indicate negative vertical velocities. The dashed line in (a) shows the baseline of the cross section given in Fig. 5

Citation: Monthly Weather Review 132, 7; 10.1175/1520-0493(2004)132<1860:TIOTVC>2.0.CO;2

Fig. 5.
Fig. 5.

MM5-simulated θ (contour interval is 2 K) and w (contour interval is 0.25 m s−1) at 1500 UTC 6 Nov 1999 for (a) the standard terrain-following system VC1 and (c) the modified system VC2; isolines show θ; the shaded area indicates negative vertical velocity. The difference fields VC1 − VC2 are given for (b) θ (contour interval is 1 K) and (d) w (contour interval is 0.25 m s−1). (e) The orography; the baseline of the cross section is indicated in Fig. 4a

Citation: Monthly Weather Review 132, 7; 10.1175/1520-0493(2004)132<1860:TIOTVC>2.0.CO;2

Fig. 6.
Fig. 6.

(a) Vertical velocity measured by the aircraft along the flight track at 45°N between 1440 and 1600 UTC (full line) 6 Nov 1999 after applying a running mean of 50 s or 10 km to the original data. The bold dotted line indicates the simulated vertical velocity using the standard terrain-following system (VC1), and the bold full line shows the result using the modified system (VC2). (b) The orography; the baseline of the track is given in Fig. 4a

Citation: Monthly Weather Review 132, 7; 10.1175/1520-0493(2004)132<1860:TIOTVC>2.0.CO;2

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