Orography-Induced Gravity Wave Drag Parameterization in the Global WRF: Implementation and Sensitivity to Shortwave Radiation Schemes

This paper describes the implementation of the orographic gravity wave drag (GWDO) processes induced by subgrid-scale orography in the global version of the Weather Research and Forecasting (WRF) model. The sensitivity of the model simulated climatology to the representation of shortwave radiation and the addition of the GWDO processes is investigated using the KimArakawa GWDO parameterization and the Goddard, RRTMG (Rapid Radiative Transfer Model for GCMs), and Dudhia shortwave radiation schemes. This sensitivity study is a part of efforts of selecting the physics package that can be useful in applying the WRF model to global and seasonal configuration. The climatology is relatively well simulated by the global WRF; the zonal mean zonal wind and temperature structures are reasonably represented with the Kim-Arakawa GWDO scheme using the Goddard and RRTMG shortwave schemes. It is found that the impact of the shortwave radiation scheme on the modeled atmosphere is pronounced in the upper atmospheric circulations above the tropopause mainly due to the ozone heating. The scheme that excludes the ozone process suffers from a distinct cold bias in the stratosphere. Moreover, given the improper thermodynamic environment conditions by the shortwave scheme, the role of the GWDO process is found to be limited.


Introduction
The Weather Research and Forecasting (WRF) model has been evaluated in terms of regional modeling for both research and operational applications since it was first released in 2000.The capability of the regional WRF model is established over a wide temporal range; from short-range forecasts such as simulations of localized heavy rainfall and snowfall within a couple of days over Korea (i.e., [1,2]), 36-h real time forecasts in the United States [3], and simulations of typhoon and hurricane that affect synoptic fields for several days (i.e., [4,5]), to regional climate simulations of such as U.S. warm-season precipitation and East-Asia summer monsoon circulations (i.e., [6,7]).These studies support the satisfactory performance of the WRF model in various regions over the globe.except that a polar filter is applied in the global version [8].In addition, the physics options and behavior should be examined separately from the regional configuration because the intrinsic requirements for global circulation modeling, such as higher model top, and coarser resolution require further validation.
The advancement of human knowledge continues together with increasing computing resources; the cutting-edge numerical weather prediction (NWP) and climate models, however, cannot resolve all relevant scales of atmospheric phenomena.Global numerical prediction models are typically run with horizontal resolutions that cannot capture atmospheric processes smaller than about 10-100 km.Gravity wave is an unresolved process in coarse resolution models, playing an important role in transporting momentum from source regions to regions where gravity waves are dissipated or absorbed during their propagation, producing synoptic scale body forces [9].Palmer et al. [10] and McFarlane [11] noted that unresolved mountain gravity wave drag was one of the most critical causes of the systematic biases in seasonal simulations-excessive surface westerlies and a too cold pole-and suggested a GWDO parameterization for large-scale models.Since then, this subgrid-scale process of gravity waves has been an essential physical process that should be parameterized in global models to represent global circulations realistically.However, the global WRF, which is a spatial extension of the original regional WRF, currently does not include any orography-induced gravity wave drag (GWDO) parameterization.It is noted that the GWDO parameterization is not included in most regional models including the WRF since horizontal resolutions of regional models are considered to be sufficiently high to resolve gravity waves.Moreover, global models include much of stratosphere, whereas the model top is lower (i.e., typically lower than 50 hPa) for regional models.Thus, most regional models do not typically include the GWDO parameterization.
The purpose of this study is to describe the implementation of the GWDO parameterization based on Kim and Arakawa [12] (hereafter, KA GWDO) into the global WRF model and evaluate the performance of the model in simulating general features of the boreal winter climate with the KA GWDO.The KA GWDO includes the enhanced lowtropospheric gravity wave drag in addition to the upperlevel wave breaking that is traditionally incorporated into GWDO schemes.The KA GWDO was earlier implemented into the National Centers for Environmental Prediction (NCEP) Global Spectral Model (GSM) successfully and its performance was later reported by Hong et al. [13].The KA GWDO scheme went into operation at the NCEP global forecast system in 2000.Sensitivity of the simulated climatology to shortwave radiation schemes is also investigated in order to re-evaluate present physics options in the WRF model in global and seasonal configuration, which have been evaluated only in regional configuration.Section 2 describes the experimental setup and implementation of the KA GWDO parameterization, and results are discussed in Section 3. Concluding remarks are given in the final section.

The Advanced Research WRF (ARW) Model.
The Advanced Research WRF (ARW; [14]) is a community model designed for both research and forecasting, which is a fully compressible nonhydrostatic model with the Arakawa-C grid system.The model performs reasonably well for detailed numerical weather prediction (NWP) cases with real-data initial and boundary conditions.The WRF model became available with the global coverage starting from WRF version 3.0, which was released in April 2008.The model used in this study is a beta version of the ARW version 3.1 with the global domain.The global WRF utilizes the latitude-longitude grid system and then a polar filter is used to filter out small-scale waves and avoid the singularity problem at the poles.

Implementation of the KA GWDO Parameterization
Scheme.The KA GWDO scheme [12] includes the lowertropospheric enhancement of GWDO due to selective lowlevel wave breaking mainly in downstream regions with the aid of additional subgrid-scale orographic statistics: the orographic asymmetry (OA) and orographic convexity (OC).The OA measures the asymmetry and location of subgrid-scale orography relative to the model grid box and it distinguishes between the upstream and downstream regions.The OC measures how convex or sharp the subgridscale orography is by statistically relating the characteristics of the mountain waves to the subgrid-scale orography.
The KA GWDO parameterization is implemented in the WRF model following Hong et al. [13]; in Hong et al. [13] the reference level is determined as the larger value between the PBL height and 2σ h following Kim and Doyle [15], where σ h is the standard deviation of subgrid-scale terrain heights.Kim and Hong [16] demonstrated that this method in determining the reference level greatly improves the climate simulations compared with the previous method that employs the PBL height as the reference level height; we note that the new method generally elevates the reference level height.The mechanism behind the improvement is explained in Kim and Hong [16].
For utilizing the KA GWDO in the WRF model, the necessary input to the KA GWDO scheme (i.e., mean, variance, asymmetry, and convexity) is derived from a 30arcsecond resolution topography dataset [17] for global domains with 10 min., 20 min., 30 min., 1 deg., and 2 deg.resolutions.These orographic statistics are interpolated to the model grid points using one of the five-resolution datasets in the WRF Preprocessing System (WPS); prepared statistics of a comparable resolution to model grid size are used.

Experimental Setup.
Seasonal simulations are conducted for three boreal winters in December, January, and February (DJF) of 1996/1997, 1997/1998, and 1999/2000.For each winter, five ensemble runs are conducted with different initialization times of 00UTC 1-5 November to average out the unpredictable parts of the flow.Thus, one experiment The physics package includes the RRTMG scheme [18] for longwave radiation, the Yonsei University Planetary Boundary Layer (YSU PBL) [19] for vertical diffusion process, the Noah land surface model [20], the Grell-Devenyi ensemble scheme [21] for cumulus parameterization, and the WSM3 (WRF Single-Moment 3-class) scheme [22] for microphysics.In the YSU PBL, the vertical diffusion coefficients in the stable boundary layer (SBL) conditions are calculated as in the case of the unstable conditions; the coefficients are parabolic functions of heights as in the mixed layer, and the SBL top is determined by the bulk Richardson number.Kim and Hong [16] demonstrated that the interaction between the KA GWDO and YSU PBL processes is improved with the SBL parameterization mentioned above.For shortwave radiation, three different shortwave schemes are used to observe the sensitivity of the simulated climate associated with the GWDO to the shortwave radiation processes in the modeled atmosphere: the Goddard [23], RRTMG, and Dudhia [24] schemes.The physics options used for the numerical experiments are summarized in Table 1.

Results
In this study, the results are obtained from and discussed based on the composite of 3-year simulations (i.e., ensemble averages of the 15 simulations).The simulated zonal wind and temperature structures are evaluated in comparison with the reanalysis (R2) data.The shortwave process in R2 is based on Chou [25] and Chou and Lee [26], and the GWDO scheme used in the R2 is described by Alpert et al. [27].In precipitation analysis, the daily Global Precipitation Climatology Project (GPCP) data with a 1 • × 1 • spatial resolution are used for the evaluation.Hereafter, to make a clear distinction, the global WRF without the KA GWDO implementation is designated the earlier version.

3.1.
Wind and Temperature Structures. Figure 1 compares the three-winter ensemble averages of the zonal-mean zonal wind and temperature structures simulated with the Goddard (Figures 1(a) and 1(d)), RRTMG (Figures 1(b) and 1(e)) and Dudhia (Figures 1(c) and 1(f)) shortwave parameterizations in the earlier version of the global WRF that includes no effect of the GWDO (denoted by Gsw nGWD, Rsw nGWD, and Dsw nGWD, resp.).The contours in each figure represent the 3-year averaged fields from the 15 ensemble members, and the color shades denote their deviations from the reanalysis fields.As can be expected and as the results show, the earlier version of the global WRF cannot reasonably represent the typical boreal winter climatology.The model clearly shows the systematic errors in the simulated climatology-too cold pole and excessively strong westerlies over the northern hemisphere (cf. Figure 1), which is typical when GWDO is not included in general circulation models.There is no separation between the tropospheric subtropical jet and stratospheric polar night jet and also the polar night jet is overly strong due mainly to the lack of GWDO.The thermodynamic structure shows too strong meridional temperature gradient in balance with the improper wind structure; the simulated temperature of the Arctic polar stratosphere is almost about 40 K colder than that of the reanalysis.Thus, it is obvious that the earlier version of the global WRF has a systematic problem due to a missing critical process; that is, orographically induced gravity wave drag.Note that the three nGWD experiments are conducted in parallel with the three GWD experiments (i.e., Gsw GWD, Rsw GWD, and Dsw GWD) to validate the implementation of the KA GWDO in the global WRF model, and thus the sensitivity to shortwave process schemes is not discussed for these nGWD experiments.
With the KA GWDO implemented, the global WRF is able to reproduce the general mean structures of both the zonal-mean zonal wind (Figures 2(a the GWDO.Associated with these improvements in the wind fields, the cold bias of the thermodynamic structures is also reduced.In the troposphere, the simulated results are less sensitive to the shortwave schemes than those in the upper atmosphere.On the other hand, clear differences among the shortwave radiation parameterizations exist in upper levels.The subtropical jet and stratospheric polar night jet in the northern hemisphere are reasonably separated with the Goddard and RRTMG shortwave radiation processes while the two jets are unrealistically bonded to each other with the Dudhia scheme; the westerly continuously decreases as the height increases such that the magnitude of the wind is evidently underestimated at the location of the observed polar-night jet, which is entirely missing in the simulation (cf. Figure 2(c)).Moreover, in the southern hemisphere, the tropospheric westerly jet is erroneously extended into the stratosphere in the Dsw GWD experiment.This radical difference in simulating the wind structure in the middle atmosphere among the three experiments (Gsw GWD, Rsw GWD, and Dsw GWD) is related to the different thermodynamic structures that heavily rely on the shortwave heating processes.The Goddard and RRTMG shortwave schemes include ozone effects that are responsible for the typical thermodynamic structure of the stratosphere; an ozone-absorption coefficient profile is specified in the Goddard scheme according to an observed climatology, and the RRTMG scheme includes tropical/midlatitude/polar and summer/winter ozone profiles.The simulated temperature-profile inversion near the tropical and southern-hemispheric polar tropopause is shown with these two shortwave schemes due to the ozone heating effects (Figures 2(d) and 2(e)).Because of this temperature inversion, there exists meridional temperature gradient in the middle stratosphere over high latitudes, which is responsible for the presence of the northern polar night jet in the two experiments (i.e., Gsw GWD and Rsw GWD).In the Gsw nGWD and Rsw nGWD experiments, there is significant cold bias related to the extremely overestimated temperature gradient in the lower stratospheric regions associated with the excessive westerlies caused by the missing drag, as shown previously, this cold bias is alleviated by its balance with the wind reduction due to the GWDO in the two GWD experiments.
On the other hand, the Dudhia scheme does not consider the ozone effects [28] and thus cannot simulate the temperature inversion; the strong cold bias is induced throughout the stratosphere (Figure 2(f)) (note that the cold bias in the Dsw nGWD experiment is due to the absence of both the ozone heating and GWDO).Moreover, given the highlyunrealistic thermodynamic structure, the GWDO process does not improve but continues to force the unrealistic system.We note that similar results were previously reported by Kim et al. [29].They demonstrated that the underestimated ozone mixing ratio inducing an underestimation of shortwave heating can result in significant bias in zonalmean temperature and wind structures; the impact of the low ozone mixing ratio is the largest in the lower polar stratosphere, which leads to the overly strong polar night jet in the northern hemisphere and unrealistically strong extension of the tropospheric westerly jet into the stratosphere in the southern hemisphere.Consequently, when the GWDO parameterization is given wrong information from other physical process, including GWDO does not improve the simulated results even though the GWDO process itself is a critical component in climate models.The Dudhia shortwave scheme shows good performance, that is, without large systematic bias, in regional weather prediction models since the model top is usually lower than 50 hPa in the regional model application, so that the simulated results do not suffer from the absent ozone effects.
In summary, shortwave radiation significantly impacts the modeled atmosphere, especially on the upper atmospheric circulations above the tropopause mainly due to the ozone heating.The heating scheme without the ozone process undergoes a distinct cold bias in the stratosphere, which in turn results in improper wind fields balancing with the cold bias.Under the unreasonable environmental conditions, the GWDO process continuously forces the system toward an unrealistic state.

Tropical Precipitation.
In Figure 3, the simulated 3-year mean daily precipitation is compared with the daily GPCP data with a 1 • × 1 • spatial resolution.The pattern correlation (PC), biases, and Root Mean Square Error (RMSE) between each simulation and GPCP data are presented at the top of each panel.The overall performance of the global WRF model in simulating the precipitation is acceptable in the three GWD experiments regardless of the shortwave processes (e.g., Figures 3(e)-3(g)).As seen in Shimpo et al. [30], the distribution of global precipitation from the global WRF is comparable, even though the integration period differs from one to another.The model produces tropical rainfall distributions quite reasonably, compared with the observations showing the double rainbelts along the double intertropical convergence zone (ITCZ) and precipitation maximum regions over South America and South Africa.However, the model generally tends to overestimate the local rainfall maximum values over tropical regions (e.g., central South America, the northwestern ocean of Madagascar, near Sumatra, and western equatorial Pacific near the maritime continent), while it underestimates the rainfall around middle latitudes.Compared with the nGWD experiments, the inclusion of the GWDO neither significantly changes the distribution, nor improves the distribution of the precipitation.With the Goddard and RRTMG shortwave processes the statistics are slightly worse in the GWD experiments while the GWD experiment shows slightly better statistics with the Dudhia shortwave.The simulated hydroclimate shows the best results-although not significant-with the Goddard shortwave scheme in this study both with and without GWDO.Figure 4 shows the zonal mean of the 3-year mean daily precipitation from 60 • S to 60 • N. The model is successful in representing meridional distributions of the zonal-mean precipitation, but tends to overestimate the precipitation over the tropics, regardless of the shortwave scheme.Near the equator, the simulated daily precipitation patterns from the experiments with the shortwave schemes including ozone effects (i.e., the Goddard and RRTMG) are similar to each other while the experiment with the Dudhia scheme shows somewhat different behaviors, both with and without the KA GWDO.In other words, the experiments with the Goddard and RRTMG schemes commonly produce less rainfall than the experiment with the Dudhia scheme so that the amounts are closer to observations than that with the Dudhia scheme.

Concluding Remarks
The orographic gravity-wave drag (GWDO) process induced by subgrid scale orography is implemented in the global version of Weather Research and Forecasting (WRF) model.The sensitivity of the simulated climatology to the representation of shortwave radiation with the GWDO process in the modeled atmosphere is investigated using the Kim-Arakawa GWDO (KA GWDO) parameterization and the Goddard, RRTMG, and Dudhia shortwave radiation schemes.
With the KA GWDO parameterization implemented, the climatology from the global WRF is relatively well simulated in the troposphere; the zonal-mean zonal wind and temperature structures are realistically represented.In the stratosphere, however, the performance of the model widely varies according to the representations of shortwave processes mainly due to the ozone heating.The scheme that excludes the ozone process induces a distinct cold bias in the stratosphere, and modeled wind fields balance with the unreasonable thermodynamic fields.The already unrealistic system due to the deficiency in the heating scheme is continuously impelled by the GWDO process.This result supports the notion that the success of a particular physics parameterization scheme in atmospheric models depends not only on the accuracy of the particular scheme itself but also on the success of other physical processes [16].In view of the precipitation, the global WRF also well represents the overall patterns of the tropical precipitation but the model tends to overestimate (underestimate) the precipitation at the tropical (mid-latitude) regions.It is found that the simulated meridional precipitation distributions differ according to the shortwave schemes depending on the presence of ozone effects.
The KA GWDO is implemented in the WRF model based on this study and became available starting from the WRF version 3.1, which was released in April 2009.

Figure 1 :
Figure 1: Three-winter ensemble averages (contours) of the zonal-mean zonal wind (upper panels) and temperature (lower panels) structures simulated from the (a), (d) Gsw nGWD, (b), (e) Rsw nGWD, and (c), (f) Dsw nGWD experiments with the earlier version of global WRF without the KA GWDO implementation.Differences from the NCEP reanalysis (R2) are color shaded.

Figure 2 :
Figure 2: As in Figure 1, but with the new version of global WRF including the KA GWDO parameterization.

1 )Figure 3 :
Figure 3: Comparison of 3-year averaged daily precipitation (mm day −1 ) obtained from (a) observations, (b), (c), (d) the experiments without the KA GWDO scheme and with three different shortwave radiation processes, and (e), (f), (g) the experiments including the KA GWDO scheme and with three different shortwave radiation processes.

Figure 4 :
Figure4: The zonal-mean of the 3-year mean daily precipitation (mm day −1 ) obtained from the three nGWD (dotted lines) and three GWD (solid lines) experiments with the Goddard (green lines), RRTMG (blue lines), and Dudhia (red lines) shortwave radiation schemes, respectively.

Table 1 :
A summary of the physics options used in the numerical experiments."-" denotes the same option as that in the Gsw nGWD experiment.Initial conditions are forced by the NCEP-Department of Energy (DOE) (NCEP-DOE) Reanalysis II (R2) data on the 2.5 • × 2.5 • global grid.The National Oceanic and Atmospheric Administration (NOAA) Optimal Interpolation Sea Surface Temperature (OISST) is used as the surface boundary conditions every 24 hours.The horizontal resolution of 1.875 • × 1.875 • is used, which is comparable to the 200 km resolution along the equator.The 38-layer Eta level system is used with the model top at 10 hPa.Intervals between the adjoining vertical levels are determined not to exceed 1 km or to be comparable to 1 km.