Interaction between the orography-induced gravity wave drag and boundary layer processes in a global atmospheric model

GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L12809, doi:10.1029/2008gl037146, 2009 Interaction between the orography-induced gravity wave drag and boundary layer processes in a global atmospheric model Young-Joon Kim 1 and Song-You Hong 2 Received 30 December 2008; revised 12 May 2009; accepted 19 May 2009; published 20 June 2009. [1] This study investigates the behavior of the orographic gravity-wave drag (GWDO) processes induced by sub-grid scale orography in response to the representation of boundary layer mixing in a global atmospheric model. The sensitivity of simulated climatology to the representation of stable boundary layer (SBL) processes associated with GWDO processes in the modeled atmosphere is investigated using the Kim-Arakawa GWDO parameterization scheme. It is found that the impact of the boundary layer structure is pronounced in the upper atmospheric circulations above the tropopause through the interaction between the boundary layer mixing and GWDO processes, even though the direct impact of the SBL structure is confined to near surface layer. This finding reinforces the notion that the success of a particular physics parameterization scheme in atmospheric models relies heavily on the interaction of a physical process with another, which should be properly considered in developing physics parameterization schemes for atmospheric models. Citation: Kim, Y.-J., and S.-Y. Hong (2009), Interaction between the orography-induced gravity wave drag and boundary layer processes in a global atmospheric model, Geophys. Res. Lett., 36, L12809, doi:10.1029/2008gl037146. 1. Introduction [2] With the continuing advancement of human knowledge together with the advent of powerful computing resources, it is becoming more feasible to represent the physical processes of the atmosphere more accurately and more efficiently in numerical weather prediction (NWP) and general circulation models (GCMs). Contemporary NWP and climate models are now fairly successful in reproducing major observed mean features of the atmosphere. However, the skill of seasonal prediction using dynamic models is still not satisfactory as compared with that by statistical methods [e.g., Shukla et al., 2000]. Aside from the theoretical deficiencies in formulating atmospheric processes, even the most powerful available computing architectures still cannot run typical NWP models or climate models fast enough to resolve all relevant scales of the atmospheric motion. The subgrid-scale processes shorter than the model s effective grid spacing thus need to be parameterized. [3] The parameterization of subgrid-scale physical processes is regarded as one of the most uncertain aspects in 1 Marine Meteorology Division, Naval Research Laboratory, Monterey, California, USA. 2 Department of Atmospheric Sciences and Global Environment Laboratory, Yonsei University, Seoul, South Korea. Copyright 2009 by the American Geophysical Union. 0094-8276/09/2008GL037146 current atmospheric numerical models [Arakawa, 2004]. Model results vary considerably depending on a particular parameterization scheme utilized in a model, as is revealed in numerous studies on GCM intercomparison [e.g., Sperber and Palmer, 1996; Shukla et al., 2000; Kang et al., 2002]. For example, in the studies by Shukla et al. [2000] and Kang et al. [2002] on the predictability of seasonal forecast models, the internal variability of models with different physics is extreme even though these models share an identical dynamic core. [4] Although the theoretical concept used in a particular parameterization scheme for a specific physical process is physically reasonable, its performance can be unsatisfactory when we do not fully understand the interaction among the physical processes in models as well as in nature. In this study, we demonstrate an example of such an interaction issue in the parameterization of physical processes for atmospheric models. The present study compares the simulated winter climatology in a GCM by modulating selected parameters in two physical parameterization schemes; of gravity-wave drag process induced by subgrid-scale orography (GWDO) and planetary boundary layer (PBL) process. The focus is on the impact of GWDO on the simulated zonal mean climatology of the zonal wind and temperature, which is greatly influenced by the representation of the stable boundary layer (SBL) mixing process. Section 2 describes the experimental setup, and experiment results are discussed in section 3. Concluding remarks are given in the final section. 2. Experimental Setup [5] The model used for this study is a version of the National Centers for Environmental Prediction (NCEP) global spectral model [Kanamitsu et al., 2002a] used for Medium-Range Forecast (MRF), and the experimental setup closely follows the study of Hong et al. [2008], which includes the implementation by Kim [1996] of lowertropospheric enhancement of GWDO due to selective low-level wave-breaking with the aid of additional orographic statistics [Kim and Arakawa, 1995] (hereinafter referred to as KA). By integrating short- and medium-range forecasts as well as seasonal simulations, Hong et al. [2008] examined the impact of enhanced lower-tropospheric KA GWDO against traditional GWDO due to upper-level wave breaking documented by J. Alpert et al. (Sensitivity of cyclogenesis to lower tropospheric enhancement of gravity wave drag using the environmental modeling center medium range model, paper presented at 11th Conference on Numerical Weather Prediction, American Meteorological Society, Norfolk, Virginia, 19 23 August 1996). They reported improvements of the simulated seasonal climate L12809 1of5

Table 1. A Summary of the Experiments and the 3-Year Ensemble-Averaged Global Wave Stress at the Reference Level and 500, 100, and 50 hpa Height Global Eddy PCs PC Experiment Reference Level Implementation Stable Boundary Layer Mixing PBL Height (m) Wave Stress (N/m 2 ) 500 hpa 100 hpa 50 hpa ogwobl Kim [1996] Hong et al. [2006] 371.1 0.0168 0.855 0.666 0.349 ogwnbl Kim [1996] Hong [presented paper, 2007] 514.7 0.0167 0.857 0.749 0.550 ngwobl Hong et al. [2008] Hong et al. [2006] 368.3 0.0221 0.888 0.734 0.470 ngwnbl Hong et al. [2008] Hong [2007] 502.7 0.0192 0.889 0.754 0.545 by including the KA GWDO scheme in the horizontal distribution of the large-scale fields, such as precipitation and geopotential heights. They concluded that the enhanced lower-level GWDO should be parameterized properly in global atmospheric models for NWP and seasonal prediction. It is noted here that Hong et al. [2008] employs an enhanced SBL mixing in the PBL scheme, which is described below. [6] The PBL scheme used in this study is the Yonsei University (YSU) PBL scheme [Hong et al., 2006]. The YSU scheme considers the entrainment flux above the PBL top height, h, which expresses the penetration of entrainment flux above h irrespective of local stability. Note that the algorithm by Hong et al. [2006] does not contain a specific formulation for the SBL. In other words, the turbulence mixing within the SBL is treated as free atmospheric diffusion by computing the diffusion coefficient K = l 2 f(ri)(@u/@z) as functions of the mixing length l, the stability function f(ri) represented in terms of the local gradient Richardson number Ri, and the vertical wind shear @U/@z. In the new SBL scheme by S.-Y. Hong (Stable boundary layer mixing in a vertical diffusion scheme, paper presented at Fall Conference, Korea Meteorological Society, Seoul, 25 26 October 2007), the vertical diffusion coefficient K = kw s z(1 z/h) 2 is computed as in the case of unstable conditions in the YSU PBL, where k is the von Karman constant (=0.4) and w s the mixed layer velocity scale, and z is the height from the surface. The major differences between the current and new SBL schemes are that the new scheme includes i) the computation of h using bulk Ri greater than 0, and ii) the cubic profile of the eddy diffusivity coefficients with height. The magnitudes of the coefficients in the new scheme can be smaller or larger than those in the old scheme. It is, however, expected that the SBL height in the new scheme is always greater than that from the old scheme. [7] Hong et al. [2008] recognized that the assumption of an SBL is critical for the KA GWDO scheme to perform adequately. In this study, the impact of the choice of the reference level in the KA scheme on a simulated seasonal climatology is evaluated with the two SBL parameterizations in combination with two different ways to implement the reference level that represents the state of low-level flow (for the KA GWDO parameterization, Table 1), which determines the initial height and magnitude of wave stress. Results from the experiments with the KA scheme using two different reference level determinations are evaluated by changing the SBL mixing in the YSU PBL scheme. Unlike the SBL formulation, the determination of the reference level still remains uncertain to define physically and is largely regarded as an engineering problem although great efforts have been made for improvement. We do not attempt to address this fundamental issue in this study and limit our discussion to the impact of the different methods. The ogw (denoting old GWD reference level) experiments compute the reference level following the original setup of Kim [1996] based on the height of the PBL, whereas the ngw (i.e., new GWD reference level) experiments take the greater value of the PBL height and the doubled value of the standard deviation of the subgrid-scale orography as implemented by Hong et al. [2008] following Kim and Doyle [2005]. [8] All the seasonal simulations are performed for boreal winters in December/January/February (DJF) for the years 1996/1997, 1997/1998, and 1999/2000. To estimate and filter out the unpredictable part of the flow, five-member ensemble runs are performed. The ensemble runs are initialized at 00 UTC 1, 2, 3, 4, and 5 November. Each simulation thus consists of 15 runs. Initial conditions are derived from the NCEP Reanalysis II [Kanamitsu et al., 2002b] data with a resolution of 2.5. As the surface boundary condition, the observed sea surface temperature data were used with a resolution of 1 during the simulation period. The model employs a resolution of T62L28 (triangular truncation at horizontal wave number 62 and 28 terrain-following vertical levels). The composites of the three-year simulations are presented and discussed. 3. Results and Discussion [9] Figure 1 compares the zonally-averaged zonal wind and temperature fields, which were obtained with the old (ogwobl experiment; Figures 1a and 1b) and new (ogwnbl experiment; Figures 1c and 1d) SBL mixing schemes, and both with the original implementation of the KA GWDO scheme, i.e., using the PBL height to determine the reference level following Kim [1996]. These fields are the averages over the three years obtained from the 15- member ensembles. The biases, denoted by color shading, are three-year averages of the deviations of the simulations from the corresponding reanalysis in each year. It was confirmed that areas of difference fields (color shading) are statistically significant with the level of significance greater than 95% (not shown). The zonal wind and temperature biases in the ogwobl experiment (Figures 1a and 1b) are exorbitant as shown by the difference from the reanalysis. Most noticeably, there is no separation between the polar night and subtropical jet streams, and there is significant temperature bias in the stratosphere, especially in the high latitudes. In fact, the simulated climatology from the ogwobl experiment (Figures 1a and 1b) is similar to that 2of5

Figure 1. Three-winter mean ensemble averages (contours) of (a, c, e) the zonal mean zonal wind and (b, d, f) temperature obtained from the experiments with the original implementation of the KA GWDO scheme and with the old (Figures 1a and 1b) and new (Figures 1c and 1d) SBL mixing scheme. Superimposed color shades are the differences from the NCEP reanalysis. The differences between the two experiments are shown in Figures 1e and 1f. with no GWDO parameterization due to the seriously underestimated wave stress at the reference level and aloft. [10] The biases are reduced considerably by replacing the old SBL mixing with the new one in the ogwnbl experiment (Figures 1c and 1d) although they are still quite large. The new SBL scheme helps greatly reduce the excessive biases (although not sufficiently) by enhancing the mixing in the PBL (Figures 1e, and 1f) and thus raising the height of the PBL (Table 1). In the KA GWDO scheme, the wave stress at the reference level, t 0, is proportional to a cubic power of the horizontal wind speed for large Froude number when low-level wave breaking is active, generating drag (t 0 / U 0 3 ; the subscript 0 for U denotes a low-level average). This implies that the GWDO process interacts closely with the SBL process in the modeled atmosphere. Since the reference level is around the PBL height (h) inthe ogw experiments, the wave stress at the reference level may have been underestimated when h becomes very low directly affecting (mostly reducing) the wave drag in the upper levels. The large difference between the two experiments (see also Figures 1e and 1f) demonstrates the fact that the performance of a parameterization scheme, in our case a GWDO parameterization scheme, depends strongly on other physics parameterization, in this case, a PBL mixing scheme. [11] Figure 2 compares the ensemble simulations obtained with the old (ngwobl, Figures 2a and 2b) and new (ngwnbl, Figures 2c and 2d) SBL mixing schemes, and with the reference level for the initial wave stress determined following the method by Kim and Doyle [2005] as used by Hong et al. [2008]. Both the ngwobl and ngwnbl experiments generally reproduce the seasonal mean state of the zonal-mean zonal wind and temperature, which is large improvement over the simulation with the original GWDO reference level (Figure 1). The mid-latitude jet streams in both hemispheres and temperature distributions depict a typical climatological distribution of the winds and temperature. [12] A noticeable improvement is found in the northern polar stratosphere when the new SBL mixing scheme is used (Figures 2c and 2d) in comparison with the old scheme (Figures 2a and 2b; see also the difference fields, Figures 2e and 2f). The magnitude of the correction in these experiments with the new GWDO scheme is not sufficient to compensate for the entire bias present in the simulation with the old GWDO scheme, such as the excessive westerly winds above the tropospheric jets, strong easterly winds in the tropical upper troposphere, and cold bias above the tropopause, which may be due to deficiencies in other physical parameterizations. The enhanced SBL mixing in ngwnbl results in further deceleration of the polar night jet (Figure 2e) and warming of the lower polar stratosphere (Figure 2f), which suggests that GWDO is more active with the new SBL scheme. Excessive westerlies above the 3of5

Figure 2. As in Figure 1, but with the new way to implement the KA GWDO scheme. tropospheric jets are weakened by about 10%. The cold bias in the polar areas in the northern hemisphere is significantly reduced by about 40% while the bias is slightly larger in the southern subtropical stratosphere. [13] It is noteworthy that, while the direct influence of the SBL processes in the model physics is limited to near the surface, the overall impact is propagated into the middle atmosphere. The reason can be deduced again from the fact that the KA GWDO scheme interacts closely with the SBL structure. For ngw experiments, the low-level average is taken between the surface and the greater of the doubled standard deviation of subgrid-scale orography (2s) and the PBL height (h) following Kim and Doyle [2005]. In typical nocturnal boundary conditions over land, U 0 increases as the depth for the average increases. [14] Comparison of Figures 1 and 2 reveals that the impact of the change in the GWDO reference level determination on the simulated climate is significant with any SBL mixing method. The wave stress at the reference level, t 0, was likely underestimated in the ogw experiments (Figure 1 and Table 1), but is systematically larger in the ngw experiments (Figure 2 and Table 1) due to better determination of the reference level in the KA scheme, allowing more gravity waves to escape the lower atmosphere, propagate upwards and break, generating drag. [15] Figure 3 compares among the experiments the diurnal variations of the averaged h over a Tibetan plateau area. It is seen that h is larger at given time in the nbl experi- Figure 3. Three-winter ensemble averages of the diurnal variation of the PBL height over a Tibetan plateau area (60 120E, 20 60N) obtained from the ngwnbl (thick solid line), ngwobl (thick dashed line), ogwnbl (thin solid line) and ogwobl (thin dashed line) experiments. The value of 2s for this area is 626.36 m (dash-dotted straight line). 4of5

ments, but is lower than the 2s value of 626.36 m. With ngw, when h becomes very low over land, typically at night, the height of the reference level for calculating the wave stress is exclusively determined by the 2s term since h <2s (note that h values in Figure 3 are averages over time and ensembles, and they can vary greatly at a specific time and case, leading to h >2s). The use of the new SBL scheme along with ngw, therefore, generally results in higher reference level due to either/both higher PBL or/ and high value of 2s, and improves (weakens) the polar night jet through improved wave breaking, as compared with that of the old SBL scheme. The alleviation of the cold bias in the polar stratosphere in the northern hemisphere can be described by the thermal wind relation associated with GWDO around the polar night jet. [16] On the other hand, Table 1 also shows that the wave stress at the reference level is larger in ngwobl than in ngwnbl, which includes enhanced SBL mixing, but the skill is higher with ngwnbl. This is because a larger wave stress at the reference level does not improve the simulation if overestimated although that sometimes looks beneficial near the surface (but with side effects) in global atmospheric models through increased total drag [Kim, 2007]. What is important is an optimal vertical variation of an adequate amount of the reference-level wave stress. [see, e.g., Kim et al., 2003]. [17] Finally, Table 1 compares the three-year ensemble averages of weather forecast skill in terms of the global geopotential height eddy pattern correlation (PC) coefficients at selected heights. It is seen that the improvements in the simulations discussed in this study correlate well with the global PC scores. The skill for the ngwnbl experiment is higher than other experiments especially at higher altitudes, except at 50 hpa compared with ogwnbl. Based on these results, we find that the interaction between GWDO and PBL processes is better represented by the new method determining the reference level for the KA GWDO when used together with the new enhanced SBL mixing scheme (i.e., ngwnbl). In order for the improved method for the reference level for the GWDO parameterization to work properly, the SBL mixing should be represented reasonably well. 4. Concluding Remarks [18] This study demonstrates that the performance of the KA GWDO parameterization in the NCEP MRF model depends strongly upon how the SBL mixing processes are represented in the vertical diffusion parameterization as well as upon how the reference level itself is determined. In other words, the interaction between the PBL and GWDO processes plays an important role in properly representing the drag processes. The new SBL parameterization in the NCEP MRF model tends to produce higher PBL height in stable conditions, which leads to an improvement in the performance of the KA scheme by enhancing the GWDO activity, especially at upper levels. [19] The core formulations of the KA GWDO scheme and the new SBL mixing scheme were separately validated by an extensive database obtained from explicit simulations (the former by Kim and Arakawa [1995] and Kim and Doyle [2005], and the latter by S.-Y. Kim et al., Test of revised YSU PBL model within WRF-Chem model, paper presented at the 8th WRF users workshop, National Center for Atmospheric Research, Boulder, Colorado, 23 27 June 2008, available at http://wrf-model.org and others). It is difficult, if not impossible, to properly represent each physical process in a numerical atmospheric model, due not only to the limitation in our knowledge and technology in representing its effect, but also to complex combined feedback from all the parameterizations in the model. This study showed an example that individually small improvements in representing the SBL mixing and the reference level result synergically in large improvements in the simulated climate, which is highly sensitive to the interaction between the SBL and GWDO processes. [20] One of the challenges for atmospheric modelers to face in developing the next generation atmospheric models may well be how to effectively merge (or strongly couple) various model components, currently represented separately in the models. [21] Acknowledgments. Y.J.K. was supported by the Office of Naval Research under ONR Program Element 0601153N. This study was also partially supported by the Korean Foundation for International Cooperation Science and Technology (KICOS) through a grant provided by the Korean Ministry of Science and Technology (MOST) in 2008, and by the project Development of the numerical prediction technique for the improved military weather support through a grant provided by the Republic of Korea Air Force (ROKAF) in 2009. The comments from J. Doyle are appreciated. The comments from the anonymous reviewers were helpful. References Arakawa, A. (2004), The cumulus parameterization problem: Past, present, and future, J. Clim., 17, 2493 2525. Hong, S.-Y., J. Choi, E.-C. Chang, H. Park, and Y.-J. Kim (2008), Lower tropospheric enhancement of gravity wave drag in a global spectral atmospheric forecast model, Weather Forecast., 23, 523 531. Hong, S.-Y., Y. Noh, and J. Dudhia (2006), A new vertical diffusion package with an explicit treatment of entrainment processes, Mon. Weather Rev., 134, 2318 2341. Kanamitsu, M., et al. (2002a), NCEP dynamical seasonal forecast system, Bull. Am. Meteorol. Soc., 83, 1019 1037. Kanamitsu, M., W. Ebisuzaki, J. Woollen, S.-K. Yang, J. J. Hnilo, M. Fiorino, and G. L. Potter (2002b), NCEP-DOE AMIP-II reanalysis (R-2), Bull. Am. Meteorol. Soc., 83, 1631 1643. Kang, I.-S., et al. (2002), Intercomparison of atmospheric GCM simulated anomalies associated with the 1997/98 El Niño, J. Clim., 15, 2791 2805. Kim, Y.-J. (1996), Representation of subgrid-scale orographic effects in a general circulation model. Part I: Impact on the dynamics of simulated January climate, J. Clim., 9, 2698 2717. Kim, Y.-J. (2007), Balance of drag between the middle and lower atmospheres in a global atmospheric forecast model, J. Geophys. Res., 112, D13104, doi:10.1029/2007jd008647. Kim, Y.-J., and A. Arakawa (1995), Improvement of orographic gravity wave parameterization using a mesoscale gravity-wave model, J. Atmos. Sci., 52, 875 1902. Kim, Y.-J., and J. D. Doyle (2005), Extension of an orographic drag parametrization scheme to incorporate orographic anisotropy and flow blocking, Q. J. R. Meteorol. Soc., 131, 1893 1921. Kim, Y.-J., S. D. Eckermann, and H.-Y. Chun (2003), An overview of the past, present and future of gravity-wave drag parameterization for numerical climate and weather prediction models, Atmos. Ocean, 41, 65 98. Shukla, J., et al. (2000), Dynamic seasonal prediction, Bull. Am. Meteorol. Soc., 81, 2593 2606. Sperber, K. R., and T. N. Palmer (1996), Interannual tropical rainfall variability in general circulation model simulations associated with the Atmosphere Model Intercomparison Project, J. Clim., 9, 2727 2750. S.-Y. Hong, Department of Atmospheric Sciences, Yonsei University, Seoul 120-749, South Korea. (shong@yonsei.ac.kr) Y.-J. Kim, Marine Meteorology Division, Naval Research Laboratory, 7 Grace Hopper Avenue, Stop 2, Monterey, CA 93943-5502, USA. 5of5