The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010
Numerical simulation of turbulence structures in the neutralatmospheric surface layer with a mesoscale meteorological model, WRF Yasuo Hattoria, Chin-Hoh Moeng b, Hiromaru Hirakuchic, Shuji Ishiharad, Soichiro Sugimotoe, Hitoshi Sutof a
Central Research Institute of Electric Power Industry, Chiba, Japan,
[email protected] b National Center of Atmospheric Science, Colorado, USA,
[email protected] c Central Research Institute of Electric Power Industry, Chiba, Japan,
[email protected] d Denryoku Computing Center, Chiba, Japan,
[email protected] e Central Research Institute of Electric Power Industry, Chiba,
[email protected] f Central Research Institute of Electric Power Industry, Chiba,
[email protected] ABSTRACT: The performance of turbulence simulations in the neutral-atmospheric boundary layer, especially near the ground, is investigated using a widely-used numerical weather forecasting model WRF at very fine resolutions. The horizontal grid spacing Δh is varied from 50 m to 300 m. An idealized condition is set; the terrain is flat and the surface roughness is homogeneous with periodic lateral boundary conditions. Comparison between a large-eddy simulation (WRF-LES) and WRF simulation with a planetary boundary layer (PBL) scheme shows that the predicted turbulence characteristics near the ground depend strongly on the turbulence scheme. With LES, as the grid becomes finer, the intensities of the resolvable velocity fluctuations increase as expected; however only with Δh = 50 m the LES solution begins to agree well with observations. On the other hand, with the PBL scheme the intensities of the “resolvable-scale” velocity fluctuations remain the same regardless of grid resolutions. Of all the simulations performed, only the LES with Δh = 50 m can capture the commonly observed streak structure near the ground. 1 INTRODUCTION A better understanding of turbulence phenomena near the ground in the neutralatmospheric boundary layer is of practical interest not only for numerical weather predictions but also in wind-engineering applications. Most international codes and standards for wind-resistance design provide procedures for assessing turbulence statistics of strong wind under neutral conditions (Ishikawa, 2004). However, the statistics estimated with respective codes and standards show considerable scatter for same terrain conditions, and this scatter has caused uncertainties in the wind-load predictions (Zhou et al., 2002). A source of the scatter might be “detached eddies” (or mesoscale phenomena) in the atmospheric boundary layer; detached eddies, which have a larger scale than turbulence of windshear, can modify turbulence characteristics near the ground as suggested by Högström et al. (2002), which was supported by observations (Drobinski et al., 2004; 2007) and a windtunnel experiment (Hattori et al., 2010), but the effects of overlying detached eddies on the turbulence structure near the ground have not been clearly understood yet, because of the difficulty in obtaining multi-point simultaneous velocity fluctuations with observations and in confirming the scale-similarity with experiments.
The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010
To understand the mesoscale-turbulence interaction, we adopt a widely-used mesoscale meteorological model WRF with fine-resolutions to study turbulence phenomena in the atmospheric boundary layer. This approach has provided new knowledge about turbulence of the convective boundary layer (Golaz et al., 2005), over complex terrain (Weigel et al., 2007; Michioka and Chow, 2008), and in a hurricane boundary layer (Zhu, 2008). However, the subgrid-scale turbulence in fine-resolution WRF simulations poses a major problem (e.g. Takemi and Rotunno, 2003; Chow et al., 2006; Moeng et al., 2007; Wang et al., 2009), and its development still remains a topic of interest. In this study, we focus on the effects of grid resolutions and turbulence modeling approaches on the predicted turbulence characteristics when the grid resolution of WRF approaches the dominant turbulent eddy sizes. We carry out WRF simulations of an idealized neutral PBL, with a horizontal grid spacing Δh varied from 50 m to 300 m. On one hand, this range of grid spacing is too coarse for the LES approach of the neutral PBL where the energy-dominant turbulent eddies are on the order of 100 m. On the other hand, this grid spacing is too fine for WRF to adopt the RANS (which predicts ensemble-mean statistics) modeling approach, i.e., a PBL turbulence scheme. With no proper theory to handle turbulence for WRF with this grid spacing, we will use both turbulence approaches, compare their predicted turbulence statistics, study their grid dependence, and verify them with observations. 2 EXPERIMENT SETUP We consider an idealized neutral PBL, which is similar to that of previous studies by Andren and Moeng (1994), Moeng and Sullivan (1994) and Moeng et al. (2007). The terrain is flat and the surface roughness is homogeneous with periodic lateral boundary conditions. The computational domain is 6 × 6 km2 in horizontal directions and 2 km in vertical direction. The geostropic wind speed and the Coriolis parameter f are set to 10 ms-1 and 10-4 s1 , respectively. The initial potential temperature is constant (300 K) below the boundary layer height (≅ 1000 m), and the capping inversion is imposed above it. The momentum flux at the ground is given by using Monin-Obukov similarity theory with the roughness height of 0.1 m. The heat flux at the ground is set to zero for neutral condition. We use the Advanced Research WRF (version 3.1), which has been widely used all over the world for numerical weather prediction. The model details are described in Skamarock et al. (2008). We choose the fifth- and third-order differencing schemes for horizontal and vertical advection terms and the third-order Runge-Kutta scheme with small time step for time integration for all simulations. The WRF model is used in two modes: One is WRF-LES where the 3-dimensional eddy viscosity predicted by the TKE equation for the 1.5-order turbulence closure is used to represent subgrid-scale diffusion and no PBL scheme is used. The other is the conventional WRF-weather model that uses a RANStype PBL scheme; here we chose the Mellor-Yamada-Janjic model (Janjic, 1990), which uses the root-mean-square of TKE as the turbulence velocity scale, to represent PBL turbulence, and the horizontal momentum flux is estimated by the Smagorinsky scheme with the model constant of 0.18. The horizontal grid spacing Δh is varied from 50 m to 300 m to examine grid dependency of predicted turbulence statistics. The vertical grid is the same for all simulations with grid spacing of about 25 m. We confirmed that turbulence statistics do not change significantly when the vertical grid resolution is changed from 10 m to 50 m, except below the height of 30 m.
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The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010
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Figure 1. Time evolution of surface friction velocity Uτ for LES. m, 100 m, and 300 m.
Figure 2. Time evolution of surface friction velocity Uτ for PBL scheme (MYJ model). lines are for Δh = 50 m, 100 m, and 300 m.
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The simulation was run for 10 hours ( = 3.6/f) and the statistics were estimated with averaging over the horizontal plan and over the last two hours of the simulations. The rum time (≅ 3.6/f) is quite small compared with that of Andren et al. (1994) ( = 10/f). Thus, we previously checked the time evolution of turbulence statistics during run time, and found that statistics do not show the tendency to increase or decrease against time during the last two hours. For instance, the time evolutions of surface friction velocity Uτ for LES and PBL scheme are displayed in figures 1 and 2. They imply that 10 hours may be long enough to generate a quasi-steady PBL. 3 RESULTS AND DISCUSSION 3.1 Turbulence statistics First, we examine the change in predicted turbulence statistics with grid resolutions for the LES and the PBL scheme. Figure 3 shows ensemble-averaged surface friction velocity against horizontal grid spacing Δh. Different turbulence modeling predicts different values of Uτ,; the PBL scheme yields ≅ 0.62 ms-1, which is quite larger than that from LES ( ≅ 0.50 −
The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010
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0.58 ms-1). The grid dependency appears only for the LES; the predicted from LES increases with Δh, while the with the PBL is almost independent of Δh. The value predicted from LES with Δh = 50 m agrees the most with that of previous LESs under the same conditions (Andren and Moeng, 1994; Moeng and Sullivan, 1994; Moeng et al. 2007). Figure 4 shows vertical profiles of time-averaged resolvable-scale momentum flux with velocity fluctuation , normalized by . Note that, they are estimated only with grid-scale (GS) components. Surprisingly, even the simulations with a PBL (RANS) scheme provides a considerable amount of GS turbulence flux in the boundary layer (below about z = 1000 m, where z refers to vertical distance from the ground), i. e., the maximum value of /2 reaches 0.77 at z ≅ 100 m with LES and 0.61 at z ≅ 200 m with PBL for Δh = 50 m. The PBL scheme, which is based on ensemble-averaged equations, is
The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010
Table 1. Comparison of intensity and anisotropy of velocity variance between present predictions with grid spacing Δh = 50 m and observations. LES
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Counihan (1975)
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Figure 5. Vertical profile of time-averaged velocity variances σh (horizontal grid-scale component), σz (vertical grid-scale component), σsgs (subgrid-scale component) for (a) LES and (b) PBL scheme (MYJ model). Solid-, dash-, and dot-lines are for Δh = 50 m, 100 m, and 300 m.
supposed to parameterize all turbulence effects in the sub-grid scale (SGS) component, whereas the LESs expect contributions of both GS and SGS components. The unanticipated GS momentum flux from the PBL-scheme approach may have generated extra momentum transfer and hence overestimated the surface friction velocity (Fig. 3). The overestimation of the surface friction velocity may be a source of the bias of the surface winds in the numerical weather predictions with the increase in grid resolutions. Figure 5 shows the vertical profiles of the time-averaged GS velocity variances of horizontal component , vertical component , and the SGS component , normalized with . Here, the SGS are taken to be 2/3 of SGS turbulence kinetic energy with the assumption of isotropy turbulence for small scales. When the LES approach is used, as grid resolutions become finer, the intensities of velocity fluctuations of GS components increase, whereas those of SGS components decrease. On the other hand, the intensities of the GS with the PBL scheme remain the same for all grid resolutions, and are smaller than those of LESs. The GS with the PBL scheme increase slightly with the increase in grid resolution and the magnitudes are about the same as those of LESs. As compared in Table 1, the predicted turbulence intensity and anisotropy in GS components from the LES at Δh = 50 m best agree to those of observations.
The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010
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Figure 6. Contours of instantaneous surface friction velocity with iso-surface of second invariant of velocity gradient for (a) LES and (b) PBL scheme (MYJ model). Both are for Δh = 50 m.
3.2 Structural characteristics of resolvable motions We also examine the GS structural characteristics near the ground with Δh = 50 m, which gives a general agreement of turbulence statistics between the LES and observations. Figure 6 depicts a typical example of visualized instantaneous turbulence structure by using contours of instantaneous surface friction velocity and iso-surface of second invariant of velocity gradients, which corresponds to a vortex surface. The turbulence structure simulated with the LES apparently differs from that with the PBL. The LES presents the streaky structure in the low-speed (small surface friction velocity) regions, relating to the vortex generation, whereas no streaky structure could be recognized in the PBL simulation. The auto-correlation of instantaneous streamwise-velocity against spanwise spacing, Δy, which is calculated with instantaneous velocities also clearly show the dependence of turbulence modeling. For the LES, auto-correlation near the ground (z ≅ 50 m) takes minimum value at Δy = 250 m, consistent roughly with the observed in the atmospheric surface layer (Drobinski et al., 2007). With the increases in z, the minimum value of autocorrelation becomes weak and then disappears at z ≅ 500 m. On the other hand, autocorrelation for the PBL does not clearly take a minimum value even near the ground. These results also provide the evidence that only the LES with the proper grid resolution can simulate the streak structure near the ground. From these results, we found that the subgrid-scale parameterization of turbulence in a fine-grid weather forecasting model can strongly affect the simulated turbulence structure near the ground, and the LES with horizontal grid spacing of 50 m has a capability to capture main feature of turbulence near the ground. It can simulate the streak structure near the ground, which has a spatial scale of several hundred meters in the spanwise direction, and also predict turbulence statistics quantitatively. As the WRF-LES grid spacing becomes coarse, the contribution of GS components to the turbulence is attenuated, and simultaneously that of SGS components increases. However, that increase is not enough to compensate for the reduction in the GS components. The value of horizontal grid spacing, Δh = 50 m, for simulating turbulence structure near the ground agree well with previous LESs
The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010
of shear-driven atmospheric boundary layer (e.g. Andren and Moeng, 1994; Moeng and Sullivan, 1994) and also the peak of velocity fluctuations agrees with observations (Tab. 1). It is puzzling that with a PBL (RANS) scheme, the WRF model still generates a lot of GS velocity fluctuations in the PBL over a uniform surface. The fluctuations do not change with horizontal grid spacing, and its horizontal and vertical velocity components are negatively correlated. This correlation generates a “pseudo turbulence momentum flux” and results in an overestimation of the surface friction velocity when the PBL scheme is used in WRF at a fine grid resolution. 4 CONCLUSIONS In this study, we investigated the performance of turbulence structure simulation in the neutral surface layer with a mesoscale meteorological model, Advanced Research WRF. The special attention was paid to the dependence of turbulence modeling on simulations with very fine grid resolutions (horizontal grid spacing below 300 m). To clearly understand the basic behavior of WRF, we considered an idealized surface layer with flat terrain, uniform surface roughness height, and periodic lateral boundary conditions. Comparison between large-eddy simulation (LES) and simulation with a PBL scheme clearly showed that the subrid-scale turbulence parameterization can strongly affect the predicted GS and SGS turbulence characteristics near the ground. The LES approach with a horizontal grid spacing < 50 m should be used in order to capture the proper turbulent wind properties in the neutral surface layer. Rotunno et al. (2009) have recently argued the importance of very fine resolutions for simulating gust winds in tropical cyclones with WRF. To reduce the uncertainties in the estimation of wind load, we will improve the turbulence parameterization in WRF and perform simulations under a realistic weather conditions for strong winds, as well as including the effect of detached eddies. 5 ACKNOWLEDGEMENTS The authors would like to thank Dr. Sun JuanZhen for helps of the collaboration between NCAR and CRIEPI. The authors also would like to thank Mr. Takahiro Murakami, Dr. Takenobu Michioka, Dr. Atsushi Hasimoto, and Dr. Naoto Kihara for fruitful discussions about the understanding of results. C.-H. Moeng's work is supported by the National Center for Atmospheric Research, USA, which is sponsored by the National Science Foundation. 6 REFERENCES Andren, A., Brown, A. R., Graf, J., Mason, P. J., Moeng, C.-H., Nieuwstadt, F. T. M., Schumann, U., 1994. Large-eddy simulation of a neutrally stratified boundary layer: a comparison of four computer codes. Q. J. Roy. Meteorol. Soc. 120. 1457-1484 Chow, F. K., Weigel, A. P., Street, R. L., Rotach, M. W., Xue, M., 2006. High-resolution large-eddy simulations of flow in a steep alpine valley. Part 1: methodology, verification, and sensitivity experiments. J. Appl. Meteor. Climatol. 45, 63-86. Counihan, J., 1975. Adiabatic atmospheric boundary layers: a review and analysis of data from the period 1880-1972. Atmos. Environ. 9, 871-905.
The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010
Drobinski, P., Carlotti, P., Newsom, R. K., Banta, R. M., Foster, R. C., Redelsperger, J.-L., 2004. The structure of the near-neutral atmospheric surface layer. J. Atmos. Sci. 61, 699-713. Drobinski, P., Carlotti, P., Redelsperger, J.-L., Banta, R. M., Masson, V., Newsom, R., 2007. Numerical and experimental investigation of the neutral atmospheric surface layer. J. Atmos. Sci. 64, 137-156. Golaz, J.-C., Wang, S., Doyle, J. D., Schmidt, J. M., 2005. COAMPS-LES: model evaluation and analysis of second-and third-moment vertical velocity budgets. Boundary-Layer Meteorology 116, 487-517 Grant, A. L. M., 1992. The structure of turbulence in the near-neutral atmospheric boundary layer. J. Atmos. Sci. 49, 226-239. Hattori, Y., Moeng, C.-H., Suto, H., Tanaka, N., Hirakuchi, H., 2010. Wind-tunnel experiment on logarithmic-layer turbulence under the influence of overlying detached eddies. Boundary-Layer Meteorology 134, 269-283. Högström, U., 1990. Analysis of turbulence structure in the surface layer with a modified similarity formulation for near neutral conditions. J. Atmos. Sci. 47, 1949-1972. Högström, U., Hunt, J. C. R., Smedman, A.-S., 2002. Theory and measurements for turbulence spectra and variances in the atmospheric neutral surface layer. Boundary-Layer Meteorology 103,101-124. Ishikawa, T., 2004. A study on wind load estimation method considering dynamic effect for overhead transmission lines. ph.D thesis, Waseda University, 259 pp. Kunkel, G. J., Marusic, I., 2006. Study of the near-wall-turbulent region of the high- Reynolds-number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375-402. Michioka, T., Chow, F. K., 2008. High-resolution large-eddy simulations of scalar transport in atmospheric boundary layer flow over complex terrain. J. Applied Meteorol. Climatology 47, 3150-3169. Moeng, C.-H., Sullivan, P., 1994. A comparison of shear- and buoyancy-driven planetary boundary layer flows. J. Atmos. Sci. 51, 999-1022. Moeng, C.-H., Dudhia, J., Klemp, J., Sullivan, P., 2007. Examining two-way grid nesting for large eddy simulation of the PBL using the WRF model. Monthly Weather Review 135, 2295-2311. Janjic, Z. I., 1990. The step-mountain coordinate: physical package. Monthly Weather Review 188, 14291443. Rotunno, R., Chen, Y., Wang, W., Davis, C., Dudhia, J., and Holland, G. J., 2009. Large-eddy simulation of an izdealized tropical cyclone. Bull. American Meteorological Soc. 90, 1783-1788. Skamarock, W. C., Klemp, J. B., Dudhia, J., Gill, D. O., Barker, D. M., Duda, M. G., Huang, X.-Y., Wang, W., Powers, J.G., 2008. A description of the advanced research WRF version 3. NCAR/TN-475+STR, 113pp Takemi, T., Rotunno, R., 2003. The effects of subgrid model mixing and numerical filtering in simulations of mesoscale cloud systems. Monthly Weather Review 131, 2085-2101. Wang, H., Skamarock, W. C., Feingold, G., 2009. Evaluation of scalar advection schemes in the advance research WRF model using large-eddy simulations of aerosol-cloud interactions. Monthly Weather Review 137, 2547-2558. Weigel, A. P., Chow, F. K., Rotach, M. W., 2007. The effect of mountainous topography on moisture exchange between the “surface” and the free atmosphere. Boundary-Layer Meteorology 125, 227-244. Zhou, Y., Kijewsk, T., Kareem, A., 2002, Along-wind load effects on tall buildings: comparative study of major international codes and standards. J. Struct. Eng. 126, 788-796. Zhu, P., 2008. Simulation and parameterization of the turbulent transport in the hurricane boundary layer by large eddies. J. Geophysical Res. 113, D17104.
