On the Ability of the WRF Model to Reproduce the Surface Wind Direction over Complex Terrain

Transcription

1 1610 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 52 On the Ability of the WRF Model to Reproduce the Surface Wind Direction over Complex Terrain PEDRO A. JIM ENEZ Division de Energías Renovables, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas, Madrid, Spain, and Mesoscale and Microscale Meteorology Division, National Center for Atmospheric Research,* Boulder, Colorado JIMY DUDHIA Mesoscale and Microscale Meteorology Division, National Center for Atmospheric Research,* Boulder, Colorado (Manuscript received 4 October 2012, in final form 22 February 2013) ABSTRACT The ability of the Weather Research and Forecasting (WRF) model to reproduce the surface wind direction over complex terrain is examined. A simulation spanning a winter season at a high horizontal resolution of 2 km is compared with wind direction records from a surface observational network located in the northeastern Iberian Peninsula. A previous evaluation has shown the ability of WRF to reproduce the wind speed over the region once the effects of the subgrid-scale topography are parameterized. Hence, the current investigation complements the previous findings, providing information about the model s ability to reproduce the direction of the surface flow. The differences between the observations and the model are quantified in terms of scores explicitly designed to handle the circular nature of the wind direction. Results show that the differences depend on the wind speed. The larger the wind speed is, the smaller are the wind direction differences. Areas with more complex terrain show larger systematic differences between model and observations; in these areas, a statistical correction is shown to help. The importance of the grid point selected for the comparison with observations is also analyzed. A careful selection is relevant to reducing comparative problems over complex terrain. 1. Introduction Topography produces strong modifications of the synoptic-scale circulation, leading to high spatial variability in the surface flow over areas of complex terrain (Whiteman 2000). This effect makes simulation by mesoscale models (Pielke 2002) challenging since relevant topographic features are poorly represented, even at high horizontal resolutions of a few kilometers (e.g., Rife et al. 2004; Jimenez and Dudhia 2012). Indeed, the effects associated with the topography that are not explicitly resolved by the models need to be parameterized to have a more realistic formulation of the surface * The National Center for Atmospheric Research is sponsored by the National Science Foundation. Corresponding author address: Pedro A. Jimenez, Mesoscale and Microscale Meteorology Division, National Center for Atmospheric Research, 3450 Mitchell Ln., Boulder, CO jimenez@ucar.edu circulations (Mesinger et al. 1996; Wood et al. 2001; Beljaars et al. 2004; Rontu 2006; Jimenez and Dudhia 2012). For instance, Jimenez and Dudhia (2012, hereinafter JD12) found that the effects produced by the resolved and unresolved topography both need to be parameterized to obtain appropriate simulations of the surface wind speed over complex terrain with the Weather Research and Forecasting model (WRF; Skamarock et al. 2008). Previous evaluations have mainly focused on the reproducibility of the surface wind speed or the wind components (e.g., Zagar et al. 2006; Rife and Davis 2005; Lazic et al. 2010; JD12). This focus is mainly a consequence of the large relevance of the wind speed for several applications such as the generation of electricity from wind. The more difficult statistical treatment of the wind direction because of its circular nature (Mardia and Jupp 1999) also seems to have contributed to this relative lack of studies that focus on the wind direction. As a result, the reproducibility of the surface wind direction by mesoscale models is still a topic for research DOI: /JAMC-D Ó 2013 American Meteorological Society

2 JULY 2013 J I M ENEZ AND DUDHIA 1611 with wide implications for very different applications such as the transport of pollutants over a region, the extinction of forest fires, or even exploration of the adequacy of assimilating surface wind observations into operational forecasts. The purpose of this study is to analyze the ability of WRF to reproduce the surface wind direction over complex terrain. Statistical techniques that are specifically designed for circular variables are used in the assessment. The simulation of JD12 is used in the analysis to complement the previous findings and thus to provide a complete characterization of the surface wind reproducibility over complex terrain. Special emphasis is paid to quantify the representativeness errors that are associated with the use of the wind from the nearest grid point during the evaluation (Jimenez et al. 2010a; JD12). This choice is not always the most appropriate to represent the wind characteristics at a given site, and it may introduce errors that can be mitigated by using nearby grid points in the comparison. 2. Experimental setup The surface wind observations used in the study consist of quality-controlled hourly records acquired at 10 m above ground level over the Comunidad Foral de Navarra (CFN; Jimenez et al. 2010b), a region with complex terrain that is located in the northeastern Iberian Peninsula (Fig. 1a). The topography of the CFN is more complex in the north than in the south, where the terrain is mostly flat. The observational sites are located in very different topographic conditions that range from sites distributed over the plains (red circles in Fig. 1a) to those near mountaintops (green) or in valleys in complex terrain (blue). The WRF simulations of JD12 span the winter of 2001/02 (December February), and the atmospheric evolution over the CFN was simulated at a high horizontal resolution of 2 km. Four domains, with two-way nesting, were used to progressively reach the desired horizontal resolution. The simulations were performed in a reforecast mode in which the model was initialized at 0000 UTC of each day of the selected winter season and was run for 48 h. The output is recorded every hour, with the first day being discarded as a spinup of the model. Data from the operational analysis performed every 6 h at 18 horizontal resolution at the National Centers for Environmental Prediction (the final analysis, or FNL) were used as initial and boundary conditions. The parameterization of the effects that the subgridscale orography produced on the flow led to improved simulations of the surface wind speed. In particular, the representation of the drag exerted by the unresolved topography as well as the increase in speed of the flow over mountains and hills led to a reduction of the mean absolute error from 1.85 to 0.72 m s 21. These effects were introduced in the model formulation by modulating the surface friction as a function of the topographic conditions. The parameterization is now included in the official WRF release. The impact on the surface wind direction estimations is small, however, although systematic improvements occur over the plains. The simulation that includes the parameterization of the filtered topographic effects is herein used to inspect the reproducibility of the wind direction. The wind from the nine grid points that are nearest to the observational sites is compared with the observations to provide a precise evaluation of the model that includes the influence of potential representativeness errors. Several scores are examined. The difference Dd between each pair of simulated and observed wind directions is defined as 8 < d WRF if d WRF # j180j Dd 5 d : WRF if d WRF d WRF if d WRF,2180 This definition assigns positive (negative) differences if the WRF direction is rotated clockwise (counterclockwise) with respect to the observed records. The values of Dd are therefore in the range [21808, 1808]. Aside from the information provided by the distribution of Dd, the root-mean-square error (RMSE) is analyzed. The RMSE is defined as 2 RMSE å n i51 3 (Dd i ) 2 7 n 5 where n is the number of pairs of observed and simulated wind directions. The relative RMSE is therefore defined as RMSE relative 5 RMSE/1808. The mean absolute error (MAE), defined as MAE 5 å n i51 jdd i j, n was also used in the evaluation. Results are similar to those obtained with the RMSE, providing more robustness to the findings presented herein. 3. Results The RMSE and the median of Dd for noncalm winds are shown in Figs. 1a and 1b, respectively. The wind 1/2,

3 1612 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 52 FIG. 1. (left) RMSE and (right) median of Dd calculated with those wind direction records associated with observations having (a),(b) nonzero wind speed and (c),(d) wind speed higher than or equal to 3 m s 21. The white (black) circles in (b) and (d) represent clockwise (counterclockwise) biases. The colors highlight the topographic conditions of the observational sites [see the legend in (c)]. direction from the nearest grid point to the observational sites is used in this comparison. The RMSE is larger in the north than in the south of the region (Fig. 1a), which indicates poorer reproducibility of the wind direction in areas of complex terrain (blue sites) than in the regions with more gentle topography (red). The RMSE is about 608 (808) over the plains (complex terrain), yielding a relative RMSE of 33% (44%). Sites located at mountaintops (green) show the best scores, with an RMSE and relative RMSE of ;508 and 28%, respectively. The median of Dd is near zero in the plains of the south (Fig. 1b), indicating a good representation of the frictional turning. Positive/negative values in the north suggest the presence of systematic differences between observations and WRF (wind direction biases) over complex terrain, however. Several studies have pointed out a dependence of the wind direction variability on the inverse of the wind speed (e.g., Joffre and Laurila 1988; Davies and Thomson 1999). This dependence is responsible for larger differences between consecutive wind direction records at low wind speeds than at higher ones (Mahrt 2011). The dataset presented here displays this relationship (Fig. 2). The changes span the whole range of possible values of [2180, 180] for wind speeds lower than about 2 m s 21, with a progressively smaller range of variation for higher

4 JULY 2013 J I M ENEZ AND DUDHIA 1613 FIG. 2. Wind direction change vs the wind speed calculated with the observations from all of the observational sites. A relationship of the standard deviation of the wind direction change equal to 100 times the inverse of the wind speed is shown for comparison (dashed lines). FIG. 3. Mean RMSE of the wind direction vs the wind speed threshold for stations located at different topographic conditions (see legend and Fig. 1a for the spatial distribution of the stations). The dotted lines show results for the nearest grid point, whereas the dashed lines show results for the nearest grid point after a statistical correction of the simulation. wind speeds. This structure suggests a dependence of the wind direction differences between model and observations on the wind speed, because it can be argued that large variations are more difficult to predict. To inspect this possibility, the scores are recalculated by only using Dd values that are associated with wind speeds of higher than or equal to 3 m s 21. The results are shown in Figs. 1c and 1d. As expected, the RMSE decreases when the wind speed threshold is increased (Fig. 1c). The RMSE is about 308 (508) over the plains (complex terrain), which is responsible for an RMSE relative of 17% (28%). Certain sites in the north reveal a weaker dependence on wind speed, however. The RMSEs here do not decrease as much as those in the plains. The larger values of the median of Dd that occur at these sites (Fig. 1d) suggest the presence of wind direction biases even at high wind speeds. A summary of the previous results is shown in Fig. 3, which presents the RMSE as a function of the wind speed threshold for the stations located in the plains, the more complex terrain areas, and the mountaintops (dotted lines). It is clear that the RMSE decreases as a function of the wind speed. The reduction is moderate at the mountains for the wind speed range shown. The RMSE is progressively lower for larger wind speeds, however, which are in turn more frequent at these windy locations (not shown). This dependence is consistent with results found at wind farms that are located on top of ridges (Carvalho et al. 2012). It is interesting to notice that for high wind speeds the RMSE tends to be flatter over complex terrain (blue dotted line) than over the plains (red dotted line), indicating a weaker dependence of the wind direction differences on the wind speed. This could be a consequence of the biases that seem to occur at certain sites in the northern part of the region (Fig. 1d). The distribution of Dd for large wind speeds (higher than or equal to 3 m s 21 ) at the different observational sites supports this hypothesis (Fig. 4a). At larger wind speeds, Dd concentrates around zero for the plains (red), but important deviations are evident for some of the stations located over complex terrain (blue). The mountain locations show an intermediate behavior (green). To evaluate the influence that potential representativeness errors introduce in the evaluation, the observations are compared with the simulated wind direction from the nine grid points that are nearest to the observational sites. The difference between the lowest and highest RMSE at each observational site is shown in Fig. 5. It is clear that the regions of complex terrain show a larger sensitivity than do the plains to the point used for the comparison. The differences can be as large as 208 at certain sites. Given the high sensitivity to the point selected for comparison, the question arises as to whether the nearest grid point is a good approximation or whether, on the contrary, careful selection of the point becomes necessary. Figures 6a and 6c show the improvement as a result of using the wind direction from the grid point with the lowest RMSE instead of the nearest one. Most of the time, the nearest grid point is very close to the best RMSE (Fig. 6a). Certain sites over complex terrain show potential improvements, however a point that is especially clear for strong winds (up to 458; Fig. 6c). The distribution of Dd for large wind speeds as a result of using the time series with the lowest RMSE is shown in Fig. 4b. An important reduction of the wind direction

5 1614 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 52 FIG. 5. Difference between the highest and lowest RMSE among the nine nearest grid points to each observational site. FIG. 4. Box-and-whiskers plot of Dd at the different observational sites. The squares represent the median, and the upper and lower bases of the boxes show the 75th and 25th percentiles, respectively. The whiskers indicate the 90th (upper) and 10th (lower) percentiles. Results are shown for (a) the nearest grid point, (b) the best of the nine nearest grid points, and (c) the nearest grid point after a statistical correction with simple linear regressions. Results are for wind speeds that are equal to or larger than 3 m s 21. biases can be appreciated at certain sites when compared with results from the nearest grid point (Fig. 4a). For instance, station 18 showed a bias of about 608 and now shows a small bias with the majority of the distribution within the [2458, 458] interval. This large improvement is a consequence of a better representation of katabatic winds from the surrounding mountains. In truth, all of the sites affected by representativeness errors that were identified by JD12 show a lower RMSE (excepting one at which the RMSE is the same) when the most representative grid points are used in the comparison. This result supports the importance of using wind information from the grid points that provide the best representation of the topographic conditions of the observational sites. Despite these improvements, certain sites located over complex terrain (blue) still show systematic behavior in the estimations (Fig. 4b). The systematic differences between model and observations are further inspected using a statistical correction. With the realization that in complex terrain the systematic differences may depend on the simulated flow direction, the correction consists of applying simple linear regressions to the positive/negative values of the zonal/meridional wind component. Hence, a total of four regressions are applied at each observational site, fitting the regression model with the WRF wind components as predictors and observations as predictands. The regression coefficients a and b are then used to calculate the corrected wind components. Hence, the statistical correction for the zonal wind component uses ^u 5 a 6 u WRF 6 1 b 6, where different regression coefficients are used depending on the sign of the zonal wind component from the WRF simulation. An analogous procedure is applied to the meridional wind component. The corrected wind components ^u and ^y are used to calculate the corrected wind direction, completing the process. More sophisticated

6 JULY 2013 J I M ENEZ AND DUDHIA 1615 FIG. 6. Difference between the RMSE calculated with the nearest grid point and (left) the best time series among the nearest nine grid points as well as (right) the corrected direction. Results are shown for (a),(b) nonzero wind speed and (c),(d) wind speed higher than or equal to 3 m s 21. White (black) circles indicate a better (worse) RMSE than that obtained with the wind direction from the nearest grid point. corrections have been used (Grimit et al. 2006; Bao et al. 2010) but the regressions are herein adopted to inspect the systematic differences between the observations and the simulation. The comparison with the RMSE obtained with the nearest grid point is shown in Figs. 6b and 6d. The correction does not show any noticeable impact over the plains. The regions of complex terrain reveal a better reproduction of the wind direction, however a point that is especially clear for high wind speeds (Fig. 6d). This behavior is expected when looking at the mean regression coefficients at the regions (Tables 1 and 2). The plain shows a mean a (b) coefficient that is close to 1 (0), indicating a small impact of the correction. Sites located over complex terrain tend to deviate from these values, however. The mountain sites show intermediate behavior, although important deviations become evident for the meridional wind component because of underestimation of the wind speed. Wind speed biases are also partially responsible for the noticeable variability of the coefficients within the regions. Most often, the correction is better than the improvements obtained with the use of representative grid points, although sometimes this is not the case (Fig. 6). The spatial

7 1616 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 52 TABLE 1. Mean and standard deviation (parentheses) of the slope a, calculated with the coefficients at the stations located in the plain, complex terrain, and mountaintop. Results for the negative/ positive wind components are shown. Plain Complex terrain Mountaintop y (0.4) 0.4 (0.6) 0.9 (0.7) y (0.2) 0.6 (0.4) 1.5 (0.5) u (0.3) 0.5 (0.5) 0.9 (0.7) u (0.2) 0.6 (0.5) 0.7 (0.5) structure at high wind speeds (Fig. 6d) shows a resemblance to the median of Dd that was calculated with the nearest grid point (Fig. 1d), suggesting a reduction of the biases. Indeed, the distribution of Dd from the corrected time series (Fig. 4c) is centered at 0 for most of the stations, indicating the absence of systematic behavior. The impact of the correction, and thus the influence of systematic differences between model and observations, can be better appreciated in Fig. 3. The RMSE shows important reductions over complex terrain (blue dashed line). A larger reduction can be appreciated for high wind speeds in comparison with lower ones, further reflecting the presence of important biases at high winds. Practically no improvement is found over the plains (red dashed line) and, to a lesser extent, over the mountaintops (green dashed lines) because of the absence of systematic differences there. 4. Conclusions Differences between the WRF and in situ surface wind directions are larger in magnitude over areas of complex terrain when compared with areas of flatter terrain. These differences were shown to depend inversely on the surface wind speed. Large differences are found for weak flows, with a better reproducibility of the wind direction at higher wind speeds. This difference is related to the higher variability that the wind direction shows for low-wind regimes, which makes its simulation more difficult. On the contrary, high-wind situations show a more defined circulation pattern, and the reproducibility of the wind direction increases. Systematic differences were found over complex terrain, even at high wind speeds. Some of these biases can be mitigated using the wind estimations from a grid point that is not the nearest one. A careful selection of the grid point used to represent the observed wind direction is therefore relevant to reducing the comparative problems over complex terrain. Certain locations do not suffer from this problem, however, and still show systematic differences between the observations and the simulation. TABLE 2. As in Table 1, but for the intercept in the origin b. Plain Complex terrain Mountaintop y (0.6) 20.4 (0.6) 22.6 (1.7) y (0.6) 20.4 (0.5) 20.2 (0.8) u (0.4) 20.2 (0.7) 20.2 (0.4) u (0.3) 0.0 (0.7) 0.3 (0.8) The situations leading to high wind speeds over the CFN are controlled by the interaction of the synopticscale circulations with the local topography (Jimenez et al. 2009, 2011). The synoptic circulations are usually well represented in mesoscale models, a fact that points to limitations in the representation of topography as being responsible for the wind direction biases. A horizontal resolution of 2 km is therefore not enough to represent the relevant topographic features over complex terrain. In these cases, the use of representative grid points and a subsequent direction-dependent statistical correction should provide the best estimations. Acknowledgments. This work was partially funded by project CGL C02 and was accomplished within Collaborative Agreement 09/940 between CIEMAT and NCAR. 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