Downscaling near-surface wind over complex terrain using a physicallybased statistical modeling approach

Transcription

1 1 Downscaling near-surface wind over complex terrain using a physicallybased statistical modeling approach Hsin-Yuan Huang 1, Scott B. Capps 2, Shao-Ching Huang 3, and Alex Hall 2 1 Joint Institute for Regional Earth System Science and Engineering, University of California, Los Angeles 2 Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles 3 Institute for Digital Research and Education, University of California, Los Angeles Accepted by: Climate Dynamics Corresponding author address: Hsin-Yuan Huang, 7343 Math Science Building, University of California, Los Angeles hyhuang@ucla.edu

2 Abstract A physically-based statistical modeling approach to downscale coarse resolution reanalysis near-surface winds over a region of complex terrain is developed and tested in this study. Our approach is guided by physical variables and meteorological relationships that are important for determining near-surface wind flow. Preliminary fine scale winds are estimated by correcting the course-to-fine grid resolution mismatch in roughness length. Guided by the physics shaping near-surface winds, we then formulate a multivariable linear regression model which uses near-surface micrometeorological variables and the preliminary estimates as predictors to calculate the final wind products. The coarse-to-fine grid resolution ratio is approximately 10 to 1 for our study region of southern California. A validated 3-km resolution dynamically-downscaled wind dataset is used to train and validate our method. Winds from our statistical modeling approach accurately reproduce the dynamically-downscaled near-surface wind field with wind speed magnitude and wind direction errors of less than 1.5 ms -1 and 30 degrees, respectively. This approach can greatly accelerate the production of near-surface wind fields that are much more accurate than reanalysis data, while limiting the amount of computational and time intensive dynamical downscaling. Future studies will evaluate the ability of this approach to downscale other reanalysis data and climate model outputs with varying coarse-to-fine grid resolutions and domains of interest Keywords: Near-surface wind, dynamical downscaling, statistical downscaling, complex terrain. 23

3 Introduction Wind flow patterns across the Earth s surface are shaped by forces spanning a vast range of scales throughout the atmosphere. Wind flow is a result of pressure gradients associated with weather systems at the synoptic scale and near-surface thermal contrasts due to horizontal changes in surface properties. While under the influence of these synoptic scale forces, migrating air encounters finer-scale pressure gradients resulting from topographic and surface roughness discontinuities. Accurate, high resolution wind data over long enough time periods to compile climatological statistics is important for climate change studies, pollutant dispersion evaluation, and wind energy resource assessments. Near-surface wind speed is also critical to the operations of public insurance (Changnon et al. 1999) and industrial utilities (Jungo et al. 2002). Wind observations can be compiled to produce wind statistics. However, these data are only valid at points where measurements are taken. The only way to obtain complete spatial coverage is to use reanalysis data (e.g., North American Regional Reanalysis, NARR; European Centre for Medium-range Weather Forecasts 40 Year Reanalysis, ECMWF ERA-Interim). However, the resolution of reanalysis data ranges from tens to hundreds of kilometers, resolving only major topographical features at best. In reality, wind variations over a heterogeneous surface occur at much finer scales. A downscaling technique deriving finer scale wind information from coarse scale data would be advantageous if it were accurate because it would have much more complete temporal and spatial coverage than reanalysis. Typically there are two types of methods available to downscale meteorological variables at resolutions finer than that of reanalysis data: dynamical and statistical

4 downscaling. Both methods have been widely used in atmospheric and environmental studies (Wilby and Wigley 1997). Using dynamical downscaling, one can obtain finer scale results from a regional climate model (RCM, e.g., the Weather Research and Forecasting model, WRF; the 5th-Generation Penn State/NCAR Mesoscale model, MM5, etc.) forced by coarse resolution data as initial and boundary conditions. Depending on the resolution of the regional model, this method can resolve complex topography and heterogeneous surface conditions, providing more realistic finer scale wind information for the domain of interest (Gustafson and Leung 2007). For example, Lebassi-Habtezion et al. (2011) applied the Regional Atmospheric Modeling System to downscale low-level winds and temperature for the Southern California region using the NCEP data as the initial and boundary conditions. They found that mesoscale model results (e.g., nearsurface wind and temperature) generally compared well to observations. Statistical downscaling, on the other hand, derives statistical relationships between local observations and coarse resolution reanalysis data using an empirical approach or regression analysis (e.g., Gutierrez et al. 2004; Pryor et al. 2005). Some recent studies also developed more complex approaches. For example, Sailor et al. (2000) used neural networks to connect general circulation model data and surface wind climatology observations, de Rooy and Kok (2004) applied a physically-based approach to link turbulence similarity theory and near-surface wind, and Michelangeli et al. (2009) developed a probability method to predict the temporal variability of wind distribution. Nonlinear regression and multivariable linear regression methods have also been used in some studies (e.g., Salameh et al. 2009; Curry et al. 2012; Haas and Pinto 2012).

5 Dynamical and statistical downscaling methods each have their own advantages and drawbacks. The dynamical downscaling technique provides detailed wind information following fundamental physical principles. However, it is computationally expensive and some parameterizations in regional atmospheric models have resolution thresholds beyond which they are not designed to be used. For a given spatial resolution and temporal period of interest, statistical downscaling methods require far fewer computational resources. However, they require long duration historical data, which are scarce. Also, it is not always clear that predictor variables giving the best fit for the historical observations are appropriate for other time periods. Finally, spatial coverage in statistical methods is limited to the spatial coverage of the data used to train the model. Recent studies have started to merge the benefits of dynamical and statistical downscaling methods (e.g., Vrac et al. 2007; Colette et al. 2012). In an ensemble downscaling project using multiple RCMs, Yoon et al. (2012) compared precipitation and temperature results from both dynamical and statistical downscaling methods for the cold season over the United States. Their results suggest that a hybrid system integrating both methods is able to increase the skill of model prediction. We introduce a technique which combines benefits from both dynamical and statistical methods to downscale near-surface winds across a study domain with complex terrain. The promise of the technique is that dynamical downscaling provides more accurate and realistic winds than the driving reanalysis data (e.g., Hughes and Hall 2010). We validate this promise further in this work. However, dynamical downscaling is very computationally expensive. Our approach is to perform only a limited amount of it, and then develop a physically-based statistical approach that can mimic the dynamic model behavior. Then we can easily

6 extend the dynamical outputs in time without spending significant computing time and resources. Through the use of this statistical modeling technique, one can obtain finescale winds directly from reanalysis data. These are very similar to dynamicallydownscaled results, but are at least an order of magnitude in computing time cheaper to produce. The structure of this manuscript is as follows. In Section 2, we introduce our methodology, including the study domain, the dynamical downscaling simulation, and its validation. Section 3 presents the statistical modeling approach which is comprised of a physically-based multivariable linear regression. Section 4 evaluates the performance of this statistical modeling compared to dynamically downscaled results, while section 5 summarizes the findings and outlines ongoing and future investigations Methodology 2.1 Study domain and data As shown in Figure 1, the study domain spans approximately 2.5 of latitude (San Luis Obispo to San Diego) and approximately 6.5 of longitude (122 degree W over the Pacific Ocean to just west of the Colorado River). Southern California is selected as the domain of interest because of its complex topography and diverse surface types. Its transverse and peninsular mountain ranges are geologically young and rugged, steering and modulating wind flow throughout most of the region. Elevation across Southern California ranges from zero to over 3000 m in the San Bernardino Mountains within a distance of about 150 km. In between major complexes and the Southern California Bight are vast urbanized basins separated by smaller mountains. Northeast of the rugged

7 mountain ranges is the elevated Mojave Desert (~1200 m) with a relatively uniform surface roughness and isolated, lower elevation mountain peaks. In addition to the synoptic-scale pressure gradient and topographic steering effects, near-surface wind speed magnitude is strongly affected by the underlying momentum roughness length and thermal stability. Roughness length (as represented in the dynamical model, discussed below in section 2.2) is proportional to obstacle height, and ranges from 0.01 m over the ocean to 0.8 m in urban areas in this domain. The mosaic of urban, agricultural and natural landscapes results in a diversity of surface roughness and near-surface wind distributions. Near-surface wind observations from the California Irrigation Management Information System 1 (CIMIS, black circles denote locations of stations in Figure 1) are used to evaluate the performance of the dynamic downscaling simulation. Managed by the California Department of Water Resources, CIMIS is a continuing program including over 120 automated weather stations in the state of California since The primary product of CIMIS is evapotranspiration, used to assist irrigators in efficient water resource management. However, micrometeorological variables including wind speed at 2 m height (most importantly for this study) are fed into the evapotranspiration calculation. Wind data from 25 CIMIS sites within the simulation domain are compared against model output. 2.2 Dynamical downscaling simulations The dynamical downscaling is performed using the National Center for Atmospheric Research (NCAR) WRF Model Version 3.3 (Skamarock et al. 2008). We use three nested domains. They have 58x51, 103x85 and 214x109 grid points at 27, 9 and 1

8 km resolution, with the timestep of 90, 30, and 10 seconds, respectively. The outermost domain (not shown) covers the entire state of California and a portion of the adjacent Northeast Pacific Ocean, while the middle domain (also not shown) covers roughly the southern half of the state. The innermost domain, with the finest grid resolution, is shown in Figure 1. Only one-way nesting (from the outermost domain to the innermost domain) is applied in the simulations. The vertical discretization has 44 levels up to an altitude of 50 mbar. Using the National Centers for Environmental Prediction s 3-hourly, 32 km resolution NARR 2 data (Mesinger et al. 2006) as the initial and boundary conditions to the outermost domain, we first perform two 1-year simulations (09/ /2010 and 09/ /2011) initialized at 00:00 UTC on August 30 for each year. The frequency of model output is hourly. WRF requires 6-12 hours to fully spin up (Skamarock 2004; Lo et al. 2008), thus data from the first two days are discarded as model spin up. WRF provides multiple parameterization choices. Version 3.3 includes seven shortwave and five longwave radiation schemes, 13 cloud microphysics models, nine cumulus schemes, and 11 planetary boundary layer parameterizations. In this study we use the Dudhia scheme (Dudhia, 1989) and the Rapid Radiative Transfer model (Mlawer et al. 1997) for shortwave and longwave radiative flux calculations, respectively. While the Purdue Lin scheme (Lin et al. 1983) is selected for cloud/liquid water microphysics over the entire simulation domain, the Kain-Fritsch scheme (Kain 2004) is added to include shallow cumulus in the two outer domains. The planetary boundary layer parameterization is the Mellor-Yamada-Nakanishi-Niino (MYNN, Nakanishi and Niino 2004) scheme, based on a turbulent kinetic energy closure to estimate eddy diffusivity and viscosity. Sea surface temperature is prescribed as the boundary condition over the 2

9 ocean. Over land, the NOAH land surface model is used with the 3-category urban canopy model (Chen et al. 2011). A 3-D spatial analysis nudging technique (using the NARR data) is applied on the outermost domain. Variables included in the nudging are potential temperature, humidity, and wind components above the boundary layer top. This analysis nudging restores the data in the outermost domain to the values of the driving reanalysis data with a characteristic time scale. It not only constrains the error growth in large-scale circulation during the simulation, but also improves the accuracy of dynamic downscaling (Lo et al. 2008). This model setup has been used in a previous study, Capps et al. (2014) to which the reader is referred to for more details. Output from this dynamical downscaling calculation is used to provide a realistic distribution of nearsurface wind for the development of the physically-based statistical downscaling approach. 2.3 Evaluation of dynamical downscaling results To verify that dynamic downscaling provides more realistic winds than reanalysis data, we first compare NARR and WRF daily mean wind speeds against CIMIS observations at the grid points closest to the CIMIS station locations. Because the observations are collected at 2 m above the land surface, NARR and WRF 10 m wind speeds are extrapolated to 2 m using the log-law. As seen in Figure 2a, an acceptable agreement exists between NARR and observed winds. The bulk of the temporal correlation coefficients are in the range, indicating that the large-scale NARR wind field is able to explain as much as 50% of the variance in CIMIS observations. In comparison, WRF winds match observed CIMIS winds more closely with respect to NARR. Both the spatial and temporal variations are much better correlated (Figure 2b).

10 In the case of WRF, average values of daily mean wind speed correlation coefficient, root-mean-square-error and bias across 25 sites are 0.80, 0.56 (ms -1 ) and 0.05 (ms -1 ), respectively. Time series of wind speed at two selected sites (#62 in Orange County and # 134 in the Mojave Desert, shown in Figure 1) are shown in Figures 2c and 2d, where red spots and blue lines are observations and WRF output, respectively. Both plots show a good temporal agreement between simulation outputs and observations. The correlation coefficient and root-mean-square-error at site #62 (#134) are 0.78 (0.77) and 0.62 (1.08) ms -1, respectively. More validation of this dynamical simulation configuration using other observations (e.g., data obtained from the National Climatic Data Center) can be found in Capps et al. (2014). Results of this validation give us confidence that the spatial and temporal wind variations in WRF are reasonably realistic, and more importantly that WRF downscaling provides a more realistic wind field compared to NARR. Therefore, it is worthwhile to build a physically-based statistical modeling framework to reproduce the WRF output Physically-based statistical modeling approach In this section, we describe the physically-based statistical modeling approach used to downscale daily mean near-surface wind from 32-km resolution NARR data (hereafter referred to as coarse grid ) to the 3-km resolution used in WRF simulation (hereafter referred to as fine grid ). The process involves two steps: First, we generate preliminary estimates using Monin-Obukhov similarity theory (MOST, Monin and Obukhov 1954). Second, the preliminary estimates are used in conjunction with other

11 relevant surface and micrometeorological variables (e.g., sea-level pressure and surface fluxes) of NARR data in a multivariable linear regression model to achieve final near- surface wind estimates. 3.1 Preliminary estimate Heterogeneities in surface characteristics (e.g., topography, roughness, vegetation type, etc.) play an important role in shaping near-surface meteorology, including near- surface u- and v-wind components, humidity and temperature. For example, using a series of large-eddy simulation experiments to investigate a realistic convective boundary layer, Huang and Margulis (2009) found that surface heterogeneity significantly impacts both thermal and momentum blending heights. Momentum blending height is a vertical length scale above which the influence of surface characteristics on momentum terms (e.g., horizontal velocity) vanishes below some specific value (Wieringa 1986). Following the concept introduced in de Rooy and Kok (2004), which reduced errors in 10 m wind estimates downscaled from a coarse resolution model, we assume that the variation of near-surface wind below the blending height follows Monin-Obukhov similarity theory. The wind magnitude ( u h ) at height z h above the surface can be written as: 224 u h u* k z h z h ln M, (1) z0 Lmo where u * is friction velocity, k is the von Karman constant, z 0 is surface momentum roughness height, and L mo (Garratt 1994). M is the stability function which is a function of Obukhov length

12 We can use Eqn. (1) to formulate wind speeds at 10 m (i.e., u 10 at z 10 ) and at the blending height (i.e., u bh at z bh ) in the coarse grid model. We then rearrange the two equations as: u L 10 u L L z0 M 10 Lmo bh z0 M bh Lmo ln 10 ln L bh L L, (2) where the superscript L represents data with coarse grid model. One can also write the same equation for data from the fine grid model with superscript S. Applying some algebraic operations on these two equations for coarse and fine grid models, we can rewrite 10 m wind at the fine grid resolution as: u S 10 Preliminary estimate z M M z M M S S L L ln L mo ln L L S L mo u10 u bh u.(3) S S bh L L ln bh z0 bh L mo ln bh z0 bh L mo S Note that u 10 is also our preliminary estimate. To simplify Eqn. (3), we invoke two assumptions. The first is that the blending height is fixed and is similar in the coarse and fine grid models. This means the wind magnitudes at the blending height are similar in both coarse and fine grid models (i.e., 241 u S bh u L bh ) and that the wind flow above the blending height is not significantly affected by the surface characteristics. Instead, it is dominated by atmospheric flow at largerscales. Using a similar concept to downscale near-surface wind, various values of blending height have been used (e.g., de Rooy and Kok (2004) used 140 m, Strassberg et al. (2008) used 65 m). However, McNaughton and Jarvis (1984), who used 100 m, suggest that the exact value of selected blending height is not very critical because the

13 changes in the vertical gradient are small around these heights. For this study, we select a blending height of 100 m. Thus, Eqn. (3) can be rewritten as: u S 10 u Preliminary estimate u L L z M z M z M z M S S L L ln Lmo ln L mo. (4) S S L L ln L mo ln L mo The second assumption is that the stability function is negligible. This assumption may be reasonably accurate because, if we use the daily mean wind, the instability effect on the wind profile during daytime may be roughly offset by the stability effect at night. Additionally, the order of the stability function is close to zero for a nearly neutral condition (Garratt 1994). With these two assumptions, Eqn. (4) can be further simplified as: 256 S ln 10 z ln 10 S z L S ln10ln z0 ln z0 S L z0 z0 L 0 z S L L 0 u10 Preliminary estimateu10 u 100 L ln ln 100 z 0 L L u10 u100. ln 100 ln 100 (5) On the right-hand-side of Eqn. (5), values of surface roughness for the coarse grid model L S ( z 0 from NARR) and fine grid model ( z 0 from WRF/local observations) are known and L L prescribed, and u 10 (NARR 10 m wind) and u 100 (NARR 100 m wind) are obtained from NARR wind speed data at 100 m height using a cubic spline interpolation. Eqn. (5) is essentially an expression to recover fine resolution mean wind velocity using fine resolution roughness information and coarse resolution velocities at different heights based on MOST. This preliminary estimate from Eqn. (5) is a valuable first step before further statistical modeling. It incorporates fine-scale variations in the most important

14 fixed physical parameter affecting 10 m wind ( z 0 ), and transforms wind speed information from the blending height to 10 m. Note that the value in curly braces in the L S second right-hand-side term of Eqn. (5) can be negative when z 0 is less than z 0, which is usually seen in coastal and urban areas in our study domain. However, this condition L L does not result in a negative preliminary estimate as long as the ratio of u100 u 10 does not exceed 7.6. We also perform additional examinations (not shown) to consider all possible combinations of an L mo ranging from -200 to 200 m (except an interval between -10 and 10 m representing a neutral condition) and a z 0 ranging from 0.05 to m for the L L similarity theory, and the result shows that the value of u100 u10 is less than this critical value for all cases. 3.2 Example of preliminary estimate Figures 3a and 3b present an example of the standard NARR 10 m wind magnitude on October 15, 2009, together with the NARR surface roughness. This shows NARR s poor representation of the coastline due to its coarse resolution (~32 km). The NARR surface roughness map is also unable to accurately represent the highly heterogeneous land use categories in the study domain. Urban and mountain zones, where high roughness length should be observed due to significant buildings and tall forests, are not clear. The 3-km resolution of surface roughness used in the WRF simulation is illustrated in Figure 3c. In this case, the coastline is clearly more realistic. Over land, urban areas have the highest roughness length (0.8 m) while the Mojave Desert has the lowest (less than 0.1 m). In this study, using the default setting in WRF model, we simply assign one roughness length for each land use category and one for the ocean surface (In

15 reality, roughness lengths over land may also depend somewhat on seasonally-varying vegetation height and those over the ocean surface may depend somewhat on wave height). The preliminary estimate of 10 m wind for October 9, 2009 using Eqn. 5 is shown in Figure 3d. The wind speed magnitude patterns in Figure 3d show a correspondence to those in Figure 3a, but with a discernable modulation of the coarser winds by the underlying higher resolution land category pattern. A clearer portrayal of this modulation is seen in Figure 3e, which shows the difference between the preliminary estimate and NARR 10 m wind interpolated to WRF grid resolution. Smaller values of the preliminary estimate values are simulated in urban and high elevation areas, while larger values are seen in the high desert. In major metropolitan areas, the wind speed reduction can be larger than 60 % (Figure 3f). Furthermore, the difference in roughness length between the land and sea creates a discernible gradient of wind magnitude across the coastline. Next, we will incorporate these preliminary estimates into a multivariable linear regression model to further obtain the final statistical downscaled 10 m wind field. 3.3 Multivariable linear regression model The second step of this approach is the development of a multivariable linear regression using the preliminary estimate and NARR near-surface meteorological variables as inputs. The meteorological variables are selected to include influences on winds that were missed in the preliminary estimate. Since the impact of thermal stability on 10 m wind is neglected in the previous step (i.e., neutral condition as assumed), the first variable to include in the regression model is the thermal flux. Since latent and sensible heat fluxes both contribute to the

16 energy fluxes from the surface to the atmospheric boundary layer, we combine them to create our first variable. This surface buoyancy flux is defined as: H LE w 0.61T a c l, (6) p v where H is sensible heat flux, LE is latent heat flux, is near-surface air density, T a is air temperature, and c p and l v are the specific heat of air and the latent heat of vaporization of water, respectively. Based on the momentum equation of fluid mechanics, the second variable we select in this regression model is spatial difference of sea level pressure ( Psea ) which plays an important role in both wind speed and direction. As one of many standard NARR outputs, pressure at surface is reduced to sea level using the Mesinger method (Mesinger and Treadon 1995). For each WRF grid point, mean sea level pressures of the four closest surrounding NARR points are interpolated to estimate its pressure using an inverse distance weighting method. Then, we define the sea level pressure difference between the NARR point with the highest pressure (among these four surrounding NARR points) and the WRF point as sea level pressure resulting in a change in wind velocity. Psea, which represents the change of To illustrate the relationship between these two meteorological variables and the variable we are interested in predicting (i.e., WRF 10 m wind speed), figure 4 shows maps of temporal correlation coefficient between the WRF dynamically downscaled 10 m wind speed and NARR w and Psea. Due to the difference in grid resolutions between WRF and NARR data, a simple 2-D linear interpolation is applied to NARR w and Psea prior to calculating these correlations. High positive correlations between 10 m wind speed and surface buoyancy flux are seen over ocean and desert areas.

17 Negative correlations between surface wind and buoyancy flux are seen over land, especially near major passes (Figure 1). This is primarily due to the occurrence of fast offshore winds through these passes during autumn and winter months, when buoyancy flux is relatively small. High correlations are generally seen in most locations in the correlation map of sea level pressure gradient (Figure 4b). Thus, in addition to the preliminary estimate, these two variables are selected in our regression model. Directly using variables with different units in a regression system could result in a badly-conditioned coefficient matrix. This may be especially a problem in our case because the magnitudes of the pressure difference or buoyancy flux are not of the same order and do not have the same unit as wind speed. So, borrowing from the idea of the Buckingham π dimension analysis, we apply a dimensional analysis to convert the units of all meteorological variables to be consistent with that of wind speed (ms -1 ). We can P, where 1 derive a new variable associated with the pressure difference 12 1 sea is a variable with units of ms -1, and is air density (kgm -3 ) which depends on location. We also can apply the same approach to derive another variable corresponding to the buoyancy flux 2 w 0, where 0 is a reference temperature of 290 K (close to the annual averaged temperature in our study domain). Using these proxy variables ensures the stability of the regression matrix. Therefore, we use these three variables (i.e., 1, 2 and preliminary estimate) to construct a multivariable linear regression model to produce a simple least-square estimate of WRF wind speed. A four-quadrant inverse tangent function is applied to individual wind components (i.e., u and v ) of both NARR data and WRF dynamic results to calculate wind directions between -180 and 180 degrees. An additional simple

18 linear regression model is trained and used to relate the wind directions between WRF output and NARR data Results of statistical modeling Wind estimates using the physically-based statistical modeling are presented and compared against actual WRF dynamical downscaling outputs in this section. Two experiments are performed. In the first experiment, we use the first year (09/ /2010) of dynamically-downscaled data to develop and train the statistical model, and then we evaluate the model performance over the second year (09/ /2011). Then the training and evaluation periods are swapped in the second experiment. The second year is used as the training period and the first year is as the evaluation period. Such swapping of experiments allows us to examine the statistical relationships between predictors and estimates. In the following paragraphs we first show an example of statistically modeled wind estimates and further compare against dynamical downscaling results in detail. 4.1 Example of wind estimate We first provide an example of dynamically downscaled and statistically modeled wind speed and direction distributions selected from a day in November 2010 to give a flavor of the results (Figure 5). The statistical estimates are based on the training period of 09/ /2010. Overall, the statistically modeled results (Figure 5b) resemble the 10 m wind pattern of the dynamical downscaling simulation (Figure 5a) closely. The wind field is that of a typical offshore event where katabatic winds flow off the high desert, descend as they cross the mountains and funnel through the passes. Particularly fast

19 offshore winds are blowing from the Newhall Pass out over the Santa Clarita Valley, the Oxnard Plain, and the adjacent ocean. Over the open ocean the wind is generally northerly, with a decrease in magnitude near the coast and islands. Significant wind direction changes are seen in the channels between islands and the mainland. Over land, slower wind speeds are seen in most areas, while faster winds occur in major passes and west of the San Bernardino and Santa Ana Mountains. Slower winds are also seen in industrial and residential areas due to the relatively high surface roughness associated with these land use categories. Consistent with the geographical patterns of wind speed, there are remarkable similarities in the wind distributions between dynamically downscaled (Figure 5c) and statistically modeled (Figure 5d) cases. The statistically modeled wind field slightly overestimates the frequency of slower winds, especially those with medium magnitude (4-8 ms -1 ). In general, as shown in the spatial map and wind rose distribution, the statistical modeling approach reproduces the dynamically downscaled wind results well. 4.2 Map of temporal error statistics Maps of error statistics verifying the overall skill of the statistical approach are shown in Figure 6. Two swapped experiments are performed as mentioned previously (i.e., while one year is treated for training, the other is used for evaluation), and the following results are averages of the two evaluation periods. Panel a) of this figure shows the correlation coefficient between the dynamical output and the statistical prediction. In general, large regions of high wind speed correlations (around 0.9) are seen over the Mojave Desert and the ocean surface. Somewhat slightly lower correlations in the range are seen in urban areas and coastal valleys. The Mojave Desert and ocean consist of

20 relatively homogeneous surface characteristics with small sub-grid scale variability. The NARR winds themselves are likely better correlated with WRF wind at these locations, and therefore it is expected that the statistical modeled winds would be better correlated to the dynamical results over these regions. On the other hand, winds over coastal, mountainous and urban regions could be significantly affected by small-scale variability of surface characteristics. Thus, the more difficult it is for statistical model to accurately predict winds over such complex regions. This result is consistent with the correlation coefficients of predictors shown in Figure 4. Compared to dynamical downscaling, the absolute error of the statistical modeled winds is larger over ocean than land (Figure 6b). The reason for this is that wind speed increases with a decrease in surface roughness length (see the map in Figure 3c), creating larger wind speeds over ocean than land. Since errors in statistical estimates ought to be roughly proportional to wind magnitude, larger errors are also seen over the ocean. Larger errors are seen over the deserts as well, as wind speeds are also faster there. Finally, slightly larger errors are seen in areas near mountains, which are poorly represented in coarse resolution data. The relative error map shown in Figure 6c also confirms this. While the ocean and deserts have smaller relative errors, slightly larger relative errors are seen over land between the coast and mountains. Overall, with a similar flow pattern as that shown in the WRF simulation and acceptable differences in both wind speed and direction, the statistical model reproduces the spatial distribution of near-surface wind over both ocean and land surfaces well. 4.3 Time series of spatial error statistics

21 Time series of statistics documenting the spatial relationship between dynamically downscaled and statistical modeled winds are plotted in Figure 7. The thin lines in light color and the thick lines with markers represent statistics based on daily and monthly averages, respectively. Consistent with the example shown in Figure 5, very high correlations (red line) are seen in wind speed (Figure 7a). Most values of the daily correlation coefficient are between 0.70 and 0.95, while all monthly mean values are higher than 0.8. The absolute value of the wind speed difference is shown as the blue line, which represents the mean of the absolute value of each difference between the dynamically downscaled winds and the statistically modeled wind estimates. The result shows that the largest error in monthly mean wind estimate is less than 2 ms -1, while the overall average is about 1.2 ms -1. The green line shows the bias in wind speed estimates. Here we define the bias as the simple arithmetic mean of difference, also referred to as the mean signed difference. The bias varies within a range between -1.5 and 1.5 ms -1, with monthly means close to zero, illustrating the accuracy of this physically-based statistical approach. Similar results are seen in the comparison of wind direction (Figure 7b). High correlations with values hovering around 0.9 are seen except for a few days with values lower than 0.7. The absolute difference of wind direction (blue line) is typically 20, with the largest error being no larger than 40. In general, the wind direction estimate is more accurate in summer than winter. A possible reason could be that winds blow consistently southward (i.e., northerly winds) during summer in our study domain. In winter, winds blow offshore during Santa Ana events and onshore during precipitation events, occasionally disturbing the normal wind regime (Conil and Hall 2006). Because the wind

22 direction anomalies are larger in winter, the error of the statistical model may also be larger. A similar story is seen in plot of bias (green line). The range of the daily mean bias is 30, and the bias in summer is significantly smaller than in winter. 4.4 Error statistics in terms of surface property Figure 8 shows the error statistics binned by surface elevation. The absolute value of wind speed error (Figure 8a) shows that, excluding data over the ocean surface (i.e., elevation<5 m), the error increases systematically with elevation. Relative error (Figure 8b) is generally less than 15%, and is insensitive to elevation change, consistent with Figure 6c (i.e., the errors are roughly proportional to wind magnitude). Errors in the wind direction estimate slightly increase with surface elevation (Figure 8c), probably due to dynamical effects associated with complex terrain. In mountain regions compressed winds are found on the windward side of the mountains, and the flow then expands downstream while flowing over the lee side of the mountains. Since these effects are unrelated to surface roughness, surface buoyancy, or surface pressure, the statistical model may have difficulty capturing them. Finally, we compare the statistical modeling estimates against both the observed CIMIS data and WRF dynamical downscaled results. Generally, the inter-daily wind speed variability estimated by the statistical model is higher compared to WRF (Figures 9a (site #62) and 9b (site #134)). The statistical model also frequently underestimates wind speeds at sites #134 and #64 when compared to both WRF and the observations. The root-mean-square-error between observations and statistical estimates is 0.83 and 1.39 ms -1 at site #62 and #134, respectively. These root-mean-square-errors are about ms -1 higher compared to WRF (Section 2.3). Similar results are also seen at additional

23 sites (site #64 in Figure 9c and site #208 in Figure 9d). It is not surprising that the statistical model performs slightly worse than the WRF dynamically-downscaled winds. However, because the statistical approach is trained on the WRF output, the quality of statistical estimates is comparable to the WRF results. This result implies the dependence of the statistical approach on the dynamical downscaling results. If the dynamic downscaling technique (i.e., WRF model) is not able to closely reproduce the observations, an even larger error and bias will occur in the statistical estimates. 4.5 Contribution of regression variables The bar plot in Figure 10 shows the average contribution from each regression variable to the statistical wind speed estimate in terms of land surface cover category. Data are predictor variables multiplied by their own regression coefficients. It is clear that, for most land cover types, the contribution of the preliminary estimate (red bars) is significantly larger, while the contribution of 2 (corresponding to the buoyancy flux, green bars) is the smallest. This result is expected because the fine grid surface roughness length that participates in the preliminary estimate procedure through similarity theory plays the most important role in determining 10 m wind speed. Meanwhile, this study estimates the daily mean wind, where the daytime stability effect may be offset by night time. The overall proportions of contribution from the preliminary estimate, the variable associated with the pressure difference ( 1 ), and the variable associated with the buoyancy flux ( 2 ) are roughly about 65%, 25%, and 10%, respectively. It is possible that the buoyancy flux (i.e., thermal stability condition) would be more significant if one estimated the sub-daily wind field using this statistical approach, rather than the daily- mean seen in Figure 10. Furthermore, the consideration of pressure difference could be

24 essential for places with complex terrain or land use change. An example is areas with mixed land types, for instance, where residential regions (with high roughness) are intermixed with hills and high mountains in our study domain Conclusions We develop and apply a physically-based statistical modeling approach to downscale near-surface wind from NARR data over the complex terrain of Southern California. This approach is comprised of two principal steps. First, we apply Monin- Obukhov similarity theory to generate preliminary estimates. These preliminary estimates substantially correct wind speed over areas where there is a significant mismatch in roughness length between the coarse and fine resolution data. Then, to obtain the final wind estimate, we construct a multivariable linear regression including the preliminary estimate and two meteorological variables that have significant impacts on near-surface wind speed and direction. In addition to mimicking the momentum equation of wind physics, dimensional analysis of micrometeorological variables in the multivariable linear regression approach provides unit consistency. Our statistical estimates accurately reproduce the 10 m wind fields simulated in the dynamic downscaling. The absolute value of daily averaged wind speed estimates is smaller than 1.5 ms -1, and most errors in wind direction are less than 30 degrees across the entire simulation period. The accuracy of the wind estimate using this physicallybased statistical modeling approach tends to degrade somewhat over highly complex terrain. Analysis of regression variables also shows that, for the daily-mean wind estimate

25 in this study, the contribution of the preliminary estimate dominates the magnitude of statistical wind speed and the correction of the buoyancy flux is less important. In addition to near-surface wind, this physically-based statistical modeling approach could be applied to other variables as long as there is a physical relationship between the variable of interest and other micrometeorological characteristics. In addition to wind resource applications, fine scale wind products provided here can also be used to improve estimates of related meteorological variables (e.g., surface fluxes). In this study, the resolution ratio between reanalysis data and dynamic downscaling in the statistical model is about a factor of ten (i.e., 32-km NARR data is downscaled to 3-km). However, in many climate studies and operational applications, coarse resolution data could be General Circulation Model output, where the grid resolution could be on the order of 100 km. Such coarse resolution data resolves a limited amount of physical processes, with coarser spatial and temporal resolutions, possibly reducing the amount of information available for the relationships in this physically-based statistical modeling approach. This may limit the performance of the statistical approach. Thus, in subsequent work, impacts of resolution difference between coarse and fine data on this statistical approach will be examined. To extend the application of proposed approach, we are using this framework to estimate near-surface winds for a 20-year period for both current and future climates. We would also like to compare our results with those using other state-of-the-art statistical downscaling approaches in a follow-up work Acknowledgments.

26 This work was supported by the Department of Energy Grant #DE-SC and the California Institute for Energy & Environment Grant #POEA01-A02. The authors would like to thank the reviewers for their helpful comments.

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30 Figure 1. Classifications of land cover for the study domain, which is the innermost, 3- km resolution domain of our WRF simulation. Black lines represent elevation contour lines of 1000 m (thin) and 2000m (thick) above sea level. Black markers are locations of the CIMIS observation sites. Number 62 and 134 are two CIMIS sites shown in Figure 2, and 64 and 208 are two additional sites shown in Figure 9. The percentages next to each land category on the right indicate the fraction of the entire simulation domain corresponding to the land category. A water surface (ocean and lake, shown in white) occupies about 36% of the study domain. Gray lines indicate the borders of Los Angeles and Orange counties.

31 Figure 2. 2-m daily mean wind measurements versus the model predictions: scatter plots of daily mean CIMIS observed and closest a) NARR and b) WRF grid cell wind speed over the simulation period. Marker locations designate the means over the two-year period and their colors represent the correlation coefficients of daily variability (as shown in the colorbar below). Time series of CIMIS observations (red circles) and WRF outputs (cyan lines) selected from c) site 62 and d) site 134 (site locations shown in Figure 1).

32 Figure 3. a) Daily-averaged NARR 10 m wind (ms -1 ) for October 15, 2009, b) NARR surface roughness (m), c) WRF surface roughness (m), d) the preliminary estimate of 10 m winds (ms -1 ) for October 15, 2009, e) wind magnitude difference (ms -1 ) and f) percentage difference (%) between the preliminary estimate and NARR data, interpolated to WRF grids.

33 Figure 4. Maps of the correlation coefficient between daily-averaged WRF 10 m wind speed and NARR daily averaged a) surface buoyancy flux, and b) spatial difference of sea level pressure.

34 Figure 5. Example of dynamically downscaled and statistically modeled winds for a day in November 2010: a) dynamically downscaled wind speed (ms -1 ), b) statistically modeled wind speed (ms -1 ), c) dynamically downscaled wind rose plot, and d) statistically modeled wind rose plot. In panels a) and b), arrows illustrating wind speed and direction are shown for every 10 WRF model grid points for clarity. The wind rose plot uses the meteorological convention.

35 Figure 6. Maps of a) correlation coefficient, b) absolute error (ms -1 ), and c) relative error (%) between dynamically downscaled and statistically modeled daily-averaged wind speed. Data are averages of the two swapped training and testing experiments. See text for details.

36 Figure 7. Time series of error statistics in statistically modeled results: a) wind speed (ms -1 ) and b) wind direction (in degrees) estimates. Each data point represents a comparison of spatial variations in wind at any given time. Red lines plot the correlation coefficients, blue lines, the mean absolute difference and green lines, the bias. Thin lines and thick lines with markers represent daily and monthly averages, respectively. Data are averages of the two swapped training and testing experiments.

37 Figure 8. Statistics of a) absolute value of wind speed difference (ms -1 ), b) relative error (%), and c) absolute value of wind direction difference (º) binned by surface elevation. Red lines and blue boxes represent the median and central 50% of data, respectively, and the whisker length represents a range of approximately two standard deviations.

38 Figure 9. Time series of 2-m daily mean wind CIMIS observations (red circles), WRF winds (cyan lines), and statistical modeling estimates (blue lines) selected from a) site 62, b) site 134, c) site 64, and d) site 208. Site locations are shown in Figure 1.

39 Figure 10. Averaged proportion (%) of contribution from each regression variable (i.e., 1, 2 and preliminary estimate) to statistical modeling wind speed estimate.