1. Introduction
Accurate prediction of low-level winds is essential for a number of applications, including aviation safety, operations at wind power plants, and dispersion forecasting for emergency response. In the wind energy industry, for example, operational forecasts are generated using mesoscale models in which observations from surface mesonets and twice-daily radiosonde launches are assimilated (Monteiro et al. 2009). One limitation is that the frequency of the radiosonde observations is often inadequate to capture rapidly evolving meteorological conditions aloft, and this lack of information can have a detrimental impact on low-level wind predictions.
The Next Generation Weather Radar (NEXRAD) network in the United States represents an additional source of meteorological data that could potentially be used to provide upper-air observations with high temporal and spatial resolution and thereby improve low-level wind prediction. The NEXRAD network currently consists of more than 140 Weather Surveillance Radar-1988 Doppler (WSR-88D) systems spread across the contiguous United States (Crum and Alberty 1993). Each radar in this network performs a continuous sequence of volume scans using a variety of volume coverage patterns (VCPs), depending on local weather conditions. Measurements consist of radial (i.e., line of sight) velocity and reflectivity.
The principal limitation in using the radar data is that the radial velocity measurements cannot be assimilated directly into current operational forecast models. Instead, an intermediate step is required in which 3D wind fields are first retrieved from the radar observations using either physical or statistical retrieval algorithms (Lindskog et al. 2004; Barker et al. 2004; Xu et al. 2006; Qiu and Xu 1992; Shapiro et al. 1995; Dowell et al. 2011; Potvin and Wicker 2012; Sun et al. 1991; Sun and Crook 1994, 2001; Crook and Sun 2004; Zhao et al. 2012; Xiao et al. 2005) and then assimilated into the forecast model. Four-dimensional variational data assimilation (4DVar) methods can in principle eliminate the intermediate retrieval step, but these methods are extremely computationally demanding and thus are currently impractical for operational use.
In a previous study, Fast et al. (2008) compared the performance of two entirely different methods for retrieving 3D fields of horizontal winds from single-Doppler NEXRAD observations. The two methods were the Variational Doppler Radar Analysis System (VDRAS) (Sun et al. 1991; Sun and Crook 1994, 2001; Crook and Sun 2004) and the National Severe Storms Laboratory (NSSL) two-dimensional variational data assimilation (2DVar) wind retrieval algorithm (Xu and Gong 2003; Xu et al. 2006, 2007). VDRAS uses 4DVar in conjunction with a simplified mesoscale model, whereas 2DVar is a simpler statistical retrieval algorithm that is based on the use of optimal interpolation. Fast et al. (2008) found that the wind speeds and directions obtained from both methods were usually similar when compared with radar wind profiler measurements and that neither method outperformed the other statistically. Thus, from an operations perspective, 2DVar is attractive because of its computational efficiency and relative simplicity.
Single-Doppler retrieval techniques invariably invoke various assumptions to constrain the solution space and make the problem tractable. 2DVar and VDRAS both assume flat terrain. It is reasonable to expect that significant error might occur when this assumption is violated. In the original study by Fast et al. (2008), the retrieval algorithms were evaluated over the relatively flat terrain of central Oklahoma. Our current interest is in using NEXRAD-derived winds to improve short-term low-level wind forecasts for operational wind farms in areas of complex terrain. Thus, it is important to understand the impact of complex terrain on the accuracy of single-Doppler wind field retrievals.
In the current study, we compare the accuracy of 2DVar velocity retrievals in flat and complex terrain and examine the seasonal variation in data availability over a period of approximately one year. The evaluation is conducted at two sites with very different terrain and climate characteristics. One site is located inside a functioning wind power plant in the northwestern United States in a semiarid region with complex terrain, and the other is located in a flat subtropical area on the east-central coast of Florida. Retrieved winds are compared with independent measurements from 915-MHz radar wind profilers (RWP) at both sites.
This paper is organized such that section 2 briefly describes the 2DVar algorithm. The field sites and instrumentation are discussed in section 3, and the results of the comparisons between the RWPs and the 2DVar retrievals are presented in section 4.
2. Wind retrieval algorithm
NEXRAD volume scans are formed from a series of “stacked” plan position indicator (PPI) scans at different elevation angles. It takes roughly 4–10 min to complete a single volume scan, depending on the mode of operation and the VCP. For each volume scan, a single file containing level-II data is generated. Level-II data include reflectivity and the radial (line of sight) velocity component of the scattering medium. Measurements are currently produced with a range resolution of 250 m and an azimuth resolution of 0.5°.
Next Generation Weather Radars are sensitive to scattering from a number of sources, including hydrometeors, insects, and humidity fluctuations (i.e., Bragg scattering). The radars operate in either precipitation or clear-air mode. Clear-air mode gives better sensitivity but more restricted volumetric coverage than the precipitation mode because only the lower elevation angles are used.
The 2DVar algorithm produces estimates of the horizontal velocity field from a single volume scan of level-II WSR-88D data (Xu and Gong 2003; Xu et al. 2006, 2007). Other methods, such as VDRAS, require several contiguous volume scans. The 2DVar algorithm is based on statistical interpolation (Daley 1991) and can be regarded as an extension of the traditional velocity azimuth display (VAD) technique (Browning and Wexler 1968). The first step in the 2DVar algorithm involves the application of the National Oceanic and Atmospheric Administration NSSL–National Centers for Environmental Prediction quality-control (QC) package (Gong et al. 2003, Liu et al. 2005; Zhang et al. 2005); QC involves clutter rejection and dealiasing, as well as computation of the mean wind profile for each elevation angle using the VAD method (Gong et al. 2003). On each PPI scan surface, horizontal wind vectors are estimated by assuming that the canonical form of the background error covariance tensor function is horizontally homogeneous and isotropic. 2DVar wind retrievals are performed using data from both precipitation- and clear-air-mode radar scans. The algorithm uses only PPI scans with elevation angles below 5° so that the effects of vertical motion can be neglected. For this study, the size of the retrieval domain was set to 160 km × 160 km, centered on the radar location.
The 2DVar algorithm reads in a single volume scan file containing level-II NEXRAD data and outputs a file containing the retrieved wind field. On occasion, no output is generated if all QC checks fail. These failures often occur when atmospheric conditions cause poor radar reflectivity so that gaps in the retrievals may persist for many hours.
3. Field sites and instrumentation
Wind retrievals from the 2DVar wind algorithm were compared with 915-MHz RWPs at the following two sites: the Columbia Basin Wind Energy Study (CBWES) site and the Kennedy Space Center (KSC). These sites were selected based on the availability of RWP measurements and their proximity to existing NEXRAD installations. Figure 1 shows the locations of the NEXRADs and RWPs at these two study locations. Each NEXRAD is identified by a unique four-letter designation. The KPDT radar (Pendleton, Oregon) was used to retrieve winds over the CBWES site, and the KMLB radar (Melbourne, Florida) was used to retrieve winds over the KSC sites.
Aerial images showing (a) the area between the KPDT radar and the CBWES site and (b) the KSC study area. The CBWES site is located in northeastern Oregon, and the KSC study area is located on the east-central coast of Florida. RWPs are located at the sites marked CBWES, KSC1, KSC2, and KSC3.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Aerial images showing (a) the area between the KPDT radar and the CBWES site and (b) the KSC study area. The CBWES site is located in northeastern Oregon, and the KSC study area is located on the east-central coast of Florida. RWPs are located at the sites marked CBWES, KSC1, KSC2, and KSC3.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Aerial images showing (a) the area between the KPDT radar and the CBWES site and (b) the KSC study area. The CBWES site is located in northeastern Oregon, and the KSC study area is located on the east-central coast of Florida. RWPs are located at the sites marked CBWES, KSC1, KSC2, and KSC3.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
The CBWES and KSC sites are very different with respect to climate, land use, and terrain. The CBWES field site (45.955°N, 118.688°W) is located in northeastern Oregon and within the State Line Wind Energy Center. The region surrounding the site is characterized as a dry temperate sagebrush steppe and contains areas of large rolling hills. The field site itself is situated near the top of a ridgeline. The steep slopes and narrow gullies in this area significantly affect low-level flow patterns. By contrast, the KSC site is located in a humid subtropical coastal region with little variation in terrain. The region in and around the KSC site contains a mix of urban areas, dense forests, and wetlands. Although terrain effects in and around the KCS site are minimal, complex low-level circulation patterns can occur because of the land–sea interface and the associated variability in surface roughness and thermal characteristics (Zhong and Takle 1992).
The CBWES site was located approximately 32 km north-northeast of the KPDT NEXRAD near Pendleton, as indicated in Fig. 1a. Instrumentation deployed at the CBWES site included a 60-m instrumented tower equipped with ultrasonic and propeller anemometers, a Scintec AG Model MFAS Doppler sodar, and a Vaisala, Inc., 915-MHz RWP. The RWP was supplied by the U.S. Department of Energy’s Atmospheric Radiation Measurement Program Climate Research Facility (Mather and Voyles 2013; Stokes and Schwartz 1994). All of these instruments were deployed in close proximity to one another (Berg et al. 2012; Yang et al. 2013).
The CBWES RWP was deployed and operated from December 2010 through June 2011 and was configured to run in three-beam, low-power mode with range gate spacing of 57 m, an averaging time of 30 min, and minimum and maximum range gates of 146 and 1462 m AGL, respectively. This configuration was chosen to get the finest possible time and space resolution and to minimize artifacts from the nearby radio tower, tower guy wires, and wind turbines. Data from the CBWES RWP were carefully compared with data measured using propeller and vane anemometers mounted on the 60-m-tall tower to ensure that the measurements were consistent and that the impact of the complex terrain on the RWP measurements was minimal.
The KSC study area contains a network of 915-MHz RWPs that are used to support space-flight operations and serves as one of several ground-truth stations for the National Aeronautics and Space Administration Tropical Rainfall Measuring Mission validation program (Lambert et al. 2003; Simpson et al. 1988). For this study, wind retrievals derived from the KMLB radar in Melbourne are compared with measurements from three RWPs, as indicated in Fig. 1b. These RWPs are denoted as KSC1, KSC2, and KSC3. The KSC1 (28.40°N, 80.60°W) profiler is located approximately 32 km north of the KMLB radar, and the KSC2 (28.60°N, 80.60°W) and KSC3 (28.60°N, 80.70°W) profilers are located farther to the north at distances of about 54 km from the KMLB radar.
For each volume scan, the 2DVar algorithm produces estimates of the horizontal wind field defined on a uniform horizontal grid and at vertical coordinates corresponding to the heights of the PPI scans. The algorithm was configured to also output estimates at the horizontal coordinates corresponding to the locations of RWPs within the retrieval domain. Retrievals from individual volume scans were averaged over hourly intervals in an effort to improve data quality.
Figure 2 shows representative examples of horizontal wind fields produced by 2DVar using data from the KPDT radar (Fig. 2a) and the KMLB radar (Fig. 2b). Both examples show retrievals on the lowest tilt angle of the volume scan (0.48°), and the colors indicate the level-II radial velocity data, where negative values correspond to flow toward the radar. We note that the KPDT radar (Fig. 2a) indicates a more complex flow pattern than does the KMLB radar (Fig. 2b), as is expected because of the influence of complex terrain surrounding the KPDT site. Also, the KPDT radial velocity field (and corresponding retrieval) show a large dead zone to the east and southeast of the radar as a result of terrain blocking caused by a nearby mountain range (the Blue Mountains).
Vectors showing 2DVar wind retrievals from (a) the KPDT radar at 0000 UTC 6 Jan 2011 and (b) the KMLB radar at 2300 UTC 10 Mar 2009. Both examples show retrievals on the lowest tilt angle of the volume scan (0.48°). Colors indicate the level-II radial velocity data. Negative radial velocities (greens and blues) correspond to flow toward the radar.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Vectors showing 2DVar wind retrievals from (a) the KPDT radar at 0000 UTC 6 Jan 2011 and (b) the KMLB radar at 2300 UTC 10 Mar 2009. Both examples show retrievals on the lowest tilt angle of the volume scan (0.48°). Colors indicate the level-II radial velocity data. Negative radial velocities (greens and blues) correspond to flow toward the radar.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Vectors showing 2DVar wind retrievals from (a) the KPDT radar at 0000 UTC 6 Jan 2011 and (b) the KMLB radar at 2300 UTC 10 Mar 2009. Both examples show retrievals on the lowest tilt angle of the volume scan (0.48°). Colors indicate the level-II radial velocity data. Negative radial velocities (greens and blues) correspond to flow toward the radar.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
4. Results
The comparison period at the CBWES site was limited to the relatively short deployment period of the RWP. This period extended from 8 December 2010 through 25 May 2011. For consistency, a similar-duration comparison period (from 1 December 2008 through 31 May 2009) was chosen for the KSC site. The 2DVar code was run over much longer time periods at both sites, however.
a. Retrieval availability
Figure 3 shows the monthly averaged percentage of time that 2DVar retrievals were available from the KMLB (Fig. 3a) and KPDT (Fig. 3b) radars. These results represent the retrieval availability relative to the number of volume scans in a given month. Thus, variations in radar downtime are not reflected in Fig. 3. The retrieval availability for KMLB (Fig. 3a) was computed for all of 2009. For KPDT, the retrieval availability was computed for the period from March 2010 to June 2011 (Fig. 3b).
Monthly-averaged percent availability of 2DVar retrievals from the (a) KMLB and (b) KPDT radars. Statistics are based on 2DVar runs covering all of 2009 for KMLB and covering from 1 Mar 2010 to 31 May 2011 for KPDT.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Monthly-averaged percent availability of 2DVar retrievals from the (a) KMLB and (b) KPDT radars. Statistics are based on 2DVar runs covering all of 2009 for KMLB and covering from 1 Mar 2010 to 31 May 2011 for KPDT.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Monthly-averaged percent availability of 2DVar retrievals from the (a) KMLB and (b) KPDT radars. Statistics are based on 2DVar runs covering all of 2009 for KMLB and covering from 1 Mar 2010 to 31 May 2011 for KPDT.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
For the KPDT radar (Fig. 3b), there is a distinct tendency for higher retrieval availabilities during the summer months. This is likely the result of stronger clear-air returns due to the presence of insects and/or enhanced Bragg scattering during the summer months (Melnikov et al. 2011). A similar annual cycle is observed in the retrievals obtained from the KMLB radar, although the winter minimum is much less pronounced and the overall retrieval availability is higher. For KPDT, the retrieval availability varies from ~20% in February to just over 80% in July. For KMLB, the retrieval availability varies from ~55% in March to nearly 100% from May through October.
b. Topography and climatological wind behavior
As indicated in Fig. 4, the CBWES site is located near the top of a ridgeline at an altitude of 543 m MSL. The ridge runs roughly from southeast to northwest. The terrain slopes off abruptly toward the northeast and more gradually toward the southwest of the site. The terrain height varies from ~165 to 660 m within 10 km of the site, as shown in Fig. 4.
Terrain-height variation within a 10 × 10 km2 area centered on the CBWES site. The CBWES site, which is indicated by the red dot, sits at an altitude of 543 m MSL. The color scale shows terrain height in meters above mean sea level. The terrain height over this area varies from about 165 m MSL in the northeastern corner to 660 m MSL in the southwestern corner.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Terrain-height variation within a 10 × 10 km2 area centered on the CBWES site. The CBWES site, which is indicated by the red dot, sits at an altitude of 543 m MSL. The color scale shows terrain height in meters above mean sea level. The terrain height over this area varies from about 165 m MSL in the northeastern corner to 660 m MSL in the southwestern corner.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Terrain-height variation within a 10 × 10 km2 area centered on the CBWES site. The CBWES site, which is indicated by the red dot, sits at an altitude of 543 m MSL. The color scale shows terrain height in meters above mean sea level. The terrain height over this area varies from about 165 m MSL in the northeastern corner to 660 m MSL in the southwestern corner.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Figure 5 shows the wind direction distributions from the RWP for the CBWES and KSC sites, at two levels (~200 and ~1000 m AGL). Also shown are the mean wind speeds as functions of wind direction. The CBWES site shows a strong tendency for southwesterly flow at both the 200- (Fig. 5a) and 1000-m (Fig. 5b) levels, consistent with long-term tower measurements described in Berg et al. (2012). The strongest winds also coincide with the prevailing southwesterly flow. By contrast, the KSC1 RWP shows a tendency for southeasterly flow at the 231-m level (Fig. 5c) and a bimodal wind direction distribution at the 1041-m level, with tendencies for both southeasterly and west-southwesterly flows. The southeasterly flows are believed to be associated with sea breezes (Zhong and Takle 1992), and the westerly winds aloft are believed to be associated with the influence of the midlatitude general circulation pattern. The KSC site shows a slight tendency for the strongest winds to be associated with westerly flow, which is likely due to frontal passages associated with extratropical storms during the winter months. Overall, wind speeds at KSC are considerably weaker than at the CBWES site.
CBWES and KSC1 RWP wind statistics for (a), (b) CBWES RWP computed for the period from 8 Dec 2010 to 25 May 2011 and (c), (d) KSC1 RWP computed for the period from 1 Dec 2008 to 31 May 2009. Gray bars indicate the wind direction frequency of occurrence (left axes), and the black dots represent the mean wind speed as a function of wind direction (right axes).
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
CBWES and KSC1 RWP wind statistics for (a), (b) CBWES RWP computed for the period from 8 Dec 2010 to 25 May 2011 and (c), (d) KSC1 RWP computed for the period from 1 Dec 2008 to 31 May 2009. Gray bars indicate the wind direction frequency of occurrence (left axes), and the black dots represent the mean wind speed as a function of wind direction (right axes).
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
CBWES and KSC1 RWP wind statistics for (a), (b) CBWES RWP computed for the period from 8 Dec 2010 to 25 May 2011 and (c), (d) KSC1 RWP computed for the period from 1 Dec 2008 to 31 May 2009. Gray bars indicate the wind direction frequency of occurrence (left axes), and the black dots represent the mean wind speed as a function of wind direction (right axes).
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
c. 2DVar and RWP comparison results
Comparison between the RWPs and the 2DVar retrievals required transforming the data to a common set of time and height coordinates. The KSC RWP profiles were originally reported with a 15-min resolution, and the CBWES RWP profiles were originally reported with 30-min resolution. First, hourly averages of the RWP profiles were computed to match the temporal resolution and sampling times of the retrievals. Weighted averages of the RWP data were then computed in the vertical dimension at each height at which the RWP profiles intersect the NEXRAD PPI scans. This weighted averaging procedure accounts for the beamwidth of the WSR-88D at the location of the RWP profile by assuming that the radiation pattern of the main lobe of the WSR-88D beam is well approximated by a Gaussian function (Donaldson 1965).
Figure 6 shows a comparison between the retrieved (2DVar) and observed (RWP) wind speed and direction for March 2011 at a height of 278 m above the CBWES RWP. In a similar way, Fig. 7 shows a comparison between the retrieved and observed wind speed and direction for January 2009 at a height of 365 m above the KSC1 RWP. Data shown in both Figs. 6 and 7 were obtained from the lowest elevation angle (0.48°) of the NEXRAD scans. We note that these time series only show data when both RWP observations and 2DVar retrievals are available. Gaps are largely due to the absence of 2DVar retrievals. The time series in Fig. 6 exhibit more gaps because of the lower retrieval availability at the CBWES site (see Fig. 3). Figures 6 and 7 indicate that the retrievals do a reasonably good job of tracking the RWP data at both sites. There is, however, a consistent slow bias in the 2DVar wind speeds relative to the RWP measurements.
Time series of (a) wind speed and (b) wind direction for March 2011 as measured by the CBWES RWP (plus signs) and estimated by 2DVar using KPDT data (gray dots). The height level is 278 m above the RWP.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Time series of (a) wind speed and (b) wind direction for March 2011 as measured by the CBWES RWP (plus signs) and estimated by 2DVar using KPDT data (gray dots). The height level is 278 m above the RWP.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Time series of (a) wind speed and (b) wind direction for March 2011 as measured by the CBWES RWP (plus signs) and estimated by 2DVar using KPDT data (gray dots). The height level is 278 m above the RWP.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Time series of (a) wind speed and (b) wind direction for January 2009 as measured by the KSC1 RWP (plus signs) and estimated by 2DVar using KMLB data (gray dots). The height level is 365 m above the RWP.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Time series of (a) wind speed and (b) wind direction for January 2009 as measured by the KSC1 RWP (plus signs) and estimated by 2DVar using KMLB data (gray dots). The height level is 365 m above the RWP.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Time series of (a) wind speed and (b) wind direction for January 2009 as measured by the KSC1 RWP (plus signs) and estimated by 2DVar using KMLB data (gray dots). The height level is 365 m above the RWP.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Quantitative comparisons between the 2DVar retrievals and the RWP observations were obtained by computing the mean and standard deviation of the wind speed difference, the mean wind speed percent difference, the Pearson correlation between wind speeds, the mean and standard deviation of the wind direction difference, and the root-mean-square vector difference (Holleman 2005).
A minimum wind speed threshold was applied when computing 
The results for the CBWES and KSC sites are summarized in Fig. 8 and in Table 1. Figure 8 shows profiles of 
(a) Wind speed bias, (b) wind direction bias, and (c) RMS vector difference for the CBWES site. (d) Wind speed bias, (e) wind direction bias, and (f) RMS vector difference for the KSC sites, where black, blue, and red correspond to KSC1, KSC2, and KSC3, respectively. The open squares in (c) and (f) show RMS vector differences that have been computed by rotating the 2DVar winds such that the mean wind direction bias is zero.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
(a) Wind speed bias, (b) wind direction bias, and (c) RMS vector difference for the CBWES site. (d) Wind speed bias, (e) wind direction bias, and (f) RMS vector difference for the KSC sites, where black, blue, and red correspond to KSC1, KSC2, and KSC3, respectively. The open squares in (c) and (f) show RMS vector differences that have been computed by rotating the 2DVar winds such that the mean wind direction bias is zero.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
(a) Wind speed bias, (b) wind direction bias, and (c) RMS vector difference for the CBWES site. (d) Wind speed bias, (e) wind direction bias, and (f) RMS vector difference for the KSC sites, where black, blue, and red correspond to KSC1, KSC2, and KSC3, respectively. The open squares in (c) and (f) show RMS vector differences that have been computed by rotating the 2DVar winds such that the mean wind direction bias is zero.
Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0297.1
Absolute relative difference 
The wind speed bias profile at the CBWES site (Fig. 8a) shows a consistent tendency for a slow bias in the retrieved winds. The magnitude of the bias decreases from about 1.9 m s−1 at 279 m AGL to about 1.0 m s−1 at 1416 m AGL. By contrast, all of the KSC sites show relatively small biases at the lowest levels and larger negative values with increasing altitude (see Fig. 8d).
Figures 8a and 8d also indicate fairly large values for the wind speed difference standard deviations σΔM. Most values fall in the range from 3 to 4 m s−1, with the exception of the lowest altitude at the CBWES site. Here, σΔM decreases monotonically from 4.7 m s−1 at 279 m AGL, to 4 m s−1 at 852 m AGL, to 3.8 m s−1 at 1416 m AGL. The KSC sites indicate a slight tendency for σΔM to increase with altitude. All of the KSC sites show σΔM ~ 3 m s−1 below 1 km AGL and slightly higher values in the range from 3.3 to 3.7 m s−1 at the highest levels (~1500 m AGL).
Wind direction biases 
At the CBWES site, the standard deviation of the wind direction difference distribution σΔϕ decreases monotonically from 37° at 279 m AGL to 20° at 1416 m AGL. The KSC sites show no clear trend in σΔϕ with altitude, with all values near 30°. We note that above ~850 m AGL σΔϕ is smaller at the CBWES than at the KSC sites. This is likely due to greater temporal variability in the wind direction at the KSC sites, as indicated in Fig. 5.
RMS vector differences RMS(Δu) for the CBWES and KSC sites are shown in Figs. 8c and 8f, respectively. In contrast to σΔM or σΔϕ, the RMS vector difference includes contributions from both random error and bias in the magnitude and direction of Δu. Thus, the RMS vector differences are considerably larger than σΔM, with values in the range from 4 to 5 m s−1 at the KSC sites and from 6 to 8 m s−1 at the CBWES site.
RMS vector differences are reduced somewhat when the RWP data are rotated to correct for the possible misalignment of the profiler. The open squares in Figs. 8c and 8f represent RMS vector differences with a rotation applied to the RWP data. The rotation angles for each site were computed from the average wind direction bias profiles. The effect of the rotation on RMS(Δu) is most pronounced at CBWES (Fig. 8c), where the average wind direction bias was 22°. The effect is much less pronounced at KSC1 (Fig. 8f), where the average wind direction bias was 10°, and the rotation had almost no effect at KSC2 and KSC3 (Fig. 8f), where the wind direction biases were small. As in the case of the wind speed difference standard deviation, the RMS vector difference decreases monotonically with altitude at the CBWES site. By contrast, the KSC sites show no significant variation with height.
The correlation coefficients RM and wind speed percent differences 
The mean wind speed percent difference 
5. Summary
In this study, we evaluated NEXRAD wind retrievals using NSSL’s 2DVar algorithm at two sites (CBWES and KSC) with very different terrain, climate, and land use characteristics. The evaluation was carried out by comparing 2DVar wind retrievals with RWP observations at the two locations. Results from the two sites allowed us to assess the impact of the complex terrain at the CBWES site.
The CBWES site showed a greater seasonal variation in the retrieval availability, with higher availability during the summer months. The retrieval availability from the KPDT radar (Oregon) varied from ~20% in February to just over 80% in July. For the KMLB radar (Florida), the retrieval availability varied from ~55% in March to nearly 100% from May through October.
At both sites and at most height levels, correlations in wind speed generally fell in the range from 0.7 to 0.8, indicating that the retrieved winds did a reasonable job at tracking fluctuations observed by the RWPs. Wind speed difference distributions tended to be fairly broad, with standard deviations generally in the range from 3 to 4 m s−1. Overall, the best agreement between the 2DVar retrievals and RWP observations was obtained at the KSC site. The worst agreement was found at the lowest level (279 m AGL) at the CBWES site.
Retrieval accuracy tended to improve markedly with altitude at the CBWES site and degrade with altitude at the KSC sites. The 2DVar algorithm performed equally well at the CBWES and KSC sites at an altitude of ~1400 m AGL. The retrieved wind speed at the CBWES site is biased slow relative the RWP at all altitudes; the magnitude of this bias decreases with altitude, however. By contrast, the KSC sites show the opposite trend, with very little bias at the low altitudes and slow biases at the highest altitudes.
The precise reason for the observed slow biases in the CBWES and KSC results is not known. Our results suggest that the 2DVar algorithm underestimates wind speeds when the flat-terrain assumption is violated and when data coverage is reduced. In clear air, the strength of the radar return signal generally decreases with altitude at a fixed range from the radar. This results in a degradation of the radial velocity data quality with altitude, which in turn results in reduced data coverage caused by 2DVar’s data quality-control procedures. We speculate that the increase in wind speed bias with altitude observed at the KSC site was the result of a reduction in data coverage. This same effect was present at the CBWES site as well; additional bias was superimposed at the lower altitudes because of the terrain effects, however.
Since the 2DVar algorithm assumes that the background error covariance tensor function is horizontally homogeneous and isotropic, it has difficulty dealing with the terrain-induced spatial heterogeneity in the flow at the CBWES site. We note that the terrain height varied from a minimum of 85 m near the eastern boundary of the retrieval domain to a maximum of 2260 m in the southwestern corner of the domain. The standard deviation of the terrain-height variation over the domain was 468 m.
To improve the performance of the 2DVar in areas of complex terrain, it is necessary and possible to estimate the three-dimensional terrain-dependent background error covariance functions from time series of innovation fields (obtained by subtracting the background radial velocity from the radar-observed radial velocity at each observation point), perhaps by extending the innovation method of Xu et al. (2007), and then to incorporate the estimated terrain-dependent background error covariance functions into the 2DVar with the background error covariance functions extended from 2D to 3D in a similar way as in the recently upgraded 2DVar (Xu et al. 2011). Continued research and development should be conducted in this direction.
Last, we note that the entire national network of WSR-88D systems was upgraded with dual-polarization capability in the spring of 2013. It is expected that the new polarimetric information will help to improve the retrieval availability through improved QC. In this study, the data QC technique used a simple method to identify bird-contaminated data on a volumewise basis. Work is currently under way to make use of the new polarimetric information to improve the identification of bird-contaminated measurements on a sample-by-sample basis. It is expected that this improvement will result in less data rejection and greater retrieval availability.
Acknowledgments
This work was supported by the U.S. Department of Energy (DOE) Office of Energy Efficiency and Renewable Energy and made use of instrumentation provided by the DOE Office of Biological and Environmental Research Atmospheric Radiation Measurement Program. Pacific Northwest National Laboratory is operated by Battelle for the DOE under Contract DE-AC06-76RL0 1830.
REFERENCES
Barker, D. M., W. Huang, Y.-R. Guo, A. Bourgeois, and Q. Xiao, 2004: A three-dimensional variational data assimilation system for MM5: Implementation and initial results. Mon. Wea. Rev., 132, 897–914, doi:10.1175/1520-0493(2004)132<0897:ATVDAS>2.0.CO;2.
Berg, L. K., M. Pekour, and D. Nelson, 2012: Description of the Columbia Basin Wind Energy Study (CBWES). Pacific Northwest National Laboratory Rep. PNNL-22036, 24 pp. [Available online at http://www.pnnl.gov/main/publications/external/technical_reports/PNNL-22036.pdf.]
Browning, K. A., and R. Wexler, 1968: The determination of kinematic properties of a wind field using Doppler radar. J. Appl. Meteor., 7, 105–113, doi:10.1175/1520-0450(1968)007<0105:TDOKPO>2.0.CO;2.
Carter, D. A., K. S. Gage, W. L. Ecklund, W. M. Angevine, P. E. Johnston, A. C. Riddle, J. Wilson, and C. R. Williams, 1995: Developments in UHF lower tropospheric wind profiling at NOAA’s Aeronomy Laboratory. Radio Sci., 30, 977–1001, doi:10.1029/95RS00649.
Crook, N. A., and J. Sun, 2004: Analysis and forecasting of the low-level wind during the Sydney 2000 Forecast Demonstration Project. Wea. Forecasting, 19, 151–167, doi:10.1175/1520-0434(2004)019<0151:AAFOTL>2.0.CO;2.
Crum, T. D., and R. L. Alberty, 1993: The WSR-88D and the WSR-88D Operational Support Facility. Bull. Amer. Meteor. Soc., 74, 1669–1687, doi:10.1175/1520-0477(1993)074<1669:TWATWO>2.0.CO;2.
Daley, R., 1991: Atmospheric Data Analysis. Cambridge University Press, 150 pp.
Donaldson, R. J., 1965: Resolution of a radar antenna for distributed targets. J. Appl. Meteor., 4, 727–740, doi:10.1175/1520-0450(1965)004<0727:ROARAF>2.0.CO;2.
Dowell, D. C., L. J. Wicker, and C. Snyder, 2011: Ensemble Kalman filter assimilation of radar observations of the 8 May 2003 Oklahoma City supercell: Influences of reflectivity observations on storm-scale analyses. Mon. Wea. Rev., 139, 272–294, doi:10.1175/2010MWR3438.1.
Fast, J. D., R. K. Newsom, K. J. Allwine, Q. Xu, P. Zhang, J. H. Copeland, and J. Sun, 2008: An evaluation of two NEXRAD wind retrieval methodologies and their use in atmospheric dispersion models. J. Appl. Meteor., 47, 2351–2371, doi:10.1175/2008JAMC1853.1.
Gong, J., L. Wang, and Q. Xu, 2003: A three-step dealiasing method for Doppler velocity data quality control. J. Atmos. Oceanic Technol., 20, 1738–1748, doi:10.1175/1520-0426(2003)020<1738:ATDMFD>2.0.CO;2.
Holleman, I., 2005: Quality control and verification of weather radar wind profiles. J. Atmos. Oceanic Technol., 22, 1541–1550, doi:10.1175/JTECH1781.1.
Lambert, W. C., F. J. Merceret, G. E. Taylor, and J. G. Ward, 2003: Performance of five 915-MHz wind profilers and an associated automated quality control algorithm in an operational environment. J. Atmos. Oceanic Technol., 20, 1488–1495, doi:10.1175/1520-0426(2003)020<1488:POFMWP>2.0.CO;2.
Lindskog, M., K. Salonen, H. Järvinen, and D. B. Michelson, 2004: Doppler radar wind data assimilation with HIRLAM 3DVAR. Mon. Wea. Rev., 132, 1081–1092, doi:10.1175/1520-0493(2004)132<1081:DRWDAW>2.0.CO;2.
Liu, S., Q. Xu, and P. Zhang, 2005: Identifying Doppler velocity contamination caused by migrating birds. Part II: Bayes identification and probability tests. J. Atmos. Oceanic Technol., 22, 1114–1121, doi:10.1175/JTECH1758.1.
Mather, J. H., and J. W. Voyles, 2013: The ARM Climate Research Facility: A review of structure and capabilities. Bull. Amer. Meteor. Soc., 94, 377–392, doi:10.1175/BAMS-D-11-00218.1.
Melnikov, V. M., R. J. Doviak, D. S. Zrnić, and D. J. Stensrud, 2011: Mapping Bragg scatter with a polarimetric WSR-88D. J. Atmos. Oceanic Technol., 28, 1273–1285, doi:10.1175/JTECH-D-10-05048.1.
Monteiro, C., R. Bessa, V. Miranda, A. Botterud, J. Wang, and G. Conzelmann, 2009: Wind power forecasting: State-of-the-art 2009. Argonne National Laboratory Rep. ANL/DIS-10-1, 216 pp. [Available online at http://www.dis.anl.gov/pubs/65613.pdf.]
Office of the Federal Coordinator for Meteorological Services and Supporting Research, 2006: Doppler radar meteorological observations: Part D: WSR-88D unit description and operational applications. U.S. Department of Commerce/NOAA Rep. FCM-H11D-2006, 218 pp. [Available online at http://www.ofcm.gov/fmh11/fmh11partd/pdf/FMH11D-2006.pdf.]
Potvin, C. K., and L. J. Wicker, 2012: Comparison between dual-Doppler and EnKF storm-scale wind analyses: Observing system simulation experiments with a supercell thunderstorm. Mon. Wea. Rev., 140, 3972–3991, doi:10.1175/MWR-D-12-00044.1.
Qiu, C.-J., and Q. Xu, 1992: A simple adjoint method of wind analysis for single-Doppler data. J. Atmos. Oceanic Technol., 9, 588–598, doi:10.1175/1520-0426(1992)009<0588:ASAMOW>2.0.CO;2.
Shapiro, A., E. Ellis, and J. Shaw, 1995: Single-Doppler velocity retrievals with Phoenix II data: Clear air and microburst retrievals in one planetary boundary layer. J. Atmos. Sci., 52, 1265–1287, doi:10.1175/1520-0469(1995)052<1265:SDVRWP>2.0.CO;2.
Simpson, J., R. F. Adler, and G. R. North, 1988: A proposed Tropical Rainfall Measuring Mission (TRMM) satellite. Bull. Amer. Meteor. Soc., 69, 278–295, doi:10.1175/1520-0477(1988)069<0278:APTRMM>2.0.CO;2.
Stokes, R. R., and S. E. Schwartz, 1994: The Atmospheric Radiation Measurement (ARM) Program: Programmatic background and design of the Cloud and Radiation Test Bed. Bull. Amer. Meteor. Soc., 75, 1201–1221, doi:10.1175/1520-0477(1994)075<1201:TARMPP>2.0.CO;2.
Sun, J., and A. Crook, 1994: Wind and thermodynamic retrieval from single-Doppler measurements of a gust front observed during Phoenix II. Mon. Wea. Rev., 122, 1075–1091, doi:10.1175/1520-0493(1994)122<1075:WATRFS>2.0.CO;2.
Sun, J., and A. Crook, 2001: Real-time low-level wind and temperature analysis using single WSR-88D data. Wea. Forecasting, 16, 117–132, doi:10.1175/1520-0434(2001)016<0117:RTLLWA>2.0.CO;2.
Sun, J., D. W. Flicker, and D. K. Lilly, 1991: Recovery of three dimensional wind and temperature fields from simulated Doppler radar data. J. Atmos. Sci., 48, 876–890, doi:10.1175/1520-0469(1991)048<0876:ROTDWA>2.0.CO;2.
Xiao, Q., Y.-H. Kuo, J. Sun, W.-C. Lee, E. Lim, Y.-R. Guo, and D. M. Barker, 2005: Assimilation of Doppler radar observations with a regional 3DVAR system: Impact of Doppler velocities on forecasts of a heavy rainfall case. J. Appl. Meteor., 44, 768–788, doi:10.1175/JAM2248.1.
Xu, Q., and J. Gong, 2003: Background error covariance function for Doppler radar radial-wind analysis. Quart. J. Roy. Meteor. Soc., 129, 1703–1720, doi:10.1256/qj.02.129.
Xu, Q., S. Liu, and M. Xue, 2006: Background error covariance functions for vector wind analyses using Doppler radar radial-velocity observations. Quart. J. Roy. Meteor. Soc., 132, 2887–2904, doi:10.1256/qj.05.202.
Xu, Q., K. Nai, and L. Wei, 2007: An innovation method for estimating radar radial-velocity observation error and background wind error covariances. Quart. J. Roy. Meteor. Soc., 133, 407–415, doi:10.1002/qj.21.
Xu, Q., K. Nai, and L. Wei, 2011: A real-time radar wind analysis system for nowcast application. Sixth European Conf. on Severe Storms, Palma de Mallorca, Balearic Islands, Spain, European Severe Storms Laboratory, P4(41). [Available online at http://www.essl.org/ECSS/2011/programme/abstracts/41.pdf.]
Yang, Q., L. K. Berg, M. Pekour, J. D. Fast, R. K. Newsom, M. Stoelinga, and C. Finley, 2013: Evaluation of WRF-predicted near-hub-height winds and ramp events over a Pacific Northwest site with complex terrain. J Appl. Meteor. Climatol., 52, 1753–1763, doi:10.1175/JAMC-D-12-0267.1.
Zhang, P., S. Liu, and Q. Xu, 2005: Quality control of Doppler velocities contaminated by migrating birds. Part I: Feature extraction and quality control parameters. J. Atmos. Oceanic Technol., 22, 1105–1113, doi:10.1175/JTECH1757.1.
Zhao, K., M. Xue, and W.-C. Lee, 2012: Assimilation of GBVTD-retrieved winds from single-Doppler radar for short-term forecasting of Super Typhoon Saomai (0608) at landfall. Quart. J. Roy. Meteor. Soc., 138, 1055–1071, doi:10.1002/qj.975.
Zhong, S., and E. S. Takle, 1992: An observational study of sea- and land-breeze circulations in an area of complex coastal heating. J. Appl. Meteor., 31, 1426–1438, doi:10.1175/1520-0450(1992)031<1426:AOSOSA>2.0.CO;2.
