The accuracy of winds derived from Next Generation Weather Radar (NEXRAD) level-II data is assessed by comparison with independent observations from 915-MHz radar wind profilers. The evaluation is carried out at two locations with very different terrain characteristics. One site is located in an area of complex terrain within the State Line Wind Energy Center in northeastern
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 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 fromsingle-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
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
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
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 250m and an azimuth resolution of 0.58.
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 froma 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
The 2DVar algorithmreads 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-MHzRWPs at the following two sites: the
The CBWES and KSC sites are very different with respect to climate, land use, and terrain. The CBWES field site (45.9558N, 118.6888W) is located in northeastern
The CBWES site was located approximately 32km north-northeast of theKPDTNEXRADnear
The CBWES RWP was deployed and operated from
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 MeasuringMission validation program (Lambert et al. 2003; Simpson et al. 1988). For this study, wind retrievals derived from the KMLB radar in
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 (0.488), 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
The comparison period at the CBWES site was limited to the relatively short deployment period of the RWP. This period extended from
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
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 minimumismuch 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 543m MSL. The ridge runs roughly from southeast to northwest. The terrain slopes offabruptly toward the northeast and more gradually toward the southwest of the site. The terrain height varies from ;165 to 660m within 10 km of the site, as shown in Fig. 4.
Figure 5 shows the wind direction distributions from the RWP for the CBWES and KSC sites, at two levels (;200 and ;1000m 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 aloftare 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.
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 theNEXRADPPI scans. Thisweighted averaging procedure accounts for the beamwidth of the WSR-88D at the location of the RWP profile by assuming that the radiation pattern of themain lobe of the WSR-88Dbeam is well approximated by a Gaussian function (Donaldson 1965).
The vertical weighting function is given by
where uo is the full width at half maximum of the main power lobe and du is the angular offset from the central axis of the main power lobe. For our purposes, the RWP data are averaged in the vertical dimension using
where z2DVar is the height where the WSR-88D scan interests the RWP profile and R is the distance from the NEXRAD radar to the intersection point. Vertical averaging was restricted to height layers with depths that are less than or equal to the beamwidth, using uo'0.958 (
Figure 6 shows a comparison between the retrieved (2DVar) and observed (RWP) wind speed and direction for
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).
The 2DVar and RWP wind vectors are denoted by u2DVar and uRWP, respectively. The wind speed difference is given by
where M2DVar 5 ju2DVarj and MRWP 5 juRWPj. A negative wind speed bias implies that the retrieval is biased slow relative to the RWP observations. The wind speed percent difference is defined as
The mean wind speed difference or bias is denoted by DM(z), where the average is computed at a given height level z and over the comparison periods for each site. The standard deviation of the wind speed difference and the mean wind speed percent difference are denoted by sDM(z) and DMrel(z), respectively. The strength of the linear dependence between M2DVar and MRWP at height z is quantified using the Pearson correlation coefficient,
where cov(x, y) is the covariance between x and y and sx is the standard deviation of x. The root-mean-square (RMS) vector difference is given by
The difference in wind direction between the 2DVar and RWP winds is determined by computing the angle of the retrieved wind vector relative to the RWP wind vector. The result is given by
where u and y are the eastward and northward components of the wind vector, respectively. With this definition, Df is positive when the retrieved winds are rotated clockwise relative to the RWP winds. The mean and standard deviation of the wind direction difference at height z is denoted by Df(z) and sDf(z), respectively.
A minimum wind speed threshold was applied when computing DMrel, Df(z), and sDf(z) to minimize scatter. Data for which MRWP is less than 0.5ms21 were excluded from these calculations.
The results for the CBWES and KSC sites are summarized in Fig. 8 and in Table 1. Figure 8 shows profiles of DM, Df, and RMS(Du), and Table 1 lists DMrel(z) and RM. Statistics for the CBWES site were computed for the period from
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 1.9ms21 at 279m AGL to about 1.0ms21 at 1416m 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 sDM. Most values fall in the range from 3 to 4ms21, with the exception of the lowest altitude at the CBWES site. Here, sDM decreases monotonically from 4.7ms21 at 279m AGL, to 4ms21 at 852m AGL, to 3.8ms21 at 1416m AGL. The KSC sites indicate a slight tendency for sDM to increase with altitude. All of the KSC sites show sDM ; 3ms21 below 1 km AGL and slightly higher values in the range from 3.3 to 3.7ms21 at the highest levels (;1500mAGL).
Wind direction biases Df shown in Figs. 8b and 8e generally indicate little variation with altitude. At the CBWES site (Fig. 8b) the bias is about 258 at the lowest level (279m AGL) but roughly constant (;208) at the higher levels. The KSC1 site (Fig. 8d) shows a bias of 118 that is approximately constant with altitude. The KSC2 and KSC3 (Fig. 8d) sites show much smaller, and constant, wind direction biases. The constant biases at the CBWES and KSC1 sites suggest the presence of systematic errors due to misalignments of individual profilers with respect to true north.
At the CBWES site, the standard deviation of the wind direction difference distribution sDf decreases monotonically from 378 at 279m AGL to 208 at 1416m AGL. The KSC sites show no clear trend in sDf with altitude, with all values near 308. We note that above ;850m AGL sDf 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(Du) for the CBWES and KSC sites are shown in Figs. 8c and 8f, respectively. In contrast to sDM or sDf, the RMS vector difference includes contributions from both random error and bias in the magnitude and direction of Du. Thus, the RMS vector differences are considerably larger than sDM, with values in the range from 4 to 5ms21 at the KSC sites and from 6 to 8ms21 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 fromthe average wind direction bias profiles. The effect of the rotation on RMS(Du) is most pronounced atCBWES (Fig. 8c), where the average wind direction bias was 228. The effect is much less pronounced at KSC1 (Fig. 8f), where the average wind direction bias was 108, 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 DMrel are listed in Table 1. Correlations at the CBWES site increase abruptly from 0.53 at 279m AGL to 0.70 at 852m AGL and then remain approximately constant above that level. The correlation at the KSC1 site experiences only a modest increase from 0.71 at 364m AGL to 0.77 at 1477m AGL. The correlations at the KCS2 and KSC3 sites are approximately 0.76 and show no obvious trend with altitude.
The mean wind speed percent difference DMrel decreases monotonically with altitude at the CBWES site from 56% at 279mAGLto 29% at 1416mAGL. Values at the KSC1 site range between 35% and 39%, and values at both KSC2 and KSC3 are ;40%. The mean wind speed percent differences show no obvious trend with altitude at any of the KSC sites.
In this study, we evaluated NEXRAD wind retrievals using NSSL's 2DVar algorithmat 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 fromthe 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 (
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 4ms21. 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 (279m 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 ;1400m 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 85m near the eastern boundary of the retrieval domain to a maximum of 2260m 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-contaminatedmeasurements 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
* Denotes Open Access content.
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