Impact of assimilating wind retrievals from high-frequency radar on COAMPS forecasts in the Chesapeake Bay

Wind retrievals from high-frequency radars (HFRs) provide high-density, hourly wind estimates over the ocean near the coast. These wind retrievals are a promising new source of near-surface wind estimates in coastal regions where it is difficult to deploy large networks of buoys and where scatterom-eters cannot observe because of land contamination. In addition to improving ocean monitoring, these wind retrievals are also useful in numerical weather prediction. The wind estimates are retrieved from the HFR Doppler spectra in conjunction with the Simulating WAves Nearshore (SWAN) model, HFR forward model, and HFR adjoint model. In this work, wind retrievals were generated from three Coastal Ocean Dynamics Applications Radar (CODAR) SeaSonde HFR sites located near the mouth of the Chesapeake Bay in August 2017 and assimilated in the Coupled Ocean/Atmosphere Mesoscale Prediction System ® (COAMPS) model. The impact of the assimilated HFR wind retrievals on near-surface weather forecasts is measured with adjoint-derived forecast sensitivity observation impact (FSOI) and a comparison to forecasts from a data-denial observing system experiment (OSE). The FSOI measurement indicates the HFR winds had neutral impact on the 12-h forecast while the OSE comparison suggests a small improvement in the 10-m u and v winds at lead times up to 36 h. Compared to a


| INTRODUCTION
Coastal high-frequency radar (HF radar or HFR) networks are routinely used to observe surface ocean currents and have been used for this purpose for decades (Barrick et al., 1977;Harlan et al., 2010;Paduan & Graber, 1997). Recent efforts have exploited the HFR Doppler spectrum, in conjunction with an ocean wave and HFR adjoint model, to estimate above-surface winds near the coast (Muscarella et al., 2021). These wind retrievals provide broad, offshore wind estimates in areas that are sparsely observed by buoys and ships and in areas that are too close to shore for satellite scatterometers to be effective. The prospect of widespread above-surface wind estimates in coastal waters is an exciting advancement for applications such as estimating offshore wind energy (Wang et al., 2019), search-and-rescue and naval operations (Futch & Allen, 2019), and supplements other wind datasets used in numerical weather prediction (Eyre et al., 2022). Blaylock et al. (2022, hereafter B22) assimilated HFR wind retrievals generated at the Southern California Bight into a numerical weather prediction (NWP) model and showed that these wind retrievals provided a beneficial impact to the forecast as measured by the forecast sensitivity observation impact (FSOI; Langland & Baker, 2004) statistic and reductions in the self-analysis root-mean-square-error (RMSE) of 10-m winds compared to a data-denial observing system experiment (OSE).
To further understand the impact of HFR-derived wind retrievals on NWP, we produced an additional set of wind retrievals for the month of August 2017 using three HFR sites at the mouth of the Chesapeake Bay following the methods described by Muscarella et al. (2021) and B22. We then assimilated a data-thinned subset of these wind retrievals into the Coupled Ocean/Atmosphere Mesoscale Prediction System ® (COAMPS) model and evaluated the impact on the forecasts, as done by B22. The purpose of this paper is to (1) increase understanding of the impact of assimilating HFR wind retrievals on NWP forecasting, (2) compare results with B22 findings, and (3) describe challenges and new insights of assimilating HFR wind retrievals that were not realized in B22's first experiment.
The methods of this study and how it extends the work of B22 are described in Section 2. Section 3 discusses the impact of assimilating HFR winds on the forecasts and compares these results with those from B22. Section 4 summarizes the work and the implications for the use of HFR wind retrievals in future data assimilation efforts.

| DATA AND METHODS
Unlike typical weather radar, which is configured to measure precipitation, the purpose of coastal HF radars is to measure backscatter from surface ocean waves. HF radars generate vertically polarized electromagnetic waves on the order of 12 m wavelength (for 25 MHz systems), which "attach" to the sea surface and scatter back to the source off ocean waves of 6 m wavelength-known as Bragg scattering. Following the methods of Muscarella et al. (2021) and B22, HFR wind retrievals were generated at the mouth of the Chesapeake Bay from Doppler spectra collected by three Coastal Ocean Dynamics Applications Radar (CODAR) SeaSonde HFR sites-VIEW, FLND, and SUNS-operating at 25 MHz (Figure 1b). The F I G U R E 1 (a) Three nested COAMPS domains centered over the Chesapeake Bay with 36, 12, and 4 km grid spacing for the outer, middle, and inner nest, respectively (blue outlines). Model topography shaded according to scale. (b) The inner nest where the FSOI and OSE metrics are evaluated with the location of the three HFR sites (white triangles), the footprint of the HFR wind retrievals (orange-hatched area), and the location of CBBV2 (red circle). raw HFR data are sampled at $2 Hz and Fourier transformed with a 1024-sample window, which results in a Doppler spectrum every $4 min, each containing 1024 Doppler frequencies sampled from À2 to 2 Hz. These are then averaged to get an hourly estimate. For comparison, the raw HFR data from the B22 experiment only contained 512 samples and used a network of 10 sites operating at 12 or 13 MHz, which produced wind retrievals over a larger footprint.
To produce an hourly estimate of the 10-m wind field derived from the HFR Doppler spectra, it is necessary to first estimate the spectra using a background wind field, the Simulating WAves Nearshore (SWAN) wave model (Booij et al., 1999), and an HFR forward model (Muscarella et al., 2021;. In this study, the background wind field was supplied by forecasts from the operational COAMPS On-Scene model. It is worth noting that the background winds could have instead been obtained from a different numerical weather model. This resulting first guess of the SWAN wave model Doppler spectra was compared to the Doppler spectra observed by the HFR system. The error between the estimated Doppler spectra and the observed Doppler spectra then feeds the HFR and SWAN adjoint models to find a solution that is consistent with the model dynamics but closer to the observed spectra. By way of a descent algorithm, an update to the 10-m wind field is retrieved that is enhanced by the HFR observations. This process was used to produce hourly estimates of the 10-m wind field within the HFR observation footprint (Figure 1b). Generating wind estimates from HFR Doppler spectra in this manner is analogous to approaches for estimating winds from other platforms like CyGNSS level 1 observables (Cardellach et al., 2020). For a comprehensive description of the method used to retrieve winds from HFR, see Muscarella et al. (2021) and the appendix of B22.
Prior to generating the wind retrievals, the raw HFR signal was processed to remove poor quality signal caused by land contamination. To focus the SWAN-HFR grid toward water locations, we use coastline bearing angles, as reported by the HFR site operators, to mask the HFR signal affected by land contamination. From this masked grid, we utilize only the HFR signal returned from over the water. This bearing angle masking was not utilized in the B22 study due to the simpler coastline in that study region. In addition, the Doppler spectra from the HFR site VIEW were not used on August 8 due to significant environmental noise.

| HFR wind retrieval quality
It is difficult to evaluate the quality of the HFR wind retrievals due to the lack of comparable observations. There is one in situ observation site located on the pier of the Chesapeake Bay Bridge-Tunnel known as CBBV2, which was maintained by the National Oceanographic and Atmospheric Administration National Ocean Service ( Figure 1b) and is within the HFR footprint. We evaluated the quality of the HFR wind estimate by comparing it to two different sources: winds observed at CBBV2 and background winds from a 6-h forecast COAMPS model that did not assimilate the HFR winds (CTRL). To avoid confusion, the background winds referred to here are not the winds from the operational COAMPS On-Scene forecasts used earlier to feed the SWAN model. The details of this control COAMPS simulation, which is one of the inputs in the COAMPS-4DVar data assimilation, is described later in Section 2.2. (It is worth noting that the control COAMPS experiment is a 4D-Var system, while the operational COAMPS On-Scene model is a 3D-Var system.) Since the CBBV2 winds are measured at 6.1 m above the surface, the wind speeds were adjusted to 10 m using the power-law wind-profile relationship to conform to the 10-m winds represented by the HFR wind retrieval and background wind field of the lowest model level (Hsu et al., 1994).
By visual inspection of Figure 2, one will see that the HFR wind retrievals and COAMPS background winds are similar in direction and magnitude to those observed at CBBV2 throughout much of the month of August 2017. The complex correlation coefficients (Kundu, 1976) between the vector wind measured by CBBV2, the HFR retrieval, and the COAMPS model background are summarized in Table 1. The amplitude of the complex correlation coefficient is a value between 0 and 1, where 1 means the two time series wind vectors are perfectly correlated. The phase angle "theta" is the relative mean angle of rotation between the two time series-positive (negative) angles indicate that the first time series is rotated counter-clockwise (clockwise) from the second time series. The correlation coefficients between the HFR and the model background relative to the winds observed at CBBV2 are roughly equal-0.627 and 0.645, respectively-and the angle of rotation is within a few degrees. The HFR retrieval is more correlated to the model background winds with an amplitude of 0.790 and a phase angle of only À2.729 . One possible interpretation of this is that the HFR wind retrievals are more similar to the model background than they are to the winds observed at CBBV2. Although this evaluation only represents HFR winds at a single location, this detail may help interpret the FSOI results presented later.
To show that the HFR winds are not significantly different from the background winds at CBBV2, we look at the RMSE for different ranges of observed wind speeds ( Figure 3). Relative to the observed winds at CBBV2, the HFR and background wind RMSEs for the u wind, v wind, and wind speed are less than 2.5 mÁs À1 for the times when the observed wind speed is less than 5 mÁs À1 (Figure 3a,b), while the RMSE is slightly higher for observed winds 5-8 mÁs À1 (Figure 3c). The highest RMSE occurs at times when the observed wind speed is greater than 8 mÁs À1 (Figure 3d). The background wind RMSE is slightly less than the HFR wind retrieval at all wind speeds. However, this difference is generally not significant. We also note that the COAMPS model does not assimilate observations from CBBV2. Therefore, this is not the reason for the lower RMSE of the background winds compared to the HFR winds at this location. We also compared the HFR wind retrievals against winds measured at two buoys near the northwest edge of the HFR footprint (44072 and YKRV2) and found the results were similar to those at CBBV2 (not shown). We acknowledge that these measures only evaluate the wind quality at a few isolated locations within the domain. In the future, we hope to generate HFR wind retrievals for more coastlines and compare them with more buoys.

| HFR data assimilation
Our purpose in creating the HFR wind retrievals is to assimilate the data into numerical weather prediction models. We followed the experiment design used by B22 to evaluate the impact of assimilating HFR wind retrievals in the Chesapeake Bay on COAMPS forecasts. These experiments were completed with the uncoupled atmospheric COAMPS model (Hodur, 1997) with boundary conditions from the Navy Global Environmental Model (NAVGEM; Hogan et al., 2014) and Navy Coupled Ocean Data Assimilation (NCODA) for its ocean analysis (Cummings, 2005). The hourly HFR winds within the ±3 h window of the cycle time were assimilated into the F I G U R E 2 (a) The 10-m wind speed (black line and gray shading) and wind direction (squares) observed by CBBV2. Wind direction squares are colored according to their corresponding wind speed, according to the scale. (b) The 10-m wind speed (black line) and wind direction (squares) from the quality-controlled HFR wind retrieval at the location nearest CBBV2. For comparison, the gray shaded region is the wind speed at CBBV2 and thin vertical lines show the departure of the HFR wind direction from the CBBV2 wind direction. (c) as in (b) except for the 10-m winds from the CTRL COAMPS background. COAMPS model (Hodur, 1997) using the COAMPS-4DVar assimilation system (Rosmond & Xu, 2006;Xu, 2013), where the background field is determined from the 3-9 h forecast trajectories (the 6-h window centered on the 6-h forecast). All other observations used operationally (e.g., rawinsonde, aircraft, satellite-derived winds, etc.) were also assimilated. The simulation was run for three nested domains-with 36, 12, and 4 km grid spacing-centered over the Chesapeake Bay (Figure 1a) with 60 vertical levels for the month of August 2017, cycled every 6 h, and produced forecasts out to 36 h. The 36 and 12 km nests use the Kain-Fritsch convective parameterization. To allow for model spin up, the first cycle began at 0000 UTC July 30 and the last cycle was 0000 UTC September 2, 2017. The COAMPS model was run for this period for two different cases: (1) a control case (CTRL) that did not assimilate HFR winds, and (2) an experimental case (EXP) that was the same as the CTRL with the addition of the assimilated HFR wind retrievals. HFR wind retrievals were available starting with the 0600 UTC August 1, 2017, cycle for every hour until 0600 UTC August 31. All HFR wind retrievals are contained within the inner-most nest ( Figure 1b). As in B22, the observation error for the HFR wind retrievals was set to 4 mÁs À1 , which is a conservative estimate for the observation error that is not actually known due to limited data. Before the assimilation cycle in the EXP simulation, the HFR wind retrievals underwent basic quality control checks and were thinned by superobservation (Berger & Forsythe, 2004;Janji c et al., 2018;Ochotta et al., 2005;Pauley, 2003). In B22, the HFR winds were available at $3 km grid spacing and were superobbed to $15 km grid spacing. In this experiment, the HFR winds are available at $1 km spacing (because the frequency at which the Chesapeake Bay HFR network operates is different from F I G U R E 3 Root-mean-square error of the CTRL COAMPS background (green) and HFR (blue) u wind, v wind, and wind speed relative to the wind observed at CBBV2 for (a) 0-2 mÁs À1 , (b) 2-5 mÁs À1 , (c) 5-8 mÁs À1 , and (d) 8 mÁs À1 and greater. Error bars indicate 95% confidence interval determined by bootstrapping. Number of samples within each wind speed bin, n, as indicated in the title of each panel. the frequency used in B22) and were also superobbed to a grid spacing of $15 km to match the spatial observation spacing of B22. Doing this reduced the wind field to 19 points within the HFR footprint.
The COAMPS-4DVar system enables us to generate the FSOI statistics for all observations at once to evaluate the impact individual observations have on the simulation's forecasts. The FSOI in this study follows the metric used in B22 and measures the impact each observation had on reducing the error in the dry energy norm of the 12-h forecast for the area within the inner nest and lowest model level. The cumulative impact of the superobbed HFR wind retrievals for each forecast cycle is the sum of the FSOI for each HFR u and v wind assimilated in the forecast cycle. As explained in B22, a negative FSOI indicates that the error in the forecasted dry energy norm is reduced by the inclusion of the HFR wind retrievals, and thus the HFR wind retrievals were collectively beneficial to the forecast for that cycle. Conversely, a positive FSOI indicates the error in the dry energy norm was increased due to the assimilation of the HFR winds and suggests the HFR wind retrievals were not beneficial. The overall impact of an observation network can be determined by the average of its impacts across many cycles of the simulation.
We also evaluate the model in terms of an observing system experiment (OSE) by comparing the forecasts between the CTRL and EXP simulations to evaluate the impact of the HFR wind retrievals on the integrated forecasts of 10 m wind, 2 m temperature, and 2 m dew point. The forecasts in the inner-most nest are compared to each simulation's analysis (self-analysis) to be consistent with the FSOI metric, which also bases forecast error on the model's own analysis. The RMSE and Pearson correlation coefficient (CORR) of the forecasts relative to the verifying analysis were computed using the Model Evaluation Tools developed by the Developmental Testbed Center (Brown et al., 2020; https://dtcenter.org/ community-code/model-evaluation-tools-met). Evaluating model forecasts with both FSOI and OSE can give a greater understanding of the impact certain observation types have on the forecasts than when only one evaluation method is used.

| RESULTS AND DISCUSSION
We first discuss the impact of the HFR wind retrievals on the forecasts in terms of the FSOI as measured in the EXP simulation. Figure 4a shows a time series of the HFR's cumulative impact on the 12-h forecast dry energy norm for each forecast cycle. As is common among other observing platforms, the impact of HFR wind retrievals varies between forecast cycles and is not always beneficial. In this experiment, the average FSOI of the HFR wind retrievals is 3.60 Â 10 À6 JÁkg À1 , which is slightly non-beneficial but is an order of magnitude less than the beneficial impacts seen in B22 where the HFR FSOI was À3.15 Â 10 À5 JÁkg À1 . Because the average impact is so small compared to B22, we interpret these results as having a neutral impact. When FSOI is grouped by initialization time, the 1200 UTC cycle tends to have a slight beneficial impact on average, while other times have a slight non-beneficial impact on average (not shown). When testing for statistical significance, however, we found that the impact at different initialization times is not statistically significant between each other and is not statistically different from zero, suggesting again that the impact from assimilating the HFR wind retrievals is neutral for all initialization times when using the FSOI metric.
The overall neutral impact could be related to the fact that there were far fewer wind retrievals assimilated in this Chesapeake Bay study compared to B22. In B22, an average of 317 HFR wind retrievals were assimilated per cycle, whereas this study only averaged 101 HFR wind retrievals per cycle (see Figure 4a). Furthermore, we expected that including the HFR winds in the assimilation would not add much value to the forecasts since they likely added little, if any, correction over the background wind, as we observed at CBBV2. Had the HFR wind retrievals been more different from the background, we may have seen more impact (positive or negative) from these wind retrievals.
Tracing FSOI results to specific causes is difficult because of the non-linear interdependence of observations on one another in the assimilation process, but we can still identify general patterns in the HFR's FSOI for different wind regimes. Beneficial or non-beneficial impacts are represented across the full range of wind speeds and wind directions (Figure 4b,c). The HFR's FSOI tendency seems to be less dependent on the wind speeds since there are roughly an equal number of beneficial and non-beneficial wind observations for different magnitudes of wind speed ( Figure 4b). As shown in B22, there is evidence that FSOI may have some dependence on wind direction. In this study, HFR winds from the southeast to southwest tend to have more non-beneficial impact, while winds from the northeast to east more often correspond to having a beneficial impact (Figure 4c). For example, the HFR wind retrievals' impact on the cycle initialized at 1200 UTC on August 29, 2017 (see Figure 4a) had the most beneficial FSOI (À1.11 Â 10 À3 JÁkg À1 ) when the winds were from the northeast (see Figure 2). The cycle where HFR winds had the most non-beneficial impact occurred in the 0600 UTC cycle on August 7, 2017 (see Figure 4a), where the FSOI of the HFR wind retrievals was 1.16 Â 10 À3 JÁkg À1 with winds primarily from the south (see Figure 2).
It is also informative to evaluate the impact of assimilating HFR wind retrievals from the perspective of an OSE. For both the EXP and CTRL simulations, the RMSE and CORR statistics were computed from selfanalysis for each model cycle in the month of August 2017 and for each forecast lead time (F06, F12, F18, F24, F30, and F36). The mean difference of each statistic between the two simulations-EXP minus CTRLgrouped by lead time illustrates the changes in the integrated forecast variables when HFR winds are assimilated in the EXP simulation ( Figure 5). The changes in RMSE and CORR are small, but the EXP simulation did have improvements over the CTRL simulation for the 10-m u and v wind components (Figure 5a,b). Specifically, the RMSE for each wind component was up to about 0.1 mÁs À1 lower in the EXP simulation than the CTRL for all the forecast lead times and is statistically different from zero at the 95% confidence interval for many of those lead times as measured by the paired difference t-test. This RMSE reduction due to assimilating HFR wind retrievals is of the same magnitude as the RMSE reduction seen in B22. There is also a slight improvement in the 10-m u and v CORR, where the CTRL case was on average less correlated to the analysis than the EXP case at all lead times, though not all lead times are statistically different from zero. We also note that there is no significant trend in the RMSE or CORR by lead times.
These OSE results demonstrate that the slight improvements in the u and v winds extend throughout all forecast lead times and not just the 12-h lead time when the FSOI is evaluated. There is no measured improvement in the 2-m temperature forecasts since neither the RMSE nor the CORR change between the two simulations ( Figure 5c). The 2-m dew point temperature does show a slight improvement in the RMSE, but the CORR is unchanged (Figure 5d). As stated in B22, we argue that although the mean improvement in the 10-m wind forecasts is small, the indicators that assimilating the HFR wind retrievals is even slightly beneficial to the forecasts is encouraging for future efforts when wind retrievals may be generated for much longer coastlines.
F I G U R E 4 (a) Total FSOI of the HFR observations for each cycle during the month of August 2017. Green and gray bars indicate cycles where the sum of the HFR observations were beneficial (negative) and non-beneficial (positive), respectively. Error bars denote the 95% confidence interval determined by bootstrapping. Blue bars are the total number of HFR u and v wind retrievals assimilated each cycle. (b) Histogram of assimilated HFR wind retrievals by wind speed, grouped by those that were beneficial (green) and those that were nonbeneficial (hatched gray). (c) as in (b) except for wind direction.

| SUMMARY
We applied the methods used by B22 to estimate nearsurface winds from an HFR network at the mouth of the Chesapeake Bay and assimilated the wind retrievals into the COAMPS model. We compared the HFR wind retrievals with in situ observations and tested the impact of assimilating HFR wind retrievals on forecasts of nearsurface variables using FSOI and OSE methods. The insight gained from the FSOI and OSE evaluations highlights the benefits of evaluating numerical weather prediction forecasts with a variety of methods.
The neutral impact of the HFR wind retrievals as measured by the FSOI may be related to the quantity and quality of the wind observations. Related to data quantity, the available HFR wind retrievals cover a relatively small geographical area (as compared to B22), and the influence of these near-surface observations may not have had widespread influence on the whole inner-nest domain at a 12-h forecast (the area and lead time the FSOI was measured for). In future studies, it may be beneficial to also consider the FSOI at additional lead times. Related to data quality, while we do not expect every observation to be beneficial, complex ocean currents and winds in an estuary may compromise the quality of HFR wind retrievals for wind speeds greater than 8 mÁs À1 . HFR wind retrievals may be better applied in areas with simpler coastline geometries than an estuary and for conditions with weak to mild winds. It also appears the HFR wind retrievals during this period were not significantly different from the model background, resulting in a small impact on the forecasts. Despite the neutral impact measured by FSOI, the results from the OSE suggest overall small improvements to the forecasts of u and v wind speed with improvements similar to what was seen in B22, even with a smaller HFR footprint.
With small impacts seen from assimilating a small area of HFR wind retrievals, we hypothesize that more impact could be achieved if HFR wind retrievals were generated from a larger network of HFR sites that covered a longer stretch of coastline. We are also working toward a bistatic implementation which could further F I G U R E 5 Change in mean root-mean-square-error (RMSE; orange square markers) and Pearson correlation coefficient (CORR; green circle markers) at each forecast lead time for (a) 10-m u wind, (b) 10-m v wind, (c) 2-m air temperature, and (d) 2-m dew point temperature. Error bars show the 95% confidence interval determined by the paired difference t-test. RMSE values below zero indicate EXP had a lower RMSE than CTRL. CORR values above zero indicate EXP had a higher correlation coefficient than CTRL. increase the range of HFR wind retrievals. Extending the use of HFR networks to generate wind retrievals for numerical weather prediction can help fill the offshore observation gap, make the total observing network in coastal environments more robust by adding an additional source of wind estimation, and potentially improve forecasts in coastal regions.

ACKNOWLEDGEMENTS
This research was performed while the lead author held a National Research Council Research Associateship award at the Naval Research Laboratory and was supported by the Office of Naval Research under program element 0603801N. We are grateful for the computing resources provided by the Navy Department of Defense Supercomputing Resource Center that made this research possible. The HF radar wind retrieval generation research was funded by the Office of Naval Research Marine Meteorology and Space program under contract N00014-17-C-7021.