Assimilating Near-Surface Wind Retrievals from High-Frequency Radars

Brian K. Blaylock aResearch Associateship Program, National Research Council, Washington, D.C.

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Daniel P. Tyndall bMarine Meteorology Division, Naval Research Laboratory, Monterey, California

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Philip A. Muscarella cSRI International, Ann Arbor, Michigan

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Kelsey Brunner cSRI International, Ann Arbor, Michigan

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Abstract

High-frequency radars (HFR) are traditionally used in coastal environments to observe ocean current and wave characteristics. With an HFR forward model, HFR adjoint model, and the Simulating Waves Nearshore model, HFR Doppler spectra observations were used to estimate near-surface winds in the Southern California Bight in October 2017. The HFR 10-m wind retrievals were assimilated into the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) with the COAMPS four-dimensional variational (4DVar) assimilation system to integrate the HFR wind retrievals into the initial conditions. Impact of the HFR-derived winds on the forecast are evaluated in terms of adjoint-derived forecast sensitivity observation impact (FSOI), and by an observing system experiment that compared forecasts from simulations that assimilated the HFR wind retrievals to a control simulation that excluded HFR winds. The addition of the HFR-estimated wind observations reduced the error in the forecasted dry energy norm in the lowest model level and also contributed to small improvements in the 10-m wind field over a 25-day experiment. The potential benefit of this new method to estimate near-surface ocean winds near the coast for data assimilation and improved numerical weather prediction is an exciting advancement in remote sensing of coastal winds and expands the benefit of existing HFR networks beyond their intended use. More importantly, wind fields retrieved from HFR have the potential to fill an observation gap near the shoreline where ship and buoy observations are sparse and scatterometer observations are unavailable due to land contamination.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Brian Blaylock, brian.blaylock.ctr@nrlmry.navy.mil

Abstract

High-frequency radars (HFR) are traditionally used in coastal environments to observe ocean current and wave characteristics. With an HFR forward model, HFR adjoint model, and the Simulating Waves Nearshore model, HFR Doppler spectra observations were used to estimate near-surface winds in the Southern California Bight in October 2017. The HFR 10-m wind retrievals were assimilated into the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) with the COAMPS four-dimensional variational (4DVar) assimilation system to integrate the HFR wind retrievals into the initial conditions. Impact of the HFR-derived winds on the forecast are evaluated in terms of adjoint-derived forecast sensitivity observation impact (FSOI), and by an observing system experiment that compared forecasts from simulations that assimilated the HFR wind retrievals to a control simulation that excluded HFR winds. The addition of the HFR-estimated wind observations reduced the error in the forecasted dry energy norm in the lowest model level and also contributed to small improvements in the 10-m wind field over a 25-day experiment. The potential benefit of this new method to estimate near-surface ocean winds near the coast for data assimilation and improved numerical weather prediction is an exciting advancement in remote sensing of coastal winds and expands the benefit of existing HFR networks beyond their intended use. More importantly, wind fields retrieved from HFR have the potential to fill an observation gap near the shoreline where ship and buoy observations are sparse and scatterometer observations are unavailable due to land contamination.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Brian Blaylock, brian.blaylock.ctr@nrlmry.navy.mil

1. Introduction

Wind observations that are assimilated in operational numerical weather prediction (NWP) models typically come from a variety of platforms that include aircraft, rawinsondes, satellite, and surface observations (Fig. 1). Observations of offshore winds, however, are traditionally limited to ships and moored or drifting buoys. While there would be many benefits from an increased spatial distribution of observed offshore winds, a sufficient increase in the number of traditional in situ observing platforms over the ocean is improbable. Satellite scatterometers do provide broad coverage of ocean winds, but scatterometers are limited by infrequent satellite overpasses and are inadequate near the coastline because of land contamination. Instead, we must consider different approaches to expand offshore wind observations.

Fig. 1.
Fig. 1.

(a) Operationally assimilated wind observations near the Southern California Bight for a 6-h window centered at 1200 UTC 5 Oct 2017, colored by observation platform. (b) As in (a), but only the near-surface wind observations and aircraft observations below 100 m. The pink hatch-shaded area is the observation footprint of the HFR network available during the CASPER-West field study with a range of ∼50 km from shore.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

For decades, high-frequency radar (HFR) networks have been an important platform to remotely sense ocean currents and wave characteristics up to 200 km from shore (Barrick et al. 1977; Paduan and Graber 1997; Harlan et al. 2010; Paduan and Washburn 2013; Mantovani et al. 2020). At present, HFR networks in the United States provide processed ocean current vectors through the Integrated Ocean Observing System (IOOS; https://hfradar.ioos.us/) for much of the U.S. coastline (Harlan et al. 2010). These types of ocean observations have been assimilated into ocean current and wave models to improve ocean forecasts (Breivik and Satra 2001; Gopalakrishnan and Blumberg 2012; Yu et al. 2012; Ngodock et al. 2015; Isern-Fontanet et al. 2017; Chao et al. 2018; Hernandez-Lasheras et al. 2021). Even in coupled ocean–atmosphere models, assimilating HFR currents can lead to improved tropical cyclone forecasts (Li and Toumi 2018). Beyond observing the ocean surface, the potential of estimating near-surface ocean winds from HFR has been recognized since the early days of HFR use (Barrick 1971; Paduan and Graber 1997; Kirincich 2016). Such wind estimates derived from HFR could effectively fill the coastal wind observation gap where scatterometers cannot observe and in situ ocean observations are scarce (Fig. 1b). While not used operationally, there have been some attempts to estimate the near-surface wind field from HFR power spectra. For example, Kirincich (2016) used wind observations from autonomous vehicles to calibrate an empirical relationship between HFR power and winds, and Zeng et al. (2016) use buoy data to train an artificial neural network to estimate wind speed from HFR.

In this work, we implement a different approach to estimate the 10-m wind field by using the adjoint of an HFR model and the observed HFR Doppler spectra. This approach exploits an existing HFR network to provide higher temporal and spatial resolution wind fields than scatterometers and better spatial resolution than ships and buoys without the need for additional observation equipment. While the HFR-retrieved wind field could be used for many ocean monitoring applications, the purpose of this study is to investigate the feasibility of assimilating HFR wind retrievals in an NWP model and assess their impact on weather forecasts.

Data assimilation is a necessary element in NWP as it constrains the model initial state by observations (Kalnay 2002; Bannister 2017). Among other advances in NWP, high-resolution models are enabled by high-resolution observations (Simonin et al. 2014). One approach for improving mesoscale weather forecasts is to assimilate new observations that improve the model’s initial conditions (Gustafsson et al. 2018). The consequent impact of those observations on the analysis and forecast improvements are typically quantified by observing system experiments (OSEs). Such OSEs are used to show that incremental improvements in NWP capabilities may come by the assimilation of additional and novel observations (Zeng et al. 2021). Under this assumption, we assimilate wind fields retrieved from an HFR network to improve the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) model’s initial state and subsequent forecasts. Hourly wind fields were generated from a network of 10 HFR systems in the Southern California Bight (Figs. 1b and 2) for 1–21 October 2017 during the Coupled Air–Sea Processes and Electromagnetic Ducting Research (CASPER-West) field experiment (Wang et al. 2018). These additional offshore wind retrievals and improved forecasts are not only useful in areas trafficked by ships or developed for wind energy, but the benefits extend to society living along the coast where the land–sea contrast plays an important role in atmospheric processes such as sea breezes.

Fig. 2.
Fig. 2.

(a) The 10-m vector winds from HFR wind retrievals (white barbs) and conventional surface wind observations (black barbs) at 1200 UTC 7 Oct 2017 with HFR wind speed, shaded according to scale. Half and full wind barbs indicate 2.5 and 5 m s−1, respectively. (b) Normalized Doppler spectra error, shaded according to scale, at 1200 UTC 7 Oct 2017. Triangles are the locations of the 10 HFR sites. Yellow circle is the location of buoy 46053 (see Fig. 3). (c),(d) As in (a) and (b), but for 0000 UTC 13 Oct 2017.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

This paper is organized as follows: Section 2 describes the near-surface wind dataset retrieved from an HFR network; section 3 describes the OSE setup, COAMPS model, and data assimilation system. The consequent impact of the HFR wind retrievals on the forecasts are presented and discussed in section 4 followed by a summary in section 5. Specific details about how the HFR wind dataset was created is given in the appendix.

2. HFR wind retrievals

Near-surface wind vectors were estimated from HFR Doppler spectra data in conjunction with the Simulating Waves Nearshore (SWAN) wave model (Booij et al. 1999; Walker and Brunner 2021) and HFR forward and adjoint models. In this experiment, we use 10 HFR sites with 12.2- or 13.4-MHz transmission frequencies which provide an observation footprint of backscatter between the shore and about 50 km from the shore in the Southern California Bight (Fig. 2). To estimate the 10-m winds from the HFR Doppler spectra, we first estimate the wave spectrum with a 3-km SWAN model (Walker and Brunner 2021), which estimates the prevalence of wind-generated waves. SWAN received boundary condition wind forcing from a 6-km operational COAMPS On-Scene forecast (COAMPS-OS), ocean currents from the 3-km Navy Coastal Ocean Model (NCOM), and assimilated wave data from six buoys available from the National Data Buoy Center (NDBC). The SWAN model is cycled every 12 h with continuously updating boundary conditions from the COAMPS-OS and NCOM models for a 24-h forecast. The SWAN model produces hourly estimates of the wave spectrum which are used as input for the first- and second-order Bragg-scattering HFR Doppler spectrum model that estimates the HFR spectrum (Rogers et al. 2012; Muscarella et al. 2018, 2020a,b). The error between the SWAN-estimated Doppler spectrum and the observed HFR Doppler spectrum is input for the HFR and SWAN adjoint models. Finally, a descent algorithm produces a best fit of the model to the observations that results in an improved estimate of the 10-m wind field. Through this process, the first-guess 10-m wind field originally supplied to the SWAN model by COAMPS-OS is enhanced with new information from the HFR observations. The resultant HFR wind retrieval is provided at hourly intervals (e.g., Figs. 2a,c) that can be assimilated in NWP. Additional details on the production of the HFR wind field are given in the appendix.

Quality control and superobservation

The HFR wind retrievals are subject to errors for reasons that include radar sighting, radar interference, and inconsistencies between the HFR model and SWAN model and the adjoint. The HFR data quality is also affected by the sea state (Wei et al. 2020). Before assimilating the HFR wind retrievals into COAMPS, we apply some basic quality control checks to remove potentially erroneous or poor wind data and thin the dataset by superobservation.

Quality control checks flagged the HFR wind retrievals for extreme wind speeds, outlier winds, and large innovations (the difference between observation and the model background). One additional quality control check, called the normalized Doppler spectra error check, removed winds where there were large deviations between the HFR observed Doppler spectra and the SWAN model estimated Doppler spectra (with HFR assimilated). Where normalized Doppler spectra error is high, our confidence in the quality of the derived wind data is low because there is a mismatch between the simulated SWAN Doppler spectra and observed HFR Doppler spectra. This mismatch in the spectra data is potentially related to inconsistencies between the model and observations and higher-order (third order, fourth order, etc.) scattering that is not represented by the HFR model. For this study, we flag HFR winds where normalized Doppler spectra error is greater than 50 (unitless) since that normalized value tended to flag similar winds as other quality control checks. For example, none of the HFR winds failed the normalized Doppler spectra error check at 0000 UTC 13 October 2017 (Fig. 2d) but many winds in the center of the HFR footprint failed this check at 1200 UTC 7 October 2017 (Fig. 2b). This parameter may be adjusted in future studies with additional investigation of appropriate threshold values for this quality control check and for different HFR networks.

After the data quality control checks, but prior to the assimilation cycle, the HFR wind retrievals are thinned by superobservation. In the experiments we present, the HFR wind field was “superobed” from its original grid spacing of 3–15 km by averaging all observations that passed the quality control check within a 15 km × 15 km grid if at least two observations had passed quality control checks within the box. Reducing the amount of assimilated HFR data by superobservation is necessary for the same reasons it is done for satellite-observed winds—it reduces computational requirements, reduces uncorrelated error, and helps mitigate the effects of correlated error from the high-resolution wind field (Pauley 2003; Berger and Forsythe 2004; Ochotta et al. 2005; Berger et al. 2011; Janjić et al. 2018; Duan et al. 2018).

Comparisons of the prepared HFR u and υ wind retrievals and COAMPS background u and υ winds to those observed at buoy 46053 (see Fig. 2b) help diagnose the quality of the data being assimilated, at least at a single point (Figs. 3 and 4). (Other buoys exist in the area but are either outside the HFR footprint or do not measure winds.) The HFR wind retrievals at times provide an improvement over the COAMPS background and the various quality control checks successfully flag some HFR winds that are opposite in direction to those observed at the buoy, such as on 11 and 19 October 2017 (Fig. 3). However, the quality controlled HFR wind at this location do not always agree with the buoy observations.

Fig. 3.
Fig. 3.

(a) Time series of u wind observed at buoy 46053 (black line), HFR “superobed” u wind retrievals that passed and failed quality control checks (blue and grey dots, respectively), and u wind from the COAMPS background without HFR assimilated (green line). (b) As in (a), but for υ wind.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

Fig. 4.
Fig. 4.

(a) Mean error of the “superobed” HFR u wind retrievals that passed quality control checks (blue) and COAMPS background u wind (green) relative to buoy 46053 (see Fig. 2) at the location of the buoy each hour of the day for 1–22 Oct 2017. Error bars indicate 95% confidence interval. (b) As in (a), but for υ wind.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

The error of the quality controlled and “superobed” HFR wind retrievals relative to the buoy averaged for each hour shows that the HFR wind retrievals have the lowest error between 1800 and 0400 UTC, while 0500–1700 UTC has less agreement when the HFR tends to have a stronger northeast (offshore) component than is observed at the buoy (Fig. 4). Some reasons for the disagreement between the buoy and HFR wind retrievals might be biases in the buoy data, biases in the COAMPS background from which HFR winds were in part derived, or differences in the represented wind height—HFR wind retrievals are at 10 m and the anemometer of the buoy is at 4 m. The COAMPS background, without HFR winds assimilated, also has errors relative to the buoy, and these errors are not significantly different from the HFR error relative to the buoy at this location except for 0400–0600 UTC in the u wind and 1200–1300 UTC in the υ wind. This indicates that the HFR wind retrievals assimilated are generally not significantly different than the error of the COAMPS background.

3. COAMPS experiment design

We devised an OSE to evaluate the impact of HFR wind retrievals assimilated into the COAMPS model (Hodur 1997). For a control, we ran uncoupled atmospheric COAMPS simulations with the Navy Coupled Ocean Data Assimilation (NCODA) ocean analysis (Cummings 2005), Navy Global Environmental Model (NAVGEM) boundary conditions (Hogan et al. 2014), and assimilate all operational observations while excluding the HFR wind retrievals. This control case is then compared to additional simulations that include the HFR wind data in the assimilation cycle. To allow time for model spinup, each simulation began at 0000 UTC 29 September 2017 and cycled every 6 h for 25 days until 0000 UTC 23 October 2017. HFR observations were assimilated starting with the 0600 UTC cycle on 1 October until 1800 UTC 21 October. Each cycle produced a 36-h forecast.

All COAMPS simulations were run for the same domain centered over the Southern California Bight with three nested domains at 36-, 12-, and 4-km grid spacing (Fig. 5). All HFR wind retrievals are contained within the innermost nest (Fig. 5b). Data assimilation is done by the COAMPS-4DVar assimilation system with a 6 h observation window (Rosmond and Xu 2006; Xu 2013). Since the HFR wind retrievals are available hourly, HFR winds are assimilated from seven distinct observation times in each assimilation cycle (i.e., the −3, −2, −1, 0, +1, +2, +3 h relative to the analysis time).

Fig. 5.
Fig. 5.

(a) COAMPS model terrain height, shaded according to scale, with 36-, 12-, and 4-km nests. (b) The innermost nest centered over the Southern California Bight. FSOI and OSE statistics are evaluated for this area. Hatched area is the HFR observation footprint.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

To test appropriate strategies for assimilating the HFR wind retrievals, we ran several experiments with adjustments to parameters like observation error, the reduction in data volume by superobservation, and quality control thresholds. From these early experiments, we learned that changes in the prescribed observation error were responsible for the largest changes in the impact the HFR wind retrievals had on the forecasts. The observation error primarily controls the degree to which the assimilation system fits the analysis to the observations. In this paper, we only present results from three experiments that had the same quality control thresholds and superobservation density, but with the HFR observation errors set to 2, 4, and 8 m s−1 referred to as HFRxE2, HFRxE4, and HFRxE8, respectively. For reference, scatterometer wind observations in operational COAMPS simulations are assigned an error of 2.8 m s−1 with all other wind observation errors ranging from 1.8 and 5.5 m s−1.

Forecast evaluation metrics

The influence of assimilating the HFR wind retrievals on the COAMPS forecast quality are evaluated in terms of adjoint-derived forecast sensitivity observation impact (FSOI) relative to all other observations for each simulation experiment. Forecasts are also evaluated within the context of a typical OSE with self-analysis comparisons of atmospheric variables of the experiments with HFR data assimilated to the control simulation without HFR data.

FSOI, as described by Langland and Baker (2004), provides a means to quantitatively compare the impact of individual observations assimilated regardless of observation type or variable (see also Baker and Langland 2007). The FSOI capability is enabled through the COAMPS-4DVar adjoint. For each experiment, the FSOI of each observation assimilated within the model domain is evaluated for its impact on the forecast relative to the model analysis. The use of self-analysis in adjoint-based impact measurements is supported by Privé and Errico (2019). The error metric evaluated is the reduction in error of the 12-h forecast dry energy norm—a unit of energy per area for the variables of temperature, pressure, and wind. Similar to Eq. (4.1) in Ehrendorfer and Errico (1995), the dry energy norm in COAMPS is defined as
E=12Dzbotztop[u2+υ2+cpTrT2+RdTr(ppr)2]dσzdD,
where Rd is the dry gas constant, cp is specific heat at constant pressure, T is temperature, Tr is the reference temperature 300 K, p is pressure, pr is the reference pressure 1000 hPa, u and υ is the wind vector, integrated over the domain horizontal extent D and vertical sigma layers σz between ztop and zbot. We limit the FSOI cost function to evaluate this measure for only the lowest model layer over the entire innermost nest (Fig. 5b). Thus, we limit our evaluation of all observations to their individual impact on the forecast near the surface for a limited area as we desire to only measure the impact on the forecasts in the inner nest where the HFR observations are located, and not the outer domains. Although impact of observations extends throughout the model’s volume, focusing the FSOI cost function to a specific area and level helps isolate the measured impact of observations to a specific area of interest and is analogous to the OSE approach that evaluates forecasts at certain levels and regions.

Impact of assimilating the HFR wind retrievals is also evaluated in terms of an OSE data-withholding experiment (Aberson 2011; Lin et al. 2017; James and Benjamin 2017; James et al. 2020). The OSE evaluation method provides an additional perspective related to the integrated effect of the HFR winds on the forecasts at different lead times for specific model output variables. For the control and three HFR experiments, we use the Model Evaluation Tools (Brown et al. 2020) to compute the 10-m wind root-mean-square error (RMSE) of each forecast cycle and lead time against the experiment’s own analysis (self-analysis). This evaluation is limited to the same horizontal extent as the FSOI cost function [the area of the innermost nest (Fig. 5b)] and is consistent with the FSOI method that also uses the simulation’s own analysis as the verifying analysis. These RMSE statistics from the control and HFR experiments are then compared against each other at each model run and lead time.

4. Results and discussion

a. Forecast sensitivity observation impact

FSOI was configured to measure the contribution of each individual observation to reducing error in the dry energy norm for the 12-h forecast for the area of the lowest model level within the innermost nest relative to the simulation’s analysis. By convention, negative FSOI is beneficial to a forecast because the observation reduced the error. For each forecast cycle, the FSOI of individual observations are summed together by observation platform (e.g., satellite surface winds, rawinsonde, aircraft profile, aircraft level flight, HFR). The summed FSOI for each group of each cycle include all observed variables made by that group (i.e., temperature, humidity, wind, etc.) Throughout the experiment, observations assimilated anywhere in the model domain tend to have greater impact—positive or negative—near the FSOI verification layer than observations further away from the verification layer, which we expect should happen (not shown).

The 25-day mean FSOI of each observation group illustrates the overall impact of the different observations in four COAMPS experiments (Fig. 6a). One property of FSOI is that adding or modifying observations will affect the measured impact for all other observations (Baker and Langland 2007). This accounts for the differences in mean FSOI between experiments for all observation groups, and not just in the mean FSOI of the HFR group. For example, mean FSOI for aircraft is different between experiments even though all experiments assimilated the same aircraft observations.

Fig. 6.
Fig. 6.

(a) Mean FSOI, (b) mean FSOI per observation, and (c) mean observation count for each observation group for the control simulation (black) and HFR experiments (shades of blue). Error bars indicate the 95% confidence interval.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

Profiles from aircraft contribute the most beneficial impact in all COAMPS experiments due in part to the large number of observations (Figs. 6a,c). Notably, there are a large number of aircraft profile observations near the FSOI evaluation layer with the presence of major airports in Los Angeles within the innermost model nest (e.g., see Fig. 1b). This result agrees with previous studies that show the importance of aircraft data for numerical weather prediction, even for forecasts near the surface (e.g., James et al. 2020). Surface ocean observations from buoys and ships had the most degrading impact on the forecasts in the lowest model level for all experiments, mostly attributed to a span of times when these observations had consistent nonbeneficial impact during 15–16 October, which is manifest by the large 95% confidence interval. During that same period, surface satellite wind observations compensated with beneficial impact (not shown).

The HFR wind retrievals had some beneficial impact, similar in impact to the satellite surface winds, with the most benefit occurring in HFRxE2 and least benefit in HFRxE8. Over the study period, the mean HFR impact is −7.25 × 10−6 J km−1 in HFRxE8, −3.15 × 10−5 J kg−1 in HRFxE4, and −5.62 × 10−5 J kg−1 in HFRxE2. Thus, in part due to the lower specified observation errors, the HFRxE2 had the most beneficial impact. However, HFRxE2 was also more susceptible of having assimilation cycles with nonbeneficial impact, as indicated by the large spread in the 95% confidence interval. HFRxE8 has very little impact due to the larger assumed observation errors, as the data were given little weight in adjusting the analysis.

There are very few HFR wind retrievals relative to the number of observations made by other observation groups. HFR provided on average only 317 additional observations each cycle while observation from all aircraft within the full model domain provide an average of over 108 000 observations that contribute to each model analysis. When FSOI for each observing group is normalized by the total number of observations at each time and averaged across time, the HFR wind retrievals in HFRxE2 and HFRxE4 have more impact per observation than the other observing systems (Fig. 6b). Of the three HFR experiments, HFRxE2 had the highest mean benefit per observations (−1.9 × 10−7 J kg−1 per observation), albeit a wide confidence interval. HFRxE4 had less impact per observation (−9.2 × 10−8 J kg−1), but still more than the other observation groups, and HFRxE8 had even less impact per observation (−1.6 × 10−8 J kg−1). The HFR observations in HFRxE2 and HFRxE4 have greater impact per observation than other observation groups; this is partially due to the way the cost function used to determine FSOI is specified. The volume that FSOI is computed over contains the entirety of the HFR observations; most other observations from other platforms are located above the lowest model level or outside of the innermost nest. Still, these results suggest the assimilated HFR winds have some beneficial impact on the forecasts near the surface where they were assimilated. Expanding the number of HFR observations to cover a larger area could be beneficial to surface forecasts near the coastline.

Assimilating HFR winds across a broad region is consistent with Langland (2005), who recommends the assimilation of many observations with small to moderate impacts over a few observations with large impacts. Relative to the number of buoys available within the HFR footprint, HFR provides a large quantity of observations over a broad area. The large quantity of moderately impactful HFR observations makes it more likely that the HFR platform as a whole is more beneficial than not. Conversely, the nonbeneficial impact of a platform with limited observations was likely manifest in this study for the few surface ocean observations assimilated within the innermost nest. As with satellite wind observations and commercial aircraft that have expanded observations in many areas, we expect that expanding the observation of near-surface winds to cover a larger area along coastlines with HFR will further increase benefit to the forecasts. An additional benefit of assimilating a new observing system in NWP is that this also increases the robustness of the total observing network as it reduces the potential negative impact when a single observing system becomes unavailable for any reason.

To examine the impact of HFR winds on specific forecasts throughout the experiment, we consider the summed FSOI for all assimilated HFR wind retrievals at each model cycle for HFRxE4 (Fig. 7a). Like other observing platforms, all HFR wind retrievals are not collectively beneficial every forecast cycle. While we would not expect a good observing system to always have beneficial impact, the overall FSOI averaged across the study period (−3.15 × 10−5 J kg−1) is slightly beneficial which suggests the HFR wind retrievals add some benefit to the forecast for the time period in their present configuration and application. There appears to be some dependence on the impact of the HFR winds on the time of day they are assimilated. On average, analyses when HFR provide the most beneficial impact tend to occur at 1200 UTC and is more often nonbeneficial for the 0000 UTC analysis (Fig. 7b). This time dependence on observation impact may be somewhat related to the flow direction of assimilated winds.

Fig. 7.
Fig. 7.

(a) Total FSOI for the HFR wind retrievals for each model cycle in experiment HFRxE4. Negative FSOI (green) indicate runs where the HFR wind retrievals had a net beneficial impact on the 12-h forecast. Positive FSOI (pink) indicate runs where the HFR wind retrievals had a nonbeneficial impact on the 12-h forecast. (b) Mean FSOI for the HFR wind retrievals by forecast cycle. Error bars indicate 95% confidence interval.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

Forecast sensitivity to HFR wind retrievals may be related to the ability of the HFR system to accurately observe winds in certain flow directions or times of day. Consideration of the analysis times when the HFRxE4 FSOI was most beneficial (Figs. 8a–c) and most nonbeneficial (Figs. 8d–f) reveals spatial and temporal variations in FSOI at each “superobed” observation location during the assimilation window. For the analysis time when HFR had the best total FSOI, the flow direction at 1200 UTC 15 October was generally north to northeast (offshore) with the greatest benefit coming from the stronger winds in the center of the HFR footprint (Fig. 8a). The analysis time with the third best FSOI (Fig. 8c) had similar flow direction at 1200 UTC 9 October and enhanced benefit for the observations close to the center of the HFR footprint (some points are missing due to quality control). The time with the second best FSOI (Fig. 8b) had different flow characteristics at 0600 UTC 16 October with more beneficial impact from the northerly flow on the western side of the HFR footprint as opposed to the areas with northwest flow with neutral impact. The two analysis times the HFR had the most nonbeneficial FSOI (Figs. 8d,e) the flow was westerly (alongshore) and both occurred at 0000 UTC. One possible reason for the FSOI dependence on flow direction could be biases in the COAMPS or adjoint model for different flow regimes that impact the FSOI. Flow direction and time of day, however, are not always good estimators of whether the HFR FSOI will be beneficial or nonbeneficial, as demonstrated by the third worst analysis time (Fig. 8f) when the flow at 1800 UTC 9 October was very similar to the first and third best analysis times with mostly east and northeast winds (Figs. 8a,c). Because many factors can influence the FSOI of an observation network at each analysis, the evaluation of the observing network should be judged based on its performance over time rather than by discrete analysis times.

Fig. 8.
Fig. 8.

HFR vector winds averaged over the 6-h assimilation window centered at the analysis time indicated and total FSOI for HFRxE4, colored according to scale, at each “superobed” HFR data point. Half and full wind barbs indicate 2.5 and 5 m s−1, respectively. (a)–(c) The three analyses when HFR has the most beneficial FSOI and (d)–(f) the three analysis times when HFR had the most nonbeneficial FSOI (see Fig. 7).

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

b. Observation system experiment forecast comparison

We have examined the impact of the HFR wind retrievals on the 12-h forecasts based on FSOI in the lowest model layer for the COAMPS experiments relative to other observations. This section examines the impact of assimilated HFR wind retrievals on the integrated forecasts from the OSE perspective that evaluates the forecasts of the three HFR experiments to the control that did not assimilate HFR winds. The RMSE for wind, temperature, and dewpoint are computed by self-analysis for the inner nest of each COAMPS simulation and all forecasts lead times. Since the measured differences in 2-m temperature and dewpoint were negligible (not shown), we only focus our discussion on the results for 10-m wind speed.

Differences between the HFRxE4 and control experiment 12-h forecasts of 10-m u and υ wind RMSE varies throughout the experiment, and it is not clear that the 10-m wind forecasts in HFRxE4 performs better than the control over the time period (Fig. 9). However, when considering the mean RMSE difference averaged across all runs in the experiment at each lead time, it is clearer that the experiments with HFR wind retrievals assimilated have smaller RMSE in near-surface wind than the control experiment (Fig. 10). For the 10-m wind forecasts, there is a mean reduction in up to 0.1 m s−1 RMSE at all lead times for the three experiments, except for the 6-h forecast for HFRxE2 (Fig. 10). The 95% confidence interval in the mean of the differences indicate these reduced RMSE is significant for a few of the lead times, specifically the u wind at F12 for HFRxE2 and HFRxE4 and at F36 for all three experiments. The reduced RMSE for the υ wind is only significant for the lead times after F24 in EFRxE2. While HFRxE2 generally provides more improvement in wind RMSE than the other two experiments, it also had a wider confidence interval. We acknowledge these average improvements are small, but it is important that the assimilation of HFR wind data into COAMPS did not degrade the forecasts. Impacts at other vertical levels between the surface and 500 hPa were inconclusive.

Fig. 9.
Fig. 9.

Self-analysis RMSE of the innermost nest for (a) 10-m u wind and (b) 10-m υ wind for the 12-h forecast for the HFRxE4 experiment (orange) and control experiment (black). Dashed blue line indicates the date HFR data began to be assimilated.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

Fig. 10.
Fig. 10.

Mean difference in RMSE by lead time between the control experiment and the three HFRx experiments (shades of orange) for (a) 10-m u wind and (b) 10-m υ wind. Values below zero indicate HFRx had lower RMSE than the control. Error bars show 95% confidence interval.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

5. Summary

There exists a need for additional near-surface ocean wind observations along coastlines where scatterometers are unavailable and buoys are scarce. We have demonstrated the potential for HFR networks to fill that gap by using the full backscattered spectral data from an existing HFR network in Southern California to estimate near-surface winds out to about 50 km from shore. We have also demonstrated the ability to assimilate the HFR wind retrievals in the COAMPS model and investigated the impacts of the HFR winds on the coastal forecasts. This study is the first time HFR wind retrievals have been generated with an HFR adjoint model and is the first time HFR wind retrievals have been assimilated in any NWP model. The use of HFR wind retrievals is an exciting advancement in coastal NWP, especially since it takes advantage of existing ocean observational networks and uses them beyond their intended purposes. HFR networks are becoming more prevalent around the globe (Roarty et al. 2019), and as new networks are installed the potential for additional coastal wind observations useful for NWP is also expanded.

We have assimilated HFR wind retrievals for a relatively small area and evaluated its impact from two perspectives—adjoint-derived FSOI and OSE comparisons to a control run. Although these initial results show small improvements in forecasted surface winds between simulations with and without HFR winds assimilated, they suggest that assimilating HFR wind retrievals can provide beneficial impact to forecasts on average over a length of time of about three weeks. Expanding the wind-retrieval capabilities to more HFR networks optimized for wind retrievals have the potential to benefit high-resolution NWP along the coastlines and make the total observing system of the coastal environment more robust. The beneficial impact of HFR wind retrievals on forecasts varies across the HFR footprint from run to run and improved use of the data may come from improved quality control checks. Some limitations to the HFR winds are systemic and more research is needed to evaluate the data quality under different types of HFR operating and weather conditions.

In this initial experiment, we have only used a limited amount of data available from the HFR network. HFR systems often operate with a range of frequencies that provide observations at different ranges and resolutions. We only had access to a limited amount of these data, but future work should investigate the use of other frequencies available to retrieve winds at greater distances from shore than we have generated in this work. We also desire to improve the quality of the HFR wind data and better quantify the observation error to address bias. This will lead to better quality control checks so that good data are not flagged and the unreliable data within the HFR footprint are not assimilated. This is challenging because each HFR network requires ongoing calibration. Another challenge is that there are few conventional observations to validate HFR wind retrievals. In this current study, we could only compare the HFR wind retrievals at a single buoy point. Further investigation of HFR wind retrievals for additional time periods in larger regions where more observations for validation are available will be needed to help quantify errors. This could be accomplished through field study with carefully placed observations or by evaluating many months of HFR wind speeds against wind speeds observed by synthetic aperture radar.

The development of HFR-derived wind field for real-time applications is still in the early stages before becoming operationally feasible. We have tested the methods in this study with retrospective runs, but the application of this work depends on cooperation from the HFR network managers, regular access to necessary Doppler spectra data from the HFR networks, applying the HFR models for different HFR network configurations and frequencies, and developing real-time capabilities. Despite these challenges, the potential benefit of HFR wind retrievals for data assimilation and improved NWP along the coast is an exciting advancement in the remote sensing of coastal winds and expands the benefit of the existing and future HFR networks located around the world.

Acknowledgments.

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 thank Libe Washburn and Brian Emery at the University of California, Santa Barbara (UCSB), for providing the HFR spectra data required for this research, Arie Knoll for work with wave forecasting during the CASPER-West experiment, and Dave Walker and Dave Lyzenga for writing the original HFR forward and HFR adjoint models. We are also grateful for the computing resources provided by the Navy Department of Defense Supercomputing Resource Center that made this research possible. Map tiles by Stamen Design (http://maps.stamen.com), under CC BY 3.0.

Data availability statement.

The NWP forecast data used in this project are too large to host on a public repository but can be provided upon request. The COAMPS atmospheric model and its data assimilation system is a licensed technology owned by the Naval Research Laboratory. NAVGEM boundary conditions and all observation files used by COAMPS, except for the HFR dataset, are available through www.usgodae.org. The HFR Doppler spectra dataset is a level 0 data product that is not routinely reported but can be obtained directly from the site operators.

APPENDIX

Generating HFR Wind Retrievals

Here, we discuss the formulation and implementation of the HFR Doppler spectrum assimilation based on SWAN version 41.20 to generate improved coastal wind estimates. This appendix only presents the equations and formulation of the HFR wind retrieval and not a full derivation. For a full derivation, see Muscarella et al. (2021). This model has been implemented to use the spatially variable wave spectra calculated by the SWAN model, as well as the Doppler spectra data from ground wave HFR sites. The initial implementation has been tested in the Southern California Bight during the CASPER-West experiment (October 2017).

a. HFR Doppler spectrum model

The Doppler spectrum σ^ from a cross-loop HFR system is defined as the sum of the first- and second-order Bragg scattering contributions as
σ^(ω,r)=σ^1(ω,r)+σ^2(ω,r),
where the first-order scattering is
σ^1(ω,r)=64πk04   ϕ1ϕ2wn(ϕ)m=±1{[kS(k,x)δ(kmkb)dk]×δ(ωkbumωb)dk}dϕ.
The spatial locations for the first order each contain a near-surface current contribution, which imparts a Doppler shift of Δω = ku. The second-order scattering is defined as
σ^2(ω,r)=64πk04ϕkkwn(ϕ)m=±1|Γ(ω,k,k,x)|2S(k,x)S(k,x)×δ(k+mkb+k)δ(ωωd)dkdkdϕ,
where k′ = mkbk, ωd = kbu + k + mωk, Γ is the coupling coefficient, and m, m′ = +1 and −1 for approaching and receding waves, respectively. See Table A1 for a list and description of all variables.
Table A1

Variable symbols and descriptions.

Table A1

b. Observed HFR Doppler wave spectra

Noisy and uncalibrated observational HFR data can be represented as
s=σCn+eσ=Cn|se|
where Cn is a fixed calibration constant, and e is the noise. In practice, e can be estimated from the extreme upper- and lower-frequency bands, away from the Bragg peaks. The absolute value is used to prevent small negative spectral densities.
We next define our cost function, using the derivative in frequency of the difference in the log of the predicted and observed spectral density, as
J=rω{ω[logσ^log(Cn|se|)]}2dωdr=rω[ω(logσ^log|se|)]2dωdr.
The main advantage of specifying the cost function in this way is that it is insensitive to the unknown calibration constant.

c. Wave spectra from Bragg spectrum gradients

The Doppler spectrum has two components that are summed to produce the complete spectrum. The two components are treated separately and then combined. After taking the first variation with respect to S and integrating by parts, we get the first-order gradient of the high-frequency spectrum error with respect to the wave spectrum as
Sd1(k,x)=ϵwn(ϕ)rm=±1{1σ^1(ω,r)2ω2[logσ^1(ω,r)log|s(ω,r)e|]δ(kmkb)}ω=mωb+kbu.
Here we integrated in ω, evaluating the integrand at the shifted Bragg frequencies. The gradient term is then assigned at the Bragg wave-vector locations in the wave spectral domain and in the spatial domain.
The second-order gradient of the HFR spectrum error with respect to the wave spectrum is
Sd2(k,x)=ϵwn(ϕ)rm=±1{1σ^2(ω,r)2ω2[logσ^2(ω,r)log|se|]}ω=ωd2|Γ(ωd,k,k,x)|2S(kmkb,x).
The resulting error in the Doppler spectrum at the Bragg frequencies is mapped to a correction in the wave spectrum at k and scaled by the scattering coefficient and the spectral density at the resonant wavenumber.

d. Adjoint models

The adjoint of the SWAN model for the adjoint wave spectra A, is defined as
AtC˜˜A=(δSδE)ASd,
where Sd is the HFR Doppler spectrum error w.r.t. the wave spectrum and ˜ and C˜ are the wave-energy propagation velocities and the wave–current interactions, respectively. The first variation of the cost function J w.r.t. the wind is
δU10J=TR[S1σδSδU10ds+ϕw(U10U10init)]δU10dxdt,
computed where the vector nature of the wind is accepted. This equation governs the reduction in J that will result from a change in U10. To reduce J we set δU10, the incremental change to the wind, to
δU10(x,t)=α[S1σδSδU10Ads+ϕw(U10U10init)],
where α is positive.

e. Implementation during CASPER-West

A SWAN model was set up for the Northern California Bight (Fig. A1). Wind forcing from a 6-km COAMPS-OS and surface currents from a 3-km NCOM are utilized as inputs to the wave model. Additionally, NDBC wave buoy data were assimilated into SWAN to correct the open boundary wave conditions during the study period (Walker and Brunner 2021). Here we utilize the data from 10 Coastal Ocean Dynamics Application Radar (CODAR) coastal HFR sites in order to estimate the surface-wind forcing for a portion of the month of October 2017 (Fig. A1).

Fig. A1.
Fig. A1.

CODAR HFR sites (diamonds) and the SWAN wave model domain (outlined bounding box) during the CASPER-West experiment.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

The HFR data require some initial preprocessing in order to select a usable set of range samples and average over a specified number of these samples, average the Doppler spectra over time, and write out the data in a form that is more easily read into the HFR adjoint model. The raw HFR data are sampled at ∼2 Hz and Fourier transformed with a 512-sample window, which results in a Doppler spectrum every ∼4 min, each containing 512 Doppler frequencies sampled from −1 to 1 Hz. Useful comparisons between observations and predictions were from an average of three range cells and a 1-h time interval.

The algorithm structure for the SWAN HFR assimilation system contains numerous processing steps and components. Figure A2 lays out the complete flowchart for the system. The forward SWAN model ingests wind vectors at 10-m height from COAMPS-OS as well as bathymetry data and produces a wave spectrum estimate. The HFR first- and second-order Doppler spectrum model ingests the SWAN wave spectrum estimate along with ancillary HFR metadata (site frequency, location, etc.) and generates an HFR Doppler spectrum estimate. This SWAN HFR estimate is then compared to the observed HFR spectrum data. The error between these sources then forces the HFR Doppler adjoint model to produce an effective wave spectrum error. The wave spectrum error forces the SWAN adjoint model. This loop is iterated until a descent algorithm produces a best fit of the model to the observations. This process allows for improved estimates of the wind and wave fields.

Fig. A2.
Fig. A2.

Flowchart for the SWAN-HFR assimilation system used to generate HFR wind retrievals.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

Figure A3 shows an example comparison of the range-Doppler plots for the Refugio State Beach (RFG1) HFR site (see Fig. A1). The Bragg peaks associated with the first- and second-order signals are clearly visible in both the predicted and observed fields. Similar plots can be generated for all the HFR sites throughout October 2017 and show that the predicted SWAN HFR Doppler model does a reasonable job of estimating the observed HFR data.

Fig. A3.
Fig. A3.

Doppler-range HFR dBZ for (top) antenna 1 and (bottom) antenna 2 at RFG1 (see Fig. A1) at 1700 UTC 3 Oct 2017. (a),(d) The predicted fields from the SWAN Doppler model. (b),(e) The observed HFR data. (c),(f) The differences between the predicted and observed fields. The first- and second-order Bragg peaks are visible in both the predicted and observed range Doppler plots.

Citation: Journal of Atmospheric and Oceanic Technology 39, 4; 10.1175/JTECH-D-21-0062.1

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  • Fig. 1.

    (a) Operationally assimilated wind observations near the Southern California Bight for a 6-h window centered at 1200 UTC 5 Oct 2017, colored by observation platform. (b) As in (a), but only the near-surface wind observations and aircraft observations below 100 m. The pink hatch-shaded area is the observation footprint of the HFR network available during the CASPER-West field study with a range of ∼50 km from shore.

  • Fig. 2.

    (a) The 10-m vector winds from HFR wind retrievals (white barbs) and conventional surface wind observations (black barbs) at 1200 UTC 7 Oct 2017 with HFR wind speed, shaded according to scale. Half and full wind barbs indicate 2.5 and 5 m s−1, respectively. (b) Normalized Doppler spectra error, shaded according to scale, at 1200 UTC 7 Oct 2017. Triangles are the locations of the 10 HFR sites. Yellow circle is the location of buoy 46053 (see Fig. 3). (c),(d) As in (a) and (b), but for 0000 UTC 13 Oct 2017.

  • Fig. 3.

    (a) Time series of u wind observed at buoy 46053 (black line), HFR “superobed” u wind retrievals that passed and failed quality control checks (blue and grey dots, respectively), and u wind from the COAMPS background without HFR assimilated (green line). (b) As in (a), but for υ wind.

  • Fig. 4.

    (a) Mean error of the “superobed” HFR u wind retrievals that passed quality control checks (blue) and COAMPS background u wind (green) relative to buoy 46053 (see Fig. 2) at the location of the buoy each hour of the day for 1–22 Oct 2017. Error bars indicate 95% confidence interval. (b) As in (a), but for υ wind.

  • Fig. 5.

    (a) COAMPS model terrain height, shaded according to scale, with 36-, 12-, and 4-km nests. (b) The innermost nest centered over the Southern California Bight. FSOI and OSE statistics are evaluated for this area. Hatched area is the HFR observation footprint.

  • Fig. 6.

    (a) Mean FSOI, (b) mean FSOI per observation, and (c) mean observation count for each observation group for the control simulation (black) and HFR experiments (shades of blue). Error bars indicate the 95% confidence interval.

  • Fig. 7.

    (a) Total FSOI for the HFR wind retrievals for each model cycle in experiment HFRxE4. Negative FSOI (green) indicate runs where the HFR wind retrievals had a net beneficial impact on the 12-h forecast. Positive FSOI (pink) indicate runs where the HFR wind retrievals had a nonbeneficial impact on the 12-h forecast. (b) Mean FSOI for the HFR wind retrievals by forecast cycle. Error bars indicate 95% confidence interval.

  • Fig. 8.

    HFR vector winds averaged over the 6-h assimilation window centered at the analysis time indicated and total FSOI for HFRxE4, colored according to scale, at each “superobed” HFR data point. Half and full wind barbs indicate 2.5 and 5 m s−1, respectively. (a)–(c) The three analyses when HFR has the most beneficial FSOI and (d)–(f) the three analysis times when HFR had the most nonbeneficial FSOI (see Fig. 7).

  • Fig. 9.

    Self-analysis RMSE of the innermost nest for (a) 10-m u wind and (b) 10-m υ wind for the 12-h forecast for the HFRxE4 experiment (orange) and control experiment (black). Dashed blue line indicates the date HFR data began to be assimilated.

  • Fig. 10.

    Mean difference in RMSE by lead time between the control experiment and the three HFRx experiments (shades of orange) for (a) 10-m u wind and (b) 10-m υ wind. Values below zero indicate HFRx had lower RMSE than the control. Error bars show 95% confidence interval.

  • Fig. A1.

    CODAR HFR sites (diamonds) and the SWAN wave model domain (outlined bounding box) during the CASPER-West experiment.

  • Fig. A2.

    Flowchart for the SWAN-HFR assimilation system used to generate HFR wind retrievals.

  • Fig. A3.

    Doppler-range HFR dBZ for (top) antenna 1 and (bottom) antenna 2 at RFG1 (see Fig. A1) at 1700 UTC 3 Oct 2017. (a),(d) The predicted fields from the SWAN Doppler model. (b),(e) The observed HFR data. (c),(f) The differences between the predicted and observed fields. The first- and second-order Bragg peaks are visible in both the predicted and observed range Doppler plots.

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