Impact Study of Assimilating Fengyun-3 GNSS-R Ocean Surface Winds in the Weather Research and Forecasting Model: Sensitivity Analysis on Observation Error Specifications

Highlights

What are the main findings?

• Optimal assimilation of FY-3E GNSS-R winds in WRF is achieved using a static observation error of 6 m/s without data thinning.
• GNSS-R wind assimilation significantly improves atmospheric analyses, with impacts extending from the surface up to 700 hPa in a sensitivity experiment and higher levels in cycling OSEs.

What are the implications of the main findings?

• The dense along-track sampling of GNSS-R observations requires careful observation error specification, which plays a critical role in data assimilation.
• The observation error configuration and OSEs provide a practical reference for assimilating GNSS-R winds in WRF, and can be extended to other NWP systems.

Abstract

The Global Navigation Satellite System Reflectometry (GNSS-R) technique provides global ocean surface wind observations unaffected by rainfall with high spatiotemporal resolution. The Fengyun-3E (FY-3E) mission, as the first operational GNSS-R satellite in China, offers low-latency data suitable for numerical weather prediction (NWP). However, the dense along-track sampling of GNSS-R winds poses challenges for observation error specification in data assimilation. In this study, FY-3E GNSS-R winds are assimilated into the Weather Research and Forecasting (WRF) model to investigate the impacts of different observation error configurations. Both static and dynamic error specifications, with and without data thinning, are evaluated through a sensitivity experiment and subsequent Observing System Experiments (OSEs). The results indicate that using a static observation error of 6 m/s without data thinning achieves the best performance. Under this configuration, GNSS-R winds influence atmospheric analyses from the surface up to approximately 700 hPa in a single assimilation case, while cycling experiments further extend the impact vertically and spatially. These findings highlight the importance of appropriate observation error specification for dense GNSS-R data and provide a practical reference for their assimilation in WRF, with potential applicability to other NWP systems.

1. Introduction

Ocean surface winds play a crucial role in numerical weather prediction (NWP) and data assimilation systems. Since it is difficult to establish meteorological observation stations over the ocean, conventional measurements have mainly relied on in situ observations from ships and buoys. With the development of remote sensing technology, spaceborne instruments such as scatterometers and synthetic aperture radars have emerged as powerful tools for monitoring ocean surface winds [1,2,3,4,5]. Their key advantage lies in the satellite-based configuration, which enables broad, near-global coverage and the generation of consistent long-term records of ocean surface winds [6].

In recent years, Global Navigation Satellite System Reflectometry (GNSS-R) has been developed as a novel approach for retrieving ocean surface winds [7,8,9,10,11]. GNSS-R utilizes the L-band signals transmitted by navigation satellite constellations, exploiting their forward reflections from the sea surface to retrieve wind speed. Compared with other remote sensing techniques, GNSS-R passively utilizes freely available GNSS signals without the need for active transmission. The receivers are lightweight and low-power, making them suitable for deployment on a larger number of small satellites, thereby reducing the overall cost. The availability of multiple platforms also leads to a much higher temporal revisit rate for GNSS-R observations. Furthermore, the L-band signals used by GNSS-R penetrate clouds and heavy precipitation, making the technique robust under different weather conditions [12,13].

Several GNSS-R missions have been launched to demonstrate and operationalize this technique. The Technology Demonstration Satellite-1 (TDS-1) carrying the SGR-ReSI receiver was launched in 2014. NASA’s Cyclone Global Navigation Satellite System (CYGNSS), launched in 2016, is the first GNSS-R mission specifically designed to monitor ocean surface winds in tropical cyclone (TC) regions [14]. The mission consists of a constellation of eight microsatellites placed in low-inclination orbits, enabling frequent revisit times over the TC regions. In addition, Spire Global operates a series of CubeSats equipped with GNSS-R technology for Earth observation, covering atmospheric, oceanic, and land-surface parameters [15].

The BuFeng-1, launched on 5 June 2019, is the first Chinese GNSS-R satellite mission [16]. The Fengyun-3 (FY-3) satellite constellation, equipped with the Global Navigation Satellite System Occultation Sounder II (GNOS-II) and operated by the China Meteorological Administration (CMA), was launched between 2021 and 2023. It represents the first operational GNSS-R mission, with an average data latency less than 3 h, integrating both GNSS radio occultation (RO) and GNSS-R observations from multiple GNSS constellations [17]. Building on the FY-3 GNOS-II, the Tianmu-1 commercial constellation was launched between 2023 and 2024. It consists of 22 small satellites with GNSS RO and GNSS-R capability for atmospheric, oceanic and terrestrial applications [18,19].

GNSS-R wind observations from most missions are collected at a sampling rate of 1 Hz, with an effective spatial resolution of 25 km. The measurements are taken at specular points, and the spacing between consecutive observations is about 6 km along the satellite track due to the velocity of the receiver. As a result, GNSS-R provides dense along-track sampling, while its spatial resolution remains coarser (grid size of 6 km and resolution 25 km as shown in Figure 1). The dense sampling does not imply higher spatial resolution. This is different from many other sensors which provide observations on a 25 km grid, such as scatterometers [20]. Conventional scatterometers transmit microwave toward the ocean surface and measure the normalized radar backscatter returned. Since scatterometer wind retrieval requires observations from multiple azimuth angles and adopts fan-beam or conical scanning, several measurements are combined into a wind vector cell, resulting in a typical 25 km grid.

Due to the unique characteristics of GNSS-R observations, appropriate handling of observation error is particularly important in assimilation [21]. A three-dimensional variational (3DVAR) data assimilation method is adopted in this study. Equation (1) shows the mathematical formulation of the 3DVAR assimilation,

$$J\left(x\right)={\displaystyle \frac{1}{2}}{\left(x-x^b\right)}^T{B}^{-1}\left(x-x^b\right)+{\displaystyle \frac{1}{2}}{\left(y-H\left(x\right)\right)}^T{R}^{-1}\left(y-H\left(x\right)\right)$$

(1)

where $x$ denotes the model state, $x^b$ denotes the background, $y$ represents the observations, $H$ is the observation operator, and $H\left(x\right)$ is the model simulated observation. $B$ is the background error covariance, and $R$ is the observation error covariance. In the Weather Research and Forecasting Data Assimilation (WRFDA) system, $R$ is assumed to be diagonal, which implies that each observation independently contributes to the analysis. When two observations are close, their errors may in reality exhibit spatial correlations. But under the assumption, each GNSS-R observation is treated as completely independent, and such correlations are neglected, which may lead to repeated counting of observational information and overestimating of the observation weight. Therefore, the optimal observation error specified in WRFDA is an effective error, rather than a pure retrieval or instrumental error.

In general, three common approaches are used to address these dense-sampling datasets: thinning, error inflation, and superobservation [22]. Thinning selects a single observation within each grid cell while discarding the others, which reduces error correlations but sacrifices a considerable amount of information. Error inflation retains all points but increases their assigned errors, therefore requires further evaluation. Superobservation averages the data within a grid cell, enabling more efficient use of information, though at the expense of smoothing local features. These methods are intended to reduce error correlations and improve the representativeness of the assimilation and forecasting. However, no unified standard currently exists, and both the choices of assimilation method and error specification vary considerably among studies.

Previous data assimilation studies of GNSS-R ocean winds have demonstrated a wide range of practices using CYGNSS data, as summarized in

Table 1. Strategies of observation error setting for GNSS-R winds in different studies.

Reference	Observation Type	Model and System	Strategy of Observation Error Settings
Majumdar and Atlas [23]	Simulated	WRF & GSI	Simulated errors with typical values of 2–4 m/s.
McNoldy and Annane [24]	Simulated	HWRF & GSI	Errors inversely proportional to antenna gain.
Zhang and Pu [25]	Simulated	HWRF & GSI	Thinned to 27 km, errors were estimated by comparing CYGNSS winds with the hurricane NR.
Lin and Yang [26]	Simulated	UWIN-CM & WRF-LETKF	2 m/s (<20 m/s) and 10% (>20 m/s).
Leidner and Annane [27]	Simulated	HWRF & GSI	Simulated errors with typical values of 2–4 m/s.
Cui and Pu [28]	Real	HWRF & GSI	Thinned at 25 km. The observation error was set to 2.1429 m/s.
Li and Mecikalski [29]	Real	WRF & WRFDA	Thinned to 25 km; 2 m/s (<20 m/s) and 10% (>20 m/s).
Mueller and Annane [30]	Real	HWRF & GSI	Inflating observation errors by a factor of 5.
Pu and Wang [31]	Real	HWRF & GSI	Observations thinned to 25 km; 2 m/s for CYGNSS V2.1 data and 3 m/s for V3.0 data.

. Majumdar and Atlas [23] assimilated simulated data with prescribed observation errors of 2–4 m/s using the WRF model with the Gridpoint Statistical Interpolation (GSI) data assimilation system. The experiments employed four nested grids with horizontal resolutions of 27, 9, 3, and 1 km. McNoldy and Annane [24] assimilated CYGNSS simulated ocean wind speeds in the Hurricane Weather Research and Forecasting (HWRF) model and GSI system with resolutions of 25 km (and 12.5 km in finer regions), with observation errors set inversely proportional to antenna gain. Zhang and Pu [25] also used HWRF and GSI to assimilate simulated GNSS-R winds thinned to the model grid resolution, with observation errors specified to match the characteristics of the nature run (NR). The correlation between the NR errors and the observation errors was found to be 84%. Lin and Yang [26] specified 2 m/s errors for winds below 20 m/s and 10% of wind speed for winds above 20 m/s in the Unified Wave INterface-Coupled Model (UWIN-CM) and the Weather Research and Forecasting model–Local Ensemble Transform Kalman Filter data assimilation system (WRF-LETKF), without thinning. Leidner and Annane [27] set observation errors equal to those of Majumdar and Atlas [23], utilizing the HWRF model and GSI system. By combining calibration and retrieval errors, they generated simulated CYGNSS wind speeds that exhibit realistic observational error characteristics. Cui and Pu [28] applied a static observation error of 2.1429 m/s and thinned real observation data to 25 km resolution in the WRF model and GSI system. Li and Mecikalski [29] adopted a similar threshold-based strategy in the WRF model and WRFDA system, but additionally applied distance-weighted averaging within each grid cell. Using the HWRF model with the GSI data assimilation system, Mueller and Annane [30] excluded winds above 15 m/s and inflated the observation error by a factor of five. Also in the HWRF-GSI framework, Pu and Wang [31] thinned CYGNSS winds to 25 km and assigned observation errors of 2 m/s for V2.1 data and 3 m/s for V3.0 data.

These examples illustrate that the treatment of observation error for GNSS-R wind speeds in the data assimilation is highly diverse and heuristic. A systematic sensitivity analysis of different error specifications for GNSS-R winds remains to be investigated. Most studies have adopted fixed, unitary error settings without fully exploring their impacts on assimilation and forecasts. Furthermore, those studies have primarily focused on the assimilation impacts of CYGNSS data in tropical cyclone environments, while relatively few investigations focus on non-cyclone regions.

In this study, we utilize the GNSS-R ocean surface wind speed product from FY-3E/GNOS-II to conduct sensitivity experiments with different observation error specifications on non-TC scenarios. Our objective is to identify an optimal error treatment strategy that improves the use of GNSS-R winds in the data assimilation system by avoiding observation overweighting. We first design a single-case assimilation experiment with multiple error configurations to assess their impact on the analysis. Building on these results, we then conduct observing system experiments (OSEs) to systematically evaluate how different error settings affect forecasts and to identify the best one. The remainder of this paper is organized as follows. Section 2 introduces the forecast model and assimilation system, as well as datasets used in this paper. Section 3 presents different GNSS-R wind error settings and their impacts in a single assimilation case. Section 4 presents the OSEs and discusses the results. Finally, Section 5 provides the conclusions and a summary of the study.

2. WRF Model and Data

2.1. WRF Forecast and Data Assimilation Systems

In this study, we employ the Weather Research and Forecasting (WRF) model version 4.3.1 together with the three-dimensional variational WRF Data Assimilation (WRFDA 3DVAR) system. The WRF model, primarily designed for mesoscale weather prediction, has been continuously developed and refined over the past two decades. The Advanced Research WRF (ARW) core is suitable for a wide range of applications, spanning spatial scales from meters to thousands of kilometers. To initiate forecasts, the model requires both background and lateral boundary conditions.

The WRFDA system is used to ingest observations and update the initial conditions of WRF within the OSEs. It provides both 3DVAR and 4DVAR assimilation capabilities and supports a variety of observational datasets, including conventional observations, radar measurements, and satellite retrievals.

The background data were obtained from the NCEP FNL analysis with a spatial resolution of 0.1° and a temporal resolution of 6 h. This product is generated by the Global Data Assimilation System (GDAS), which continuously ingests observational data from the Global Telecommunications System (GTS) and other sources.

2.2. FY-3E GNSS-R Ocean Surface Wind Observations

The FY-3E GNOS-II GNSS-R ocean surface winds are the major observations in the assimilation study of this paper [32]. The retrieved wind product is derived by empirical geophysical model functions using multiple variables derived from multi-constellation (GPS, BeiDou, and Galileo) measurements. The wind product demonstrates high accuracy over the global low-to-moderate wind regime (0–25 m/s) and is suitable for global NWP applications. The validation result against ECMWF ERA5 10 m winds is shown in Figure 2. The overall wind error is under 1.5 m/s.

In this paper, we propose two methods to estimate the observation error of FY-3E GNSS-R winds. The first one is the “static” method, i.e., setting the errors of all wind observations as a constant value. The second one is the “dynamic” method where the observation error is empirical function of wind speed and signal-to-noise ratio (SNR). A look-up table was developed for the relationship trained from actual measurements as shown in Figure 3. As expected, the error increases as wind speed increases, and decreases as SNR increases generally.

2.3. Validation Datasets: ECMWF ERA5 and HSCAT Wind Data

Two types of reference datasets were used in this study. The first is ERA5, the fifth-generation ECMWF reanalysis, which provides a comprehensive set of global atmospheric and surface variables on multiple levels, with a horizontal resolution of 0.25°. The second dataset is the scatterometer winds of the Haiyang-2B (HY-2B) satellite (HSCAT). The Ku-band scatterometer can provide accurate global ocean surface wind observations at a spatial resolution of 25 km [33,34]. HY-2B scatterometer winds are not assimilated in any models in this study, and thus can be regarded as an independent dataset for validation.

It should be noted that both datasets have limitations when used as the comparison data. ERA5 is a model-based reanalysis product; it contains model-related uncertainties and smoothing effects. Scatterometer winds, on the other hand, suffer from rainfall contamination and observation noise.

3. A Case Study of Assimilating GNSS-R Wind Speed

3.1. Experiment Description

In this section, FY-3E GNSS-R ocean surface winds were assimilated. The quality control of the data was implemented using the “quality_flag” variable in each file. The 24 h WRF forecast initialized by the NCEP FNL analysis served as the background, with a horizontal resolution of 0.25° and 41 vertical levels. The lateral boundary conditions were also obtained from the FNL. The default static background error statistics (cv_option = 3) were applied. They are precomputed climatological estimates derived from long-term model forecasts and are commonly used in WRFDA applications. The use of them provides a stable framework for evaluating the impact of a new kind of observation. The assimilation experiment was conducted over the western Pacific Ocean region at 0600 UTC on 23 August 2022. This analysis time is also the initial analysis for the following OSEs in Section 4, which include 16 assimilation–forecast cycles. The model domain (25.7° S–49.4° N, 133.2° E–144.2° W) consisted of 300 × 300 horizontal grid points, as shown in Figure 4a. The GNSS-R wind observations during the assimilation window are shown in Figure 4b. The WRF model employed the Thompson microphysics scheme, the RRTMG longwave and shortwave radiation schemes, the MYJ planetary boundary layer scheme with the corresponding surface layer parameterization, and the Grell–Devenyi cumulus parameterization. Cloud–radiation interaction and convective–radiative feedback were both activated.

The experiment was divided into two groups based on whether the data thinning was applied. In the group of data thinning, wind observations were thinned to a 25 km grid using the nearest-to-grid point thinning method. Within each group, the impacts of different static and dynamic observation error settings on the assimilation performance were investigated.

For the static observation errors, six constant values were prescribed: 24.00, 9.00, 6.00, 4.00, 2.00, and 0.01 m/s. By progressively reducing the error values, the relative weight of the observations in the assimilation was increased, allowing us to explore the interplay between static error settings and thinning strategies and to identify optimal configurations. The extreme values were included to examine how the analysis response when observation confidence is set low (large errors) versus high (small errors). These settings also enabled us to assess whether increasing the static error could substitute for thinning.

For dynamic observation errors, initial values average 1.5 m/s, close to the wind speed RMSE from the validation result in Figure 2. To avoid overfitting without thinning, multiple inflation factors were introduced in the experiments. Specifically, the initial dynamic error was multiplied by factors of 4, 5, and 6. This design enabled us to evaluate whether inflated dynamic errors can, under certain specifications, play a role similar to thinning in improving assimilation performance.

Two datasets, ECMWF ERA5 and HSCAT winds, were used for validation. Using both datasets in parallel allowed us to examine the sensitivity of assimilation results to different error characteristics. The scatterometer errors primarily originate from the instrument noise and retrieval algorithms, whereas reanalysis errors arise from model background uncertainties and the data assimilation system. The root-mean-square error (RMSE) of the background and analysis compared with the validation datasets is used as the metric for evaluation.

3.2. Results

Figure 5 summarizes the RMSEs between the analysis and two references (HSCAT and ERA5) under different observation error settings. The following results are based on this single assimilation case. For the static error experiments, smaller observation errors substantially degrade the analyses, while moderate values (6–9 m/s) yield better performance. Referenced to HSCAT winds, the optimal result is achieved after thinning with observation error of 9 m/s. Referenced to ERA5 data, the best result is obtained at observation error of 6 m/s after thinning.

For dynamic errors, with all observations included, RMSE with HSCAT decreases monotonically as the inflation factor increases from 1 to 6. Furthermore, data thinning could still improve the analyses; factor 5 after thinning indicates the smallest RMSE. For ERA5 reference, the minimum RMSE appears at a factor of 6 with thinning.

Overall, these results highlight those moderate static errors (6–9 m/s) are generally optimal, and dynamic error inflation can partially compensate for error correlations within the experimental configuration. Data thinning exhibits a stable performance and has a positive impact in experiment.

Next, we choose several settings, which perform reasonably well, to evaluate the impact of observation errors on analyses in detail.

• GNSSR6_CTRL: GNSS-R wind speeds are assimilated with a static observation error of 6 m/s.
• GNSSRdy_CTRL: GNSS-R wind speeds are assimilated with dynamic observation errors inflated by a factor of 4.
• thinGNSSR4_CTRL: GNSS-R wind speeds are assimilated with a static observation error of 4 m/s and data thinning applied.

Observation error settings were selected based on the following considerations. Without thinning, a moderate static error of 6 m/s was chosen because it performed well. For the dynamic error, an inflation factor of 4 was applied because error inflation is necessary and this factor produces a matched magnitude to the static error of 6 m/s. Since the averaged retrieval error of FY-3E GNSS-R winds is approximately 1.5 m/s. With thinning, a static error of 4 m/s was used because thinning can partially mitigate overfitting, allowing a smaller static error.

Figure 6 presents the RMSEs of observation-minus-background (O–B) and observation-minus-analysis (O–A) departures. In all situations, O–A values are smaller than O–B. The O–B distribution is more scattered and elliptical, while the O–A distribution is more linear, indicating better agreement with observation. Among the three experiments, the small O–A RMSE in thinGNSSR4_CTRL reflects a strong pull of analysis toward observation.

From the background overlaid with observations, the four GNSS-R wind speed tracks that fall inside the domain are mostly located in low-speed areas (Figure 7a). A high-surface-wind-speed region can be identified near 150° E, 30° N. After assimilation, analysis shows no substantial changes compared with background, indicating that the basic dynamical balance of the flow has been preserved (Figure 7b–d).

To further examine the impact of assimilation, difference between analysis and background was focused. In Figure 7e–g, several key regions can be identified. The pictures reveal that the main changes induced by assimilation occur in the low-speed regions. One notable area is centered near 28° N, 197° W, where the analysis speed exceeds background by more than 5 m/s. Among the experiments, GNSSRdy_CTRL shows the largest positive differences, whereas thinGNSSR4_CTRL exhibits the smallest. Combined with the earlier O–A results, this reveals a consistent pattern. GNSSRdy_CTRL shows the least consistency with the observations, and it also deviates most from background. Conversely, analysis closest to the observations (thinGNSSR4_CTRL) remains most similar to background. So different observation error settings produce distinct impacts on analysis, and the affected areas align with the observation swaths.

The RMSE between background and reference ERA5 is 1.314 m/s; the others are 1.51 m/s, 1.56 m/s, and 1.42 m/s for GNSSR6_CTRL, GNSSRdy_CTRL, and thinGNSSR4_CTRL respectively. From Figure 8, most surface wind speed differences originate from the assimilated influence of observation. Low-speed areas measure a stronger impact, particularly in GNSSRdy_CTRL, because the prescribed observation errors in this experiment decrease with wind speed, which enhances the influence of low-speed observations during assimilation. One region differs: 23°–37° N, 183°–200° W, in the red box. Although observations also pass through this area and their speed departures from background are small, assimilation still produces a noticeable speed increase. This region lies on the southern flank ahead of a trough, where upper-level winds are strong.

From Figure 9, the RMSE profiles (solid lines) from different experiments at 0600 UTC on 23 August 2022 indicate that the impact of assimilating surface wind speed is primarily confined to the boundary layer and extends upward to approximately 700 hPa. Above this level, the influence of assimilation rapidly diminishes and becomes negligible. In this single assimilation experiment, thinGNSSR4_CTRL achieves the lowest overall RMSE, followed by GNSSR6_CTRL, while GNSSRdy_CTRL shows the smallest improvement. The RMSE is large near the surface, decreases with height to a minimum around 700 hPa, and then increases again at higher levels. This vertical structure suggests that the constraint introduced by surface-wind assimilation is mainly concentrated in the lower troposphere and weakens with altitude, with the background error increasingly dominating aloft.

The dashed lines follow the same trend as the RMSE profiles and denote the upper and lower bounds of the uncertainty range. The shaded regions represent ±1 standard deviation of the RMSE profiles at each pressure level, quantifying the variability across different samples. Above 700 hPa, the spread becomes small and tends to overlap among experiments, indicating a more consistent error structure in the upper levels. Overall, a narrower envelope indicates more consistent model performance, whereas a wider envelope suggests stronger variability associated with changes in atmospheric conditions and observation coverage. Therefore, the shaded regions provide a quantitative measure of the stability of the RMSE profiles across different experiments.

4. Observing System Experiments

4.1. Experiment Description

The OSE is a standard approach in data assimilation for assessing the impact of specific observing systems by selectively withholding or including them in assimilation–forecast cycles. It provides a quantitative measure of the contribution of observations to numerical weather prediction (NWP) models. In this study, we conducted OSEs to evaluate the assimilation of FY-3E GNSS-R ocean surface winds under different error specifications, with the objectives of identifying optimal error settings and demonstrating the potential contribution of GNSS-R wind data to NWP. Each experiment in the OSEs employed an assimilation window of ±3 h and a cycling interval of 6 h. Forecasts were integrated to 120 h, with a total of 16 assimilation–forecast cycles conducted. The first assimilation cycle begins at 0600 UTC on 23 August 2022, and the last one begins at 0000 UTC on 27 August 2022. The physics, planetary boundary layer, and other schemes are the same as the assimilation case study.

The OSEs in this study consists of four parallel experiments: CTRL (a control baseline, no observations are assimilated), GNSSR6_CTRL, GNSSRdy_CTRL and thinGNSSR4_CTRL. Among those experiments, GNSSR6_CTRL and GNSSRdy_CTRL compare the static and dynamically inflated error settings. thinGNSSR4_CTRL assesses whether thinning, which mitigates error correlations among dense GNSS-R observations, combined with stronger observational weighting, can further improve forecasts.

4.2. Results

Figure 10 shows the ocean surface wind speed RMSE time series of the forecasts for different experiments, when evaluated using ERA5 and HSCAT winds. When comparing to ERA5 (Figure 10a), GNSSR6_CTRL exhibits the smallest errors compared to the others throughout the 120 h forecasts. CTRL and thinGNSSR4_CTRL show nearly identical RMSEs, increasing steadily from about 1.7 m/s at 6 h to about 2.0 m/s at 120 h. GNSSRdy_CTRL performs the worst, with errors exceeding 2.1 m/s after 72 h. The result is similar when comparing to HSCAT, shown in Figure 10b, indicating that GNSSR6_CTRL is the best error setting. The curves in Figure 10b are more fluctuating, due to the limited number of collocations between GNSS-R and HSCAT data at certain times.

Figure 11 shows the mean vertical profiles of wind speed RMSE from the averaged analyses, referenced to ERA5 data. The solid lines represent the RMSE profiles averaged over all assimilation times for each experiment. GNSSR6_CTRL yields the smallest mean RMSE among the four experiments, which is better than the others at any height. All experiments exhibit a broadly similar pattern. Below approximately 700 hPa, RMSE increases with height and then decreases, with maximum values not exceeding 2.4 m/s. Above 700 hPa, RMSE first increases and then decreases again, with maximum mean values exceeding 4.5 m/s. For CTRL, GNSSRdy_CTRL, and thinGNSSR4_CTRL, differences are most evident in the lower troposphere: between 1000 and 850 hPa. thinGNSSR4_CTRL shows lower RMSE than GNSSRdy_CTRL. Above 850 hPa, the RMSE profiles of the three experiments converge and become nearly indistinguishable.

To assess whether the assimilation of GNSS-R wind data improves the consistency of the analyzed geopotential height fields with the reference, we examined the anomaly correlation coefficients (ACCs) of geopotential meters at 850 hPa between the forecasts and ERA5 (Figure 12). The results show that GNSSR6_CTRL exhibits the highest correlation, remaining above 0.97 throughout and showing a relatively stable trend. Both CTRL and thinGNSSR4_CTRL display a more rapid decline after 54 h, with similar performance. GNSSRdy_CTRL has the lowest correlation, dropping rapidly after 72 h, but ACCs still stabilizes above 0.94.

Overall, these results demonstrate that GNSS-R data can significantly improve NWP forecasts when appropriate observation error settings are used, and it is validated using two independent reference datasets in the OSEs. Different error settings were shown to have large impacts on the assimilation results. A constant wind speed error of 6 m/s without thinning was found to be the best error setting where the forecasts were significantly improved compared to the control experiment.

5. Discussion

The experiments in this study were designed to examine the role of observation error. The single assimilation case reflected the response to different GNSS-R wind error settings, while the OSEs further evaluated whether and how these differences could lead to forecast impacts. The comparison among GNSSR6_CTRL, GNSSRdy_CTRL, and thinGNSSR4_CTRL indicates that assimilating dense GNSS-R winds requires a balance between observational constraints and the model background. The sensitivity experiments demonstrate that the observation error used in WRFDA should be regarded as an effective observation error rather than only as instrumental or retrieval uncertainty.

The relationship between data thinning and error inflation further highlights the balance between reducing correlated information and retaining dense observations. In WRFDA, thinning could reduce the influence of observation in fact. However, it also removes part of the dense sampling information, which is one of the advantages of GNSS-R observations. In OSEs, thinGNSSR4_CTRL does not outperform GNSSR6_CTRL, although it shows a stronger adjustment in the single assimilation case. This suggests that retaining all observations with a larger static error can provide more stable forecasts than thinning with stronger observation weights.

The dynamic error provides another useful comparison. We could set different observation errors based on wind speed; the higher the wind speed, the larger the observation error. Therefore, low-speed observations may receive relatively large weights because the dynamic error decreases under low-wind conditions. In this case, many GNSS-R tracks were located in low-speed regions, which contributed to stronger local increments, especially in GNSSRdy_CTRL. The dynamic error gives more weight to low-speed regions but underestimates high-speed regions, so the static observation error performs better than the dynamic error.

For vertical levels, the effect of assimilation remains limited. In the single assimilation case, the influence of GNSS-R wind assimilation is confined below around 700 hPa. In the OSEs, assimilation could produce broader impacts, such as the improved vertical RMSE profiles and higher 850 hPa geopotential height ACCs in GNSSR6_CTRL. This indicates that assimilation of just GNSS-R surface winds can still contribute to higher levels in forecasting if their observation errors are properly specified.

A limitation of this study is that conventional observations were not incorporated into the control experiment, as the main objective of this work is to study the sensitivity of the assimilation results to different observation error specifications, rather than as a complete representation of an operational data assimilation system.

6. Conclusions

This study investigates the impact of assimilating Fengyun-3 GNSS-R ocean surface wind observations into the WRF model through OSEs with different observation error specifications. A key feature of GNSS-R is the track-wise and exceptionally dense distribution of observations at specular points compared to other remote sensing techniques, which poses a challenge to properly specifying observation errors in the data assimilation system.

We first examined the effects of different observation error configurations in a single assimilation case of GNSS-R wind speeds. Based on these results, representative error settings were selected for a series of OSEs. Results indicate that the assimilation performance is highly sensitive to observation error specifications. The OSEs demonstrated that a static error of 6 m/s without thinning is the optimal error configuration for GNSS-R wind speed assimilation in the WRF system. This optimal value should be interpreted as an effective observation error within the data assimilation system, rather than solely the intrinsic uncertainty of GNSS-R winds. It reflects the combined effects of dense along-track sampling, which introduces spatially correlated information, as well as representativeness errors and the use of a static background error covariance. In this context, inflating the observation error provides a practical way to balance the relative contributions of observations and background, leading to improved assimilation performance. Under this configuration, GNSS-R wind speed data can influence near-surface forecasts up to about 700 hPa in a single assimilation case, while in the OSEs the impact propagates to higher atmospheric levels, exhibiting a broader range of influence. Although the optimal observation error specification here is tailored to the WRF model, the analytical framework can be extended to other NWP models or data assimilation systems.

Overall, this study offers new insights into the assimilation of Fengyun-3 GNSS-R winds in regional forecasting systems. It emphasizes both the potential and the current limitations of assimilating GNSS-R wind data in NWP and points to the need for refined assimilation strategies.

Future work should focus on optimizing the joint assimilation of both GNSS-R and conventional observations. Further assimilation and forecast experiments for more special weather systems such as tropical cyclones, with different intensities, tracks, and environmental flow patterns, are needed to assess the robustness and general applicability of the present findings. In addition, the incorporation of flow-dependent background error covariances may further facilitate the vertical propagation of GNSS-R information and enhance its influence in the upper atmosphere.