TDS-1 GNSS reflectometry wind geophysical model function response to GPS block types

ABSTRACT This paper presents the TDS-1 GNSS reflectometry wind Geophysical Model Function (GMF) response to GPS block types. The observables were extracted from Delay Doppler Maps (DDMs) after taking the receiver antenna gains effects and GNSS-R geometry effects into account. Since the DDM is affected by GPS EffectiveIsotropic Radiated Power (EIRP), we first investigate the sensitivity of observables to the GPS block. Additionally, the observables at high SNRs are more sensitive to wind speed, but the spatial coverage at high signal to noise ratios (SNRs) is lower, while DDMs at low SNRs have the opposite characteristics. To balance the accuracy and spatial coverage, the DDM datasets are divided into two parts: high SNR (>0 dB) and low SNR (>−10 dB and ≤0 dB) to develop wind GMF. Then, the influences of GPS block on wind speed retrieval both at high and low SNR is analyzed. Results show that the block types have impacts on wind GMF and the use of a prior GPS block can contribute to a better wind speed retrieval both at high and low SNR. Compared with ASCAT, the Root Mean Square Error (RMSE) value of wind speed retrieval at high and low SNR are 2.19 m/s and 3.13 m/s, respectively, when all TDS data are processed without distinguishing GPS block types. However, if the TDS data are separately processed and used to develop wind GMF through different blocks, both the accuracy and correlation coefficient can be improved to some extent. Finally, the influence of significant height of the swell (Hs) on SNR observables is analyzed, and it is demonstrated that there is no obvious linear or nonlinear relationship between them.


Introduction
Obtaining accurate ocean wind field is significant for atmospheric, oceanographic and climatic research. For instance, the ocean wind field affects the interaction between sea and air, the evaporation rate of seawater, and the formation of storms. Furthermore, accurate ocean wind field estimation and its monitoring play a key role in marine engineering, maritime shipping, and maritime rescue. Currently, the common methods of ocean wind field retrieval are through the use of microwave radiometers and scatterometers. Coriolis WindSat, as an example of a microwave radiometer, uses the emissivity from ocean surface to derive wind field. Besides, scatterometers transmit a range of electromagnetic signal frequencies, such as ASCAT, ERS-1/2 (C-band, ~5 GHz), and QuickSat (Ku-band, ~14 GHz) to the earth surface. Then, the reflected signals through a Bragg scattering mechanism of the surface capillary waves present over largescale ocean waves from earth surface are received. Scatterometry uses these reflected signals to retrieve the wind speed and direction. It is known that radiometers and scatterometers can accurately provide ocean wind field information. However, they are restricted to large-scale deployments due to high equipment costs. Under severe weather conditions, such as heavy rain, the results of scatterometer are significantly affected by the use of high-frequency microwave signals (C-band, Ku-band) (Stiles and Yueh 2002;Portabella et al. 2012).
GNSS-R exploits GNSS signals reflected on the Earth surface in a forward bistatic radar configuration, which has developed as a remotely sensed technique that can measure ocean surface winds (Garrison, Katzberg, and Hill 1998;Garrison et al. 2002;Komjathy et al. 2004;Zhou et al. 2006;Cardellach et al. 2011;Rodriguez-Alvarez et al. 2013;Wang et al. 2016;Asgarimehr, Wickert, and Reich 2018). As a consequence of the frequency used by GNSS systems (L-band), GNSS-R observations are less sensitive to atmospheric rain attenuation (Balasubramaniam and Ruf 2020). The utilization of GNSS signals for ocean scatterometry has been put forward by Hall and Cordey (Hall and Cordey 1988). In July 1991, for the first time, Auber et al. have successfully collected and tracked GPS reflected navigation signals from an aircraft (Auber, Bibaut, and Rigal 1994). In 1993, Martin-Neira proposed the use of GPS signals as an alternative to radar altimeters by measuring the sea surface height (SSH), the so-called passive reflectometry and interferometry system (PARIS) (Martín-Neira 1993). Recently, several studies have focused on using GNSS, which reflected navigation signals for ocean remote sensing, such as SSH (Lowe et al. 2002;Ruffini et al. 2004;Liu, Jiang, and Zhou 2008;Nogues-Correig et al. 2010), sea ice (Gleason 2010;Alonso-Arroyo, Zavorotny, and Camps 2016;Yan and Huang 2016;Llaveria et al. 2021), and soil moisture Chew et al. 2016;Chew and Small 2020;Yan et al. 2020). This paper focuses on GNSS-R ocean wind speed retrieving.
In 1998, the first experiment for GNSS-R ocean wind field retrieving was carried out via airborne (Garrison, Katzberg, and Hill 1998). Although many GNSS-R experiments installed in ground and airborne have been conducted, there is still limited global coverage. In order to prove the GNSS-R capability for global covering, the United Kingdom-Disaster Monitoring Constellation (UK-DMC) was operated in 2003. With its payload of the GNSS Receiver Remote Sensing Instrument (SGR-ReSI), the UK-DMC satellite has been developed as a new GNSS reflectometry mission. It has demonstrated the correlation among wind, wave, and GNSS-R signals, but its data were inadequate to completely show the ocean wind field retrieving potentiality of GNSS-R (Gleason 2006;Gleason et al. 2005;Clarizia et al. 2009;Li and Huang 2014). To further study the use of satellitebased GNSS-R for Earth observation, the TDS-1 satellite was launched on 8 July 2014, which successfully demonstrated the ocean wind field retrieval capabilities through GNSS-R. (Foti et al. 2015). With the success of TDS-1, the GNSS-R mission Cyclone Global Navigation Satellite System (CYGNSS) has been started on 15 December 2016. CYGNSS has been designed to measure hurricane parameters (Ruf et al. 2012(Ruf et al. , 2016. The revised version of SGR-ReSI is one instrument installed in CYGNSS. This contribution attempts to improve GNSS-R wind speed retrieving with TDS-1 data. Many studies have used TDS-1 data to retrieve ocean wind speed using numerous retrieving algorithms Lin et al. 2019;Clarizia et al. 2014;Foti et al. 2017). In general, algorithms based on Signal Noise Ratio (SNR) of Delay Doppler Maps (DDMs) are effective in retrieving the wind speed. DDMs at high SNRs are more sensitive to wind speed, but their spatial coverage is lower at high SNRs, while DDMs at low SNRs have an opposite behavior. The quality of the GNSS-R signal may be affected by GPS EIRP, which is affected by the incident angle, the sea surface roughness, transmit power and receiving antenna gain, the reflection geometry (i.e. wind direction) and the incoming swell. Different GPS blocks are now operating on different GPS transmits such as block IIR, IIR-M designed by Lockheed Martin and IIF designed by Boeing. Due to different transmit powers, antenna patterns, and attitudes, different blocks have limited publicly available features, which makes it extremely difficult to evaluate the effect of each GPS EIRP on DDMs (Said et al. 2019). Therefore, it is crucial to investigate the TDS-1 wind speed retrieving compacity under different GPS blocks.
To analyze the influence of different GPS blocks at high SNR and low SNR on wind speed retrieval, here, we present the relationship between wind speed retrievals and GPS blocks. Then, the observables were used to develop GMF according to the given GPS block. Since the DDMs are affected by the sea state, such as the significant height of the swell (Hs), the influence of Hs on SNR observables is also analyzed. The structure of the rest of this paper is organized as follows: In Section 2, the datasets and the preparation of the analysis are described. Section 3 shows the method of wind speed retrieval from the DDM. Section 4 shows the wind speed retrieval performance with different GPS blocks at both high and low SNR and the influence of Hs on SNR observables. Finally, Section 5 gives concluding remarks.

Theory of wind speed retrieval from DDMs
Based on DDMs, many methods and algorithms for wind speed retrieving have been presented in previous work. The DDM from the ocean surface is modeled as where Y τ; f ð Þ j j 2 h i represents the GNSS power scattered by the ocean surface as a function of the time delay τ and the frequency offset f . P t and G t are the GNSS transmitter power and antenna gain, respectively, and G r is the receiver antenna gain. λ is the carrier wavelength. T i is the coherent integration time. Λ 2 and S 2 are the components of the Woodward Ambiguity Function (WAF) in delay (triangular function) and delay Doppler frequency (sinc function, the attenuation due to Doppler misalignment), respectively. R t and R r are the transmitter-to-surface and surface-to-receiver ranges, respectively. dA denotes the surface element of the scattering area A. σ 0 symbolizes the normalized bistatic radar cross-section (NBRCS), which is related to the roughness of the glistening zone. σ 0 can be used to retrieve the ocean wind speed. Assuming that the cross-section is constant over the glistening zone, the average crosssection σ 0 h i can be rewritten as In dB, Equation (2) becomes where P r is the received power.
is the integral term. Equation (3) corrects the following effects: (1) the transmitter power P t and its antenna gain G t , (2) the receiver antenna gain G r , (3) distance from specular point (SP) to transmitter and receiver (R t and R r ), (4) the scattering area (the glistening zone, A).
As mentioned above, since GPS satellites are operating in a number of blocks, there are different P t and G t defined EIRPs. Different GPS block types may affect the distribution of σ 0 h i, which need to be accounted for. Since there are no accurate estimates of EIRP in TDS-1 datasets, here, we develop the GMFs according to different GPS block type. Since it is time consuming to accurately calculate the integral term, we replace it with an approximation named CF (correction factor). To obtain high quality data, the data with incident angle (θ) less than 35° is used for analysis (Soisuvarn et al. 2016).
In Equation (4), 1=G r corrects the effects of (2); R 2 t � R 2 r corrects the effects of (3); and cosðθÞ corrects the effects of (4). Thus, the equation becomes where AGSP represents the antenna gain at the specular point. k1 and k2 are constants. In this study, Equation (5) is used to develop a GMF. P r is computed from DDM. Two receiver observables, SNR and SMN (signal minus noise), which are proportional to P r , can be used for wind speed retrieval ). Therefore, for simplicity, P r is replaced with SNR in this paper. Thus, Equation (5) becomes where k1 and k2 are equal to 0.8 and 0, respectively. SNRc represents the corrected SNR. The raw SNR and SMN are computed by where s DDM represents the average power in signal box (3 Doppler bins × 1 delay bin, see Figure 1), and n DDM stands for the average power box measured in a noise box (20 Doppler bins × 20 delay bins, see Figure 1; the approximate resolution size is 20 km) in the signalfree area. Figure 1 shows an example of a DDM from the SGR-ReSI instrument. The dimensions (resolution) of it are 20 bins in Doppler frequency (500 Hz spacing) and 128 bins in delay (0.25 chip spacing). Due to system noise and sea ice effects, the DDM from SGR-ReSI does not always exhibit the "horseshoe" shape, as shown in Figure 1, but a garbled situation as shown in Figure 2. In Figure 2, the characteristic horseshoe shape is lost in the noise. Therefore, quality control (QC) is required to remove these inferior quality DDMs before wind speed retrieval. Comparing Figures 1 and 2, the fluctuations are relatively small in the DDM noise box, which show the characteristic "horseshoe" shape in Figure 1, while the fluctuations of noisy DDMs are large in Figure 2. These noisy DDMs usually exist in the observables at high incident angles and low AGSP. Therefore, the DDMs withincident angles larger than 35° and AGSPs less than 0 dB are considered for further analysis. Besides, the DDMs with the difference between the maximum and minimum values greater than 10,000 in the noise box are also removed.
To balance the accuracy and spatial coverage, the process of wind speed retrieval is as follows. First, DDM datasets are divided into two parts: high SNR (>0 dB) and low SNR (>−10 dB and ≤0 dB). Then, QC is applied to filter out poorquality data both at high and low SNR datasets. After correcting the receiver antenna gain effects and GNSS-R geometry effects, the remaining datasets are divided into different parts according to different GPS blocks to develop GMF and to retrieve wind speed. Finally, the influence of Hs on SNR observables is analyzed.

UK TechDemoSat-1
In this study, the datasets from TDS-1, ASCAT and ECMWF are used. TDS-1 can process GPS reflected signals into DDMs, from which ocean roughness and wind field can be retrieved. TDS-1 has been operated in two modes, including Unmonitored Automatic Gain Control (UAGC) (from September 2014 to April 2015) and Fixed Gain Mode (FGM) (After May 2015). Since the receiver absolute powers operated in UAGC were unknown, the receiver operated in FGM is more effective for calibration purposes. Both modes can generate DDMs, which belong to level 1b data in the TDS-1 datasets. Besides the L1b dataset, TDS-1 datasets also provide levels 0 and 2 datasets, including raw data and wind speeds . The level 1b data, from May 2015 to May 2016, is used in this study. In order to avoid the influence of sea ice, the ocean data at latitudes between ±55° are used. The datasets are available at http://merrbys.co.uk/.

Advanced scatterometer
The ASCAT, operating at a frequency of 5.255 GHz (C-band), is one of the instruments using vertically polarized antennas. As an aperture radar, ASCAT The three missions have been operated by the European organization for the Exploitation of Meteorological Satellites (EUMETSAT). It generates radar beams on both sides of the satellite ground track, which illuminates as wide as 550 km swaths (separated by about 700 km). As the satellite moves along its orbit, each swath provides measurements of radar backscatter from the ocean surface on a 25 km or 12.5 km grid, which is divided into 21 or 41 so-called wind vector cells (WVCs). In this way, ASCAT provides 25-km and 12.5-km products for the effective swath width to 525 km (21 × 25) or 512.5 km (41 × 12.5), respectively. Compared with buoys data, the RMSE of ASCAT wind speed data is less than 1.72 m/s (Bentamy 2008). The ASCAT data are available from the Physical Oceanography Distributed Active Archive Center (https://podaac.jpl.nasa.gov/). In this study, the ASCAT dataset is matched with the TDS-1 dataset applying the following criteria: time ≤30 minutes and distance ≤25 km in space.

ECMWF
For each hour a day, the fifth-generation ECMWF atmospheric reanalysis of the global climate so-called ERA5 provides wind speed, the Hs, and pressure levels. Reanalysis combines modeled data with observations from across the world to a globally complete and consistent dataset by using the physics laws. The ECMWF dataset can be downloaded from the European Center for Medium-Range Weather Forecasts (https://www.ecmwf.int/). In this study, the wind speed and Hs from ERA5 are used for analysis. The ERA5 data is matched with the TDS-1 dataset applying the following criteria: time ≤30 minutes and latitude and longitude ≤0.25°.

GMF and wind speed retrieval results against ASCAT/ECMWF winds at high SNR
As mentioned above, the data at high SNR with SNRs >0 dB are used to develop GMF. Figures 3  and 5 show SNRc against ASCAT/ECMWF wind speed matchup dataset randomly used for training (75% of samples) all GPS blocks and each GPS block as well as GMF. Outliers are removed according to the three sigma rules. Figures 4 and 6 show the wind speed retrievals against ASCAT/ECMWF winds for the remaining independent test subset (25% of samples) for all GPS blocks and each GPS block. Similar trends of GMFs and wind speed results are found in each GPS block. For further analysis, Table 1 shows the results against ASCAT and ECMWF at high SNRs.
In general, although the winds from ECMWF especially at low winds are more discrete than ASCAT for all GPS blocks, the GMF trends and the wind speed retrieval results versus ASCAT and ECMWF are similar. It is worth mentioning that most of the on-orbit GPS satellites are the types of Block IIR and Block IIF, thus having more training or test samples for these two kinds of blocks. Compared with ASCAT and ECMWF, their accuracy values of wind speed retrieval are 2.19 m/s and 1.88 m/s, respectively, when all TDS data are processed without distinguishing GPS block types. However, if the TDS data are separately processed and used to develop wind GMF through different blocks, both the accuracy and correlation coefficient can be improved to some extent. Block IIA and block IIR-A show smaller RMSEs of 1.48 m/s and 1.47 m/s for ASCAT and 1.69 m/s and 1.51 m/s for ECMWF, which may be attributed to the following two reasons. On the one hand, the wind speeds of blocks IIA and IIR-A are mostly concentrated at lower speed (<15 m/s). On the other hand, the numbers of available samples of these two block types are much smaller than the other blocks.

GMF and wind speed retrieval results against ASCAT/ECMWF winds at low SNR
Likewise, the data at low SNR with 10 dB < SNR ≤ 0 dB are used to develop GMF. Figures 7 and 9 show the SNRc against ASCAT/ECMWF wind speed matchup dataset randomly used for training (75% of samples) all GPS blocks and each GPS block. Different from the GMF form at high SNR, the GMF form at low SNR is a linear model. Figures 8 and 10 show the wind speed retrievals against ASCAT/ECMWF winds for the     remaining independent test subset (25% of samples) of all GPS blocks and each GPS block. Table 2 shows the results against ASCAT and ECMWF at low SNR. Note that the GMF in this section is Linear model. The reason for choosing linear model is that the Linear model has better performance with smaller RMSE and higher correlation coefficient compared with other functions, e.g. exponential and power Law. In addition, GMFs from low SNR do not cross the center point of the contour like high SNR. The reason is that if the GMF crosses the center point, the slope of the GMF at high wind will be very large, which will lead to a large wind speed range corresponding to one SNRc and severely decrease the wind speed retrieval accuracy. Therefore, Figures 7 and 9 show GMFs corresponding to the minimum RMSEs and maximum correlation coefficients. Compared with ASCAT and ECMWF, the accuracy values of wind speed retrieval are 3.13 m/s and 2.74 m/  s, respectively, when all TDS data are processed without distinguishing GPS block types. The performance at low SNR data is poorer than the performance at high SNR due to the high wind speed data at low SNR larger than that of high SNR. On the other hand, it also demonstrates that the quality of SNR data is better than that of low SNR data. Since there are many winds (>13 m/s) that deviate from the GMF, the RMSE of block IIA is larger than that of all blocks in ECMWF, thus leading to poor GMF and small correlation coefficients. However, the samples of low SNR with 202344 and 197612 for ASCAT and ECMWF, respectively, are larger than the samples of high SNR, 67825 and 110265 for ASCAT and ECMWF, respectively, which can maintain large spatial coverage. Furthermore, similar to high SNR, if the TDS data are separately processed and used to develop wind GMF through different blocks, both the accuracy and correlation coefficient can be improved at low SNR. In addition, our analysis was done with TDS, which only has one antenna and one observatory limited publicly available characterizations, specifically related to their actual transmit power, antenna patterns, and attitude. This calibration issue may be attributed to the unknown GPS transmit powers from different PRNs, not correctly accounted for in the bistatic radar equation. Because TDS-1 has limited publicly available characterizations specifically related to their actual transmit power and antenna patterns, we can only analyze the influence of different GPS blocks on wind speed retrieval.

Observable versus sea state
As described in (Soisuvarn et al. 2016), the DDM is affected not only by wind field but also by the sea state such as swell. Therefore, it is worth investigating the relationship between observables and other parameters other than wind. Here, we consider the sensitivity of observables to Hs. Figure 11(a) shows the relationship between Hs and SNR. As shown in Figure 11(a), there are a lot of lower SNRs (<−10 dB) between 0 m and 4 m of Hs. Thus, it is necessary to use QC to filter out poor DDMs. To more intuitively see the effect of Hs on the observables, Figure 11(b) shows the relationship between ECMWF wind speed and mean SNR at different Hs. As the wind speed  increases, the SNR decreases. When Hs is greater than 6 m, the SNR changes drastically due to the limited number of samples . Since SNRc is applied to develop GMF, it is worth to analyze whether the SNRc is influenced by Hs. Figure 12 shows the relationship between ECMWF Hs and SNRc. In general, the SNRc decreased with Hs. Hs is mainly distributed in 0-4 m, and the SNRc are clustered around 252.5 dB. There is no obvious linear or nonlinear relationship between SNRc and Hs in the concentrated part. However, adding a Hs for the corrected factor into GMF into a discrete part may contribute a better wind speed retrieval, which needs further study.

Conclusions
In this paper, the TDS-1 GNSS reflectometry wind geophysical model function response to GPS block was proposed. First, the method of wind speed retrieval from DDMs was presented. To balance the accuracy and spatial coverage, this method divided DDM datasets into two parts: high SNR (>0 dB) and low SNR (>−10 dB and ≤0 dB) to develop wind GMF. During the progress, the observable was accounted for by the receiver antenna gain effects and GNSS-R geometry effects. After correcting the above elements, the sensitivity of the corrected SNR (SNRc) to GPS block was investigated. Then, the SNRc was used to develop GMF by using different GPS blocks. Finally, the influence of Hs on SNR observables is analyzed.
The results show that although the winds from ECMWF are more discrete than ASCAT for all GPS blocks especially at low winds, the GMF trends and the wind speed retrieval results versus ASCAT and ECMWF are similar. The block types have impacts on wind GMF and the use of a prior GPS block can contribute to a better wind speed retrieval at both high and low SNR. Compared with ASCAT, the RMSE values of wind speed retrieval at high and low SNR are 2.19 m/s and 3.13 m/s, respectively, when all TDS-1 data are processed without distinguish GPS block types. However, if the TDS-1 data  are separately processed and used to develop wind GMF through different blocks, both the accuracy and correlation coefficient can be improved to some extent. Although the performance of low SNR is poorer than high SNR, the samples of low SNR is larger than high SNR, which can maintain large spatial coverage.