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Article

How Does Wind Influence Near-Nadir and Low-Incidence Ka-Band Radar Backscatter and Coherence from Small Inland Water Bodies?

by
Jessica V. Fayne
1,* and
Laurence C. Smith
2
1
Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI 48109, USA
2
Department of Earth, Environmental, and Planetary Sciences, Brown University, Providence, RI 02903, USA
*
Author to whom correspondence should be addressed.
Remote Sens. 2023, 15(13), 3361; https://doi.org/10.3390/rs15133361
Submission received: 26 April 2023 / Revised: 21 June 2023 / Accepted: 26 June 2023 / Published: 30 June 2023
Browse Figures
Graphical abstract
"> Figure 1
<p>(<b>A</b>) The 2017 AirSWOT data collection (black lines) was acquired as a part of the Arctic Boreal Vulnerability Experiment (ABoVE) Airborne Campaign (AAC) beginning in North Dakota, USA, and flying north through Western Canada to Alaska, USA, before returning south along an overlapping flight path. The inset highlights a snapshot (1 July 2017) of the spatial variability of wind speeds from ERA-5 Reanalysis over several lakes in southern Northwest Territories and northern Alberta. Cumulative density plots demonstrate (<b>B</b>) the distribution of water body areas to be examined in this study and (<b>C</b>) the distribution of wind speeds covered by different incidence angles.</p> "> Figure 2
<p>A workflow chart for this study demonstrates two paths of analysis. The primary research seeks to identify the sensitivity of Ka-band radar backscatter and coherence to wind speed and directional variability, and to what extent this variability influences the accuracy of retrieved water surface elevations. The secondary research assesses global wind speed trends over lakes to determine the likelihood that SWOT and other Ka-band InSAR sensors such as AirSWOT will be able to produce accurate water surface elevations globally.</p> "> Figure 3
<p>Comparison of AirSWOT Ka-band VV backscatter with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Backscatter consistently increases with increasing wind speeds across all incidence angles. Wind speeds 3 m/s or higher for incidence angles between 3 and 8.6 degrees achieve the minimum ideal value to consistently separate water from land or other wet surfaces (&gt;10 dB). The first incidence angle category (0.05–0.1 radians, 2.8–5.7 degrees) is most comparable to SWOT due to similar viewing geometry. This second category shows consistently high backscatter, 15 dB, for wind speeds greater than 3 m/s.</p> "> Figure 4
<p>Comparison of AirSWOT Ka-band coherence with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Coherence consistently increases with increasing wind speeds across all incidence angles. Wind speeds 3 m/s or higher for incidence angles between 2.9 and 17.2 degrees achieve the minimum ideal value for producing high-quality AirSWOT elevations (&gt;0.75). The first incidence angle category (0.05–0.1 radians, 2.8–5.7 degrees), while most comparable to SWOT due to similar viewing geometry, does not have the highest coherence due to the AirSWOT antenna pointing having been focused near 12.9 degrees. Due to the antenna pointing, the highest coherence is identified in the third category (0.15–0.2 radians, 8.6–11.4 degrees), with coherence values exceeding 0.85 for wind speeds greater than 3 m/s. Wind speeds of 3–7 m/s are much more likely to produce highly coherent data, important for reducing horizontal and vertical errors in the computed elevation product.</p> "> Figure 5
<p>Comparison of AirSWOT Ka-band VV backscatter with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Backscatter consistently increases with increasing wind speeds across lake areas. Small lakes, 0.0625–0.25 km<sup>2</sup>, show significantly lower backscatter on average, up to 5 dB lower, compared with larger water bodies, even in high wind conditions.</p> "> Figure 6
<p>Comparison of AirSWOT Ka-band coherence with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Coherence consistently increases with increasing wind speeds across lake areas. Small lakes, 0.0625–0.25 km<sup>2</sup>, show significantly lower coherence on average, up to 0.25 lower, compared with larger water bodies, even in high wind conditions, though increasing wind speeds reduce the difference between small and larger water bodies.</p> "> Figure 7
<p>An incomplete distribution of wind directions and speeds occurred during the NASA ABoVE AirSWOT flight campaigns (8 July–17 August 2017). During these flight acquisitions, high wind speeds occurred at wind directions 210–320 degrees, while directions 30–150 degrees experienced lower wind speeds. Wind directions between 320 and 30 degrees (winds from the north) rarely occurred during the AirSWOT flight acquisitions. A statistical assessment of the influence of wind direction on the AirSWOT Ka-band backscatter and coherence is not possible due to this insufficient diversity of wind direction/wind speed combinations during the flight campaigns.</p> "> Figure 8
<p>Global wind speeds over the SWOT observable Prior Lake Database (PLD). ERA-5 monthly reanalysis of 10 m height wind speeds during 2022 was compared with the global PLD. The frequency of wind speed occurrence across PLD lake areas is distributed into 10th, 25th, 50th, 75th, and 90th percentile groups with the mean. Using monthly averages, 75% of PLD lake areas met or exceeded the minimum required wind speeds for high backscatter and coherence, which are necessary to retrieve accurate water surface elevations. The average wind speed for lakes around the globe in 2022 is 4.03 m/s.</p> ">
Versions Notes

Abstract

:
While many studies have been conducted regarding wind-driven Ka-band scattering on the ocean and sea surfaces, few have identified the impacts of Ka-band scattering on small inland water bodies, and fewer have identified the influence of wind on coherence over water. These previous studies have been limited in spatial scale, covering only large water bodies >25 km2. The recently launched Surface Water and Ocean Topography (SWOT) mission is the first Ka-band InSAR satellite designed for mapping water surface elevations and open water areas for rivers as narrow as 100 m and lakes as small as 0.0625 km2. Because measurements of these types are novel, there remains some uncertainty about expected backscatter amplitudes given wind-driven water surface roughness variability. A previous study using the airborne complement to SWOT, AirSWOT, found that low backscatter and low coherence values were indicative of higher errors in the water surface elevation products, recommending minimum thresholds for backscatter and coherence for filtering the data to increase the accuracy of averaged data for lakes and rivers. We determined that the global average wind speed over lakes is 4 m/s, and after comparing AirSWOT backscatter and coherence data with ERA-5 wind speeds, we found that the minimum required speed to retrieve high backscatter and coherence is 3 m/s. We examined 11,072 lakes across Canada and Alaska, with sizes ranging from 350 m2 to 156 km2, significantly smaller than what could be measured with previous Ka-band instruments in orbit. We found that small lakes (0.0625–0.25 km2) have significantly lower backscatter (3–5 dB) and 0.20–0.25 lower coherence than larger lakes (>1 km2). These results suggest that approximately 75% of SWOT observable lake areas around the globe will have consistently high-accuracy water surface elevations, though seasonal wind variability should remain an important consideration. Despite very small lakes presenting lower average backscatter and coherence, this study asserts that SWOT will be able to accurately resolve the water surface elevations and water surface extents for significantly smaller water bodies than have been previously recorded from satellite altimeters. This study additionally lays the foundation for future high-resolution inland water wind speed studies using SWOT data, when the data become available, as the relationships between wind speed and Ka-band backscatter reflect those of traditional scatterometers designed for oceanic studies.

Graphical Abstract">

Graphical Abstract

1. Introduction

The water–air interface is an important component in tracking and modeling changes in the water and energy cycles through wind-driven surface water dynamics [1,2]. Wind induces waves and seiches and increases evaporation rates over lakes, for example [3,4]. Recent studies have identified that global wind speeds have increased from 3.13 m/s in 2010 to 3.30 m/s in 2017 [5], and increasing winds are driving more intense hurricane rainfall [6], providing increased importance to the study of global winds. Inland surface winds are highly variable over space and time due to topographic relief and boundary layer frictional resistance from surface features such as trees and buildings, which reduce wind velocity. Because of the spatially varying nature of wind speed over land, the availability of high-resolution datasets of airflow over inland water bodies would increase the accuracy of models focused on atmospheric dynamics and the water cycle.
Radar remote sensing offers unique capabilities for tracking spatial and temporal variations in wind-induced surface water roughness, including the estimation of wave heights and wind velocities over water. Such retrievals are traditionally obtained through scatterometry over oceans [7,8]. Classic scatterometry studies were conducted to establish geophysical model functions (GMFs) relating wind parameters to water surface scattering over ocean surfaces via the mechanism of wind-driven water surface roughening [7,8,9,10,11,12]. Due to oblique viewing geometries and poor calibration for SAR-wind GMFs, few have used SAR imagery to assess surface water scattering [13,14].
While SAR sensors offer high spatial resolution and focused imagery over inland water compared with scatterometers, to our knowledge, there has been no attempt to quantitatively assess wind-induced roughness of multiple small inland water bodies (less than 1 km2) using SAR data. For this reason, the potential influence of wind on Ka-band returns for small inland water from the recently launched Surface Water and Ocean Topography (SWOT) satellite, the world’s first hydrology-focused InSAR mission, remains unquantified. SWOT was developed by NASA and Centre National D’Etudes Spatiales (CNES) with contributions from the Canadian Space Agency (CSA) and the United Kingdom Space Agency, and was launched on 16 December 2022 from Vandenberg Space Force Base. Preliminary experiments demonstrated that AirSWOT (an experimental airborne Ka-band precursor to SWOT, see [15,16]) SAR backscatter returns over inland surface water bodies appear to be sensitive to emergent vegetation and wind [17,18,19,20]. For accurate SWOT and AirSWOT data retrievals of water surface elevation (WSE) and inundation extent, inland water bodies must present strong signal returns (backscatter) and internally consistent transmit/receive signals (interferometric coherence). AirSWOT observations over Canada and Alaska have produced water surface elevations that do not quite meet the designed accuracy standard of 10 cm [18,19,20,21,22] due in part to low backscatter (“dark water”) and low coherence from water surfaces [22]. Furthermore, pre-launch assessments of SWOT’s potential vulnerability to dark-water returns over small inland water bodies use traditional scatterometry models developed for oceans using coarse-resolution Ka-band radar data from precipitation satellite GPM (5 km) and altimetry satellite AltiKa (12 km), with minimum lake areas of 25 km2 [8,23,24,25,26,27], a scale far coarser than most inland water bodies. Using high-resolution optical remote sensing, [28] reported an average area of just 26 m2 for ~85,000 lakes across Canada and Alaska.
SWOT uses a Ka-band (35.75 GHz frequency, 8.8 mm wavelength) interferometer called the Ka-band Radar Interferometer (KaRIn), a bistatic SAR system with near-nadir incidence angles (~0.6 to ~4°) over a wide swath (two 50 km swaths, one on either side of a nadir altimeter), allowing it to produce high-resolution (10–50 m) water surface elevations [29]. Interferometry (InSAR) uses the timing of incident and received radar pulses to triangulate objects on the ground, producing a map of elevations (Figure 3 in [29]). Radar backscatter signals change with the changing geometries, and because water surfaces are rapidly changing due to wave dynamics (or lack of waves), the resultant backscatter data will also be influenced. Because of the relatively short wavelength of SWOT, compared with P-, L-, C-, and X-band sensors (wavelengths greater than 1 cm), the Ka-band instrument has increased sensitivity to small capillary waves and thus wind speeds [8,23,24,25,26,27], and has the potential to be used to study vegetation [17].
The SWOT satellite is designed to image water bodies with a minimum area of 250 m2, while AirSWOT is capable of imaging water bodies with a minimum area of 10 m2 [22,29]. Because of the influence of local topography and diverse water body shapes and sizes, we suspect that existing Ka-band scattering models designed for features greater than 10 km2 may not be sufficient for modeling the impacts of surface wind friction velocities for millions of smaller water bodies which will be observed by SWOT. Understanding the relationship between wind speed, wind direction, and radar backscatter will increase our ability to estimate the quality of SWOT observations prior to the flyover and improve planning capabilities for airborne AirSWOT data acquisitions. Studying how wind speeds influence radar backscatter and coherence can help estimate and improve the performance of derived InSAR elevation estimates. Figure 1 highlights the flight path of the AirSWOT data collected during the 2017 summer field campaign and the sampling of the water features in this study. While this work seeks to improve our understanding of the performance of Ka-band InSAR sensors for estimating water surface elevations, the simultaneous work of quantifying the relationship between Ka-band backscatter and wind characteristics for small water bodies will enable future investigations of wind–water friction velocities for assessing hyper-local evaporation and water vapor transport.
This study assesses the influence of wind on Ka-band scattering over lakes to improve predictions of InSAR-based water surface elevation accuracies and for the suitability of SWOT and AirSWOT to be used in future wind analyses and retrievals. SWOT was recently launched, and its data have not yet been made available to the public for analysis. Average global wind speeds are calculated over SWOT observable lakes, compared with AirSWOT Ka-band backscatter data to identify if average wind speeds are sufficient to produce high enough Ka-band scattering returns to produce accurate elevations. Scattering observations are examined from 11,072 water features across Alaska and western Canada and ~22,000 km2 of AirSWOT flights for the NASA Arctic-Boreal Vulnerability Experiment (ABoVE) [22]. The areas of these water features range from 350 m2 to 156 km2, including lakes too small to detect from AltiKa and GPM. A workflow chart describing the methodology of this study is shown in Figure 2.
Using reference wind speed and direction data from modeled and in situ data sources, and Ka-band backscatter, coherence, and flight heading data from AirSWOT, we correlate wind and radar data to identify scattering sensitivities to wind speed and direction. For incidence angles 0–17°, we determine that (1) wind speeds 3 m/s or higher are required for strong backscatter and coherence, leading to higher-accuracy elevation data, (2) SWOT minimum small lakes average 5 dB lower backscatter and 0.25 lower coherence than lakes larger than 1 km2, (3) the AirSWOT data used in this study do not capture enough varying conditions of wind direction to be comparable with Ka-band wind direction GMFs and theoretical models, and (4) global average lake wind speeds are 4 m/s. We conclude with a discussion on further implications of Ka-band SAR data for wind speed assessments and InSAR water surface elevation retrievals for SWOT.

2. Materials and Methods

2.1. Materials

2.1.1. AirSWOT Ka-Band Interferometric Synthetic Aperture Radar

The airborne SWOT (AirSWOT) platform supports a Ka-band interferometric wide-swath altimeter, called the Ka-band SWOT Phenomenology Radar (KaSPAR), which is used to produce high-resolution maps of water surface elevations [30]. AirSWOT was developed as a complement to SWOT to understand surface phenomenological interactions and to test and design radar and InSAR algorithms at Ka-band [15,16]. While AirSWOT has collected small datasets over various parts of the United States [18,19,20,21], the largest published AirSWOT collection to date is from an airborne flight and field campaign conducted from 8 July to 17 August 2017 for the NASA Arctic Boreal Vulnerability Experiment (ABoVE) [22,31,32]. The collection acquired ~22,000 km2 km of flight lines spanning 23° in latitude, ranging from North Dakota through Canada to Alaska and back again. The collection covered over 40,000 inland water bodies [33]. These lakes have varying sizes, orientations, shapes, and prevailing wind conditions. Though the available radar data used in this study have a nominal incidence angle range of ~3–27° (some observations cover 0.5–3°), higher incidences are removed from this study, limiting the analysis to 3–17°. These incidence angles were removed in accordance with recommendations from previous studies [22] and to accommodate the expected lower values of random error (0.02) across the selected range of incidence angles (~2° to ~18°) [15]. After filtering, the number of water bodies remaining to be studied here is 11,072. The radar data products used in the analysis are incidence angle, noise subtracted and calibrated VV backscatter, total coherence, and un-gridded geolocation (LLHE) processed by the NASA Jet Propulsion Laboratory (JPL) and presented in [22]. These data have a gridded pixel spacing of 3.6 m, an average swath width of 4 km, and an average flight altitude of 9.5 km. The 2017 ABoVE AirSWOT products are freely available for download at https://daac.ornl.gov/cgi-bin/dsviewer.pl?ds_id=1646 (accessed on 25 April 2023). For technical descriptions of the AirSWOT instrument configuration and these data products, see [15,16,22].

2.1.2. SWOT Prior Lake Database (PLD)

The SWOT Prior Lake Database (PLD) contains shapefiles of global lakes generated from moderate-resolution Landsat imagery (30 m) and is based on the CIRCA-2015 Lake product, which used 3300 Landsat 8 images to map global lakes [34]. The CIRCA-2015 product was subsequently updated to become the PLD using the GeoDAR: Georeferenced Global Dams and Reservoirs dataset [35]. The global lake database will be used in this assessment to identify the prevalence of lake wind speeds high enough to produce strong signal scattering to produce high-accuracy SWOT water surface elevations.

2.1.3. Modeled and In Situ Wind Parameters

Wind speed and direction data from three different datasets were used to compare with AirSWOT data. Reanalysis data from the European Center for Medium-Range Weather Forecasts (ECMWF) ERA5 hourly (and monthly averaged) data on single levels from 1940 to present (Copernicus Climate Change Service, 2023, accessed 15 April 2023 [36,37]) comprise the primary wind speed and direction reference dataset. The ERA-5 hourly and monthly data used in this study include 25 km resolution geolocated U- and V-component wind speeds at 10 m heights, which are converted to total wind speed (Equation (1)) and wind direction (Equation (2)) as follows:
V → = u 2 + v 2
ϕ = 180 + 180 π ∗ a t a n 2 v , u % %   360
To include and prioritize in situ wind speed and direction measurements where available, we used hourly and sub-daily in situ meteorological stations around Wood Buffalo National Park [38] and from approximately 40 more sparsely placed in situ stations throughout western Canada and Alaska from Copernicus Global land surface atmospheric variables from 1755 to 2020 from comprehensive in-situ observations (Copernicus Climate Change Service, 2022, accessed on 24 March 2022; https://cds.climate.copernicus.eu/cdsapp#!/dataset/insitu-observations-surface-land?tab=overview). These in situ measurements were spatially integrated with the gridded ERA-5 data to form a single combined wind parameter dataset, as explained in the next section. Because these sites do not have consistent measurements for all time steps, the number of total in situ stations integrated into the regularly gridded ERA-5 modeled data varies between 20 and 80 stations for each time step across the study domain.

2.2. Methods

2.2.1. Extract Ka-Band Radar Backscatter and Coherence over More Than 11,000 Inland Water Bodies

To compare AirSWOT backscatter and coherence from small inland water surfaces with wind speed and direction, we use a camera-based reference water mask acquired simultaneously with AirSWOT radar data [33]. The water mask is derived from 1 m optical imagery from a Cirrus Designs Digital Camera System (DCS) mounted on the AirSWOT Beechcraft Super King Air B200 aircraft, consisting of 40,000 open-water polygons with areas ranging from 40 m2 to 156 km2 [33]. This water mask was used to retrieve radar variables (backscatter and coherence) and wind variables (wind speed and direction) within these independently identified water body polygons and filtered and sorted by incidence angle, enabling analysis of 11,072 remaining water features.

2.2.2. Interpolate Local Wind Speed and Direction

Gridded wind speed and wind direction data were produced by integrating three reference wind datasets. Because the AirSWOT swaths are 4 km wide, narrower than the 25 km ERA-5 data, we resampled the ERA-5 data to a 5 km grid and added sparsely located and temporally varying in situ stations to produce hourly wind speed and direction datasets. The 5 km hourly data were produced by converting the ERA-5 gridded raster data into geolocated-pixel-centroid points, which are combined with the geolocated in situ points from Wood Buffalo and Copernicus datasets. The combined points from the three datasets are spatially interpolated to a 5 km grid, leaving the majority of the resampled ERA-5 data values similar or identical to the original dataset, except for near in situ stations.

2.2.3. Compare AirSWOT Ka-Band SAR Backscatter and InSAR Coherence with Wind Speed by Incidence Angle and Lake Area

Wind speed values were extracted for each of the point coordinates corresponding to the radar data extracted from within the predefined water features. We separated (binned) wind speeds into seven 1 m/s categories (from 0 to 7 m/s) for comparison with AirSWOT Ka-band backscatter and coherence values, using box plots as in Rodriguez et al. (2018) [26]. The resultant incidence angle and lake area box plots revealed how increasing wind speeds influence AirSWOT Ka-band backscatter and coherence over inland lakes.

2.2.4. Compare AirSWOT Ka-Band SAR Backscatter and InSAR Coherence with Wind Direction

Wind direction was similarly derived from the point corresponding to the nearest neighbor radar point within the water features. Additionally, we assessed the heading of the AirSWOT aircraft to offset the flight heading from the wind direction. The flight heading is formatted as −180 to 180 degrees, which we shifted by adding 180 to make the range 0 to 360 to match the wind direction data. Wind influences scattering in reference to the flight path as upwind (0 degrees), downwind (180/−180), and crosswind (−90/90). We calculated these azimuthal wind values relative to the flight heading using a simple offset described in Equation (3):
ϕ W i n d A z i m u t h = 180 − φ F l i g h t − φ W i n d
Azimuthal wind directions were separated into 10-degree bins (from −180 to 180 degrees), and box plots were generated using the observed backscatter and coherence. These box plots enable comparison of observed AirSWOT backscatter–wind azimuth relationships to a theoretical sinusoidal relationship reported in a classic earlier modeling study (i.e., a three-cosine model, as in Giovanangeli et al., 1991 [10]).

2.2.5. Identify Global Lake Wind Speeds

At the global scale, monthly wind speeds were assessed at the native 25 km resolution and extracted using the SWOT PLD lake dataset. Monthly wind speeds for 2022 were assessed for the global lakes in the PLD. Because the PLD data are in polygon format, and the global wind speeds have a coarser raster resolution, PLD lakes were first aggregated and filtered on a 5 km grid and then converted points for direct extraction. Because of this aggregation step, many small lakes within a 5 km cell are represented as a single lake-area feature, and very large lakes that encompass multiple 5 km cells are represented as multiple lake-area features. The 5 km cell size was selected for aggregating the lakes to reduce the computational cost of global meter-scale lake analysis while ensuring that lakes smaller than the 25 km ERA-5 pixels are not significantly undercounted.

3. Results

3.1. Interpolate Local Wind Speed and Direction

We produced 5 km hourly raster files representing wind speed and direction covering Canada and Alaska. Their full extent spans 50 degrees to 70 degrees north latitude, and 60 to 180 degrees west longitude. Figure 1 presents a close-up of these wind speed data. Because of the spatially and temporally varying availability of the in situ stations (i.e., 20–80 stations have uneven observations across 20 degrees latitude, 120 degrees longitude, and 1500 h), the in situ data rarely cover AirSWOT observation regions, severely hampering their utility. Nonetheless, the in situ data are included, where possible, and the ERA-5 modeled data have even temporal and spatial coverage for this study (the pixel size is 5 km, but the resolution remains 25 km in most areas).

3.2. Compare AirSWOT Ka-Band SAR Backscatter and InSAR Coherence with Wind Speed by Incidence Angle and Lake Area

Strong relationships were found between wind speed and Ka-band backscatter and coherence, as seen in Figure 2. Radar backscatter increases with wind speed, with relatively low values (averaging around −3 to 5 dB) associated with wind speeds <3 m/s. The first incidence angle bin (0.05–0.1 radians, 2.8–5.7°), which approximates SWOT incidence angles (~0.5–4.1°), suggests that hourly mean wind speeds of ~0 m/s yield a median backscatter of ~0 dB. At 7 m/s, the median backscatter increases to ~15 dB. This overall increase in backscatter for wind speeds >3 m/s manifests across all incidence angles, despite the expected incidence-angle-dependent decrease in scattering (Figure 3). Even the fifth incidence angle bin, midway across the AirSWOT swath (0.25–0.3 radians, 14.3–17.2°), exhibits backscatter increases from ~−10 dB to ~3 dB.
To obtain backscatter values that are consistently 10–20 dB, wind speeds must ideally reach 3 m/s or higher, suggesting that Ka-band InSAR data may not yield useful WSE retrievals when winds are below 3 m/s. This recommendation is further corroborated by comparing wind speed with AirSWOT interferometric coherence (Figure 4). For accurate estimation of water surface elevation from AirSWOT or SWOT data, coherence over water bodies should be high (ideally ~0.75–1). Our comparison of wind speeds with AirSWOT coherence demonstrates consistently high coherence, greater than 0.75, for incidence angles 0.05–0.3 radians (2.9–17.2 degrees) when wind speeds are 3 m/s or greater.
Comparing water body sizes rather than instrument viewing geometry similarly reveals differences in radar backscatter strength and coherence (Figure 5 and Figure 6). Small water body areas, 0–0.0625 km2, show significantly lower backscatter (Figure 5) and coherence (Figure 6) compared to larger water bodies greater than 1 km2. Note that the SWOT expected minimum observable water body size is 0.0625 km2 (62,500 m2). Within the SWOT observable range, 0.0625–0.25 km2 water bodies similarly exhibit lower backscatter (up to 5 dB lower) and coherence (up to 0.25 lower) than large water bodies.

3.3. Compare AirSWOT Ka-Band SAR Backscatter and InSAR Coherence with Wind Direction

Upon conducting the wind direction analysis, we found an insufficient number of samples spanning a necessary diversity of wind directions and speeds to compare with the AirSWOT radar observations, shown in Figure 7. More specifically, we found abundant high wind speed observations for only a small subset of wind directions (210–320 degrees), and low wind speeds dominated by another subset of wind directions (30–150 degrees). A clear relationship was found between wind direction and wind speed, which can only be explained by a seasonal effect (stronger winds from the southwest). Due to this relatively narrow range of wind direction/speed combinations, together with the fixed azimuthal headings of the long, 2017 AirSWOT flight lines acquired over a relatively short period of time, we are unable to assess the influence of wind direction on either backscatter or interferometric coherence from the 2017 ABoVE AirSWOT data collection.

3.4. Identify Global Lake Wind Speeds

The monthly average global lake wind speed in 2022 was 4.03 m/s (Figure 8), 22% faster than the previously reported average speed of 3.3 m/s including land [5]. This average is provided excluding the North American Great Lakes, which, when included, increase the global lake wind speed average to 4.26 m/s, 29% higher than average wind speeds combining land and water. An analysis of historical data sampled every 10 years from 1940 to 2020 yields average lake wind speeds of 3.97 m/s and 4.17 m/s when great lakes are included. Backscatter and coherence analysis suggest a minimum average wind speed of 3 m/s to produce backscatter and coherence values sufficient to retrieve consistently accurate water surface elevations from SWOT and AirSWOT. Using monthly averages from ERA-5, we found that 75% of PLD lake areas meet the speed criterion throughout the year.

4. Discussion and Conclusions

The 2017 AirSWOT flight experiment provides a rare trove of Ka-band backscatter and interferometric coherence imagery [22,31], as well as simultaneous near-infrared camera imagery and open-water classifications [33], allowing over 11,072 inland water bodies across Alaska and western Canada to be assessed for their sensitivities to wind speeds and directions. By comparing AirSWOT Ka-band radar returns from these water bodies with a resampled ERA-5 reanalysis wind speed and direction product, we identify robust relationships between wind speed, backscatter, and coherence. These trends are generally consistent across different incidence angle ranges, albeit with lower backscatter and coherence at larger (i.e., more oblique) incidence angles. Due to the under-sampling of different wind direction/wind speed combinations during the 2017 AirSWOT flight campaign, we are unable to provide a comparative analysis of wind direction. Additionally, while there is a clear sensitivity of backscatter from wind speed variability, robust GMFs cannot be produced given the prevailing wind direction for the region and the short acquisition duration, leading to a limited number of samples overall. Because wind direction contributes to backscatter variability [10], improved knowledge of wind directions would reduce the uncertainty in the retrieved wind speeds.
Our analysis of the 2017 AirSWOT Ka-band data suggests lower-accuracy water surface elevations are likely under low wind conditions (<2 m/s). Referencing best practices for high-accuracy Ka-band InSAR retrievals of water surface elevation (i.e., >5 dB backscatter and >0.8 coherence, [22]), we conclude that wind speeds of 0–3 m/s wind produce unacceptably low backscatter (<0 dB) and coherence (~0.25) across all incidence angles. Wind speeds of ~3 m/s and higher produce high values of SAR backscatter (>10 dB) and interferometric coherence (>0.8) optimal for water surface elevation retrieval. Very small lakes (less than 0.25 km2) demonstrate poorer performance across wind speed ranges.
On the global scale, lake wind monthly averages demonstrate that lakes have high average wind speeds, around 4.03 m/s, and 75% of lake areas meet or exceed the 3 m/s minimum to produce sufficient water surface elevations (Figure 8). Because this analysis divided lakes into 5 km lake cells, it is possible that a portion of a lake exhibits higher scattering than another portion (for example, 75% of a lake has high scattering, and 25% is too dark). Due to the SWOT lake processing algorithm, the part of the lake with high scattering is sufficient to provide enough data to produce a high-quality elevation for the whole lake, on average. This means that 25% of whole lakes will not necessarily have poor-quality elevations, but that whole lakes might not have even coverage, depending on local wind speeds. A previous study found that global wind speeds are increasing [5], suggesting that lakes might experience stronger backscatter in the future, driven by higher average winds.
Our study characterizes Ka-band radar returns from small inland water bodies (350 m2–155 km2), which are critically important to the SWOT satellite mission’s success. SWOT uses wide-swath Ka-band interferometry with 10–70 m spatial resolution to estimate areas and surface elevations of millions of inland water bodies as small as 250 m × 250 m (62,500 m2). Previous studies using GPM and AltiKa data focused on much larger water bodies or ocean surfaces, with emphasis on estimating wave heights and shapes for much higher wind speeds (up to 20 m/s) [8,23,25]. Nonetheless, our results agree with a high-resolution (600 m × 36 m) scatterometry study over the Gulf of Mexico, which determined that wind speeds of >2–3 m/s are necessary to retrieve meaningful radar returns [12]. Similarly, a bridge-mounted Ka-band system identified very strong backscatter (20 dB) from a river surface at wind speeds >2–3 m/s [29]. This study lends further support to the notion that wind speeds of ~3 m/s or more may be necessary for the successful retrieval of water surface elevations over small inland water bodies from SWOT.
Previous scatterometry studies focused on large water bodies and open oceans having background surface wave roughness higher than the roughness seen from smaller water bodies, asserting minimum speeds of 2 m/s [8,12,25]. However, this study points to slightly higher wind speeds (i.e., at least 3 m/s) for successful water surface elevation retrieval over small inland water bodies. The 1 m/s difference between these studies may be explained by the absence of internal turbulence or wave trains on small lakes, unlike the open ocean. Wind shadowing from surrounding topographic relief and frictional resistance from surrounding vegetation also dampen wind speeds over small inland water bodies, requiring a higher atmospheric wind speed to achieve comparable water surface roughening. Future studies on radar backscattering should incorporate high-resolution (sub-kilometer) DEM and land-cover-based wind speed modeling to account for fine-scale phenomena induced by localized topographic and frictional resistance factors. Other limitations of our analysis include a dearth of observational data reflecting multiple wind directions relative to the fight heading.
Regardless of these limitations, we conclude that AirSWOT Ka-band InSAR data are sensitive to wind speeds, producing higher-quality backscatter and InSAR coherence data when wind speeds reach and exceed 3 m/s. Based on an analysis of global climate data, approximately 75% of lake areas are expected to meet this criterion. Unlike scatterometry studies, the goal of this research is not to produce new GMFs but to assess Ka-band wind sensitivities as related to AirSWOT and SWOT water surface elevation retrieval accuracies. Further, studies of wind-induced sources of error and uncertainty will aid in data-screening protocols and quality assessment for AirSWOT and SWOT Ka-band water surface elevation retrievals. Future research on surface scattering from radars not designed for scatterometry will create opportunities for high-resolution wind monitoring, enabling greater advancements in the study of water–air interactions and the water cycle, such as investigations of limnology and evaporation. Finally, this paper builds a foundation for wind speed retrievals from SWOT, providing high-spatial-resolution wind speed data from inland water bodies that can be used in data assimilation and operational weather monitoring. SWOT was developed by NASA and Centre National D’Etudes Spatiales (CNES) with contributions from the Canadian Space Agency (CSA) and the United Kingdom Space Agency, and was launched on 16 December 2022 from Vandenberg Space Force Base. As of this manuscript’s writing, SWOT data have not been made publicly available for analysis. Future research aims to build upon this foundational assessment of wind speed using available SWOT data.

Author Contributions

J.V.F.: Conceptualization, Project administration, Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing—original draft, Writing—review and editing; L.C.S.: Funding acquisition, Resources, Supervision, Writing—review and editing. All authors have read and agreed to the published version of the manuscript.

Funding

This work was funded by the NASA Surface Water and Ocean Topography Science Team Program (grant number 80NSSC20K1144) managed by Nadya Vinogradova Shiffer, a NASA Future Investigators in Earth and Space Science and Technology (FINESST) graduate fellowship (grant number 80NSSC19K1377).

Data Availability Statement

All data presented in this study are available publicly available as indicated in the materials and methods sections. Readers may contact the author with questions after reviewing the in-text links and citations.

Acknowledgments

The 2017 ABoVE AirSWOT data were processed using software developed at the Jet Propulsion Laboratory. We would like to thank the AirSWOT data producers and SWOT algorithm specialists at NASA JPL, Albert Chen, Curtis W. Chen, Michael Denbina, Brent Williams, and Xiaoqing Wu, for contributing to the production of the data, supporting this study, and providing feedback on the preliminary stages of this work. A portion of this work was performed at the University of California, Los Angeles, in the Department of Geography; we would also like to thank the Department of Geography for providing physical computing resources in support of this research. We also would like to thank the anonymous reviewers and editors for their work reviewing this manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. (A) The 2017 AirSWOT data collection (black lines) was acquired as a part of the Arctic Boreal Vulnerability Experiment (ABoVE) Airborne Campaign (AAC) beginning in North Dakota, USA, and flying north through Western Canada to Alaska, USA, before returning south along an overlapping flight path. The inset highlights a snapshot (1 July 2017) of the spatial variability of wind speeds from ERA-5 Reanalysis over several lakes in southern Northwest Territories and northern Alberta. Cumulative density plots demonstrate (B) the distribution of water body areas to be examined in this study and (C) the distribution of wind speeds covered by different incidence angles.
Figure 1. (A) The 2017 AirSWOT data collection (black lines) was acquired as a part of the Arctic Boreal Vulnerability Experiment (ABoVE) Airborne Campaign (AAC) beginning in North Dakota, USA, and flying north through Western Canada to Alaska, USA, before returning south along an overlapping flight path. The inset highlights a snapshot (1 July 2017) of the spatial variability of wind speeds from ERA-5 Reanalysis over several lakes in southern Northwest Territories and northern Alberta. Cumulative density plots demonstrate (B) the distribution of water body areas to be examined in this study and (C) the distribution of wind speeds covered by different incidence angles.
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Figure 2. A workflow chart for this study demonstrates two paths of analysis. The primary research seeks to identify the sensitivity of Ka-band radar backscatter and coherence to wind speed and directional variability, and to what extent this variability influences the accuracy of retrieved water surface elevations. The secondary research assesses global wind speed trends over lakes to determine the likelihood that SWOT and other Ka-band InSAR sensors such as AirSWOT will be able to produce accurate water surface elevations globally.
Figure 2. A workflow chart for this study demonstrates two paths of analysis. The primary research seeks to identify the sensitivity of Ka-band radar backscatter and coherence to wind speed and directional variability, and to what extent this variability influences the accuracy of retrieved water surface elevations. The secondary research assesses global wind speed trends over lakes to determine the likelihood that SWOT and other Ka-band InSAR sensors such as AirSWOT will be able to produce accurate water surface elevations globally.
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Figure 3. Comparison of AirSWOT Ka-band VV backscatter with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Backscatter consistently increases with increasing wind speeds across all incidence angles. Wind speeds 3 m/s or higher for incidence angles between 3 and 8.6 degrees achieve the minimum ideal value to consistently separate water from land or other wet surfaces (>10 dB). The first incidence angle category (0.05–0.1 radians, 2.8–5.7 degrees) is most comparable to SWOT due to similar viewing geometry. This second category shows consistently high backscatter, 15 dB, for wind speeds greater than 3 m/s.
Figure 3. Comparison of AirSWOT Ka-band VV backscatter with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Backscatter consistently increases with increasing wind speeds across all incidence angles. Wind speeds 3 m/s or higher for incidence angles between 3 and 8.6 degrees achieve the minimum ideal value to consistently separate water from land or other wet surfaces (>10 dB). The first incidence angle category (0.05–0.1 radians, 2.8–5.7 degrees) is most comparable to SWOT due to similar viewing geometry. This second category shows consistently high backscatter, 15 dB, for wind speeds greater than 3 m/s.
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Figure 4. Comparison of AirSWOT Ka-band coherence with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Coherence consistently increases with increasing wind speeds across all incidence angles. Wind speeds 3 m/s or higher for incidence angles between 2.9 and 17.2 degrees achieve the minimum ideal value for producing high-quality AirSWOT elevations (>0.75). The first incidence angle category (0.05–0.1 radians, 2.8–5.7 degrees), while most comparable to SWOT due to similar viewing geometry, does not have the highest coherence due to the AirSWOT antenna pointing having been focused near 12.9 degrees. Due to the antenna pointing, the highest coherence is identified in the third category (0.15–0.2 radians, 8.6–11.4 degrees), with coherence values exceeding 0.85 for wind speeds greater than 3 m/s. Wind speeds of 3–7 m/s are much more likely to produce highly coherent data, important for reducing horizontal and vertical errors in the computed elevation product.
Figure 4. Comparison of AirSWOT Ka-band coherence with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Coherence consistently increases with increasing wind speeds across all incidence angles. Wind speeds 3 m/s or higher for incidence angles between 2.9 and 17.2 degrees achieve the minimum ideal value for producing high-quality AirSWOT elevations (>0.75). The first incidence angle category (0.05–0.1 radians, 2.8–5.7 degrees), while most comparable to SWOT due to similar viewing geometry, does not have the highest coherence due to the AirSWOT antenna pointing having been focused near 12.9 degrees. Due to the antenna pointing, the highest coherence is identified in the third category (0.15–0.2 radians, 8.6–11.4 degrees), with coherence values exceeding 0.85 for wind speeds greater than 3 m/s. Wind speeds of 3–7 m/s are much more likely to produce highly coherent data, important for reducing horizontal and vertical errors in the computed elevation product.
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Figure 5. Comparison of AirSWOT Ka-band VV backscatter with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Backscatter consistently increases with increasing wind speeds across lake areas. Small lakes, 0.0625–0.25 km2, show significantly lower backscatter on average, up to 5 dB lower, compared with larger water bodies, even in high wind conditions.
Figure 5. Comparison of AirSWOT Ka-band VV backscatter with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Backscatter consistently increases with increasing wind speeds across lake areas. Small lakes, 0.0625–0.25 km2, show significantly lower backscatter on average, up to 5 dB lower, compared with larger water bodies, even in high wind conditions.
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Figure 6. Comparison of AirSWOT Ka-band coherence with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Coherence consistently increases with increasing wind speeds across lake areas. Small lakes, 0.0625–0.25 km2, show significantly lower coherence on average, up to 0.25 lower, compared with larger water bodies, even in high wind conditions, though increasing wind speeds reduce the difference between small and larger water bodies.
Figure 6. Comparison of AirSWOT Ka-band coherence with wind speed (0–7 m/s) over ~11,000 small inland water bodies in western Canada and Alaska. Coherence consistently increases with increasing wind speeds across lake areas. Small lakes, 0.0625–0.25 km2, show significantly lower coherence on average, up to 0.25 lower, compared with larger water bodies, even in high wind conditions, though increasing wind speeds reduce the difference between small and larger water bodies.
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Figure 7. An incomplete distribution of wind directions and speeds occurred during the NASA ABoVE AirSWOT flight campaigns (8 July–17 August 2017). During these flight acquisitions, high wind speeds occurred at wind directions 210–320 degrees, while directions 30–150 degrees experienced lower wind speeds. Wind directions between 320 and 30 degrees (winds from the north) rarely occurred during the AirSWOT flight acquisitions. A statistical assessment of the influence of wind direction on the AirSWOT Ka-band backscatter and coherence is not possible due to this insufficient diversity of wind direction/wind speed combinations during the flight campaigns.
Figure 7. An incomplete distribution of wind directions and speeds occurred during the NASA ABoVE AirSWOT flight campaigns (8 July–17 August 2017). During these flight acquisitions, high wind speeds occurred at wind directions 210–320 degrees, while directions 30–150 degrees experienced lower wind speeds. Wind directions between 320 and 30 degrees (winds from the north) rarely occurred during the AirSWOT flight acquisitions. A statistical assessment of the influence of wind direction on the AirSWOT Ka-band backscatter and coherence is not possible due to this insufficient diversity of wind direction/wind speed combinations during the flight campaigns.
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Figure 8. Global wind speeds over the SWOT observable Prior Lake Database (PLD). ERA-5 monthly reanalysis of 10 m height wind speeds during 2022 was compared with the global PLD. The frequency of wind speed occurrence across PLD lake areas is distributed into 10th, 25th, 50th, 75th, and 90th percentile groups with the mean. Using monthly averages, 75% of PLD lake areas met or exceeded the minimum required wind speeds for high backscatter and coherence, which are necessary to retrieve accurate water surface elevations. The average wind speed for lakes around the globe in 2022 is 4.03 m/s.
Figure 8. Global wind speeds over the SWOT observable Prior Lake Database (PLD). ERA-5 monthly reanalysis of 10 m height wind speeds during 2022 was compared with the global PLD. The frequency of wind speed occurrence across PLD lake areas is distributed into 10th, 25th, 50th, 75th, and 90th percentile groups with the mean. Using monthly averages, 75% of PLD lake areas met or exceeded the minimum required wind speeds for high backscatter and coherence, which are necessary to retrieve accurate water surface elevations. The average wind speed for lakes around the globe in 2022 is 4.03 m/s.
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Fayne, J.V.; Smith, L.C. How Does Wind Influence Near-Nadir and Low-Incidence Ka-Band Radar Backscatter and Coherence from Small Inland Water Bodies? Remote Sens. 2023, 15, 3361. https://doi.org/10.3390/rs15133361

AMA Style

Fayne JV, Smith LC. How Does Wind Influence Near-Nadir and Low-Incidence Ka-Band Radar Backscatter and Coherence from Small Inland Water Bodies? Remote Sensing. 2023; 15(13):3361. https://doi.org/10.3390/rs15133361

Chicago/Turabian Style

Fayne, Jessica V., and Laurence C. Smith. 2023. "How Does Wind Influence Near-Nadir and Low-Incidence Ka-Band Radar Backscatter and Coherence from Small Inland Water Bodies?" Remote Sensing 15, no. 13: 3361. https://doi.org/10.3390/rs15133361

APA Style

Fayne, J. V., & Smith, L. C. (2023). How Does Wind Influence Near-Nadir and Low-Incidence Ka-Band Radar Backscatter and Coherence from Small Inland Water Bodies? Remote Sensing, 15(13), 3361. https://doi.org/10.3390/rs15133361

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