1. Introduction
Coastal communities face potential dangers due to the formidable waves and powerful surges that accompany storms. These natural phenomena present significant risks, endangering the safety and well-being of those residing in coastal areas of the North American Great Lakes (hereafter referred to as the Great Lakes). For example, with winds hitting 20 m/s in Muskegon, Michigan, Lake Michigan’s eastern shore, waves surpassed 3 m in height on 5 December 2017 [
1]. This severe storm followed another record of extreme weather in Lake Superior in October, when a buoy in Lake Superior north of Marquette, Michigan, recorded a highest wave of 8.8 m during a high wave event on 24 and 25 October 2017, according to the National Data Buoy Center (NDBC) database. Two people were swept into the lake at Black Rocks, a lookout point in Presque Isle Park north of Marquette [
2]. Given these circumstances, the quality of numerical wave models such as WAVEWATCHIII
® (hereafter WW3) [
3] holds great significance, as it plays a pivotal role as the foundation of NOAA’s operational Great Lakes Waves-Unstructured Forecast System version 2.0 (GLWUv2) [
4,
5] in providing wave forecast guidance and warnings for the Great Lakes region. Accurate forecasts enable coastal communities to take precautionary measures to safeguard their properties against potential damages.
In the Great Lakes region, most of the in situ observations of significant wave height (SWH) used to evaluate GLWUv2 are provided by NDBC buoys. However, the buoys are regularly retrieved from the lakes during winter to avoid damage from the ice cover. Therefore, the lack of buoy data in winter leaves the accuracy of the wave model unverified for winter periods. To fill this gap in wave model evaluation, wave data detected by satellites are utilized as an alternative data source.
The ATL13 Along Track Inland Surface Water Data provided by the Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2 ATL13) contains SWH measurements over inland water bodies, including the Great Lakes region [
6]. The data offer a potential source for evaluating the accuracy and effectiveness of GLWUv2 in SWH predictions within the Great Lakes for the following three reasons: First, the ICESat-2 ATL13 data products provide the SWH data over unfrozen areas of the Great Lakes during the winter, which makes it competent in complementing the winter data gaps. Second, the ICESat-2 produces a high density of SWH data along its operational track. According to the data over the Great Lakes region in this study, the density of the SWH is approximately 11.8 data points per kilometer. The inland water heights are processed in segments that contain a minimum of approximately 100 signal photons to ensure the segment accurately characterizes the water surface. As such, the segments vary in length from approximately 30 m to 100 m [
6]. Therefore, the ICESat-2 ATL13 data products provide the information about water surface conditions at an unprecedentedly high resolution compared with other satellite measurements, such as those produced by the China–France Oceanography Satellite (CFOSAT), whose spatial resolution (nadir beam) is around 70 to 80 km [
7], and the Global Navigation Satellite System-Reflectometry (GNSS-R) data, which provide SWH estimates at a resolution of 27.8 km × 27.8 km (0.25° × 0.25°) [
8]. Third, the data products from ICESat-2 demonstrate high precision. As presented in the Algorithm Theoretical Basis Document for ATL13 [
9], the overall ensemble error per 100 inland water photons is estimated as 6.1 cm, derived from the root-mean-square of five error sources: radial orbit error, tropospheric delay error, forward scattering error, geolocation knowledge uncertainty, and ATLAS (Advanced Topographic Laser Altimeter System) ranging precision per photon. Therefore, it is worth exploring the potential of the ATL13 data products of ICESat-2 in physical wave model verification for the Great Lakes.
Although it has been over 5 years since ICESat-2’s launch (15 September 2018), the SWH data in its ATL13 product have not been broadly explored and applied for examining wave conditions over large water bodies. Most studies regarding the ICESat-2 ATL13 product focus on its inland water orthometric height data, while its SWH data are only treated as auxiliary information. For example, Luo et al. [
10] estimated lake water level on the Tibetan Plateau by subtracting the SWH from the orthometric height of the ATL13 dataset. They evaluated how taking SWH into consideration would affect estimating the change rates of water level. Similarly, Liu et al. [
11] used the ICESat-2 ATL13 product to monitor the lake water levels in the Yellow River Basin by also subtracting the SWH from the orthometric water level to obtain the true water level, but found this greatly increased the standard deviation of the water level measurements and thus increased the uncertainty of the water volume change calculation, compared to disregarding the effect of SWH. An et al. [
12] evaluated the performance of seven ongoing satellite (ICESat-2 included) altimetry missions for measuring inland water levels of the Great Lakes, and concluded that the stability of the average deviation (bias) of the ICESat-2 is the best in inland water level measurements, but the mean root-mean-square error (RMSE) of ICESat-2 is slightly higher than satellites Jason-3 and Sentinel-6. They also pointed out that ICESat-2 has an exceptionally high spatial resolution among the seven satellites. However, their study did not explore the use of SWH data of the ICESat-2 ATL13 product for studying wave conditions in the Great Lakes.
Despite their promising potential, the SWH data of the ICESat-2 ATL13 product remain unexamined. It is necessary to assess their data quality and accuracy before being applied in evaluating the numerical wave model prediction results. Some studies have conducted similar work and investigated the data quality of SWH data provided by other satellites. According to Yang and Zhang’s study [
13], the RMSE is about 0.2–0.3 m for the comparison of satellite Sentinel-3A SWH with NDBC buoy data, and that of satellite Sentinel-3B is about 0.18–0.3 m, across the global ocean. Li et al. [
14] assessed the performance of the SWH data of the China–France Oceanography Satellite (CFOSAT) in the South China Sea, a unique sea area characterized by a semi-enclosed basin and multi-reef terrain. Compared against observations from mooring or buoy sites, they found that the average correlation coefficient is as high as 0.87, and the average RMSE is 0.47 m in the relatively open and deep areas of the South China Sea. However, the SWH data would be affected by coastlines, topography, and monsoons in certain cases. Moreover, Durrant et al. [
15] validated SWH data from Jason-1 and Envisat satellite altimetry against NDBC buoy data across the globe. The Jason-1 SWH was reported to have a bias of −0.010 m, an RMSE of 0.227 m, and a correlation coefficient of 0.983, and the Envisat SWH was reported to have a bias of 0.036 m, an RMSE of 0.219 m, and a correlation coefficient of 0.986. In addition, Peng and Jin [
8] estimated the global ocean SWH using space-borne CYGNSS GNSS-R data through the relationship between the square root of the signal-to-noise ratio data of the CYGNSS delayed Doppler map and the SWH, then compared it with buoy-measured data from NDBC. The correlation coefficient between the estimated value and the SWH observation of a buoy is 0.9539, the bias is −0.0496 m, and the RMSE is 0.2761 m. Although all of the above four studies focused on ocean waves, none of them evaluated satellite SWH measurements, particularly in the Great Lakes. Actually, such research remains fairly rare based on our search among academic articles.
Based on the reasons above, this study evaluated the quality of the ICESat-2 ATL13 significant wave height data in the Great Lakes region using the regular buoy measurements sourced from the National Data Buoy Center (NDBC) and the Seagull platform of the Great Lakes Observing System (Seagull GLOS), within two time intervals: April 2021 to December 2021, and May 2022 to October 2022. Then, this study assessed the model quality of GLWUv2 by comparing its retrospective forecast simulations with the ICESat-2 ATL13 significant wave height data in the Great Lakes, and also with emerging low-cost Spotter buoys that have enabled rare winter wave measurements in recent years. This study will fill a critical data gap of wave conditions for the Great Lakes during winter by verifying the accuracy of the ICESat-2 ATL13 significant wave height data. The work will ultimately contribute by providing better wave predictions that improve the preparedness of the people and industries of the Great Lakes communities for dangerous high wave conditions.