Satellite altimeters transmit microwave pulses toward the sea surface below and measure “waveforms”, i.e., time series of the power of received backscattered echoes (Figure 1
a). Under the presence of sea surface waves, microwave pulse signals reflected at the wave crests reach back to the satellite earlier than ones reflected at the wave troughs. This temporal discrepancy is represented as the leading edge rise time, i.e., duration of the leading edge slope of the waveform, and thus enables to measure significant wave height (SWH). Since the mid-point of the leading edge slope would represent the wave-averaged sea surface, the distance between the satellite and the sea surface at nadir, which will be converted to the sea surface height (SSH), is calculated from the round-trip delay time of the radar pulses at the midpoint of the leading edge.
Measurements of SWH by satellite altimeters have been reported quite accurate in open oceans e.g., [1
], but they have not been fully discussed in areas near lands. This is partly because altimeter measurements are often unreliable in coastal areas [3
]. In so-called “retracking” processes, an idealized model is fitted to observed perturbed waveforms (Figure 1
a). The Brown mathematical model is most commonly used as the idealized model in open oceans, but it assumes homogeneous reflectance within a footprint of an altimeter [3
]. This assumption, however, tends to be broken in coastal areas since sources of inhomogeneous reflectance (e.g., ships, lands, slicks, or calm water in small bays) are often present within a footprint. Therefore, altimeter measurements in coastal areas could be contaminated by such sources within a footprint.
In this decade, however, new retracking algorithms have been developed to accurately treat coastal altimetry data e.g., [3
]. Especially, so-called “subwaveform retrackers”, such as Adaptive Leading Edge Subwaveform (ALES) retracker, are promising and widely used in these days [5
]. The subwaveform retrackers analyze only a part of the waveform near the leading edge slope (i.e., subwaveform estimation window) to reduce possible contaminations of extraordinary microwave reflections from areas of inhomogeneous reflectance within a footprint (Figure 1
a). Recently, another subwaveform retracker is proposed by [6
] (Wang, Ichikawa, and Wei, 2019; hereinafter referred as “WIW19”) that refers sequentially assembled waveforms of all along-track points, i.e., a radargram (Figure 1
b), to find a largest subwaveform estimation window size that is not affected by contaminated echoes. Use of these retracking algorithms have been reported to significantly improve coastal altimetry measurements.
Another reason why coastal altimetry SWH measurements are not fully discussed is due to strong spatial gradient of wave heights in coastal areas [1
]. In coastal areas where spatial scales are generally small, it is unrealistic to expect spot buoy measurements, along-track altimeter measurements, and gridded wave model results to be all compatible with each other. In this study, therefore, we choose the Celebes Sea as the study area. The Celebes Sea is a deep marginal sea so that spatial gradient would be less significant than in coastal areas near lands. Nevertheless, frequent contaminations of altimeter measurements by presence of areas of smooth sea surface have been reported even in the center of the Celebes Sea, 200 km away from lands, so that performance of subwaveform retrackers could be fully examined [6
In the present study, Jason-2 SWH datasets in the Celebes Sea determined by three retracking algorithms were compared with each other and also with a wave model. Details of Jason-2 data and algorithms are described in Section 2
, together with descriptions of the wave model. The inter-comparisons of Jason-2 datasets are first described in Section 3.1
, then they are compared with wave model results (Section 3.2
). Discrepancies of the retracking algorithms are discussed in Section 4.1
. In addition, representability of the wave model is discussed in Section 4.2
, followed by conclusions in Section 5
2. Materials and Methods
The Celebes Sea was selected for the study area in the present study. The Celebes Sea is a deep (most area is over 2000 m) semi-enclosed sea located between 1°N and 6°N (Figure 2
). In general, wind speed is low and waves are calm, and these conditions often produce areas of quite smooth sea surface, which contaminate altimeter waveforms as stronger echo intensity than the surrounding areas within a footprint (also known as “sigma0 blooms” [8
]). Smooth areas are frequently found even in the middle of the sea away from islands, and thus altimeter measurements in the Celebes Sea are often corrupted [6
In this study, the 20 Hz Sensor Geophysical Data Records (SGDR; Version d) of the Jason-2 altimeter waveforms in the Celebes Sea were used [9
]; four tracks are available in the Celebes Sea, as shown in Figure 2
. The dataset covers the period from July 2008 to April 2015. Together with the original SGDR SWH dataset determined from full-length waveforms, two SWH datasets using subwaveform retracking algorithms are investigated in this study.
One is ALES retracker, which adjusts the subwaveform estimation window size proportional to the SWH estimation [5
]. Since ALES uses only a small part of the trailing edge slope (no more than 20 gates in calm sea states; Figure 1
b) that is necessary to accurately fit the Brown model, it is less likely affected by contaminations in the trailing edge slope.
The other is WIW19 retracker, which requires a series of adjacent waveforms: unlike SGDR and ALES that process each single waveform independently, WIW19 uses radargrams to determine the estimation window size [6
]. Since contaminations from a smooth area can be recognized in the neighboring waveforms as far as the area is included in a footprint (Figure 1
b), radargrams enable it easier to identify these contaminations. In WIW19, the subwaveform estimation window size is extended as long as possible unless contaminated echoes are included, and then the Brown model is fitted excluding the contaminated trailing edge outside the estimation window (Figure 1
a). Note that the subwaveform estimation window size of WIW19 is significantly variable, depending on the relative locations of the nadir observation point to contamination sources (Figure 1
b). Although WIW19 is a subwaveform retracker, it could use full-length waveform as SGDR if no contamination sources were present within a footprint and thus the whole echoes in a waveform were uncontaminated.
In the fitting process of the Brown model, two subwaveform retrackers uses the Nelder-Mead optimization approach [4
], whereas SGDR uses Maximum Likelihood Estimator (MLE4) [8
]. Note that four unknown parameters of the Brown model are estimated in both SGDR and WIW19, whereas ALES does not directly estimate the slope of the trailing edge, which is related to the attitude (mispointing angle) of an altimeter.
In order to eliminate obvious outliers in SGDR and ALES datasets, several quality-control filters [6
] have been applied to 20 Hz data in this study (Table 1
). These criteria are recommended ones in Jason-2 Products Handbook [9
], except that zero SWH data are excluded in the present study. For WIW19, we eliminated waveforms whose uncontaminated trailing edge is shorter than 5 gates, in order to keep reasonable fitting to the Brown model [6
In order to compare these Jason-2 SWH data with wave fields numerically calculated from wind fields, wave hindcasts were conducted with a 3rd-generation wave model, WAVEWATCH III version 3.14 (WW3) [11
]. The WW3 was driven by the surface wind field estimated by the NCEP Climate Forecast System Reanalysis (CFSR version 2) [12
] and water depths were obtained from ETOPO1 bathymetry database. The hindcast covers the 5-month period from January through May 2014.
For all calculations, we used the same parameterization schemes for the three main source terms: wind input, nonlinear spectral transfer, and dissipation. For the wind input and wave dissipation, the source term package by [13
] was used. We employed the discrete interaction approximation (DIA) method [14
] for the nonlinear interaction term. The shallow water source terms were not included. For spatial propagation of the wave spectrum, the default third-order advection scheme is used. For all these, the default settings were used.
The model has a nested domain with grid resolutions of 1/2° for the outer nest (covering the Global Oceans excluding the poles) and 1/12° for the inner nest (Indonesian Seas: 97.5°E–129.0°E, 9.0°S–15.0°N; the domain is indicated in Figure 2
). The frequency domain was set to 30 bins logarithmically spaced from 0.041 to 0.65 Hz (relative frequency of 10%) whereas the directional resolution was set to 10°. WW3 wave model products for the inner nest were stored hourly which was used for the comparison with Jason-2 data.
Excellent agreement between WW3 model and both altimeter and buoy data has been reported in open ocean e.g., [15
]. The correlation coefficients between 1/4° WW3 model and GDR SWH data of several altimeters exceed 0.9 in most areas [16
], although they slightly decrease to 0.8 in the equatorial area. In the comparison in [16
], however, worst correlations are found in the Indonesian Seas as significantly low as approximately 0.5; worst agreement with the altimetry SWH data in the Indonesian Seas is also found in wave hindcasts of another model (European Center for Medium-Range Weather Forecasts) [18
]. On the other hand, [17
] reported that agreement between 1/20° WW3 model and strictly quality-controlled altimetry SWH data that eliminate all suspicious observations [2
] is good even when the Indonesian Seas are included. From comparisons between tropical coastal buoys and WW3 models with different resolutions (1/2°, 1/5°, and 1/20°), [17
] also concluded that correlation values do not change significantly from coarser grids to finger grids, in contrast that the root-mean-squared (RMS) differences decrease by increasing the resolution of the grids; note that temporal variations of wind waves are mainly determined by wind fields themselves and that these models in [17
] commonly use the same NCEP wind fields. Therefore, the different correlation coefficients in [16
] and [17
] would be due to discrepancy of the quality of the altimeter data, not the resolution of WW3 models. These results suggest that the capability of Jason-2 retrackers for SWH can be assessed by correlation coefficients with WW3 models, as a consistency with wave fields numerically determined from the NCEP wind fields. At the same time, they also suggest that the resolution of WW3 models may affect the other statistics such as the RMS differences with the altimetry data. In the present study, therefore, the ability of the 1/12° WW3 model to represent basic wave physics in the Celebes Seas will be alternately further discussed in Section 4.2
For comparisons, WW3 SWH values are extracted at the point and time of Jason-2 20 Hz observations; linear interpolations of 1/12° grids and one-hour intervals are used. Figure 3
shows examples of SWH variations along Track 190 in a standard calm sea state or in a rougher sea state. Even in the calm sea state (Figure 3
a), and for all algorithms, 20 Hz altimetry SWH data are so noisy that all 20 Hz SWH values (both Jason-2 altimetry data and WW3 model data) are averaged in this study over 51 along-track points to produce 18 km separations along tracks; small scale structures of SWH less than 18 km are not treated in the present study since they are not well represented in the model. In the averaging process, outliers in a 18-km block are removed based on the Median Absolute Deviation (MAD) [2
]; namely, an observed value
is discarded as an outlier if its deviation from the median value
is larger than three times of MAD, where MAD is defined as
. After this MAD filter, the mean number of data points used in an 18-km block becomes 45.8 for WIW19, 46.9 for ALES, 43.4 for SGDR and 50.4 for WW3 model: if the number of data is less than 25, the corresponding 18-km averaged value is discarded. Mean standard deviations of 18-km averages were 0.42 m for WIW19, 0.35 m for ALES, and 0.50 m for SGDR, while it was 0.008 m for WW3 model.
In the Celebes Sea where waveforms of satellite altimeters are often contaminated, two subwaveform retrackers, ALES and WIW19, are applied to Jason-2 20 Hz SGDR data. The estimated SWH datasets are first compared with the original SGDR SWH data that use full-length waveforms. Using radargrams, or a series of adjacent waveforms along Jason-2 tracks, WIW19 can provide an optimal index (the uncontaminated trailing edge length) how Jason-2 observation points are close to contamination sources such as slicks and lands.
When observations are close to these contamination sources, SGDR tends to estimate unrealistic SWH values with respect to two subwaveform retrackers, since contaminated echoes near the leading edge ruin the full-waveform SGDR retracker. Meanwhile, the subwaveform retrackers avoid to use contaminated echoes within the trailing edge of the waveforms, so that their SWH estimations are not affected by the presence of contamination sources. These contaminated observations could be filtered by sigma0 criteria since they tend to have larger sigma0 values as “sigma0 blooms”. Strict sigma0 filtering certainly reduces SWH outliers and improves data quality, but unnecessarily removes uncontaminated observations at the same time.
When uncontaminated full-length waveforms are available, all algorithms are well correlated, except that ALES retracker has a positive bias in a calm sea state (SWH < 1 m), whose state is not unusual in the calm semi-enclosed Celebes Sea. Due to this positive bias, ALES data include no SWH estimations smaller than 0.4 m, which is rather unrealistic in this calm study area. Under the calm sea state condition, ALES limits the subwaveform estimation window size to less than six gates, even though a longer window size were actually available since observations are uncontaminated. In other words, although a short estimation window size of ALES subwaveform retracker is useful to avoid potential contaminations in the trailing edge slope, it could be too short in the calm sea state to properly fit the Brown model to a waveform with the steep leading edge. Meanwhile, WIW19 retracker extends the size of the uncontaminated estimation windows as long as possible.
For moderate sea states (SWH > 1.5 m), agreement of two subwaveform retrackers using the Nelder-Mead fitting method (WIW19 and ALES) are excellent despite that the subwaveform estimation window sizes are significantly different. On the other hand, WIW19 tends to estimate slightly larger SWH values than SGDR that uses MLE4 fitting, although both use the similar estimation window sizes. Therefore, for uncontaminated altimeter observations in moderate sea states, choices of the fitting algorithms would influence the similarity of the results more significantly than the estimation window sizes.
These datasets are then compared with WW3 model results, resulting in good agreement especially when comparisons are limited to uncontaminated Jason-2 observations. Note, however, that WIW19 retracker can achieve similar agreement with all available observations without such strict limitation, providing better data availability; data availability would be especially important e.g., in assimilating fast-varying SWH field in coastal areas.
The agreement, however, becomes worse if swells from the Pacific is excluded in the WW3 model, suggesting that the swells are almost always present in the Celebes Sea, in spite of its semi-enclosed nature. Comparisons with individual Jason-2 data also reveal discrepancies that may be caused by insufficiency of the present WW3 model calculated from the NECEP wind fields, such as displacements of locally-confined SWH events with respect to Jason-2 tracks. Together with improved quality of the altimetry SWH data, higher resolutions of both wave models and wind fields would further improve wave fields descriptions in semi-enclosed coastal seas.