An Improved Adaptive Multi-Scale Peak Detection Retracker for River Level Estimation Based on Sentinel-6 Fully Focused SAR Data

Abstract

Satellite altimetry technology has been widely used for the observation of oceans and inland water bodies. At present, fully focused synthetic aperture radar (FF-SAR) data, which significantly enhances along-track resolution, has good prospects for river level estimation. However, FF-SAR data with large data volumes have more complex waveforms, which brings more challenges to waveform retracking. This study developed an improved adaptive multi-scale peak detection (ImpAMPD) retracker based on Sentinel-6 FF-SAR data. Initially, sub-waveforms are identified and extracted from each waveform. Subsequently, the data are segmented according to the number of gates and the minimum gate length. Finally, retracking calculations are performed on the segmented sub-waveforms to determine river levels. In this study, the in situ data from six river sections with different features in the middle and upper reaches of the Yangtze River were used to validate the accuracy of the ImpAMPD retracker and to perform a comparison of this developed retracker with three existing retrackers (OCOG, PTR, SAMOSA+). The results indicate that the ImpAMPD retracker can fully utilize the advantage of the high posting rate of FF-SAR data to process the complex multi-peak waveforms on the river surface, accurately extract the correct water surface signals, and achieve highly precise river level estimation. The best accuracy results were obtained in four river sections, namely, Zhicheng, Shashi, Hankou, and Huantan, with STDDs of 0.18 m, 0.26 m, 0.47 m, and 0.36 m, respectively. The ImpAMPD retracker is highly automated and adaptable to rivers of varying widths, providing robust support for river level monitoring and flood management.

1. Introduction

Satellite altimetry has been widely utilized for Earth observation, particularly for estimating water surface elevation (WSE) in coastal and inland water bodies and monitoring river discharge and extreme flood events [1]. The limitation of conventional pulse-limited altimeters is their along-track resolutions, i.e., their ability to distinguish between two targets along the surface and the footprint size (several kilometers) [2]. Delay/Doppler altimeters, by transmitting pulses at a high pulse repetition frequency (PRF) to ensure coherence, significantly increase the number of independent observations obtained from individual scatterers on the surface and enhance the along-track resolution by an order of magnitude [3,4,5]. The first generation of high PRF altimeters operated in a closed burst mode [6], such as CryoSat-2, with a PRF of 19 kHz and an azimuth resolution of approximately 300 m. In contrast, new altimetry missions, such as Sentinel-6, utilize a nearly continuous pulse transmission approach with a PRF of 9–10 kHz [7], which allows them to operate in an interleaved mode, eliminating the need to group pulses into bursts, reducing along-track ambiguities, and significantly improving measurement accuracy [8].

In 2017, Egido and Smith [9] developed the fully focused SAR time–domain back-projection (FF-BP) algorithm, which can enhance the along-track resolution to its maximum theoretical limit, approximately half the length of the antenna along the track. The FF-BP algorithm can distinguish targets in highly heterogeneous scenes but suffers from high computational effort. In 2018, Guccione et al. [10] proposed the two-dimensional (2D) frequency–domain FF-SAR (FF-WK) algorithm, introduced an approximate solution based on the Omega-Kappa algorithm, and demonstrated its effectiveness for both closed burst (e.g., CryoSat-2) and open burst modes (e.g., Sentinel-6). The FF-WK algorithm significantly improved computational efficiency, and its maintaining accuracy is comparable to that of the FF-BP algorithm. In 2024, Hernández-Burgos et al. [6] explored the FF-WK algorithm for Sentinel-6 to derive and extensively validate the final expression for the focused single-look waveforms of ideal point targets and demonstrate the algorithm’s versatility and its potential applications in different environments (e.g., open ocean, sea ice).

The accuracy advantage of FF-SAR data has been initially tested in application areas. In 2022, Kleinherenbrink et al. [11] utilized CryoSat-2 FF-SAR data to estimate water levels in Dutch lakes and canals, demonstrating that these data can measure ditches only a few meters wide. When the ditch signal has a sufficiently high signal-to-noise ratio, the measurement accuracy can achieve a sub-decimetric level. Feng et al. [12] evaluated the measurement accuracy of Sentinel-3A altimetry data over the west coast of the North Atlantic Ocean and showed that FF-SAR data accuracy is consistently better than the LRM data and comparable or slightly better compared to standard UFSAR products. Schlembach et al. [13] utilized FF-SAR processed Sentinel-6 Michael Freilich (S6-MF) coastal altimetry data to verify that FF-SAR improves the accuracy by 29% relative to UFSAR at 1–3 km from the coast in complex environments. Additionally, the performance of waveform retrackers applied to FF-SAR data has been evaluated. Ehlers et al. [14] applied high posting rate FF-SAR waveform data along the coast and found that coastal clutter could be filtered out more efficiently to improve data quality, and discussed the applicability of different UFSAR retrackers (e.g., SAMOSA).

The FF-SAR algorithm has good prospects for river level estimation, but the terrain around the rivers is complex, and the interference suffered by the echo is serious [11] and the improvement of the along-track resolution also brings more challenges to the waveform processing of FF-SAR data. The accuracy performance of existing retrackers on FF-SAR data needs to be further evaluated, and new retrackers that can fully utilize the advantages of FF-SAR data need to be explored. In this study, the FF-SAR algorithm is applied to Sentinel-6 altimetry data, and an improved adaptive multi-scale peak detection (ImpAMPD) retracker for FF-SAR waveform features is developed, and compared with an offset center of gravity (OCOG) [15], point target response (PTR) [16], and SAMOSA+ [17] retrackers to evaluate and analyze their performance in the middle and upper reaches of the Yangtze River. PTR retracker is the SINC model that is only employed with a PTR function to fit with the waveform. Various factors affecting accuracy (e.g., river width, posting rate) were thoroughly discussed, and river level time series for different river sections from 2020 to 2024 were obtained, which are intended to provide support for river level monitoring.

The remainder of the paper is structured as follows: Section 2 introduces the study area and data sources, including Sentinel-6 altimetry data, its FF-SAR data processing workflow, and in situ data for accuracy validation. Subsequently, the paper provides a detailed analysis of the FF-SAR waveform characteristics in combination with the geomorphology of each study area and describes the design process of the ImpAMPD retracker. Section 3 analyzes the results of the segmented sub-waveforms and evaluates the accuracy of the water level time series obtained by different retrackers at virtual stations with different river widths. Temporal and spatial changes in river levels in the middle and upper reaches of the Yangtze River from 2020 to 2024 are also analyzed. Section 4 discusses the performance of FF-SAR data in river level estimation, the impact of interfering signals on waveforms, and the effectiveness of various retrackers. Finally, Section 5 provides a summary of the paper.

2. Materials and Methods

2.1. Study Area

In this study, a section of the middle and upper reaches of the Yangtze River was selected as the study area, which is located at 28° and 33.5°N and 105° and 116.5°E, spanning Sichuan, Chongqing, Hubei, and Henan, and has a subtropical climate with an average annual temperature of 14–18 °C and annual precipitation ranging from 1000 to 1400 mm. Influenced by the monsoon climate, the spatial and temporal distribution of precipitation in the Yangtze River basin is uneven, with large interannual variations and seasonal concentration, leading to frequent flooding. The middle and upper reaches of the Yangtze River are highly flood-prone and vulnerable areas, making hydrological data essential for understanding runoff changes within the basin.

Six study sections (virtual stations) with different river widths and geomorphological features were established along the middle and upper reaches of the Yangtze River in this study, and the virtual station is defined at the intersection between the satellite reference ground track and the river centerline. From west to east, four sections, including Zhutuo, Zhicheng, Shashi, and Hankou, are located on the main stream of the Yangtze River, while two sections, including Jingziguan and Huantan, are situated on tributaries. The Sentinel-6 overpass trajectories for each section are illustrated in Figure 1. The details of the in situ data and river widths are provided in

Table 1. Details of six study sections.

Study Section	Duration 1	Coordinates 2 (N, E)	Width (m)	Landscape 3	Slope 4 (m/km)	Mode 5
Zhicheng	8 January 2022–11 February 2024	30.30, 111.50	(1800, 2000)	Sandbar, Pond	0.201	Relative
Shashi	8 January 2022–10 February 2024	30.31, 112.23	(600, 1600)	Sandbank, Pond	0.096	Relative
Hankou	1 January 2022–25 January 2024	30.56, 114.29	(1400, 2000)	Bridge, Pond, Ships	0.031	Relative
Zhutuo	31 December 2020–23 December 2021	29.01, 105.85	(300, 500)	Shoal, Pond	0.929	Relative
Jingziguan	24 December 2020–26 December 2021	33.25, 111.01	(50, 150)	Shoal	1.513	Relative
Huantan	22 September 2022–10 February 2024	31.80, 113.05	(50, 90)	Pond	0.631	Relative

¹ Duration of the in situ data. ² Location of the in situ station. ³ The surrounding landscape that can interfere with the waveform. ⁴ Slope is the channel gradient of a river. ⁵ Relative mode is the elevation relative to the local system of these in situ data.

.

Based on river width, Zhicheng, Shashi, and Hankou are classified as large-width rivers, Zhutuo as a medium-width river, and Jingziguan and Huantan as small-width rivers. Different geomorphological features in each section (Table 1) may cause varying degrees of “contamination” to the waveforms. For instance, within the river channel, features such as sandbars, bridges, and ships docked or navigating in marinas can contribute to contamination. Additionally, on both sides of the river, large shoals that accumulate water bodies and numerous small ponds [18] scattered along the bank significantly affect the waveforms.

2.2. Data

2.2.1. Altimeter Data and Processing

The data used in this study were derived from the Sentinel-6 satellite launched on 21 November 2020, with a repeat cycle of 10 days and 127 orbits per cycle [19]. The data are Sentinel-6 L1a products from December 2020 to February 2024 and were processed into FF-SAR datasets using the FF-WK algorithm [20,21]. The processing steps are as follows:

• Zero-padding the raw data in the along-track direction. The Sentinel-6 satellite operates in an interleaved mode with a dynamic pulse repetition frequency (PRF), so interpolation was employed to maintain a constant pulse repetition interval (PRI);
• Performing the Fourier transforms of the dataset in the along-track direction, one by one in the range direction;
• Solving for the stationary phase point (SPP) [10,22];
• Along-track compression, including the multiplication of the transformed dataset by the focusing operator sample-by-sample;
• Complete focusing using double inverse Fourier transforms by applying the inverse Fast Fourier Transform (IFFT) algorithm to the azimuth and the Fast Fourier Transform (FFT) algorithm to the range direction;
• Compensating across the track.

In Sentinel-6 FF-SAR processing, it is unnecessary to implement Stolt interpolation to focus the remaining range positions [6]. The FFSAR single-looked waveforms were first generated using a synthetic aperture of 2.3 s. With Sentinel-6, this corresponds to an along-track resolution of 0.85 m on the ground. Then, the waveforms were averaged at 160 Hz, 640 Hz, and 1280 Hz to reduce the noise (also called multi-look).

2.2.2. Auxiliary Data

The daily in situ data for each station between December 2020 and February 2024 were obtained from the Water Level Yearbook of China and the National Rainfall Information website (Table 1). Additionally, the river centerline and slope data were acquired from the SWOT River Database (SWORD).

2.3. Methods

2.3.1. Analysis of River FF-SAR Waveform Features

Although the FF-SAR algorithm significantly improves the posting rate, increases the number of nadir points, and better meets the needs of river level monitoring, the complex terrain of river surfaces and their surroundings can cause various interferences in the waveforms, and these echo signals from different objects are manifested in the form of sub-wave peaks, which ultimately makes the waveforms present the multi-peak pattern, leading to difficulties in determining sub-wave peak signals from the water surface of the river.

This study utilizes Sentinel-6 1280 Hz data, which contains more information for analyzing waveform features. The satellite images (left) and radargrams (right) for each study section are presented in Figure 2. The dark blue boxes indicate river surface signals, where the river morphology is evident, and the river water surface signals can be determined. Interfering signals can be categorized into two types; one is the non-river surface signals represented by ponds (red boxes), which have high strength but are discontinuous in the azimuth direction and can distinctly separate from river surface signals in the range direction; the other is the interfering signals from the surface of river represented by sandbars and bridges, which are high in intensity, and more continuous in the azimuth direction, neighboring with the river water surface signals in the range direction, and generally appearing shaded in radargrams, making it difficult to distinguish between them. As shown in Figure 3, the radargrams of the Shashi section reveal the river’s complex echo signals, numerous and strong interfering sub-wave peaks, and the continuity of the river water surface sub-wave peaks (red retracking line).

Overall, in the azimuth direction, the river exhibits the most continuous morphology among the landforms in the study area. Therefore, the river water surface signals (manifested as sub-wave peaks) are usually more numerous in the overall waveforms relative to the irregular disturbing objects. In the range direction, echo signals from different objects can be distinguished in each waveform, determined by the radar altimeter’s pulse scattering mechanism. Consequently, there will be higher frequencies concentrated within a certain range, and the continuity of sub-wave peaks, representing different echo signals, will also be manifested in the azimuth direction of the waveforms (see Figure 3). Thus, the sub-wave peak signals of the river water surface have the highest continuity, especially after the high posting rate of FF-SAR processing. The number of waveforms has greatly increased, and the above waveform features will be more significant.

2.3.2. ImpAMPD Retracker

Based on the analysis of FF-SAR waveform features, the core hypothesis of this study is that the sub-wave peaks corresponding to river water surfaces exhibit the highest continuity. Adaptive multi-scale sub-wave peak extraction decomposes complex echoes into sub-wave peaks from the river water surface or interfering objects. According to the core hypothesis and prior knowledge (in Section 2.3.1), sub-wave peaks representing a specific object are concentrated within a certain gate range. Therefore, by applying effective waveform segmentation and statistical methods, sub-wave peaks representing the river water surface can be extracted. Notably, since waveform segmentation is performed on sub-wave peaks, the gate length of the sub-waveform to which a sub-wave peak belongs can serve as a criterion for segmentation.

This study develops a more suitable retracker for river multi-peak waveforms, which realizes the accurate extraction of sub-wave peak waveforms from the river water surface in order to obtain highly precise river water levels.

The steps of the ImpAMPD retracker are illustrated in Figure 4 as follows:

• To select daily overpass waveform data for the river segments in the study sections to obtain multiple waveform data;
• To extract multi-scale adaptive sub-wave peaks to accurately identify multiple strong sub-wave peak signals from each waveform based on the Local Maxima Scalogram (LMS) method [23] The key of this method is to construct an $\mathrm{L}\times \mathrm{N}$ local maxima matrix ${\left(m_{k,i}\right)}_{\mathrm{L}\times \mathrm{N}}$ for each waveform. The extraction process is as follows:
  Step 1: Calculate the local maxima of the waveform using a moving average window, where the window length $w_k$ varies according to $\left\{w_k=2k+1|k=\mathrm{1,2},\dots ,L\right\}$. The local maxima $m_{k,i}$ for different window lengths $w_k$: are determined by (1):

  $$m_{k,i}=\left\{\begin{array}{c}0, \\ r+1,\end{array}\right.{\displaystyle \genfrac{}{}{0pt}{}{x_{i-1}>x_{i-k-1}\cap x_{i-1}>x_{i+k-1}}{\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}}}$$

  (1)

  where $r$ is a random number in the range [0, 1], $k$ is the $k$-th waveform in the along-track direction, and $x$ is the power waveform. L = 5 is the optimal setting for peak detection in this study. The values of $m_{k,i}$, at $i=1,\dots ,k+1$ and $i=N-k+2,\dots ,N$ are set to $r+1$. Based on this, a local maxima matrix $M={\left(m_{k,i}\right)}_{\mathrm{L}\times \mathrm{N}}$ can be constructed.
  Step 2: Calculate the sum of each row of the local maxima matrix $M$, denoted as $\gamma =\left[{\gamma }_1,{\gamma }_2,{\dots ,\gamma }_L\right]$.

  $${\gamma }_k=\sum _{i=1}^N{m}_{k,i},k=1,\dots ,L$$

  (2)

  The row-wise summation $\gamma =\left[{\gamma }_1,{\gamma }_2,{\dots ,\gamma }_L\right]$ contains information about the scale-dependent distribution of zeros (thus, local maxima). The global minimum of $\gamma$, denoted as $\lambda =argmin\left({\gamma }_k\right)$, represents the dimension with the most local maxima. Additionally, use $\lambda$ to reorganize the local maxima matrix LMS by removing all elements $m_{k,i}$ that satisfy $k>\lambda$, resulting in a new matrix ${M_r=\left(m_{k,i}\right)}_{\lambda \times \mathrm{N}}$.
  Step 3: To determine the peaks of the waveform by calculating the column-wise standard deviation ${\sigma }_i$ of each column of the matrix $M_r$ according to (3).

  $${\sigma }_i={\displaystyle \frac{1}{\lambda -1}}{\left[\sum _{k=1}^{\lambda }{\left(m_{k,i}-{\displaystyle \frac{1}{\lambda }}\sum _{i=1}^{\lambda }{m}_{k,i}\right)}^2\right]}^{{\displaystyle \frac{1}{2}}}$$

  (3)

  The index $i$ that satisfies ${\sigma }_i=0$ represents the bins of the detected peak. This value is designated as the stopping point of the sub-waveform ${stopgate}_i$. For each waveform, $stopgate=\left[{stopgate}_1,{stopgate}_2,\dots ,{stopgate}_N\right]$ can be determined.
  Additionally, to determine the starting point of each sub-waveform, the waveform is normalized with the maximum power. Subsequently, the power difference of the normalized waveform’s consecutive gates is calculated to obtain the power difference waveform. Finally, for each sub-waveform stopping point ${stopgate}_i$, the power difference waveform is searched from back to front. The first gate with a power value below 0.001 is identified as the corresponding sub-waveform starting point ${startgate}_i$.
  Following the aforementioned steps, the same search is performed for all sub-waveform stopping points in $stopgate$, and ultimately, the sub-waveform starting points $startgate=\left[{startgate}_1,{startgate}_2,\dots ,{startgate}_N\right]$ are calculated, forming N sub-waveforms together with $stopgate$. Considering that some situations may have sub-waveform widths of only 2–3 bins, which are too narrow for retracking calculations, it is necessary to extend several bins forward or backward to form new sub-waveforms. Previous studies have demonstrated that a sub-waveform width of at least five bins is optimal [24,25]. Therefore, the difference between the end and start gates is calculated to verify the sub-waveform length. For special sub-waveforms, two bins are extended either backward or forward;
• Sub-waveform information statistics. After the multi-scale adaptive sub-wave peak extraction, each row of the waveforms is traversed in the azimuth direction. Using the obtained start and end gates of each sub-waveform, the gate length of each sub-waveform is calculated and recorded in the $AllGateLengths$ array. The frequency of each gate length and its corresponding occurrence are then counted. Subsequently, the smallest gate length is selected from the top three most frequent gate lengths, denoted as the minimum gate length $minGateLength$;
• Sub-waveform segmentation. The number of segments in the waveforms is determined based on the number of gates.

  $$numSegments=binnum/minGateLength$$

  (4)

  Each segment may contain multiple sub-wave peaks. To further remove interfering signals, the minimum gate length is halved, referred to as the narrow gate scheme, while the original gate length is referred to as the wide gate scheme. Each waveform is traversed to determine the segment of each sub-wave peak gate position. The top three segments with the most sub-wave peaks are identified, and the start and end gate positions and corresponding row numbers are recorded, denoted as $rows$;
• Retracking of sub-waveform segments. Retracking is performed for each type of sub-waveform segment, and the corresponding height ($R_{retrack}$) is calculated. First, each sub-waveform is traversed to obtain its $startgate$, $stopgate$, and $rows$. A temporary row (referred to as newRow) of the same size as a single waveform is created, with all values initialized to 0. The sub-waveform values are subsequently assigned to the corresponding gate positions in newRow. Thereafter, the PTR and Threshold retrackers are applied to the waveform in newRow. The Threshold is an extension of the OCOG retracker, defined as Threshold = thres·OCOG. The standard deviation and median of the heights for each sub-waveform segment are calculated, and heights exceeding three times the standard deviation from the median are removed. This outlier exclusion step is repeated three times. Finally, the water level ($H$) at several nadir points for the day is determined using the following formula [25],

  $$H=Alt-Range-N_{geoid}-R_{iono}-R_{st}-R_{wet}-R_{dry}-R_{retrack}$$

  (5)

  where $Alt$ is the satellite altitude, $Range$ is the distance between the altimeter and the water surface, $R_{iono}$ is the ionospheric correction, $R_{st}$ is the solid earth tide, $R_{wet}$ is the wet troposphere, $R_{dry}$ is the dry troposphere, and $N_{geoid}$ is the geoid height with respect to the ellipsoid, for which the 2008 Earth Gravitational Model (EGM2008) is used. Except for $R_{retrack}$, all the above corrections are included in Sentinel-6 L2 products;
• Removing outliers for heights in the along-track direction. The heights for the same day are extracted based on the corresponding orbit number. The nearest neighbor linear interpolation method is employed to filter outliers. Subsequently, the average of the heights in the along-track direction is calculated and used as a baseline to exclude outliers beyond ±8 m;
• Slope correction and river level time series construction. Due to the slope of the river surface and the distance deviations of several nadir points during the observation period (see Figure 1), it is necessary to calculate the distance from each nadir point along the river centerline to the virtual station. Using the cumulative distance difference ($∆Distance$) and the slope ($Slope$), the correction value to adjust the along-track water levels at the virtual station is calculated. The formula is given as follows:

  $$H_{correct}=H+\left(Slope·∆Distance\right)$$

  (6)

  The median, mean, and standard deviation of the along-track water levels are then calculated. The standard deviation of along-track water levels is recorded as alStd.

2.3.3. Annual Change Rate of River Levels

To estimate the river level trend, this study simplifies the periodic series fluctuations into annual and semi-annual cycles. The formula is as follows [26]:

$$H\left(t\right)+v=a+bt+ccos\left(2\pi t\right)+dsin\left(2\pi t\right)+ecos\left(4\pi t\right)+fsin\left(4\pi t\right)$$

(7)

where $t$ is time in years, $a$ is a constant term, $b$ is the annual rate of water level change (m/y), $c,d$ are the coefficients for the annual cycles, $e,f$ are the coefficients for the semi-annual cycles, $v$ represents the fitting error. These parameters are determined using the nonlinear least squares method.

3. Results

This study utilized FF-SAR data with posting rates of 160 Hz, 640 Hz, and 1280 Hz to analyze their impact on algorithm accuracy. For the proposed ImpAMPD retracker, as described in Section 2.3.2, the narrow gate scheme involves halving the minimum wave gate length, denoted as Narrow_ImpAMPD, while the original minimum gate length is termed the wide gate scheme, denoted as Wide_ImpAMPD. The ImpAMPD_OCOG algorithm suffix indicates the threshold (thres) choices of 40%, 45%, and 50%.

3.1. Sub-Waveform Segment Analysis

As described in Section 2.3.2, during the implementation of the ImpAMPD retracker, the segments with the most sub-wave peaks and their corresponding sub-waveforms are identified and recorded. These top three types of segments are considered in this study as potential signals from the river water surface due to their high number of sub-wave peaks. Here, Shashi is an example of how to analyze the segment results of the ImpAMPD_OCOG retracker (50% threshold) under the narrow gate scheme at 1280 Hz.

The specific performance is detailed below:

• The first segment has the highest number of sub-wave peaks, and the second and third segments have significantly lower numbers of sub-wave peaks than the first segment;
• Figure 5 and Figure 6 illustrate that the water level generated in the first segment is the most consistent with the in situ data, while the water level generated in the second segment has a low frequency of monitoring, a large range of elevation fluctuations, a high along-track standard deviation, and a large difference between the generated water level and in situ data;
• For the 1280 Hz_N_ImpAMPD waveform segment, the minimum gate length is 2. The first segment is mostly the 72nd–74th segments, which corresponds to the range of the dark blue box in Figure 2b, while the second segment is mostly the 62nd–66th segments, which corresponds to the range of the red box in Figure 2b, indicating that the sub-wave peaks in the second segment are the interfering signals from the non-river surfaces.

In general, the first segment with the highest number of sub-wave peaks can be directly adopted as the correct segment. However, based on the design of the ImpAMPD retracker, if the result of the first segment is very poor (based on the along-track standard deviation and the number of water levels), secondary segments can be considered according to the actual performance of the waveforms in the study area, which may occur in areas with the small river width where the signal percentage of the river water surface is not significant.

3.2. Accuracy Verification

In this study, we obtained and compared the accuracy of various retrackers (ImpAMPD, OCOG, PTR, SAMOSA+) in different study sections and at different posting rates, and the accuracy validation results are detailed in Appendix A.

Table 2. The best retracking result for each virtual station.

Virtual Station	Best Retracker 1	STDD (m)	CC 2	MalStd 3 (m)
Zhicheng	1280 Hz_N_ImpAMPD_OCOG_40	0.47	0.96	0.091
	160 Hz_SAMOSA+	0.53	0.94	0.311
Shashi	1280 Hz_N_ImpAMPD_OCOG_50	0.26	1.00	0.106
	160 Hz_SAMOSA+	1.02	0.93	0.325
Hankou	1280 Hz_N_ImpAMPD_OCOG_50	0.18	1.00	0.081
	160 Hz_SAMOSA+	1.52	0.90	0.264
Zhutuo	1280 Hz_N_ImpAMPD_OCOG_50	0.33	0.99	0.058
	160 Hz_SAMOSA+	0.30	0.99	0.064
Jingziguan	1280 Hz_W_ImpAMPD_PTR	0.83	0.83	0.060
	640 Hz_OCOG	0.73	0.47	0.054
Huantan	640 Hz_W_ImpAMPD_OCOG_40	0.36	0.41	0.015
	160 Hz_SAMOSA+	0.37	0.36	0.012

¹ For each virtual station, the first row is the best retracking result of ImpAMPD, and the second row is that of other retrackers. ² Correlation coefficient. ³ Mean of the along-track standard deviations.

demonstrates the results of the retrackers with the best accuracy at each virtual station. The comparison of the river level time series for each retracker with the in situ data are shown in Figure 6, and the comparison of the correlations is shown in Figure 7.

In Appendix A, STDD (Standard Deviation of Differences) denotes the standard deviation of the difference between the monitored water levels obtained by each retracker and the in situ data on the same day. NO. denotes the number of samples of each retracker involved in the accuracy verification. MalStd denotes the mean of the along-track standard deviations obtained by the retracker during the monitoring period. The along-track standard deviation (alStd) indicates the standard deviation of the single-day water levels and can reflect the accuracy of the river levels obtained from different retrackers; the more outliers in the river levels for a single day, the larger the alStd value for that day is.

3.2.1. Accuracy of the ImpAMPD Retracker

As shown in Table 2, the ImpAMPD retracker exhibits favorable results at six virtual stations, especially the best accuracy Zhicheng, Shashi, Hankou, and Huantan with the STDDs of 0.47 m, 0.26 m, 0.18 m, 0.36 m, respectively. Although the best results were not achieved in Zhutuo and Jingziguan, they are similar to the best accuracy obtained by the existing retrackers and have the best correlation with the in situ data in Jingziguan. Specifically, only the in situ data for the year 2021 were collected in Zhutuo and Jingziguan, and the Jingziguan virtual station is located downstream of the dam, where the river width is narrow, and its waveforms are subject to significant interference.

As seen in Appendix A, the ImpAMPD_OCOG retracker has the best accuracy, and each thresholding results have a positive correlation between the STDD and MalStd, so MalStd can be used to assist in the threshold selection for this retracker.

The ImpAMPD_PTR retracker exhibits the lowest MalStd at all virtual stations and even reaches the millimeter-level accuracy in Huantan, indicating good and robust performance. In large and medium-width rivers, the narrow gate scheme of the ImpAMPD retracker exhibits high accuracy, whereas, in small-width rivers, the wide gate scheme proves more effective. In Zhicheng, Shashi, Hankou, Zhutuo, and Huantan, the accuracy of the N_ImpAMPD retracker is higher than that of the W_ImpAMPD retracker when the posting rate is higher, and the opposite trend is observed in Jingziguan.

3.2.2. Comparative Analysis of Different Retrackers

Among the existing retrackers, the SAMOSA+ retracker performed best at five virtual stations, and its accuracy was close to that of the best OCOG retracker in Jingziguan.

In large-width rivers, the ImpAMPD retracker has excellent performance, and the existing retrackers are poor. It is concluded that the existing retrackers are weak in identifying the correct signals from waveforms with multiple peaks, resulting in more outliers in the elevation series and higher STDD. Similarly, the W_ImpAMPD retracker has a larger minimum gate length and more interfering sub-waveforms in the selected segments, leading to more erroneous elevations, especially at a higher posting rate. In contrast, the N_ImpAMPD retracker can effectively eliminate interfering signals and significantly increase the number of correct signals at a higher posting rate, resulting in higher accuracy.

With the narrowing of the river width, the existing retrackers perform better. The improvement in the amount of data by the FF-SAR algorithm is weakened with the narrowing of the river width, so the performance of the ImpAMPD retracker is limited, especially for the narrow gate scheme, which also excludes some correct signals when removing interfering signals through the gate position. In this case, the correct signals are not easy to recognize due to their insufficient quantity. However, the wide gate scheme considers signals in a larger range of gates, which increases the number of correct signals to some extent, so the accuracy is better. On the other hand, the nadir points of the narrow-width rivers are less, and the number of outliers in the series obtained by existing retrackers is reduced accordingly, resulting in better accuracy.

3.3. Water Level Time Series Analysis

Figure 8 illustrates the river level time series obtained by the ImpAMPD and SAMOSA+ retrackers for different virtual stations. The monitored water levels have been zero-mean normalized, and the relative water levels at observation points greater than 0 m are higher than the average water levels during the monitoring period, and the values below 0 m are lower than the average water levels.

3.3.1. Main Stream of the Yangtze River

From upstream to downstream, the water level series in Zhutuo, Zhicheng, Shashi, and Hankou exhibit similar seasonal variation characteristics. During the summer flood season, short-term flood peaks significantly exceeding the annual average water level are common, whereas the winter dry seasons often show consistently low water levels. In general, the water levels in the middle and upper reaches of the Yangtze River are relatively high from May to October every year, with a significant rise from June to September and reaching the peak between August and October. Conversely, from November to April, the water levels are relatively low, with the lowest water levels observed between December and March. It is worth mentioning that the flood season in 2022 is significantly earlier compared to 2021 and 2023.

During the monitoring period, the water levels exhibited a declining trend, with the highest rate of decline observed in Shashi at −0.923 m/y. Overall, the further downstream, the greater the range of fluctuations in water levels (

Table 3. The trends for changes in river levels at six virtual stations during 2020–2024.

Virtual Station	Monitoring Period	Annual Rate of Change (m/y)	Variance of River Levels (m)	No.
Zhutuo	21 December 2020–14 February 2024	−0.17	5.15	98
Zhicheng	27 December 2020–11 February 2024	−0.56	6.32	96
Shashi	27 December 2020–10 February 2024	−0.92	9.54	93
Hankou	30 December 2020–25 January 2024	−0.77	11.97	89
Jingziguan	24 December 2020–28 January 2024	−0.13	5.67	78
Huantan	27 December 2020–10 February 2024	0.15	7.14	73

) and the higher the rate of decline.

3.3.2. Tributaries of the Yangtze River

The Jingziguan hydrological station is the inflow control station of the Danjiangkou reservoir, and the river section by the virtual station is located downstream of the dam, so the artificial storage characteristics of the river level changes are obvious, such as during the period from December 2021 to March 2023 (see Figure 8e), the river levels of the virtual stations was a long-term low value and displayed a declining trend at −0.13 m/y.

In Huantan, the virtual station is located upstream of the dam, resulting in stable water level changes with significant artificial storage characteristics. During the monitoring period, the river levels at this virtual station were high, trending upwards at 0.15 m/y.

4. Discussion

4.1. Performance of FF-SAR Data in River Level Estimation

The primary advantage of the FF-SAR algorithm is its capacity to increase the posting rate, resulting in an increase in the number of waveforms obtained along the track direction (azimuth) within a certain observation range. Consequently, the larger the range, the more significant the increase in the number of waveforms is, and the range size is expressed as the size of the river width in the river scenario.

In the waveforms, signals from the river water surface are termed correct signals, whereas non-river water surface signals are termed interfering signals. Interfering signals derived from sandbars, bridges, ships within the river channel, or ponds and floodplains on both sides of the river channel. The proportion of the two types of signals in the waveforms determines the quality of the waveform, which varies depending on the study area. Generally, in large-width rivers, the river extent is larger, and the percentage of correct signals in the azimuth direction is relatively high. Conversely, in small-width rivers, the percentage of correct signals is relatively low.

Overall, the FF-SAR algorithm increases the data volume. The larger the original data volume, the more the data volume is boosted by the high posting rate added to it. Therefore, the FF-SAR algorithm also increases the interference signals. If the original data contain a high proportion of interference signals, a higher posting rate will exacerbate difficulties in water level monitoring.

4.2. Impact of Interfering Signals on Waveforms

In the range direction, the interfering signals degrade the quality of waveforms, i.e., altering the shape of individual waveforms. These signals increase the number of sub-wave peaks in a single waveform. When there are too many strong sub-wave peaks, it is difficult to identify the only correct sub-wave peak signal, leading to errors in the retracking results of individual waveforms. The impact of interfering signals in the range direction can be extended to the azimuth direction so that the erroneous elevations retracked by individual waveforms will manifest as outliers in the along-track elevation series. For FF-SAR data, when the waveform quality of the study area is certain, an increase in the number of along-track waveforms will result in more errors in the along-track elevation series. When the number of errors reaches a certain threshold, it is difficult to determine them as outliers.

Interfering signals from various sources exhibit distinct features in waveform intensity (see Figure 2 and Figure 3). The strongest interferences from water surface signals beyond the river, such as ponds and ditches near the river, exhibit strong sub-wave peak signals in the range direction of individual waveforms. Kleinherenbrink [11] also found that neighboring ponds and small lakes exhibit strong sub-wave peak signals in the waveforms that are difficult to eliminate when monitoring water levels, which is not conducive to waveform retracking. However, in the azimuth direction, the small area of ponds will result in a low continuity of interfering signals. In contrast, interfering signals from beaches on both sides of the river, sandbars in the river, and bridges within the footprint are high in intensity and shaded. These objects not only exhibit strong sub-wave peak signals in the range direction of waveforms but also are relatively continuous in the azimuth direction. Nevertheless, the results of this study indicate that such interfering signals and the correct signals are still distinguishable in the range direction, although they are adjacent to each other.

4.3. Comparison of Retrackers’ Performance

4.3.1. The Existing Retrackers

The three existing retrackers (OCOG, PTR, SAMOSA+) used in this study perform waveform retracking of individual waveforms only in the range direction (one-dimensional). The fundamental concept underlying these retrackers is to refine the range measurement either by fitting a physical model to the waveform and extracting the range information or identifying a point in the waveform that is considered representative of the height measurement [27]. These retrackers are sensitive to waveform variations and can be significantly affected by peaks within the waveform. Due to the complexity and interference in river waveforms, these algorithms frequently retrack incorrect sub-wave peaks, resulting in wrong elevation results.

Specifically, the OCOG retracker determines the retracking bin based on the overall shape of the individual waveform. However, the presence of multiple interfering objects along the range direction of the river surface can readily cause retracking errors. In Shashi (see Figure 2 and Figure 3), there are sandbanks and ponds on both sides of the river, causing multi-peak waveforms, which lead to the poor accuracy of the OCOG retracker. The PTR retracker initializes with the maximum value of the main peak signal and utilizes the local optimum of the individual waveform as the retracking bin. However, the presence of specular reflective objects, such as ponds, with significantly higher signal reflection intensities compared to the river, can induce errors. This is most evident in Huantan, where the PTR retracker’s accuracy is the poorest. The SAMOSA+ retracker selects the peak position of a moving point-wise product in a subset of 20 consecutive waveforms after aligning them for tracker shift. However, when interfering objects exhibit continuity, it can cause significant errors. For example, in Hankou, there is a bridge and a large pond on the west bank, whose contamination is continuous, resulting in poor performance of the SAMOSA+ retracker. In contrast, in Zhutuo, the interfering objects are small and sparse, leading to better results from the SAMOSA+ retracker.

In large-width rivers, the single-day elevation series contains more outliers, and the number of outliers increases with a higher posting rate. In such cases, whether by taking the mean and median or removing the outliers and then selecting the middle of the series and averaging the data, it is difficult for the erroneous values to be regarded as outliers and removed. Therefore, the high posting rates are detrimental to the accuracy of the existing retrackers in large-width rivers. Conversely, small-width rivers have fewer data and fewer outliers, leading to better performance of the existing retrackers, and appropriately increasing the posting rate may have a positive effect (e.g., Jingziguan).

4.3.2. The ImpAMPD Retracker

The ImpAMPD retracker performs waveform retracking on the overall waveforms in both the range and azimuth directions (two-dimensional). By segmenting sub-waveforms, it strips the correct and erroneous signals in the range direction and identifies them based on the continuity of correct signals, weakening the impact of interfering signals.

In large-width rivers, when the posting rate is higher, the number of correct values in the azimuth direction is also higher, which makes it easier to recognize, and, therefore, the ImpAMPD retracker performs better. However, in small-width rivers, the smaller the river width and the smaller the data volume, the weaker the data volume enhancement effect of the FF-SAR algorithm (as described in Section 4.1), and the more it will weaken the performance of the ImpAMPD retracker. Therefore, in such cases, the accuracy of the ImpAMPD retracker is comparable to or slightly better than that of existing retrackers (see Appendix A), and its advantage is not significant.

For the selection of gate scheme, the narrow gate scheme has a better performance in large-width rivers; as illustrated in Figure 2, the morphology of the river can be reflected in the radargrams, i.e., the surface signals of the river in the dark blue box. However, these signals are not all correct signals from the water surface; there are many interfering signals (e.g., shaded strong signals). The average gate length in the range direction in the dark blue box is approximately 10 bins, so only finer segmentation can weaken the impact of interfering signals. By utilizing the FF-SAR algorithm, correct signals are usually identified due to their largest number.

As the river width decreases, the wide gate scheme gradually outperforms the narrow gate scheme. This is because the finer segmentation strips out both interfering and correct signals. As described in Section 3.1 in the case of Shashi, the first segment typically lies between the 72nd and 74th gates (see Figure 3), while the second segment lies between the 62nd and 66th gates; the two segments are not adjacent to each other in the range direction, and there are correct signals in the neighboring segments of the first segment. Due to the reduction of data volume caused by the narrower river width, the number of correct signals in the first segment of the narrow gate scheme becomes insufficient, while the wide gate scheme expands the length of the minimum gate, considering more correct signals and resulting in better algorithm performance. Therefore, when applying the ImpAMPD algorithm to large- and medium-width river sections using high posting rate data, the narrow gate scheme is recommended, while the wide gate scheme is more suitable for small-width (below 200 m) river sections.

In summary, in large-width rivers, the large data volume comprises numerous correct and erroneous signals, so identifying the correct signals and eliminating the impact of outliers is the key to waveform retracking algorithms. In small-width rivers, the data volume is smaller, and there are fewer erroneous signals, so it is more important to consider more correct signals in waveform retracking.

5. Conclusions

In this study, an improved adaptive multi-scale peak detection (ImpAMPD) retracker was developed based on Sentinel-6 FF-SAR data by deeply analyzing the waveform characteristics of the river surface, extracting multi-scale adaptive sub-wave peaks, performing sub-waveform statistics and segment processing to identify and extract the water surface signals of the river from the waveforms in both the range and azimuth directions. The in situ data from six river sections with different features (e.g., river width, morphology, surrounding landscape) in the middle and upper reaches of the Yangtze River were used to validate the accuracy of this retracker, and three existing retrackers (OCOG, PTR, SAMOSA+) were compared. The results indicate that the ImpAMPD retracker can fully utilize the advantage of the high posting rate of FF-SAR data and efficiently process the complex multi-peak waveforms on the river surface to achieve highly precise river level estimation. The ImpAMPD retracker is highly automated and easy to implement, and it can be adapted to rivers of various scales and river widths. The best accuracy results were obtained in four river sections, namely, Zhicheng, Shashi, Hankou, and Huantan, with STDDs of 0.18 m, 0.26 m, 0.47 m, and 0.36 m, respectively. Among the ImpAMPD retrackers, the ImpAMPD_OCOG retracker exhibits the best accuracy; the ImpAMPD_PTR retracker demonstrates good accuracy and more robust performance; the narrow gate scheme of the ImpAMPD retracker performs well in large-width rivers, while the wide gate scheme is suitable for small-width rivers. It is worth mentioning that the SAMOSA+ retracker performs best among the three existing retrackers. The existing retrackers generally perform well in small-width rivers but poorly in large-width rivers. Moreover, the increase in posting rate has a negative effect on the performance of the existing retrackers in large-width rivers. Finally, the ImpAMPD retracker is also applicable to other water bodies, such as lakes. The performance of this retracker with other satellite altimetry SAR data will be explored in future research. Furthermore, there is a certain relative distance between the in situ stations and virtual stations in this study, so accuracy validation results may still have some errors.