Partially empirical model-based water depth retrieval in shallow sea using GF5-AHSI hyperspectral remote sensing data: a case study on Meizhou Bay in Fujian Province, China

Abstract

Bathymetric mapping using quantitative remote sensing techniques is a crucial research domain for accurately retrieving oceanic depths. This study uses GF5-AHSI hyperspectral remote sensing data to evaluate the accuracy of three semi-empirical models for shallow water depth retrieval: single-band, multi-band, and band-ratio models. The methodology involved parameter extraction, optimal band selection, and combining bands to create the models. A Pearson correlation analysis was conducted to assess parameter sensitivity, optimizing the models for water depth retrieval. The models’ precision was evaluated by comparing their outputs with actual underwater topography measurements from Meizhou Bay, Fujian Province. Error margins in estimated water depths ranged from 10% to 50% across the three models, with accuracy generally improving at greater depths. Among the models, the band-ratio model showed the highest reliability, followed by the multi-band model, and the single-band model was the least reliable. However, in depths greater than 30 m, the single-band model’s error margin could be reduced to within 10%, surpassing the performance of the multi-band and band-ratio models. A spectral reflectance sensitivity test revealed variations in reflectance across different water depths, with a slight increase in the near-infrared band due to water turbidity. To further improve model accuracy, strategies must be implemented to mitigate the interference of suspended sediments and reduce noise, thereby enhancing the reliability of water depth retrieval.

Graphical abstract

Keywords

GF5-AHSI / water depth retrieval / Pearson correlation coefficient / partially theoretical and empirical model

1 Introduction

Mapping underwater bathymetry plays a vital role in marine environmental exploration, supporting a wide range of activities such as topographic surveys, geomorphological research, safe navigation, and coastal management—including fisheries, marine transportation, and infrastructure development (Shen et al., 2016; Kutser et al., 2020; Li et al., 2023; Ma et al., 2023). Traditionally, bathymetric mapping has relied on techniques such as sonar, sounding hammers, and rods, typically conducted from ship-based platforms (Giordano et al., 2016; Rogers et al., 2020; Grøn et al., 2021; Borrelli et al., 2022). The conventional methods require substantial knowledge of hydrology, geology, and geomorphology, as well as extensive fieldwork and repeated measurements, which is labor-intensive, time-consuming, and costly. In shallow waters, the accuracy of conventional methods is further compromised due to the frequent need for manual intervention (Cheng et al., 2021; He et al., 2021). Moreover, the limited time available for ship navigation in shallow waters, due to risks like stranding during low tide, significantly constrains the efficiency of conventional methods. For areas shallower than −5 m, measurements can only be conducted at high tide, further limiting data collection opportunities (Lafon et al., 2002). As a result, ship-based sound detection proves inefficient for large-scale, rapid bathymetry updates, particularly in shallow coastal waters.

The exploration of nearshore water depth has become a crucial focus in oceanic remote sensing research (Ashphaq et al., 2021; Hsu et al., 2021). Advances in multispectral, hyperspectral, and radar sensing technologies have improved detection capabilities, surpassing traditional ship-based methods (Jay and Guillaume, 2014). Pioneering work on remote sensing of shallow water topography, notably LiDAR, was introduced in 1969 (Hickman and Hogg, 1969), setting the stage for future innovations. The integration of big data analytics platforms like Google Earth Engine (GEE) has further advanced data processing and water depth retrieval methods (Li et al., 2021; Chen et al., 2022; Merchant, 2023). Traditional water depth retrieval models, including analytical, statistical, and hybrid approaches, primarily based on multispectral data, have been widely tested, validated, and refined over decades (Arabi et al., 2020; Kutser et al., 2020; Nan et al., 2020; Zhang et al., 2020b). One notable contribution came from the Environmental Research Institute of Michigan (ERIM) in the United States, which developed a remote sensing theory based on seabed reflection in conjunction with multispectral data (Ceyhun and Yalçın, 2010). Since the 1980s, Chinese researchers have made significant strides in water depth detection using multispectral images from spaceborne and airborne sensors (Liu and Feng, 2025). Studies have been conducted in diverse regions, such as the South China Sea’s Yongshu Reef and the Arctic coastal plain of Alaska, utilizing data from MODIS, HJ satellites, Gaofen-1, and TM images (Dang and Ding, 2003; Li et al., 2015; Chen et al., 2017). Recently, there has been a shift from multispectral to hyperspectral and active optical remote sensing techniques for water depth detection. This transition includes innovations like the integration of multi-source, multi-temporal images, and the combination of passive and active remote sensing methods (Nan et al., 2020). While active remote sensing offers higher accuracy, it is often more costly and complex. Conversely, passive optical remote sensing, with its extensive data sets and long-term records, holds significant potential for broader application, though it still requires enhancements in accuracy.

Gaofen-5 (GF-5), China’s first hyperspectral satellite, is equipped with an Advanced Hyperspectral Imager (GF5-AHSI) for high-precision Earth and oceanic observations across a wide spectral range, from ultraviolet to long-infrared wavelengths (Zhang et al., 2020a; Chen et al., 2021). Hyperspectral remote sensing, with its narrow 5 nm spectral intervals, offers superior spectral resolution compared to multispectral sensing, enabling more accurate detection of subtle variations, such as water depth (Vandermeulen et al., 2017). The enhanced spectral detail minimizes issues like spectral ambiguity, improving the retrieval models’ accuracy for water depth (Marcello et al., 2018). Despite minor spectral differences in seawater, hyperspectral data can detect finer changes in the marine environment. In applications such as monitoring oceanic conditions in the South China Sea and the south-eastern coastal regions of China, GF-5 has proven to be invaluable (Wen et al., 2024). It has contributed significantly to improving marine environmental monitoring, providing precise measurements of water depth, sea surface temperature, and other key indicators essential for coastal management and marine ecosystem protection (Chen et al., 2019; Wan et al., 2020; Hou et al., 2022; Yang et al., 2022).

Common methods for hyperspectral water depth extraction include the look-up table method, spectral differential statistical model, neural network model, and partially-analytical model (Louchard et al., 2003; Mobley et al., 2005; Hedley et al., 2009). The look-up table method requires detailed numerical simulations and accurate optical property matching (Kutser et al., 2020). The spectral differential statistical model addresses spectral noise but is limited by complex physical mechanisms (Kutser et al., 2020). However, its application in hyperspectral water depth extraction is limited due to the complexity of the physical mechanisms associated with spectral information (Zhang et al., 2020b). Neural networks, like the HOPE model, are widely used but may overestimate depth in low-reflectance areas and demand high computational effort (Lee et al., 1999; Petit et al., 2017). In contrast, empirical algorithms based on band ratios offer a simpler, more efficient approach, with broader applicability across multispectral and hyperspectral data, yielding improved accuracy (Paredes and Spero, 1983; Pattanaik et al., 2015; Roelfsema et al., 2018; Garcia et al., 2020; Hsu et al., 2021; Roy and Das, 2022).

We leverage GF5-AHSI hyperspectral remote sensing data to develop three partially empirical models for shallow water depth retrieval. These models are based on the principles of radiative energy reflection and transfer at the air-sea interface, extending conventional optical remote sensing techniques for water depth detection. We created single-band, multi-band, and band-ratio models, and evaluated their accuracy using field-measured water depth data from Meizhou Bay in Fujian Province. Our aim is to enhance the performance of water depth retrieval in both shallow and deeper waters by comparing the strengths and limitations of each model investigated. Through comparison, we seek to improve the applicability of spaceborne hyperspectral data for precise water depth detection in diverse marine environments.

2 Materials and methods

2.1 Study area

Fujian Province, located on the Chinese southeast coast directly opposite Taiwan Island, features one of the longest coastlines in China, extending approximately 3800 km as part of China’s extensive 34000 km coastline (Pattanaik et al., 2015). With a coastline meander ratio of 1:7.01, Fujian has the most intricate coastline in China, comprising 125 harbors of various sizes, 22 of which are deep-water ports (Liu and Xue, 2024). Seven of these ports, including Meizhou Bay, have been developed to accommodate deep-water berths capable of handling vessels over 50000 DWT (Fig. 1). Meizhou Bay, situated between Putian City and Quanzhou City in Fujian Province, is a semi-enclosed, elongated bay that stretches approximately 33 km from north to south and 30 km from east to west. The bay’s coastline spans around 289 km, with Quanzhou City and Putian City contributing 162 km and 127 km, respectively. Of the total coastline, 134 km is utilized by the harboring industry, while the remaining 83 km supports urban and tourism development. Covering an aquatic area of about 516 km², Meizhou Bay has approximately 374 km² lying below the mean low water level.

2.2 Data sets

2.2.1 Remote sensing data

Water depth inversion was performed using data from the Advanced Hyperspectral Imager (AHSI) onboard the Gaofen-5 (GF-5) satellite, with a spatial resolution of 30 m. The data was collected on November 12, 2019, and is available at Land Satellite Remote Sensing Application Center website. The AHSI provides comprehensive spectral coverage, including visible to near-infrared (VNIR) wavelengths from 400 to 745 nm across 150 bands with a spectral resolution of 5 nm, and short-wave infrared (SWIR) wavelengths from 710 to 2500 nm across 180 bands with a spectral resolution of 10 nm.

2.2.2 Field measured water depth data

On December 16, 2019, we collected 288 bathymetric data points through hydrographic surveys, as shown in Figs. 1 and 2(b). The measurements, ranging from 0.1 to 64 m, represent the shallow water depths outlined in Table 1. To facilitate model development and validation, the data set was divided into training and validation subsets in a 2:1 ratio, with 194 samples allocated for model training and 94 for validation. Statistical comparisons of key descriptive metrics—maximum, minimum, mean, and standard deviation—confirmed that the two subsets were statistically similar, supporting the validity of the dividing approach (Table 1). To assess the spatial distribution of the samples, Ripley’s K function was applied. The results indicated that the overall data set, along with its training and validation subsets, maintained highly similar spatial characteristics across different scales. No significant clustering or excessive uniformity was found, confirming that the sample partitioning was spatially balanced (Fig. 2(b)). Additionally, the water depth distributions of the training and validation sets demonstrated strong consistency, following similar patterns (Fig. 2(c)). In addition, tidal data were obtained at Chongwu station, covering the same study region. Both the bathymetric and tidal data were standardized to the Wusong datum to maintain consistency across analyses (Zhang et al., 2021).

3 Methods

3.1 Data pre-processing

The GF-5 AHSI data set was pre-processed to integrate visible, near-infrared, and shortwave spectral ranges, for subsequent modeling and analysis. The data underwent a series of pre-processing steps. First, radiometric calibration was applied to correct sensor-related variations. This was followed by atmospheric correction according to established protocols (Zhao et al., 2020). To address the BRDF effects, the Ross-Li BRDF model was employed for correction. Finally, orthorectification was carried out to correct geometric distortions (Su et al., 2021). Using the PIE-Hyp 6.3 framework, this pre-processing involved several key steps: assessing spectral quality, resolving mixed pixels, classifying images, detecting specific targets, and integrating themes to combine the hyperspectral data with spatial information effectively (Jiang et al., 2023). During band selection, redundant bands and those affected by strong water vapor absorption were identified and excluded, resulting in the removal of four SWIR bands and 20-five bands affected by water vapor. The final exclusion of SWIR bands in the range of 2300 to 2500 nm was made due to the significant sensor artifacts, and 276 bands remained (Fernández-Habas et al., 2022).

Further steps included radiometric normalization, atmospheric correction, geospatial rectification, and signal enhancement (Zhao et al., 2020; Su et al., 2021). Radiometric normalization converted raw digital numbers (DNs) into reflectance values, using established methodologies (Honkavaara et al., 2012). Atmospheric correction was performed using the 6S module within PIE, parameterized with satellite metadata (Kotchenova et al., 2006). The 6S model was specifically chosen due to its suitability for the complex atmospheric conditions and varying water characteristics. Compared to other correction methods like FLAASH, the 6S model is more sensitive to aerosol and water vapor parameters. Geospatial rectification ensured accurate location data for the GF5-AHSI imagery. To further refine the data set, a Pearson correlation analysis was performed to evaluate the relevance of the bands for depth estimation, ensuring that only the most informative spectral bands were used in the water depth retrieval process. Signal enhancement, including filtering and noise reduction, was applied to improve data quality (Dai et al., 2020a; Dai et al., 2021). For water detection, bands 38 (548.66 nm) and 110 (856.60 nm) of the GF5-AHSI imagery were used to calculate the Normalized Difference Water Index (NDWI), with a threshold of 0.1 to identify water features. For a comprehensive description of these procedures, please refer to the work of Dai et al. (2020b).

3.2 Pearson correlation coefficient analysis

The Pearson correlation coefficient, denoted as ρ, quantifies the degree of linear association between two stochastic variables and is bounded within the interval of [−1, +1] (Nan et al., 2020; Yao et al., 2020). The magnitude of ρ reflects the correlation’s intensity, with values closer to +1 or −1 signifying stronger positive or negative linear relationships, respectively, and a value of 0 denoting the absence of a linear connection. To illustrate, consider two n-dimensional vectors, X=\left[X_1,X_2\dots X_n\right] and Y=\left[Y_1,Y_2\dots Y_n\right]; the Pearson correlation coefficient is computable via the following equation:

(1)\rho (X,Y)=\frac{\mathrm{c}\mathrm{o}\mathrm{v}(X,Y)}{{\sigma }_X{\sigma }_Y}=\frac{{\displaystyle \sum _{i=1}^n(X_i-\overline{X})(Y_i-\overline{Y})}}{\sqrt{{\displaystyle \sum _{i=1}^n(X_i-\overline{X}{)}^2}}\sqrt{{\displaystyle \sum _{i=1}^n(Y_i-\overline{Y}{)}^2}}},

where X_i is the selected bands, Y_i is the water depth, \overline{X} is the average of the selected bands, \overline{Y} is the average water depth.

3.3 Water depth model

3.3.1 Single-band model

The univariate model, referred to as the single-band attenuation model, uses a singular spectral band from remote sensing imagery to retrieve bathymetric data. The commonly used formulas are expressed as (Jawak et al., 2015; Arabi et al., 2020)

(2)Z=\frac{1}{k_f}[\ln (L-L_{i\mathrm{\infty }})-\ln R_{ib}-\ln C_i],

where Z is the water depth, k_t is the effective attenuation coefficient of water, f is the geometric factor for the path length of light propagation in water, L_i is the band radiation received by the sensor, L_{t\mathrm{\infty }} is radiometric brightness values at maximum water depth in the study area, R_ib is the bottom reflectance of water bodies, and C_i is a composite quantity determined by solar irradiance, water bodies, atmospheric transmittance.

In a limpid aquatic environment characterized by uniform water quality, the performance of the single-band model in depth retrieval is commendably high, provided that the substrate reflectivity and the water’s attenuation coefficient remain invariant. Nevertheless, this monochromatic depth model fails to account for the diffuse scattering of light within the aqueous medium. Presuming X=L_i-L_{i\mathrm{\infty }}, the formulation can be efficaciously condensed as

(3)Z=a\mathrm{l}\mathrm{n}X+b,

where a and b are two empirical parameters, Z is the water depth value, and X is the radiation in the i-band minus the radiant brightness value at the deepest part of the study area.

3.3.2 Multi-band model

The multi-band approaches to bathymetric retrieval employ a minimum of two spectral bands. This method enhances the single-band model by assuming uniform substrate reflectance across different water bodies within identical spectral bands, with other parameters correspondingly equivalent (Roy and Das, 2022):

(4)Z=a_0+a_1\ln X_1+a_2\ln X_2,

(5)X_i=L_i-L_e,i=1,2,

where Z is the water depth value. a₀, a₁, and a₂ are empirical regression coefficients, which can be obtained through regression analysis of the surface reflectance and the measured water depth data. X₁ and X₂ are the reflectance of the two different bands minus the deepest reflectance. L_i is radiation received by the sensor at band i. L_i∞ is radiometric brightness values at maximum water depth in the study area.

3.3.3 Band-ratio model

The band-ratio bathymetric model is underpinned by a straightforward theoretical framework. Its formulation can be derived from the computation of the quotient between two monochromatic band models (Yao and Shi, 2015; Chen et al., 2017):

(6)Z=\frac{1}{k_i^1-k_i^2}\left(\ln \frac{C_i^1}{C_i^2}+\ln \frac{R_{b1}}{R_{b2}}\right)-\ln \frac{L_i^1-L_{i\mathrm{\infty }}^1}{L_i^2-L_{i\mathrm{\infty }}^2},

where \ln {\displaystyle \frac{C_i^1}{C_i^2}}+\ln {\displaystyle \frac{R_{b1}}{R_{b2}}} is a constant value determined by the water environment of the study area. {\displaystyle \frac{1}{k_i^1-k_i^2}}is the difference between the attenuation coefficients of the two bands and remains essentially constant. In water depth retrieval, this value is mainly influenced by water conditions, the atmosphere, and other factors. The simplified expression is

(7)Z=a\mathrm{l}\mathrm{n}{\displaystyle \frac{x_1}{x_2}}+b,

where a and b are two empirical parameters. Z is the water depth value. x₁ and x₂ are the reflectance of two bands.

3.4 Accuracy evaluation

The measured bathymetry was adjusted for tidal variations to align with the Wusong datum, following the methodology articulated by Zhang et al. (2021). Subsequently, the coefficient of determination (R²), root mean square error (RMSE), and mean relative error (MRE) were employed to assess the precision of the bathymetric retrieval models. The indicators of accuracy were calculated using the following formulas:

(8)R^2=1-\frac{{\displaystyle \sum _{i=1}^n{\left(H_i-G_i\right)}^2/(n-m-1)}}{{\displaystyle \sum _{i=1}^n{\left(H_i-\overline{H}\right)}^2/(n-1)}},

(9)\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{\left(H_i-G_i\right)}^2}}{n}},

(10)\mathrm{M}\mathrm{R}\mathrm{E}=\frac{{\displaystyle \sum _{i=1}^n\left|H_i-G_i\right|/H_i}}{n},

where H_i is the measured value, \overline{H} is the mean measured value; G_i is the predicted value; n is the number of monitoring points; and m is the number of independent variables. The closer the value of R² is to 1, the smaller the RMSE and MRE are, indicating that the higher the model accuracy (Mi et al., 2022).

4 Results

4.1 Spectral reflectance establishment

The image quality of the GF-5 AHSI data is improved after applying the 6S model for atmospheric correction, particularly in the visible and shortwave infrared spectral ranges. We effectively minimized atmospheric interferences, such as water vapor absorption and aerosol scattering. This improvement allows the spectral reflectance of water bodies and vegetation to be captured with greater accuracy, providing a true representation of the spectral characteristics of ground features.

The improved spectral curves clearly corrected the impact of atmospheric effects on the original images. We selected three observation points to illustrate changes in spectral curves before and after atmospheric correction. Among these, points A and B represent water pixels, and point C represents a vegetation pixel (Fig. 3). In the water pixels (points A and B), a distinct reflection peak at 530 nm is visible on the spectral curve, and the near-infrared band shows significant absorption. This occurs because water strongly absorbs light in this band, resulting in reduced reflectance. After atmospheric correction, the reflectance in the near-infrared band decreases further, aligning more closely with expected water characteristics (Figs. 3(b) and 3(c)). For the vegetation pixel (point C), the uncorrected curve displays unstable reflectance in the near-infrared band, largely due to atmospheric interference. Following correction, the near-infrared reflectance markedly increases, revealing the high reflectance typical of vegetation and presenting a standard vegetation spectral curve (Fig. 3(d)). This process yielded surface reflectance values that more accurately represent real-world conditions.

4.2 Bands correlation test and model establishment

To identify optimal spectral bands for bathymetric modeling, Pearso’s correlation analysis was conducted to examine the relationship between bathymetric data and spectral band reflectance. Figure 4 illustrates the correlations between transformed spectral reflectance and measured bathymetric values, using ratio, logarithmic, and first-order differential transformations, and Fig. 5 showcases the selected ten bands with the highest correlations. The analysis of original spectral reflectance (Fig. 4(a)) revealed that bands B41 (561.461 nm) to B47 (587.173 nm) were highly correlated with bathymetric data (correlation coefficients exceeding 0.9). Notably, band B46 (574.317 nm) exhibited the strongest correlation coefficient (−0.905) and served as the primary variable in both univariate and multivariate modeling. The correlation of band B45 (578.603 nm) was second, and both B45 and B46 were selected as variables for multivariate modeling (Fig. 5(a)). Further examination of band B46 using ratio transformations identified bands B37 (544.396 nm) and B39 (552.914 nm) as significantly correlated, with coefficients above 0.8 (Fig. 4(b)). The ratio of B37/B46 demonstrated the highest correlation with bathymetric data, with a coefficient of 0.817 (Fig. 5(b)), and was selected for ratio-based modeling. In contrast, the correlation patterns for logarithmic transformations mirrored those of the original spectral data, while first-order differential transformations produced substantial noise and low correlation values (Figs. 4(d) and 5(d)). As a result, these transformation methods were excluded from further consideration in modeling.

Based on the selected bands of spectral reflectance and the corresponding training groups of water depth values, the regression analysis using Eqs. (11), (12), and (13) yield.

(i) The established single-band water depth model (Fig. 6(a)) is

(11)Z=-13.685\times \mathrm{l}\mathrm{n}\left(B46-0.0048\right)-16.337,R^2=\mathrm{0.741.}

(ii) The established band-ratio water depth model (Fig. 6(b)) is

(12)Z=65.457\times \mathrm{l}\mathrm{n}\left(B37/B46\right)-8.037,R^2=\mathrm{0.797.}

(iii) The established multi-band water depth model (Fig. 6(c)) is

(13)\begin{array}{rl}Z=& -42.872\times \mathrm{l}\mathrm{n}\left(B45-0.006\right)+24.840\\ & \times \mathrm{l}\mathrm{n}\left(B46-0.0048\right)-24.852,R^2=\mathrm{0.770.}\end{array}

4.3 Results of water depth retrieval

The comparative analysis of the three water depth retrieval models, as implemented within the PIE-Hyp platform and represented by Eqs. (11), (12), and (13), is shown in Fig. 7. All models successfully replicate the overall patterns of water depth distribution in shallow marine environments, as illustrated in Figs. 7(a), 7(b), and 7(c). Additionally, all three models exhibited standard deviations within 15, as depicted in Figs. 7(d), 7(e), and 7(f). However, differences become apparent in depths less than 30 m when comparing the band-ratio model with the single-band and multi-band models (Figs. 7(g), 7(h), 7(i), 7(j), 7(k), and 7(l)). Closer to the coast, the single-band and multi-band models estimate depths ranging from 10 to 15 m, while the band-ratio model predicts shallower depths of less than 10 m (Figs. 7(g), 7(i), and 7(k)). At depths greater than 30 m, the multi-band model primarily estimates depths between 30 and 35 m, in contrast to the single-band and band-ratio models, which estimate depths of 20−25 m and 25−30 m, respectively (Figs. 7(h), 7(j), and 7(l)).

The performance of the three models was evaluated by comparing their ability to delineate areas across different water depth intervals, ranging from 10 to 60 m at 5-m increments, as shown in Fig. 8. The analysis indicates that both the single-band and multi-band models most frequently estimate water depths within the 10−15 m range, representing 22.11% and 23.10% of their respective data. These models show the least frequency in depths less than 10 m, with 0.83% for the single-band model and 1.00% for the multi-band model. In contrast, the band-ratio model shows its highest frequency of water depth estimates also in the 10−15 m range, at 17.51%. However, its lowest frequency is observed in the 55−60 m range, accounting for 0.82%. This comparative assessment highlights the distinct performance characteristics of each model across the specified depth intervals.

4.4 Accuracy evaluation

The accuracy of the developed three bathymetric inversion models was assessed using key statistical metrics, including the R², RMSE, and MRE. The results, shown in Fig. 9, indicate that both the multi-spectral and band-ratio algorithms performed better than the single-band approach in terms of predictive accuracy. Notably, the band-ratio model achieved the highest accuracy, with an R² of 0.871, the lowest MRE of 29.61%, and an RMSE of 7.756. Overall, all models yielded RMSE values below 8 m and R² values above 0.79, demonstrating their capability to provide reliable water depth estimations.

To conduct a comprehensive analysis, the MRE of each model was evaluated using water depth data from test sites, categorized into four strata: 0−5, 5−15, 15−30, and > 30 m, as shown in Table 2. The results indicate a general trend of decreasing modeling error with increasing water depth. However, the mixed theoretical and empirical models demonstrated significant MREs, particularly in the precision test samples. In the 0−5 m depth range, all models exhibited low accuracy, with average errors exceeding 50%. This could be due to nearby human activities and underwater geological factors affecting the readings. For the 5−15 m depth range, the MRE for depth estimation decreased to about 30%, a reduction of more than 40%, reflecting a notable improvement in both precision and predictive performance. Accuracy continued to improve in the 15−30 m range, with MREs stabilizing around 24%, showing a slight increase of approximately 5% in model retrieval accuracy. At depths greater than 30 m, all models performed well, with MREs averaging around 23%, indicating proficient depth estimation capabilities. Overall, the analysis suggests that the mixed theoretical and empirical models are effective for estimating water depths in areas deeper than 5 m, demonstrating their suitability for marine environments with varying depths.

The comparative analysis assesses the performance of 94 test samples across different modeling frameworks, as shown in Fig. 9. The first model, a simple univariate approach, was constructed using the spectral bands that had the highest correlation with water depth. Despite its simplicity, this model exhibited a substantial MRE of 31.37%, indicating limited accuracy. However, it performed best for depths exceeding 30 m, where it showed the lowest MRE among the models tested. The linear regression in Fig. 9(a) shows a strong coefficient of determination (R² = 0.797) for this univariate model, but there is a systematic underestimation, as most data points fall below the parity line. In contrast, a multivariate model, which requires more parameters, was approximated with a simpler bivariate model in our study. As shown in Fig. 9(b), the bivariate model outperforms the univariate one, achieving an R² of 0.831 and a more balanced distribution of residuals around the parity line, indicating improved accuracy. Future research could benefit from developing more complex multivariate models with additional predictive variables to further enhance the precision of water depth retrieval. Lastly, the band ratio model, illustrated in Fig. 9(c), achieved the highest coefficient of determination (R² = 0.871), indicating minimal differences between estimated and observed depths. This model effectively reduces errors associated with surface conditions and bottom heterogeneity, making it particularly useful in intermediate depth ranges of 15−30 m. Its performance underscores its potential for improving water depth retrieval methods in similar environments.

5 Discussion

5.1 Influence of band selections

The advantage of hyperspectral remote sensing lies in its ability to separate the electromagnetic spectrum into numerous narrow bands often ranging from tens to hundreds (Kummerow et al., 2022). This division allows for the capture of detailed spectral reflectance data, which enhances the characterization of environmental features. However, the large number of bands often leads to data that are highly correlated and redundant. To address these challenges, data reduction techniques are essential to identify and retain the most relevant spectral bands (Dai et al., 2020a). Each spectral band exhibits a different sensitivity to water depth, affecting the development and performance of bathymetric retrieval models (Kennedy et al., 2021; Roy and Das, 2022). We quantify the relationship between spectral bands and water depth using the absolute value of the Pearson correlation coefficient, with higher values indicating stronger predictive ability and greater model accuracy. In this study, we calculate the Pearson correlation coefficients for each spectral band with respect to water depth and select bands based on their highest absolute values. For the multi-band model, we incorporate additional bands that also show significant correlation with water depth. This process culminates in the development of a linear regression model that uses the reflectance of the selected bands to estimate bathymetry, improving the accuracy of water depth retrieval (Zhou et al., 2023).

To evaluate the effectiveness of the selected spectral bands in improving water depth retrieval, we employed a single-band model using three bands with strong negative correlations: B48 (−0.899), B40 (−0.897), and B39 (−0.894). Table 3 presents the regression parameters (a, b), the R², and the RMSE used for accuracy assessment. The regression analysis revealed an inverse relationship between the parameters a and b in the single-band model. Accuracy assessment showed that RMSE decreased while R² increased, indicating an inverse correlation between model accuracy and parameter variability. Moreover, the RMSE was inversely proportional to the absolute value of the correlation coefficient; as the correlation coefficient’s magnitude decreased, RMSE increased, aligning with previous theoretical findings (Niroumand-Jadidi et al., 2018). Since the correlation coefficients for bands B48, B40, and B39 are lower than that of B46, the models based on these bands exhibit reduced accuracy compared to the model using B46. This outcome highlights the importance of selecting bands with higher correlation coefficients for achieving more precise water depth retrieval.

5.2 Model reliability assessment

The theoretical framework offers the most precise and broadly applicable approach among the three main remote-sensing methods for estimating water depth (Jawak et al., 2015). However, it requires numerous parameters and involves complex calculations. On the other hand, the statistical model is easier to develop and computationally simple, but its use is limited across different coastal environments due to its lack of adaptability. The hybrid model, which combines theoretical and empirical components, reduces reliance on empirical parameters, making calculations simpler while improving accuracy in depth estimation (Kutser et al., 2020). As a result, this hybrid approach has become the preferred method for retrieving water depth information through remote sensing.

We assessed the effectiveness of commonly used hybrid theoretical-empirical models, including single-band, multi-band, and band-ratio models, as detailed in Table 4, for broader application in water depth retrieval. The single-band model integrates both physical dynamics and empirical relationships. However, its limitations include significant inaccuracies and the need for unknown coefficients, restricting its applicability primarily to clear, shallow waters. The multi-band variation, a simpler form, decreases dependence on correlation coefficients and remains less affected by changes in water type and seabed reflectance. Meanwhile, the band-ratio model effectively compensates for variations in water quality and seabed characteristics, making it robust across different environments. Comparative analysis shows that all three models perform comparably to analytical methods at depths of 0–5 m and beyond 30 m. Among these, the band-ratio model generally delivers the highest accuracy, followed by the multi-band and single-band models. Interestingly, at depths greater than 30 m, the single-band model demonstrates a MRE 10% lower than that of the band-ratio model, indicating its superior precision in deeper waters.

Parameters were obtained using a straightforward regression analysis, allowing for the subsequent estimation of water depth. While the single-band water depth retrieval model uses a simple equation with low computational demands, its practical application is limited by the complexities of aquatic environments and factors that compromise the reliability of depth measurements. Applying this model requires careful error evaluation, particularly in areas with varying water quality. Differences in water quality and seabed composition significantly affect depth estimation: the former influences the radiation attenuation coefficient, while the latter alters reflectance. To address these challenges, a multi-band ratio model, combining two single-band models, can be employed. This approach reduces the impact of variables such as solar zenith angle, tidal changes, and satellite orientation, enhancing the accuracy of depth estimation results.

5.3 Other possible influencing factors

The estimation of water depth using hyperspectral remote sensing is a complex process influenced by various factors. Key contributors to the accuracy include the sensor’s specifications, atmospheric conditions affecting radiative transfer, and the way light propagates through water (Jay et al., 2017). One major challenge is the glare effect, where the sensor captures sunlight reflecting off the ocean surface, known as specular reflection (Avrahamy et al., 2019). This reflection can dominate the signal, often due to Fresnel reflection, making accurate depth retrieval difficult. Additionally, coastal areas present unique challenges for water depth inversion. Light reflected from the seabed near shorelines is often influenced by tides and wave action, which can cause variability in the reflected signal. This effect is particularly pronounced in shallow waters, where dynamic coastal processes can significantly alter the optical properties of the water column (Russell et al., 2019).

In shallow marine environments, complex benthic dynamics arise from the interplay of biological and physical processes, leading to unique seabed reflectance characteristics (Chennu et al., 2013). For modeling purposes, the seabed was treated as a Lambertian reflector; however, elements like coral reefs that do not conform to this assumption can cause approximation errors (Minghelli-Roman and Dupouy, 2014). The accuracy of water depth retrieval is influenced mainly by two factors: the relative reflectance of the seabed and the water column above, which affects the sensitivity of spectral bands to depth; and the interaction between seabed morphology and the water’s inherent optical properties, which impacts the bands’ response to changes in these properties. To reduce the impact of seabed variations on depth estimation, optimal spectral bands and ratios were identified using the Pearson correlation coefficient. Future research should incorporate specific data on seabed types and reflectance, which could serve as prior knowledge or constraints in the model, thereby improving its accuracy. Furthermore, integrating multi-temporal and multi-source remote sensing data could enhance spatial resolution through advanced data fusion and downscaling techniques, providing a more detailed understanding of shallow sea environments (Zhang et al., 2023).

5.4 The potential applications of hyperspectral water depth retrieval

Hyperspectral remote sensing for bathymetric estimation offers a major improvement over traditional hydrographic survey methods by allowing for broad and rapid mapping of underwater topography (Gawehn et al., 2020). However, the accuracy of depth retrieval from remote sensing is still lower than that achieved with multi-beam echosounder surveys. Despite this limitation, hyperspectral remote sensing provides valuable data in shallow waters that are difficult to access and survey with conventional hydrographic techniques. In clear waters with uniform seabed reflectivity, hyperspectral remote sensing can map depths up to 30 m or more. While its depth accuracy does not yet match the precision of multi-beam sonar (Niroumand-Jadidi et al., 2018), it can still be useful for preliminary assessments of underwater features. Furthermore, remote sensing plays a crucial role in identifying submerged landscapes and detecting obstacles in areas that are challenging for direct survey methods. This makes it a valuable tool in complementing traditional approaches, particularly in complex or inaccessible environments.

The use of remote sensing technology for estimating water depth is gaining increased scholarly attention, driven by advancements in data processing and obtaining techniques (Nan et al., 2020). However, the accuracy of these remote-sensing-derived bathymetric models is often limited by dynamic marine conditions, atmospheric influences, seabed characteristics, and other environmental factors (Jay et al., 2017). Current models struggle with a high MRE exceeding 50% in shallow waters (0−5 m), indicating that the relationship between hyperspectral data and water depth is not adequately captured by simple linear regression. In coastal areas heavily influenced by human activity and complex water quality, existing models fail to fully account for the impact of suspended sediments, underwater ecosystems, and sensor characteristics, which are critical factors in signal attenuation. The variability of optical attenuation across different spectral bands and water depths significantly affects the accuracy of depth information retrieved. To improve model performance under varying turbidity conditions, segmentation methods and water quality-specific thresholds are used to reduce the impact of dissolved substances. The complexity of remote-sensing-based bathymetry requires an interdisciplinary approach that integrates knowledge from geology, optics, and marine sciences (Andréfouët and Bionaz, 2021). Addressing these challenges calls for targeted data collection and innovative methodologies.

6 Conclusions

This research addresses a critical gap in the application of hyperspectral remote sensing techniques for bathymetric retrieval, with a focus on data from the GF5-AHSI sensor aboard the Chinese remote-sensing satellite. The study introduces an innovative approach that integrates model-based selection methods and Pearson correlation analysis to identify optimal spectral bands, thereby enhancing the precision of water depth retrieval.

By developing and comparing semi-theoretical and empirical water depth retrieval models—spanning single-band, multi-band, and band-ratio methods—this study provides a comprehensive evaluation of model performance across varying depths. The results reveal significant errors in shallow waters, with inaccuracies exceeding 30% at depths between 0 and 5 m. However, the accuracy improves in deeper waters (15−30 m), where the MRE decreases to approximately 20%. The comparative assessment of the models shows that the band-ratio approach delivers the highest accuracy and reliability among the methods evaluated. In contrast, the single-band model provides the least precision overall. However, for depths exceeding 30 m, the single-band model outperforms the band-ratio approach due to its improved retrieval precision at greater depths. The sensitivity analysis of spectral reflectance revealed significant changes in reflectance values across different water depths, with slight increases observed in the near-infrared spectrum at specific points. These variations are likely influenced by differences in sediment concentration within the water column and disturbances on the water surface.

For future research in hyperspectral remote-sensing-based bathymetric retrieval, efforts should focus on enhancing the understanding of the fundamental processes involved. This includes examining the impact of suspended particulates, refining data to minimize noise, and prioritizing key information. Such improvements are essential for achieving greater accuracy in water depth retrieval, especially in the shallow waters.

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