Optimization and Evaluation of Widely-Used Total Suspended Matter Concentration Retrieval Methods for ZY1-02D’s AHSI Imagery

: Total suspended matter concentration ( C TSM ) is an important parameter in aquatic ecosystem studies. Compared with multispectral satellite images, the Advanced Hyperspectral Imager (AHSI) carried by the ZY1-02D satellite can capture finer spectral features, and the potential for C TSM retrieval is enormous. In this study, we selected seven typical Chinese inland water bodies as the study areas, and recalibrated and validated 11 empirical models and two semi-analytical models for C TSM retrieval using the AHSI data. The results showed that the semi-analytical algorithm based on the 697 nm AHSI-band achieved the highest retrieval accuracy ( R 2 = 0.88, average unbiased relative error = 34.43%). This is because the remote sensing reﬂectance at 697 nm was strongly inﬂuenced by C TSM , and the AHSI image spectra were in good agreement with the in-situ spectra. Although further validation is still needed in highly turbid waters, this study shows that AHSI images from the ZY1-02D satellite are well suited for C TSM retrieval in inland waters. Methodology, Formal analysis, P.Z.; Funding acquisition, Resources, Writing—original P.Z.; Writing—review and Y.L.


Introduction
More than 40% of the world's population lives in coastal areas or along rivers and lakes [1], while the water quality of numerous water bodies has deteriorated in recent decades owing to intensified human activities. In particular, the widespread problem of microplastics in water bodies poses a potential threat to the health of people [2]. Inland waters are more fragile than marine ecosystems because of their more confined nature and lower ecological stability [3]. Total suspended matter is a widely used water quality parameter in aquatic environmental studies, which mainly refers to solids suspended in water bodies, including inorganic substances that are insoluble in water, organic substances, sediment, and microorganisms [4]. The presence of suspended matter alters the distribution of light intensity in the water body, affecting the growth of aquatic vegetation and thus the distribution of primary productivity and biomass in the water body [5].
Water quality monitoring based on in-situ measurements usually only represents the status of stations. It is costly and difficult to provide continuous large-scale monitoring over time. With the rapid development of remote sensing technology, large-scale and long timeseries remote sensing products are increasingly being used [6,7]. Satellite image-based C TSM retrieval can effectively overcome the shortcomings of traditional methods and is being Table 1. Specifications of commonly used satellite-based hyperspectral sensors [27][28][29].

Sensor Spectral Range (nm) Spectral Bands Spectral Resolution (nm) Spatial Resolution (m) Swath Width (km)
Hyperion 357-2576 220 10  The main purpose of this study is to test the capability of the ZY1-02D AHSI for total suspended matter retrieval in inland waters, and thereby identify the optimal model that can be applied to AHSI data of ZY1-02D. Section 2 describes the data and retrieval strategy, Section 3 the data processing methods and alternative models, and Section 4 the calibration and validation results of the selected model. An experimental discussion is presented in Section 5 and conclusions are drawn in Section 6.

R rs and C TSM Field Measurements
From May 2019 to July 2021, 9 field experiments were carried out in 7 inland lakes and reservoirs of China. Details of the study areas and measurement information are given in Table 2. Specifically, 7 field experiments conducted in 2019 include a total of 97 sets that have C TSM of 2.6-49 mg/L. In-situ data of these 97 sampling sites were used as calibration sets. Three field experiments conducted in 2020 and 2021 include 37 sampling sites in Taihu Lake, Yuqiao Reservoir, and Qinghai Lake, with C TSM ranging from 1.9 to 53.5 mg/L. Field measurements at these 37 sampling sites were used as validation sets. As one of the five major freshwater lakes in China, Taihu Lake has a water area of about 2338 km 2 . Nevertheless, it is a typical shallow lake, with an average water depth of about 1.9 m [30]. Baiyangdian Lake is an important natural lake in northern China, and located in the middle of the Daqing River Basin. It has a water area of about 366 km 2 and an average depth of about 3.6 m. Qinghai Lake, the largest inland lake in China, is located in the northeastern part of the Tibetan Plateau, with an area of approximately 4553 km 2 . Yuqiao Reservoir, also known as Cuiping Lake, is 15 km long from east to west and 5 km wide from north to south, with a total watershed area of approximately 2060 km 2 with a water depth of approximately 4.7 m [31]. Other reservoirs can be found in northern China, with water surface areas ranging from tens to hundreds of square kilometers, and their water quality is generally good. The locations and sample points of the 3 study areas which have AHSI concurrent images are shown in Figure 1.
The main indicators collected were C TSM and in-situ spectra. C TSM was measured by the drying and weighing method. After obtaining surface water samples in the field, the samples were brought back to the laboratory within 24 h. In the laboratory, water samples were filtered using a 0.45 µm pore size filter membrane and dried to a constant mass at 103-105 • C. Repeated drying, cooling, and weighing was done until the difference between two weighing results was less than or equal to 0.4 mg/L [32]. The sampling time and the statistical information of C TSM are shown in Table 2. While collecting water samples, in-situ spectra were collected using an ASD Field Spec Pro spectrometer according to the above-water method [33]. Remote sensing reflectance spectra were calculated by measuring the reference plate radiance (L p (λ)), sky radiance (L sky λ), and water surface radiance (L u λ). For L u λ measurements, the viewing zenith angle was 40 • downward, and the azimuth angle was 135 • away from the sun azimuth. The viewing zenith angle was 40 • upward for L sky λ measurements, and the azimuth angle was the same as for L u λ measurements. The reference plate radiance was measured by aiming at the center of the reference plate vertically downward. For the water surface radiance measurements at each sampling site, we performed 10 replicate measurements and checked the results. Anomalous spectra caused by random solar flares may be present in the measured result. These anomalous results were discarded, and the remaining spectra were averaged.
The above-water remote sensing reflectance was calculated by the following equation: where ρ p is the standard panel reflectance calibrated in the laboratory and the ρ sky is the air-water interface skylight reflectance. As shown in Table 2, a total of 134 sets of data were obtained, including R rs and C TSM . Among them, 97 of the sampling points with earlier sampling times had no concurrent images, and they only had the in-situ measured R rs and C TSM . So, they were used for the original calibration of the C TSM estimation model. The in-situ measured R rs of these sampling points are shown in Figure 2. In addition to this, there are 37 sampling points which have AHSI concurrent images and their locations are shown in Figure 1. The in-situ R rs and C TSM of these points were used to validate the calibrated model. In-situ measured R rs for these sampling points are shown in Figure 3.

Concurrent ZY1-02D Image Acquisition
The ZY1-02D satellite AHSI images were selected based on the field measurement time ±1 d, and stable meteorological conditions. Specifically, all in-situ measurements of Taihu Lake and Yuqiao Reservoir were measured within 3 h of the ZY1-02D satellite overpasses. Images of Qinghai Lake were acquired 1 day after the in-situ measurements. Since Qinghai Lake is a deep lake (average water depth of 21 m), and the meteorological condition is stable during the in-situ measurements and satellite image acquisition, the C TSM is relatively stable in this study region. Therefore, the in-situ measurements in Qinghai Lake are counted as match-ups despite the 1-day difference between them. All images were acquired around 11:00 a.m. local time with less than 10% cloud coverage. To match the image R rs with in-situ R rs , a 3 × 3 pixel window centered at the posistion of the sampling points was used. If the coefficient of variation (i.e., standard deviation/mean) was less than 0.40 in the window, the central pixel of the 3 × 3 pixel window was selected as a match-up [34].
AHSI concurrent images R rs of 37 validation points in Taihu Lake, Yuqiao Reservoir and Qinghai Lake were used to verify the accuracy of AHSI image retrieval C TSM .

AHSI Band R rs Simulations
For hyperspectral sensors with narrow band widths, the spectral response function (SRF) in each band is usually described using the Gaussian function [35,36] as follows: where λ i is the central wavelength of each band, ∆λ i is the FWHM of each band. For AHSI sensors, VNIR and SWIR have FWHMs of 8.76 and 16.26 nm, respectively. Based on SRF, the in-situ R rs can be converted to AHSI band-equivalent R rs using the following equation: where f i (λ) is the SRF of ith band, λ max and λ min represent the maximum and minimum wavelengths in this band, respectively. According to Equation (3), the conversion of in-situ R rs to AHSI-band R rs can be achieved.

C TSM Model Development Using the In-Situ Dataset
Two methods are usually used to estimate C TSM using remote sensing reflectance: 1. The relationship between R rs and C TSM , which is an empirical algorithm. They are classified into single-band and multi-band algorithms; 2. The backscatter coefficient (b bp ) can be estimated by remote sensing reflectance, and then the relationship between b bp and C TSM can be established, which is a semi-analytical method. The typical models of the different algorithms are presented below.

Empirical Algorithm
• Single-band empirical models As the C TSM in water increased, the reflectance of the water in the VNIR band also increased gradually. The reflection peaks of the spectra of water with different C TSM appeared at 580-700 nm. Among the related studies, red-band retrieval has been the most frequently used [7][8][9]. However, when the C TSM is excessively high, the reflectance of the visible region tends to saturate [37]. To avoid this phenomenon, there are models that change the retrieval wavelength to the NIR band [14,17].

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Multi-band empirical models With increasing C TSM in water, the wavelength of the reflection peak shifts towards the long-wave direction. Therefore, the band-ratio model can be established using the reflection peak of the red-NIR bands and the low reflectance of the blue-green bands. Because of the strong absorption at 940 nm and 1130 nm, the choice of reflection peak wavelength is mostly <850 nm, such as in Doxaran_02 [37], He_13 [13], and Hou_17 [38].
By constructing spectral feature parameters, the absorption and reflection characteristics of the spectral profile can be effectively highlighted for accurate C TSM retrieval. Spectral characteristic parameters are available in various forms. One of the typical combinations is the spectral absorption characteristics obtained by the spectral absorption index or the spectral envelope method, also known as the baseline model, such as in Kuster_16 [39] and Liu_18 [40]. In addition, the three-band model (Zhang_10 [10]) and the normalized model (Zhang_10_1 [41]) have also been developed and are applicable for different water bodies.
All the empirical models and their utilized bands or spectral indices are listed in Table 3. Table 3. Wavelength or spectral combinations used in empirical methods.

Model Type Model Name Band or Spectral Index Source
Single-band model R rs (705) [14] Multi-bands models Doxaran_02

Semi-Analytical Algorithm
The backscattering coefficient (b bp ) at specific wavelengths is closely linked to C TSM [15]. At present, the b bp of water bodies is mostly estimated based on semi-analytical methods, which are more stable than empirical models owing to the incorporation of physical-optical principles [42]. Therefore, the method of estimating C TSM based on b bp has higher stability and applicability. In this study, we consider 2 types of semi-analytic algorithms: QAAbased and Nechad C TSM retrieval methods. They were applied to the ZY1-02D AHSI data, and the accuracies were evaluated.

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QAA-based C TSM retrieval method There are two main steps in this method: 1. Calculate b bp using the QAA; and 2. build an empirical model between b bp and C TSM .
In this study, we calculated b bp using two original QAA models (QAA_V5 and QAA_V6) and three improved models (Le_09 [43], Mishra_14 [44], and Jiang_21 [45]). Among them, the reference wavelength of QAA_V5 is 555 nm [46], whereas the reference wavelength of QAA_V6 is shifted to 670 nm to adapt to highly turbid or eutrophic waters [47]. The steps involved in the two types of QAA methods are listed in Table 4. In addition, other scholars have modified the QAA model to adapt to inland water bodies with complex optical properties, such as adjusting the empirical formula [43,44,48] and developing a new semi-analytical algorithm to replace the original empirical algorithm part [49]. Table 4. Steps of the two original types of quasi-analytical algorithm (QAA) method. Step Property Table 4, r rs (λ) is the remote sensing reflectance below the water surface, a(λ) is the total absorption coefficient, and b bw (λ) is the backward scattering coefficient of pure water. The major difference between QAA_V5 and QAA_V6 is that a(λ) is calculated differently. The b bp (λ) calculated by the algorithm was then linked to the C TSM .
Linear models were used to retrieve the C TSM because of the linear relationship between b bp and C TSM: where a and b are the coefficients of the linear model obtained by calibrating the calibration dataset. Because the Jiang_21 model was obtained from a calibration dataset with a wider C TSM range [45], the origin linear model was used directly in this study and was not recalibrated.

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Nechad retrieval method Nechad_10 retrieval model is a simplified model based on reflectance, which links single-band reflectance to TSM concentration. It has been successfully applied to watercolor satellite sensors such as SeaWiFS and MODIS [15], its main formulas are as follows: where A = a np /b * bp , a np represents the non-particulate absorption and b * bp represents the constant TSM-specific particulate backscatter. A ρ and B ρ were obtained by nonlinear fitting and reparametrized based on the calibration dataset used in this study. C = b * bp /a * p , a * p represents the constant TSM-specific particulate absorption coefficient, which is determined by the IOPs and is independent of R rs . therefore, the Nechad rated C ρ values were used directly [15].

Calibration and Validation
First, the parameters of the empirical and semi-analytical models were calibrated based on the in-situ R rs and in-situ C TSM from 97 calibration datasets. Second, the calibrated models were validated using in-situ R rs and in-situ C TSM from 37 validation datasets. Three indicators, i.e., the coefficient of determination (R 2 ), root mean square error (RMSE), and average unbiased relative error (AURE), were used for accuracy analysis and were calculated as follows: where n is the number of samples,ŷ i is the model estimated value, y i is the in-situ measurement value, and y is the mean value of the in-situ measurements.

C TSM Retrieval Based on AHSI Images
After testing the empirical and semi-analytical models based on in-situ data, to retrieve the C TSM from AHSI images, we first performed atmospheric correction of the images and extracted the water region. Then, the best empirical and semi-analytical models were applied to the AHSI images, and finally the accuracy evaluation of the image retrieval results was achieved by the in-situ measured C TSM .

AHSI Image Preprocessing
Pre-processing of the AHSI images is a prerequisite for estimating the total suspended matter concentration, including atmospheric correction and water body extent extraction. First, the Digital Number (DN) values were converted into apparent radiances using radiometric calibration coefficients. Second, atmospheric correction was performed using the FLAASH atmospheric correction tool. In the FLAASH module, most of the parameters were set according to the official documentation [50]. For the ZY1-02D hyperspectral data, the sensor altitude was set to 778 km, and we chose the 940 nm water vapor retrieval band.
Using the ZY1-02D surface reflectance (ρ) images retrieved from FLAASH, the automated water extraction index (AWEI) was calculated as follows [51]: The delineation of water bodies was then achieved using the OTSU method [52] based on the AWEI. To correct the skylight effect and retrieve remote sensing reflectance from surface reflectance images, an image-based method for remote sensing reflectance estimation [53] was applied as follows: where R rs (λ) represents the remote sensing reflectance of the image; ρ(λ) represents the surface reflectance; and min(ρ N IR : ρ SW IR ) represents the minimum surface reflectance in the NIR and SWIR bands, respectively, where ρ N IR and ρ SW IR use the mean ρ in the AHSI bands of 720-730 nm and 1530-1630 nm, respectively.

AHSI-Retrieved C TSM Accuracy Assessment
After the consistency check between AHSI image R rs and in-situ R rs , the models were validated using the AHSI image-derived R rs from the validation dataset. Then, models with high accuracy were applied to AHSI images. It should be noted that in-situ R rs was converted to band-equivalent R rs in the AHSI bands by the method in Section 3.1.
For the accuracy analysis of the satellite-ground spectral consistency, the spectral angle cosine was calculated as follows: where n is the number of samples and y i j andŷ i j are the in-situ R rs and AHSI image R rs of samples i and band j, respectively.
Based on the pre-processed AHSI images, C TSM was retrieved using the best empirical and semi-analytical method and 37 matched points were used to evaluate the accuracy of the image retrieval C TSM using R 2 , RMSE, and AURE.

Accuracy Assessment of ZY1-02D Image Atmospheric Correction
The accuracy of the image-derived remote sensing reflectance affected the accuracy of the estimated C TSM . Therefore, the accuracy evaluation of ZY1-02D image-derived R rs was conducted for the main bands utilized in the C TSM retrieval models using R 2 and AURE. The results are shown in Table 5. Table 5. Accuracy analysis of the ZY1-02D image-derived R rs . Among the major bands utilized by the models, 551 nm had the lowest AURE of 18.84%, which was the band with the highest agreement between image remote sensing reflectance and in-situ remote sensing reflectance. As can be seen from Figures 2 and 3, the energies of 551 and 560 nm were higher than that of other wavelengths; therefore, they were relatively less affected by noise. Similarly, the red bands of 645-700 nm were also relatively high in energy and received relatively little noise impact, with AUREs of approximately 30%. It is known from the remote sensing principle that the shorter the wavelength, the weaker the penetration ability, while the atmosphere has a strong scattering effect in the blue band. Therefore, the consistency of the 490 nm satellite spectrum was poor compared with the red and green bands; however, the AURE was still controlled at 32.60%. The NIR band after 750 nm was lower in energy, and there was only a very small reflection peak at 800 nm, which was more affected by noise; therefore, its relative error was also relatively high.

ZY1-02D Bands (nm) R rs (490) R rs (551) R rs (560) R rs (645) R rs (697) R rs (748) R rs (774) R rs (800) R rs (816) R rs (842)
Subsequently, the spectral angle cosine was calculated separately for the satelliteground spectra of each study area to determine the spectral consistency in different study areas, as shown in Table 6. The mean values of the spectral angle cosine in all three regions were >0.9, indicating that the AHSI image spectra were in good agreement with the in-situ spectra.

C TSM Estimation from In-Situ Measurements by Empirical Models
First, we tested 11 empirical models, which were divided into two categories: Singleband and multi-bands models. Among the empirical models, the selected bands for each model were adapted according to the AHSI bands. For the model calibration, we compared the model equation of the original literature, and four types of fitting functions: linear, exponential, logarithmic, and power functions. The model with the highest R 2 was chosen as the best fitting model. In addition, the fitting function should be monotonous to avoid estimation anomalies. The calibration and validation results of the models are presented in Table 7 and Figure 4. In the empirical models, the calibration of the single-band model based on the NIR band after 700 nm was generally good, with R 2 > 0.85. Among the multi-band models, the baseline model was generally better; the Kuster_16_2 model (R 2 = 0.83) was the best calibrated multiband model. The results of the other multiband models were generally lower.
From the validation results, the Zhang_10 ratio model had the best validation results, with the lowest AURE of 19.08%. The single-band model was also generally good, with a validation AURE of approximately 20%. Among the multi-band models, Kuster_16 showed better results on the validation set, with AURE < 30%, whereas the validation results of the Liu_18 model were poor and not applicable to the estimation of C TSM in inland waters. The ratio model still performed poorly in the validation set. Determining the optimal empirical model applicable to AHSI images requires further validation.

C TSM Estimation from In-Situ Measurements by Semi-Analytical Models
b bp values were calculated using QAA and its improved models for indirect estimation of the total suspended matter concentration. The Jiang_21 model established the relationship between the b bp and C TSM over a wider range of C TSM . Therefore, the parameters were not re-rated. Other models re-rated the relationship between b bp and C TSM based on calibrated datasets to enable the estimation of C TSM . The Nechad_10 model showed the best calibration results at 697 nm with parameters A ρ and B ρ : 934.09 (g/m 3 ) and 4.39 (g/m 3 ), respectively. C TSM was then retrieved based on image-derived R rs using various semianalytical models. The calibration and validation results of C TSM estimated on the ZY1-02D match-ups are shown in Table 8 and Figure 5.
In the QAA-based C TSM retrieval method, even though the Le_09 and Mishra_14 models achieved the highest R 2 in the calibration dataset, QAA_v5 achieved the optimal performance in the validation dataset. This was mainly due to the utilization of the 551 nm band, for which the image-derived R rs was reasonably accurate.
The accuracy of the Nechad_10 model gradually improved as the wavelength shifted toward the long wave direction, and the highest validation accuracy was achieved at 697 nm. Generally, the difference in the C TSM estimation accuracy between the two types of semi-analytical models was insignificant.

C TSM Estimation from AHSI Images
To investigate the applicability of different models to satellite images, optimal singleband and multi-band empirical models, the QAA_V5 based model, and Nechad_10 (697 nm) model were applied to the image-derived R rs of match-ups, and the validation accuracy results are shown in Table 9. The best results are shown in Figure 6. Table 9. Validation results of the best C TSM retrieval models based on the AHSI images R rs . Optimal results are shown in bold. Based on the Nechad_10 (697 nm) model, the total suspended matter concentration distributions were produced for the three study areas (Figure 7). The overall trend of C TSM in Taihu Lake decreased from northwest to southeast, while most rivers entering the lake are located along the northwestern coast of Taihu Lake. The confluence of the rivers increases the movement of the lake, resulting in higher C TSM at the northwest of Taihu Lake, while the central and eastern parts are less affected by this trend [41]. The C TSM in Yuqiao Reservoir did not vary considerably, with low C TSM values in the center of the reservoir and high C TSM values along the northern coast due to human activities [31]. The highest C TSM existed in the eastern part of the reservoir, where the Lin River entered the lake, reaching >13 mg/L. Due to the limited coverage of the AHSI image, only the C TSM in the central region of Qinghai Lake was estimated. The overall C TSM in Qinghai Lake was very low, mostly approximately 3 mg/L. The suspended matter concentration was low in the middle of the lake, and showed an increasing trend from the center of the lake to the lake shore.

Evaluation of C TSM Estimation Methods for AHSI Images
Based on calibration and validation results (Table 9), the final model chosen in this study was the Nechad_10(697) model, which achieved the highest accuracy among all the Nechad_10 models with different bands. As revealed by the in-situ C TSM estimation results in Table 8, the AURE brought by the Nechad_10(697) is 28.92% (Figure 5b). Considering the uncertainties in AHSI image-derived R rs , we compared the image-derived C TSM with that estimated based on in-situ R rs . The corresponding results are shown in Figure 8, which suggests the error brought by the image-derived R rs uncertainty is 13.64%. Figure 8. Comparison of C TSM validation results from in-situ R rs retrieval and AHSI R rs retrieval based on the Nechad_10(697) model.
In addition, Figure 5b demonstrates the accuracy of C TSM retrieval based on in-situ measure R rs . Most of the validation points are distributed along the 1:1 line. B ρ in the Nechad_10(697) model is represented as the intercept of the fitting line, as C TSM is equal to B ρ when R rs is zero. Therefore, the retrieved C TSM is more sensitive to the parameter B ρ when the C TSM is low. This results in the Nechad_10(697) model overestimating the C TSM for Qinghai Lake as its C TSM is generally lower than B ρ , but a good retrieval for Yuqiao Reservoir and Taihu Lake. Therefore, the Nechad_10(697) model may bring relatively large errors for C TSM retrieval in clear water bodies.
The C TSM retrieval results of AHSI images showed an overall underestimation in the Taihu Lake region. According to the studies of Doxaran et al. [37] and Petus et al. [9], spectral saturation is more likely to occur when using wavelengths less than 600 nm to estimate C TSM in regions with greater than 100 mg/L. However, the wavelengths and C TSM chosen in this manuscript are not in this range. The high accuracy of image remote sensing reflectance is a prerequisite for accurate estimation of C TSM . In the experiment, the AURE between the in-situ R rs and the AHSI image R rs at 697 nm reached 29.17% (Figure 9). When these two types of data were applied to TSM concentration estimation, it caused a 13.64% difference in the AURE of the C TSM retrieval results. Based on the scatterplot of the spectrum at 697 nm, the underestimation is more likely due to the AHSI image's uncertainties in atmospheric correction. Overall, the Nechad_10 (697 nm) model provided the best prediction for AHSI images in the validation of Taihu Lake, Yuqiao Reservoir, and Qinghai Lake. However, during the model calibration and validation, most sampling sites had a C TSM of less than 50 mg/L. Thus, the calibrated model parameters may not be applicable in regions with higher C TSM . Although these sampling sites were located in lakes and reservoirs of varying sizes in China, the representativeness of the sampling areas is still limited. For example, the salt lakes in the Qinghai-Tibet Plateau or the lakes in the Mongolian Plateau were not included [54]. Studies have shown that saline lakes tend to have a higher C TSM than freshwater lakes [55]. Saline lakes have longer water exchange times, and their absorption characteristics may be significantly altered in the process of microbial degradation. Therefore, retrieval models based on freshwater lakes may not be applicable in these areas. To sum up, when applying AHSI images to retrieve C TSM , the Nechad model may be unable to achieve optimal performance in all inland waterbodies. More in-situ measurements are needed for further development of the C TSM retrieval model to be applied on ZY1-02D AHSI images.

Comparison of C TSM Retrieval with Multispectral Sensors
To verify that AHSI has advantages for C TSM retrieval compared with multispectral sensors, a comparison was made with estimated C TSM based on band R rs of Landsat-8 OLI, Sentinel-2 MSI, and Sentinel-3 OLCI. Since no images of Landsat-8, Sentinel-2, or Sentinel-3 were acquired for the study areas on the same date of the ZY1-02D overpasses, this comparison was conducted using in-situ measured R rs .
First, band R rs of the Landsat-8 OLI, Sentinel-2 MSI, and Sentinel-3 OLCI were simulated using their respective SRFs and the in-situ measured R rs . Second, parameters in the optimal empirical and semi-analytical models (i.e., the Zhang_09 model and the Nechad_10 model) were recalibrated based on the calibration dataset of the simulated band R rs . The same as in Sections 4.2 and 4.3, the 97 and 37 datasets were used for model calibration and validation, respectively. Third, simulated bands of R rs of the 37 datasets were then respectively applied to Zhang_09 and Nechad_10 models for C TSM estimation. Finally, accuracy analysis was conducted for estimated C TSM using the simulated band R rs of these multispectral sensors, and then compared with the AHSI results in Tables 7 and 8.
In terms of the Zhang_09 model, Sentinel-2 MSI acquired the best performance among the three multispectral sensors. Specifically, the 783 nm band of MSI was used and achieved an AURE of 21.58%, which is slightly higher than the AURE of AHSI (21.48%). For the Nechad_10 models established on band R rs of the multispectral sensors, the highest validation accuracy was also obtained by Sentinel-2 MSI with an AURE of 31.17%, which is also greater than that of AHSI (28.92%). This indicates that the AHSI's narrow bands can help to improve the accuracy of C TSM retrieval models.

Conclusions
The new-generation hyperspectral imaging spectrometer AHSI onboard the ZY1-02D satellite has continuous narrow spectral bands of 400-2500 nm, and can capture fine spectral features, thereby showing great potential for inland water C TSM retrieval. In this study, we recalibrated 13 widely used empirical and semi-analytical C TSM retrieval models using in-situ AHSI equivalent spectra of six typical inland water bodies in China. Validations based on in-situ spectra showed that the Zhang_10 model in the empirical model achieved the lowest AURE, (i.e., 19.08%). Two semi-analytical models established with the green and red bands, the QAA_V5-based model and the Nechad_10(697) model, had similar accuracy with AUREs of 25.96% and 28.92%, respectively. In terms of the validation based on the AHSI image-derived R rs of 36 match-ups, Nechad_10(697) achieved the best retrieval accuracy (AURE of 34.43%). This is owing to the robustness of the model, as well as the highly accurate AHSI band R rs at 697 nm.
Overall, the spectral and spatial resolution of ZY1-02D AHSI images makes it a useful data source for C TSM retrieval of inland water bodies. With the advancement of atmospheric correction accuracy and model optimization based on a larger range of in-situ data, the accuracy of C TSM retrieval based on ZY1-02D AHSI images will be further improved.