Abstract
The suspended sediment concentration （SSC） is an extremely important property for water monitoring. Since machine learning technology has been successfully applied in many domains， we combined the strengths of empirical algorithms and the artificial neural network （ANN） to further improve remote sensing retrieval results. In this study， the neural network calibrator （NNC） based on ANN was proposed to secondarily correct the empirical coarse results from empirical algorithms and generate fine results. A specialized regularization term has been employed in order to prevent overfitting problem in case of the small dataset. Based on the Gaofen-5 （GF-5） hyperspectral remote sensing data and the concurrently collected SSC field measurements in the Yangtze estuarine and coastal waters， we systematically investigated 4 empirical baseline models and evaluated the improvement of accuracy after the calibration of NNC. Two typical applications of NNC models consisting baseline model calibration and temporal calibration have been tested on each baseline models. In both applications， results showed that the calibrated D’Sa model is of highest accuracy. By employing the baseline model calibration， the root mean square error （RMSE） decreased from 0.1495 g/L to 0.1436 g/L， the mean absolute percentage error （MAPE） decreased from 0.7821 to 0.7580 and the coefficient of determination （
Due to the optical reflectance， scattering and absorption of different substances， distinct optical properties of the surface reflectance have the great capabilities of extracting the information of the water quality parameter
The suspended sediment concentration （SSC） is an extremely important property for water monitoring， which is the consequence of aquatic degradation and soil erosion for deforestation and urbanization. The SSC is typically defined as the total concentration （g/L or mg/L） of both organic and inorganic matter suspended in the water because of the turbulenc
Recently， with the improvement of computational power and the development of machine learning technology， rather complex WQP retrieval problems can be solved. The artificial intelligence technology holds the advantage of retrieving different water parameters based on a single machine learning algorithm. Plenty of implementations of machine learning algorithms such as multilinear regressio
In recent years， many new satellites equipped with advanced imagers， which can obtain increasing spatial coverage， spectral resolution and spectral range， have been launched for general or specific purpose
In this study， we systematically investigated the SSC retrieval in the Yangtze estuarine and coastal waters by implementing several empirical baseline models based on the GF-5 hyperspectral images and SSC field measurements collected simultaneously. A neural network calibrator （NNC） for double calibration was proposed to combine the advantages of ANN and the traditional empirical algorithms. This combination can compensate the inherent errors of the empirical models and reduce the data that ANN requires. In order to prevent the overfitting problem， an identity function was pretrained and a specialized regularization term was employed. Two typical applications of the NNC model including baseline model calibration and temporal calibration have been investigated based on 4 baseline algorithms. With the small size of dataset， a moderate improvement of accuracy has been achieved in both applications. Finally， the entire hyperspectral images on target date were processed using the algorithms with the highest accuracy to analyze the distribution of SSC and finish the reality check. This paper provides a universal secondary calibration method based on ANN to minimize the inherent errors of baseline models.
The Yangtze Estuary is selected as the area to investigate SSC retrieval algorithms. The Yangtze River， the longest river in Euro-Asian continent， rises in the Tibetan Plateau， flows generally 6300 km to the East China Sea and generates the Yangtze Estuary. The prosperous Yangtze Estuary， the geographically largest， most densely populated and industrialized area of China， plays an important role in geochemical cycles for a considerable amount of sediment suspended in the Yangtze River. The suspended sediment load per year from the Yangtze River reaches approximately 480 million tons and nearly 40% of the load is deposited in the Yangtze Estuary making it an extremely highly turbid regio
The Yangtze Estuary starts from Xuliujing and ends at the East China Sea， presenting a “three-order bifurcation and four outlets into the sea” pattern. The Yangtze Estuary is firstly divided by the Chongming Island and Hengsha Island into the North and the South Branch. Then the South Branch is secondly separated by Changxing Island and Hengsha Island into the North and South Channel. Finally， the South Channel is split into the North Passage and the South Passage by Jiuduansha wetlan
Fig. 1 Locations of 14 SSC field measurements on March 27 （blue）， May 24 （brown） and 31 October （black） 2019 near the Yangtze estuarine and coastal waters. The stars and diamonds represent the field measurements collected by the buoy stations and ships， respectively
图1 长江河口卫星地面SSC同步实测位置示意图
GF-5 satellite， launched on May 9 2018， denotes a polar-orbiting satellite of a series of China High-resolution Earth Observation System （CHEOS） satellites of the China National Space Administration， which has taken an AHSI designed and developed by Shanghai Institute of Technical Physics （SITP）， Chinese Academy of Science
The space-borne hyperspectral images were preprocessed in ENVI software as follows： orthorectification， radiometric calibration， atmospheric correction， masking and water extractio
The GF-5 hyperspectral images contain the necessary information， i.e.， the Rational Polynomial Coefficients （RPCs）， to complete the photogrammetric processing. The ENVI RPC Orthorectification tools use RPC information and a high-resolution digital elevation model （DEM） to create a geometrically corrected image.
The conversion from the quantized DN of raw imagery into at-aperture radiance （） is a linear transformation described in
| . | （1） |
The next step is atmospheric correction which removes or decreases the influence of the atmospheric scattering， absorption and reflection and translates the at-aperture radiance to the surface reflectance signatur
Open water body can be identified via the Normalized Difference Water Index （NDWI） method， as in
| ， | （2） |
where Green and NIR represent the surface reflectance of green and near-infrared （NIR） bands， respectively. In our experiment， wavelengths of 895 and 565 nm were selected as the NIR and green bands respectively by observing and comparing the surface reflectance curves of water body with those of other terrain types.
Based on the preprocessed AHSI data and field measurements， the entire procedures of the SSC retrieval are shown in
Fig. 2 Flow diagram for the entire SSC retrieval process.
图2 SSC反演流程图
There are generally three approaches for quantitative remote sensing of WQPs： the empirical， analytical and semi-analytical approache
| ， | （3） |
where A and B represent the fitting coefficients.
Nechad et al. presented that the single band model can provide a robust SSC retrieval accuracy for case II turbid waters based on appropriate band selection around 700 nm. The recommended linear form of this algorithm is as follow
| ， | （4） |
where Best Band denotes the band selected using exhaustive search method. In order to translate this algorithm from MERIS， MODIS and SeaWIFS sensors to GF-5 AHSI， we tested entire 48 bands from 600 - 900 nm to locate the Best Band.
Similar to the Nechad model， Ruhl et al. derived and tested a single band exponential algorithm measured in the very turbid San Francisco Bay， Californi
| . | （5） |
In this research， the algorithm was built based on field measurements collected from 1994 to 1998 with SSC values ranging from 0 to over 400 mg/L. This algorithm obtained
Considering the model developed by Loisel et al. in the highly turbid Mekong River Delta with SSC maximum values over 5000 mg/L， three bands （489， 557 and 668 nm） are utilized here to adapt to the GF-5 AHS
| ， | （6） |
where A， B and C are the fitting parameters.
Our intuition of designing NNC is combining the complementary advantages between empirical models and ANN. Compared to empirical models which lack certain complex nonlinear features， NNC obtains the great capability of the ANN in extracting potential features and generating highly complex nonlinear functions. However， the ANN model requires a large dataset to prevent overfitting problem， which is hard to be satisfied in the field of remote sensing. In order to prevent the overfitting problem， the simple empirical models with just a few parameters can help ANN to reduce the required parameter number. By using transfer learning， our ANN is first trained to learn an identity function， aiming at learning the hypothesis of baseline models which require fewer parameters. Following this intuition， we proposed the NNC which takes the coarse results of baseline models as input and generate the calibrated fine results.
Usually， the ANN model consists of a collection of the connected neurons （or nodes） and corresponding weights assigned with links in the multilayer structure which typically includes an input layer， one or more hidden layers and an output layer. In this work， we aim to secondarily calibrate the baseline SSC results and generate more precise results. In detail， the input of ANN is one baseline retrieval result and the output takes the corresponding field measurement as the label. Thus， a classical three-layer feed forward network with one node in the input layer and one node in the output layer was employed to update each input to a better output. Further， the number of nodes in the hidden layer should be small in order to reduce network parameters and prevent the overfitting problem. In our experiment， a hidden layer containing 10 nodes was selected for the small size of parameters and enough nonlinear expression ability. Finally， a sigmoid function was added after the output layer for activation. Below， we formulate the general form of ANN. In the feed forward process of prediction， the node vector of the former layer is multiplied with corresponding network parameters， added to a bias and then activated by the sigmoid function to obtain the node vector of the latter layer， as follows：
| ， | （7） |
| ， | （8） |
| ， | （9） |
where is the sigmoid function， is the activated node vector of layer l， is the network parameter matrix from layer l to （l+1）， is a bias value from layer l to （l+1） and is the hypothesis value of the output layer with x being the input value. Specifically， given Sl nodes in the layer l， the shape of is and the shape of is .
The cost function （or loss） describes the error between the prediction values and the ground truth. The back propagation （BP） algorithm has been employed to iteratively minimize the cost function and complete the training process. Furthermore， we developed a distinct cost function with the purpose of optimizing the baseline model accuracy. The basic cost function is shown in
| ， | （10） |
where N represents the number of training data， is the hypothesis values in the output layer， x is the baseline predictions in the input layer and y is the values of the field measurements. The regularization term is often used to penalize network parameters and improve the generalization ability of the ANN model. Here， a specialized regularization term is added to the cost function：
| ， | (11) |
where λ is the regularization hyperparameter controlling the degree of penalty， L is the layer number of the input and hidden layers， is the number of nodes in the layer l and represents the network parameter linking the layer l node p to the layer （l+1） node j. An extra network based on identity function， i.e. inputs equal to outputs， was pre-trained to obtain the initial parameters which provide the initial hypothesis based on baseline models to guarantee accuracy improvement after the secondary calibration.
A systematical investigation of two typical applications of NNC including baseline model calibration and temporal calibration has been presented. As for the baseline model calibration， aiming to compensate the inherent errors of the baseline models， the field measurements from 31 October 2019 were used both for fitting the baseline model and the secondary calibration of the NNC model. As for the temporal calibration， the purposes are the specialization of the parameterized historical model to adapt to the specific new field measurement data and the correction of inherent baseline errors. In this case， the baseline model was fitted as the historical model based on the in situ data from 27 March and 24 May 2019. Then， an extra linear calibration （LC） model was fitted to assign prediction results of the historical model to results on the specific date by using the data from 31 October 2019. Finally， the NNC model was trained based on the data from 31 October 2019 to secondarily calibrate the historical model to adapt to the specific date.
In order to gain better understanding of the various models， the accuracy for calibration and validation can be statistically evaluated by the three indices， root mean square error （RMSE）， the mean absolute percentage error （MAPE） and the coefficient of determination （
| ， | （12） |
| ， | （13） |
where N is the total number of samples， is the estimated value and is the field measurement value. The RMSE maintains the same unit as the in situ data and thus is intuitive and representative of the size of error. Besides， because of the disproportionate weight given by the squaring process， the RMSE is sensitive to occasional large errors and performs well in the situation with no outliers. As expressed in relative meaning， this statistical measurement can be compared widely across distinct data ranges. It is notable that the MAPE puts a heavy penalty on errors of small SSC values due to the ratio form， which leads to a significant complement of the RMSE.
| ， | （14） |
where SSR is the sum of squares for regression， RSS is the residual sum of squares， SST is the total sum of squares and
（1） The first step is to select a reasonable number of training data. Mention that the number should be greater than the free degree of baseline models and less than the total number of the dataset minus 3 to obtain the valid
（2） The next step is to find out all the possible situations via combination to pick training data from the total dataset and the number of situations here is .
（3） After completing the division to different training and validation groups， each statistical parameter for validation of the groups can be calculated and the average is taken as the final evaluated accuracy.
It is indicated that every possible combination of the training and test data groups can account for the final average accuracy. However， due to fast growing rate of factorial function， this improved k-fold cross validation method can only be considered in the small size of dataset.
In our research， field measurements of SSC have been collected concurrently to the GF-5 overpass based on the aforementioned method. The total 14 in situ SSC data measured on buoy stations and ships using drying and filtration process and optical backscattering method respectively was statistically analyzed in a line chart as shown in
Fig. 3 Line chart of total in situ SSC data. The number 1~7， 8~10， 11~14 samples were measured on 31 October， 24 May and 27 March 2019， separately. A separation line （purple） is plotted to highlight the water samples 1~7 used for the final retrieval. The blue to yellow colors of dots intuitively show the low to high SSC levels. The lines drew in blue and orange represent the origin SSC values of all 3 days and sorted SSC values of 31 October 2019， respectively
图3 实测SSC数据. 点1~7， 8~10， 11~14分别代表了2019年10月31日，5月24日和3月27日的结果. 紫色分隔线用于突出点1~7，点的蓝色到黄色反映了从低到高的SSC浓度，蓝色和橙色线分别代表了原始SSC数值和排序后的2019年10月31日SSC数值.
The preprocessed surface reflectance curves extracted in the highly likely estuarine spots of low， middle and high SSC values on each individual date are shown in
Fig. 4 Spectra of the surface reflectance in the research region on 27 March （a） 24 May （b） and 31 October （c） 2019. The dotted， dashed and solid lines represent the low， middle and high SSC values， respectively （d） some surface reflectance spectra extracted from different typical ground objects on 31 October 2019
图4 不同时间的光谱反射率曲线. 2019年（a） 3月27日 （b） 5月24日 （c） 10月31日. 点线、虚线、实线线型分别代表了低、中、高的SSC浓度值 （d）不同典型地物的反射率光谱曲线（2019年10月31日）
According to documented locations of the 7 water samples on 31 October 2019， the preprocessed surface reflectance curves of GF-5 images are shown in
Fig. 5 The 7 examples of preprocessed surface reflectance spectra for different SSCs measured on 31 October 2019
图5 7种SSC浓度的反射率光谱曲线（2019年10月31日）
In normal case that only in situ data on targeting date is available， NNC can be easily implemented to improve the accuracy of baseline models through compensating the inherent errors of the baseline models. By selecting the in situ data of 31 October 2019 as the whole dataset and using the improved k-fold cross validation method with 4 as the size of the training dataset， the SSC retrieval results of the baseline models and NNC are shown in the
From the results， it is noticeable that the accuracy of the baseline model has been enhanced moderately for all RMSE， MAPE and
In order to overcome the problem of overfitting， a wide range of hyperparameter λ in the regularization term has been employed to test the generalization ability of the NNC model and thus the optimum λ of the best generalization performance of NNC is selected. The dependence relationships of λ and corresponding RMSE， MAPE，
Fig. 6 The relationships between the regularization hyperparameter λ， RMSE， MAPE and
图6 在基线模型校正应用中的正则化参数λ， RMSE， MAPE and R2 （a）D’Sa模型 （b）Nechad模型 （c）Ruhl模型 （d）Loisel模型
Fig. 7 The scatter diagrams （left） between the predicted values and field measurement values and the NNC calibration curves （right） for D’Sa （a）， Nechad （b）， Ruhl （c） and Loisel （d） models in the application for baseline model calibration
图7 在基线模型校正应用中的预测值与实测值散点图（左）和NNC校正曲线（右）， （a）D’Sa模型， （b）Nechad模型， （c）Ruhl模型， （d）Loisel模型
When the baseline models calibrated and validated based on extra historical data are available， the NNC model can be used to adjust the existing model to adapt to specific date with an extra LC step. Our intuitive of the temporal calibration is that adding extra historical information may generate better results. By selecting 4 as the size of the training set and using the improved k-fold cross-validation method， the application for temporal calibration was tested. The results of SSC retrieval based on historical baseline models are shown in
Significant improvement of RMSE and R2 in most models can be obtained after the double calibration. Although the RMSE in D’Sa increases （from 0.1218 to 0.1352 g/L） after NNC in temporal calibration， the value decreases （from 0.1436 to 0.1352 g/L） compared to the result in baseline model calibration. The R2 in Loisel decreases （from 0.3685 to 0.3037）， mainly because the great error after LC cannot be well calibrated by NNC. Specifically， the complex non-monotonic Loisel model leads to the overfitting problem in our small dataset and causes the great error after LC. Besides， the NNC only has limit calibration ability due to the small dataset and prevention of overfitting. Thus， a drop in R2 is observed in Loisel model. With a larger dataset， the NNC may achieve better results in temporal calibration. In terms of MAPE， the MAPE of most models decreases because the redistribution in the LC process may cause big relative errors when predicting small SSC values. Aiming at the visualization of the NNC model， the relationships of the predicted values and the field measurements for each baseline model have been plotted in
Fig 8 The scatter diagrams （left） between the predicted values and field measurement values and the NNC calibration curves （right） for D’Sa （a）， Nechad （b）， Ruhl （c） and Loisel （d） models in the application for temporal calibration
图8 在时间校正应用中的预测值与实测值散点图（左）和NNC校正曲线（右）， （a）D’Sa模型， （b）Nechad模型， （c）Ruhl模型， （d）Loisel模型
From the inverse results of the two applications， the D’Sa model of the temporal calibration with the highest accuracy （RMSE=0.1352 g/L， MAPE=0.7817 and
Fig. 9 SSC retrieval results of the baseline model （a） and NNC double calibration （b） using the D’Sa model in the application of temporal calibration based on the GF-5 images in the Yangtze estuarine and coastal waters on 31 October 2019. For result comparison， the magnified images of the region of interest （ROI） labelled in the red area are provided in the top left of each picture. The green star and pink diamond denote the samples with 0.14 and 0.63 g/L SSC values， respectively
图9 2019年10月31日长江河口的SSC反演结果， （a）基线D'Sa模型， （b） NNC校正模型， 图中红色框内区域放大于左上角，其中绿色和粉色标注分别代表了0.14 g/L和 0.63 g/L反演值
This study shows that the great learning capability of the ANN can be utilized to improve the accuracy in the SSC retrieval process. As mentioned above， moderate improvement can be observed， indicating the effectiveness of NNC. By employing the baseline model calibration， all three assessment parameters in four models obtain increment in precision. By employing the temporal calibration， RMSE and
Generally， the ANN model requires substantial data to drive and even very complicated models can be extracted by the great learning and reasoning abilities of ANN. However， considering the limitation of the dataset size， there may be the risks of overfitting. Hence， in order to prevent the overfitting problem， several aforementioned methods have been designed and employed. First， our proposed NNC takes the advantage of the small size of parameters of the simple baseline models. By using transfer learning， our NNC is first trained to learn an identity function， which reduces the data size that ANN requires. Second， a regularization term is added in the loss function of ANN to test the generalization ability. Third， the best hyperparameter λ is selected to obtain the model with the best generalization performance. Fourth， the improved k-fold cross-validation method is used to obtain low-variance accuracy estimation results and avoid the high-variance risks due to the limited dataset. In addition， 4 baseline models of different types and 3 accuracy assessment parameters were tested to ensure the reliability of our research.
This study shows that the great learning capability of the ANN can be utilized in the double calibration process to improve the accuracy of the SSC retrieval. In this paper， the proposed double calibration system is able to correct both linear and nonlinear errors of the baseline models based on ANN with a specialized regularization term. Our method obtained a moderate improvement of accuracy in both applications. For the two typical applications including baseline model calibration and temporal calibration， 4 distinct baseline models and corresponding NNC models have been systematically investigated using the GF-5 AHSI images and the concurrently collected field measurements. The results show D’Sa model is of highest accuracy in both applications. By employing the baseline model calibration， RMSE decreased from 0.1495 g/L to 0.1436 g/L， MAPE decreased from 0.7821 to 0.7580 and
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