Remote sensing nonlinear three-variable water depth inversion method

Abstract

Aiming at the problem of low water depth inversion precision caused by neglecting the characteristics of non-uniform attenuation, water surface reflection, water body attenuation and water bottom reflection because only exponential attenuation of light in water transmission is considered in a remote sensing water depth inversion process, the transmission process and physical characteristics of sunlight on the water surface, the water body and the water bottom are analyzed; three key factors of water surface reflectivity, water body transparency and water bottom reflectivity of water depth inversion are summarized, and a remote sensing nonlinear three-variable water depth inversion method is provided. Through comparison and verification of a Moroat island test field, a logarithmic ratio model, a ratio logarithmic model and a multiband model, the model can effectively improve the precision of remote sensing inversion of water depth.

Description

Technical Field

[0001] The invention relates to the field of remote sensing water depth inversion, and in particular to a satellite multi-spectral remote sensing water depth inversion method. Background Art

[0002] In nearshore areas, the satellite image radiance and water depth generally show a nonlinear relationship, and the results of traditional linear model fitting are difficult to invert the accurate water depth. For this reason, a large number of patents have been developed based on this nonlinear relationship to study and construct reasonable water depth inversion models to invert water depth. Basically, they are divided into two categories: one is based on the principle of exponential attenuation of light in water, using the characteristics of different depths of blue / red, blue / near infrared, green / red, and green / near infrared to invert different water depths and water body characteristics, construct a multi-band water depth inversion model, and use satellite remote sensing images to invert water depth, such as a water depth inversion method based on the permeable band ratio factor (ZL201110035432.2). However, this type of method simply uses different bands of multi-spectrum, and does not consider the influencing factors of water depth, such as the reflectivity of the water surface and bottom and the attenuation coefficient of water to light, resulting in low accuracy of inverted water depth; the other type is to construct a ratio logarithm or logarithmic ratio model based on the exponential attenuation of blue-green light in water and a logarithmic relationship with water depth, which is used to invert water depth from satellite images, such as the remote sensing water depth inversion tidal height correction method (ZL202110391470.5) and a shallow sea water depth inversion method based on Sentinel-2A images (ZL202111400522.7). This type of method also only considers the exponential attenuation characteristics of blue-green light in water, and does not consider the influence of impurities, water surface and bottom reflectivity in water, which also leads to low accuracy and large error in inverted water depth. In summary, these two existing water depth inversion methods only use the exponential attenuation characteristics of visible light transmission in water, and do not consider the influence of different bottom materials and water surface reflectivity in water.

[0003] To this end, the present invention selects water surface reflectivity, bottom reflectivity and water body transparency to construct a nonlinear three-variable water depth inversion method based on the linear relationship between blue-green light and water surface reflectivity and bottom sediment, and a nonlinear relationship with water body transparency. The model parameters are optimized using the least squares method and the minimum gradient descent method to obtain a remote sensing nonlinear three-variable water depth inversion model (referred to as "remote sensing nonlinear three-variable model") to invert the water depth. Summary of the invention

[0004] The traditional linear model only utilizes the exponential attenuation characteristics of visible light transmission in water, and does not consider the influence of different bottom materials, water bodies, and water surface reflectivity in water, resulting in low water depth inversion accuracy and large errors. The present invention proposes a remote sensing nonlinear three-variable water depth inversion method, which selects water surface reflectivity, bottom material reflectivity and water body transparency, constructs a nonlinear three-variable model, and uses multispectral satellite remote sensing images to invert higher-precision water depth.

[0005] The specific steps are as follows:

[0006] S1: First calculate the water surface reflectivity, bottom reflectivity and water transparency.

[0007] S1-1: Extract water areas using normalized water index, i.e. formula (1)

[0008] (1)

[0009] In the formula, NDWI is the normalized water index. A value greater than 0 indicates water areas, and a value less than 0 indicates other areas. B is the blue band reflectance, R NIR is the reflectivity in the near-infrared band.

[0010] S1-2: After extracting the water area using formula (1), use formula (2) to calculate the water surface reflectivity

[0011] (2)

[0012] Where P is the water surface reflectivity, L is the water surface radiance, and L max To extract the maximum radiance of the water surface, L min To extract the minimum radiance of the water surface.

[0013] S1-3: Based on the attenuation characteristics of blue-green light in water, the water transparency is calculated using formula (3).

[0014] (3)

[0015] Where D T is the water transparency, D is the known water depth difference between points S1 and S2, L S1 and L S2 The radiation brightness is known for points S1 and S2 respectively.

[0016] S1-4: Calculate the bottom reflectivity using formula (4)

[0017] (4)

[0018] In the formula, R b is the reflectivity of the bottom, L max To extract the maximum radiance of the water surface, L this is the water surface radiance at the current point, D m D is the depth difference between the current point water depth and the maximum radiance of the water surface in the extracted water area, T For water transparency.

[0019] S2: Constructing a water depth inversion model

[0020] (4)

[0021] Where y is the water depth, x is the eigenvector, i.e. (x1, x2, x3), x1, x2, x3 are the water surface reflectivity P, water transparency D respectively. T and the bottom reflectivity R b ,ω T is the weight vector, sigmod(▪) is the exponential mapping marker, and b is the bias vector.

[0022] S3: Inversion model parameters.

[0023] S3-1: Initialize ω to (ω1, ω2, ω3), ω1, ω2 and ω3 are three random numbers in [-1, 1], and b is (0, 0, 0).

[0024] S3-2: Calculate the predicted water depth .

[0025] (5)

[0026] S3-2: Calculate the i-th predicted water depth in the sample error function L(ω, b) The measured water depth y (i) The error l (i) .

[0027] (6)

[0028] In the formula, n is the number of samples, i is the number of the i-th sample, and l (i) (ω, b) is the i-th predicted water depth The measured water depth y (i) of error.

[0029] S3-3: Use partial derivatives to solve the error function L(ω, b) parameters of the sample and update the original parameters ω, b to obtain the optimal parameter values ​​ω*, b*.

[0030] (7)

[0031] In the formula, η represents the learning rate, which is generally a decimal between 0 and 1.

[0032] S4: Data set consisting of existing feature vector x and water depth y data Optimize model parameters and construct a remote sensing nonlinear three-variable water depth inversion model.

[0033] S5: Inversion of water depth using the constructed remote sensing nonlinear three-variable model.

[0034] The benefits of the present invention are as follows: (1) the water transparency is used to take into account not only the exponential attenuation of light in water, but also the incomplete exponential attenuation of light in water; (2) the water surface transmittance and bottom reflectance are taken into account; (3) a remote sensing nonlinear three-variable water depth inversion method is proposed, water surface transmittance, bottom reflectance and water transparency are selected as characteristic variables, a remote sensing nonlinear three-variable model is constructed, and multispectral satellite remote sensing images are used to invert higher-precision water depth. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is the principle of remote sensing nonlinear three-variable water depth inversion

[0036] Figure 2 The experimental process

[0037] Figure 3 Molokai Island Test Site

[0038] Figure 4 The depth of the Molokai test site

[0039] Figure 5 The logarithmic ratio inversion of water depth

[0040] Figure 6 This is a scatter plot of the logarithmic ratio inversion depth and the laser radar measured depth

[0041] Figure 7 is the water depth inverted by the ratio logarithmic model

[0042] Figure 8 The scatter plot of water depth inverted by the ratio logarithmic model and water depth measured by lidar

[0043] Fig. 9 It is the multi-band model to invert water depth

[0044] Fig.10 This is a scatter plot of water depth inverted by multi-band model and water depth measured by lidar

[0045] Fig.11 The remote sensing nonlinear three-variable model is used to invert water depth

[0046] Fig.12 The scatter plot of water depth inverted by remote sensing nonlinear three-variable model and water depth measured by lidar DETAILED DESCRIPTION

[0047] The principle, experiment and steps of the present invention are further described in detail below with reference to the accompanying drawings for the specific implementation of the present invention.

[0048] Combination Figure 1 , illustrating the principle of this embodiment:

[0049] The light emitted by the sun passes through the atmosphere and hits the water surface. Part of the light is reflected on the water surface, and the other part penetrates the water surface, is absorbed and scattered by chlorophyll, yellow matter and non-pigment particles in the water, reaches the bottom of the water to form a reflection, and then is absorbed and scattered by chlorophyll, yellow matter and non-pigment particles in the water, penetrates the water surface and the atmosphere, and is finally received by the satellite sensor. In this process, water surface reflection, water body attenuation and bottom reflection are the three most important key factors in signal generation. Therefore, the influencing factors of water depth inversion are simplified to key factor 1: water surface reflectivity, key factor 2: water body transparency and key factor 3: bottom reflectivity. According to their relationship with water depth, a remote sensing nonlinear three-variable water depth inversion method is proposed, and a remote sensing nonlinear three-variable model is constructed.

[0050] Combination Figure 2 , describing the experimental process of this embodiment:

[0051] S1: This example uses a Landsat 9 image and performs image preprocessing such as radiometric calibration, atmospheric correction, and water area clipping. Landsat 9 images can be downloaded for free from the official website of the United States Geological Survey (USGS) (https: / / earthexplorer.usgs.gov / ). In this experiment, a total of 1 Landsat 9 L2 image was downloaded, corresponding to February 24, 2022. The detailed information of each band of the Landsat 9 image is shown in Table 1.

[0052] Table 1 Landsat 9 image parameters

[0053]

[0054] Landsat 9 L2 products, L2 products have been officially calibrated and atmospherically corrected. Therefore, no additional preprocessing is required. In ENVI, you can directly open the TIF format data of each band in the downloaded image data file.

[0055] S2: Combination Figure 3 and Figure 4 , illustrating the test field and water depth of this embodiment.

[0056] S2-1: Combination Figure 3 The test site of this embodiment is located on Molokai Island, the fifth largest island in Hawaii, USA, located in the Hawaiian Islands in the central Pacific Ocean, with a coastline of 142 km and an area of ​​673 km. 2 It has a tropical marine climate, with abundant precipitation throughout the year, concentrated in summer and autumn. The industries are mainly tourism and agriculture. The coastal areas are less affected by human activities, and the water is relatively clear. The study area is , .

[0057] S2-2: Combination Figure 4 , which illustrates the water depth of the test field of this embodiment. It uses the water depth measured by manned airborne laser radar, and obtains the water depth data at the time of satellite transit after tidal correction (combined with the tidal data corresponding to the time of satellite image acquisition) and other preprocessing. The shallowest water depth of the test field is 0m, and the maximum water depth is -37.39m. The water depth change trend gradually deepens from southeast to northwest, and the change becomes faster and faster with the increase of depth.

[0058] S3: Combine the water surface reflectivity extracted by formula (1), the water transparency extracted by formula (2) and the bottom reflectivity extracted by formula (3) to create a data set, which is divided into training data and verification data.

[0059] S4: Combining the entire process of solar radiation passing through the atmosphere, crossing the water surface, reaching the bottom of the water, and being transmitted to the satellite sensor, the key factors of remote sensing water depth inversion are analyzed, and a remote sensing nonlinear three-variable water depth inversion method is proposed. The water surface reflectivity, water transparency, and bottom reflectivity are used as characteristic variables to construct a remote sensing nonlinear three-variable model.

[0060] S5: Combination Figure 5 , 7 , 9 and 11, which illustrate that based on the training data of S3, the least square method and minimum gradient descent method are used to optimize the parameters of water depth inversion models such as the log-ratio model, the log-log ratio model, the multi-band model and the remote sensing nonlinear three-variable model, and the corresponding water depth inversion model is constructed to invert the water depth.

[0061] S5: Combination Figure 6 , 8 , 10, 12, the actual water depth (verification data) and the water depth inverted by the logarithmic ratio model, the ratio logarithmic model, the multi-band model and the remote sensing nonlinear three-variable model were analyzed by scatter plot, and the R of the water depth inverted by different models in the test field was calculated. 2 , RMSE and MAE, as shown in Table 2. As can be seen from Table 2, at the Molokai Island test site, the maximum depths of the depth inversion model and the depth measured by the lidar are: remote sensing nonlinear three-variable model > logarithmic ratio model > multi-band model > ratio logarithmic model; R 2 The RMSE from high to low is: remote sensing nonlinear three-variable model > logarithmic ratio model > multi-band model > logarithmic ratio model; the MAE from low to high is: remote sensing nonlinear three-variable model > logarithmic ratio model > multi-band model > logarithmic ratio model.

[0062] Table 2 Comparative analysis of water depth inversion between real water depth and logarithmic ratio model, logarithmic ratio model, multi-band model and remote sensing nonlinear three-variable model

[0063]

[0064] S6: According to the inversion statistical results of S5, the remote sensing nonlinear three-variable model of the present invention has the best effect.

[0065] In summary, the present invention can improve the accuracy of water depth inversion to a certain extent, making the inverted water depth closer to the real water depth, and also more practical and valuable.

[0066] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0067] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A remote sensing nonlinear three-variable water depth inversion method, which is characterized by the following steps: S1: First calculate the water surface reflectivity, bottom reflectivity and water transparency S1-1: Extract water areas using normalized water index, i.e. formula (1) (1) In the formula, NDWI is the normalized water index. A value greater than 0 indicates water areas, and a value less than 0 indicates other areas. B is the blue band reflectance, R NIR is the reflectivity in the near-infrared band; S1-2: After extracting the water area using formula (1), use formula (2) to calculate the water surface reflectivity (2) Where P is the water surface reflectivity, L is the water surface radiance, and L max To extract the maximum radiance of the water surface, L min To extract the minimum radiance of the water surface; S1-3: Based on the attenuation characteristics of blue-green light in water, the water transparency is calculated using formula (3); (3) Where D T is the water transparency, D is the known water depth difference between points S1 and S2, L S1 and L S2 The radiances of points S1 and S2 are known respectively; S1-4: Calculate the bottom reflectivity using formula (4) (4) In the formula, R b is the reflectivity of the bottom, L max To extract the maximum radiance of the water surface, L this is the water surface radiance at the current point, D m D is the depth difference between the current point water depth and the maximum radiance of the water surface in the extracted water area, T For water transparency; S2: Constructing a water depth inversion model (4) Where y is the water depth, x is the eigenvector, i.e. (x1, x2, x3), x1, x2, x3 are the water surface reflectivity P, water transparency D respectively. T and the bottom reflectivity R b ,ω T is the weight vector, sigmod(▪) is the exponential mapping index, and b is the bias vector; S3: Inversion model parameters S3-1: Initialize ω to (ω1, ω2, ω3), ω1, ω2 and ω3 are three random numbers in [-1, 1], and b is (0, 0, 0); S3-2: Calculate the predicted water depth ; (5) S3-2: Calculate the i-th predicted water depth in the sample error function L(ω, b) The measured water depth y (i) The error l (i) ; (6) In the formula, n is the number of samples, i is the number of the i-th sample, and l (i) (ω, b) is the i-th predicted water depth The measured water depth y (i) The error of S3-3: Use partial derivatives to solve the error function L(ω, b) parameters of the sample and update the original parameters ω, b to obtain the optimal parameter values ​​ω*, b*; (7) In the formula, η represents the learning rate, which is generally a decimal between 0 and 1; S4: Data set consisting of existing feature vector x and water depth y data Optimize model parameters and construct a remote sensing nonlinear three-variable water depth inversion model; S5: Invert water depth using the constructed remote sensing nonlinear three-variable water depth inversion model.

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