A method for calculating soil heat flux under a two-dimensional framework of soil temperature - elevation

Abstract

The present invention relates to a method for calculating soil heat flux under a two-dimensional framework of soil temperature - elevation, belonging to the field of remote sensing measurement of soil heat flux. It includes: S1 obtaining remote sensing images, elevation, and surface emissivity data of the study area and preprocessing them; S2 calculating the change rate of surface temperature with vegetation cover at each pixel using the remote sensing surface temperature and remote sensing vegetation cover within a rectangular window centered on each pixel; S3 separating the soil temperature at each pixel from the remote sensing surface temperature using the change rate of surface temperature with vegetation cover at each pixel; S4 constructing a two-dimensional framework with elevation as the horizontal axis and soil temperature as the vertical axis, dividing the elevation range into several intervals, and determining the lowest and highest soil temperatures within each sub-interval; S5 solving the change rates of the lowest and highest soil temperatures with elevation based on S4; S6 solving the change rate of soil temperature with elevation at each pixel from the change rates in S5; S7 inputting the pixel change rate and soil temperature in S6 into the soil heat diffusion equation to calculate the soil heat flux.

Description

Technical Field

[0001] The present invention relates to a remote sensing measurement method for soil heat flux, and particularly to a remote sensing calculation method for soil heat flux by means of the relationship between soil temperature and elevation. Background Art

[0002] Soil heat flux is an important parameter characterizing the net heat exchange between the surface soil and the deep soil, and to a certain extent reflects the strength of heat acquisition or release by the soil in different ecosystems. Soil heat flux is an important part of the surface energy balance, reflecting the income and expenditure of surface energy, and affecting the energy conversion between the land and the atmosphere and the estimation of surface evapotranspiration in the process of the surface water cycle. Therefore, the surface soil heat flux is crucial for the energy balance of the ecosystem, the surface microclimate, the microscale biophysical environment of the vegetation roots, and the comprehensive management of regional water resources. Accurately estimating soil heat flux is of great significance for the research on surface energy balance, surface evapotranspiration estimation, and regional hydro-ecology.

[0003] At present, the estimation methods for surface soil heat flux mainly include climatological estimation mainly based on station specifications, heat conduction and improvement, soil column heat content, and empirical integration, the combination method of measured soil heat flux and heat storage, the average soil thermocouple method, the harmonic method, the heat conduction equation correction method, and the semi-order method. Most of these methods are based on the observation of surface soil heat flux at the point scale, and use soil temperature to estimate soil heat flux. However, when the thermal properties of the soil heat flux plate are different from those of the adjacent soil, or when the parameters calibrated by the point-scale soil heat flux observation are used to calculate the soil heat flux with significantly different soil thermal properties, large errors will occur. In addition, for large-scale observations, it is not very realistic to arrange high-density heat flux plates or soil temperature sensors, and the demand for observation data limits the popularization and application of these methods.

[0004] The rapidly developing remote sensing technology has the characteristics of comprehensiveness, macroscopy, dynamics, continuous monitoring, and short update cycle, and can obtain large-area and continuous observation data, and can provide a large amount of surface spatial distribution information at the regional scale. The methods for estimating soil heat flux based on remote sensing data are divided into two types. One is to estimate soil heat flux by means of the empirical relationship established between the ratio of soil heat flux to net radiation or sensible heat flux and the surface parameters retrieved by remote sensing. The other is to directly use a semi-theoretical model with remote sensing data to estimate the surface soil heat flux. The empirical relationships relied on in the empirical method, such as the relationship between soil heat flux and net radiation, sensible heat flux, etc., vary with different underlying surfaces, and the surface parameters included in the empirical relationships are also often different. For different research regions, the applicability of these empirical methods is also limited.

[0005] Therefore, it is crucial to effectively and fully utilize remote sensing information at the regional scale to quickly and quantitatively estimate the surface soil heat flux in order to better meet the data requirements of the soil heat flux in the hydrological and ecological fields at the regional scale. Especially in the remote sensing evapotranspiration model, the soil heat flux, as an important energy input component, is often linearly segmented from the net radiation and linearly processed. Currently, there is an urgent need to develop an accurate quantitative remote sensing estimation method. For this purpose, a method for measuring the soil heat flux in a two-dimensional framework of soil temperature - elevation is invented. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides a method for measuring the soil heat flux in a two-dimensional framework of soil temperature - elevation.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A method for measuring the soil heat flux in a two-dimensional framework of soil temperature - elevation, comprising the following steps:

[0009] S1: Calculate the change rate of the surface temperature with vegetation cover at each pixel using the remote sensing surface temperature and remote sensing vegetation cover within a rectangular window centered on each pixel;

[0010] S2: Separate the soil temperature at each pixel from the remote sensing surface temperature using the change rate of the surface temperature with vegetation cover at each pixel;

[0011] S3: Construct a two-dimensional framework with elevation as the horizontal axis and soil temperature as the vertical axis, divide the elevation range into several intervals, and determine the lowest and highest soil temperatures within each sub-interval;

[0012] S4: Solve the change rate of the lowest and highest soil temperatures with elevation based on S3;

[0013] S5: Solve the change rate of the soil temperature with elevation at each pixel from the change rate in S4;

[0014] S6: Input the change rate at each pixel in S5 and the soil temperature into the soil heat diffusion equation to measure the soil heat flux.

[0015] As a further preferred technical solution, S1 is specifically:

[0016] α = P -1 B′T IJ

[0017] α = [α 0 , α 1 , α 2 , α 3 ′

[0018]

[0019] T IJ = [T i-Wj-W , …, T i+Wj-W , T i-Wj-W+1 , …, T i-Wj+W , …, T i+Wj+W ′

[0020] In the formula, W represents the length of the rectangular window, i and j represent the per-pixel positions, B is an orthogonal matrix, P is a non-singular upper triangular matrix, α represents the coefficient vector at the pixel (i, j), and T IJ represents the sequence of land surface temperatures within the rectangular window centered on the pixel (i, j), and BP represents the matrix of vegetation cover F within the rectangular window centered on the pixel (i, j).

[0021] As a further preferred technical solution, the S2 is specifically as follows:

[0022]

[0023]

[0024] In the formula, T ij represents the land surface temperature at the pixel (i, j), ε ij represents the land surface emissivity at the pixel (i, j), ε sij represents the bare soil emissivity at the pixel (i, j), F ij represents the vegetation coverage at the pixel (i, j), T sij represents the bare soil temperature at the pixel (i, j), T s represents the bare soil temperature of the study area.

[0025] As a further preferred technical solution, the S3 includes the following steps:

[0026] S31: Construct a two-dimensional framework with elevation as the horizontal axis and soil temperature as the vertical axis;

[0027] S32: Determine the maximum elevation and the minimum elevation within the study area, and divide the elevation range into several intervals, specifically:

[0028]

[0029] H = [H 1 … H n … H N ′

[0030]

[0031]

[0032] Wherein, minH is the minimum elevation in the study area, maxH is the maximum elevation in the study area, N is the number of intervals for dividing the elevation range, and H n represents the median elevation of the nth sub-interval , and represents the elevation width of each sub-interval;

[0033] S33: Determine the lowest soil temperature within each sub-interval, specifically:

[0034] min_T = [minT 1 … minT n … minT N ′

[0035]

[0036] Wherein, x and y represent the positions of the pixels, and H xy represents the elevation value at the pixel (x, y), T sxy represents the surface temperature at the pixel (x, y) where the elevation is in the nth sub-interval, {T sxy} represents the set composed of all T sxy , minT n represents the minimum value in {T sxy}, and min_T represents the vector composed of {minT n}; 1≤n≤N ;

[0037] S34: Determine the lowest and highest soil temperatures within each sub-interval, specifically:

[0038] max_T = [maxT 1 … maxT n … maxT N ′

[0039]

[0040] Wherein, maxT n represents the maximum value in {T sxy}, and max_T represents the vector composed of {maxT n}; 1≤n≤N ;

[0041] As a further preferred technical solution, the said S4 includes the following steps:

[0042] S41: Based on S3, solve the change rate of the lowest soil temperature with elevation, specifically:

[0043]

[0044]

[0045] In the formula, β = [β 0 β 1 ′ represents the change rate of the lowest soil temperature with elevation;

[0046] S42: Solve for the change rate of the highest soil temperature with elevation based on S3, specifically:

[0047]

[0048] In the formula, κ = [κ 0 κ 1 ′ represents the change rate of the highest soil temperature with elevation.

[0049] As a further preferred technical solution, the S5 includes the following steps:

[0050] S51: Calculate the lowest soil temperature corresponding to the elevation value of each pixel, specifically:

[0051] T min_o = β 1 H o + β 0

[0052] In the formula, H o represents the elevation value of each pixel, and T min_o represents the lowest soil temperature corresponding to the elevation value of each pixel;

[0053] S52: Calculate the highest soil temperature corresponding to the elevation value of each pixel, specifically:

[0054] T max_o = κ 1 H o + κ 0

[0055] In the formula, T min_o represents the highest soil temperature corresponding to the elevation value of each pixel.

[0056] As a further preferred technical solution, the S6 includes the following steps:

[0057] S61: Calculate the change rate of the soil temperature with the elevation value at each pixel, specifically:

[0058]

[0059] In the formula, T s_o represents the soil temperature of each pixel, and ν represents the change rate of the soil temperature with the elevation value at each pixel;

[0060] S62: Calculate the surface soil temperature at each pixel, specifically:

[0061] τ o = T s_o + νD

[0062] In the formula, D represents the depth (m) of the surface soil at each pixel, and τ o represents the soil temperature at the soil depth D;

[0063] S63: Calculate the soil heat flux at each pixel, specifically:

[0064] G = K(T s_o - τ o )D = -KνD

[0065] In the formula, K represents the thermal conductivity (W / m 2 / K), and G represents the measured soil heat flux (W / m 2 ).

[0066] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0067] 1) Currently, there is no method for directly measuring soil heat flux by remote sensing. The present invention fills this gap by using the remote sensing thermal infrared surface temperature and elevation two-dimensional framework technology;

[0068] 2) The present invention proposes a local rectangular window high-order polynomial regression method for solving the change of surface temperature with vegetation cover;

[0069] 3) The present invention proposes an elevation-surface temperature dual hybrid interpolation method for quantifying the relationship between the surface and the surface layer temperature;

[0070] 4) The present invention requires less data and does not require observation. The soil heat flux can be measured only by using remote sensing surface temperature and elevation data, which is convenient and fast. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 is a flowchart of the method in the embodiment provided by the present invention; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0072] The following will combine the drawings and embodiments to detail the basic idea, technical features and beneficial effects of the present invention. It should be noted that the used drawings only show the preferred embodiments of the present invention, not all of them. Those of ordinary skill in the art can also obtain other related drawings based on this embodiment without creative work.

[0073] As Figure 1 shown, the technical process in the embodiment provided by the present invention includes the following steps:

[0074] S1 Obtain remote sensing images, elevation, and surface emissivity data of the study area and preprocess them;

[0075] S2 calculates the change rate of surface temperature with vegetation cover at each pixel using the remote sensing surface temperature and remote sensing vegetation cover within a rectangle window centered on each pixel;

[0076] S3 separates the pixel soil temperature from the remote sensing surface temperature using the change rate of surface temperature with vegetation cover at each pixel;

[0077] S4 constructs a two-dimensional framework with elevation as the horizontal axis and soil temperature as the vertical axis, divides the elevation range into several intervals, and determines the lowest and highest soil temperatures within each sub-interval;

[0078] S5 solves the change rates of the lowest and highest soil temperatures with elevation based on S4;

[0079] S6 solves the change rate of soil temperature with elevation at each pixel from the change rates in S5;

[0080] S7 inputs the pixel change rate and soil temperature in S6 into the soil heat diffusion equation to measure the soil heat flux.

[0081] In one embodiment, in S1, the remote sensing image of the study area should include near-infrared band, red band, and thermal infrared band. Exemplarily, the remote sensing image can be selected from Landsat-5 TM, Landsat-7 ETM+, or Landsat8 OLI and TIRS sensors (https: / / ladsweb.modaps.eosdis.nasa.gov / ) or HJ-1B CCD camera and infrared camera (https: / / www.gscloud.cn / search);

[0082] In one embodiment, in S1, the elevation data can be selected from SRTM3, with a spatial resolution of 90m, global coverage, and can be downloaded through https: / / ladsweb.modaps.eosdis.nasa.gov / ;

[0083] In one embodiment, in S1, the surface emissivity can be selected as the ASTER GEDv3 dataset, which is the mean of surface emissivity derived from all cloud-free ASTER images between 2000 and 2008, with a spatial resolution of 100m, global coverage, and can be downloaded through https: / / ladsweb.modaps.eosdis.nasa.gov / ;

[0084] In one embodiment, in S1, the preprocessing includes elevation spatial resolution resampling, surface emissivity adjustment, and inversion of the thermal infrared band of surface temperature for remote sensing;

[0085] The elevation spatial resolution resampling is to resample the spatial resolution of the digital elevation to the spatial resolution of the remote sensing thermal infrared band;

[0086] The adjustment of the surface emissivity is preferably:

[0087]

[0088]

[0089] In the formula, ε is the emissivity of the thermal infrared band, ε 13 is the surface emissivity of band 13 in the ASTER GEDv3 product, ε 14 is the surface emissivity of band 14 in the ASTER GEDv3 product, VI, VI min 、VI max are the vegetation indices, the minimum value of the vegetation index, and the maximum value of the vegetation index calculated from the near-infrared and red bands of the selected remote sensing image, VI a 、VI a_min 、VI a_max are the mean value of the vegetation index, the minimum value of the mean value of the vegetation index, and the maximum value of the mean value of the vegetation index calculated from the near-infrared and red bands of ASTER;

[0090] The inversion of the surface temperature in the remote sensing thermal infrared band is preferably a single-channel algorithm, specifically:

[0091]

[0092]

[0093] L λ =0.0370588DN + 3.2

[0094] In the formula, T is the surface temperature (K) of the remote sensing thermal infrared band obtained by inversion, DN is the digital value of the thermal infrared band of the remote sensing image, and L λ represents the radiation of the remote sensing thermal infrared band (W / (m 2 sterμm), γ 2 is 1282.71K, γ 1 is 666.09mW cm - 2 sr -1 μm -1 ,T B is the brightness temperature (K) of the on-satellite remote sensing thermal infrared band, λ is the wavelength of the effective radiation 11.5μm, and ρ is a constant 1.438×10 -2 m K.

[0095] In one embodiment, in S2, calculating the change rate of the surface temperature with respect to the vegetation cover at each pixel by using the remotely sensed surface temperature and remotely sensed vegetation cover within a rectangular window centered on each pixel specifically includes:

[0096] α = P -1 B′T IJ

[0097] α = [α 0 , α 1 , α 2 , α 3 ′

[0098]

[0099] T IJ =[T i-Wj-W , …, T i+Wj-W , T i-Wj-W+1 , …, T i-Wj+W , …, T i+Wj+W ′

[0100] In the formula, W represents the length of the rectangular window, i and j represent the positions of each pixel, B is an orthogonal matrix, P is a non-singular upper triangular matrix, α represents the coefficient vector at pixel (i, j), and T IJ represents the sequence of surface temperatures within the rectangular window centered on pixel (i, j), and BP represents the matrix of vegetation cover F within the rectangular window centered on pixel (i, j).

[0101] In one embodiment, in S3, separating the soil temperature of each pixel from the remotely sensed surface temperature by using the change rate of the surface temperature with respect to the vegetation cover at each pixel specifically includes:

[0102]

[0103]

[0104] In the formula, T ij represents the surface temperature at pixel (i, j), ε ij represents the surface emissivity at pixel (i, j), ε sij represents the bare soil emissivity at pixel (i, j), F ij represents the vegetation coverage at pixel (i, j), T sij represents the bare soil temperature at pixel (i, j), and T s represents the bare soil temperature of the study area.

[0105] In one embodiment, in S4, the steps of constructing a two-dimensional framework with elevation as the horizontal axis and soil temperature as the vertical axis, dividing the elevation range into several intervals, and determining the lowest and highest soil temperatures within each sub-interval include the following steps:

[0106] S41: Construct a two-dimensional framework with elevation as the horizontal axis and soil temperature as the vertical axis;

[0107] S42: Determine the maximum elevation and minimum elevation in the study area, and divide the elevation range into several intervals, specifically:

[0108]

[0109] H = [H 1 …H n …H N ′

[0110]

[0111]

[0112] In the formula, minH is the minimum elevation in the study area, maxH is the maximum elevation in the study area, N is the number of intervals for dividing the elevation range, H n represents the elevation median of the nth sub-interval , represents the elevation width of each sub-interval;

[0113] S43: Determine the lowest soil temperature within each sub-interval, specifically:

[0114] min_T = [minT 1 …minT n …minT N ′

[0115]

[0116] In the formula, x and y represent the positions of the pixels, H xy represents the elevation value at the pixel (x, y), T sxy represents the surface temperature at the pixel (x, y) where the elevation is in the nth sub-interval, {T sxy} represents the set composed of all T sxy minT n represents the minimum value in {T sxy}, min_T represents the vector composed of {minT n} 1≤n≤N ;

[0117] S44: Determine the lowest and highest soil temperatures within each sub-interval, specifically:

[0118] max_T = [maxT 1 …maxT n …maxT N ′

[0119]

[0120] Wherein, maxT n represents the maximum value in {T sxy}, and max_T represents the vector composed of {maxT n}. 1≤n≤N

[0121] In one embodiment, in S5, the step of solving the change rates of the lowest and highest soil temperatures with respect to elevation based on S4 includes the following steps:

[0122] S51: Solving the change rate of the lowest soil temperature with respect to elevation based on S4, specifically:

[0123]

[0124]

[0125] Wherein, β = [β 0 β 1 ′ represents the change rate of the lowest soil temperature with respect to elevation;

[0126] S52: Solving the change rate of the highest soil temperature with respect to elevation based on S4, specifically:

[0127]

[0128] Wherein, κ = [κ 0 κ 1 ′ represents the change rate of the highest soil temperature with respect to elevation.

[0129] In one embodiment, in S6, the step of solving the change rate of the soil temperature with respect to elevation at each pixel based on the change rates of S5 includes the following steps:

[0130] S61: Calculating the lowest soil temperature corresponding to the elevation value of each pixel, specifically:

[0131] T min_o = β 1 H o + β 0

[0132] Wherein, H o represents the elevation value of each pixel, and T min_o represents the lowest soil temperature corresponding to the elevation value of each pixel; ​

[0133] S62: Calculate the highest soil temperature corresponding to the elevation value per pixel, specifically:

[0134] T max_o = κ 1 H o + κ 0

[0135] In the formula, T min_o represents the highest soil temperature corresponding to the elevation value per pixel.

[0136] In one embodiment, in the said S7, the step of inputting the per-pixel change rate of S6 and the soil temperature into the soil heat diffusion equation to measure the soil heat flux includes the following steps:

[0137] S71: Calculate the change rate of the soil temperature with the elevation value at each pixel, specifically:

[0138]

[0139] In the formula, T s_o represents the soil temperature of each pixel, and ν represents the change rate of the soil temperature with the elevation value at each pixel;

[0140] S72: Calculate the surface soil temperature at each pixel, specifically:

[0141] τ o = T s_o + vD

[0142] In the formula, D represents the depth (m) of the surface soil layer at each pixel, and τ o represents the soil temperature at the soil layer depth D;

[0143] S73: Calculate the soil heat flux at each pixel, specifically:

[0144] G = K(T s_o - τ o )D = -KνD

[0145] In the formula, K represents the thermal conductivity (W / m 2 / K), and G represents the measured soil heat flux (W / m 2 ).

[0146] A method for measuring soil heat flux in a two-dimensional soil temperature - elevation framework proposed by the present invention has the following advantages:

[0147] 1) By means of the digital elevation model, high-spatial-resolution remote sensing measurement of soil heat flux over a large area is realized, filling the gap in direct remote sensing measurement of soil heat flux;

[0148] 2) A closed equation for extracting soil temperature was constructed by combining the land surface temperature and vegetation cover within a local window centered pixel by pixel;

[0149] 3) At present, both digital elevation models and remote sensing thermal infrared can cover the globe. Therefore, the present invention can estimate the global soil heat flux with high spatial resolution.

[0150] It should be noted that those of ordinary skill in the art can make various modifications and substitutions to the preferred embodiments given by the present invention. However, within the spirit and principles of the present invention, these changes cannot depart from the protection scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating soil heat flux under a two-dimensional framework of soil temperature - elevation, characterized in that, it includes the following steps: S1: Calculate the change rate of surface temperature with vegetation cover at each pixel by using the remotely sensed surface temperature and remotely sensed vegetation cover within a rectangular window centered on each pixel, specifically: α = P -1 B'T IJ α＝[α 0 ,α 1 ,α 2 ,α 3 ]′ T IJ = [T i-Wj-W , …, T i+Wj-W , T i-Wj-W+1 , …, T i-Wj+W , …, T i+Wj+W ′ where W represents the length of the rectangular window, i and j represent the per-pixel positions, Β is an orthogonal matrix, Ρ is a non-singular upper triangular matrix, α represents the coefficient vector at pixel (i, j), and T IJ represents the sequence of land surface temperatures within the rectangular window centered at pixel (i, j), and ΒΡ represents the matrix of vegetation cover F within the rectangular window centered at pixel (i, j); S2: Separate the soil temperature at each pixel from the remotely sensed surface temperature by using the change rate of surface temperature with vegetation cover at each pixel, specifically: where, T ij represents the land surface temperature at pixel (i, j), ε ij represents the land surface emissivity at pixel (i, j), ε sij represents the bare soil emissivity at pixel (i, j), F ij represents the vegetation coverage at pixel (i, j), T sij represents the bare soil temperature at pixel (i, j), T s represents the bare soil temperature of the study area; S3: Construct a two-dimensional framework with elevation as the horizontal axis and soil temperature as the vertical axis, divide the elevation range into several intervals, and determine the lowest and highest soil temperatures within each sub-interval; S4: Solve the change rate of the lowest and highest soil temperatures with elevation based on S3; S5: Solve the change rate of soil temperature with elevation at each pixel from the change rate in S4; S6: Input the change rate at each pixel in S5 and the soil temperature into the soil heat diffusion equation to calculate the soil heat flux.

2. The method according to claim 1, characterized in that, S3 includes the following steps: S31: Construct a two-dimensional framework with elevation as the horizontal axis and soil temperature as the vertical axis; S32: Determine the maximum elevation and minimum elevation within the study area, and divide the elevation range into several intervals, specifically: In the formula, minH is the minimum elevation in the study area, maxH is the maximum elevation in the study area, N is the number of intervals for dividing the elevation range, and H n represents the median elevation of the nth sub-interval , and represents the elevation width of each sub-interval; S33: Determine the lowest soil temperature within each sub-interval, specifically: min_T=[minT 1 …minT n …minT N ′ where x and y represent the positions of pixels, and H xy represents the elevation value at the pixel (x, y), and T sxy represents the land surface temperature at the pixel (x, y) where the elevation is in the n-th sub-interval, {T sxy} represents the set composed of all T sxy , minT n represents the minimum value in {T sxy}, and min_T represents the vector composed of {minT n} 1≤n≤N ; S34: Determine the lowest and highest soil temperatures within each sub-interval, specifically: max_T = [maxT 1 …maxT n …maxT N ′ where maxT n represents the maximum value in {T sxy}, and max_T represents the vector composed of {maxT n} 1≤n≤N .

3. The method according to claim 1, characterized in that, S4 includes the following steps: S41: Solve the change rate of the lowest soil temperature with elevation based on S3, specifically: where β = [β 0 β 1 ′ represents the rate of change of the lowest soil temperature with elevation; S42: Solve the change rate of the highest soil temperature with elevation based on S3, specifically: where κ = [κ 0 κ 1 ′ represents the change rate of the highest soil temperature varying with elevation.

4. The method according to claim 1, characterized in that, S5 includes the following steps: S51: Calculate the lowest soil temperature corresponding to the elevation value of each pixel, specifically: T min_o = β 1 H o + β 0 Where H o represents the elevation value per pixel, and T min_o represents the lowest soil temperature corresponding to the elevation value per pixel; S52: Calculate the highest soil temperature corresponding to the elevation value of each pixel, specifically: T max_o = κ 1 H o + κ 0 where T min_o represents the highest soil temperature corresponding to the elevation value per pixel.

5. The method according to claim 1, characterized in that, S6 includes the following steps: S61: Calculate the change rate of soil temperature with elevation value at each pixel, specifically: where T s_o represents the pixel-by-pixel soil temperature, and ν represents the change rate of the soil temperature with respect to the elevation value at each pixel; S62: Calculate the surface soil temperature at each pixel, specifically: τ o = T s_o + νD where D represents the depth of the surface soil at each pixel, with the unit of m, and τ o represents the soil temperature at the soil depth D; S63: Calculate the soil heat flux at each pixel, specifically: G = K(T s_o - τ o )D = - KνD where K represents the thermal conductivity in the unit of W / m 2 / K, and G represents the measured soil heat flux in the unit of W / m 2 .

Images