Mountain area surface temperature daily scale extension physical model considering terrain and proximity effect

Abstract

The invention discloses a mountainous area surface temperature daily scale extension physical model considering terrain and proximity effect, belongs to the field of thermal infrared quantitative remote sensing research, considers the influence of the terrain on short wave radiation and long wave radiation, and considers the radiation contribution of the long wave radiation of ambient atmosphere on a target pixel at the same time. A heat conduction equation and an energy balance equation are combined, a mountain area surface temperature daily scale expansion four-parameter physical model capable of being used for mountain area complex terrains is constructed, and four parameters comprise a factor mu which links the environment temperature and the environment stress intensity, factors eta 0 and eta 1 which are closely related to weather and climate backgrounds, and thermal penetration P. The invention develops a mountainous area surface temperature daily scale expansion physical model considering terrain and proximity effect, and the mountainous area high spatial resolution surface temperature at any time in the day can be obtained only through sporadic thermal observation values (greater than or equal to 4 thermal observation values).

Description

Technical Field

[0001] This invention relates to the field of infrared quantitative remote sensing, specifically to a diurnal extended physical model of surface temperature in mountainous areas that takes into account topography and proximity effects. Background Technology

[0002] Land surface temperature (LST) is a key physical quantity in the Earth's surface system, reflecting the combined effects of interactions between land, ocean, and atmosphere. It plays an indispensable role in studying the exchange of matter and energy between the Earth's surface and atmosphere, global ocean circulation, climate anomalies, resource and environmental monitoring, and the urban heat island effect, and is widely applied in many basic disciplines and major applied fields. Furthermore, LST is an important land surface parameter among the fundamental climate variables identified by the United Nations Framework Convention on Climate Change and the World Meteorological Organization, impacting numerous global social challenges, including the United Nations Sustainable Development Goals (SDGs). Mountainous areas are highly sensitive to global climate change and serve as a significant indicator. At the same time, mountainous areas account for approximately 24% of the global land surface and have complex topographic structures. Therefore, accurate estimation of LST in mountainous areas is crucial for ecological environment monitoring and climate change research.

[0003] Furthermore, the complex geometry of mountainous areas significantly impacts longwave radiation at the high spatial resolution pixel scale; however, mountains cover approximately 24% of the global land area. Therefore, accurately retrieving mountain surface temperature is crucial for studying both local and global climate change. High-resolution mountain surface temperature data is vital for remote sensing applications such as ecological conservation, climate change research, mountain evapotranspiration estimation, and satellite remote sensing.

[0004] Satellite sensors acquire instantaneous surface temperatures. High temporal resolution (MLST) mountain surface temperatures (MLST) within a day has significant scientific value and application prospects for improving evapotranspiration and hydrological process simulations, optimizing land surface processes and meteorological models, supporting climate change and ecological environment monitoring, and promoting disaster monitoring in plateau and mountainous areas. Meanwhile, how to estimate the MLST at any given moment within a day using instantaneous, sporadic thermal observations is of even greater interest. This is crucial for estimating daily, monthly, or annual average LSTs and has practical application value for dynamically monitoring changes in the thermal environment of mountainous areas. Therefore, studying the response mechanism of mountainous terrain and proximity effects to the diurnal temperature cycle (DTC) in mountainous areas, and developing a diurnal scale extension model suitable for mountainous surface temperatures, is worthy of attention.

[0005] In summary, quantifying the long-wave radiation patterns of neighboring pixels is crucial for accurately retrieving high spatial resolution surface temperatures in mountainous areas. Constructing a scientifically sound and high-precision modeling theory for the diurnal expansion of surface temperatures in mountainous areas is not only a core task of satellite thermal infrared remote sensing technology in the study of mountainous thermal environments, but also key to a deeper understanding of climate and environmental issues in mountainous regions. Acquiring high spatiotemporal resolution MLST (Multi-Layer Thermal Sensing) data can enhance the monitoring capabilities of mountainous thermal environments, enabling it to play a significant role in climate change research, thermal anomaly monitoring, and surface energy balance analysis, possessing profound practical significance and broad application prospects. Summary of the Invention

[0006] To address the aforementioned problems, the purpose of this invention is to provide a physical model for diurnal expansion of surface temperature in mountainous areas that considers topography and proximity effects, thereby achieving high-precision diurnal expansion estimation of surface temperature in mountainous areas with high spatial resolution.

[0007] To achieve the above objectives, this invention provides a diurnal extended physical model of surface temperature in mountainous areas that considers topography and proximity effects. The specific steps include: S1. Considering topographic and proximity effects, and combining the heat conduction equation and energy balance equation, construct a daily-scale extended analytical model of surface temperature in mountainous areas. A notable feature of this invention is the development of a diurnal extended physical four-parameter model, which, without increasing the number of solution parameters, also considers the influence of slope, aspect, and proximity effects on target pixels in complex mountainous terrain. First, a physical analytical model is constructed, based on which a diurnal extended physical (MDTC) model for surface temperature suitable for complex mountainous terrain is built. It is assumed that the mountainous surface satisfies the heat conduction equation and boundary conditions, where the heat conduction equation is expressed as follows: In the formula, This represents partial differential operations. T It's temperature. t It is time. x It's about depth. d It's the slope. f Where is the slope aspect and D is the thermal diffusivity; meanwhile, the boundary conditions of the MDTC model are governed by the energy balance (SEB) equation, which is expressed as follows: In the formula, NSR It is the net radiation at the Earth's surface. H It is sensible heat flux. LE It is latent heat flux. G It is soil heat flux.

[0008] Furthermore, the net surface radiation (NSR) can also be expressed as the sum of the net shortwave surface radiation (NSSR) and the net longwave surface radiation (NSLR), as follows: According to the definition of NSSR, it can be represented in the following form: In the formula, This indicates direct solar radiation. This indicates the contribution of the surrounding terrain to the shortwave radiation of the target pixel. Represents surface reflectance. Indicates the surface emissivity. This represents the long-wave radiation emitted by the atmosphere to the Earth's surface. This indicates the contribution of the surrounding terrain to the long-wave radiation of the target pixel. This indicates that the pixel itself emits radiation.

[0009] According to the definition of NSLR, it can be represented as: In the formula, This represents the long-wave radiation emitted by the atmosphere to the Earth's surface. Indicates long-wave diffuse radiation. Indicates long-wave reflected radiation. This indicates the contribution of the surrounding terrain to the long-wave radiation of the target pixel. This indicates that the pixel itself emits radiation. It represents the surface emissivity.

[0010] Therefore, NSR can be further expressed as: This invention considers the effects of shortwave and longwave radiation on target pixels; therefore, the net surface radiation (NSR) can be further simplified as follows: Based on the above derivation and assumptions, the SEB equation for complex mountainous terrain can be transformed into: In the formula, R environmet The longwave radiative forcing of the target pixel's ambient atmosphere and adjacent terrain can be expressed as: R up This represents the upward longwave radiation, and its expression is as follows: By considering the influence of mountainous terrain and proximity effects, the energy balance process in mountainous areas was derived and described in detail, providing a theoretical basis for further constructing explicit expressions and parameterization schemes for diurnal-scale extended models in mountainous areas.

[0011] S2. Parameterize the diurnal scale extended analytical model of surface temperature in mountainous areas to obtain a diurnal scale extended physical model of surface temperature in mountainous areas containing four parameters. Based on the above theoretical analysis, the topographic effects of direct solar radiation and downward shortwave radiation, the contributions of atmospheric and adjacent topographic longwave radiation, upward longwave radiation, and boundary conditions are essentially implicit functions, making them difficult to directly apply to diurnal extended models of surface temperature in mountainous areas. Therefore, it is urgent to describe them through parameterization. The specific parameterization scheme is as follows: (1) Parameterization of direct solar radiation; in, Direct solar radiation, Z is the solar constant, and Z is the solar zenith angle. Atmospheric attenuation; in, This is the Earth's rotational angular velocity. The coefficients of the first equation are... The coefficients of the second equation; For mountainous areas considering slope and aspect, cos Z It can be improved to consider the cosine of the solar incidence angle cosZ, which is corrected for slope and aspect. m : in, For the coefficients of the third process, The coefficients of the fourth equation are... The coefficients of the fifth equation; in, f Slope direction, Geographical latitude, The solar declination, d Slope; Due to the complex topography and geometric relationship between the sun and the mountainous terrain, the solar radiation received by pixels in mountainous areas should satisfy the following relationship: In the formula, cosZ>0 indicates that the sun is above the horizon, and cosZ m >0 indicates that the pixel can receive direct solar radiation, and M(Z)>0 indicates that atmospheric attenuation is positive.

[0012] (2) Parameterization of the topographic effect of downlink shortwave radiation; The influence of terrain on the downlink shortwave radiation of a target pixel mainly originates from the surrounding visible pixels. This invention uses the downlink shortwave radiation contribution of the target pixel's eight neighboring pixels to approximate the impact of terrain on the target pixel. Assuming that in mountainous areas, the target pixel and its neighboring pixels have the same downlink shortwave direct radiation and albedo, the contribution of neighboring pixels to the target pixel's downlink shortwave radiation due to terrain can be expressed as: In the formula, i Represents the target cell number. j Represents the cell numbers surrounding the target cell ( j =8, indicating the 8 pixels surrounding the target pixel. SVF Indicates the visibility factor of the sky. Represents the surface reflectance of adjacent pixels. This represents the direct solar radiation of adjacent pixels. This represents the average surface reflectance of adjacent pixels. This represents the average direct solar radiation received by adjacent pixels. This indicates that the target pixel receives downwave radiation contributions from neighboring pixels; (3) Parameterization of longwave radiation contributions from the atmosphere and adjacent topography; Under illumination, the forcing effect of environmental radiation on MLST is relatively smaller compared to direct solar radiation. However, in shaded areas or at night, environmental forcing is the main driver of MLST variation. Therefore, this invention considers the longwave radiation effects of the environment and the longwave radiation contribution from topography. This invention employs a coefficient... m The intensity of long-wave radiation stress in the environment is linked to a virtual ambient temperature, expressed as: In the formula, Indicates the environmental stress coefficient. T environment This is a virtual ambient temperature, derived from the contribution of long-wave radiation from the nearby atmosphere and terrain, in shadow areas where there is no direct solar radiation. T environment The temporal variation reflects the temporal variation of environmental forcing. In practical applications, T environment It can be replaced by near-surface temperature or LST without considering topographic effects; near-surface temperature can well represent long-wave downward radiation within the hemispherical range.

[0013] (4) Parameterization of uplink longwave radiation; Because uplink longwave radiation is influenced by various factors such as spatial heterogeneity of surface emissivity, topographic effects, and atmospheric conditions, its acquisition typically relies on remote sensing inversion or atmospheric radiative transfer models, resulting in significant uncertainties in acquisition accuracy and spatiotemporal resolution. To reduce modeling complexity and enhance model applicability, this paper introduces a simplification method, approximating uplink longwave radiation as a linear function of surface temperature. This assumption has been widely adopted in previous studies and can, to some extent, characterize the dominant influence of surface thermal state on uplink radiation. In the formula, h 0 and h 1 represents two linear coefficients. h 0 indicates the first linear coefficient. h 1 represents the second linear coefficient. Fourier series expansion is used to solve the heat conduction equation. To be applicable to Fourier transform, since the dynamic changes in surface temperature over a multi-day period do not have strict periodicity, the upward long-wave radiation coefficient is further expressed as a time-dependent coefficient. t The linear function, Huang et al. h 1 represents time. t The linear function, considering the effect of environmental forcing, does not add new parameters to be solved, and still uses the coefficients. h 1 is represented as: In the formula, or 0 indicates the first coefficient of upward longwave radiation. or 1 represents the second coefficient of upward longwave radiation; (5) Parameterization of boundary conditions; The complex topographic relief of mountainous areas significantly affects the spatiotemporal distribution of solar radiation, particularly manifested in the spatial non-uniformity of sunshine duration (the duration of continuous solar illumination). Due to differences in slope and aspect, the time windows for receiving solar radiation vary significantly across pixels, thus influencing the surface energy balance. Sunshine duration has been proven to be one of the important boundary conditions affecting surface temperature changes; therefore, a boundary condition function for sunshine duration can be constructed based on topographic parameters and introduced into the diurnal-scale extended model of surface temperature to more accurately characterize the differences and dynamic responses of solar radiation and longwave radiation among different topographic units. In the formula, k represents thermal conductivity. Indicates the boundary driving function; Under illumination conditions, the following should be satisfied: In the formula, Indicates the diurnal variation phase angle, Describes the boundary condition function. This represents the domain of the phase angle under illumination conditions. Under non-light conditions, including shadows and night, the following should be satisfied: In the formula, This represents the domain of the phase angle under non-illuminated conditions. The cosine of the effective solar zenith angle on the slope; This invention will f ( oh d t Expanding according to Fourier series, then f ( oh d t This can be represented as: In the formula, n Indicates the harmonic sequence number or the number of harmonics. n Fourier series of order components; A n and B n It is by f ( ωt The coefficients of the two Fourier series determined by Ω are jointly determined by solar radiation, mountain geometry, and environmental stress; Ω refers to the domain of the solar radiation state on the Earth's surface, which is related to the position of the sun and the surface geometry. Indicates the sign of the phase angle integral; In complex mountainous terrain, it is difficult to directly achieve the expression. f ( ωt The analytical formula for the coefficients. This invention employs a discretization method to estimate the numerical solution of the coefficients of two Fourier series, which can be expressed as: In the formula mSee d t It is the integration domain, set M =1000, Give d t =2 π / M ; Therefore, the analytical expression of the heat conduction equation is: In the formula, f n This is the phase offset value. MLST ( 0 ,t , d , f The expression is the developed diurnal-scale extended model of surface temperature in mountainous areas, suitable for complex terrain, denoted as the MDTC model. The average daily surface temperature The attenuation factor for the nth harmonic is... As an obligatory term, For the nth order phase lag, P This refers to thermal flux. The model links intraday time-series MLST with four parameters, including the environmental stress coefficient. m First coefficient of uplink longwave radiation or 0 and the second coefficient of upward longwave radiation or 1. Thermal flux P This equation, based on physical processes, provides a physical basis for estimating the surface temperature in mountainous areas at any given time during the day. The four parameters have clear physical meanings: ① Environmental stress coefficient. m It is a coefficient that links ambient temperature and the intensity of environmental stress; ② First coefficient of uplink longwave radiation or 0 and the second coefficient of upward longwave radiation or 1. Closely related to meteorological and climatic background; ③ P It is thermal flux, which represents the inertia of a substance to heat. The larger the value, the less affected it is by the disturbance of surrounding heat, and vice versa.

[0014] S3. Input the observed surface temperature values ​​of the target mountain area, and determine four parameters—environmental stress coefficient, first coefficient of upward longwave radiation, second coefficient of upward longwave radiation, and thermal penetration—through the daily-scale extended physical model of surface temperature in the mountain area. Estimate the surface temperature at any time in the target mountain area and complete the construction of the daily-scale extended physical model of surface temperature in the mountain area. The surface temperature observation value ; Therefore, the present invention employs the above-mentioned extended physical model of mountain surface temperature on a diurnal scale that considers topography and proximity effects, and has the following beneficial effects: 1) This invention elucidates the effect of the three-dimensional structural features of complex mountain terrain on the long-wave radiation transmission process of mountain pixels, quantifies the influence of terrain effect and proximity effect, and constructs a diurnal extended analytical model of mountain surface temperature.

[0015] 2) This invention analyzes the impact of complex terrain on the diurnal variation of surface temperature in mountainous areas, realizes the construction of a diurnal scale extended model of surface temperature in mountainous areas under clear sky conditions, improves the description of the diurnal variation characteristics of surface temperature in mountainous areas, and provides a rigorous theoretical basis and data support for the refined study of climate change in mountainous areas. Attached Figure Description

[0016] Figure 1This is a flowchart of a diurnal extended physical model of surface temperature in mountainous areas that takes into account topography and proximity effects, according to the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0018] like Figure 1 As shown, this invention provides a diurnal extended physical model of surface temperature in mountainous areas that considers topography and proximity effects, specifically including the following steps: S1. Considering topographic and proximity effects, and combining the heat conduction equation and energy balance equation, construct a daily-scale extended analytical model of surface temperature in mountainous areas. A notable feature of this invention is the development of a diurnal extended physical four-parameter model, which, without increasing the number of solution parameters, also considers the influence of slope, aspect, and proximity effects on target pixels in complex mountainous terrain. First, a physical analytical model is constructed, based on which a diurnal extended physical (MDTC) model for surface temperature suitable for complex mountainous terrain is built. It is assumed that the mountainous surface satisfies the heat conduction equation and boundary conditions, where the heat conduction equation is expressed as follows: In the formula, This represents partial differential operations. T It's temperature. t It is time. x It's about depth. d It's the slope. f Where is the slope aspect and D is the thermal diffusivity; meanwhile, the boundary conditions of the MDTC model are governed by the energy balance (SEB) equation, which is expressed as follows: In the formula, NSR It is the net radiation at the Earth's surface. H It is sensible heat flux. LE It is latent heat flux. G It is soil heat flux.

[0019] Furthermore, the net surface radiation (NSR) can also be expressed as the sum of the net shortwave surface radiation (NSSR) and the net longwave surface radiation (NSLR), as follows: According to the definition of NSSR, it can be represented in the following form: In the formula, This indicates direct solar radiation. This indicates the contribution of the surrounding terrain to the shortwave radiation of the target pixel. Represents surface reflectance. Indicates the surface emissivity. This represents the long-wave radiation emitted by the atmosphere to the Earth's surface. This indicates the contribution of the surrounding terrain to the long-wave radiation of the target pixel. This indicates that the pixel itself emits radiation.

[0020] According to the definition of NSLR, it can be represented as: In the formula, This represents the long-wave radiation emitted by the atmosphere to the Earth's surface. Indicates long-wave diffuse radiation. Indicates long-wave reflected radiation. This indicates the contribution of the surrounding terrain to the long-wave radiation of the target pixel. This indicates that the pixel itself emits radiation. It represents the surface emissivity.

[0021] Therefore, NSR can be further expressed as: This invention considers the effects of shortwave and longwave radiation on target pixels; therefore, the net surface radiation (NSR) can be further simplified as follows: Based on the above derivation and assumptions, the SEB equation for complex mountainous terrain can be transformed into: In the formula, R environmet The longwave radiative forcing of the target pixel's ambient atmosphere and adjacent terrain can be expressed as: R up This represents the upward longwave radiation, and its expression is as follows: By considering the influence of mountainous terrain and proximity effects, the energy balance process in mountainous areas was derived and described in detail, providing a theoretical basis for further constructing explicit expressions and parameterization schemes for diurnal-scale extended models in mountainous areas.

[0022] S2. Parameterize the diurnal scale extended analytical model of surface temperature in mountainous areas to obtain a diurnal scale extended physical model of surface temperature in mountainous areas containing four parameters. Based on the above theoretical analysis, the topographic effects of direct solar radiation and downward shortwave radiation, the contributions of atmospheric and adjacent topographic longwave radiation, upward longwave radiation, and boundary conditions are essentially implicit functions, making them difficult to directly apply to diurnal extended models of surface temperature in mountainous areas. Therefore, it is urgent to describe them through parameterization. The specific parameterization scheme is as follows: (1) Parameterization of direct solar radiation; in, Direct solar radiation, Z is the solar constant, and Z is the solar zenith angle. Atmospheric attenuation; in, This is the Earth's rotational angular velocity. The coefficients of the first equation are... The coefficients of the second equation; For mountainous areas considering slope and aspect, cos Z It can be improved to consider the cosine of the solar incidence angle cosZ, which is corrected for slope and aspect. m : in, For the coefficients of the third process, The coefficients of the fourth equation are... The coefficients of the fifth equation; in, f Slope direction, Geographical latitude, The solar declination, d Slope; Due to the complex topography and geometric relationship between the sun and the mountainous terrain, the solar radiation received by pixels in mountainous areas should satisfy the following relationship: In the formula, cosZ>0 indicates that the sun is above the horizon, and cosZ m >0 indicates that the pixel can receive direct solar radiation, and M(Z)>0 indicates that atmospheric attenuation is positive.

[0023] (2) Parameterization of the topographic effect of downlink shortwave radiation; The influence of terrain on the downlink shortwave radiation of a target pixel mainly originates from the surrounding visible pixels. This invention uses the downlink shortwave radiation contribution of the target pixel's eight neighboring pixels to approximate the impact of terrain on the target pixel. Assuming that in mountainous areas, the target pixel and its neighboring pixels have the same downlink shortwave direct radiation and albedo, the contribution of neighboring pixels to the target pixel's downlink shortwave radiation due to terrain can be expressed as: In the formula, i Represents the target cell number. j Represents the cell numbers surrounding the target cell ( j =8, indicating the 8 pixels surrounding the target pixel. SVF Indicates the visibility factor of the sky. Represents the surface reflectance of adjacent pixels. This represents the direct solar radiation of adjacent pixels. This represents the average surface reflectance of adjacent pixels. This represents the average direct solar radiation received by adjacent pixels. This indicates that the target pixel receives downwave radiation contributions from neighboring pixels; (3) Parameterization of longwave radiation contributions from the atmosphere and adjacent topography; Under illumination, the forcing effect of environmental radiation on MLST is relatively smaller compared to direct solar radiation. However, in shaded areas or at night, environmental forcing is the main driver of MLST variation. Therefore, this invention considers the longwave radiation effects of the environment and the longwave radiation contribution from topography. This invention employs a coefficient... m The intensity of long-wave radiation stress in the environment is linked to a virtual ambient temperature, expressed as: In the formula, Indicates the environmental stress coefficient. T environment This is a virtual ambient temperature, derived from the contribution of long-wave radiation from the nearby atmosphere and terrain, in shadow areas where there is no direct solar radiation. T environment The temporal variation reflects the temporal variation of environmental forcing. In practical applications, T environment It can be replaced by near-surface temperature or LST without considering topographic effects; near-surface temperature can well represent long-wave downward radiation within the hemispherical range.

[0024] (4) Parameterization of uplink longwave radiation; Because uplink longwave radiation is influenced by various factors such as spatial heterogeneity of surface emissivity, topographic effects, and atmospheric conditions, its acquisition typically relies on remote sensing inversion or atmospheric radiative transfer models, resulting in significant uncertainties in acquisition accuracy and spatiotemporal resolution. To reduce modeling complexity and enhance model applicability, this paper introduces a simplification method, approximating uplink longwave radiation as a linear function of surface temperature. This assumption has been widely adopted in previous studies and can, to some extent, characterize the dominant influence of surface thermal state on uplink radiation. In the formula, h 0 and h 1 represents two linear coefficients. h 0 indicates the first linear coefficient. h 1 represents the second linear coefficient. Fourier series expansion is used to solve the heat conduction equation. To be applicable to Fourier transform, since the dynamic changes in surface temperature over a multi-day period do not have strict periodicity, the upward long-wave radiation coefficient is further expressed as a time-dependent coefficient. t The linear function, Huang et al. h 1 represents time. t The linear function, considering the effect of environmental forcing, does not add new parameters to be solved, and still uses the coefficients. h 1 is represented as: In the formula, or 0 indicates the first coefficient of upward longwave radiation. or 1 represents the second coefficient of upward longwave radiation; (5) Parameterization of boundary conditions; The complex topographic relief of mountainous areas significantly affects the spatiotemporal distribution of solar radiation, particularly manifested in the spatial non-uniformity of sunshine duration (the duration of continuous solar illumination). Due to differences in slope and aspect, the time windows for receiving solar radiation vary significantly across pixels, thus influencing the surface energy balance. Sunshine duration has been proven to be one of the important boundary conditions affecting surface temperature changes; therefore, a boundary condition function for sunshine duration can be constructed based on topographic parameters and introduced into the diurnal-scale extended model of surface temperature to more accurately characterize the differences and dynamic responses of solar radiation and longwave radiation among different topographic units. In the formula, k represents thermal conductivity. Indicates the boundary driving function; Under illumination conditions, the following should be satisfied: In the formula, Indicates the diurnal variation phase angle, Describes the boundary condition function. This represents the domain of the phase angle under illumination conditions. Under non-light conditions, including shadows and night, the following should be satisfied: In the formula, This represents the domain of the phase angle under non-illuminated conditions. The cosine of the effective solar zenith angle on the slope; This invention will f ( oh d t Expanding according to Fourier series, then f ( oh d t This can be represented as: In the formula, n Indicates the harmonic sequence number or the number of harmonics. n Fourier series of order components; A n and B n It is by f ( ωt The coefficients of the two Fourier series determined by Ω are jointly determined by solar radiation, mountain geometry, and environmental stress; Ω refers to the domain of the solar radiation state on the Earth's surface, which is related to the position of the sun and the surface geometry. Indicates the sign of the phase angle integral; In complex mountainous terrain, it is difficult to directly achieve the expression. f ( ωt The analytical formula for the coefficients. This invention employs a discretization method to estimate the numerical solution of the coefficients of two Fourier series, which can be expressed as: In the formula mSee d t It is the integration domain, set M =1000, Give d t =2 π / M ; Therefore, the analytical expression of the heat conduction equation is: In the formula, f n This is the phase offset value. MLST ( 0 ,t , d , f The expression is the developed diurnal-scale extended model of surface temperature in mountainous areas, suitable for complex terrain, denoted as the MDTC model. The average daily surface temperature The attenuation factor for the nth harmonic is... As an obligatory term, For the nth order phase lag, P This refers to thermal flux. The model links intraday time-series MLST with four parameters, including the environmental stress coefficient. m First coefficient of uplink longwave radiation or 0 and the second coefficient of upward longwave radiation or 1. Thermal flux P This equation, based on physical processes, provides a physical basis for estimating the surface temperature in mountainous areas at any given time during the day. The four parameters have clear physical meanings: ① Environmental stress coefficient. m It is a coefficient that links ambient temperature and the intensity of environmental stress; ② Coefficient or 0 and or 1. Closely related to meteorological and climatic background; ③ P It is thermal flux, which represents the inertia of a substance to heat. The larger the value, the less affected it is by the disturbance of surrounding heat, and vice versa.

[0025] S3. Input the observed surface temperature values ​​of the target mountain area, and determine four parameters—environmental stress coefficient, first coefficient of upward longwave radiation, second coefficient of upward longwave radiation, and thermal penetration—through the daily-scale extended physical model of surface temperature in the mountain area. Estimate the surface temperature at any time in the target mountain area and complete the construction of the daily-scale extended physical model of surface temperature in the mountain area. The surface temperature observation value ; The MDTC model developed in this invention requires at least four surface temperature observations, and the daily average surface temperature... T d This can be used as an initial input value; the average LST from sporadic observations can be taken. However, this requires a certain distribution of the observed values ​​within the day. Generally, the phase difference between two temperatures should be exactly [value missing]. The optimal time is when the surface temperature (LST) is at its best. Theoretically, by using four or more sporadic LST data points throughout the day, these four parameters can be determined, and the MLST of the mountainous surface temperature at any time of day can be estimated.

Claims

1. A diurnal extended physical model for surface temperature in mountainous areas, considering topography and proximity effects, characterized in that, Includes the following steps: S1. Considering topographic and proximity effects, construct a diurnal extended analytical model of surface temperature in mountainous areas; The diurnal-scale extended analytical model of surface temperature in mountainous areas includes heat conduction equations and energy balance equations. The terrain effects include slope, aspect, and sky visibility factors; The proximity effect includes shortwave radiation and longwave radiation; S2. Parameterize the diurnal scale extended analytical model of surface temperature in mountainous areas to obtain a diurnal scale extended physical model of surface temperature in mountainous areas containing four parameters. The parameterization includes: parameterization of direct solar radiation, parameterization of the topographic effect of downwave shortwave radiation, parameterization of the contribution of atmospheric and adjacent topographic longwave radiation, parameterization of upwave longwave radiation, and parameterization of boundary conditions. The boundary conditions include boundary conditions under illumination conditions and boundary conditions under non-illumination conditions. The four parameters are: environmental stress coefficient, first coefficient of uplink longwave radiation, second coefficient of uplink longwave radiation, and thermal penetration. S3. Input the observed surface temperature values ​​of the target mountain area. The scale-extended physical model determines four parameters: environmental stress coefficient, first coefficient of upward longwave radiation, second coefficient of upward longwave radiation, and thermal penetration. It estimates the surface temperature at any time in the target mountain area and completes the construction of the daily scale-extended physical model of the mountain surface temperature. The surface temperature observation value indivual.

2. The extended physical model of diurnal surface temperature in mountainous areas considering topography and proximity effects as described in claim 1, characterized in that, In S1, the diurnal extended analytical model of mountain surface temperature includes a heat conduction equation and an energy balance equation. The expression for the heat conduction equation is as follows: In the formula, This represents partial differential operations. T Indicates temperature. x Indicates depth, t Indicates time, d Indicates slope, φ Indicates the slope aspect, and D represents the thermal diffusivity; The energy balance equation is expressed as follows: In the formula, NSR represents the net surface radiation. This indicates direct solar radiation. This indicates the contribution of the surrounding terrain to the shortwave radiation of the target pixel. Represents surface reflectance. Indicates the surface emissivity. This represents the long-wave radiation emitted by the atmosphere to the Earth's surface. This indicates the contribution of the surrounding terrain to the long-wave radiation of the target pixel. This indicates that the pixel itself emits radiation.

3. The extended physical model of diurnal surface temperature in mountainous areas considering topography and proximity effects as described in claim 1, characterized in that, In S2, the expression for the direct solar radiation parameter is: in, This indicates direct solar radiation. Z represents the solar constant, and Z represents the solar zenith angle. Indicates atmospheric decay; Considering the slope and aspect of mountainous areas, cosZ is improved to cosZ of the cosine of the solar incidence angle that takes into account the slope and aspect correction. m The expression is: in, The coefficients representing the third-party process, Denotes the coefficients of the fourth equation. Denotes the coefficients of the fifth equation; in, φ Indicates slope direction. Indicates geographical latitude, Indicates the solar declination. d Indicates slope, Represents the Earth's angular velocity of rotation. t Indicates time.

4. The diurnal extended physical model of mountain surface temperature considering topography and proximity effects according to claim 1, characterized in that, In S2, the parameterized expression for the downlink shortwave radiation is: In the formula, i Indicates the target cell number. j This indicates the pixel numbers surrounding the target pixel, which are preset values. Represents surface reflectance. Represents a pixel j Surface reflectivity Represents the target pixel i Surface reflectance, SVF represents the sky visibility factor. Represents the target pixel i Direct solar radiation, Represents a pixel j Direct solar radiation, Represents the target pixel i The contribution of downlink shortwave radiation, This represents the average value.

5. A diurnal extended physical model for mountainous surface temperature considering topography and proximity effects as described in claim 1, characterized in that, In S2, the boundary conditions include boundary conditions under illumination conditions and boundary conditions under non-illumination conditions. The functional expression for the boundary conditions under illumination conditions is: In the formula, Indicates the diurnal variation phase angle, t Indicates time, Describes the boundary condition function. This represents the domain of the phase angle under illumination conditions. Indicates the effective solar zenith angle on the slope. This represents the environmental stress coefficient, where Z is the solar zenith angle. Represents surface reflectance. This indicates direct solar radiation. This indicates the contribution of the surrounding terrain to the shortwave radiation of the target pixel. T environment Indicates the virtual ambient temperature; The boundary condition function expression under non-illuminated conditions is: In the formula, This represents the domain of the phase angle under non-illuminated conditions.

6. The diurnal extended physical model of mountain surface temperature considering topography and proximity effects according to claim 1, characterized in that, In S2, the expression for the diurnal extended physical model of mountain surface temperature, which includes four parameters, is obtained as follows: In the formula, MLST ( 0 , t , d , φ The expression is an extended diurnal model of surface temperature in mountainous areas, suitable for complex terrain. This represents the average daily surface temperature. n Indicates the harmonic sequence number. This represents the attenuation factor of the nth harmonic. Indicates a mandatory item. This indicates the nth-order phase lag. P Indicates thermal flux. t Indicates time, d Indicates slope, φ Indicates slope direction. h 1 indicates the second linear coefficient. Indicates the diurnal variation phase angle, n Indicates the harmonic sequence number. A n Denotes the coefficients of the first Fourier series. B n This represents the coefficients of the second Fourier series.

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