JEOS RP ISSN03 | Page 335

328

J. Eur. Opt. Society-Rapid Publ. 22, 32( 2026)

Table 1. Sample separability calculation results.

according to Fresnel ' s theorem; h r is the zenith angle of the reflection direction; β is the tilt rate of the small surface element. To accurately characterize the reflection properties of the land surface, the Rahman-Pinty-Verstraete( RPV) semi-empirical BRDF model is introduced [ 25 ], which can be expressed as:

BRDF land ðh i; h v; u cos h k�1 i

� cosh k�1 v

¼ r 0 exp bpð Þ

1�k ðcosh i � cosh v Þ ½ Š h ð h i; h v; u Þ ð8Þ

where r 0 represents the reflection intensity, k represents the surface anisotropy characteristics, h i is the solar zenith angle, h v is the observed zenith angle, φ is the relative azimuth angle, b is forward and backscattering, p( X) isthe direction cosine function, and h( θ i, θ v, φ) isthebackscattering enhancement term.

2.4 Temporal temperature extension of land based on meteorological data

To characterize the rapid temperature changes of land features and overcome the limitation that satellite inversion results only represent typical moments, this paper introduces land surface meteorological data to obtain high temporal resolution temperature information, providing support for the temporal reconstruction and model expansion of land surface temperature.

2.4.1 Land surface temperature data acquisition by the meteorological bureau

The land temperature field is key data for the simulation of infrared characteristics of a scene. The near-real-time product datasets from the China Land Surface Data Assimilation System( CLDAS-V2.0) are selected to obtain surface meteorological temperatures at different times. The data format is NetCDF, and the time resolution is 1 hour. Taking the data from 11:00 am on October 24, 2023 as an example, the land surface temperature is shown in Figure 5a.

Background temperature is interpolated using Ordinary Kriging( OK) [ 26 ]. OK interpolation, also known as spatial local interpolation, is a method based on semi-variogram theory and structural analysis to provide unbiased optimal estimation of regionalized variables within a finite region. OK interpolation for a single spatial moment is defined as:

^Z ðx 0 Þ ¼ Xn k i Zx ð i Þ ð9Þ i¼1

Þ Figure 4. Land surface classification result.

where ^Z( x 0) is the value of the location to be predicted; Z( x i) is the actual measured value at the i-th location; n is the number of actual measured values in the prediction area; and λ i is the weight at the i-th location, the weight [ 26 ] can be expressed as: 8

><

>:

X n

i¼1

X n

j¼1 k i ¼ 1 � k j c x i; x j þ l ð xi; x 0 Þ; i ¼ 1; 2;...; n: ð10Þ

where γ( x i, x j) is the variogram between points i and j; γ( x i, x 0) is the variogram between point i and point 0 to be estimate; μ is the Lagrange multiplier. When using the OK interpolation method, the sample variogram must first be calculated. Then, an appropriate theoretical model for variogram is selected based on its type for simulation. Finally, a linear estimate of the point to be estimated is performed based on the simulated variogram. The sample variogram [ 27 ] is defined as:

cðhÞ ¼ 1 2NðhÞ ¼ X NðhÞ

½ Zx ð i þ hÞ�Zx ð i ÞŠ 2 ð11Þ i¼1

where N( h) is the number of all data pairs with a vector distance of h in the spatial dataset; x i is the coordinate vector of the i-th data point; and h is the vector distance, representing the magnitude and direction of the distance. The spatio-temporal OK interpolation is defined as:

T 0 ðt i Þ ¼ ^Z ðx 0; t i Þ ¼ X n k kZx ð k; t i Þ ð12Þ k¼1

where T 0( t i) is the OK-predicted baseline temperature at the i-th time instant. Z( x k, t i) is the actual measured temperature at location x k and time t i; λ k is the weight assigned to the k-th measured point x k for estimating the value at