Introduction

Due to the limitation in the orbital configuration of satellites and also the design of remote sensing sensors, it is not possible to have spatial resolution and short-term visiting period at the same time. As a result, different algorithms have been presented to integrate the data of different sensors. In this research, the images of Bands 2 to 7 of Landsat 8 were divided into three homogeneous, semi-homogeneous and heterogeneous regions using Iso Data classification. In each class, micro-scale classification was done using STARFM and ESTARFM algorithms, and then a method based on fractal geometry was presented for spatio-temporal micro-scale based on the triangular prism fractal dimension rule.

Methodology

In this research, bands 2 to 7 of Landsat 8 were divided into three homogeneous, semi-homogeneous, and heterogeneous regions using Iso Data classification and the concept of entropy. Madis was executed. Then micro-scale analysis was done using two algorithms STARFM and ESTARFM in each classification class. In order to carry out micro-mapping based on fractal geometry, first after each image on the dates before and after the prediction time of Landsat and MADIS image and the time of MADIS prediction in different step sizes with the method of determining the dimension of triangular prism calculation. By using the relationship between the fractal in the times before and after the forecast date and the relationship between the fractal after in a photo from Madis (representative with time repetition) and Landsat (representative with better spatial resolution) after the image before this prediction. was hit Using inverse numerical calculations and the rule of Heron's triangle, the radiance value of each pixel was found at the predicted time. The new method designed for fractal geometry gave the best results in homogeneous and semi-homogeneous regions.

Results and discussion

The strongest performance in the homogeneous region was related to the method based on fractal geometry with an average error percentage of 2.323% among all bands, and the weakest performance was related to the ESTARFM method with an error percentage of 4.316. In the semi-homogeneous region, the best performance with an error percentage of 3.368% was related to the method based on fractal geometry and the weakest performance was related to the STARFM method with an error percentage of 6.546 among all bands. In the heterogeneous region, the strongest performance was related to the ESTARFM method with an error percentage of 3.804 and the weakest performance was related to the STARFM method with an error percentage of 8.634 among all bands.

The performance of micro-scale methods in visible bands was generally stronger than their performance in mid- and near-infrared bands. The best results among all bands and regions based on the weighted average of the results related to the method based on fractal geometry with an error percentage of 3.699 and the weakest related to the STARFM method with an error percentage of 6.757. Also, the data with a longer time interval had better performance in the micro-exponential scale compared to the data with a shorter time interval.

Conclusion

In this research, exponential micro-scale was done based on STARFM and ESTARFM algorithms and based on fractal geometry on Bands 2-7 of Landsat 8 and its comparison with actual images on the expected date had the following results in summary:

• The three methods examined in this research had acceptable results in microscale.

• In all methods, the method based on fractal geometry had the best results, followed by ESTARFM and finally STARFM was the weakest.

• In the evaluation of all bands, exponential micro-scale in the homogeneous and semi-homogeneous region with the fractal method has higher accuracy than the STARFM and ESTARFM methods.

• In the evaluation of all bands, exponential micro-scale in the heterogeneous region with the ESTARFM method has a higher accuracy than the method based on fractal geometry and STARFM.