## 4 Experiment
### Results and Discussion
#### 4.2.4 MODIS-NDVI Downscaling Based on the Elastic Window
A stratified sampling strategy was employed, where 2 out of 14 Landsat scenes were selected and points were randomly scattered to obtain values of fine curves and original curves for different land cover types, as shown in Table 5. In total, there were 3738 sampling points in 2010. The original values of the MODIS-NDVI curve were considered the true values. Three measures, namely variance, mean difference, and correlation coefficient, were used to assess the similarity between the constructed curve and the original curve. The variance calculation is shown in Formula (9), where \(n\) represents the total number of periods in the NDVI time series, and \(\Delta\)NDVI represents the difference between the two curves during the corresponding period. The parameter \(\Delta\mu\) represents the average value of the NDVI difference between the two curves, as shown in Formula (10). The correlation coefficient  
Figure 10: The generated fine-resolution NDVI images of the Shandong Province (China) of 2010 in row–major order via the elastic window. calculation is shown in Formula (11), where n represents the total number of periods in the temporal NDVI, \(a\) represents the generated NDVI curve, and \(b\) represents the low-spatial-resolution curve. The parameters \(\mu_{a}\) and \(\mu_{b}\) represent the NDVI means of the fine curve and the low-spatial-resolution curve, respectively. \[\sigma=\sqrt{\frac{\sum\limits_{i=1}^{n}{(\Delta\text{NDVI}_{i}-\Delta\mu)}}{n- 1}} \tag{9}\]  
\[\Delta\mu=\frac{1}{n}{\sum\limits_{i=1}^{n}{(\Delta\text{NDVI}_{i})}} \tag{10}\]  
\[c=\frac{\sum\limits_{i=1}^{n}{(\text{NDVI}_{(a,i)}-\mu_{a})(\text{NDVI}_{(b,i)}- \mu_{b})}}{\sqrt{\sum\limits_{i=1}^{n}{(\text{NDVI}_{(a,i)}-\mu_{a})}^{2}}\sqrt {\sum\limits_{i=1}^{n}{(\text{NDVI}_{(b,i)}-\mu_{b})}^{2}}} \tag{11}\]  
The statistical distribution of the constructed NDVI and the original NDVI for the main land cover categories at the sampling points in 2010 is presented in Figure 12. It can be observed that the mean difference of NDVI values (Figure 12A) in the sampled land  
Figure 11: The generated NDVI curves of typical land cover class in the Shandong Province (China), where (**a**) denotes built-up, (**b**) denotes crop, (**c**) denotes forest, (**d**) denotes grass, (**e**) denotes water, and (**f**) denotes wetland. cover types follows a normal distribution. Generally, the constructed NDVI curve has higher values than the original NDVI curve, with an average increase in approximately 0.16 points across all points. Except for forest land types, the standard deviation (Figure 12B) for all other types is around 0.1, and the correlation coefficients (Figure 12C) for each sampling point are generally above 0.9. Based on the local climate characteristics of the study area, it can be inferred that vegetation growth was stagnant during the specified period. Consequently, this image may not comprehensively reflect the accurate vegetation distribution in the area. When this image is used as the basis for generating classification maps, it may introduce errors and hurt the classification results of ground objects. Therefore, some errors were introduced into the generated high-spatial-resolution NDVI dataset in this specific scenic area. \begin{table}
\begin{tabular}{c c c c} \hline
**Year** & **Land Cover** & **Sampling Point Number of 119034** & **Sampling Point Number of 122035** \\ \hline
2010 & Crop & 455 & 622 \\
2010 & Forest & 417 & 228 \\
2010 & Grass & 193 & 252 \\
2010 & Water & 348 & 240 \\
2010 & Built-up & 565 & 418 \\ \hline \end{tabular}
\end{table} 
Table 5: The numbers of sampling points of two areas and the according land cover types.