*2.3.1 Experiment*

As the best indicator of the status of vegetation growth and vegetation coverage, the normalized difference vegetation index is widely used in the study of environmental (climate) changes, crop yield estimation, and other fields. Among existing vegetation index products, the moderate resolution imaging spectroradiometer

(MODIS) vegetation index products are highly valued for their ease of use, ready availability, global coverage, and continuous phase. They have been widely used in studies of forest fires [24, 25], grassland vegetation growth [26, 27], drought [28, 29], land desertification [30], and other studies involving ecological environment monitoring. The maximum spatial resolution of MODIS vegetation index products, however, is only 250 m. The validation of this remote sensing land surface parameter is an important issue that cannot be avoided [31–33] and needs to be carried out by means of scale conversion. The most representative MODIS NDVI product, namely, MOD13 Q1, will be studied in this paper, which will also focus on establishing a downscaled model of NDVI and validating the MOD13 Q1 product

*Establishing the Downscaling and Spatiotemporal Scale Conversion Models of NDVI Based on…*

This is the experiment. A Landsat8 OLI NDVI image (**Figure 1**) was utilized to validate a MODIS NDVI image (MOD13 Q1, **Figure 2**) with nearest imaging time in Xiamen, China. Based on the downscaling formulas in Section 2.2, the MOD13 Q1 image of Xiamen was directly downscaled by ⅛ multiples, and the 30 m downscaled NDVI was obtained as **Figure 3**. The histograms of the original and processed NDVI images are drawn as **Figure 4**, and the statistics and correlation coefficients of the NDVI images are presented in **Table 1**. Based on these data, the downscaled results

1.Compared with the real 30 m OLI NDVI image, the 30 m downscaled MOD13 Q1 image has smaller differences in maximum value, minimum value, mean value, and variance. The correlation coefficient between the two images is 0.93, which is highly correlated. The overall quality of the NDVI image obtained by downscaling the MOD13 Q1 image is considered to be good,

were evaluated and the MOD13 Q1 image was validated.

By analyzing **Figures 1**–**4** and **Table 1**, it is found that:

indicating that the overall quality of MOD13 Q1 is good.

based on it.

**Figure 3.**

*30 m downscaled image of MOD13 Q.*

*DOI: http://dx.doi.org/10.5772/intechopen.91359*

*2.3.2 Result analysis*

**45**

**Figure 1.** *30 m OLI NDVI image.*

**Figure 2.** *240 m MOD13 Q1 image.*

*Establishing the Downscaling and Spatiotemporal Scale Conversion Models of NDVI Based on… DOI: http://dx.doi.org/10.5772/intechopen.91359*

**Figure 3.** *30 m downscaled image of MOD13 Q.*

**2.3 Experiment and result analysis**

*Fractal Analysis - Selected Examples*

As the best indicator of the status of vegetation growth and vegetation coverage, the normalized difference vegetation index is widely used in the study of environmental (climate) changes, crop yield estimation, and other fields. Among existing vegetation index products, the moderate resolution imaging spectroradiometer

*2.3.1 Experiment*

**Figure 1.**

**Figure 2.**

**44**

*240 m MOD13 Q1 image.*

*30 m OLI NDVI image.*

(MODIS) vegetation index products are highly valued for their ease of use, ready availability, global coverage, and continuous phase. They have been widely used in studies of forest fires [24, 25], grassland vegetation growth [26, 27], drought [28, 29], land desertification [30], and other studies involving ecological environment monitoring. The maximum spatial resolution of MODIS vegetation index products, however, is only 250 m. The validation of this remote sensing land surface parameter is an important issue that cannot be avoided [31–33] and needs to be carried out by means of scale conversion. The most representative MODIS NDVI product, namely, MOD13 Q1, will be studied in this paper, which will also focus on establishing a downscaled model of NDVI and validating the MOD13 Q1 product based on it.

This is the experiment. A Landsat8 OLI NDVI image (**Figure 1**) was utilized to validate a MODIS NDVI image (MOD13 Q1, **Figure 2**) with nearest imaging time in Xiamen, China. Based on the downscaling formulas in Section 2.2, the MOD13 Q1 image of Xiamen was directly downscaled by ⅛ multiples, and the 30 m downscaled NDVI was obtained as **Figure 3**. The histograms of the original and processed NDVI images are drawn as **Figure 4**, and the statistics and correlation coefficients of the NDVI images are presented in **Table 1**. Based on these data, the downscaled results were evaluated and the MOD13 Q1 image was validated.

#### *2.3.2 Result analysis*

By analyzing **Figures 1**–**4** and **Table 1**, it is found that:

1.Compared with the real 30 m OLI NDVI image, the 30 m downscaled MOD13 Q1 image has smaller differences in maximum value, minimum value, mean value, and variance. The correlation coefficient between the two images is 0.93, which is highly correlated. The overall quality of the NDVI image obtained by downscaling the MOD13 Q1 image is considered to be good, indicating that the overall quality of MOD13 Q1 is good.

of the product release. Therefore, the histogram is reasonable to a certain degree in the larger value area. At the same time, the histogram distribution of the difference image indicates that the pixel values are distributed in the range [1, 1] and the distribution pattern is low on both sides and high in the middle (approximately a value of 0), which also indicates that the downscaled image

*Establishing the Downscaling and Spatiotemporal Scale Conversion Models of NDVI Based on…*

2.Further, the analysis of **Table 1** shows that the maximum value of the

only occupies a small space and does not affect the overall evaluation

According to the above analysis, the overall quality of the MOD13 Q1 downscaled image is good, indicating that the overall quality of MOD13 Q1 is good. In the NDVI range of values from 0.2 to 0.6, MOD13 Q1 is overestimated, and its discrimination ability of NDVI difference is low, which should be taken into account in

Based on the fractal iterated function system, downscaling models of remote sensing land surface parameters can be established. The models can then be merged with more ancillary data, which relate to the scale effects of land surface parameters. Therefore, the models are of benefit for obtaining accurate downscaled results. In summary, although the breadth and depth of the fractal IFS application in establishing RS land surface parameters downscaling models is still insufficient, the inherent physical meaning and the advantages of the dynamic process expression of this method confer great potential on it, which needs further investigation. It is expected to become a new universal method for quantitative downscaling of RS land surface parameters and lead to the discovery of new research methods.

**3. Establishing spatiotemporal scale conversion models of RS land surface parameters based on multi-fractal theory and method**

**3.1 Review of establishing spatiotemporal scale conversion models of RS land**

The phase is an important feature of RS images. When the phase changes, the spectrum of the objects in the image changes accordingly. Then, the parameters calculated based on the spectral information will also change, such as surface reflectivity, NDVI, and so on. The temporal response of RS land surface parameters will be further reflected in the variation of its spatial scale conversion model, i.e.,

In order to quantitatively characterize the phase characteristics of spatial scale effects, that is, to establish a spatiotemporal scale conversion model (also called a spatiotemporal scaling fusion model), scholars combined the advantages of higher temporal-resolution feature of low spatial-resolution images and higher

difference image exceeds the range of [1, 1]. This may be due to a certain error which is caused by the MOD13 Q1 and OLI image during preprocessing process (atmospheric correction, geometric correction, etc.), which causes a large difference in pixel values between the MOD13 Q1 downscale image and the OLI NDVI image. However, the analysis of **Table 1** shows that the mean and variance of the difference image are small, so the above abnormal situation

and the real image are highly consistent.

*DOI: http://dx.doi.org/10.5772/intechopen.91359*

conclusion.

practical applications.

**surface parameters**

**47**

the phase characteristics of spatial scale effects.

**2.4 Discussion**

**Figure 4.**

*Histograms of original and processed NDVI images. (a) MOD13 Q1, (b) 30 m downscaled MOD13 Q1, (c) OLI NDVI, (d) difference image between* **Figures 3** *and 1 (***Figure 3Figure 1***).*


*Note: The correlation coefficient is the one between the downscaled MOD13 Q1 and the OLI NDVI.*

#### **Table 1.**

*Statistics of original and processed NDVI images.*

Comparing **Figure 4(a)** and **(b)**, there is a certain similarity between the distribution patterns of the two images, which indicates that the downscaled image retains the spatial distribution structure of the original image to a good degree, which proves to some extent that the original MOD13 Q1 image is of good quality. In addition, comparing **Figure 4(b)** and **(c)**, it is found that the downscaled NDVI image has a higher proportion in the vicinity of the zero value (mainly artificial features) than the real image. In the range of 0.2–0.6, the difference is greater. The downscaled image generally has a higher proportion in this range of values, and the histogram is smoother, indicating that the image recognition of the NDVI difference is not high. Referring to the correlation between **Figure 4(b)** and **(a)**, it is known that MOD13 Q1 also has these problems within the abovementioned range of values. Analysis of the original MOD13 Q1 image shows that it is a 16-day NDVI composite product, and each pixel takes the maximum value of NDVI within 16 days as the result

*Establishing the Downscaling and Spatiotemporal Scale Conversion Models of NDVI Based on… DOI: http://dx.doi.org/10.5772/intechopen.91359*

of the product release. Therefore, the histogram is reasonable to a certain degree in the larger value area. At the same time, the histogram distribution of the difference image indicates that the pixel values are distributed in the range [1, 1] and the distribution pattern is low on both sides and high in the middle (approximately a value of 0), which also indicates that the downscaled image and the real image are highly consistent.

2.Further, the analysis of **Table 1** shows that the maximum value of the difference image exceeds the range of [1, 1]. This may be due to a certain error which is caused by the MOD13 Q1 and OLI image during preprocessing process (atmospheric correction, geometric correction, etc.), which causes a large difference in pixel values between the MOD13 Q1 downscale image and the OLI NDVI image. However, the analysis of **Table 1** shows that the mean and variance of the difference image are small, so the above abnormal situation only occupies a small space and does not affect the overall evaluation conclusion.

According to the above analysis, the overall quality of the MOD13 Q1 downscaled image is good, indicating that the overall quality of MOD13 Q1 is good. In the NDVI range of values from 0.2 to 0.6, MOD13 Q1 is overestimated, and its discrimination ability of NDVI difference is low, which should be taken into account in practical applications.

#### **2.4 Discussion**

Based on the fractal iterated function system, downscaling models of remote sensing land surface parameters can be established. The models can then be merged with more ancillary data, which relate to the scale effects of land surface parameters. Therefore, the models are of benefit for obtaining accurate downscaled results.

In summary, although the breadth and depth of the fractal IFS application in establishing RS land surface parameters downscaling models is still insufficient, the inherent physical meaning and the advantages of the dynamic process expression of this method confer great potential on it, which needs further investigation. It is expected to become a new universal method for quantitative downscaling of RS land surface parameters and lead to the discovery of new research methods.
