**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 surface parameters**

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., the phase characteristics of spatial scale effects.

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

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

1.672050 1.088930 0.029594 0.027916 —

*Histograms of original and processed NDVI images. (a) MOD13 Q1, (b) 30 m downscaled MOD13 Q1,*

**NDVI images Maximum Minimum Mean Variance Correlation**

MOD13 Q1 0.999100 0.561500 0.397400 0.001100 — 30 m downscaled MOD13 Q1 0.999950 0.999793 0.326412 0.206495 0.937449

**coefficient**

*(c) OLI NDVI, (d) difference image between* **Figures 3** *and 1 (***Figure 3Figure 1***).*

OLI NDVI 0.984436 0.961210 0.299418 0.227313

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

**Figure 4.**

**Table 1.**

**46**

Difference image (**Figure 3Figure 1**)

*Statistics of original and processed NDVI images.*

*Fractal Analysis - Selected Examples*

spatial-resolution feature of medium spatial-resolution images, and carried out a series of studies on spatiotemporal fusion of remotely sensed surface parameters such as surface reflectance [34], land surface temperature [35, 36], vegetation indexes [37], leaf area index [38], and so on. And then Huang et al. [39] reviewed this and presented the systematic achievements in theory and application. From the theoretical basis of spatiotemporal scale conversion fusion (the spatial scale consistency of the time-phase variation model and the time consistency of the spatial downscaling model) to the type division of the spatiotemporal scale conversion fusion algorithms (the algorithms based on features' components, the algorithms based on surface spatial information, the algorithms based on features' temporal change, and the combination algorithms of the ones above), and then to the key problems and challenges encountered in existing research (the imaging geometry and radiation characteristics, differences between multi-source RS images, the complexity of subpixel unmixing models, the complexity of features' temporal change models, etc.), and the possible development trend in future (improvement in the versatility and robustness of the algorithms), he made a detailed and in-depth explanation, so that we have a more comprehensive understanding of the development of spatiotemporal scale conversion fusion research. In fact, in addition to this method, the multi-fractal method has important potential to solve the above problems [21, 40]. The following is an example of NDVI analysis and how to establish a spatiotemporal scale conversion model (or spatiotemporal scaling fusion model) based on multi-fractal theory and method.

embodied as a parameter in the model. This model is more universal than the downscaling model based on the single phase image. To obtain a medium to high spatial resolution NDVI image of a certain phase during vegetation growth, the corresponding phase and the low spatial resolution NDVI image of the phase are brought into the model calculation. Of course, this method requires the research object to have a more significant phase or time periodicity, and the established

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

poral scaling. The implementation idea is similar with Section 2.2, while the *r* function changes. The *r* functional parameters may need to be recalibrated when the spatial distribution of vegetation cover changes obviously with time (e.g., sowing stage, heading stage, maturity stage, etc.). Therefore, *r* function will be merged with temporal parameters of NDVI distribution, such as LAI. And the multi-fractal model of NDVI spatiotemporal scaling should be a function of NDVI to capture

Besides, there is another method of multi-fractal modeling of NDVI spatiotem-

Although the multi-fractal theory and method has advantages in constructing a spatiotemporal scale conversion model of RS land surface parameters, the theory and implementation of this method are more complicated, and few research cases are currently seen. However, this method is expected to become a new method for the construction of spatiotemporal scale conversion model of RS land surface

Taking normalized difference vegetation index (NDVI) as an example, the establishment of scaling models based on fractal theory was described and analyzed in the paper. It was concluded that fractal iterated function system was an effective methodology to establish downscaling models for remote sensing land surface parameters such as NDVI and multi-fractal modeling may be a novel methodology to establish spatiotemporal scale conversion models for land surface parameters

This work was supported by the National Natural Science Foundation of China "Coupling of NDVI's up-scaling and down-scaling fusing with ground objects classification" (No. 41601350), the Natural Science Foundation of Fujian Province, China "Research on NDVI's scaling fusing with ground objects classification" (No. 2017J05069), and the "Scientific Research Climbing Plan" Project from Xiamen University of Technology "Spatial Distribution Estimation and Dynamic Monitoring of Soil Organic Matter Based on Multi-source and Heterogeneous Data"

spatiotemporal scale conversion model is more accurate.

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

temporal changes in relation to ancillary data such as LAI.

parameters, which is worthy of further study.

**4. Conclusions**

such as NDVI in the future.

**Acknowledgements**

(No. XPDKT19010).

**49**

### **3.2 Spatiotemporal scale conversion models of NDVI based on multi-fractal theory and method**

As the best indicator of vegetation growth status and vegetation coverage, NDVI has typical phenological characteristics. This means that in the same area where the surface cover type is unchanged, the physiological characteristics and external forms of the plant can change significantly in different growth stages, and this change will be directly reflected in the changes in image spectrum and NDVI of the surface. Furthermore, the NDVI spatial scale conversion model based on RS images of different growth periods (i.e., different phases) will also change. How to effectively reflect the influence of the phase characteristics of RS images on the construction of this model and then construct a more universal NDVI spatial scale conversion model that can be integrated with surface phenological features, namely, NDVI spatiotemporal scale conversion model? This issue has important research value. Kim and Barros [21] proposed the idea of multi-fractal method for multi-temporal remote sensing soil moisture spatial down-scaling model to describe the phase characteristics of soil moisture spatial down-scaling, but did not do specific research.

Referring to the existing knowledge, the specific method of establishing the NDVI spatiotemporal scale conversion model is given here: first, analyze the surface condition of the study area, determine the type of the main cover of the study area, and based on its phenological knowledge, select enough low and medium-high spatial resolution images finely corresponding to important "nodes" of vegetation throughout the growing season; secondly, the NDVI spatial downscaling models for different growing stages "nodes" are constructed based on the down-scaling methods such as fractal IFS; third, according to multi-fractal theory and method, using the time phase as a factor in the fractal dimension calculation method, the models corresponding to each growth stages are "fused" to obtain a unified and full growth period NDVI scale conversion model (i.e., NDVI spatiotemporal scale conversion model). At this time, the time phase (i.e., different growth stages) has been

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

embodied as a parameter in the model. This model is more universal than the downscaling model based on the single phase image. To obtain a medium to high spatial resolution NDVI image of a certain phase during vegetation growth, the corresponding phase and the low spatial resolution NDVI image of the phase are brought into the model calculation. Of course, this method requires the research object to have a more significant phase or time periodicity, and the established spatiotemporal scale conversion model is more accurate.

Besides, there is another method of multi-fractal modeling of NDVI spatiotemporal scaling. The implementation idea is similar with Section 2.2, while the *r* function changes. The *r* functional parameters may need to be recalibrated when the spatial distribution of vegetation cover changes obviously with time (e.g., sowing stage, heading stage, maturity stage, etc.). Therefore, *r* function will be merged with temporal parameters of NDVI distribution, such as LAI. And the multi-fractal model of NDVI spatiotemporal scaling should be a function of NDVI to capture temporal changes in relation to ancillary data such as LAI.

Although the multi-fractal theory and method has advantages in constructing a spatiotemporal scale conversion model of RS land surface parameters, the theory and implementation of this method are more complicated, and few research cases are currently seen. However, this method is expected to become a new method for the construction of spatiotemporal scale conversion model of RS land surface parameters, which is worthy of further study.
