*2.1. Study Area*

Caohai (104◦10 –104◦20 E, 26◦47 –27◦52 N), in Guizhou Province, is a typical karst plateau wetland lake. It is located on the south side of the county seat of Yi, Hui, and Miao Autonomous County, Weining County, northwest Guizhou Province, and it provides a habitat for rare birds such as *Grus nigricollis*, unique to China (Figure 1). It is a complete and typical karst plateau small watershed, which requires frequent monitoring using remote sensing images. The terrain of the study area is the highest in the east, higher in the southwest, and the lake area is situated in the middle. The water outlet of the watershed is in the northwest, with an average elevation of 2171.7 m and a watershed area of approximately 96 km<sup>2</sup> [33,34]. The land use types in the region are complex and diverse, mainly including construction land, forest land, cultivated land, rivers, and lakes. As it is located in the karst plateau area of Southwest China and belongs to the humid subtropical plateau monsoon climate, the study area has poor light conditions, heavy rainfall, and cloud cover all year round. These factors lead to a serious lack of optical remote sensing image data, especially high-resolution data, and there is an urgent need for high-spatiotemporalresolution images in daily production and scientific research activities [35–37].

**Figure 1.** Location of the study region. (1) Land–water boundary area, (2) mountainous area, (3) urban area.

#### *2.2. Data Sources*

PS is the world's largest micro satellite group, consisting of hundreds of Dove (10 cm × 10 cm × 30 cm) satellites. PS data (https://www.planet.com/markets/educationand-research/, 15 March 2022) have a spatial resolution of 3 to 5 m, and the satellite can acquire data every day, with a short coverage period and fast update speed [38,39]. GF-2 is the first civil optical remote sensing satellite successfully launched by China in 2014, with a

spatial resolution better than 1 m. It is the civil land observation satellite with the highest resolution in China. The GF-2 data come from the China Resources Satellite Application Center (http://www.cresda.com/CN/, 17 March 2022), the revisit period is 5 days, and the coverage period is 69 days [40–42].

This study selected the PS data of 2 scenes imaged on 15 April 2021 and 10 July 2021, and the GF-2 data of 2 scenes imaged on 15 April 2021 and 13 July 2021. Due to the limitation of revisit cycle, GF-2 does not have the image of 10 July 2021, so the scene with the closest time (13 July 2021) was selected. Among them, the GF-2 data for 15 April were used as the input known high-resolution low-temporal data. PS data for 15 April served as input known high-temporal low-resolution data. The PS data for 10 July were used as the high-temporal low-resolution data in the prediction period to simulate the high-resolution data in the corresponding period, and the GF-2 data for 13 July were used as the verification data for accuracy evaluation.

The data were radiometrically corrected using ENVI 5.3 software, and atmospheric correction was performed with the FLAASH Atmospheric correction module. Second, the PS data were converted to a UTM 50N/WGS84 projection and coordinate system and resampled to 1 m resolution using the nearest neighbor method. Finally, rectification was performed via the RPC Orthorectification Workflow tool to make the two images perfectly match. Finally, they were cropped to the same experimental area as the GF-2 data. In this study, four multispectral bands of GF-2 data and the corresponding PS band were selected as experimental bands. The specific band ranges are shown in Table 1.

**Table 1.** GF-2 PMS and PS image spectral ranges.


#### *2.3. Methods*

2.3.1. FSDAF Model

FSDAF integrates the method of mixed pixel decomposition and a weighting function, and provides better prediction results for changes in regional ground object types. The main steps are as follows: (1) classify the high-spatial-resolution images at time *tb*; (2) use the reflectivity change of the PS image to estimate the time change of the corresponding ground object type from *tb* to *tp*; (3) use the category temporal change obtained in the previous step to predict the high-resolution image located in the *tp* period and calculate the residual error of each pixel prediction of the PS image; (4) use the thin plate spline (TPS) function to predict the high-resolution image at time *tp*; (5) calculate the residual distribution based on the thin-plate spline function; (6) use the neighborhood information to obtain the final prediction of the GF-2 image [25,27].

$$P\_{\text{high}}(\mathbf{x}\_{\text{ij}}, y\_{\text{ij}}) = B\_{\text{high}}(\mathbf{x}\_{\text{ij}}, y\_{\text{ij}}) + \sum\_{k=1}^{n} \left[ w\_k \times \Delta R(\mathbf{x}\_k, y\_k) \right] \tag{1}$$

$$
\Delta P\_{\text{high}}(\mathbf{x}\_{ij\prime} y\_{ij}) = \varepsilon\_{\text{high}}(\mathbf{x}\_{ij\prime} y\_{ij}) + \Delta R\_{\text{high}}(a) \tag{2}
$$

In the formula, Δ*Phigh*, *xij*, *yij*- is the pixel change value at time *tb* and time *tp*; *εhigh*, *xij*, *yij*is the residual of the high-spatial-resolution image assigned to the *j*-th pixel by the *i*-th pixel of high temporal resolution; Δ*Rhigh*(*a*) is the change value of surface cover type *a* of the high-spatial-resolution data between time *tb* and time *tp*; *Phigh*, *xij*, *yij*is the pixel value of the high-temporal-resolution image at time tp; *Bhigh*, *xij*, *yij*is the pixel value of the high-temporal-resolution image at time *tb*; *wk* is the weight value of the *k*-th similar pixel; Δ*R*(*xk*, *yk*) is the change value of pixel resolution at time *tb* and time *tp*. The residual

value between the cell value of the base date and the cell value of the forecast date is calculated as follows:

$$
\varepsilon\_{\text{high}}(x\_{i\bar{j}\prime}y\_{i\bar{j}}) = m \times \varepsilon(x\_{i\prime}y\_{i\prime}) \times \mathcal{W}(x\_{i\bar{j}\prime}y\_{i\bar{j}}) \tag{3}
$$

$$\varepsilon(\mathbf{x}\_{i}, y\_{i}) = \Delta P\_{low} \left( \mathbf{x}\_{i\circ}, y\_{i\circ} \right) - \frac{1}{m} \left[ \sum\_{j=1}^{m} P\_{t\_{p}}^{TP} \left( \mathbf{x}\_{i\circ}, y\_{i\circ} \right) - \sum\_{j=1}^{m} B\_{high} \left( \mathbf{x}\_{i\circ}, y\_{i\circ} \right) \right] \tag{4}$$

$$\mathcal{W}(x\_{\text{ij}}, y\_{\text{ij}}) = \mathbb{C}\mathcal{W}(x\_{\text{ij}}, y\_{\text{ij}}) / \sum\_{k=1}^{n} \mathbb{C}\mathcal{W}(x\_{\text{ij}}, y\_{\text{ij}}) \tag{5}$$

$$\mathcal{CN}(\mathbf{x}\_{ij\prime}, y\_{ij}) = P\_{t\_p}^{SP} \left( \mathbf{x}\_{ij\prime} y\_{ij} \right) - P\_{t\_p}^{TP} \left( \mathbf{x}\_{ij\prime} y\_{ij} \right) + \varepsilon (\mathbf{x}\_{i\prime} y\_i) \times \left[ 1 - H I \times \varepsilon(\mathbf{x}\_{i\prime} y\_i) \right] \tag{6}$$

In the formula, *m* is the total number of high-spatial-resolution image pixels corresponding to the high-temporal-resolution image pixels (*xi*, *yi*); *ε*(*xi*, *yi*) is the residual between the *i*-th pixel value predicted due to the time difference between the high spatial resolution at time *tb* and time *tp*; *CW*, *xij*, *yij*is the weight of the assigned residual; *W*, *xij*, *yij*is the weight of *CW*, *xij*, *yij*normalized; Δ*Plow*, *xij*, *yij*is the pixel change value of the high-temporal-resolution image between time *tb* and time *tp*; *PTP tp* , *xij*, *yij*- is the pixel value of the high-spatial-resolution image at time *tp* predicted by the time difference; *PSP tp* , *xij*, *yij*- is the pixel value of the high-spatial-resolution image at time *tp* predicted after TPS optimization parameters; *HI* is the homogeneity coefficient, i.e., in the moving window, when the *k*-th high-spatial-resolution pixel (with a high temporal resolution) and the moving center pixel , *xij*, *yij*have the same land cover type, *HI* is taken as 1; otherwise, *HI* takes a value of 0.
