**3. Results**

#### *3.1. Relationship Between the DN Values and Spectral Reflectance*

A desirable fitting function of the DN values and the spectral reflectance should meet two requirements: (1) when the reflectance reaches zero, the DN value should also reach zero, and (2) the relationship should be nonlinear because of gamma correction. In the study by Lebourgeois et al. [23], the relationship between the DN values in the raw and the compressed image format is logarithmic. Inspired by their result, we adopted the following fitting function for spectral calibration:

$$\frac{1}{2}y = a \left[ \ln(x+1) \right]^{\frac{1}{2}} \tag{4}$$

where *x* is the DN value of ground targets, *y* is spectral reflectance, and *a* and *b* are fitting coefficients. Equation (4) guarantees that the pixel reflectance is always positive.

This function produced a robust regression fit to the spectral reflectance of the ground targets observed in the Brooksvale Park (Figure 4) and the Yale Playground (Figure 5). The coefficients of determination (*R*2) for Brooksvale Park were greater than 0.60 (*p* < 0.05) and those for the Yale Playground were greater than 0.40 (*p* < 0.05). For Brooksvale Park, all of the data points followed the fitting line closely. For the Yale Playground, there were two outliers: a yellow pavement mark, and a red brick (Figure 5). Such discrepancy may be indicative that these ground targets were not Lambertian reflectors. The view angle of the spectrometer was nadir. If the drone was relatively stable during the flight, the camera was levelled, and if only central pixels were used to form the mosaic, the camera angle would also be perfectly nadir. However, because the mosaic had pixels from other parts of the original photos, and because the camera position could deviate from the vertical, the actual camera angle viewing these targets may differ from the nadir. For this reason, a BRDF is required to correct for the non-Lamberstian behaviors, which is beyond the scope of this study.

**Figure 4.** Regression fit between the band DN value and band reflectance of ground targets in Brooksvale Park. Panels (**<sup>a</sup>**–**<sup>c</sup>**) are for clear sky conditions, and (**d**–**f**) are for overcast sky conditions under which the spectrometer measurement took place. Also shown are the regression equation, coefficient of determination (*R*2), and the confidence level (*p*).

**Figure 5.** The description is the same as in Figure 4 except for the location being Yale Playground. Arrows indicate outliers discussed in the text.

#### *3.2. Landscape Visible-Band and Shortwave Albedo*

Applying the calibration functions (Figure 4d–f) obtained under overcast sky conditions to the pixels in Brooksvale Park, we obtained a landscape-level mean visible band albedo of 0.086 ± 0.110 (Table 3). The landscape visible band albedo of Yale Playground was 0.037 ± 0.063 according to the drone measurement. Here, the drone albedo was obtained using the clear-sky calibration functions (Figure 5a–c). The reader is reminded that the standard deviations here were computed from the albedo values of the pixels in the mosaics, and they therefore are indication of the variations across the landscapes, rather than uncertainties of our estimation.


**Table 3.** Comparison of drone-derived and Landsat 8 visible and shortwave band albedo under clear and overcast sky conditions for the Brooksvale Park and the Yale Playground. Refer to Supplementary Figures S3–S6 for the spatial distributions of these albedo values.

c and o represent clear and overcast sky conditions, respectively; SN and SV represent that the shadow on the Yale Playground were taken as non-vegetation and vegetation, respectively.

The ratio of the shortwave to the visible band albedo of the non-vegetation and vegetation ground targets, are shown in Table 4. To estimate the shortwave albedo at the landscape scale, we first performed a classification of the mosaicked images. The results are illustrated in Figure S2. The vegetation and non-vegetation pixels occupied 61% and 39% of the land area in Brooksvale Park, respectively. Their visible band albedo values were multiplied by the conversion factors obtained for the vegetation and non-vegetation ground targets under overcast conditions, respectively, to obtain the shortwave albedo values. Averaging over the whole scene yielded a landscape shortwave albedo of 0.332 ± 0.527 under an overcast sky condition.

**Table 4.** Ratio between the shortwave and visible band albedo obtained with the spectrometer for the vegetation and non-vegetation targets of the Brooksvale Park and the Yale Playground.


At the Yale Playground, a large portion of the pixels were in shadow, with low band reflectance. The spectral information in the three visible bands was insufficient for the classifier to identify which of these pixels were vegetation, and which were non-vegetation. Therefore for the Yale Playground, the image was divided into three classes: vegetation (25%), non-vegetation (50%), and shadow (25%). For the vegetation and non-vegetation pixels, the conversion factors obtained under clear sky conditions were used to estimate their shortwave albedo. For the pixels in shadow, the conversion factors obtained under overcast sky conditions were more appropriate. Since the pixels in shadows were not identifiable, we first assumed that all of them were vegetation (grass, SV), and by applying the conversion factor for vegetation (5.29), we arrived at an estimate of the landscape albedo of 0.061 ± 0.076. We then assumed that all of the pixels in shadows were non-vegetation (SN), obtaining a landscape albedo estimate of 0.054 ± 0.074. These two estimation did not differ by much. The actual albedo value of Yale Playground should fall between these two bounds.
