## 3 Radiometric and Geometric Calibration and Corrections
### Radiometric Calibration and Corrections
In all four bands, the linear transformation changed the D-value considerably, shifting the distribution of the PS data to align more closely with the Sentinel data (Figure 4). Regardless of the difference between the untransformed values (coarser dash) and the Sentinel distribution (solid line), the adjusted PS distribution (finer dash) is nearly coincident with the Sentinel distribution in all cases, indicating that the linear transformation was successful in matching the distributions. However, it should be noted that these adjustments are relative corrections that normalize the imagery [29], they do not necessarily correct the absolute radiometric quality of the imagery. Multi-date radiometric normalization of PS images has also been achieved through identifying pseudo-invariant spectral features using multivariate alteration detection (MAD; [35]). With MAD, a regression equation can be developed between images in a time series and used to transform all pixels in the image [24]. More advanced approaches have involved multi-scale machine learning techniques to correct for radiometric inconsistencies between Planet acquisitions. For example, [PERSON] & [PERSON] [7] promote a technique called Cubesat Enables Spatio-Temporal Enhancement Method (CESTEM), which utilizes a non-parametric model tree regression approach to construct band-specific relations between Planet and Landsat 8. CESTEM has been applied mainly in agricultural environments [36; 37]. Fusion methods have also been tested to leverage the higher fidelity spectral consistency of Sentinel-2 images while taking advantage of the high spatial reso  
Figure 3: Density plots of Planet (dashed lines) compared to corresponding Harmonized Landsat Sentinel-2 (HLS) (solid lines) for (**a**) blue, (**b**) green, (**c**) red, and (**d**) nir bands. Data were derived from a scene captured on 8 October 2020 in western Colorado, USA [38.88N, \(-\)107.05W]. lution of the PS data [38; 39]. For example, [PERSON] and [PERSON] [40] used a state-of-the-art super-resolution residual convolutional neural network simultaneously fuse (sharpen) and radiometrically normalize the PS data. In addition to general pixel-based radiometric inconsistencies within and between PS images, there can also be corrupt lines, bands, and other data quality issues such as clouds. Planet provides two 'usable data mask' assets (udm and udm2) that allow researchers to mask out unusable data or bands. Line-filling methods, such as those used to fill Landsat ETM+ SLC-off gaps (e.g., [41]), may be transferable to PS images. [PERSON] et al. [42] corrected corrupt bands in PS images using unmixing-based denoising, based on the technique by [PERSON] et al. [43]. [PERSON] et al. [44] used the MODIS nadir bidirectional reflectance distribution function adjusted reflectance data to correct the PS data and then generate an improved invalid pixel mask by combining Planet's udm with their own results. Users have also developed cloud and cloud-shadow detection algorithms to assist with masking these radiometric inconsistencies [45; 46]. In sum, it is best to first review the udm/udm2 assets to determine known data quality issues before performing any additional corrections or analyses. Figure 4: Empirical cumulative density functions of untransformed PS (Planet) and adjusted PS (Adj. Planet) through a Sentinel-2 based linear transformation for **(a)** blue, (b) green, (c) red, and **(d)** nir bands. Values are compared using the Kolmogorov–Smirnov test’s \(D\) statistic, which is nonnegative with values closer to 0 signaling similar distributions and larger numbers signaling dissimilar distributions. The image used was captured near Manhattan, KS, USA.