## 3 Radiometric and Geometric Calibration and Corrections
### Radiometric Calibration and Corrections  
Radiometric effects can arise in PS images internally from platform, sensor, and calibration differences and externally from atmospheric and environmental effects. Planet performs sensor/radiometric and atmospheric corrections, but the procedures vary by product/processing level (Table 2). Since each sensor has a unique relative spectral response and is sensitive to different parts of the spectrum, even well-calibrated sensors will produce different radiance values [9]. Planet's atmospheric correction algorithm utilizes look up tables generated from a range of atmospheric conditions (i.e., water vapor and temperature profiles, aerosol types, aerosol optical depth), geometry (solar zenith angle, satellite zenith angle, azimuth angle difference, elevation), surface conditions, and spectral conditions, and atmospheric corrections are applied using standard atmospheric models with MODIS water vapor, ozone, and aerosol data. However, there are limitations to note. A single, global aerosol model is used with all scenes assumed to be captured at sea level and exhibiting Lambertian scattering, which fails to account for stray light and adjacency effects [17]. Additionally, the MODIS scenes on which the model is built are sometimes unavailable, and the approach does not correct for haze and thin cirrus clouds. These limitations result in reflectance values that are not always compatible with reference values (e.g., from Landsat 8 or Sentinel-2), even when scenes are captured the same day. Figure 3 compares density plots for PS and harmonized Landsat-Sentinel data (HLS) for four bands (RGB-NIR) for images captured on the same day. From these figures, it is possible to see the considerable differences in the reflectance distributions between the Planet and HLS data, particularly for the blue and green bands. While the red and near infrared bands are more similar, there are still inconsistencies between the acquisitions. These graphs importantly highlight the spectral differences between the PS and Landsat/Sentinel data and demonstrate how direct comparisons of the data are untenable. While Planet continues to improve radiometric calibration of individual sensors including in-orbit calibration [5; 9], additional radiometric adjustments are still vital for many applications, particularly when mosaicking scenes. In situations where only a single PS image is being utilized, established atmospheric correction methods such as dark object subtraction [28] have been used by researchers to compensate for radiometric irregularities [20]. Empirical line calibration [29] could also be used for absolute radiometric correction since the placement of black and white targets in the field is feasible given the small size of PS pixels and the frequent satellite pass-overs. However, in cases where many images are needed to cover the study area, this approach would prove unwieldy. For situations where multiple PS images are being utilized, studies have employed normalization approaches to improve radiometric consistency by adjusting pixel values based on higher-quality sensors such as Landsat and Sentinel. Most often, a linear scaling function is used to shift PS values to match surface reflectance values from the reference sensor [30; 31; 32; 33; 34]. The linear scaling takes the form:  
\[y_{trans}\ =\ ay_{orig}\ +b \tag{1}\]  
where \(y_{trans}\) is the transformed PS reflectance, \(y_{orig}\) is the original PS reflectance, and \(a\) and \(b\) are multiplicative and additive constants that can be determined through substituting \(y_{orig}\) with the reflectance value of a co-located, reference standard pixel (e.g., Sentinel or Landsat). Linear scaling will shift PS reflectances to match a reference standard, such as in Figure 4, which shows cumulative density functions and Kolmogorov-Smirnov D-statistics comparing the distributions.