## 1 Introduction

Table 3: Thematic map legend of the ATCOR-2/3/4 spectral pre-classification [71; 72; 73], whose output product is identified as “image_hcw.bsq” (hcw = haze/cloud/water and snow) map. According to [PERSON] and [PERSON], “pre-classification as part of the atmospheric correction has a long history, e.g., as part of NASA’s processing chain for MODIS”, e.g., refer to [57]. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Label**} & \multicolumn{3}{c}{**Spectral Rule (based on reflectance measured at Landsat TM central} \\  & & wave bands, 18 is located at 0.48 nm, b2 at 0.56 nm, b3 at 0.66 \(\mu\)m, b4 at \\  & & 0.83 μm, b5 at 1.6 μm, b7 at 2.2 μm)**Pseudocolor** \\ \hline
1 & Snow/ice & b4/b3 \(<\) 1.3 ANDb \(\geq\) 0.2 ANDb5 \(<\) 0.12 \\
2 & Cloud & b4 \(>\) 0.25 ANDb0.85 \(<\) 0.15 \\
3 & Bright bare soil/sand/cloud & b4 \(\geq\) 0.15 ANDb1.3 \(\leq\) b4/b3 \(\leq\) 3.0 \\
4 & Dark bare soil & b4 \(>\) 0.15 ANDb1.3 \(\leq\) b4/b3 \(\leq\) 3.0 \\
5 & Average vegetation & b4/b3 \(>\) 3.0 ANDb1.3 \(\leq\) 0.0 ANDb2.0 \(\leq\) b4 \(\leq\) 0.45 \\
6 & Bright vegetation & b4/b3 \(\geq\) 3.0 ANDb(b2/b3 \(\geq\) 0.8 OR b3 \(\leq\) 0.15) ANDb1.3 \(\leq\) 0.08 \\
7 & Dark vegetation & b4/b3 \(\geq\) 3.0 ANDb(b2/b3 \(\geq\) 0.8 OR b3 \(\leq\) 0.15) ANDb3.0 \(\leq\) 0.08 \\
8 & Yellow vegetation & b4/b3 \(\geq\) 2.0 ANDb2 \(\geq\) b3 ANDb3 \(\geq\) 8.0 ANDb4/b5 \(\geq\) 1.5* \\
9 & Mix of vegetation/soil & b2 \(\leq\) 0.5 \(\leq\) b4/b3 \(\leq\) 3.0 ANDb5 \(\leq\) 0.5 ANDb4 \(\geq\) 0.15 \\
10 & Asphal/dark sand & b4/b3 \(\leq\) 1.6 ANDb0.5 \(\leq\) b3 \(\leq\) 0.2 ANDb0.0 \(\leq\) b4 \(\leq\) 0.2* \\
11 & Sand/bare soil/cloud & b4/b3 \(\leq\) 2.0 ANDb4 \(\leq\) 0.15 ANDb2 \(\leq\) 0.15* \\
12 & Bright sand/bare soil/cloud & b4/b3 \(\leq\) 2.0 ANDb4 \(\leq\) 0.15 ANDb4 \(\leq\) 0.258 OR b5 \(\geq\) 0.30* b) \\
13 & Dry vegetation/soil & (1.7 \(\leq\) b4/b3 \(\leq\) 2.0 ANDb4 \(\geq\) 0.25*) OR (1.4 \(\leq\) b4/b3 \(\leq\) 2.0 \\  & & ANDb7/b5 \(\leq\) 0.83) \\
14 & Sparse veg./soil & (1.4 \(\leq\) b4/b3 \(\leq\) 1.7 ANDb4 \(\geq\) 0.25*) OR (0.4 \(\leq\) b4/b3 \(\leq\) 2.0 \\  & & ANDb7/b5 \(\leq\) 0.83 ANDb5/b4 \(\geq\) 1.2*) \\
15 & Turbid water & b4 \(\leq\) 0.11 ANDb5 \(\leq\) 0.05* \\
16 & Clear water & b4 \(\leq\) 0.2 ANDb5 \(\leq\) 0.02* \\
17 & Clear water over sand & b3 \(\geq\) 0.02 ANDb3 \(\geq\) b4 \(\leq\) 0.005 ANDb5 \(\leq\) 0.02* \\
18 & Shadow & \\
19 & Not classified (outliers) & \\ \hline \hline \end{tabular}  
* These expressions are optional and only used if band b5 is present. b: Decision rule depends on presence of band b5. c: Decision rule depends on presence of band b7.  
\end{table} 
Table 4: Rule set (structural knowledge) and order of presentation of the rule set (procedural knowledge) adopted by the prior knowledge-based MS reflectance space quantizer, eligible for MS reflectance space hyperpolyhedralization into MS color names, called Spectral Classification of surface reflectance signatures (SPECL), implemented within the ATCOR commercial software toolbox [71; 72; 73]. Figure 11: Sen2 Cor flow chart for ESA Level 2 product generation from Sentinel-2 imagery [11; 12; 44], same as in the Atmospheric/Topographic Correction for Satellite Imagery (ATCOR) commercial software toolbox [71; 72; 73]. While sharing the same system design, ESA Sen2 Cor and ATCOR differ at the two lowest levels of abstraction, known as algorithm and implementation [76] (refer to Section 1). First, a scene classification map (SCM) is generated from top-of-atmosphere reflectance (TOARF) values. Next, class-conditional MS image radiometric enhancement of TOARF into surface reflectance (SURF) values, synonym for bottom-of-atmosphere (BOA) reflectance values, corrected for atmospheric, adjacency and topographic effects is accomplished in sequence, stratified by the same SCM product generated at first stage from TOARF values. More acronyms in this figure: AOT = aerosol optical thickness, DEM = digital elevation model, LUT = look-up table.