## 4 Results
### Grid-Level FRP
#### 4.3.2 Underestimation of MODIS Grid FRP and Adjustment Models  
The relationship between MODIS and VIIRS grid FRP, characterized as the median FRP ratio of VIIRS to MODIS, varies with satellite VZA and grid size (Figure 8 and Table 1). Generally, the FRP ratio decreases slightly along VZA for grid size finer than 0.5\({}^{\circ}\) (Figure 8a-c), remains nearly constant at a grid size of 0.5\({}^{\circ}\) (Figure 8d, as also indicated by the fitted model and small r\({}^{2}\) showing in Table 1), but increases for the grid size coarser than 0.5\({}^{\circ}\) (Figure 8e-g). At the finest grid size of 0.05\({}^{\circ}\), the FRP ratio indicates that MODIS and VIIRS grid FRP are generally comparable in view angles close to nadir but VIIRS grid FRP becomes smaller in large view angles, although the ratio at individual grids varies largely from 0.1-10 (Figure 8a). As the grid grows to 0.25\({}^{\circ}\), a commonly used resolution in biomass-burning emissions inventories, MODIS grid FRP on average is underestimated by 14-31% in all view angles relative to VIIRS grid FRP according to the FRP ratio (Figure 8c), in which MODIS misses 20% of VIIRS sum FRP (Figure 6b). At the coarsest grid size of 5\({}^{\circ}\), the FRP ratio also reveals that MODIS FRP underestimation generally increases from 69-130% with VZA (Figure 8g). Consequently, the underestimation of MODIS grid FRP increases with the increase in grid size and VZA.  
The VIIRS-to-MODIS FRP ratio is a function of satellite VZA at a grid size, which provides empirical relationships to adjust the underestimation of MODIS FRP partly at different resolutions (Table 1). All the best-fit models for the seven grid sizes show a high coefficient of determination (r\({}^{2}\) 0.67) and small root-mean-square error (RMSE) (<0.146). Interestingly, the parameter \(\beta_{0}\), the bias of FRP ratio, which measures the degree of underestimation of MODIS grid FRP in nadir (VZA = 0\({}^{\circ}\)) underestimation of MODIS grid FRP (in nadir with VZA = 0\({}^{\circ}\)), increases significantly from 1.05 to 1.69 as grid size grows from the finest to the coarsest.  
Figure 7: VIIRS fire detection count and FRP distributions in the matched and not-matched 0.25\({}^{\circ}\) grids across Africa. (**a**) The stacked histogram shows the percent of the matched (red) and not-matched (blue) VIIRS fire detections in every 5\({}^{\circ}\) MODIS VZA from nadir to the scan edge, and the yellow line displays the cumulative percentage of the not-matched VIIRS fire detections to all the fire detections contemporaneously observed by VIIRS I-band. (**b**) VIIRS FRP frequency density distributions in the matched (red cycle) and not-matched (blue triangle) grids. The gray dash line shows the location of 2 MW FRP.  
Figure 8: Derived best-fitted models (Equation (3)) at seven grid resolutions: (**a**) 0.05\({}^{\circ}\), (**b**) 0.1\({}^{\circ}\), (**c**) 0.25\({}^{\circ}\), (**d**) 0.5\({}^{\circ}\), (**e**) 1.0\({}^{\circ}\), (**f**) 2.5\({}^{\circ}\), and (**g**) 5.0\({}^{\circ}\). Gray solid dots represent the matched grids, blue solid cycles and bars are the median, 10 th, and 90 th percentiles of the FRP ratio in every 1\({}^{\circ}\) MODIS VZA, and the red solid line is the best-fitted model. Note that the \(y\)-axis uses logarithmic scale for visualization purposes.