# Local resolution weighting Local resolution weighting (LRW) combines acquisitions pixel by pixel and gives more weight to the acquisitions that resolve the terrain more finely at that pixel. s1bursts follows Small et al. (2022)[^1] and applies the method to backscatter and coherence alike. # Why mountains need it A radar looks sideways, so the ground resolution of a mountain slope depends on how the slope faces the sensor. A slope facing the sensor is compressed into few pixels and coarsely resolved. A slope facing away is stretched over many pixels and finely resolved, unless it is so steep that it lies in radar shadow. Ascending and descending orbits look from opposite sides, so each resolves slopes that the other resolves poorly. # The weights The `scattering_area` band of an RTC product contains the normalized ground area A_i that acquisition i observes in each pixel. Its inverse is the local resolution, r_i = 1/A_i. At each pixel, the weights are the local resolutions, normalized to sum to one over the M acquisitions with a valid observation there: W_i = \frac{r_i}{\sum\_{j=1}^{M} r_j} The composite of a measured value x is the weighted mean x_c = \sum\_{i=1}^{M} W_i \\ x_i , or the weighted median or quantile with `aggregation="median"` or a quantile level. The weights depend only on the viewing geometry, so x can be backscatter \gamma^0 or coherence. A coherence product has no scattering area of its own, so each pair is weighted by the RTC product of its primary acquisition, which is why [compose_coherence_lrw()](../reference/resolution_weighter.ResolutionWeighter.md#s1bursts.resolution_weighter.ResolutionWeighter.compose_coherence_lrw) takes RTC products as well. An acquisition in radar shadow has no valid area there and does not count toward M. Bursts of the same orbit and date are mosaicked first, so the overlap of neighboring bursts counts once. The edge of every burst is dropped, because multilooking or the coherence window darkens it. `burst_edge_trim` turns this off, and its width follows the looks or window and the grid spacing. Each pixel is taken from the burst whose data edge is farther away, which splits every overlap at its midline, as SNAP's TOPSAR-Deburst and TOPSAR-Merge do. A pixel's scattering area comes from the same burst as its value, or for coherence from the RTC product of that burst. # Capping the local resolution Close to radar shadow, A_i approaches zero and r_i grows without bound, although the simulated area is least reliable there. `clip_max_resolution` sets a cap r\_\text{max} and uses \min(r_i, r\_\text{max}) in place of r_i in the weights, so that one acquisition cannot dominate such pixels. No cap is applied by default. For scale, flat terrain has a local resolution of about 0.6 to 1.0. # The quality layers The number of observations (`QA-NUM`) is M, the number of acquisitions that contributed to each pixel. The composite quality map (`QA-CQM`) is the local resolution of the composite: the inverse of the mean scattering area, weighted as the composite is: \text{CQM} = \left( \sum\_{i=1}^{M} W_i \\ A_i \right)^{-1} A higher value means a finer resolution. The quality map describes the viewing geometry only, not the accuracy of the measured value. With a median or quantile, it is still the weighted mean from [The weights](#the-weights), so it describes the weighting rather than the acquisitions that supplied each value. ## Footnotes [^1]: Small, D., Rohner, C., Miranda, N., Ruetschi, M., & Schaepman, M. E. (2022). Wide-area analysis-ready radar backscatter composites. *IEEE Transactions on Geoscience and Remote Sensing*, 60, 5201814.