# Coupled Spatiotemporal Characterization of Monsoon Cloud Cover and Vegetation Phenology
## 3 Results
### Application to the Example Dataset
Geographic partitioning is again present, clearest in PC 1 vs. 2. Western Forests (WF) and Eastern Forests (EF) form nearly distinct clusters, with some intermediate gradation. Central forests are not sufficiently distinct to form an additional EM. Eastern Nejd (EN) and Western Nejd (WN) pixels grade toward a single null EM. The PC 3 vs. 2 projection forms a phase plane with Nejd pixels at the center and wadis on the circumference. EM time series for 101 pixel averages shown in lower right. Time series are vertically offset to emphasize synchrony of phenological responses to the monsoon; order of time series does not imply higher or lower values. EOFs for both regions shown on right side. The other temporal endmembers form clear corners on the scatterplot of dimensions 3 vs. 2. This combination of dimensions is fortuitous, as its geometry corresponds nearly directly to the geography of Jabal Al Qara. The forests and grasslands are clearly distinct from each other along an axis oblique to either of the individual dimensions. Furthermore, the eastern and western portions of the ranges are distinct from each other along an axis that is nearly perpendicular to the forest-grassland axis. This results in a boxy character to the dimension 3 vs. 2 scatterplot. Individual forest subsystems are identifiable from the temporal feature space. Each curvilinear collection of pixels grading from the lower edge to the upper edge of the dimension 3 vs. 2 projection corresponds to a spatially coherent set of pixels grading from the base of an individual wadi up through higher elevations to the grasslands that immediately surround it. The full Jabal Al Qara region can thus be considered a composition of distinct phenolic subsystems that grade in a continuum from east to west. These individual wadi subsystems also radiate outward from the null endmember in the dimension 1 vs. 2 and 1 vs. 3 projections. Samples of 1001 pixel time series were chosen from each of the endmember regions in the temporal feature space. In every case, these pixels cluster in geographic space to form endmember regions that are (nearly) spatially contiguous. The pixel time series for each region were then averaged together to form one mean endmember time series representative of that spatiotemporally distinct region. The five averages of these 5005-pixel time series concisely represent the spatiotemporal variability of all 33,729-pixel time series in the Jabal Al Qara subset of the NDVI image stack. The time series for each of the Jabal Al Qara endmembers is shown in the lower right. For display purposes, the 17 years for each endmember time series were again averaged together to form a single representative year. While each statistically distinct region has a similar average annual cycle, variations in the amplitude of post-monsoon greenness and rate of senescence are clearly visible. These variations will be discussed below. The temporal feature space for Jabal Al Qamar (Figure 2B) exhibits substantially less complexity than the temporal feature space for Jabal Al Qara. While the forests are again distinct, the minimal spatial extent of the grasslands results in the feature space grading directly from forested wadis into the sparsely vegetated Nejd. Two distinct Nejd corners are evident in the dimension 1 vs. 2 space. However, these are clearly grading toward a single Null endmember. These continua would have merged together if the spatial extent of the analysis had been expanded further inland. The time series for each of the Jabal Al Qamar endmembers, as well as the low-order EOFs, are shown in the lower right of Figure 2B. Examination of the dimension 1 vs. 2 projection of the Jabal Al Qamar dataset also demonstrates much sharper spatial clustering than in the Jabal Al Qara. While a continuum does exist between the eastern and western forests of Jabal Al Qamar, the transition zone between them is narrower and more abrupt than in Jabal Al Qara.