# Coupled Spatiotemporal Characterization of Monsoon Cloud Cover and Vegetation Phenology
## 3 Results  
### Application to the Example Dataset  
In the case of our example time series, for both the Jabl Al Qara and the Jabl Al Qamar \(>50\%\) of the variance is present in the first three dimensions of the transformed data. Scatterplots showing the first three dimensions of the temporal feature space are shown in Figure 2. In these scatterplots, each point represents the time series of an image pixel (or many similar pixels), with the position determined by the relative contribution of the three dominant Principal Components. The geometrical relation between clusters of points in these scatterplots visually depicts the statistical similarity in cycles of cloud cover and vegetation phenology among distinct geographical pixels. In this way, the transformed temporal feature space efficiently characterizes the dominant spatiotemporal patterns in the dataset by showing them in an easily interpreted image. Interactive examination of these scatterplots can reveal important features of the dataset. Figure 2A shows the Jabl Al Qara temporal feature space, endmembers, and associated low-order EOFs. The full 17-year time series of EOF 1 is shown in the upper right, while the median years of EOFs 1, 2, and 3 are shown in the lower right. EOF 1 can be understood to represent the average annual cycle and EOFs 2 and 3 can be considered as the most pervasive modulations of this cycle. These modulations principally alter the amplitude and timing of post-monsoon senescence. The geometrical structure of the temporal feature space is characterized by corners and relatively sharp edges. The pixel time series at the corners are the temporal endmembers (tEMs) of the feature space, representing the most statistically distinct temporal patterns. The continuum that is bounded by the endmembers is indicative of gradations among the extreme temporal patterns associated with endmember pixels at the corners and edges. The sharp edges suggest that most of the pixels in the image can be well represented by linear combinations of a relatively small number of endmember temporal patterns. As is typical with temporal feature spaces, the first Principal Component dimension represents the overall amplitude of the pixel time series. Six distinct temporal endmembers are identifiable from the Jabl Al Qara feature space. The endmember time series are shown in the lower right, while their locations are shown on the Principal Component scatterplots. Most of these corners are most clearly visible from the projection showing dimensions 2 vs. 3 (upper right). Some corners are obscured from ready identification in the other projections, since they plot above or below the plane of the page and are therefore projected onto one another in a two-dimensional plot. The two temporal endmembers that are most distinct in the dimension 1 vs. 2 scatterplot are the Null and Western Forest endmembers. The Null endmember corresponds to pixels with essentially no vegetation and is analogous to the origin of the feature space. The Western Forest, on the other hand, shows the highest amplitude phenology of all temporal patterns in Jabl Al Qara. The ready identification of the maximum and minimum amplitude phenological cycle using dimensions 1 and 2 is intuitive since the first dimension of an EOF transform corresponds to the temporal mean. These endmembers occupy positions that are indistinguishable at the bottom of the dimension 3 vs. 2 scatterplot, from which all of the other endmembers are identified. Figure 2: **(A)** Jabal Al Qara temporal feature space. PC 3 vs. 2 most clearly shows geographically meaningful partitioning. Eastern Grasslands (EG) and Forests (EF), left, grade to Western Grasslands (WG) and Forests (WF), right. Distinct Central Grasslands (CG) also exist, but no analogous central forests are present. WF overprints the Nejd (N) in the 3 vs. 2 projection. Endmember time series for 1001 pixel averages chosen from corresponding corners of the TTS are shown in lower right. (**B**) Jabal Al Qamar TFS.