# Coupled Spatiotemporal Characterization of Monsoon Cloud Cover and Vegetation Phenology
## 1 Introduction  
Monsoons influence a wide range of ecologically and societally important landscapes. The annual reversal of winds characteristic of monsoon climates generally results in strong seasonality in patterns of rainfall, temperature, and humidity [1]. Because these parameters are often linked to plant physiology, wild and managed vegetation communities alike rely on the monsoon for cues associated with leaf out, growth, and senescence [2]. Mean and interannual variability of the monsoon ultimately controlsoverarching ecosystem parameters like nutrient pulses [3; 4] and net primary production [5; 6]. Where they are present, monsoons drive phenology. Significant year-to-year variations in the timing, duration, and spatial extent of seasonal rains can occur in monsoon environments [7]. Because of the relationship between precipitation and plant growth, the interannual variability of the monsoon can cause fluctuations in vegetation abundance and phenological timing (e.g., [8]). Interannual variability (along with the potential for multi-year trends) in monsoon environments is a question of significant interest to the biogeoscience community, policymakers, and the public, because of the potential implications for management of coupled human-natural systems (e.g., [9; 10; 11]). However, accurate quantification of variability and/or trends in monsoon environments requires consistent measurements of the biogeophysical system across both space and time. Optical satellite imaging is one source of abundant, intercalibrated measurements of the atmosphere and Earth surface. Multispectral sensors like MODIS (the Moderate Resolution Imaging Spectroradiometer) [12], Landsat [13], and Sentinel-2 [14], measure reflected solar radiance in order to provide estimates of Earth's reflectance. Field and laboratory reflectance spectra of many Earth materials have been measured, allowing for accurate, spatially and temporally explicit inference of the abundance of these materials from multispectral imagery (e.g., [15; 16; 17]). Decades of satellite observations now exist and are of sufficient quantity and quality to support robust spatiotemporal analysis. This data archive is freely available, global in scope, and growing with improving resolution in space and time as new satellite constellations become operational and future missions are planned. This work presents an approach to spatiotemporal analysis that relies on a single parameter to reliably discriminate between green vegetation, soil, and clouds. The parameter that we use is the Normalized Difference Vegetation Index (NDVI) [18]. Differences in NDVI among these three common Earth materials are due to their fundamental physical and chemical properties. The broad consistency of the multispectral reflectance properties of these materials, as well as the generality of their relative seasonal cycles, suggests that this approach is likely to be sufficiently general to be profitably applied in other monsoon environments worldwide. Our analytic approach begins by applying Empirical Orthogonal Function (EOF) analysis [19] to an image time series of NDVI. EOF analysis is a commonly used tool in climatology, meteorology, and oceanography [20; 21; 22]. We then extend the traditional EOF analysis by using the topology of the Temporal Feature Space (TFS) composed of the low order Principal Components to characterize the continuum of temporal patterns that are present in the image time series, as described by [23]. The combination of the topology of the temporal feature space, its geographic manifestation as spatial Principal Components, and the structure of the temporal EOFs provides a basis for separating deterministic spatiotemporal patterns from stochastic variability without the need for _a priori_ assumptions about the form of the spatial or temporal processes that may or may not be represented in the data. Subsequent investigation of the resulting temporal feature space allows for discrimination among regions with statistically distinct monsoonal-phenological cycles.