A Contextual Mann‐Kendall Approach for the Assessment of Trend Significance in Image Time Series

One of the most common problems in estimating trends in image time series is the presence of contaminants such as clouds. There are many techniques for estimating robust trends but evaluating the significance of the trends can be difficult due to this increased variance. This article presents a novel approach called the Contextual Mann‐Kendall (CMK) test for assessing significant trends. This test uses the principle of spatial autocorrelation to characterize geographical phenomena, according to which a pixel would not be expected to exhibit a radically different trend from neighboring pixels. The procedure removes serial correlation through a prewhitening process. Then, similar to the logic of the Regionally Averaged Mann‐Kendall (RAMK) test, it combines the information from neighboring pixels while adjusting for cross‐correlation. CMK was compared with the Mann‐Kendall (MK) test in which contextual information was not involved for the mean annual NDVI over 22 years (1982–2003) in West Africa. With the MK test, ～11% of the study area showed significant (p < 0.001) trends which increased to 16% when tested using the CMK test. Thus the CMK test produces a result that makes intuitive sense from a geographical perspective and enhances the ability to detect trends in relatively short time series.     

Implications of space-time orientation for Principal Components Analysis of Earth observation image time series

A time series of geographic images can be viewed from two perspectives: as a set of images, each image representing a slice of time, or as a grid of temporal profiles (one at each pixel location). In the context of Principal Components Analysis (PCA), these different orientations are known as T-mode and S-mode analysis respectively. In the sparse literature on these modes it is recognized that they produce different results, but the reasons have not been fully explored. In this paper we investigate the interactions between space-time orientation and standardization and centering in PCA. Standardization refers to the eigenanalysis of the inter-variable correlation matrix rather than the variance-covariance matrix while centering refers to the subtraction of the mean in the development of either matrix. Using time series of monthly anomalies in lower tropospheric temperature from the Microwave Sounding Unit (MSU) as well as in CO₂ in the middle troposphere from the Atmospheric Infrared Sounder (AIRS), we show that with T-mode PCA, standardization has the effect of giving equal weight to each time step while centering has the effect of detrending over time. In contrast, with S-mode PCA, standardization has the effect of giving equal weight to each location in space while centering detrends over space. Further, in the formation of components, S-mode PCA preferences patterns that are prevalent over space while T-mode PCA preferences patterns that are prevalent over time. The two orientations thus provide complementary insights into the nature of variability within the series.