Nature research paper: Oceanic climate changes threaten the sustainability of Asia’s water tower
denotes the maximum amplitude of all standardized indices in this study. Because the maximum scale for all standardized indices is in the range −3 to 3, we applied maxFurthermore, to determine the spatial patterns of the trends, we used the modified Mann–Kendall trend analysis as implemented in the R package modifiedmk. This analysis was conducted at the scale of individual grid cells and covers the period 2003–2016.
Maximum covariance analysis was performed to further verify the covariation between spatial matrixes for any pair of indices. The spatial and temporal coefficients were calculated as follows: $${\bf{L}}=\left[\begin{array}{ccc}{{\bf{L}}}_{1} & \cdots \, & {{\bf{L}}}_{1}\\ \vdots & \ddots & \vdots \\ {{\bf{L}}}_{{\boldsymbol{m}}} & \cdots \, & {{\bf{L}}}_{m}\end{array}\right]$$
$${\bf{R}}=\left[\begin{array}{ccc}{{\boldsymbol{R}}}_{1} & \cdots & {{\bf{R}}}_{1}\\ \vdots & \ddots & \vdots \\ {{\bf{R}}}_{{\boldsymbol{q}}} & \cdots & {{\bf{R}}}_{q}\end{array}\right]$$ $${{\bf{C}}}_{l,r}=\frac{1}{N}{\bf{L}}{{\bf{R}}}^{{\rm{T}}}{\boldsymbol{=}}{\bf{U}}{\boldsymbol{\Sigma }}{{\bf{V}}}^{{\rm{T}}}$$$${{\rm{PC}}}_{r,q}{\boldsymbol{=}}{{\bf{V}}}_{q}^{{\rm{T}}}{\bf{R}}$$
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