Statistical analysis

Kendall trend test method was used to detect the changes of IWP and its major driving factors, which has been widely applied to evaluate changing trends of time series in hydrometeorology^32,33. The specific calculation procedure given by Kendall and Syuart³⁴ and Mann³⁵ is as follows:

For a data series x₁, x₂, …, x_n, the number of all pairs of observations that x_i < x_j (j > i), say p, should be determined first. The ordered (i, j) subsets are (i = 1, j = 2, 3, …, n), (i = 2, j = 3, 4, …, n) … (i = n − 1, j = n), and n is the length of data series.

The basic statistic τ is expressed as:

where E(τ) = 0; .

The test statistic N is defined as

where N converges rapidly to a standard normal distribution. And N_1-α/2 is a threshold at a given significance level (α) that can be obtained from the Standard Normal Distribution Table. If is greater than N_1-α/2, the changing trend is statistically significant at the significance level α, a positive N denotes an increasing trend while negative denotes decreasing.

The concept of average annual growth rate was used to analyze the annual growth range of IWP and its major driving factors. The average annual growth rate is calculated as:

where, is the average annual growth rate (%), Y₁, Y_n is the values of the first and last year of the study period or sub-period, respectively. The correlation analysis was conducted by SPSS 21 software (IBM SPSS Inc., USA).