Page 39 - AJWEP-22-4

Spatiotemporal variability and climate forcing mechanisms

1, x x j denoted V , and is obtained by integrating the square of

i
ar
a j 12 3,, ,..., i (VII) the wavelet coefficient over the time translation domain b.
ij
0, x x j
i
2.3.3. RF modeling
Here, S is the cumulative number of times the value The RF algorithm – an ensemble learning framework
k
at time i exceeds the value at time j. When k = 1, S = 0. initially conceptualized by Breiman – operates through
1
Assuming the time series is randomly independent, the parallelized decision trees to enhance predictive
statistical variables are defined as: accuracy while enabling robust quantification of feature
importance. By implementing a bagging technique,
20
E S )
k
UF S ( k k ,,...,23 n (VIII) the model iteratively generates bootstrapped training
k
VarS ( k ) subsets and incorporates stochastic feature selection
during tree construction, ultimately aggregating
where UF is the test statistic, with UF = 0; E(S ) predictions through majority voting to mitigate
k
k
1
and Var(S ) are the mean and variance of cumulative overfitting risks. For this investigation, multivariate
k
S . For a time series X , X , orX that is independent and feature importance analysis was performed using the
n
1
2
k
identically distributed, E(S ) and Var(S ) are calculated Ranger package within the tidymodels environment,
k
k
as: systematically identifying the dominant drivers
underlying the spatiotemporal dynamics of WER and
nn ( 1 ) SER.
ES( k ) Furthermore, existing studies 22,23 have shown that

4 (IX)
)(
VarS ( ) nn ( 12 n 5 ) the decrease in cloud cover, increases in atmospheric
k 72 water vapor, and interannual variations in monsoon
circulation are the main causes of direct changes in
The UF statistic is computed in the forward direction SER and WER. Therefore, nine climatic factors were
of the time series X , X , …, X , while UB is computed selected for attribution analysis, including temperature,
n
1
2
in reverse order. At a significance level of α = 0.05, precipitation, cloud fraction, relative humidity, and
the critical value is 1.96. If |UF|>1.96, a significant ASC.
trend is indicated. Specifically, if UF > 0, the sequence
shows an upward trend, UF < 0 indicates a downward 3. Results
trend, and UF = 0 indicates no trend. If UF > 1.96,
the sequence shows a significant upward trend; if UF 3.1. Temporal variation characteristics of WER and
<−1.96, it exhibits a significant downward trend. An SER
intersection point between the positive sequence (UF) In this study, two indicators (EWED and annual TSR)
and negative sequence (UB) curves within the critical were used, in combination with the Mann–Kendall trend
values indicates the mutation start time. test and spectral analysis methods, to map the temporal
evolution of EWED and annual TSR in NWC from 1961
2.3.2. Wavelet analysis to 2019 (Figures 2 and 3). The trend analysis results
To calculate the real part of the wavelet, this study used the (Figure 2A and B, Table 1) showed that both EWED and
Morlet continuous complex wavelet as the basis function annual TSR in NWC exhibited a significant decreasing
(i.e., the comr function). 12,21 It is expressed as follows: trend over the period 1961 – 2019, with average annual
decline rates at 0.598 W·m ·a (R = 0.718) and 5.663
−1
2
−2
2
2
−1
−2

2 iF e X MJ·m ·a (R = 0.429), respectively. The Mann–Kendall
comr x F b (X) trend test results indicate that the interannual variations
F b in EWED and annual TSR in NWC over the past half-
century can be divided into three stages: A slow increase
stage (stage I), a slow decrease stage (stage II), and a
ab
Vara f , 2 db (XI) rapid decrease stage (stage III). The specific results are
as follows: For EWED, stage I spanned 1961 – 1984,
and for annual TSR, it spanned 1961 – 1975. During
where F is the center frequency, and F is the this period, the UF values were mostly >0, indicating
b
e
frequency bandwidth. The wavelet square difference is an increasing trend. Stage II spanned 1985 – 1992
Volume 22 Issue 4 (2025) 31 doi: 10.36922/AJWEP025190147