Multiscale Correlation Analysis between Wind Direction and Meteorological Parameters in Guadeloupe Archipelago
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area and Data Description
2.2. Multi-Scale Multidimensional Correlation Analysis
2.2.1. MEMD
- 1.
- A suitable set of direction vectors are generated by sampling on a unit hyper-sphere;
- 2.
- The projection of the dataset are calculated along the direction vector for all k;
- 3.
- Temporal instants are identified corresponding to the maxima of projection for all k;
- 4.
- is interpolated to obtain multivariate envelope curves for all k;
- 5.
- The mean of envelope curves is calculated by ;
- 6.
- The “detail” is extracted using . If fulfils the stoppage criterion for a multivariate IMF, the above procedure from step (1) onwards is applied upon the residue series (i.e., ). Otherwise, steps from (2) onwards are repeated upon the series .
2.2.2. HSA
2.2.3. TDIC
- 1.
- All time series data are decomposed using MEMD;
- 2.
- The periodicities of the IMFs of the two time series of concern are compared and the IMFs with nearly same mean periodicity are selected;
- 3.
- The ITs of both IMFs (of similar scale) are identified by HT;
- 4.
- The minimum sliding window size () is identified as the maximum of ITs between the two signals at the current position , i.e., ;
- 5.
- The sliding window is then fixed as where n is any positive number (a multiplication factor for minimum sliding window size). In general, n is selected as 1 [46];
- 6.
- IMF1 and IMF2 are given as two IMFs of nearly the same mean period pertaining to two different time series. The TDIC of the pair of IMFs can be found out as at any , where is the correlation coefficient of two time series;
- 7.
- Student’s t-tests are performed to investigate whether the difference between the correlation coefficient and zero is statistically significant or not;
- 8.
- Steps 4 to 7 are repeated iteratively till the boundary of the sliding window exceeds the end points of the time series.
3. Results and Discussion
3.1. MEMD Analysis
3.2. Instantaneous Frequency of Meteorological Parameters (IMFs)
3.3. TDIC Analysis
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Rainfall | Temperature | Relative Humidity | ||||
---|---|---|---|---|---|---|
Modes | (Days) | V (%) | (Days) | V (%) | (Days) | V (%) |
IMF1 | 2.905 | 38.974 | 2.671 | 5.536 | 2.687 | 19.992 |
IMF2 | 4.885 | 20.720 | 4.872 | 5.000 | 4.978 | 16.638 |
IMF3 | 8.742 | 17.364 | 8.659 | 5.550 | 8.659 | 13.764 |
IMF4 | 16.459 | 8.236 | 15.887 | 2.911 | 16.917 | 9.980 |
IMF5 | 31.500 | 5.265 | 31.500 | 3.656 | 33.218 | 8.820 |
IMF6 | 60.900 | 2.547 | 57.094 | 1.584 | 60.900 | 3.796 |
IMF7 | 101.500 | 2.202 | 114.188 | 1.259 | 114.188 | 4.085 |
IMF8 | 203.000 | 0.776 | 203.000 | 12.268 | 203.000 | 5.074 |
IMF9 | 304.500 | 3.633 | 365.400 | 60.834 | 304.500 | 16.740 |
IMF10 | 609.000 | 0.130 | 913.500 | 1.260 | 609.000 | 1.039 |
IMF11 | 1827.000 | 0.004 | 913.500 | 0.005 | 1827.000 | 0.031 |
Residue | LT | 0.150 | LT | 0.139 | LT | 0.041 |
Solar radiation | Wind speed | Wind direction | ||||
Modes | (Days) | V (%) | (Days) | V (%) | (Days) | V (%) |
IMF1 | 2.687 | 31.998 | 2.659 | 13.060 | 2.699 | 29.116 |
IMF2 | 4.885 | 15.998 | 4.911 | 14.761 | 4.885 | 18.601 |
IMF3 | 8.869 | 12.871 | 8.659 | 17.381 | 8.659 | 17.494 |
IMF4 | 17.075 | 9.077 | 16.761 | 15.065 | 16.917 | 10.567 |
IMF5 | 34.472 | 7.192 | 32.053 | 13.015 | 32.625 | 8.337 |
IMF6 | 60.900 | 2.249 | 63.000 | 5.008 | 60.900 | 3.432 |
IMF7 | 107.471 | 0.941 | 107.471 | 2.962 | 101.500 | 3.068 |
IMF8 | 228.375 | 4.901 | 203.000 | 3.214 | 182.700 | 2.666 |
IMF9 | 365.400 | 13.829 | 365.400 | 14.635 | 365.400 | 3.752 |
IMF10 | 913.500 | 0.547 | 913.500 | 0.685 | 913.500 | 1.121 |
IMF11 | 1827.000 | 0.011 | 1827.000 | 0.014 | 913.500 | 0.003 |
Residue | LT | 0.388 | 1827.000 | 0.200 | LT | 1.842 |
Parameters | Pearson Correlation |
---|---|
vs. R | 0.11 |
vs. T | −0.04 |
vs. | 0.32 |
vs. | −0.08 |
vs. U | −0.29 |
Rainfall | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Wind Direction | IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | IMF9 | IMF10 | IMF11 | Residue |
IMF1 | 0.085 | −0.003 | −0.009 | 0.003 | −0.009 | −0.008 | −0.015 | −0.003 | −0.006 | −0.005 | −0.004 | 0.006 |
IMF2 | −0.004 | 0.166 | 0.023 | −0.004 | −0.006 | 0.006 | −0.001 | 0.011 | −0.003 | −0.003 | −0.001 | 0.002 |
IMF3 | −0.008 | 0.004 | 0.101 | 0.021 | 0.000 | −0.015 | −0.006 | −0.001 | −0.007 | −0.004 | −0.005 | 0.010 |
IMF4 | 0.003 | 0.000 | −0.016 | −0.050 | 0.040 | 0.003 | 0.004 | −0.003 | −0.016 | −0.017 | −0.011 | −0.019 |
IMF5 | 0.012 | −0.015 | 0.016 | −0.007 | −0.050 | 0.047 | 0.010 | 0.022 | 0.002 | 0.017 | 0.000 | 0.006 |
IMF6 | −0.009 | −0.020 | 0.021 | 0.015 | −0.045 | 0.023 | 0.038 | 0.045 | −0.002 | −0.020 | −0.019 | 0.007 |
IMF7 | −0.010 | −0.007 | −0.019 | −0.008 | −0.016 | 0.009 | 0.288 | 0.054 | −0.066 | 0.031 | 0.044 | −0.008 |
IMF8 | −0.004 | −0.006 | −0.007 | 0.007 | 0.028 | 0.056 | 0.178 | 0.690 | −0.104 | 0.036 | 0.041 | 0.144 |
IMF9 | −0.038 | 0.004 | 0.000 | 0.009 | 0.016 | 0.031 | −0.071 | −0.006 | 0.744 | 0.115 | 0.038 | 0.056 |
IMF10 | −0.018 | −0.002 | 0.009 | 0.003 | 0.007 | 0.026 | −0.024 | 0.014 | 0.233 | 0.816 | 0.664 | −0.014 |
IMF11 | −0.018 | −0.001 | 0.012 | −0.002 | 0.001 | −0.002 | −0.051 | −0.004 | 0.184 | 0.765 | 0.880 | −0.318 |
Residue | 0.004 | −0.005 | −0.015 | 0.015 | 0.007 | −0.004 | 0.048 | −0.047 | −0.097 | −0.007 | 0.228 | −0.993 |
Wind direction | Temperature | |||||||||||
IMF1 | −0.153 | 0.012 | 0.020 | −0.027 | 0.008 | 0.011 | 0.023 | 0.011 | −0.002 | 0.012 | 0.009 | 0.008 |
IMF2 | 0.003 | −0.204 | −0.057 | 0.000 | 0.005 | −0.008 | 0.012 | −0.013 | 0.005 | −0.007 | −0.009 | 0.012 |
IMF3 | 0.020 | −0.039 | −0.228 | −0.045 | −0.009 | −0.005 | 0.017 | −0.001 | −0.002 | 0.000 | −0.001 | 0.003 |
IMF4 | 0.002 | 0.011 | −0.006 | −0.186 | −0.008 | 0.030 | 0.015 | −0.004 | −0.001 | 0.015 | 0.019 | 0.015 |
IMF5 | 0.013 | 0.015 | −0.001 | −0.074 | −0.188 | 0.007 | 0.018 | −0.002 | 0.004 | −0.018 | −0.005 | −0.027 |
IMF6 | 0.006 | −0.005 | 0.004 | 0.002 | 0.059 | −0.245 | −0.078 | 0.046 | −0.027 | 0.023 | 0.016 | −0.005 |
IMF7 | 0.003 | −0.004 | 0.003 | 0.003 | 0.019 | −0.022 | 0.505 | 0.088 | 0.003 | −0.019 | −0.002 | −0.007 |
IMF8 | 0.020 | −0.002 | 0.002 | 0.013 | 0.018 | −0.004 | 0.171 | −0.059 | −0.225 | 0.038 | 0.134 | 0.044 |
IMF9 | −0.019 | 0.001 | 0.003 | −0.008 | 0.022 | 0.080 | −0.039 | −0.023 | 0.117 | −0.004 | 0.028 | 0.001 |
IMF10 | −0.012 | −0.005 | −0.002 | −0.016 | 0.009 | 0.036 | −0.018 | 0.001 | 0.134 | 0.776 | 0.780 | −0.162 |
IMF11 | −0.005 | −0.007 | −0.007 | −0.016 | 0.010 | 0.048 | −0.003 | −0.026 | 0.028 | 0.630 | 0.721 | −0.147 |
Residue | −0.003 | 0.002 | 0.010 | −0.013 | −0.004 | 0.015 | −0.054 | 0.031 | 0.076 | 0.002 | −0.197 | 0.941 |
Wind direction | Relative humidity | |||||||||||
IMF1 | 0.199 | −0.004 | −0.008 | 0.014 | −0.007 | 0.005 | −0.021 | 0.004 | 0.005 | −0.012 | −0.011 | 0.002 |
IMF2 | 0.014 | 0.386 | 0.057 | −0.004 | −0.001 | 0.002 | −0.004 | 0.012 | −0.004 | 0.002 | 0.000 | 0.003 |
IMF3 | −0.016 | 0.041 | 0.304 | 0.063 | −0.009 | −0.004 | 0.007 | 0.018 | −0.007 | 0.002 | 0.002 | 0.012 |
IMF4 | 0.000 | −0.006 | 0.029 | 0.345 | 0.081 | −0.007 | −0.016 | 0.014 | 0.002 | −0.021 | −0.013 | −0.029 |
IMF5 | 0.007 | −0.013 | 0.012 | 0.045 | 0.200 | 0.088 | 0.004 | 0.016 | 0.009 | 0.017 | 0.004 | 0.019 |
IMF6 | 0.007 | −0.004 | 0.005 | 0.009 | −0.012 | 0.151 | 0.155 | 0.017 | 0.010 | 0.017 | 0.015 | −0.003 |
IMF7 | −0.013 | −0.004 | −0.012 | −0.008 | 0.001 | 0.011 | 0.454 | 0.084 | −0.063 | −0.001 | 0.016 | −0.017 |
IMF8 | −0.004 | −0.003 | −0.013 | 0.007 | 0.003 | 0.007 | 0.055 | 0.398 | 0.123 | 0.003 | −0.061 | 0.119 |
IMF9 | −0.033 | 0.001 | 0.001 | 0.011 | 0.015 | 0.039 | −0.068 | 0.030 | 0.760 | 0.111 | 0.015 | 0.093 |
IMF10 | −0.004 | −0.010 | 0.001 | 0.017 | 0.007 | 0.075 | −0.011 | −0.014 | 0.042 | 0.107 | 0.022 | 0.010 |
IMF11 | −0.017 | −0.003 | 0.009 | −0.002 | 0.002 | 0.003 | −0.051 | −0.016 | 0.165 | 0.753 | 0.889 | −0.309 |
Residue | 0.003 | −0.010 | −0.025 | 0.015 | 0.012 | 0.023 | 0.020 | −0.073 | −0.119 | 0.001 | 0.271 | −0.894 |
Wind direction | Solar radiation | |||||||||||
IMF1 | −0.056 | −0.002 | 0.014 | −0.012 | 0.006 | 0.008 | 0.007 | 0.001 | 0.007 | 0.006 | 0.008 | −0.010 |
IMF2 | 0.007 | −0.128 | −0.026 | 0.003 | 0.001 | −0.006 | −0.009 | −0.008 | 0.001 | −0.004 | −0.002 | −0.007 |
IMF3 | 0.003 | −0.008 | −0.093 | 0.002 | −0.006 | 0.000 | 0.004 | −0.004 | 0.002 | 0.013 | 0.013 | −0.002 |
IMF4 | 0.002 | 0.007 | 0.004 | −0.015 | −0.005 | 0.005 | −0.003 | −0.008 | 0.013 | 0.009 | 0.003 | 0.006 |
IMF5 | −0.002 | −0.001 | −0.022 | 0.051 | 0.152 | 0.008 | 0.004 | 0.017 | −0.023 | −0.006 | 0.006 | −0.018 |
IMF6 | 0.006 | 0.010 | −0.009 | −0.016 | 0.059 | 0.202 | −0.071 | 0.026 | −0.043 | −0.001 | 0.009 | 0.000 |
IMF7 | 0.007 | −0.002 | 0.005 | 0.018 | −0.001 | −0.031 | −0.349 | −0.144 | 0.023 | −0.010 | −0.018 | 0.007 |
IMF8 | 0.013 | 0.005 | 0.005 | −0.010 | 0.010 | −0.049 | 0.048 | −0.270 | −0.261 | 0.000 | 0.089 | −0.047 |
IMF9 | 0.005 | −0.001 | −0.002 | −0.005 | 0.015 | 0.066 | −0.004 | −0.030 | −0.533 | −0.047 | −0.008 | −0.063 |
IMF10 | 0.000 | −0.008 | −0.020 | −0.002 | 0.014 | 0.051 | 0.007 | −0.014 | −0.015 | 0.215 | 0.171 | −0.203 |
IMF11 | 0.017 | −0.002 | −0.017 | −0.002 | 0.003 | 0.026 | 0.048 | −0.003 | −0.183 | −0.612 | −0.707 | 0.254 |
Residue | −0.004 | 0.004 | 0.013 | −0.014 | −0.006 | 0.008 | −0.050 | 0.040 | 0.087 | −0.003 | −0.224 | 0.977 |
Wind direction | Wind speed | |||||||||||
IMF1 | −0.085 | 0.012 | 0.007 | −0.025 | 0.001 | 0.012 | 0.002 | 0.011 | −0.010 | 0.008 | 0.013 | 0.004 |
IMF2 | 0.000 | −0.096 | −0.066 | −0.002 | 0.002 | −0.009 | 0.000 | −0.006 | 0.005 | 0.009 | 0.010 | −0.006 |
IMF3 | 0.021 | −0.035 | −0.294 | −0.058 | −0.030 | −0.014 | 0.000 | −0.014 | −0.010 | −0.015 | −0.014 | −0.004 |
IMF4 | −0.006 | 0.011 | −0.012 | −0.465 | −0.014 | 0.039 | 0.024 | −0.009 | −0.018 | 0.013 | 0.011 | 0.011 |
IMF5 | 0.005 | 0.000 | 0.010 | −0.098 | −0.489 | −0.065 | −0.002 | 0.002 | 0.009 | −0.018 | −0.018 | −0.019 |
IMF6 | −0.003 | −0.009 | 0.016 | 0.019 | −0.061 | −0.480 | −0.093 | −0.066 | −0.011 | −0.001 | −0.009 | 0.002 |
IMF7 | 0.003 | 0.001 | −0.006 | 0.018 | −0.026 | −0.097 | −0.265 | −0.076 | −0.022 | 0.031 | 0.015 | 0.020 |
IMF8 | 0.001 | −0.002 | 0.001 | −0.008 | −0.035 | −0.006 | −0.039 | −0.383 | −0.111 | 0.026 | 0.084 | −0.080 |
IMF9 | 0.022 | 0.000 | −0.006 | −0.011 | −0.004 | 0.042 | 0.041 | −0.003 | −0.749 | −0.104 | −0.029 | −0.060 |
IMF10 | −0.003 | 0.014 | 0.018 | −0.008 | −0.013 | −0.086 | 0.012 | 0.049 | 0.083 | 0.065 | 0.023 | 0.059 |
IMF11 | 0.007 | 0.009 | 0.010 | 0.008 | −0.010 | −0.044 | 0.027 | 0.048 | −0.025 | −0.532 | −0.675 | 0.157 |
Residue | −0.001 | 0.008 | 0.018 | −0.001 | −0.009 | −0.047 | 0.046 | 0.042 | 0.055 | 0.089 | 0.056 | −0.256 |
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Plocoste, T.; Sankaran, A. Multiscale Correlation Analysis between Wind Direction and Meteorological Parameters in Guadeloupe Archipelago. Earth 2023, 4, 151-167. https://doi.org/10.3390/earth4010008
Plocoste T, Sankaran A. Multiscale Correlation Analysis between Wind Direction and Meteorological Parameters in Guadeloupe Archipelago. Earth. 2023; 4(1):151-167. https://doi.org/10.3390/earth4010008
Chicago/Turabian StylePlocoste, Thomas, and Adarsh Sankaran. 2023. "Multiscale Correlation Analysis between Wind Direction and Meteorological Parameters in Guadeloupe Archipelago" Earth 4, no. 1: 151-167. https://doi.org/10.3390/earth4010008
APA StylePlocoste, T., & Sankaran, A. (2023). Multiscale Correlation Analysis between Wind Direction and Meteorological Parameters in Guadeloupe Archipelago. Earth, 4(1), 151-167. https://doi.org/10.3390/earth4010008