Spatiotemporal Scaling Effect on Rainfall Network Design Using Entropy
Abstract
:1. Introduction
2. Methodology
2.1. Spatiotemporal Scale
2.2. Kriging
2.3. Entropy
2.4. Optimization of Network Design
2.5. Study Area and Data
3. Result and Discussion
3.1. Validation of Kriging Estimates
3.2. Uncertainty Distributed in Space
3.3 Spatial Scale Effect
3.4. Temporal Scale Effect
3.5. Optimal Rain Gauge Station Network of the NTUEF Area
4. Conclusions
- (1)
- It exhibits different locations for first prioritized candidate rain gauges between spatiotemporal scales.
- (2)
- The effect of spatial scales is insignificant in comparison to temporal scales for network design. From the joint entropy value, the difference between hourly and monthly scales is more significant than the six dry, wet months and annual rainfall. However, the difference is significant across the spatial scale.
- (3)
- A smaller number and a lower percentage of required stations (PRS) are needed to reach stable joint entropy of long duration (six months or year) at finer spatial scale. Compromising the accuracy and network density, we suggest the optimal network design comprising of 13 candidate stations be suitable across all spatiotemporal scales.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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No. | Rain Gauge Station | Elevation (m) | TM2 (m) | Hourly Rainfall for Typhoon Events (mm) | Monthly Rainfall (mm) | Annual Rainfall (mm) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Easting | Northing | Maximum | Minimum | Mean | Standard Deviation | Maximum | Minimum | Mean | Standard Deviation | Maximum | Minimum | Mean | Standard Deviation | |||
1 | AliShan | 2,413 | 230,043 | 2,600,476 | 123.0 | 0.0 | 25.8 | 25.6 | 3,346.0 | 0.0 | 336.6 | 438.1 | 5,886.7 | 2,196.5 | 4,039.2 | 1,140.9 |
2 | Mt. Jade | 3,845 | 245,030 | 2,598,435 | 64.0 | 0.0 | 14.7 | 13.4 | 2,189.9 | 0.0 | 254.8 | 299.0 | 4,705.2 | 1,702.7 | 3,058.2 | 830.3 |
3 | Xitou Nursery | 1,169 | 228,583 | 2,618,722 | 110.0 | 0.0 | 17.0 | 20.6 | 1,770.0 | 0.0 | 202.3 | 246.1 | 4,053.0 | 1,291.0 | 2,455.3 | 673.5 |
4 | Jushan-NTU | 156 | 216,693 | 2,628,383 | 145.0 | 0.0 | 10.2 | 18.1 | 1,173.0 | 0.0 | 181.0 | 214.8 | 2,821.6 | 1,355.1 | 2,221.0 | 449.4 |
5 | Shueli-NTU | 295 | 234,893 | 2,633,571 | 123.5 | 0.0 | 10.5 | 17.2 | 1,512.5 | 0.0 | 150.7 | 200.4 | 2,816.0 | 2,12.5 | 1,835.9 | 724.6 |
6 | Nemoupu-NTU | 509 | 233,987 | 2,620,868 | 125.5 | 0.0 | 11.2 | 15.8 | 1,008.0 | 0.0 | 153.3 | 175.4 | 2,805.0 | 946.0 | 1,820.9 | 491.0 |
7 | Heshe-NTU | 780 | 237,830 | 2,609,920 | 74.0 | 0.0 | 11.2 | 14.3 | 1,258.0 | 0.0 | 154.2 | 185.0 | 2,688.5 | 1,062.0 | 1,855.9 | 498.8 |
8 | Chinshueigao-NTU | 520 | 227,576 | 2,629,098 | 100.0 | 0.0 | 9.2 | 14.5 | 1,271.6 | 0.0 | 187.6 | 222.1 | 4,275.0 | 680.5 | 2,234.6 | 852.4 |
9 | Hsingouko | 2,540 | 236,749 | 2,597,543 | 112.5 | 0.0 | 16.8 | 15.9 | 2,203.0 | 0.0 | 241.7 | 294.0 | 4,524.5 | 787.0 | 2,828.7 | 1,068.2 |
10 | Dann | 1,528 | 224,672 | 2,619,646 | 75.5 | 0.0 | 8.6 | 11.2 | 945.0 | 0.0 | 180.7 | 197.9 | 3,154.0 | 773.0 | 2,088.8 | 627.1 |
11 | Jushan | 151 | 217,157 | 2,629,012 | 170.0 | 0.0 | 8.9 | 16.9 | 1,133.5 | 0.0 | 177.6 | 207.3 | 3,205.0 | 613.0 | 2,047.8 | 611.7 |
12 | Wanshian | 2,403 | 240,080 | 2,613,075 | 85.0 | 0.0 | 12.8 | 15.0 | 1,633.5 | 0.0 | 208.3 | 247.9 | 3,642.0 | 924.0 | 2,421.6 | 832.5 |
13 | Phoenix Garden | 878 | 227,485 | 2,625,117 | 141.0 | 0.0 | 11.9 | 18.4 | 1,292.0 | 0.0 | 218.2 | 235.6 | 3,671.0 | 948.0 | 2,522.5 | 741.5 |
14 | Xitou Observation | 1,771 | 229,514 | 2,617,731 | 61.0 | 0.0 | 9.2 | 9.6 | 1,053.5 | 0.0 | 192.8 | 203.2 | 3,139.0 | 909.5 | 2,219.5 | 629.0 |
15 | Long-Shen Bridge | 339 | 236,100 | 2,630,858 | 130.5 | 0.0 | 9.0 | 15.0 | 900.0 | 0.0 | 164.5 | 179.4 | 2,812.5 | 1,133.5 | 1,921.2 | 653.3 |
16 | Ji-Ji | 235 | 226,257 | 2,636,039 | 103.5 | 0.0 | 8.3 | 13.2 | 975.0 | 0.0 | 188.7 | 210.0 | 3,100.5 | 1,504.5 | 2,256.7 | 923.4 |
17 | GuanShan | 1,780 | 240,135 | 2,601,472 | 81.5 | 0.0 | 14.8 | 15.4 | 1,171.5 | 0.0 | 227.7 | 225.2 | 3,695.9 | 1,296.5 | 2,444.9 | 820.9 |
18 | Pasture | 2,677 | 237,860 | 2,597,660 | 136.0 | 0.0 | 18.3 | 17.4 | 2,383.5 | 0.0 | 304.1 | 387.7 | 5,218.8 | 1,653.5 | 3,719.5 | 1,025.3 |
19 | Shenmu Village | 1,595 | 233,125 | 2,603,668 | 91.5 | 0.0 | 16.4 | 17.0 | 2,141.5 | 0.0 | 260.1 | 330.5 | 4,649.5 | 1,653.5 | 3,114.4 | 1,664.2 |
20 | Chungshinlun | 661 | 219,839 | 2,625,192 | 63.5 | 0.0 | 9.4 | 12.6 | 1,075.0 | 0.0 | 231.0 | 264.0 | 3,682.0 | 1,554.5 | 2,731.8 | 1,468.3 |
21 | Shueli | 593 | 234,295 | 2,636,644 | 110.0 | 0.0 | 10.2 | 17.5 | 911.0 | 0.0 | 193.9 | 218.3 | 3,094.0 | 1,451.0 | 2,341.8 | 1,276.9 |
22 | Fongchiou | 1,151 | 237,647 | 2,618,491 | 84.5 | 0.0 | 11.1 | 14.3 | 1,211.0 | 0.0 | 166.9 | 210.1 | 2,938.0 | 1,088.0 | 2,021.5 | 1,114.5 |
23 | ShangAn | 781 | 236,321 | 2,625,167 | 66.0 | 0.0 | 8.6 | 12.2 | 804.5 | 0.0 | 162.0 | 190.1 | 2,914.0 | 1,193.0 | 1,973.3 | 1,074.3 |
24 | Hsin-shin Bridge | 897 | 235,680 | 2,606,957 | 96.5 | 0.0 | 14.2 | 17.2 | 1,751.5 | 0.0 | 193.9 | 266.1 | 3,277.5 | 1,291.0 | 2,425.1 | 1,297.9 |
25 | Dongpu | 887 | 241,493 | 2,606,091 | 67.0 | 0.0 | 10.2 | 11.8 | 1,307.0 | 0.0 | 169.6 | 219.2 | 2,917.0 | 1,107.0 | 2,092.9 | 1,138.7 |
26 | Siluang | 1,001 | 237,315 | 2,628,058 | 78.5 | 0.0 | 10.7 | 15.5 | 963.5 | 0.0 | 186.7 | 217.3 | 3,061.0 | 1,313.5 | 2,193.8 | 1,218.5 |
27 | Xitou office | 1,156 | 228,453 | 2,619,028 | 56.0 | 0.0 | 13.5 | 12.9 | 1,218.5 | 0.0 | 223.2 | 277.4 | 4,005.5 | 1,125.5 | 3,053.3 | 1,369.3 |
28 | TienDi | 787 | 230,728 | 2,624,199 | 53.5 | 0.0 | 11.3 | 12.6 | 1,360.5 | 0.0 | 140.3 | 266.4 | 3,122.5 | 137.0 | 2,326.5 | 973.3 |
29 | GuangHsin | 645 | 225,917 | 2,625,831 | 49.5 | 0.0 | 9.8 | 12.2 | 1,190.5 | 0.0 | 238.9 | 286.9 | 3,628.5 | 329.0 | 3,124.5 | 1,299.3 |
30 | No.3 Gully | 1,185 | 228,811 | 2,619,174 | 25.0 | 0.0 | 4.2 | 5.7 | 776.0 | 0.0 | 167.2 | 180.2 | 3,339.5 | 712.5 | 1,937.0 | 907.2 |
31 | Neihu elementary school | 772 | 227,181 | 2,623,316 | 52.0 | 0.0 | 9.8 | 11.7 | 1,214.5 | 0.0 | 201.6 | 258.7 | 3,560.5 | 901.0 | 3,090.3 | 1,157.6 |
32 | Lower University Gully | 1,197 | 227,492 | 2,618,456 | 106.0 | 0.0 | 15.1 | 16.8 | 1,663.0 | 0.5 | 255.6 | 402.7 | 3,956.0 | 222.5 | 3,334.2 | 1,207.7 |
33 | Wushio | 1,495 | 225,450 | 2,620,064 | 32.0 | 0.0 | 7.3 | 7.5 | 2,296.5 | 0.0 | 212.4 | 394.3 | 3,941.0 | 610.0 | 3,400.8 | 1,221.4 |
34 | Yashanpin | 1,390 | 233,383 | 2,611,144 | 86.0 | 0.0 | 17.5 | 19.4 | 1,872.5 | 0.0 | 269.3 | 367.1 | 4,221.0 | 2,264.5 | 3,534.0 | 1,478.1 |
35 | Alibudon | 1,208 | 235,227 | 2,609,712 | 31.5 | 0.0 | 4.8 | 7.9 | 823.5 | 0.0 | 135.8 | 162.1 | 2,876.0 | 530.5 | 1,549.0 | 780.0 |
36 | Salishian | 1,216 | 241,259 | 2,602,664 | 61.5 | 0.0 | 10.3 | 12.3 | 1,211.5 | 0.0 | 208.0 | 274.3 | 3,284.5 | 824.5 | 1,941.2 | 799.8 |
37 | Neuchangpin | 1,306 | 237,549 | 2,606,292 | 83.0 | 0.0 | 13.8 | 16.5 | 1,500.0 | 0.0 | 185.3 | 247.9 | 2,672.5 | 1,768.5 | 2,302.8 | 1,008.6 |
38 | Shenmu | 1,315 | 235,142 | 2,602,259 | 75.0 | 0.0 | 12.9 | 15.5 | 1,490.5 | 0.5 | 297.5 | 413.5 | 3,885.0 | 425.0 | 2,185.3 | 955.8 |
39 | 32-compartment | 1,823 | 240,123 | 2,602,231 | 59.0 | 0.0 | 15.6 | 13.5 | 1,714.5 | 0.0 | 223.5 | 298.9 | 3,073.0 | 2,050.5 | 2,318.0 | 1,157.2 |
40 | 30-compartment | 2,097 | 238,588 | 2,603,814 | 66.0 | 0.0 | 14.8 | 14.4 | 1,725.0 | 0.0 | 227.2 | 341.3 | 4,294.0 | 1,134.5 | 2,903.7 | 1,244.7 |
41 | 29-compartment | 2,298 | 233,408 | 2,596,924 | 80.5 | 0.0 | 20.2 | 20.7 | 2,307.5 | 0.0 | 347.0 | 466.6 | 5,450.5 | 974.5 | 3,453.3 | 1,774.8 |
42 | 20-compartment | 967 | 233,765 | 2,615,241 | 72.0 | 0.0 | 12.8 | 15.1 | 1,372.5 | 15.0 | 174.8 | 282.1 | 2,010.0 | 603.0 | 1,456.5 | 573.6 |
43 | 21-compartment | 1,280 | 231,832 | 2,618,174 | 99.5 | 0.0 | 22.3 | 24.4 | 2,243.5 | 7.0 | 296.3 | 433.4 | 2,946.0 | 2,048.5 | 2,518.5 | 1,023.4 |
44 | 22-compartment | 892 | 230,636 | 2,618,475 | 79.0 | 0.0 | 13.7 | 17.1 | 1,403.0 | 3.0 | 198.1 | 259.8 | 2,859.5 | 1,859.5 | 2,129.6 | 877.4 |
45 | 24-compartment | 1,278 | 231,635 | 2,621,701 | 107.0 | 0.0 | 18.9 | 21.2 | 2,042.0 | 0.0 | 171.1 | 339.8 | 2,820.5 | 442.0 | 1,582.8 | 797.0 |
46 | 13-compartment | 454 | 231,953 | 2,629,686 | 51.5 | 0.0 | 7.9 | 11.0 | 708.5 | 8.5 | 178.2 | 193.9 | 2,728.5 | 1,003.5 | 1,870.9 | 804.6 |
47 | 16-compartment | 1,002 | 232,038 | 2,630,932 | 71.0 | 0.0 | 10.6 | 14.9 | 303.0 | 2.5 | 114.4 | 203.5 | 1,473.5 | 508.5 | 1,058.4 | 458.3 |
48 | 17-compartment | 454 | 230,194 | 2,632,283 | 51.0 | 0.0 | 8.9 | 10.4 | 343.0 | 0.0 | 166.6 | 259.3 | 1,403.0 | 409.5 | 1,110.8 | 300.3 |
49 | 11-compartment | 1,228 | 230,931 | 2,626,757 | 60.0 | 0.0 | 12.9 | 14.5 | 915.0 | 21.0 | 216.6 | 207.2 | 2,998.0 | 1,402.0 | 2,219.9 | 929.7 |
50 | 9-compartment | 1,213 | 232,127 | 2,628,823 | 57.0 | 0.0 | 10.4 | 12.3 | 755.0 | 21.5 | 216.4 | 189.2 | 2,391.5 | 1,301.5 | 1,839.6 | 762.0 |
Typhoon | Date | Maximum Wind (m/s) | Rainfall Duration (h) | Damage (Billion, NT) |
---|---|---|---|---|
Herb | 29 July–1 August 1996 | 53 | 44 | 39.3 |
Toraji | 28–31 July 2001 | 38 | 24 | 14.7 |
Mindulle | 28 June–3 July 2004 | 45 | 72 | 6.5 |
Kalmeigi | 16–18 July 2008 | 33 | 32 | 3.4 |
Silaku | 11–16 September 2008 | 51 | 75 | 5.6 |
Marakot | 5–10 August 2009 | 40 | 96 | 47.7 |
Saola | 30 July–3 August 2012 | 38 | 42 | 16.2 |
Temporal Scale | b (Sill, mm2) | a (Range Parameter, m) | Kriging Variance (mm2) |
---|---|---|---|
Hour | 165 ± 292 | 40,243 ± 25,538 | 21 ± 62 |
Month | 23,529 ± 67,316 | 39,481 ± 67,316 | 3,154 ± 7,760 |
Dry six months | 43,209 ± 52,813 | 50,926 ± 22,708 | 3,198 ± 4,184 |
Wet six months | 583,324 ± 560,410 | 39,499 ± 27,171 | 64,250 ± 58,808 |
Annual | 645,623 ± 654,175 | 31,337 ± 29,685 | 104,080 ± 107,613 |
Scale | Candidate Station Number | Hour | Month | Six Dry Months | Six Wet Months | Year |
---|---|---|---|---|---|---|
1-km | 346 | 126 (36.4%) | 143 (41.3%) | 3(0.9%) | 2(0.6%) | 4 (1.1%) |
3-km | 45 | 26 (57.8%) | 28 (62.2%) | 5(11.1%) | 3(6.7%) | 4 (8.9%) |
5-km | 20 | 14 (70.0%) | 13 (65.0%) | 6(30%) | 3(15%) | 3 (15.0%) |
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Wei, C.; Yeh, H.-C.; Chen, Y.-C. Spatiotemporal Scaling Effect on Rainfall Network Design Using Entropy. Entropy 2014, 16, 4626-4647. https://doi.org/10.3390/e16084626
Wei C, Yeh H-C, Chen Y-C. Spatiotemporal Scaling Effect on Rainfall Network Design Using Entropy. Entropy. 2014; 16(8):4626-4647. https://doi.org/10.3390/e16084626
Chicago/Turabian StyleWei, Chiang, Hui-Chung Yeh, and Yen-Chang Chen. 2014. "Spatiotemporal Scaling Effect on Rainfall Network Design Using Entropy" Entropy 16, no. 8: 4626-4647. https://doi.org/10.3390/e16084626