# Spatial Frequency Analysis by Adopting Regional Analysis with Radar Rainfall in Taiwan

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{i}> 6 were set as discordant grids and removed for further analysis. A K-means cluster analysis using scaled at-site characteristics was used to group the QPESUMS grids in Taiwan into 22 clusters/sub-regions based on their characteristics. Spatially, homogeneous subregions with QPESUMS data produce more detailed homogeneous subregions with clear and continuous boundaries, especially in the mountain range area where the number of rain stations is still very limited. According to the results of z-values and L-moment ratio diagrams, the Wakeby (WAK), Generalized Extreme Value (GEV), and Generalized Pareto (GPA) distributions of rainfall extremes fitted well for the majority of subregions. The Wakeby distribution was the dominant best-fitted distribution, especially in the central and eastern regions. The east of the northern part and southern part of Taiwan had the highest extreme rainfall especially for a 100-year return period with an extreme value of more than 1200 mm/day. Both areas were frequently struck by typhoons. By using grid-based (at-site) as the basis for assessing regional frequency analysis, the results show that the regional approach in determining extreme rainfall is very suitable for large-scale applications and even better for smaller scales such as watershed areas. The spatial investigation was performed by establishing regions of interest in small subregions across the northern part. It showed that regionalization was correct and consistent.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, is located in Southeast Asia’s Western Pacific (between Japan and the Philippines). Taiwan has a long and narrow shape, with the Central Mountain Range extending across the middle of the country. The mountainous area with elevations greater than 1000 m comprises 32% of the island, while hills and plateaus with elevations between 100 and 1000 m encompass 31% of the island, and the rest of the island is flat with elevations of less than 100 m (Figure 1).

#### 2.2. Data

#### 2.3. L-Moment approach

#### 2.4. Discordancy Measure

#### 2.5. K-Means Clustering

#### 2.6. Heterogeneity Measure

_{1}did not fulfill the criterion, the site inside the region needed to be modified to meet the requirements for becoming an approved homogenous region. Ref. [15] then proposed several region changes, including the following: (1) relocating a site or a few sites within a region; (2) subdividing the region; (3) merging two or more regions and redefining groups; (4) breaking up the region by reassigning its sites to other regions; and (5) removing a site or sites from the data.

#### 2.7. Selection of Candidate Distributions

_{4}is the standard deviation of regional average sample L-kurtosis estimated as

^{DIST}| is sufficiently close to zero, with |Z

^{DIST}| being less than or equal to 1.64. If there are more than one acceptable distribution, the one with the lowest |ZDIST| is considered to be the best distribution.

#### 2.8. Estimation of Rainfall Quantiles

#### 2.9. Accuracy Assessment

#### 2.10. Regional and Grid-Based Estimates for Watershed Scale

_{i}and y

_{i}are the individual grids indexed with i, X and Y are the regional and at-site (grid-based) datasets.

## 3. Results & Discussion

#### 3.1. Screening the Data

_{i}= D(u

_{i}), should tell us how distant u

_{i}is from the center of the area in respect to its size. Large D

_{i}values suggest that the ith site should be examined further for the potential of data errors, or that the prospect of relocating the site should be considered.

_{i}values are more likely to be found in large regions. In any case, regardless of the size of these values, it is recommended to study the data for the locations with the highest D

_{i}values [15].

_{i}of more than 3 and the second using a critical value of >6. Figure 4a,b show the discordant spatial grid distribution (D

_{i}> 3) and a graph of the relationship between L-skewness and L-CV. A total number of 801 of 22,787 grids is categorized as discordant (3.52% of total grids). The spatial distribution of discordant grids is almost evenly distributed throughout the region, but a continuous significant discordant grid is seen in the southeastern area.

_{i}values > 3 (discordant) did not affect the homogeneity of the region after clustering and heterogeneity tests. therefore, we continued the second analysis by increasing the critical D

_{i}limit by >6. Based on this critical value, 171 of 22,787 grids are categorized as discordant (0.75%) (see Figure 4c,d). Grids with discordant value greater than 6 greatly affects the homogeneity of the region. The region that was originally homogeneous shifted to heterogeneous, especially in the southeastern region.

#### 3.2. Identification of Homogeneous Regions

_{i}and H

_{1}) defined in Equations (5) and (9) were calculated to see if they are spatially continuous and physically reasonable. When the estimated heterogeneity measure (H

_{1}) surpasses the critical value, which indicates “potentially” and “definitely” heterogeneous, K-means then will be used to regroup the grids in the region into smaller regions. This process was repeated until no further separation of heterogeneous regions was possible. Occasionally, the discordance measure suggested that several surrounding grids within a region are discordant with the remainder of the region. In this case, the homogenous regions were manually refined by using subjective adjustments as described in the methodology section. Examining the discordant grids showed several natural and physically defensible modifications to the clusters, leading to more homogeneous clusters after accounting for the topographical and geographic patterns of the average annual maximum series.

#### 3.3. Selection of Distribution Models

#### 3.4. Estimation of Regional Quantiles

#### 3.5. Accuracy Result

#### 3.6. Spatial Mapping of Extreme Rainfall

#### 3.7. Regional and Grid-Based Estimates for Watershed Scale

^{2}within drainage area and a total of 5103 grids for the three homogeneous subregions. More specifically, of the 322 grids within the Touqian watershed, 145 grids are located in subregion 4 (10.67 % of total SR-4 grids), 101 grids are located in subregion 5 (5.59 % of total SR-5 grids), and 76 grids are located in subregion 11 (3.92 % of total of total SR-11 grids).

#### 3.8. Small-Scale Spatial Investigation

## 4. Conclusions

_{i}= 6, 171 of 22,787 grids (0.75%) were discordant. Taiwan’s south-eastern coastal grid with a discordant value of 6 affects the region’s homogeneity. Based on L-moment ratio diagrams and z-values, Wakeby (WAK), GEV, and GPA extreme rainfall distributions are best for most subregions (goodness-of-fit measures). In the central and eastern regions, the Wakeby distribution is dominant and best-fitting. Estimating rainfall quantiles based on the best-fitted distribution for each sub-region increased the range of variation from 0.80–0.99 to 1.71–3.35 in a 100-year return period. This result explains why quantile estimate variation increases with return period. Sub-regions 1, 7, 11, and 22 have the highest regional growth curves in the higher return period, while sub-regions 13, 19, and 20 have the lowest. The relative regional RMSE values and 90% error bounds show that regional quantile uncertainty increases with return period, demonstrating that quantile estimations are accurate when return periods are less than 100 years. The index-flood method was used to create the spatial distribution of rainfall quantiles for several return periods (2 years, 5 years, 10 years, 20 years, 50 years, and 100 years), considering the regional growth curve as a regional scale and the annual maximum rainfall as site-specific. Two areas receive significantly more extreme rainfall than others. The southern region (sub-regions 10, 14, 15, 19, and 20) is in Tainan City, Chiayi County, Kaohsiung City, and Pingtung County. Regional frequency analysis may yield more precise estimates of rainfall quantiles than at-site analysis, not only for larger areas but also for smaller-scale areas. A region of interest has been established to determine if regionalization in the north is accurate. Each sub-coefficient regions of variation is lower than the entire RoI’s. The regionalization was accurate and consistent. According to the findings, the use of radar-rainfall in the estimation of extreme rainfall using a regional approach is highly recommended in other regions with unreliable or relatively few and uneven rain gauges, particularly in catchment areas that require frequency analysis for water-related infrastructure that is typically not covered by sufficient rain gauges.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Overeem, A. Climatology of Extreme Rainfall from Rain Gauges and Weather Radar; Wageningen University: Wageningen, The Netherlands, 2009. [Google Scholar]
- Chang’A, L.B.; Kijazi, A.L.; Mafuru, K.B.; Nying’Uro, P.A.; Ssemujju, M.; Deus, B.; Kondowe, A.L.; Yonah, I.B.; Ngwali, M.; Kisama, S.Y.; et al. Understanding the Evolution and Socio-Economic Impacts of the Extreme Rainfall Events in March-May 2017 to 2020 in East Africa. Atmos. Clim. Sci.
**2020**, 10, 553–572. [Google Scholar] [CrossRef] - Rahman, H.T.; Mia, E.; Ford, J.D.; Robinson, B.E.; Hickey, G.M. Livelihood exposure to climatic stresses in the north-eastern floodplains of Bangladesh. Land Use Policy
**2018**, 79, 199–214. [Google Scholar] [CrossRef] - Wei, L.; Hu, K.-H.; Hu, X.-D. Rainfall occurrence and its relation to flood damage in China from 2000 to 2015. J. Mt. Sci.
**2018**, 15, 2492–2504. [Google Scholar] [CrossRef] - Alias, N.E.B. Improving Extreme Precipitation Estimates Considering Regional Frequency Analysis. Ph.D. Thesis, Kyoto University, Kyoto, Japan, 2014. [Google Scholar] [CrossRef]
- Liu, J.; Doan, C.D.; Liong, S.-Y.; Sanders, R.; Dao, A.T.; Fewtrell, T. Regional frequency analysis of extreme rainfall events in Jakarta. Nat. Hazards
**2015**, 75, 1075–1104. [Google Scholar] [CrossRef] - Feng, Z.; Leung, L.R.; Hagos, S.; Houze, R.A.; Burleyson, C.D.; Balaguru, K. More frequent intense and long-lived storms dominate the springtime trend in central US rainfall. Nat. Commun.
**2016**, 7, 13429. [Google Scholar] [CrossRef] - Fawad, M.; Yan, T.; Chen, L.; Huang, K.; Singh, V.P. Multiparameter probability distributions for at-site frequency analysis of annual maximum wind speed with L-Moments for parameter estimation. Energy
**2019**, 181, 724–737. [Google Scholar] [CrossRef] - Harka, A.E.; Jilo, N.B.; Behulu, F. Spatial-temporal rainfall trend and variability assessment in the Upper Wabe Shebelle River Basin, Ethiopia: Application of innovative trend analysis method. J. Hydrol. Reg. Stud.
**2021**, 37, 100915. [Google Scholar] [CrossRef] - Kim, D.-I.; Han, D.; Lee, T. Reanalysis Product-Based Nonstationary Frequency Analysis for Estimating Extreme Design Rainfall. Atmosphere
**2021**, 12, 191. [Google Scholar] [CrossRef] - Tung, Y.-S.; Wang, C.-Y.; Weng, S.-P.; Yang, C.-D. Extreme index trends of daily gridded rainfall dataset (1960–2017) in Taiwan. Terr. Atmos. Ocean. Sci.
**2022**, 33, 8. [Google Scholar] [CrossRef] - Mamoon, A.A.; Rahman, A. Uncertainty Analysis in Design Rainfall Estimation Due to Limited Data Length: A Case Study in Qatar. In Extreme Hydrology and Climate Variability; Elsevier Inc.: Amsterdam, The Netherlands, 2019. [Google Scholar] [CrossRef]
- Su, B.; Kundzewicz, Z.; Jiang, T. Simulation of extreme precipitation over the Yangtze River Basin using Wakeby distribution. Theor. Appl. Climatol.
**2009**, 96, 209–219. [Google Scholar] [CrossRef] - Gaál, L.; Kyselý, J.; Szolgay, J. Region-of-influence approach to a frequency analysis of heavy precipitation in Slovakia. Hydrol. Earth Syst. Sci.
**2008**, 12, 825–839. [Google Scholar] [CrossRef] - Hosking, J.R.M.; Wallis, J.R. Regional Frequency Analysis; Cambridge University Press: Cambridge, UK, 1997. [Google Scholar] [CrossRef]
- Greenwood, J.A.; Landwehr, J.M.; Matalas, N.C.; Wallis, J.R. Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form. Water Resour. Res.
**1979**, 15, 1049–1054. [Google Scholar] [CrossRef] - Hosking, J.R.M. L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics. J. R. Stat. Soc. Ser. B (Methodol.)
**1990**, 52, 105–124. [Google Scholar] [CrossRef] - Eldardiry, H.; Habib, E. Examining the Robustness of a Spatial Bootstrap Regional Approach for Radar-Based Hourly Precipitation Frequency Analysis. Remote Sens.
**2020**, 12, 3767. [Google Scholar] [CrossRef] - Li, M.; Li, X.; Ao, T. Comparative Study of Regional Frequency Analysis and Traditional At-Site Hydrological Frequency Analysis. Water
**2019**, 11, 486. [Google Scholar] [CrossRef] - Gaál, L.; Kyselý, J. Comparison of region-of-influence methods for estimating high quantiles of precipitation in a dense dataset in the Czech Republic. Hydrol. Earth Syst. Sci.
**2009**, 13, 2203–2219. [Google Scholar] [CrossRef] - Malekinezhad, H.; Nachtnebel, H.; Klik, A. Comparing the index-flood and multiple-regression methods using L-moments. Phys. Chem. Earth Parts A/B/C
**2011**, 36, 54–60. [Google Scholar] [CrossRef] - Gado, T.; Hsu, K.; Sorooshian, S. Rainfall frequency analysis for ungauged sites using satellite precipitation products. J. Hydrol.
**2017**, 554, 646–655. [Google Scholar] [CrossRef] - Modarres, R.; Sarhadi, A. Statistically-based regionalization of rainfall climates of Iran. Glob. Planet. Chang.
**2011**, 75, 67–75. [Google Scholar] [CrossRef] - Santos, M.; Fragoso, M.; Santos, J.A. Regionalization and susceptibility assessment to daily precipitation extremes in mainland Portugal. Appl. Geogr.
**2017**, 86, 128–138. [Google Scholar] [CrossRef] - Yin, Y.; Chen, H.; Xu, C.-Y.; Xu, W.; Chen, C.; Sun, S. Spatio-temporal characteristics of the extreme precipitation by L-moment-based index-flood method in the Yangtze River Delta region, China. Theor. Appl. Climatol.
**2016**, 124, 1005–1022. [Google Scholar] [CrossRef] - Mulaomerović-Šeta, A.; Blagojević, B.; Imširović, Š.; Nedić, B. Assessment of Regional Analyses Methods for Spatial Interpolation of Flood Quantiles in the Basins of Bosnia and Herzegovina and Serbia. In Lecture Notes in Networks and Systems; Springer: Berlin, Germany, 2022; Volume 316. [Google Scholar] [CrossRef]
- Overeem, A.; Buishand, T.A.; Holleman, I. Extreme rainfall analysis and estimation of depth-duration-frequency curves using weather radar. Water Resour. Res.
**2009**, 45, W10424. [Google Scholar] [CrossRef] - Sarmadi, F.; Shokoohi, A. Regionalizing precipitation in Iran using GPCC gridded data via multivariate analysis and L-moment methods. Theor. Appl. Climatol.
**2015**, 122, 121–128. [Google Scholar] [CrossRef] - Goudenhoofdt, E.; Delobbe, L.; Willems, P. Regional frequency analysis of extreme rainfall in Belgium based on radar estimates. Hydrol. Earth Syst. Sci.
**2017**, 21, 5385–5399. [Google Scholar] [CrossRef] - Yeh, H.-F.; Chang, C.-F. Using Standardized Groundwater Index and Standardized Precipitation Index to Assess Drought Characteristics of the Kaoping River Basin, Taiwan. Water Resour.
**2019**, 46, 670–678. [Google Scholar] [CrossRef] - Wu, C.-C.; Kuo, Y.-H. Typhoons Affecting Taiwan: Current Understanding and Future Challenges. Bull. Am. Meteorol. Soc.
**1999**, 80, 67–80. [Google Scholar] [CrossRef] - Chen, H.-W.; Chen, C.-Y. Warning Models for Landslide and Channelized Debris Flow under Climate Change Conditions in Taiwan. Water
**2022**, 14, 695. [Google Scholar] [CrossRef] - Chang, F.-J.; Chiang, Y.-M.; Tsai, M.-J.; Shieh, M.-C.; Hsu, K.-L.; Sorooshian, S. Watershed rainfall forecasting using neuro-fuzzy networks with the assimilation of multi-sensor information. J. Hydrol.
**2014**, 508, 374–384. [Google Scholar] [CrossRef] - Chiou, P.T.; Chen, C.-R.; Chang, P.-L.; Jian, G.-J. Status and outlook of very short range forecasting system in Central Weather Bureau, Taiwan. In Applications with Weather Satellites II; SPIE: Washington, DC, USA, 2005; pp. 185–196. [Google Scholar] [CrossRef]
- Chang, R.-C.; Tsai, T.-S.; Yao, L. Intelligent Rainfall Monitoring System for Efficient Electric Power Transmission. In Information Technology Convergence; Springer: Dordrecht, The Netherlands, 2013; pp. 773–782. [Google Scholar] [CrossRef]
- Neykov, N.M.; Neytchev, P.N.; Van Gelder, P.H.A.J.M.; Todorov, V.K. Robust detection of discordant sites in regional frequency analysis. Water Resour. Res.
**2007**, 43, W06417. [Google Scholar] [CrossRef] - Hosking, J.R.M. Regional Frequency Analysis Using L-Moments. 2019. Available online: https://cran.r-project.org/package=lmomRFA (accessed on 12 July 2021).
- Lin, G.-F.; Chen, L.-H. Identification of homogeneous regions for regional frequency analysis using the self-organizing map. J. Hydrol.
**2006**, 324, 1–9. [Google Scholar] [CrossRef] - Alem, A.M.; Tilahun, S.A.; Moges, M.A.; Melesse, A.M. A regional hourly maximum rainfall extraction method for part of Upper Blue Nile Basin, Ethiopia. In Extreme Hydrology and Climate Variability; Elsevier: Amsterdam, The Netherlands, 2019; pp. 93–102. [Google Scholar] [CrossRef]
- Rao, A.R.; Srinivas, S.S. Regionalization of Watersheds: An Approach Based on Cluster Analysis; Springer Science & Business Media: Berlin, Germany, 2008. [Google Scholar] [CrossRef]
- Abdi, A.; Hassanzadeh, Y.; Talatahari, S.; Fakheri-Fard, A.; Mirabbasi, R. Regional drought frequency analysis using L-moments and adjusted charged system search. J. Hydroinformatics
**2017**, 19, 426–442. [Google Scholar] [CrossRef] - Wright, M.J.; Houck, M.H.; Ferreira, C.M. Discriminatory Power of Heterogeneity Statistics with Respect to Error of Precipitation Quantile Estimation. J. Hydrol. Eng.
**2015**, 20, 04015011. [Google Scholar] [CrossRef] - Khan, S.A.; Hussain, I.; Hussain, T.; Faisal, M.; Muhammad, Y.S.; Shoukry, A.M. Regional Frequency Analysis of Extremes Precipitation Using L-Moments and Partial L-Moments. Adv. Meteorol.
**2017**, 2017, 6954902. [Google Scholar] [CrossRef] - Busababodhin, P.; Seo, Y.A.; Park, J.-S.; Kumphon, B.-O. LH-moment estimation of Wakeby distribution with hydrological applications. Stoch. Environ. Res. Risk Assess.
**2016**, 30, 1757–1767. [Google Scholar] [CrossRef] - Rahman, M.; Hassan, R.; Buyya, R. Jaccard Index based availability prediction in enterprise grids. Procedia Comput. Sci.
**2010**, 1, 2707–2716. [Google Scholar] [CrossRef] - Chang, P.-L.; Zhang, J.; Tang, Y.-S.; Tang, L.; Lin, P.-F.; Langston, C.; Kaney, B.; Chen, C.-R.; Howard, K. An Operational Multi-Radar Multi-Sensor QPE System in Taiwan. Bull. Am. Meteorol. Soc.
**2021**, 102, E555–E577. [Google Scholar] [CrossRef] - Hu, C.; Xia, J.; She, D.; Xu, C.; Zhang, L.; Song, Z.; Zhao, L. A modified regional L-moment method for regional extreme precipitation frequency analysis in the Songliao River Basin of China. Atmos. Res.
**2019**, 230, 104629. [Google Scholar] [CrossRef] - Chen, L.-H.; Hong, Y.-T. Regional Taiwan rainfall frequency analysis using principal component analysis, self-organizing maps and L-moments. Hydrol. Res.
**2012**, 43, 275–285. [Google Scholar] [CrossRef] - Szolgay, J.; Parajka, J.; Kohnová, S.; Hlavčová, K. Comparison of mapping approaches of design annual maximum daily precipitation. Atmos. Res.
**2009**, 92, 289–307. [Google Scholar] [CrossRef] - Rossi, F.; Fiorentino, M.; Versace, P. Two-Component Extreme Value Distribution for Flood Frequency Analysis. Water Resour. Res.
**1984**, 20, 847–856. [Google Scholar] [CrossRef] - Gabriele, S.; Arnell, N. A hierarchical approach to regional flood frequency analysis. Water Resour. Res.
**1991**, 27, 1281–1289. [Google Scholar] [CrossRef] - De Luca, D.L.; Galasso, L. Stationary and Non-Stationary Frameworks for Extreme Rainfall Time Series in Southern Italy. Water
**2018**, 10, 1477. [Google Scholar] [CrossRef] - Hao, W.; Hao, Z.; Yuan, F.; Ju, Q.; Hao, J. Regional Frequency Analysis of Precipitation Extremes and Its Spatio-Temporal Patterns in the Hanjiang River Basin, China. Atmosphere
**2019**, 10, 130. [Google Scholar] [CrossRef] - Beguería, S.; Vicente-Serrano, S.M. Mapping the Hazard of Extreme Rainfall by Peaks over Threshold Extreme Value Analysis and Spatial Regression Techniques. J. Appl. Meteorol. Clim.
**2006**, 45, 108–124. [Google Scholar] [CrossRef] - Prudhomme, C.; Reed, D.W. Mapping Extreme Rainfall in a Mountainous Region Using Geostatistical Techniques: A Case Study in Scotland. Int. J. Climatol.
**1999**, 19, 1337–1356. [Google Scholar] [CrossRef] - Su, S.-H.; Kuo, H.-C.; Hsu, L.-H.; Yang, Y.-T. Temporal and Spatial Characteristics of Typhoon Extreme Rainfall in Taiwan. J. Meteorol. Soc. Jpn. Ser. II
**2012**, 90, 721–736. [Google Scholar] [CrossRef] - Malekinezhad, H.; Zare-Garizi, A. Regional frequency analysis of daily rainfall extremes using L-moments approach. Atmósfera
**2014**, 27, 411–427. [Google Scholar] [CrossRef] - Wang, Z.; Zeng, Z.; Lai, C.; Lin, W.; Wu, X.; Chen, X. A regional frequency analysis of precipitation extremes in Mainland China with fuzzy c-means and L-moments approaches. Int. J. Clim.
**2017**, 37, 429–444. [Google Scholar] [CrossRef]

**Figure 3.**Site-characteristics used in K-means clustering (Latitude and Longitude, Elevation, The average of Annual Maximum Series, and 5-year Rainfall.

**Figure 4.**Spatial distribution of QPESUMS discordant grids in Taiwan; (

**a**). Discordant grids using D

_{i}> 3 as critical; (

**b**). L-skewness and L-CV plot for D

_{i}> 3 (red dots represent discordant grids); (

**c**). Discordant grids using D

_{i}> 6; (

**d**). L-skewness and L-CV plot for D

_{i}> 6 (red dots represent discordant grids).

**Figure 6.**The division of 22 homogeneous subregions using QPESUMS in Comparison with Chen and Hong, (2012) [48]’s homogeneous subregions using Rain Gauges in Taiwan.

**Figure 10.**Extreme rainfall for at-site frequency analysis using the GEV distribution and regional frequency analysis at 50-year return period.

**Figure 11.**Comparison of the average extreme rainfall for at-site and regional frequency analysis at 50-year return period.

**Figure 14.**Extreme rainfall of six sub-regions within region of interest and the whole region of interest at 5-year.

Region/Sub-Region | Number of Grids | L-Moment Ratios | H_{1} | ||
---|---|---|---|---|---|

t | t_3 | t_4 | |||

North | |||||

1 | 711 | 0.33 | 0.24 | 0.17 | −2.01 |

2 | 453 | 0.22 | 0.21 | 0.11 | −0.62 |

3 | 509 | 0.19 | 0.18 | 0.15 | −0.67 |

4 | 1359 | 0.25 | 0.28 | 0.17 | −0.14 |

5 | 1806 | 0.28 | 0.15 | 0.10 | −1.86 |

6 | 606 | 0.24 | 0.20 | 0.16 | −1.27 |

West | |||||

7 | 980 | 0.32 | 0.34 | 0.17 | −5.83 |

8 | 1186 | 0.26 | 0.19 | 0.10 | −5.33 |

9 | 1961 | 0.27 | 0.26 | 0.20 | −7.71 |

10 | 1150 | 0.26 | 0.25 | 0.14 | 0.85 |

Center | |||||

11 | 1938 | 0.32 | 0.29 | 0.08 | −4.97 |

12 | 1344 | 0.25 | 0.11 | 0.10 | −4.90 |

13 | 826 | 0.23 | 0.00 | 0.06 | −6.01 |

14 | 474 | 0.22 | 0.07 | 0.05 | −1.19 |

15 | 567 | 0.17 | 0.11 | 0.20 | −6.87 |

East | |||||

16 | 2231 | 0.25 | 0.08 | 0.06 | −5.21 |

17 | 652 | 0.25 | 0.17 | 0.09 | 0.07 |

South | |||||

18 | 1629 | 0.19 | 0.09 | 0.12 | −3.63 |

19 | 609 | 0.16 | 0.10 | 0.12 | −6.49 |

20 | 1283 | 0.16 | 0.05 | 0.08 | −3.25 |

21 | 265 | 0.25 | 0.20 | 0.07 | −2.55 |

22 | 248 | 0.35 | 0.30 | 0.14 | 0.92 |

**Table 2.**GoF measures (Z-test), best fit Distribution, and parameter distribution of 22 homogenous Sub-Regions in Taiwan.

Reg | Goodness-of-Fit Measures | Best Fit Distribution | Parameter Estimates for Distributions Accepted at the 0.90 Level | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

GLO | GEV | GNO | PE3 | GPA | ξ/μ | α/σ | K/β | γ | δ | ||

North | |||||||||||

1 | 7.44 | 0.61 | −2.28 | −7.59 | −16.25 | GEV | 0.71 | 0.42 | −0.11 | ||

2 | 18.58 | 11.54 | 9.70 | 5.99 | −4.92 | WAK | 0.48 | 0.68 | 0.32 | 0.00 | 0.00 |

3 | 7.45 | −0.08 | −1.17 | −3.90 | −16.92 | GEV | 0.84 | 0.27 | −0.01 | ||

4 | 13.00 | 5.05 | −0.08 | −9.14 | −15.97 | GNO | 0.88 | 0.38 | −0.58 | ||

5 | 34.65 | 17.03 | 16.09 | 11.85 | −20.90 | WAK | 0.30 | 1.04 | 0.49 | 0.00 | 0.00 |

6 | 5.87 | −1.60 | −3.35 | −7.00 | −18.90 | GEV | 0.79 | 0.33 | −0.05 | ||

West | |||||||||||

7 | 19.51 | 14.45 | 8.66 | −1.41 | −0.68 | GPA | 0.37 | 0.62 | −0.02 | ||

8 | 31.21 | 18.77 | 16.39 | 11.10 | −9.58 | WAK | 0.35 | 0.58 | 2.62 | 0.58 | −0.17 |

9 | 1.52 | −7.88 | −13.01 | −22.24 | −33.28 | GLO | 0.89 | 0.24 | −0.26 | ||

10 | 19.89 | 11.13 | 7.17 | −0.05 | −10.72 | PE3 | 1.00 | 0.50 | 1.48 | ||

Center | |||||||||||

11 | 63.27 | 53.04 | 45.54 | 32.36 | 25.38 | WAK | 0.32 | 0.74 | 0.10 | 0.00 | 0.00 |

12 | 30.61 | 13.51 | 14.22 | 11.95 | −21.70 | WAK | 0.24 | 2.03 | 7.43 | 0.70 | −0.34 |

13 | 35.70 | 16.95 | 21.79 | 21.79 | −16.88 | WAK | 0.18 | 2.61 | 8.57 | 0.92 | −0.69 |

14 | 29.02 | 16.95 | 18.71 | 18.19 | −6.53 | WAK | 0.36 | 0.92 | 1.90 | 0.42 | −0.30 |

15 | −11.39 | −20.36 | −19.99 | −21.20 | −38.83 | WAK | 0.40 | 2.43 | 5.54 | 0.20 | 0.11 |

East | |||||||||||

16 | 56.21 | 32.30 | 34.29 | 32.08 | −15.90 | WAK | 0.26 | 1.17 | 5.37 | 0.83 | −0.50 |

17 | 24.58 | 14.92 | 13.61 | 10.26 | −6.62 | WAK | 0.36 | 0.56 | 2.58 | 0.58 | −0.21 |

South | |||||||||||

18 | 23.65 | 1.61 | 5.38 | 3.62 | −36.65 | GEV | 0.86 | 0.30 | 0.12 | ||

19 | 12.97 | 1.83 | 2.73 | 1.61 | −20.65 | PE3 | 1.00 | 0.29 | 0.60 | ||

20 | 37.51 | 16.77 | 20.29 | 19.72 | −23.01 | WAK | 0.50 | 1.00 | 2.47 | 0.25 | −0.16 |

21 | 20.74 | 14.78 | 13.42 | 10.58 | 1.01 | GPA | 0.41 | 0.79 | 0.34 | ||

22 | 13.01 | 9.74 | 7.04 | 2.33 | 0.68 | GPA | 0.28 | 0.77 | 0.07 |

**Table 3.**Similarity index between grid-based and regional frequency analysis for Touqian watershed and Taiwan.

Return Period | Touqian | Taiwan | ||
---|---|---|---|---|

NCC | JSI | NCC | JSI | |

2-year | 0.980 | 0.935 | 0.977 | 0.917 |

5-year | 0.989 | 0.916 | 0.965 | 0.912 |

10-year | 0.990 | 0.914 | 0.946 | 0.899 |

20-year | 0.990 | 0.888 | 0.929 | 0.890 |

50-year | 0.990 | 0.858 | 0.907 | 0.880 |

100-year | 0.989 | 0.839 | 0.892 | 0.874 |

1000-year | 0.988 | 0.795 | 0.849 | 0.855 |

**Table 4.**Extreme rainfall statistics of six sub-regions within region of interest and the whole region of interest.

Sub-Region | Region of Interest | Whole ROI | ||||
---|---|---|---|---|---|---|

Mean | Std Dev | CV | Mean | Std Dev | CV | |

1 | 361.51 | 49.78 | 13.77 | 363.95 | 67.23 | 18.47 |

2 | 345.39 | 59.00 | 17.08 | |||

3 | 399.03 | 38.45 | 9.64 | |||

4 | 291.57 | 35.03 | 12.01 | |||

5 | 409.32 | 63.94 | 15.62 | |||

6 | 311.17 | 23.14 | 7.44 |

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**MDPI and ACS Style**

Chang, C.-H.; Rahmad, R.; Wu, S.-J.; Hsu, C.-T. Spatial Frequency Analysis by Adopting Regional Analysis with Radar Rainfall in Taiwan. *Water* **2022**, *14*, 2710.
https://doi.org/10.3390/w14172710

**AMA Style**

Chang C-H, Rahmad R, Wu S-J, Hsu C-T. Spatial Frequency Analysis by Adopting Regional Analysis with Radar Rainfall in Taiwan. *Water*. 2022; 14(17):2710.
https://doi.org/10.3390/w14172710

**Chicago/Turabian Style**

Chang, Che-Hao, Riki Rahmad, Shiang-Jen Wu, and Chih-Tsung Hsu. 2022. "Spatial Frequency Analysis by Adopting Regional Analysis with Radar Rainfall in Taiwan" *Water* 14, no. 17: 2710.
https://doi.org/10.3390/w14172710