# Assessing Future Rainfall Intensity–Duration–Frequency Characteristics across Taiwan Using the k-Nearest Neighbor Method

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of the Study Cases

_{short}), 24-h and 25-year events (event

_{long}), 1-h events (D1), 24-h events (D24), 2-year events (T2), and 25-year events (T25), as shown in the contingency table (Table 1). It should be noted that because the observed data has the periods of record of 20 years, only events with the 25-year return period and associated results are assessed in this study.

#### 2.2. Framework of Rainfall Projection

#### 2.3. Algorithm of the k-NN Method Used in the Study

_{p}between the observed and the generated consecutive n-day rainfall event is estimated using Equation (1). To determine the weights w

_{t}in Equation (1), while optimization methods can be used, this study adopts the reciprocal of the variance as the weights to estimate the distance with neighbors, as shown in Equation (2) [36]. The reciprocals of the variances are used as weights to allow more flexibility in selecting the most-alike historical events for the originally existed large variation of the n

_{th}day rainfall amount:

_{t}is the generated daily rainfall on the t

_{th}day of the consecutive n-day event; o

_{t,p}is the observed daily rainfall on the t

_{th}day of the p

_{th}historical event in the pool with a total of f events; w

_{t}are the weights. Notice that the events in the pool are extracted from the defined window period. In this study, the month of the generated daily rainfall is chosen as the window period.

_{p}with rank one (r = 1), is selected. The hourly rainfall h

_{q,t′}is determined by Equation (3), and the ratio of rainfall amount for each hour ($\frac{{h}_{q,t}}{{o}_{t,r=1}}$) is derived from the selected observed event:

_{q,t’}represents hourly rainfall simulated for the q

_{th}hour on the t

_{th}day; o

_{t,r = 1}is the total rainfall amount of the t

_{th}day of the observations; and h

_{q,t}is the hourly rainfall for the q

_{th}hour on the t

_{th}day from the observations. Here the observations refer to the nearest observed neighboring n-day rainfall event.

_{max}in the same month. Afterwards, either one of the following two possible conditions is determined for the generation of future hourly rainfall, as shown in Equations (4) and (5):

- (1)
- If D
_{max}is larger than half of m, then the m-day is divided into two sets, namely a and b days ($m=a+b$). All possible combinations of a and b are tried. After the m-day event is divided into new combinations, the distance d_{p}(Equation (1)) of historical and simulated a- and b-day events are summed up as Equation (4). The optimal a and b are determined when the minimal distance is obtained:$${d}_{p}{}^{\prime}={d}_{p,a}+{d}_{p,b},\forall \left(a,b\right)\mathrm{if}{D}_{max}\ge \frac{m}{2}$$ - (2)
- If D
_{max}is smaller than half of m, D_{max}is used to divide the m days as many times as possible. The m-day event becomes D_{max}+ … + D_{max}+ c, where c equals to m minus a multiple of D_{max}. With the new combination, the distance d_{p}(Equation (1)) of historical and simulated D_{max}-day events are calculated as well as c-day events (m = ${D}_{max}+\dots +{D}_{max}+c$). When the minimal d_{p}is obtained using Equation (5), the most alike multiple D_{max}-day and c-day events are determined and used as references to generate future hourly rainfall for the m-day event:$${d}_{p}{}^{\u2033}={d}_{p,{D}_{max}}+\cdots +{d}_{p,{D}_{max}}+{d}_{p,c},\mathrm{if}{D}_{max}\frac{m}{2}$$

## 3. Results and Discussion

_{short}) and 24-h events in the 25-yr return period (events

_{long}), to examine the variation among locations and scenarios. Next, the influences of return periods and durations on rainfall intensities are analyzed.

#### 3.1. Rainfall Variation among Locations and Scenarios

_{short}for the near- and far-future are depicted in Figure 4 and Figure 5, respectively. Both the rainfall intensities and the percentage changes compared to the observation in 1986–2005 are illustrated. The projected rainfall intensity of events

_{short}is about 30–65 mm/h in the near future (Figure 4), while a slight increase is found for the far future (Figure 5). It is found that the variation of rainfall intensities among the locations is larger than that among the scenarios. After converting to change percentages, the variations among the scenarios become equally prominent, indicating deviation of the future rainfall intensities from the past. The projected rainfall-intensity changes of −10~20% were found in the near and far future. Comparing the results of RCP 2.6 and 8.5, opposite signs which show obvious difference between the two scenarios are found at Kaohsiung (− to +), Hengchun (− to +), and Chenggong (+ to −). Changes are intensified under RCP 8.5 for most other stations, except for Zhuzihu, Taipei, Hsinchu and Alishan, although no obvious difference are found for the two scenarios.

_{short}. It is because the ventilation is good, and the height exceeds the zone where moisture is condensed. On the other hand, the altitudes and weather conditions of the stations are more even in southern and eastern Taiwan.

_{long}for the near and far-future are depicted in Figure 7 and Figure 8, respectively.

_{long}compared to events

_{short}. For future studies, events with longer return periods than 25-yr return periods should better be analyzed using record of the observed data longer than 20 years to disclose more information.

#### 3.2. Association between Return Periods/Durations and Rainfall Intensities

## 4. Conclusions

_{short}) and with 24-h duration and 25-yr return period (events

_{long}), were discussed. For events

_{short}, the projected rainfall-intensity changes of 10~20% were found under future scenarios compared to the observations. Considering the existing flood-warning thresholds, precautions of flooding are required for the frequently occurred short-duration storm events in Keelung, Danshui, Kaohsiung, and Suao, although rainfall intensities are projected to decrease from the near to the far future.

_{long}, the majority of the projected rainfall intensities exceeded the flood-warning threshold despite of the decreasing intensities compared to observation, which should be of concern. Compared to events

_{short}, the decreases in the rainfall intensities of events

_{long}are more obvious from near to far future. Among all stations, the land-subsidence regions in central and south, the landslide-sensitive mountainous region in north and central, the pluvial- and fluvial-flood prone region in north, and the regions with vulnerable infrastructures in east should be especially aware of possible long-duration extreme events. It should be noted that because the observed data has a period of record of 20 years, only the 25-yr return period are presented here; however, events with longer return periods than 25-yr return periods should better be analyzed to disclose more information of extreme events the cities face in the future.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Neumann, B.; Vafeidis, A.T.; Zimmermann, J.; Nicholls, R. Future Coastal Population Growth and Exposure to Sea-Level Rise and Coastal Flooding—A Global Assessment. PLoS ONE
**2015**, 10, e0118571. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hughes, B.; Lowe, J.A.; Nicholls, R.; Osborn, T. The impacts of climate change across the globe: A multi-sectoral assessment. Clim. Chang.
**2016**, 134, 457–474. [Google Scholar] - Nolan, P.; O’Sullivan, J.; McGrath, R. Impacts of climate change on mid-twenty-first-century rainfall in Ireland: A high-resolution regional climate model ensemble approach. Int. J. Climatol.
**2017**, 37, 4347–4363. [Google Scholar] [CrossRef] - Cheng, L.; AghaKouchak, A. Nonstationary Precipitation Intensity-Duration-Frequency Curves for Infrastructure Design in a Changing Climate. Sci. Rep.
**2015**, 4, 7093. [Google Scholar] [CrossRef] [PubMed][Green Version] - Peck, A.; Prodanovic, P.; Simonovic, S.P.P. Rainfall Intensity Duration Frequency Curves Under Climate Change: City of London, Ontario, Canada. Can. Water Resour. J. Rev. Can. Des Ressour. Hydr.
**2012**, 37, 177–189. [Google Scholar] [CrossRef] - De Paola, F.; Giugni, M.; Topa, M.E.; Bucchignani, E. Intensity-Duration-Frequency (IDF) rainfall curves, for data series and climate projection in African cities. Springer Plus
**2014**, 3, 1–18. [Google Scholar] [CrossRef][Green Version] - Olesen, J.E.; Trnka, M.; Kersebaum, K.; Skjelvåg, A.; Seguin, B.; Peltonen-Sainio, P.; Rossi, F.; Kozyra, J.; Micale, F. Impacts and adaptation of European crop production systems to climate change. Eur. J. Agron.
**2011**, 34, 96–112. [Google Scholar] [CrossRef] - Arnell, N.W.; Lloyd-Hughes, B. The global-scale impacts of climate change on water resources and flooding under new climate and socio-economic scenarios. Clim. Chang.
**2014**, 122, 127–140. [Google Scholar] [CrossRef][Green Version] - Li, C.-Y.; Lin, S.-S.; Chuang, C.-M.; Hu, Y.-L. Assessing future rainfall uncertainties of climate change in Taiwan with a bootstrapped neural network-based downscaling model. Water Environ. J.
**2018**, 34, 77–92. [Google Scholar] [CrossRef] - Huang, W.; Chang, Y.; Hsu, H.; Cheng, C.; Tu, C. Dynamical downscaling simulation and future projection of summer rainfall in Taiwan: Contributions from different types of rain events. J. Geophys. Res. Atmos.
**2016**, 121, 13–973. [Google Scholar] [CrossRef] - Wei, C.; Yeh, H.; Chen, Y.; Cheng, K. Stochastic simulation for design storm with different return periods and du-rations, annual and monthly rainfall of the National Taiwan University Experimental Forest. J. Exp. For. Natl. Taiwan Univ.
**2016**, 30, 153–176. [Google Scholar] - Chen, C.W.; Tung, Y.S.; Liou, J.J.; Li, H.C.; Cheng, C.T.; Chen, Y.M.; Oguchi, T. Assessing landslide characteris-tics in a changing climate in northern Taiwan. Catena
**2019**, 175, 263–277. [Google Scholar] [CrossRef] - Chen, Y.M.; Chen, C.W.; Chao, Y.C.; Tung, Y.S.; Liou, J.J.; Li, H.C.; Cheng, C.T. Future Landslide Characteris-tic Assessment Using Ensemble Climate Change Scenarios: A Case Study in Taiwan. Water
**2020**, 12, 564. [Google Scholar] - Richardson, C.W. Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour. Res.
**1981**, 17, 182–190. [Google Scholar] [CrossRef] - Semenov, M.A.; Barrow, E.M.; Lars-Wg, A. A Stochastic Weather Generator for Use in Climate Impact Studies; User Manual: Hertfordshire, UK, 2002. [Google Scholar]
- Mailhot, A.; Duchesne, S.; Caya, D.; Talbot, G. Assessment of future change in intensity–duration–frequency (IDF) curves for Southern Quebec using the Canadian Regional Climate Model (CRCM). J. Hydrol.
**2007**, 347, 197–210. [Google Scholar] [CrossRef] - DeGaetano, A.T.; Castellano, C.M. Future projections of extreme precipitation intensity-duration-frequency curves for climate adaptation planning in New York State. Clim. Serv.
**2017**, 5, 23–35. [Google Scholar] [CrossRef] - Cook, L.M.; McGinnis, S.; Samaras, C. The effect of modeling choices on updating intensity-duration-frequency curves and stormwater infrastructure designs for climate change. Clim. Chang.
**2020**, 159, 289–308. [Google Scholar] [CrossRef][Green Version] - Rasmussen, S.B.; Blenkinsop, S.; Burton, A.; Abrahamsen, P.; Holm, P.E.; Hansen, S. Climate change impacts on agro-climatic indices derived from downscaled weather generator scenarios for eastern Denmark. Eur. J. Agron.
**2018**, 101, 222–238. [Google Scholar] [CrossRef] - So, B.-J.; Kim, J.-Y.; Kwon, H.-H.; Lima, C.H. Stochastic extreme downscaling model for an assessment of changes in rainfall intensity-duration-frequency curves over South Korea using multiple regional climate models. J. Hydrol.
**2017**, 553, 321–337. [Google Scholar] [CrossRef] - Hassanzadeh, E.; Nazemi, A.; Elshorbagy, A. Quantile-based downscaling of precipitation using genetic program-ming: Application to IDF curves in Saskatoon. J. Hydrol. Eng.
**2014**, 19, 943–955. [Google Scholar] [CrossRef] - Mirhosseini, G.; Srivastava, P.; Fang, X. Developing Rainfall Intensity-Duration-Frequency Curves for Alabama under Future Climate Scenarios Using Artificial Neural Networks. J. Hydrol. Eng.
**2014**, 19, 04014022. [Google Scholar] [CrossRef] - Ivanov, V.Y.; Bras, R.L.; Curtis, D.C. A weather generator for hydrological, ecological, and agricultural applications. Water Resour. Res.
**2007**, 43. [Google Scholar] [CrossRef][Green Version] - Peleg, N.; Molnar, P.; Burlando, P.; Fatichi, S. Exploring stochastic climate uncertainty in space and time using a gridded hourly weather generator. J. Hydrol.
**2019**, 571, 627–641. [Google Scholar] [CrossRef] - Müller, H.; Haberlandt, U. Temporal rainfall disaggregation with a cascade model: From single-station disaggrega-tion to spatial rainfall. J. Hydrol. Eng.
**2015**, 20, 04015026. [Google Scholar] [CrossRef][Green Version] - De Luca, D.L. Analysis and modelling of rainfall fields at different resolutions in southern Italy. Hydrol. Sci. J.
**2014**, 59, 1536–1558. [Google Scholar] [CrossRef][Green Version] - Menabde, M.; Sivapalan, M. Modeling of rainfall time series and extremes using bounded random cascades and levy-stable distributions. Water Resour. Res.
**2000**, 36, 3293–3300. [Google Scholar] [CrossRef][Green Version] - Over, T.M.; Gupta, V.K. Statistical Analysis of Mesoscale Rainfall: Dependence of a Random Cascade Generator on Large-Scale Forcing. J. Appl. Meteorol.
**1994**, 33, 1526–1542. [Google Scholar] [CrossRef][Green Version] - Choi, J.; Lee, O.; Jang, J.; Jang, S.; Kim, S. Future intensity–depth–frequency curves estimation in Korea under rep-resentative concentration pathway scenarios of Fifth assessment report using scale-invariance method. Int. J. Climatol.
**2019**, 39, 887–900. [Google Scholar] [CrossRef] - Cannon, A.J.; Innocenti, S. Projected intensification of sub-daily and daily rainfall extremes in convec-tion-permitting climate model simulations over North America: Implications for future intensity–duration–frequency curves. Nat. Hazards Earth Syst. Sci.
**2019**, 19, 421–440. [Google Scholar] [CrossRef][Green Version] - Yang, X.; He, R.; Ye, J.; Tan, M.L.; Ji, X.; Tan, L.; Wang, G. Integrating an hourly weather generator with an hourly rainfall SWAT model for climate change impact assessment in the Ru River Basin, China. Atmos. Res.
**2020**, 244, 105062. [Google Scholar] [CrossRef] - Peleg, N.; Fatichi, S.; Paschalis, A.; Molnar, P.; Burlando, P. An advanced stochastic weather generator for simu-lating 2-D high-resolution climate variables. J. Adv. Modeling Earth Syst.
**2017**, 9, 1595–1627. [Google Scholar] [CrossRef] - Blenkinsop, S.; Harpham, C.; Burton, A.; Goderniaux, P.; Brouyère, S.; Fowler, H.; Fowler, H. Downscaling transient climate change with a stochastic weather generator for the Geer catchment, Belgium. Clim. Res.
**2013**, 57, 95–109. [Google Scholar] [CrossRef][Green Version] - Burton, A.; Fowler, H.; Blenkinsop, S.; Kilsby, C. Downscaling transient climate change using a Neyman–Scott Rectangular Pulses stochastic rainfall model. J. Hydrol.
**2010**, 381, 18–32. [Google Scholar] [CrossRef] - De Luca, D.; Petroselli, A.; Galasso, L. A Transient Stochastic Rainfall Generator for Climate Changes Analysis at Hydrological Scales in Central Italy. Atmosphere
**2020**, 11, 1292. [Google Scholar] [CrossRef] - Solaiman, T.A.; Simonovic, S.P. Development of Probability Based Intensity-Duration-Frequency Curves under Climate Change. Water Resour Res Rep.
**2011**, 34, 1–93. [Google Scholar] - Alam, M.S.; Elshorbagy, A. Quantification of the climate change-induced variations in Intensity–Duration–Frequency curves in the Canadian Prairies. J. Hydrol.
**2015**, 527, 990–1005. [Google Scholar] [CrossRef] - Gunawardhana, L.N.; Al-Rawas, G.A.; Al-Hadhrami, G. Quantification of the changes in intensity and frequency of hourly extreme rainfall attributed climate change in Oman. Nat. Hazards
**2018**, 92, 1649–1664. [Google Scholar] [CrossRef] - Lee, T.; Son, C.; Kim, M.; Lee, S.; Yoon, S. Climate Change Adaptation to Extreme Rainfall Events on a Local Scale in Namyangju, South Korea. J. Hydrol. Eng.
**2020**, 25, 05020005. [Google Scholar] [CrossRef] - Hosseinzadehtalaei, P.; Tabari, H.; Willems, P. Climate change impact on short-duration extreme precipitation and intensity–duration–frequency curves over Europe. J. Hydrol.
**2020**, 590, 125249. [Google Scholar] [CrossRef] - Ganguli, P.; Coulibaly, P. Assessment of future changes in intensity-duration-frequency curves for Southern Ontar-io using North American (NA)-CORDEX models with nonstationary methods. J. Hydrol. Reg. Stud.
**2019**, 22, 100587. [Google Scholar] - Muzik, I. A first-order analysis of the climate change effect on flood frequencies in a subalpine watershed by means of a hydrological rainfall–runoff model. J. Hydrol.
**2002**, 267, 65–73. [Google Scholar] [CrossRef] - Kuo, C.-C.; Gan, T.Y.; Gizaw, M. Potential impact of climate change on intensity duration frequency curves of central Alberta. Clim. Chang.
**2015**, 130, 115–129. [Google Scholar] [CrossRef] - Shukor, M.S.A.; Yusop, Z.; Yusof, F.; Sa’Adi, Z.; Alias, N.E. Detecting Rainfall Trend and Development of Future Intensity Duration Frequency (IDF) Curve for the State of Kelantan. Water Resour. Manag.
**2020**, 34, 3165–3182. [Google Scholar] [CrossRef] - Butcher, J.B.; Zi, T.; Pickard, B.R.; Job, S.C.; Johnson, T.E.; Groza, B.A. Efficient statistical approach to develop intensity-duration-frequency curves for precipitation and runoff under future climate. Clim. Chang.
**2021**, 164, 1–20. [Google Scholar] [CrossRef] - Mirhosseini, G.; Srivastava, P.; Stefanova, L. The impact of climate change on rainfall Intensity–Duration–Frequency (IDF) curves in Alabama. Reg. Environ. Chang.
**2012**, 13, 25–33. [Google Scholar] [CrossRef] - Mirhosseini, G.; Srivastava, P.; Sharifi, A. Developing Probability-Based IDF Curves Using Kernel Density Estimator. J. Hydrol. Eng.
**2015**, 20, 04015002. [Google Scholar] [CrossRef] - Field, C.B. (Ed.) Climate Change 2014–Impacts, Adaptation and Vulnerability: Regional Aspects; Cambridge University Press: Cambridge, UK, 2014. [Google Scholar]
- National Science and Technology Center for Disaster Reduction. Climate Change in Taiwan 2017: Scientific Report—The Physical Science Basis; National Science and Technology Center for Disaster Reduction: Taipei, Taiwan, 2017. [Google Scholar]
- Jhong, B.C.; Tachikawa, Y.; Tanaka, T.; Udmale, P.; Tung, C.P. A generalized framework for assessing flood risk and suitable strategies under various vulnerability and adaptation scenarios: A case study for residents of Kyoto city in Japan. Water
**2020**, 12, 2508. [Google Scholar] [CrossRef] - Lin, C.-Y.; Tung, C.-P. Procedure for selecting GCM datasets for climate risk assessment. Terr. Atmos. Ocean. Sci.
**2017**, 28, 43–55. [Google Scholar] [CrossRef][Green Version] - Hong, N.-M.; Lee, T.-Y.; Chen, Y.-J. Daily weather generator with drought properties by copulas and standardized precipitation indices. Environ. Monit. Assess.
**2016**, 188, 1–14. [Google Scholar] [CrossRef] - Willems, P.; Arnbjerg-Nielsen, K.; Olsson, J.; Nguyen, V. Climate change impact assessment on urban rainfall extremes and urban drainage: Methods and shortcomings. Atmos. Res.
**2012**, 103, 106–118. [Google Scholar] [CrossRef] - Weibull, W. A statistical Theory of Strength of Materials; IVB-Handl, Generalstabens Litografiska Anstalts Förlag: Stockholm, Sweden, 1939. [Google Scholar]
- Lu, Y.; Qin, X.S.; Mandapaka, P.V. A combined weather generator and K-nearest-neighbour approach for assessing climate change impact on regional rainfall extremes. Int. J. Climatol.
**2015**, 35, 4493–4508. [Google Scholar] [CrossRef] - Prein, A.F.; Rasmussen, R.M.; Ikeda, K.; Liu, C.; Clark, M.P.; Holland, A. The future intensification of hourly precipitation extremes. Nat. Clim. Chang.
**2017**, 7, 48–52. [Google Scholar] [CrossRef] - Cheng, K.S.; Hueter, I.; Hsu, E.C.; Yeh, H.C. A Scale-Invariant Gauss-Markov Model for Design Storm Hyetographs 1. Jawra J. Am. Water Resour. Assoc.
**2001**, 37, 723–735. [Google Scholar] [CrossRef]

**Figure 1.**Location of 21 weather stations across Taiwan for the northern, central, southern and eastern regions.

**Figure 2.**Relation between the IDF values in the historical period (1986–2005) used to verify the reliability of the K-NN method, derived based on (i) the observed daily rainfall, (ii) the projected daily rainfall, and (iii) the observed hourly rainfall.

**Figure 3.**Intensity-Duration-Frequency (IDF) curves from the k-NN method using both the simulated and observed daily precipitation of Tainan in the historical period (1986–2005).

**Figure 4.**Rainfall intensities (

**top**) and percentage changes (

**bottom**) of events with 1-h duration and 2-yr return period (events

_{short}) for the near future (2021–2040) under RCP 2.6 and RCP 8.5 for five GCMs (CCSM4, CESM1-CAM5, GISS-E2-R, HadGEM2-AO, MIROC5).

**Figure 5.**Rainfall intensities (

**top**) and percentage of changes (

**bottom**) of events with one-hour duration and two-year return period (events

_{short}) for far future (2081–2100) under RCP2.6 and RCP 8.5 for five GCMs (CCSM4, CESM1-CAM5, GISS-E2-R, HadGEM2-AO, MIROC5).

**Figure 6.**Difference of rainfall intensities (

**top**) and percentage changes (

**bottom**) of events

_{short}between the near future (2021–2040) and far future (2081–2100).

**Figure 7.**Rainfall intensities (

**top**) and percentage changes (

**bottom**) of events with 24-h duration and 25-yr return period (events

_{long}) for the near future (2021–2040) under RCP 2.6 and RCP 8.5 for five GCMs (CCSM4, CESM1-CAM5, GISS-E2-R, HadGEM2-AO, MIROC5).

**Figure 8.**Rainfall intensities (

**top**) and percentage of changes (

**bottom**) of events with twenty-four-hour du-ration and twenty-five-year return period (events

_{long}) for far future (2081–2100) under RCP2.6 and RCP 8.5 for five GCMs (CCSM4, CESM1-CAM5, GISS-E2-R, HadGEM2-AO, MIROC5).

**Figure 9.**Difference of rainfall intensities (

**top**) and percentage changes (

**bottom**) of events

_{long}between the near future (2021–2040) and far future (2081–2100).

**Figure 10.**Rainfall intensities of the 1-h events (D1) in different return periods for the four regions and four scenarios.

**Figure 11.**Rainfall intensities of events with twenty-four-hour duration (D24) changing with the return periods for the four regions and four scenarios.

**Figure 12.**Rainfall intensities of 2-yr events (T2) of different durations for the four regions and four scenarios.

**Figure 13.**Rainfall intensities of events with twenty-five-year return period (T25) changing with the durations for the four regions and four scenarios.

**Table 1.**Contingency table of the six types of events analyzed in this study (event

_{short}, event

_{long}, D1, D24, T2 and T25).

D1 | D24 | ||
---|---|---|---|

D (h) T (yr) | 1 | 24 | |

T2 | 2 | event_{short} | |

T25 | 25 | event_{long} |

Steps | Method Adopted in This Study |
---|---|

Generate daily rainfall | Richardson-type weather generator [14] |

Generate hourly rainfall | k-Nearest Neighbors (k-NN) method [36] |

Obtain rainfall intensities for events of various return periods | Weibull’s formula [54] |

Correct bias of historical simulation and future projection | Quantile-mapping-based bias correction [46] |

Parameter | Configuration |
---|---|

Window period of the neighbors | One month |

Weight for estimating the neighboring distance | Reciprocal of the variance |

Neighbor-selecting criterion | The nearest neighbors |

Number of realizations | Ten realizations of 20-yr data |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, P.-Y.; Tung, C.-P.; Tsao, J.-H.; Chen, C.-J. Assessing Future Rainfall Intensity–Duration–Frequency Characteristics across Taiwan Using the *k*-Nearest Neighbor Method. *Water* **2021**, *13*, 1521.
https://doi.org/10.3390/w13111521

**AMA Style**

Chen P-Y, Tung C-P, Tsao J-H, Chen C-J. Assessing Future Rainfall Intensity–Duration–Frequency Characteristics across Taiwan Using the *k*-Nearest Neighbor Method. *Water*. 2021; 13(11):1521.
https://doi.org/10.3390/w13111521

**Chicago/Turabian Style**

Chen, Pei-Yuan, Ching-Pin Tung, Jung-Hsuan Tsao, and Chia-Jeng Chen. 2021. "Assessing Future Rainfall Intensity–Duration–Frequency Characteristics across Taiwan Using the *k*-Nearest Neighbor Method" *Water* 13, no. 11: 1521.
https://doi.org/10.3390/w13111521