# A New Look at Storm Separation Technique in Estimation of Probable Maximum Precipitation in Mountainous Areas

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Step-Duration-Orographic-Intensification-Factor (SDOIF) Method

#### 2.2. Regional L-Moments Analysis (RLMA)

#### 2.2.1. L-Moments Approach

#### 2.2.2. The Index-Flood Procedure

#### 2.2.3. Identification of Homogenous Regions

#### 2.2.4. Selection of an Appropriate Probability Distribution

#### 2.3. Procedure of PMP Estimation

- (1)
- Estimation of rainfall quantiles via RLMA: Firstly, several homogeneous regions are identified in the target area based on historical annual maximum rainfalls, and the appropriate probability distributions for the regions are determined. Then, using the regional parameters of the identified distribution for each homogeneous region, quantile factors for the dimensionless distribution at specified recurrence intervals (or probabilities of nonexceedance) can be computed. By multiplying the quantile factors by the means of the at-site annual maximum rainfalls, the desired quantile estimates at sites are obtained.
- (2)
- Development of OIF: Rainfall quantiles with certain return periods are used to calculate the OIFs at sites in the target area according to Equation (4). Then, a grid framework covering the target area is established at a resolution which is adapted to the spatial distribution density of raingauge stations. The Kriging method, which is an interpolation procedure used to estimate a variable at unsampled locations using weighted sums of the variable at neighboring sample points, is adopted to obtain the grid-point values of OIF.
- (3)
- Storm Separation: The duration maximum rainfalls R
_{∆t}at sites are obtained based on observation data of the storms for transposition and then interpolated to the same grid framework of OIFs. At each grid point, using Equation (5) with R_{∆t}as numerator and OIF as denominator, the convergence rainfall R_{0,∆t}for each storm is achieved. - (4)
- Construction of the convergence component pattern: The spatial distribution of the convergence rainfall R
_{0,∆t}can be generalized into a set of concentric ellipses to build up the convergence component pattern. To determine the shape of the convergence component pattern, the most suitable ellipse for each convergence rainfall is drawn to fit the shape of isohyets around the rainfall center, and the aspect ratio (i.e., the ratio of the major radius to the minor radius) of each ellipse is estimated. The average of the aspect ratios over the storms is taken as the aspect ratio of the generalized convergence component pattern. Meanwhile, Depth-Area relation of each convergence rainfall is calculated. Taking the maximum area for every rainfall depth at an interval of 50mm in all storms, the Depth-Area relation of the generalized convergence component pattern is developed. - (5)
- Estimation of PMP: The convergence component pattern is transposed to the design area and coupled with (superposed onto) local OIFs. The OIFs of the design area is calculated in the same way as it is done for the target area. By multiplying the OIF by the rainfall value calculated from the isohyets of convergence component pattern at each grid point, the PMP estimates are achieved.

## 3. Study Area and Data Availability

^{2}. As the elevation map shows (Figure 2a), two-thirds of the island are occupied by mountains which are mostly located in the central-east area of the island, while plains are mainly distributed in the west part. The five main mountain ranges, including Central, Jade, Snow, Ali, and Eastern Coastal Mountain Range, run approximately in parallel from north-northeast to south-southwest through the island, with a maximum elevation of 3952 m. The Central Mountain Range (CMR), which is high and steep, forms the backbone ridge. Many studies pointed out that when a typhoon passed over the island and its vicinity, enormous amounts of rainfall occurred and were enhanced by orographic lifting of the island mountains, particularly the CMR [40,41,42,43].

^{2}. To develop the local OIF, historical 4- and 24-h annual maximum rainfall data of 73 raingauge stations in Hong Kong and Shenzhen station in Guangdong province of China located close to Hong Kong (Figure 2b) with observation periods longer than 20 years have been used. The main inflow direction of moisture during typhoon storms in Hong Kong is northeast or north [34,35], so R22, R30, and Shenzhen, located in the northern low-altitude area (red squares in Figure 2b), were selected as the base stations.

## 4. Results and Discussion

#### 4.1. Homogeneous Regions of Taiwan

#### 4.2. Rainfall Quantiles in Taiwan

#### 4.3. Orographic Intensification Factor (OIF) of Taiwan under Southwesterly Moisture Inflow

^{2}), the OIFs at sites were interpolated to the gird with a resolution of 14 km × 14 km (0.125° × 0.125°). The spatial distributions of OIFs based on annual maximum rainfalls, 100-, 200-, and 500-year rainfall quantiles (hereafter, OIF

_{am}, OIF

_{100-yr}, OIF

_{200-yr}, and OIF

_{500-yr}, respectively) are shown in Figure 4. It can be observed that, for the same duration, the spatial distribution patterns of OIF

_{am}, OIF

_{100-yr}, OIF

_{200-yr}, and OIF

_{500-yr}are similar, which illustrates that OIFs can stably reflect the influences of topography on precipitation. The areas of high OIF values are mainly in the southwestern of Ali, Jade, and Central Mountain Range, with the two highest value centers located around Ali Mountain (denoted by C1) and Weiliao Mountain (denoted by C2) and in the windward slope of the mountains with obvious topographic lifting effect under the southwesterly moisture inflow during typhoon storms. The two maximum total accumulated rainfall records during Typhoon Morakot from 5 to 10 August 2009 were observed in Ali Mountain (3059.5 mm) and Weiliao Mountain (2910.0 mm), which are consistent with these two OIF centers. Comparing to 4-h OIFs, the center values of 24-h OIFs are larger, and the contours of 24-h OIFs are denser, which indicates that the influences of topography on rainfall enhances with the increase of duration. In addition, it is found that there is another high value center of 24-h OIFs in the northeast of Taiwan, where high rainfall records were also observed in history. However, given that the OIFs were developed under southwesterly moisture inflow while the northeastern area is in the leeward side of the mountain ranges with respect to the southwesterly moisture inflow, it is not considered in question.

_{100-yr}, OIF

_{200-yr}, and OIF

_{500-yr}are denser and telling more spatial details than that of OIF

_{am}. Figure 5 gives the differences between the OIFs based on rainfall quantiles and OIF

_{am}. It is observed that, to the west windward slopes of the Central Mountain Range (CMR), as well as at the high value center around Ali Mountain, where the orographic effect is strong, 4-h OIF

_{100-yr}, OIF

_{200-yr}, and OIF

_{500-yr}are slightly higher than OIF

_{am}but slightly lower than OIF

_{am}to the east of CMR. Moreover, OIF

_{am}, OIF

_{100-yr}, OIF

_{200-yr}, and OIF

_{500-yr}are close to each other on the southwestern coastal plain. While for a longer duration of 24-h, OIF

_{200-yr}, and OIF

_{500-yr}are close to OIF

_{am}to the west and south of Taiwan, and just the OIF

_{100-yr}, which reflects the orographic effect more evidently, are higher than OIF

_{am}around Ali Mountain. This may suggest that the 100-year quantiles based on current data situation are more stable and hence of more representativeness to the Ali Mountain in terms of the rainfall intensification.

#### 4.4. Storm Separation and Construction of the Convergence Component Pattern

_{am}, OIF

_{100-yr}, OIF

_{200-yr}, and OIF

_{500-yr}separately in a 0.125° (14 km) latitude–longitude resolution grid (same as the grid framework for interpolated OIFs). Then convergence rainfalls of the four storms based on annual maximum rainfalls, 100-, 200-, and 500-year rainfall quantiles (hereafter, R

_{0(am)}, R

_{0(100-yr)}, R

_{0(200-yr)}, and R

_{0(500-yr)}, respectively) were obtained. The center values of rainfalls before and after separation are given in Table 5. The first row gives the 4- and 24-h maximum observed rainfalls (R

_{∆t}) which contain the orographic effects. It is obvious that, after removing the orographic effects, the maximum convergence rainfalls (R

_{0(am)}, R

_{0(100-yr)}, R

_{0(200-yr)}, and R

_{0(500-yr)}) are smaller than maximum R

_{∆t}of the corresponding storms. The differences between the observed rainfalls and the convergence rainfalls are larger for longer duration than that for shorter duration, which indicates that the orographic effects are stronger for longer duration. The 4-h maximum R

_{0(100-yr)}, R

_{0(200-yr)}, and R

_{0(500-yr)}are generally close and slightly smaller than maximum R

_{0(am)}. However, the 24-h maximum R

_{0(100-yr)}, R

_{0(200-yr)}, and R

_{0(500-yr)}are much larger than maximum R

_{0(am)}and increase with the increasing return periods. All these indicate that the orographic impacts on rainfall increase with increase of duration of rainfall.

_{0(am}

_{)}has the highest center value and the largest areas in every rainfall depth interval. However, it shows an opposite situation for 24-h.

#### 4.5. PMP Estimates in Hong Kong

_{am}of Hong Kong based on annual maximum rainfalls was used. The resolution of the compute grid is 0.05° × 0.05° (5 km × 5 km) which is adapted to the spatial distribution density of raingauge stations in Hong Kong. The gridded values of OIF

_{am}are presented in Figure 8. It can be seen both the maximum 4- and 24-h OIF

_{am}of Hong Kong are centered at 114.15° E, 22.4° N near Tai Mo Mountain (marked in red star), at which the centers of convergence component patterns (red ellipses in Figure 8) were placed. Then the preliminary PMP estimates for generalized R

_{0(am)}, R

_{0(100-yr)}, R

_{0(200-yr)}, and R

_{0(500-yr)}(hereafter, PMP

_{am}, PMP

_{100-yr}, PMP

_{200-yr}, and PMP

_{500-yr}, respectively) were obtained on the grid, and the isohyets of the PMP were drawn up (Figure 9). The superposition of the generalized convergence component patterns transposed from Taiwan onto the local orographic component was made at orientations of several directions. For simplicity, the results at east–west orientation shown here are for illustration.

_{am}, and along with the increasing return periods, the center values (denoted by red numbers in Figure 9) vary slightly down by about 6%–9% (see Figure 10) for 4-h. While for 24-h, it shows an upper trend and the increasing percentage of PMP

_{500-yr}is up to 11.6%. The decreasing (increasing) variation tendency of center values of 4-h (24-h) PMP is resulting from the increasing (decreasing) trend of 4-h (24-h) OIFs in the center of the convergence rain. The point PMP estimates were compared with the extreme rainfall records in Hong Kong and the world records [28,34,35] to examine their rationality. The point 4-h (24-h) PMPs exceeds the maximum 4-h (24-h) rainfall of 384.0 mm (956.0 mm) recorded at Lantau (Tai Mo Mountain) in Hong Kong but is smaller than the world record. Besides, they are smaller compared to the PMPs estimated by a revised K

_{m}-value method in Hong Kong (i.e., 558.5 mm for 4-h and 1,753.0 mm for 24-h) [49,50]. However, the PMP estimates obtained here so far are actually just embryonic PMPs, so more comparisons should be made after conducting some necessary adjustments such as moisture maximization.

## 5. Summary and Conclusions

- (1)
- For 4- and 24-h, there are similar spatial distribution patterns of OIFs on Taiwan Island based on different data samples, which implicates that the SDOIF method is a stable and effective way to separate an orographic component rainfall with spatial distribution from storm rainfalls in mountainous areas.
- (2)
- In general, OIFs obtained based on rainfall quantiles show clearer spatial details of orographic influences on rainfall and better reflect the enhancement effects in orographic intensification areas than that obtained based on annual maxima. Moreover, the separated convergence rainfalls based on rainfall quantiles, which are more accordant with the precipitation purely resulting from atmospheric systems, can be transposed in a larger area. If the convergence rainfalls are transposed and then combined with the local OIFs in design area developed based on local rainfall quantiles, it may get more accurate PMP estimates not only in terms of the center values but also the spatial pattern. Further applications and verifications in other areas with different data should be studied.
- (3)
- For different durations, the center values of OIFs and PMP estimates based on rainfall quantiles may display increasing or decreasing trends with the increase of return periods. Considering quantile estimates may become less accurate and less reliable at larger return periods with respect to the data available, the 100-year rainfall quantiles are recommended most to calculate the OIF in storm separation procedure to achieve more reliable PMP estimates. The accuracy of quantiles estimated via RLMA is influenced by the quality of data (such as number of stations, length of data series) and the validity of delineated homogeneous regions, which will affect the accuracy of OIF values and PMP estimates. If rainfall data with longer time series at more stations are available, a more detailed analysis would be taken to estimate the quantiles, then more accurate and reliable OIFs could be expected.
- (4)
- In SDOIF method, the selection of base stations has an impact on the OIF values. The OIFs computed in this study only represent the topographic effects under the rainfalls with southwesterly moisture jet hitting Taiwan. However, in the cases of estimation for other areas such as north Taiwan, OIFs under storms with other moisture inflow directions such as northeast or northwest may be applied.
- (5)
- The PMP results in this study are just preliminary PMP estimates that require further adjustments, including transposition adjustments of orientations to the prevailing moisture jet during the invasion of typhoon storms to Hong Kong and moisture maximization.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Flowchart of Probable Maximum Precipitation (PMP) estimation applying the storm separation technique using rainfall quantiles estimated via Regional L-moments Analysis (RLMA).

**Figure 2.**Elevation map of (

**a**) Taiwan Island and (

**b**) Hong Kong, and locations of the raingauge stations. Red squares indicate selected base stations for development of orographic intensification factor (OIF).

**Figure 3.**Sketch of (

**a**) 4-h and (

**b**) 24-h homogeneous regions of Taiwan and the best-fit distributions for homogeneous regions.

**Figure 4.**Spatial distribution maps of Taiwan (

**a**–

**d**) 4-h and (

**e**–

**h**) 24-h OIFs under southwesterly moisture inflow: (

**a**,

**e**) based on annual maximum rainfalls (OIF

_{am}); (

**a**,

**f**) based on 100-year rainfall quantiles (OIF

_{100-yr}); (

**b**,

**g**) based on 200-year rainfall quantiles (OIF

_{200-yr}); (

**c**,

**h**) based on 500-year rainfall quantiles (OIF

_{500-yr}). C1 and C2 indicate the high value centers of OIFs at Ali and Weiliao Mountain, respectively.

**Figure 5.**Differences of (

**a**–

**c**) 4-h and (

**d**–

**f**) 24-h OIFs based on annual maximum rainfalls, 100-, 200-, and 500-year rainfall quantiles: (

**a**,

**d**) OIF

_{100-yr}—OIF

_{am}; (

**b**,

**e**) OIF

_{200-yr}—OIF

_{am}; (

**c**,

**f**) OIF

_{500-yr}—OIF

_{am}.

**Figure 6.**Four-hour convergence rainfall isohyetal maps of storms of TCs Kalmaegi, Fanapi, Herb, and Morakot affecting Taiwan for the cases of (

**a**) annual maximum rainfalls, (

**b**) 100-year rainfall quantiles, (

**c**) 200-year rainfall quantiles, and (

**d**) 500-year rainfall quantiles. Red circles and r denote the generalized ellipses for the convergence rainfalls and their aspect ratios, respectively.

**Figure 7.**Twenty-four-hour convergence rainfall isohyetal maps of storms of TCs Herb, Morakot, Haitang, and Aere affecting Taiwan for the cases of (

**a**) annual maximum rainfalls, (

**b**) 100-year rainfall quantiles, (

**c**) 200-year rainfall quantiles, and (

**d**) 500-year rainfall quantiles. Red circles and r denote the generalized ellipses for the convergence rainfalls and their aspect ratios, respectively.

**Figure 8.**(

**a**–

**d**) 4-h and (

**e**–

**h**) 24-h generalized convergence component patterns of Taiwan storms (red ellipses) superposed on Hong Kong gridded OIFs (blue numbers, grid resolution: 5 km × 5 km) for the cases of (

**a**,

**e**) annual maximum rainfalls, (

**b**,

**f**) 100-year rainfall quantiles, (

**c**,

**g**) 200-year rainfall quantiles, and (

**d**,

**h**) 500-year rainfall quantiles.

**Figure 9.**Isohyetal maps of

**(a**–

**d**) 4-h and (

**e**–

**h**) 24-h Hong Kong embryonic PMP estimates for the cases of (

**a**,

**e**) annual maximum rainfalls, (

**b**,

**f**) 100-year rainfall quantiles, (

**c**,

**g**) 200-year rainfall quantiles, and (

**d**,

**h**) 500-year rainfall quantiles.

**Figure 10.**Variation of center values of (

**a**) 4-h and (

**b**) 24-h Hong Kong PMP based on annual maximum rainfalls, 100-, 200-, and 500-year rainfall quantiles. The percentage variations relative to PMP based on annual maxima are given in parentheses.

**Table 1.**Data periods and duration rainfall maxima of selected storms (listed with corresponding tropical cyclones—TCs) for 4- and 24-h transposition analysis.

TCs | Storm Data Period | 4-h Rainfall Maxima (mm) | 24-h Rainfall Maxima (mm) | |||
---|---|---|---|---|---|---|

Kalmaegi (2008) | 16–18 July | 496.0 | - | |||

Fanapi (2010) | 17–20 September | 435.5 | - | |||

Herb (1996) | 29 July–1 August | 415.5 | 1748.5 | |||

Morakot (2009) | 5–10 August | 404.5 | 1623.5 | |||

Haitang (2005) | 16–20 July | - | 1254.5 | |||

Aere (2004) | 24–26 August | - | 1154.0 |

**Table 2.**Numbers of sites, values of homogeneity measure ${H}_{1}$, and goodness-of-fit tests’ results, as well as the best-fit distributions for 4-h homogenous regions of Taiwan (The best fitting results of each test are highlighted in bold, and ‘-’ indicates the value of $\left|{Z}^{DIST}\right|$ exceeds 1.64.).

Homogenous Regions | Number of Sites | ${\mathit{H}}_{1}$ | ${\mathit{Z}}^{\mathit{D}\mathit{I}\mathit{S}\mathit{T}}$ | RMSE(E−5) | RE Score | Best-Fit Distribution | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

GLO | GEV | GNO | GPA | PE3 | GLO | GEV | GNO | GPA | PE3 | GLO | GEV | GNO | GPA | PE3 | ||||||

1 | 17 | 0.79 | 1.38 | −0.66 | −1.16 | - | - | 6186 | 4880 | 5139 | 9886 | 6192 | 17.0 | 17.0 | 17.0 | 9.0 | 15.0 | GEV | ||

2 | 11 | −1.09 | 1.28 | 0.05 | −0.57 | - | - | 7515 | 5153 | 5221 | 6948 | 6767 | 12.5 | 16.5 | 17.0 | 14.0 | 15.0 | GEV | ||

3 | 49 | 0.75 | - | 0.15 | −0.58 | - | - | 7216 | 5465 | 5346 | 9567 | 5718 | 10.0 | 15.5 | 20.5 | 10.0 | 19.0 | GNO | ||

4 | 19 | 0.85 | - | - | 1.38 | - | 0.21 | 9171 | 6113 | 6016 | 6712 | 6109 | 13.0 | 18.0 | 18.0 | 11.0 | 15.0 | GNO | ||

5 | 33 | 0.44 | - | 0.97 | 0.08 | - | −1.63 | 9110 | 6817 | 6873 | 8386 | 7563 | 11.0 | 18.5 | 16.5 | 11.0 | 18.0 | GEV | ||

6 | 7 | 0.13 | 1.61 | 0.10 | −0.25 | - | −0.98 | 6077 | 2391 | 2970 | 7408 | 4273 | 12.0 | 18.0 | 18.5 | 11.0 | 15.5 | GEV | ||

7 | 28 | 0.23 | - | −1.18 | −1.37 | - | - | 6731 | 5660 | 5905 | 11331 | 6718 | 18.5 | 18.5 | 17.5 | 5.0 | 15.5 | GEV | ||

8 | 17 | −0.2 | 0.60 | −1.57 | - | - | - | 6532 | 6373 | 6424 | 12,337 | 7073 | 14.5 | 18.0 | 16.5 | 9.0 | 17.0 | GEV |

**Table 3.**Numbers of sites, values of homogeneity measure ${H}_{1}$ and goodness-of-fit tests’ results, as well as the best-fit distributions for 24-h homogenous regions of Taiwan (The best fitting results of each test are highlighted in bold, and ‘-’ indicates the value of $\left|{Z}^{DIST}\right|$ exceeds 1.64.).

Homogenous Regions | Number of Sites | ${\mathit{H}}_{1}$ | ${\mathit{Z}}^{\mathit{D}\mathit{I}\mathit{S}\mathit{T}}$ | RMSE(E−5) | RE Score | Best-fit Distribution | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

GLO | GEV | GNO | GPA | PE3 | GLO | GEV | GNO | GPA | PE3 | GLO | GEV | GNO | GPA | PE3 | ||||||

1 | 15 | −1.74 | 1.15 | −0.42 | −1.05 | - | - | 6982 | 5754 | 6226 | 9678 | 7745 | 16.0 | 17.5 | 16.5 | 11.0 | 14.0 | GEV | ||

2 | 15 | −0.89 | - | - | - | −0.76 | 1.57 | 13,280 | 10,534 | 9837 | 6889 | 9068 | 7.0 | 12.0 | 14.0 | 22.0 | 20.0 | GPA | ||

3 | 51 | 0.45 | - | - | 0.80 | - | −1.15 | 9490 | 7420 | 7221 | 9114 | 7407 | 13.5 | 19.0 | 20.0 | 8.5 | 14.0 | GNO | ||

4 | 14 | −0.89 | - | - | - | −1.35 | - | 12,353 | 9400 | 8983 | 6463 | 8532 | 11.0 | 13.5 | 16.5 | 17.5 | 16.5 | GPA | ||

5 | 26 | 0.51 | - | - | - | −0.53 | - | 12,462 | 9376 | 8609 | 5716 | 7323 | 9.5 | 12.5 | 16.5 | 16.5 | 20.0 | GPA | ||

6 | 9 | −0.56 | - | 0.38 | −0.18 | - | −1.22 | 6296 | 3630 | 3595 | 7297 | 4542 | 13.0 | 15.5 | 15.5 | 15.5 | 15.5 | GNO | ||

7 | 31 | 0.58 | - | 0.11 | 0.08 | - | −0.71 | 8553 | 5841 | 6323 | 9561 | 6641 | 12.5 | 14.5 | 18.0 | 13.0 | 17.0 | GNO | ||

8 | 20 | 0.93 | - | −0.64 | 0.00 | - | −0.16 | 8259 | 6323 | 6953 | 12,169 | 7601 | 17.5 | 15.5 | 18.5 | 5.0 | 18.5 | GNO |

**Table 4.**Four and 24-h means of annual maximum rainfalls along with 100-, 200-, and 500-year rainfall quantiles of selected base stations (station 1–5) and top-ranked-rainfall stations (station 6–9).

Station | Longitude (° E) | Latitude (° N) | 4-h (mm) | 24-h (mm) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Means of Annual Maxima | Quantiles | Means ofAnnual Maxima | Quantiles | |||||||||

100-year | 200-year | 500-year | 100-year | 200-year | 500-year | |||||||

1 | Puzi | 120.25 | 23.47 | 114.8 | 252.3 | 277.1 | 310.5 | 239.9 | 623.1 | 695.2 | 793.3 | |

2 | Beimen | 120.12 | 23.27 | 101.6 | 223.4 | 245.3 | 274.9 | 224.8 | 583.8 | 651.3 | 743.3 | |

3 | Xiaying | 120.25 | 23.23 | 119.8 | 263.3 | 289.2 | 324.0 | 267.2 | 693.8 | 774.1 | 883.3 | |

4 | Yongkang | 120.23 | 23.04 | 122.9 | 270.3 | 296.8 | 332.6 | 281.1 | 730.1 | 814.6 | 929.5 | |

5 | Kaohsiung | 120.31 | 22.57 | 129.7 | 285.1 | 313.1 | 350.8 | 280.6 | 728.8 | 813.0 | 927.8 | |

6 | Xinmajia | 120.69 | 22.68 | 231.3 | 510.4 | 555.2 | 613.0 | 673.8 | 1630.8 | 1781.8 | 1979.4 | |

7 | Taiwu | 120.70 | 22.61 | 226.8 | 498.8 | 547.8 | 613.7 | 656.6 | 1589.3 | 1736.4 | 1929.0 | |

8 | Ali | 120.76 | 22.73 | 196.4 | 433.4 | 471.5 | 520.5 | 581.3 | 1406.9 | 1537.2 | 1707.6 | |

9 | Alishan | 120.81 | 23.51 | 182.2 | 478.3 | 540.6 | 628.3 | 578.7 | 1536.9 | 1625.0 | 1716.9 |

**Table 5.**Center values of the observed rainfalls (R

_{∆t}) and the convergence rainfalls (R

_{0(am)}, R

_{0(am)}, R

_{0(200-yr)}, and R

_{0(500-yr)}) for 4- and 24-h.

Rainfall Category | 4-h (mm) | 24-h (mm) | |||||||
---|---|---|---|---|---|---|---|---|---|

Kalmaegi | Fanapi | Herb | Morakot | Herb | Morakot | Haitang | Aere | ||

R_{∆t} | 496.00 | 435.50 | 415.50 | 404.50 | 1748.50 | 1623.50 | 1254.50 | 1154.00 | |

R_{0(am)} | 326.74 | 295.15 | 256.90 | 309.35 | 717.01 | 842.78 | 541.89 | 683.00 | |

R_{0(100-yr)} | 306.14 | 295.39 | 214.66 | 283.11 | 700.13 | 883.40 | 586.64 | 670.02 | |

R_{0(200-yr)} | 302.68 | 295.40 | 208.46 | 280.19 | 739.50 | 901.67 | 599.61 | 707.82 | |

R_{0(500-yr)} | 298.26 | 295.41 | 200.88 | 276.76 | 799.96 | 940.27 | 616.61 | 765.55 |

**Table 6.**Depth-Area relation of 4-h convergence component patterns based on annual maximum rainfalls, 100-, 200-, and 500-year rainfall quantiles.

Isohyets (mm) | Area (km^{2}) | ||||||
---|---|---|---|---|---|---|---|

Pattern of R_{0(am)} | Pattern of R_{0(100-yr)} | Pattern of R_{0(200-yr)} | Pattern of R_{0(500-yr)} | ||||

50 | 31,881.70 | 31,447.68 | 31,373.12 | 31,266.79 | |||

100 | 20,816.35 | 18,378.25 | 18,094.28 | 17,761.58 | |||

150 | 12,231.82 | 10,470.06 | 10,014.78 | 9605.52 | |||

200 | 3119.37 | 2237.58 | 2102.96 | 1984.52 | |||

250 | 1207.39 | 903.03 | 790.83 | 701.39 | |||

300 | 453.42 | 124.38 | 97.51 | - |

**Table 7.**Depth-Area relation of 24-h convergence component patterns based on annual maximum rainfalls, 100-, 200-, and 500-year rainfall quantiles.

Isohyets (mm) | Area (km^{2}) | ||||||
---|---|---|---|---|---|---|---|

Pattern of R_{0(am)} | Pattern of R_{0(100-yr)} | Pattern of R_{0(200-yr)} | Pattern of R_{0(500-yr)} | ||||

50 | 35,245.02 | 35,325.08 | 35,349.79 | 35,385.68 | |||

100 | 33,650.13 | 34,347.81 | 34,232.98 | 34,062.31 | |||

150 | 29,288.53 | 29,923.18 | 30,044.69 | 30,518.39 | |||

200 | 25,872.61 | 26,161.95 | 26,377.82 | 26,666.98 | |||

250 | 23,209.88 | 23,518.93 | 23,866.45 | 24,289.69 | |||

300 | 19,818.52 | 20,117.71 | 20,891.05 | 21,809.99 | |||

350 | 17,690.70 | 18,103.19 | 18,471.69 | 19,131.15 | |||

400 | 14,596.24 | 15,016.58 | 15,973.14 | 16,972.45 | |||

450 | 11,985.35 | 12,410.95 | 12,933.63 | 13,889.52 | |||

500 | 8661.74 | 8747.52 | 9278.78 | 10,006.27 | |||

550 | 6598.92 | 6668.70 | 7222.13 | 7950.74 | |||

600 | 3946.10 | 4204.51 | 4337.09 | 4511.36 | |||

650 | 2748.03 | 3064.23 | 3338.07 | 3569.35 | |||

700 | 1758.12 | 2059.28 | 2322.65 | 2704.62 | |||

750 | 912.99 | 1357.74 | 1614.58 | 1951.11 | |||

800 | 250.40 | 639.10 | 988.28 | 1351.21 | |||

850 | - | 96.63 | 305.79 | 811.66 | |||

900 | - | - | 7.69 | 236.72 |

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liao, Y.; Lin, B.; Chen, X.; Ding, H.
A New Look at Storm Separation Technique in Estimation of Probable Maximum Precipitation in Mountainous Areas. *Water* **2020**, *12*, 1177.
https://doi.org/10.3390/w12041177

**AMA Style**

Liao Y, Lin B, Chen X, Ding H.
A New Look at Storm Separation Technique in Estimation of Probable Maximum Precipitation in Mountainous Areas. *Water*. 2020; 12(4):1177.
https://doi.org/10.3390/w12041177

**Chicago/Turabian Style**

Liao, Yifan, Bingzhang Lin, Xiaoyang Chen, and Hui Ding.
2020. "A New Look at Storm Separation Technique in Estimation of Probable Maximum Precipitation in Mountainous Areas" *Water* 12, no. 4: 1177.
https://doi.org/10.3390/w12041177