# Estimation of Rainfall Associated with Typhoons over the Ocean Using TRMM/TMI and Numerical Models

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## Abstract

**:**

^{−1}, respectively. Furthermore, the correlation coefficient and root-mean-square error for convective rainfall were 0.78 and 7.25 mm·h

^{−1}, respectively, and those for stratiform rainfall were 0.58 and 9.60 mm·h

^{−1}, respectively. The main contribution of this study is introducing an approach to quickly and accurately estimate the typhoon precipitation, and remove the need for complex calculations.

## 1. Introduction

## 2. Theory

## 3. Methodology

#### 3.1. Physical Algorithm

#### 3.2. Establishing a Threshold for Rain

**Figure 5.**Histograms of the TB for the TMI in the absence of rain at 19 GHz: (

**a**) TB10V and (

**b**) TB10H.

**Figure 7.**Histograms of the TB for the TMI in the absence of rain at 37 GHz: (

**a**) TB10V and (

**b**) TB10H.

**Figure 8.**Histograms of the TB for the TMI in the absence of rain at 85 GHz: (

**a**) TB10V and (

**b**) TB10H.

Frequencies | Threshold (Mean) | Standard Deviation |
---|---|---|

10-V GHz | 175.78 K | 1.27 K |

10-H GHz | 93.78 K | 2.39 K |

19-V GHz | 218.77 K | 2.73 K |

19-H GHz | 163.46 K | 5.05 K |

21-V GHz | 248.21 K | 3.41 K |

37-V GHz | 228.09 K | 2.39 K |

37-H GHz | 175.74 K | 5.05 K |

85-V GHz | 276.17 K | 1.63 K |

85-H GHz | 260.77 K | 3.76 K |

#### 3.3. Prior PDF

^{−1}[39]. A total of 15,480 swaths and over 60 million observation data were obtained over the South China Sea and northwestern Pacific in the nine-year period. The number of RR data used in this study to construct the prior PDF was 3,115,544.

**Figure 9.**Rain rate distribution-PR (near nadir). Points marked by “+” represent the RRs near the nadir of the curve, and the solid line denotes the probability distribution.

#### 3.4. Conditional PDF

Number | Typhoon Nane | Typhoon Strength | Simulation Time (UTC) |
---|---|---|---|

1 | BOLAVEN | Strong | 2012/8/25 1800–2012/8/26 1800 |

2 | GUCHOL | Strong | 2012/6/17 0600–2012/6/17 0600 |

3 | NANMADOL | Strong | 2011/8/25 1800–2011/8/26 1800 |

4 | SONGDA | Strong | 2011/5/26 1200–2011/5/27 1200 |

5 | SINLAKU | Strong | 2008/9/12 0600–2008/9/13 0600 |

6 | PRAPIROON | Medium | 2012/10/11 1800–2012/10/12 1800 |

7 | JELAWAT | Medium | 2012/9/28 0000–2012/9/29 0000 |

8 | SANBA | Medium | 2012/9/14 1200–2012/9/15 1200 |

9 | HAIKUI | Medium | 2012/8/6 0000–2012/8/7 0000 |

10 | MUIFA | Medium | 2011/8/3 0600–2011/8/4 0600 |

11 | CHABA | Medium | 2010/10/27 1800–2010/10/28 1800 |

12 | MEGI | Medium | 2010/10/21 0000–2010/10/22 0000 |

13 | FANAPI | Medium | 2010/9/17 1200–2010/9/18 1200 |

14 | LUPIT | Medium | 2009/10/18 0000–2009/10/19 0000 |

15 | PARMA | Weak | 2009/10/4 0600–2009/10/5 0600 |

#### 3.5. Posterior PDF

## 4. Validation and Discussion

#### 4.1. Analysis of TB

No. | Typhoon Name | Scan Time (UTC) | The Range of Quantitative Analysis | Data Number | Correlation Coefficient | ||||
---|---|---|---|---|---|---|---|---|---|

North Latitude | East Longitude | ||||||||

1 | BOLAVEN | 2012/8/26 | 759 | 23 | 29 | 125 | 133 | 3437 | 0.74 |

2 | GUCHOL | 2012/6/17 | 1848 | 19.5 | 24 | 125 | 130 | 1846 | 0.87 |

3 | NANMADOL | 2011/8/26 | 842 | 15.5 | 19 | 122 | 126 | 1020 | 0.64 |

4 | SONGDA | 2011/5/27 | 609 | 17 | 22.5 | 121.5 | 126 | 1921 | 0.73 |

5 | SINLAKU | 2008/9/12 | 1912 | 22 | 26.5 | 121.5 | 125.5 | 1297 | 0.79 |

6 | PRAPIROON | 2012/10/12 | 709 | 17 | 23 | 126 | 132 | 3117 | 0.78 |

7 | JELAWAT | 2012/9/28 | 1508 | 23 | 28 | 123 | 128 | 1960 | 0.83 |

8 | SANBA | 2012/9/15 | 347 | 21.5 | 26 | 126 | 131 | 1840 | 0.8 |

9 | HAIKUI | 2012/8/6 | 1820 | 24 | 30 | 121.5 | 128 | 2589 | 0.7 |

10 | MUIFA | 2011/8/3 | 1841 | 21.5 | 27 | 128 | 134 | 2682 | 0.77 |

11 | CHABA | 2010/10/28 | 1016 | 23 | 28 | 127 | 131 | 1553 | 0.88 |

12 | MEGI | 2010/10/21 | 1330 | 21.5 | 27 | 128 | 134 | 2156 | 0.84 |

13 | FANAPI | 2010/9/18 | 620 | 21.5 | 25.5 | 123 | 128 | 1575 | 0.84 |

14 | LUPIT | 2009/10/18 | 1434 | 15 | 21 | 131 | 137 | 2307 | 0.82 |

15 | PARMA | 2009/10/4 | 2232 | 17 | 22 | 117 | 122 | 1691 | 0.72 |

#### Validation of TB Simulation

**Figure 11.**TB10V of Typhoon Nanmadol: (

**a**) TMI observation; (

**b**) Radiative Transfer for TIROS Operational Vertical Sounder (RTTOV) simulation; and (

**c**) histogram for the region within the dashed square in the preceding panels.

**Figure 12.**TB10H of Typhoon Nanmadol: (

**a**) TMI observation; (

**b**) RTTOV simulation; and (

**c**) histogram for the region within the dashed square in the preceding panels.

#### 4.2. Validation of RR Estimation

Number | Typhoon Name | Scan Time (UTC) | Orbital Number | Correlation Coefficient | RMSE |
---|---|---|---|---|---|

1 | MUIFA | 2011/08/03 1307 | 78127 | – | – |

2 | MUIFA | 2011/08/03 1940 | 78131 | 0.52 | 3.48 |

3 | MUIFA | 2011/08/04 1732 | 78146 | – | – |

4 | NANMADOL | 2011/08/29 0025 | 78524 | 0.78 | 2.67 |

5 | TEMBIN | 2012/08/23 0943 | 84141 | 0.7 | 4.63 |

6 | TEMBIN | 2012/08/26 0832 | 84187 | 0.58 | 4.27 |

7 | TEMBIN | 2012/08/27 0736 | 84202 | 0.54 | 2.36 |

8 | SANBA | 2012/09/12 0733 | 84451 | 0.44 | 6.05 |

9 | SANBA | 2012/09/14 0540 | 84481 | 0.66 | 5.97 |

10 | JELAWAT | 2012/09/28 1544 | 84706 | 0.72 | 6.14 |

#### Case Study

^{−1}) of the TMI-RR is greater than that of the PR-RR.

**Figure 13.**RR estimation for Typhoon Nanmadol: (

**a**) near-surface RR estimated by the PR (PR-RR); (

**b**) RR estimated using the Bayesian method and the TMI data (TMI-RR); and (

**c**) scatter plot of the PR-RR and TMI-RR.

^{−1}.

^{−1}, possibly because the heavy precipitation consists of individual short-range convective cells that average light precipitation in their vicinity. Finally, the maximum RR of the TMI-RR is smaller than that of the PR-RR, and the range of the second largest RR of the TMI-RR is greater than that of the PR-RR.

^{−1}. By comparing the TMI-RR and P-RR, the heavy rainfall locations are similar and match the locations of the PR-RR, and the intensity of P-RR is significantly lower than the PR-RR. The possible season for the low P-RR values less than 15 mm·h

^{−1}at high PR-RR above 25 mm·h

^{−1}is that the Figure 2 is not a production for typhoons near Taiwan. Therefore, the proposed method provides better results than the approach in directly estimating the rain rate from the attenuation index.

#### 4.3. Precipitation Type Analysis

^{−1}, and the corresponding rainfall of the TMI is less than 10 mm·h

^{−1}. The probability of heavy precipitation on a small scale is higher for convective precipitation. Regions A and B in Figure 13a,b are examples. The area which has the maximum RR is smaller than the FOV, and the RR of this area will be averaged. The PR-RR is averaged to the same horizontal resolution as the TMI. The maximum PR-RR can also be obtained by averaging it to the TMI resolution. The correlation coefficient between the TMI-RR and PR-RR is 0.78, and the root-mean-square error is 7.25 mm·h

^{−1}.

^{−1}, but the number of points of the PR-RR that reach 10–50 mm·h

^{−1}is considerably smaller. The TMI-RR data are mostly located on the left side of x = y, whereas the PR-RR values are less than 20 mm·h

^{−1}. The right side of x = y contains PR-RR values greater than 30 mm·h

^{−1}, implying that the TMI-RR values are overestimating when the PR-RR values are less than 20 mm·h

^{−1}. The TMI-RR values are underestimating when the PR-RR values are greater than 30 mm·h

^{−1}. Iguchi et al., (2000) [42] showed that there are differences in the coefficients in the reflectivity-rainfall rate relationship between different precipitation types as a result of larger raindrops in convective rain. Thus, an error in classification of convective actual type as stratiform type would lead to lower (by about 40%) estimated rainfall rate PR-RR than the actual value (and 2.5 times higher values for the opposite classification error). A possible reason for the high TMI-RR values above 20 mm·h

^{−1}at low PR-RR less than 10 mm·h

^{−1}values under stratiform rainfall is that they are errors in TRMM precipitation classification as the stratiform type while it is actually the convective type of rain, which leads to lower PR-RR values than actual RR. The correlation coefficient between the TMI-RR and the PR-RR is 0.58, and the root-mean-square error is 9.6 mm·h

^{−1}.

^{−1}is questionable because such high RR values do not occur in stratiform precipitation. However, if there is a TRMM classification error for these points, the results of the proposed method will underestimate even more significantly if they correspond to classification errors; second, the conditional PDF of Bayesian theory was constructed by considering 15 typhoons (heavy precipitation), and therefore, it is more suitable for heavy precipitation. In theory, high RR values are typical of convective precipitation. The most likely reason of the RR estimation error is that the physics in the models do not reproduce the typhoon environment well.

^{−1}are underestimated by TMI-RR, which could be explained partially by possible rainfall classification errors (actual stratiform rainfall classified as the convective type). The conclusion from Figure 15 is that stratiform rainfall (excluding possible bad classification points) is overestimated by the proposed method and convective rainfall is underestimated (including high convective PR-RR rainfall classified as stratiform from TRMM algorithms in Figure 15b).

## 5. Conclusions

^{−1}. Furthermore, the correlation coefficient of the convective RR is 0.78, and the root-mean-square error is 7.25 mm·h

^{−1}with a systematic underestimation of RR compared to PR. The correlation coefficient of the stratiform RR is 0.58, and the root-mean-square error is 9.6 mm·h

^{−1}with a systematic overestimation of RR compared to PR. The results show that the Bayesian method can be effective in estimating the RR associated with typhoons over the ocean.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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## Share and Cite

**MDPI and ACS Style**

Yeh, N.-C.; Liu, C.-C.; Chen, W.-J. Estimation of Rainfall Associated with Typhoons over the Ocean Using TRMM/TMI and Numerical Models. *Water* **2015**, *7*, 6017-6038.
https://doi.org/10.3390/w7116017

**AMA Style**

Yeh N-C, Liu C-C, Chen W-J. Estimation of Rainfall Associated with Typhoons over the Ocean Using TRMM/TMI and Numerical Models. *Water*. 2015; 7(11):6017-6038.
https://doi.org/10.3390/w7116017

**Chicago/Turabian Style**

Yeh, Nan-Ching, Chung-Chih Liu, and Wann-Jin Chen. 2015. "Estimation of Rainfall Associated with Typhoons over the Ocean Using TRMM/TMI and Numerical Models" *Water* 7, no. 11: 6017-6038.
https://doi.org/10.3390/w7116017