# On the Predictability of Daily Rainfall during Rainy Season over the Huaihe River Basin

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## Abstract

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## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

^{2}, is one of the most densely inhabited areas in China. The HRB is a significant crop area in China due to its special climate, which is characterized by warm temperate climate in the northern part and subtropical climate in the southern part. Wheat and grain production accounts for about 50% and 20% of the country’s total, respectively. The rainy season plays an important role in crop planting in the HRB. It can be pointed out from Figure 2 that rainy-season precipitation (generally from May–September in the HRB) accounts for the largest part of the annual total precipitation [25]. Consequently, investigation and prediction of rainy-season precipitation are of central importance for this area.

#### 2.2. Data Description

## 3. Methods

#### 3.1. Determination of Rainy Season

_{i}is daily precipitation data for Julian day i in one year at one station in the HRB. ${\overline{x}}_{i1}$ and ${\overline{x}}_{i2}$ are averaged values of two subsamples before and after Julian day i, respectively. n is the length of each subsample.

#### 3.2. The Bayesian Homogeneous Markov Model

#### 3.3. Bayesian Nonhomogeneous Markov Model

## 4. Results and Discussion

#### 4.1. Identification of Hidden States and Spatial Precipitation Dependence

#### 4.2. Meteorological Patterns Associated with the Hidden States

#### 4.3. Bayesian-NHMM Calibration and Validation

#### 4.3.1. Selection of Potential Predictors for Bayesian-NHMM

_{s}larger than 0.3 and p-value smaller than 0.1, in order to guarantee that correlation between rainfall and climate indices is strong and that results are significant at the 0.1 significance level.

#### 4.3.2. Seasonality

#### 4.3.3. Interannual Variability

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Determination of rainy season by multi-scale moving t-test in 2016 for the Xuchang Station in the HRB. The red value on the left represents the largest t

_{r}value. The red value on the right represents the smallest t

_{r}value.

**Figure 4.**The Bayesian-hidden Markov model network. Dependencies are denoted by arrows, with time t, here in days, going from left to right. t = 1,2, …, T.

**Figure 5.**The Bayesian-NHMM network. Dependencies are denoted by arrows, with time t, here in days, going from left to right. t = 1,2, …, T. The observed values (R_(t,S), X_t, W_(t,S)) are shown in grey boxes. The unknown parameters (δ for the transition probabilities and θ for the emission distribution), and the hidden states (Z_t) are denoted as circles. Q_t in double circles is a set of matrices including the transition probabilities from the Markov property of hidden states and the exogenous variables X_t. 3.4. Bayesian estimation.

**Figure 7.**Daily rainfall amount for four selected states. The dots in the figure demonstrate not only the location of rainfall stations but also the magnitude of daily precipitation amount.

**Figure 8.**Rainfall occurrence probability for four selected states. The dots in the figure demonstrate not only the location of rainfall stations but also the magnitude of rainfall occurrence probability.

**Figure 10.**Seasonality of states averaged over 30 years and interannual variability of states for all stations.

**Figure 12.**Comparison between seasonal cycle of observed (blue) and simulated (red) rainfall amount averaged for all stations in the period of 1987–2016.

**Figure 13.**Comparison between interannual variability of observed (blue) and simulated (red) rainfall amount averaged for all stations during the period of 1987–2016.

**Figure 14.**Comparison between interannual variability of observed (blue) and simulated (red) wet days averaged for all stations during the period of 1987–2016.

No. | Name | Longitude (E) | Latitude (N) | Elevation (m) | Onset (Julian Day) | Retreat (Julian Day) | Rainy-Season Precipitation (mm) | Annual Precipitation (mm) |
---|---|---|---|---|---|---|---|---|

1 | XuChang | 113.5 | 34.0 | 66.8 | 131 | 271 | 534.0 | 712.2 |

2 | ZhuMaDian | 114.0 | 33.0 | 82.7 | 123 | 273 | 791.6 | 925.3 |

3 | XinYang | 114.0 | 32.1 | 114.5 | 114 | 262 | 853.8 | 1081.9 |

4 | KaiFeng | 114.2 | 34.5 | 73.7 | 126 | 277 | 656.4 | 620.7 |

5 | XiHua | 114.3 | 33.5 | 52.6 | 128 | 273 | 816.6 | 786.1 |

6 | ShangQiu | 115.4 | 34.3 | 50.1 | 130 | 264 | 579.7 | 721.4 |

7 | BuYang | 115.4 | 32.5 | 32.7 | 126 | 259 | 721.7 | 906.2 |

8 | GuShi | 115.4 | 32.1 | 42.9 | 122 | 250 | 696.5 | 1055.3 |

9 | HaoZhou | 115.5 | 33.5 | 37.7 | 131 | 258 | 617.1 | 794.5 |

10 | DangShan | 116.2 | 34.3 | 44.2 | 132 | 261 | 590.9 | 738.9 |

11 | HuoShan | 116.2 | 31.2 | 86.4 | 104 | 255 | 882.8 | 1382.3 |

12 | LiuAn | 116.3 | 31.4 | 74.1 | 107 | 259 | 888.1 | 1117.8 |

13 | ShouXian | 116.5 | 32.3 | 22.7 | 124 | 256 | 660.5 | 915.4 |

14 | SuZhou | 116.6 | 33.4 | 25.9 | 133 | 258 | 679.1 | 868.3 |

15 | XuZhou | 117.1 | 34.2 | 41.2 | 141 | 261 | 639.2 | 822.6 |

16 | BengBu | 117.2 | 32.6 | 21.9 | 116 | 249 | 732.7 | 967.8 |

17 | XinYuan | 118.1 | 36.1 | 305.1 | 132 | 261 | 585.0 | 709.0 |

18 | WeiFang | 119.1 | 36.5 | 22.2 | 139 | 257 | 517.1 | 1071.1 |

19 | GanYu | 119.1 | 34.5 | 5.3 | 134 | 263 | 740.5 | 925.8 |

20 | LongKou | 120.2 | 37.4 | 4.8 | 135 | 259 | 496.5 | 591.5 |

21 | SheYang | 120.2 | 33.5 | 2 | 131 | 261 | 695.1 | 985.8 |

Predictors | Lag | r_{s} | p-Value |
---|---|---|---|

IOD | 4 | 0.342 | 0.064 |

SNAO | 5 | 0.332 | 0.079 |

Niño 1–2 | 2 | −0.314 | 0.091 |

Niño 4 | 12 | 0.297 | 0.117 |

Niño 3.4 | 9 | 0.206 | 0.283 |

NAO | 10 | −0.191 | 0.322 |

Niño 3 | 8 | 0.149 | 0.440 |

PDO | 7 | −0.054 | 0.780 |

ID | Model | Predictors |
---|---|---|

1 | Bayesian-HMM | - |

2 | Bayesian-NHMM | IOD |

3 | Bayesian-NHMM | IOD + SNAO |

4 | Bayesian-NHMM | IOD + SNAO + Niño 1–2 |

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**MDPI and ACS Style**

Cao, Q.; Hao, Z.; Yuan, F.; Berndtsson, R.; Xu, S.; Gao, H.; Hao, J.
On the Predictability of Daily Rainfall during Rainy Season over the Huaihe River Basin. *Water* **2019**, *11*, 916.
https://doi.org/10.3390/w11050916

**AMA Style**

Cao Q, Hao Z, Yuan F, Berndtsson R, Xu S, Gao H, Hao J.
On the Predictability of Daily Rainfall during Rainy Season over the Huaihe River Basin. *Water*. 2019; 11(5):916.
https://doi.org/10.3390/w11050916

**Chicago/Turabian Style**

Cao, Qing, Zhenchun Hao, Feifei Yuan, Ronny Berndtsson, Shijie Xu, Huibin Gao, and Jie Hao.
2019. "On the Predictability of Daily Rainfall during Rainy Season over the Huaihe River Basin" *Water* 11, no. 5: 916.
https://doi.org/10.3390/w11050916