# Grid-to-Point Deep-Learning Error Correction for the Surface Weather Forecasts of a Fine-Scale Numerical Weather Prediction System

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## Abstract

**:**

## 1. Introduction

## 2. Data and Method

#### 2.1. Data Description

_{2}), 2 m relative humidity ($R{H}_{2}$), and 10 m wind speed (${W}_{10}$), generated by PRUFS. With 24 forecast cycles each day, there is a total of 576 model samples (i.e., 24 × 24) per day.

#### 2.2. G2N Model

#### 2.3. Data Pre-Processing and Dataset Partitioning

#### 2.4. Model Evaluation Statistics

## 3. Results and Analysis

#### 3.1. Overall Test Results

#### 3.2. Forecast Lead Time and Daily Variation

#### 3.3. Spatial Distribution of the G2N Performances

## 4. Sensitivity Analysis of G2N to the Inputs and Learning Areas

#### 4.1. Impact of the PRUFS Forecast Input (G-Exp)

**This indicates that selecting the proper sizes of spatial structures/features is important for G2N.**If it is too small, the model will not be able to take in sufficient information on the spatial features of the PRUFS forecasts. On the other side, if the input domain size is too large, it may introduce unnecessary noises and/or information burdens that hinder the G2N training.

#### 4.2. Impact of the Sites for Multitask Learning(N-Exp)

**These results indicate that multistation learning for G2N with more stations is beneficial, not only reducing computing costs dramatically but also increasing the learning skills of the G2N model.**

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The 3 km horizontal resolution area of PRUFS and the distribution of the 311 automatic weather stations (black dots). The background color shows the height of the terrain, and the red star is the station “Jintan”, to be discussed in the later section.

**Figure 2.**Multisite (G2N, (

**a**)) and single-site (G2-One, (

**b**)) forecast error correction models for grid forecasting. (

**a**) Whole grid area as input for multisite correction of 311 sites. (

**b**) Different proportions of grid regions as input for single-point correction experiments.

**Figure 4.**Normalized frequency distributions of the PRUFS forecast errors and the G2N corrected forecast errors. The (

**a**) 2 m temperature, (

**b**) 2 m relative humidity, and (

**c**) 10 m wind speed, with error bins at 1 °C, 1%, and 0.5 m/s, respectively.

**Figure 5.**Density scatter plots of the forecast–observation pairs of the PRUFS forecasts (

**1st column**) and the G2N correction (

**2nd column**). The (

**a**,

**b**) 2 m temperature, (

**c**,

**d**) 2 m relative humidity, and (

**e**,

**f**) 10 m wind speed.

**Figure 6.**The variation of the RMSE of the PRUFS 0–24 h forecasts and the G2N correction for 2 m temperature (

**a**,

**b**), 2 m relative humidity (

**c**,

**d**), and 10 m wind speed (

**e**,

**f**) with forecast lead time (

**left panels**) and diurnal variation (

**right panels**); The horizontal coordinate of the left panels is the forecast lead time and that of the right panels is the local time.

**Figure 7.**The RMSE of the PRUFS forecasts (

**left panels**) and the G2N correction (

**middle panels**) and the corresponding G2N improvement percentages (

**right panels**, %) of 2 m temperature (

**a**–

**c**), 2 m relative humidity (

**d**–

**f**), and 10 m wind speed (

**g**–

**i**).

**Figure 8.**Horizontal distribution of the bias of the PRUFS forecasts (

**left panels**) and the G2N correction (

**right panels**) of 2 m temperature (

**a**,

**b**), 2 m relative humidity (

**c**,

**d**), and 10 m wind speed (

**e**,

**f**).

**Figure 9.**Horizontal distribution of the Pearson correlation coefficients concerning the observations of the PRUFS forecasts (

**left panels**) and the G2N correction (

**right panels**) of 2 m temperature (

**a**,

**b**), 2 m relative humidity (

**c**,

**d**), and 10 m wind speed (

**e**,

**f**).

**Figure 10.**Sub-domains containing 51 (

**a**), 101 (

**b**), and 199 (

**c**) station sites for N-exps. The red star is the station “Jintan”.

**Table 1.**The RMSE and improvement percentages (IP) (see Equation (6)) of the 2 m temperature, 2 m relative humidity, and 10 m wind speed 0–24 h forecasts corrected by G2N, averaged at all stations.

Element | Test Dataset | ||
---|---|---|---|

PRUFS | G2N | IP | |

2 m-T | 2.22 | 1.79 | 19.4% |

2 m-RH | 16.25 | 12.27 | 24.5% |

10 m-WD | 1.66 | 0.95 | 42.8% |

**Table 2.**RMSE of the 10 m wind speed of the PRUFS forecast and the correction by G2-One at Jintan and Nanjing for different input areas and the corresponding IP. The evaluation was done on all test datasets.

AreaRatios of Input Domain | PRUFS Forecasts (RMSE)-“Jintan” | G2-One Correction (RMSE)-“Jintan” | IP | PRUFS Forecasts (RMSE)-“Nanjing” | G2-One Correction (RMSE)-“Nanjing” | IP |
---|---|---|---|---|---|---|

1.0 (G2N331) | 1.47 | 0.89 | 39.5% | 1.36 | 0.97 | 28.7% |

1.0 | 1.48 | 0.98 | 33.8% | 1.37 | 1.05 | 23.4% |

0.9 | 1.48 | 0.96 | 35.1% | 1.37 | 1.04 | 24.1% |

0.8 | 1.48 | 0.96 | 35.1% | 1.37 | 1.02 | 25.5% |

0.7 | 1.48 | 0.90 | 39.2% | 1.37 | 0.98 | 28.5% |

0.6 | 1.48 | 0.97 | 34.5% | 1.37 | 1.01 | 26.3% |

0.5 | 1.48 | 0.97 | 34.5% | 1.37 | 1.01 | 26.3% |

0.4 | 1.48 | 0.98 | 33.8% | 1.37 | 1.02 | 25.5% |

0.3 | 1.48 | 0.98 | 33.8% | 1.37 | 1.02 | 25.5% |

(a) 2 m Temperature Statistics Results | |||||
---|---|---|---|---|---|

Verification | 51 | 101 | 199 | 311 | |

N-exps | |||||

G2N51 | 16.4% | ||||

G2N101 | 14.1% | 13.8% | |||

G2N199 | 19.8% | 19.8% | 21.8% | ||

G2N311 | 20.8% | 20.2% | 21.8% | 18.9% | |

(b) 2 m Relative Humidity Statistics Results | |||||

Verification | 51 | 101 | 199 | 311 | |

N-exps | |||||

G2N51 | 23.7% | ||||

G2N101 | 24% | 25.5% | |||

G2N199 | 25.7% | 27.5% | 24.6% | ||

G2N311 | 27.8% | 28.9% | 25.7% | 24.5% | |

(c) 10 m Wind Speed Statistics Results | |||||

Verification | 51 | 101 | 199 | 311 | |

N-exps | |||||

G2N51 | 44.5% | ||||

G2N101 | 46.5% | 43.4% | |||

G2N199 | 44.5% | 41.6% | 40.9% | ||

G2N311 | 47.4% | 44% | 43.9% | 42.8% |

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**MDPI and ACS Style**

Qin, Y.; Liu, Y.; Jiang, X.; Yang, L.; Xu, H.; Shi, Y.; Huo, Z.
Grid-to-Point Deep-Learning Error Correction for the Surface Weather Forecasts of a Fine-Scale Numerical Weather Prediction System. *Atmosphere* **2023**, *14*, 145.
https://doi.org/10.3390/atmos14010145

**AMA Style**

Qin Y, Liu Y, Jiang X, Yang L, Xu H, Shi Y, Huo Z.
Grid-to-Point Deep-Learning Error Correction for the Surface Weather Forecasts of a Fine-Scale Numerical Weather Prediction System. *Atmosphere*. 2023; 14(1):145.
https://doi.org/10.3390/atmos14010145

**Chicago/Turabian Style**

Qin, Yu, Yubao Liu, Xinyu Jiang, Li Yang, Haixiang Xu, Yueqin Shi, and Zhaoyang Huo.
2023. "Grid-to-Point Deep-Learning Error Correction for the Surface Weather Forecasts of a Fine-Scale Numerical Weather Prediction System" *Atmosphere* 14, no. 1: 145.
https://doi.org/10.3390/atmos14010145