# The Impact of Profiles Data Assimilation on an Ideal Tropical Cyclone Case

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. WRF-PDAF

#### 2.2. LESTKF

#### 2.3. Profile Observation Operators

## 3. Experimental Design

#### 3.1. Setup of the Twin Experiment

#### 3.2. Experimental Design for the Cost-Effective Balance

## 4. Results and Analysis

#### 4.1. Relationship between Localization Radii and Observation Densities

#### 4.2. The Most Cost-Effective Balance

^{2}) exceeding 0.99.

- The cost is defined as the deployment of observations. The cost function is defined as the linear relationship between the cost and density, i.e., $g\left(x\right)=x$. Thus, the total cost of fully deploying observations at 100% density is considered 100%, and no cost if no deployment (0 density).
- The benefit is defined as the property saved due to the reduction in the RMSE. Here, the total property can be saved is defined as a. The relationship between the property saved and the RMSE reduction in wind is linear [30,31]. The RMSE–density relationship follows Figure 4 and is denoted as r(x). Therefore, the relationship between the benefit and density is $f\left(x\right)=a-r\left(x\right)$, representing the benefit function. Thereby, when density is 100%, the benefit is a. Conversely, when density is 0, the benefit is 0.

## 5. Discussion and Conclusions

- Significance of Profile DA

- Influence of Observation Density and Localization Radius

- Practical Implications

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The RMSEs of U and V from 031200 to 070000 using different observation densities and localization radii (RMSE of U: m/s, RMSE of V: m/s).

**Figure 3.**The RMSEs of T, U, and V at 051400 using different localization radii (T: K, U: m/s, V: m/s).

Exp | Name | Member(s) | Profile Density (%) | Localization (km) | DA-Cycle (s) |
---|---|---|---|---|---|

1 | True | 1 | - | - | - |

2 | CTRL | 1 | - | - | - |

3 | ENS | 40 | - | - | - |

4 | D100L0 | 40 | 100 | 0dx | 30 |

5 | D100L3 | 40 | 100 | 3dx | 30 |

6 | D100L5 | 40 | 100 | 5dx | 30 |

7 | D100L10 | 40 | 100 | 10dx | 30 |

8 | D25L0 | 40 | 25 | 0dx | 30 |

9 | D25L3 | 40 | 25 | 3dx | 30 |

10 | D25L5 | 40 | 25 | 5dx | 30 |

11 | D25L10 | 40 | 25 | 10dx | 30 |

12 | D11L0 | 40 | 11.1 | 0dx | 30 |

13 | D11L5 | 40 | 11.1 | 5dx | 30 |

14 | D11L10 | 40 | 11.1 | 10dx | 30 |

15 | D11L20 | 40 | 11.1 | 20dx | 30 |

16 | D4L0 | 40 | 4 | 0dx | 30 |

17 | D4L5 | 40 | 4 | 5dx | 30 |

18 | D4L10 | 40 | 4 | 10dx | 30 |

19 | D4L20 | 40 | 4 | 20dx | 30 |

20 | D1L0 | 40 | 1 | 0dx | 30 |

21 | D1L5 | 40 | 1 | 5dx | 30 |

22 | D1L10 | 40 | 1 | 10dx | 30 |

23 | D1L20 | 40 | 1 | 20dx | 30 |

24 | D1L30 | 40 | 1 | 30dx | 30 |

**Table 2.**The RMSEs of T, U, and V for experiments in Table 1 at 051400.

**The numbers in bold represent the smallest values in each density group**.

Exp | Name | RMSE_T (K) | RMSE_U (m/s) | RMSE_V (m/s) |
---|---|---|---|---|

1 | True | - | - | - |

2 | CTRL | 1.112 | 1.929 | 2.063 |

3 | ENS | 0.939 | 1.799 | 1.910 |

4 | D100L0 | 0.185 | 0.294 | 0.294 |

5 | D100L3 | 0.145 | 0.233 | 0.234 |

6 | D100L5 | 0.148 | 0.229 | 0.230 |

7 | D100L10 | 0.251 | 0.337 | 0.337 |

8 | D25L0 | 0.430 | 0.553 | 0.567 |

9 | D25L3 | 0.249 | 0.361 | 0.389 |

10 | D25L5 | 0.239 | 0.339 | 0.361 |

11 | D25L10 | 0.273 | 0.361 | 0.371 |

12 | D11L0 | 0.583 | 0.790 | 0.811 |

13 | D11L3 | 0.310 | 0.418 | 0.450 |

14 | D11L5 | 0.285 | 0.393 | 0.418 |

15 | D11L10 | 0.300 | 0.396 | 0.409 |

16 | D4L0 | 0.765 | 1.21 | 1.26 |

17 | D4L5 | 0.381 | 0.468 | 0.501 |

18 | D4L10 | 0.353 | 0.454 | 0.471 |

19 | D4L20 | 0.405 | 0.513 | 0.522 |

20 | D1L0 | 0.895 | 1.617 | 1.709 |

21 | D1L5 | 0.673 | 0.710 | 0.727 |

22 | D1L10 | 0.566 | 0.580 | 0.611 |

23 | D1L20 | 0.481 | 0.563 | 0.579 |

24 | D1L30 | 0.486 | 0.666 | 0.677 |

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Shao, C.; Nerger, L.
The Impact of Profiles Data Assimilation on an Ideal Tropical Cyclone Case. *Remote Sens.* **2024**, *16*, 430.
https://doi.org/10.3390/rs16020430

**AMA Style**

Shao C, Nerger L.
The Impact of Profiles Data Assimilation on an Ideal Tropical Cyclone Case. *Remote Sensing*. 2024; 16(2):430.
https://doi.org/10.3390/rs16020430

**Chicago/Turabian Style**

Shao, Changliang, and Lars Nerger.
2024. "The Impact of Profiles Data Assimilation on an Ideal Tropical Cyclone Case" *Remote Sensing* 16, no. 2: 430.
https://doi.org/10.3390/rs16020430