# Development of Daily and Extreme Temperature Estimation Model for Building Structures Based on Raw Meteorological Data

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Hourly Meteorological Data Analysis Based on Cubic Spline Function Method (FFT)

#### 2.1. Selection of Original Meteorological Data and Spline Function Method

#### 2.2. The Principle and Implementation of Cubic Spline Function FFT Method

#### 2.2.1. The Principle of Cubic Spline Function

#### 2.2.2. Realization of Cubic Spline Function

- (1)
- Assuming n interpolation nodes as input, and a = x
_{1}< x_{2}<$\cdot \cdot \cdot $< x_{n}= b. The corresponding function values are f_{1,}f_{2,}$\cdot \cdot \cdot $, f_{n}, the boundary condition is f_{0}, f_{n}, the desired value is x_{0}. - (2)
- Calculating h
_{j}= x_{j}_{+1}− x_{j}(j = 1, 2,$\cdot \cdot \cdot $, n − 1). - (3)
- Calculating μ
_{i}, λ_{i}, d_{i}. - (4)
- Calculating μ
_{n}, λ_{0}, d_{0}, d_{n} - (5)
- Solving Equation (7) or Equation (10) by using the chasing method.
- (6)
- Outputting the expression of the cubic polynomial in each interval.
- (7)
- Using the Hanning window FFT algorithm to optimize the cubic spline curve.
- (8)
- Confirming the closed interval [x
_{j,}x_{j+1}] of x_{0}, and calculatng the interpolation s(x_{0}).

#### 2.3. Hourly Temperature Analysis

## 3. Establishment of Standard Daily Meteorological Model

#### 3.1. Standard Daily Meteorological Model

^{2}are:

#### 3.2. Extreme Daily Meteorological Model

#### 3.3. The Analysis of Daily Temperature Difference

#### 3.3.1. The Analytical C:\Users\usuario\Users\Jerry\AppData\Local\youdao\DictBeta\Application\7.2.0.0703\resultui\dict\?keyword=Method of Daily Temperature Difference

_{1}, C

_{2}can be valued according to the Table E.3.2 in the Load code for the design of building structures GB50009-2012 [13].

#### 3.3.2. The Analysis of Daily Temperature Differences in Different Recurrence Intervals in Different Months

## 4. The Establishment of Meteorological Model of Standard Year for Buildings

#### 4.1. The Temperature Meteorological Model of Standard Year

#### 4.2. Annual Temperature Analysis

## 5. Conclusions

- (1)
- As the daily temperature difference follows the extreme value type I distribution, the daily temperature differences with different recurrence intervals or in extreme weather were obtained by statistical analysis. The results from this paper can contribute to refine the Load code
- (2)
- Code for the design of building structures.
- (3)
- The temperature meteorological model of a standard year reacts to the change in regulation of the annual temperature distribution and offers parameters for the analysis of annual temperature effect.
- (4)
- The annual temperature difference calculated with the method offered by this paper is close to the value offered by the standard. This means the analytical C:\Users\usuario\Users\Jerry\AppData\Local\youdao\DictBeta\Application\7.2.0.0703\resultui\dict\?keyword=method offered by this paper is reasonable. Moreover, the calculated annual temperature difference with different recurrence interval sand in extreme weather can be used for the analysis of building structures in different recurrence intervals or in extreme weather.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Temperature meteorological model of particular day of disastrous weather in July in Beijing.

**Figure 6.**Temperature meteorological model of particular day of disastrous weather in January in Beijing.

Month | Hours | Mean Value | Variance | Standard Deviation | 50 Year Return Value | Extreme Weather Value | Month | Hours | Mean Value | Variance | Standard Deviation | 50 year Return Value | Extreme Weather Value |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

July | 1 | 25.54 | 3.38 | 1.84 | 29.33 | 29.83 | January | 1 | −5.28 | 9.18 | 3.03 | −11.52 | −12.34 |

2 | 24.90 | 3.65 | 1.91 | 28.84 | 29.35 | 2 | −5.62 | 9.03 | 3.00 | −11.81 | −12.62 | ||

3 | 24.14 | 4.28 | 2.07 | 28.40 | 28.96 | 3 | −6.11 | 9.20 | 3.03 | −12.36 | −13.18 | ||

4 | 23.72 | 4.79 | 2.19 | 28.23 | 28.82 | 4 | −6.70 | 9.56 | 3.09 | −13.07 | −13.90 | ||

5 | 23.86 | 4.44 | 2.11 | 28.21 | 28.77 | 5 | −7.27 | 10.14 | 3.18 | −13.83 | −14.69 | ||

6 | 24.31 | 3.91 | 1.98 | 28.38 | 28.91 | 6 | −7.71 | 10.78 | 3.28 | −14.47 | −15.36 | ||

7 | 24.97 | 3.77 | 1.94 | 28.97 | 29.50 | 7 | −7.89 | 11.20 | 3.35 | −14.79 | −15.69 | ||

8 | 25.78 | 4.15 | 2.04 | 29.98 | 30.53 | 8 | −6.87 | 11.85 | 3.44 | −13.96 | −14.89 | ||

9 | 26.65 | 4.85 | 2.20 | 31.19 | 31.79 | 9 | −5.41 | 13.91 | 3.73 | −13.09 | −14.09 | ||

10 | 27.54 | 5.79 | 2.41 | 32.50 | 33.15 | 10 | −4.06 | 15.14 | 3.89 | −12.07 | −13.12 | ||

11 | 28.43 | 6.86 | 2.62 | 33.83 | 34.53 | 11 | −2.83 | 15.78 | 3.97 | −11.01 | −12.09 | ||

12 | 29.28 | 7.73 | 2.78 | 35.01 | 35.76 | 12 | −1.74 | 16.69 | 4.09 | −10.16 | −11.26 | ||

13 | 30.07 | 8.12 | 2.85 | 35.94 | 36.71 | 13 | −0.82 | 17.87 | 4.23 | −9.53 | −10.67 | ||

14 | 30.73 | 8.21 | 2.86 | 36.63 | 37.40 | 14 | −0.12 | 18.51 | 4.30 | −8.98 | −10.14 | ||

15 | 31.17 | 8.69 | 2.95 | 37.25 | 38.04 | 15 | 0.22 | 18.48 | 4.30 | −8.64 | −9.80 | ||

16 | 31.00 | 8.61 | 2.93 | 37.05 | 37.84 | 16 | −0.09 | 16.87 | 4.11 | −8.55 | −9.66 | ||

17 | 30.43 | 8.22 | 2.87 | 36.34 | 37.11 | 17 | −0.78 | 14.71 | 3.84 | −8.68 | −9.71 | ||

18 | 29.62 | 7.30 | 2.70 | 35.19 | 35.92 | 18 | −1.66 | 12.49 | 3.53 | −8.94 | −9.90 | ||

19 | 28.74 | 6.14 | 2.48 | 33.85 | 34.52 | 19 | −2.59 | 10.66 | 3.26 | −9.32 | −10.20 | ||

20 | 27.96 | 5.14 | 2.27 | 32.63 | 33.25 | 20 | −3.39 | 9.72 | 3.12 | −9.81 | −10.66 | ||

21 | 27.39 | 4.55 | 2.13 | 31.78 | 32.36 | 21 | −3.96 | 10.01 | 3.16 | −10.48 | −11.33 | ||

22 | 26.95 | 4.09 | 2.02 | 31.12 | 31.66 | 22 | −4.39 | 10.49 | 3.24 | −11.06 | −11.94 | ||

23 | 26.60 | 3.73 | 1.93 | 30.58 | 31.10 | 23 | −4.75 | 10.50 | 3.24 | −11.42 | −12.30 | ||

24 | 26.25 | 3.61 | 1.90 | 30.16 | 30.67 | 24 | −5.05 | 9.89 | 3.15 | −11.53 | −12.38 |

Month | Mean Value | Standard C:\Users\usuario\Users\Jerry\AppData\Local\youdao\DictBeta\Application\7.2.0.0703\resultui\dict\?keyword=Deviation | The Daily Temperature Difference with 10 Years Recurrence Interval | The Daily Temperature Difference with 20 Years Recurrence Interval | The Daily Temperature Difference with 50 Years Recurrence Interval | The Daily Temperature Difference in Extreme Weather |
---|---|---|---|---|---|---|

January | 9.2 | 3.6724 | 14.8 | 17.2 | 20.3 | 22.6 |

February | 11.8 | 2.5364 | 15.7 | 17.4 | 19.5 | 21.1 |

March | 11.8 | 4.2237 | 18.3 | 21.0 | 24.6 | 27.2 |

April | 13.0 | 4.1063 | 19.3 | 22.0 | 25.4 | 28.0 |

May | 12.6 | 4.5861 | 19.6 | 22.6 | 26.4 | 29.3 |

June | 13.0 | 3.6358 | 18.6 | 20.9 | 23.9 | 26.2 |

July | 8.3 | 2.6888 | 12.4 | 14.2 | 16.4 | 18.1 |

August | 9.4 | 1.9732 | 12.4 | 13.7 | 15.4 | 16.6 |

September | 13.3 | 3.9548 | 19.3 | 21.9 | 25.2 | 27.7 |

October | 11.5 | 4.0917 | 17.7 | 20.4 | 23.8 | 26.4 |

November | 11.7 | 3.3483 | 16.8 | 19.0 | 21.8 | 23.9 |

December | 10.5 | 3.3849 | 15.7 | 17.9 | 20.7 | 22.9 |

Month | Mean Value | The Reference Temperature with 10 years Recurrence Interval | The Annual Temperature Difference with 10 years Recurrence Interval | The Reference Temperature with 50 years Recurrence Interval | The Annual Temperature Difference with 50 years Recurrence Interval | The Reference Temperature Offered by the Standard | The Annual Temperature Difference Offered by the Standard | The Reference Temperature in Extreme Weather (100 years) | The Annual Temperature Difference in Extreme Weather (100 years) | |
---|---|---|---|---|---|---|---|---|---|---|

January | maximum | 0.7 | 7.1 | 47.3 | 13.3 | 52.2 | — | 49.0 | 15.9 | 54.1 |

minimum | −8.5 | −11.8 | −13.1 | −13.0 | −13.5 | |||||

July | maximum | 31.7 | 35.5 | 39.1 | 36.0 | 40.6 | ||||

minimum | 23.4 | 21.1 | 20.3 | — | 20.0 |

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**MDPI and ACS Style**

Yang, J.; Yang, Y.; Zou, J.; Yang, W.
Development of Daily and Extreme Temperature Estimation Model for Building Structures Based on Raw Meteorological Data. *Appl. Sci.* **2022**, *12*, 11582.
https://doi.org/10.3390/app122211582

**AMA Style**

Yang J, Yang Y, Zou J, Yang W.
Development of Daily and Extreme Temperature Estimation Model for Building Structures Based on Raw Meteorological Data. *Applied Sciences*. 2022; 12(22):11582.
https://doi.org/10.3390/app122211582

**Chicago/Turabian Style**

Yang, Jianyu, Yongda Yang, Jiaming Zou, and Weijun Yang.
2022. "Development of Daily and Extreme Temperature Estimation Model for Building Structures Based on Raw Meteorological Data" *Applied Sciences* 12, no. 22: 11582.
https://doi.org/10.3390/app122211582