Importance of Weather Conditions in a Flight Corridor
Abstract
:1. Introduction
2. Data
2.1. Data Sources
2.2. Data Description
3. Interpolation Methods
3.1. Linear Interpolation
3.2. Kriging
3.2.1. Estimation of Kriging Weights
3.2.2. Trend
3.2.3. Scaling Factor and Function
3.3. Feedforward Neural Networks
3.4. Decision Tree
3.5. Comparison of Methods
4. Monte Carlo Simulation
- We regard the data collected by the releasing balloons as the accurate weather data and compare the interpolation results by the Ordinary Kriging with GFS data as input. The errors are defined as the difference between the balloon data and the interpolated values by Ordinary Kriging with the GFS inputs . For ,
- Quantify and investigate the dependency among the errors , , and ;
- Select bivariate copulas such that
- Generate uniform pseudo-noise based on the selected copula model;
- Generate random errors with . In this step, instead of using empirical distribution function, the kernel smoothed one is used in order to avoid purely bootstrapped observations;
- Generate weather scenarios with GFS data and errors where weather data at each location of GFS grid has the simulated error added,
- Calculate the trajectories with Ordinary Kriging interpolations and simulated weather scenarios,
4.1. Dependency
4.2. Modelling the Dependency
4.3. Empirical Margins and Random Number Generator
4.4. Trajectory Simulation Results
5. Conclusions
- the kernel method works better than machine learning methods for the meteorological data interpolation for a flight trajectory;
- even though errors in GFS data and Ordinary Kriging are inevitable, the inaccuracy of the data has a very minor impact on the trajectory, total fuel burn, and flight time.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. A Trajectory from Nantes to Athens
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Model Size | Units | Activation | cv-MSE 1 | |||
---|---|---|---|---|---|---|
Temperature (K2) | Wind Speed () | Relative Humidity (%2) | ||||
Hidden layers | Small | 50 | tanh | 652.70 | 78.07 | 599.68 |
Medium | 300 | tanh | 652.80 | 33.54 | 582.77 | |
50 | tanh | |||||
Large | 400 | tanh | 17.05 | 34.83 | 581.41 | |
100 | tanh | |||||
50 | linear | |||||
Huge | 500 | tanh | 7.16 | 33.16 | 424.28 | |
300 | tanh | |||||
100 | tanh | |||||
50 | linear |
α | 0 | 0.001 | 0.01 | 0.1 | 1 | 10 | 100 | 1000 |
---|---|---|---|---|---|---|---|---|
Temperature (K) | 9.84 | 6.03 | 7.28 | 11.07 | 18.59 | 9.50 | 29.46 | 536.56 |
Wind speed () | 38.84 | 39.36 | 39.58 | 40.50 | 39.06 | 41.16 | 77.55 | 77.69 |
Relative humidity (%) | 593.05 | 585.94 | 559.01 | 536.48 | 481.06 | 600.70 | 654.94 | 652.03 |
Methods | loo-MSE | ||
---|---|---|---|
Temperature (K2) | Wind Speed () | Relative Humidity (%2) | |
Ordinary Kriging | 11.79 | 3.53 | 69.10 |
the RBF method | 0.42 | 1.93 | 85.73 |
Neural Network | 13.05 | 47.33 | 678.50 |
Bagging | 15.04 | 16.15 | 153.29 |
GBM | 2.39 | 13.34 | 179.21 |
Linear Interpolation | 9.31 | 13.01 | 178.11 |
Temperature (K) | U-wind (m/s) | 0.12 | 0.19 | 0.08 | 0.08 (positive) |
Temperature (K) | V-wind (m/s) | −0.19 | 0.04 | −0.12 | 0.02 (negative) |
U-wind (m/s) | V-wind (m/s) | −0.13 | 0.16 | −0.10 | 0.06 (negative) |
Family | |||
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Gumbel | |||
Clayton | |||
Frank | |||
Joe |
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Chen, G.; Fricke, H.; Okhrin, O.; Rosenow, J. Importance of Weather Conditions in a Flight Corridor. Stats 2022, 5, 312-338. https://doi.org/10.3390/stats5010018
Chen G, Fricke H, Okhrin O, Rosenow J. Importance of Weather Conditions in a Flight Corridor. Stats. 2022; 5(1):312-338. https://doi.org/10.3390/stats5010018
Chicago/Turabian StyleChen, Gong, Hartmut Fricke, Ostap Okhrin, and Judith Rosenow. 2022. "Importance of Weather Conditions in a Flight Corridor" Stats 5, no. 1: 312-338. https://doi.org/10.3390/stats5010018
APA StyleChen, G., Fricke, H., Okhrin, O., & Rosenow, J. (2022). Importance of Weather Conditions in a Flight Corridor. Stats, 5(1), 312-338. https://doi.org/10.3390/stats5010018