# Performance-Based Navigation Approach Procedures with Barometric Vertical Guidance: How to Select the Air Temperature for Approach Procedure Design

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Description

_{0}= −0.0065 °C/m = standard temperature lapse rate with pressure altitude in the first layer (sea level to tropopause) of the ISA

_{0}= 288.15 K standard temperature at sea level

#### 2.1. Effective VPA and Final Approach Surface (FAS) Relationship

#### 2.2. FAS and Obstacle Clearance Height (OCH) Relationship

- No obstacles penetrate the FAS, so OCH = HL
- There are some obstacles that penetrate the FAS, so OCH = Hobs + HL

#### 2.3. OCH and Cloud Ceiling

- If OCH > cloud ceiling, then the missed approach probability is very high.
- If OCH ≤ cloud ceiling, then the missed approach probability is low

## 3. Statistical Analysis of Airport Temperatures: Theoretical Background

- Obtaining the airport temperature database for the hours of operation over a period of at least 5 years, preferably the last 5 years [25];
- Checking that the sample size is relevant;
- Plotting the database histograms;
- Fitting the probability density function to each histogram;
- Obtaining representative low temperatures.

^{2}tests, z-tests, and some exact tests. By setting the effect size values to 0.1, a 99% confidence level (α = 0.01), and 80% power, the sample size should be at least 997, as shown in Figure 5.

^{2}values. This can be considered a good fit as the density function graphically matches the histogram (see Figure 6). In fact, other temperature studies have been carried out in which the extreme value model best fits the temperature data as compared to other models [31,32].

## 4. Statistical Analysis of Airport Temperatures: Application to Selected Airports

#### 4.1. Sample Size Verification

#### 4.2. Identification of Representative Low Temperatures at the Airport

## 5. Impact of Temperature Selection on the OCH: A Practical Case

## 6. Proposed Methodology for Selecting Airport Temperature

- Determine the cloud ceiling corresponding to the expected periods of use of the approach procedure with barometric vertical guidance.
- Calculate the value of the temperature which means that 95 or 99% will be above them. Two methods:
- If a probability density function is available which clearly fits the data with an appropriate p-value, it is recommended to use the temperatures of this fit.
- If this is not possible, the corresponding 95% and 99% percentiles can be used. (The percentile method is the simplest one and is equivalent for the purpose of this application)
- Identify the temperature which corresponds to the minimum historical temperature.

- FAS calculation using the representative temperatures identified in the previous step.
- Obstacle assessment for each FAS.
- OCH calculation for each FAS.
- Compare the OCH values obtained with the cloud ceiling for the period of interest. Select OCHs lower than the cloud ceiling.
- From the OCHs selected in the previous step, identify the temperature that represents the highest percentage value.

## 7. Conclusions

- The effective VPAs corresponding to each temperature (95 and 99%) are very similar. There is no significant operational difference in terms of effective VPA.
- As far as the OCH is concerned, there are significant differences. The same obstacle can mean big differences in the value of the OCH if one lower limit of temperature or another is considered. In this case, it is convenient to carry out a detailed study and choose the temperature that offers an OCH lower than the cloud ceiling. On the other hand, obstacles of the same height, located at small distances between them measured from the threshold, can also mean large differences in the OCH value.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Effective VPA vs. final approach surface (FAS). Where: ATT: along track tolerance; α

_{FAS}: final approach surface slope; Hi: tabulated value depending on the airport elevation.

**Figure 3.**Final approach surface (FAS) vs. obstacle clearance height (OCH). Where: Hobst: obstacle height above runway threshold (THR); HL: height lost. Margin to be added depending on the aircraft category: OCH: obstacle clearance height.

Distribution | KS “D” | A^{2} |
---|---|---|

Largest Extreme Value | 0.0318951 | 95.2365 |

Logistic | 0.0654753 | 284.022 |

Normal | 0.0510042 | 300.199 |

Laplace | 0.0800149 | 644.089 |

Smallest Extreme Value | 0.100732 | 998.674 |

Probability (%) | Largest Extreme Value T (°C) |
---|---|

95 | 1.66 |

99 | −1.36 |

Percentile (%) | T (°C) |
---|---|

95 | 1.8 |

99 | −1.9 |

Airport | Sample Size | Confidence Level | Power | Effect Size (d) |
---|---|---|---|---|

Germany—Berlin | 36,050 | 99% | 80% | 0.0180 |

Austria—Vienna | 85,925 | 99% | 80% | 0.0117 |

Belgium—Brussels | 43,547 | 99% | 80% | 0.0164 |

Spain—Madrid | 84,469 | 99% | 80% | 0.0118 |

France—Paris | 83,105 | 99% | 80% | 0.0119 |

Greece—Athens | 84,018 | 99% | 80% | 0.0118 |

The Netherlands—Amsterdam | 43,804 | 99% | 80% | 0.0163 |

United Kingdom—London | 86,082 | 99% | 80% | 0.0116 |

Airport | Prob. Function | Statistic Parameter 1 | Statistic Parameter 2 | T (°C) (95%) | T (°C) (99%) | Min T ^{3} (°C) | Prob. (>) Min T |
---|---|---|---|---|---|---|---|

Germany— Berlin | Largest Extreme Value | Loc ^{1} = 7.22449 | Scale = 7.47762 | −0.98 | −4.20 | −12.8 | 100.00% |

Austria— Vienna | Normal | Mean = 11.6383 | StDev ^{2} = 8.84278 | −2.91 | −8.93 | −16 | 99.91% |

Belgium— Brussels | Normal | Mean = 11.3733 | StDev = 6.92934 | −0.02 | −4.75 | −9.7 | 99.88% |

Spain— Madrid | Largest Extreme Value | Loc = 10.9917 | Scale = 8.08852 | 1.66 | −1.36 | −5.7 | 99.97% |

France— Paris | Largest Extreme Value | Loc = 12.2801 | Scale = 7.22265 | 0.40 | −4.52 | −8 | 99.75% |

Greece— Athens | Normal | Mean = 18.8677 | StDev = 8.10409 | 5.54 | 0.01 | −3 | 99.65% |

The Netherlands— Amsterdam | Normal | Mean = 11.3334 | StDev = 6.53509 | 0.58 | −3.87 | −8.6 | 99.89% |

United Kingdom—London | Largest Extreme Value | Loc = 8.95401 | Scale = 5.66213 | 2.74 | 0.07 | −6 | 99.99% |

^{1}Location;

^{2}standard deviation;

^{3}minimum historical temperature (2016–2020).

Airport | T (°C) (95%) | Effective VPA (°) | T (°C) (99%) | Effective VPA (°) | Min T (°C) | Effective VPA (°) |
---|---|---|---|---|---|---|

Germany— Berlin | −0.98 | 2.8 | −4.20 | 2.8 | −12.8 | 2.7 |

Austria— Vienna | −2.91 | 2.8 | −8.93 | 2.8 | −16 | 2.7 |

Belgium— Brussels | −0.02 | 2.8 | −4.75 | 2.8 | −9.7 | 2.7 |

Spain— Madrid | 1.66 | 2.9 | −1.36 | 2.9 | −5.7 | 2.8 |

France— Paris | 0.40 | 2.9 | −4.52 | 2.8 | −8 | 2.8 |

Greece— Athens | 5.54 | 2.9 | 0.01 | 2.8 | −3 | 2.8 |

The Netherlands— Amsterdam | 0.58 | 2.8 | −3.87 | 2.8 | −8.6 | 2.7 |

United Kingdom—London | 2.74 | 2.9 | 0.07 | 2.8 | −6 | 2.8 |

Airport | T (°C) (95%) | Effective VPA (°) | T (°C) (99%) | Effective VPA (°) |
---|---|---|---|---|

Germany— Berlin | −0.7 | 2.8 | −5.5 | 2.8 |

Austria— Vienna | −2 | 2.8 | −6 | 2.8 |

Belgium— Brussels | 0.7 | 2.8 | −2.4 | 2.8 |

Spain— Madrid | 1.8 | 2.9 | −1.9 | 2.8 |

France— Paris | 1 | 2.8 | −2 | 2.8 |

Greece— Athens | 6 | 2.9 | 3 | 2.9 |

The Netherlands— Amsterdam | 1.1 | 2.8 | −2.2 | 2.8 |

United Kingdom—London | 2 | 2.9 | −1 | 2.8 |

Representative Temperature | FAS Height (ft) at X NM from THR | |||
---|---|---|---|---|

2 NM | 3 NM | 4 NM | 5 NM | |

95% | 349.1 | 654.8 | 960.5 | 1266.3 |

99% | 344.6 | 646.3 | 948.0 | 1249.7 |

Minimum historical temperature | 337.5 | 633.1 | 928.7 | 1224.2 |

Aircraft Category (V_{at}) | Margin Using Radio Altimeter ^{1} (Meters) | Margin Using Radio Altimeter ^{1} (Feet) | Margin Using Barometric Altimeter (Meters) | Margin Using Barometric Altimeter (Feet) |
---|---|---|---|---|

A—169 km/h (90 kt) | 13 | 42 | 40 | 130 |

B—223 km/h (120 kt) | 18 | 59 | 43 | 142 |

C—260 km/h (140 kt) | 22 | 71 | 46 | 150 |

D—306 km/h (90 kt) | 26 | 85 | 49 | 161 |

^{1}The radio altimeter margins are reproduced for the corrections to the steep angles and high airports only and not for the derivation of the OCH.

Obstacle Height (ft.) | OCH (ft.) CAT D (Position 2 NM from THR) | ||
---|---|---|---|

95% T | 99% T | Min T | |

350 | 511 | 511 | 511 |

345 | 161 | 506 | 506 |

340 | 161 | 161 | 501 |

335 | 161 | 161 | 496 |

330 | 161 | 161 | 161 |

Distance from the Obstacle to the THR (m) | OCH (ft.) CAT D (Obstacle Height 340 ft) | ||
---|---|---|---|

95% T | 99% T | Min T | |

3620 | 501 | 501 | 501 |

3649 | 161 | 501 | 501 |

3676 | 161 | 161 | 501 |

3706 | 161 | 161 | 501 |

3735 | 161 | 161 | 161 |

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**MDPI and ACS Style**

Pérez Sanz, L.; Martínez García-Gasco, C.; Pérez Maroto, M.; Pérez-Castán, J.A.; Serrano-Mira, L.; Gómez Comendador, V.F. Performance-Based Navigation Approach Procedures with Barometric Vertical Guidance: How to Select the Air Temperature for Approach Procedure Design. *Aerospace* **2023**, *10*, 337.
https://doi.org/10.3390/aerospace10040337

**AMA Style**

Pérez Sanz L, Martínez García-Gasco C, Pérez Maroto M, Pérez-Castán JA, Serrano-Mira L, Gómez Comendador VF. Performance-Based Navigation Approach Procedures with Barometric Vertical Guidance: How to Select the Air Temperature for Approach Procedure Design. *Aerospace*. 2023; 10(4):337.
https://doi.org/10.3390/aerospace10040337

**Chicago/Turabian Style**

Pérez Sanz, Luis, Carmen Martínez García-Gasco, Marta Pérez Maroto, Javier A. Pérez-Castán, Lidia Serrano-Mira, and Víctor Fernando Gómez Comendador. 2023. "Performance-Based Navigation Approach Procedures with Barometric Vertical Guidance: How to Select the Air Temperature for Approach Procedure Design" *Aerospace* 10, no. 4: 337.
https://doi.org/10.3390/aerospace10040337