In this paper we have considered two meteorological factors as an object of our research: horizontal and vertical visibility. These meteorological factors are associated with "danger thresholds", going beyond these levels (in excess or decrease) is unacceptable or undesirable. The initial values of the horizontal and vertical visibility are assumed to be equal to the values presented in the weather forecast. The results of this development can be used to solve problems related to aviation forecasting, for example, when making a decision regarding a departure or landing of the aircraft.
Introduction In this paper we consider the weather report, which is transmitted in the form of reports METAR (Meteorological Aerodrome Report — aeronautical meteorological code for transmitting reports on the actual weather at the airport) or TAF (the weather at a certain time in the future (normally from several hours to days).
The forecast TAF can be represented in the form of one or more sections, each of which begins with one of the code words: NOSIG (No significant change) – this means that there are no major weather changes in the next 2 hours; BECMG (Becoming) - sustained significant changes of weather conditions are expected; TEMPO (Temporary) - temporary significant changes of weather conditions are expected.
The values of the studied meteorological factors are modeled based on the justification of the forecast (forecast errors and probability). We took into account not only the bulk of the weather forecast but also a group of stable and temporary changes in the forecast. The main objective of this work is to determine the probability of the value of meteorological factors to go beyond the "hazard threshold".
The solution to this problem has been found under the assumption that specific implementation of meteorological factors at the time of landing (or take off) is a continuous random variable with values on a usual quantitative scale, and it has a normal distribution and that the meteorological factors are independent variables. We will consider X(t) to be some meteorological factor provided in the actual weather report (METAR) or airport weather forecast (TAF). It is a continuous onedimensional value (a mark on a quantitative scale) by which we will consider parameters of meteorological factors: horizontal visibility (in meters) at approaching of the aircraft or the height of the lower threshold of the cloud (in meters) at the terminal aerodrome [1].
The value of meteorological factor X(t) can be provided in the main part of the
forecast (defined as ), and in the group of persistent changes (they are defined as
BECMG, FM), or in the group of temporal changes (defined as TEMPO), sometimes
indicating the probability of possible changes in 40% (PROB40 ) or 30% (PROB30).
The value of meteorological factors not included into the main part of the weather
forecast will be defined as .
"Maximum hazard threshold" is associated with these meteorological factors - the
value of going beyond it (the excess or decrease) is unacceptable or undesirable, the
value of this level of "maximum danger level" is defined by [2]-[
The basic assumption of this article is the following: the definite implementation of meteorological factor X (t) at the time of landing (or take off) is a continuous random variable with values in the usual quantitative scale.
Our main problem is to find probability of the event that the value X(t) value will overcome , defined as = { ( ) > } or = { ( ) < }.
We define as the probability of the weather conditions exceeding the safety threshold.
We will assume that:
─ distribution of possible ( ) implementations are Gaussian (normal) with
parameters and , [
Calculating Estimated Probability of Weather Conditions
Let us define ( ) as the horizontal visibility (which can be in a real situation) and
will be a random variable. The variable is defined in the TAF forecast
section. The variable of the horizontal visibility ( ) ∈ Ν( ; ) has a Gaussian
(normal) distribution (with mathematical expectation and variance 2). The
variance of ( ) is determined by the forecast provision and accuracy.
According to [
} = 0.8 Hence we can derive = 0.23 ∙ .
We obtain the probability of weather conditions exceeding the safety threshold in this situation (forecast visibility of more than 800 m): where Ф(∗) is the function of the standard Gaussian distribution. Geometric illustration of the formula (2) is given in Figure 1. If the value of the forecast visibility is less than 800 meters, then the error is equal to ±200 and taking into account the reliability of 80% of the forecast, the following is true: = { − 200 < ( ) < + 200} = 0.8 Herewith we will obtain = 156 .
Then the probability of a "dangerous" weather situation is equal to: (1) (2) (3) { ( ) <
is the value of cloud conditions provided by a forecast. Forecasted clouds height means that the error is 30% of the forecast if the forecast value lies from 300 to 3
, and the error is 30 m if the forecast value We will suppose the forecast is below 300 . Given the forecast accuracy of 70%, is more than 300 , then
is 30% for accuracy and defined as 1 and 2. Herein considered values are independent variables (as the accuracy and correctness of the forecast of each value are considered) although they are weather dependent. We will define the probability of the event as: ( ) = 1 − (1 − 1)(1 − 2) Taking into account weather conditions changes, TAF forecast may be an indicator of possible changes (BECMG, FM or TEMPO). If changes are not forecasted, then NOSIG indicator may emerge. In this event in TEMPO, the value should be obtained from the weather forecast.
The emergence of the event from TEMPO is used with the indication within period from 1 to 2 that is the mixture of two weather conditions at that time and in the place: one with characteristics of the main forecast, the other from the forecast of changes. The probability of encountering TEMPO weather at the time of aircraft arrival equals: 0 = { 0.4, 0.5, 0.3,
, (10) Accordingly, the probability of finding the weather conditions forecast indicated in the main forecast equals (1 − 0
) The BECMG forecast replaces the main forecast from time 2 when there is an improvement of weather conditions and from time 1 if there is deterioration in the weather conditions with the forecast reliability of 80%.
For example, let the visibility distance be (then the real visibility is a random ), whereas the visibility distance is in TEMPO forecast (i.e. the new forecasted visibility is a random value distributed with parameters = and 1 = ∙ = { ( ) < ).
} = Then the probability of a "dangerous" weather situation is equal to: = 0 ∙ Φ ( ∙ ( − 1)) + (1 − p0)Φ ( ∙ ( − 1)) (11) Depending on the values ,
we will select pre-adapted formulas (2) or For the vertical visibility weather conditions ( ) (i.e. the clouds height) formulas 1 (4). are similar: = { ( ) < } = 1 1. Federal aviation regulations “Preparation and flight operations in civil aviation of the Russian Federation”, 2009; 128; 95 p. [in Russian] 2. ICAO. Annex. 3 to the Chicago Convention on International Civil Aviation. Meteorological Service for International Air Navigation. Appendix B. Forecast accuracy desirable from an operational point of view, 2010; 17; 218 p. 3. Analysis of the impact of Reliability on the safety of flights by type of aircraft. М., 2009.
URL: http://www.flysafety.ru/files/razdel2.pdf (Reference date: 13.10.15). 4. Status of safety in civil aviation of the States Parties of the agreement on civil aviation and the use of airspace over a ten year period (1992-200). Report of the Interstate Aviation Committee. URL: http://www.mak.ru/russian/info/doclad_bp/1992-2001/doklad_za_19922001_godi.html (Reference date: 13.10.15).