Functional networks of weather events propagation between airports

López Martín, Raúl (supervisor: Massimiliano Zanin)
Master Thesis (2022)

Meteorology and climatology are fields of high relevance, not only from a purely scientific side, but also as they affect everyday life. For example, in aviation industry they play a key role, up to the point that flights can get delayed and cancelled, and airports can even stop operating temporarily due to the atmospheric conditions. Understanding the evolution and properties of the different meteorological variables is necessary to, for example in the last mentioned area, make air travel safer and minimize disruptions.

Historically, this problem has been addressed, first, by understanding from a physical point of view the laws that rule the associated phenomena and evolution of the meteorological variables; afterwards, when solid foundations on the latter were achieved, with mathematical models able to recreate the found physical laws. In this project, we are going to use a more novel, data-based approach known as functional networks. This methodology first uses a statistical tool to find spatial and temporal relations between a given meteorological variable measured at different spatial locations, for a set of variables. Next, a complex network representation (where nodes are the spatial locations and edges represent the relations) is used to present and analyse the results. Despite the recentness of this framework, it has already been shown to produce relevant results in a wide range of scientific works on the mentioned fields. In this project, leveraging on these results, two main modifications are introduced. First, the used data set is going to be less complete than the ones commonly used, as less than two hundred of unevenly spaced spatial locations, in an extension larger than the size of the European continent, are going to be used as the sources for the time series; opposed to the very high spatial resolution commonly used in other works, where they use full grids of evenly spaced spatial locations with a separation of few tens of kilometers.

The structure of this work is going to be the following. First, the data sets are going to be extracted from the sources which are METARs (acronym of METeorological Aerodrome Reports), which taking into account these reports come as strings of characters, this repre- sents a first challenge of translating the strings to numerical values that can be manipulated and analysed. Second, filtering, interpolation suitability, interpolation, and normalization processes are going to be executed on the data so time series of the desired variables can be reconstructed, and thus used by the statistical tool to find relations between them. The used statical tool is the Granger causality, which will allow us to find “forecasting causalities” between the same variable at different spatial locations. A causality of the aforementioned kind exists if additionally using past values of the variable at a given location help to better predict present ones at another, compared to only using past values of the variable to be predicted. Third, when these relations are found for the desired variables (in this project these are temperature, difference between temperature and dew point, which is related to humidity, and wind speed; all very relevant variables for air transport operations), complex networks are built and analysed.

The results are going to be extracted via three different procedures: calculating the different metrics associated to the topology of the outcome networks, dividing them according to their edges’ properties, which takes advantages of the extra characteristics that add to the network the nodes representing spatial locations and edges representing causalities; and comparing them with different null models (Erdös-Rényi and one that respects the edge prob- ability as a function of the distance between the nodes). From these results, first, hypotheses of the physical phenomena underlying the networks are proposed: the total networks and their structure are the result of both westerlies (wind jet streams that blow from west to east in the European continent) and the closeness between spatial locations generating propaga- tion of tendencies of meteorological variables; and second, through the mentioned results, a validation of the resilience of this methodology, when working with low spatial resolution and using complex network’s metrics to obtain meaningful results, is performed.

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