Compound Events over Poland : Probabilistic Perspective

The purpose of the present study is to quantify the compound events and persistent events (e.g.,  heat waves) from probability perspectives.  Notably, the compound events are quantified by a joint frequency distribution of the two variables that are used to identify those compound events. For example, the tendency of having simultaneously warm and dry (i.e., less rains) states on the same day can be identified in the joint distribution of temperature and precipitation.  If such a tendency exists, it is identified as a local peak in the joint distribution, located at positive temperature and negative precipitation anomalies. In this manner, we objectively demonstrate the tendency of compound warm-dry events over Poland in the summer season, which has been empirically known, but not clearly quantified. In winter the opposite is true and the precipitation distribution for high positive anomalies is clearly skewed in the direction of positive anomalies of temperature confirming higher precipitation on warmer days due to the atmosphere's greater capacity for water vapor.  

Joint distributions are not necessarily between two variables of the same day. A lag can be introduced, and in this manner, it can be demonstrated that the tendency of  warm days  over Poland are frequently followed by high precipitation few days after.  A simple lag correlation suggests that such an event is most likely to happen with 5-day lag. However, in this case, there is no shift of the peak to a positive side of precipitation anomaly, but the tendency is merely identified by a long tail towards the positive precipitation anomaly in joint distribution.

The persistent events are quantified by a conditional probability: for example, a persistence of a warm state can be quantified by the conditional probability of having the same warm state a day after when this warm event has happened.
For these demonstrations, daily mean temperatures and precipitation (1966- 2024) from 48 meteorological stations obtained from the Institute of Meteorology and Water Management, National Research Institute are used.

This research is funded by the National Science Center, Poland (NCN) (grant number 2023/51/B/ST10/01926)