Statistics for Hasn’t it happened to you too: In a relaxed group, people are chatting pleasantly over an “aperitif”. The mention of “mathematics”, “physics” or even “stochastics” (probability theory) ends the conversation immediately or makes Statistics for the conversation partners break out in a cold sweat. At the very latest, “quantile”, “median” or “standard deviation” will have strangled any conversation… Unless you come across the loyal readers of our blog. Mathematics is actually quite simple. And admit it: who among you didn’t calculate their grade point average at school?
It is probably not impossible that…
You have certainly not missed it: the previously purely deterministic weather forecast (there will be this or that weather) is increasingly being replaced by probability terms such as “possible”, “probable”, “not impossible” etc. In graphics, for example, not only a (single) deterministic temperature value is given, but also an expected temperature range.
Weather and Probabilities
The weather above our heads follows a truly chaotic system, which weather models try to control using countless mathematical formulas.
Roughly simplified, a weather model works as follows: Using as much measurement data as possible (ground measurements, radio soundings, radar/satellite data, etc.), the initial state of the atmosphere is determined and the weather model is started with this data. The weather model then calculates the expected weather for the coming days. So far so good, we have a solution, i.e. a deterministic forecast.
Back to our chaotic weather: It is obvious that, despite all the philippines phone number library effort, the initial state of the weather can never be completely captured by measurements. Even when our weather model starts, there are uncertainties that “propagate” over the forecast time.
The uncertainties in weather forecasting are estimated using the ensemble method. The model is calculated several times, each time with slightly different initial conditions. Each model calculation provides a weather forecast, or more precisely a “member”. All “members” are then compared and assessed. This is where probability theory comes into play. We introduce the most important terms such as “mean”, “median”, and “quantile”.
definition of terms
Several times a day, the ECMWF IFS model produces 51 10-day forecasts, slightly changing the initial conditions. These 51 forecasts are called “members” as described above.
For any location, we will now look at the predicted 24-hour rainfall for a specific day. Let us now assume that the distribution of rainfall according to the different “members” looks like this (it is somewhat idealized for better understanding):
Example precipitation distribution of
Example precipitation distribution of the 51 “members”. Source: MeteoSwiss
We can see that the precipitation distribution is uniform and symmetrical around the maximum value of 26 mm, which is represented by “Member” No. 26.
To better illustrate the various statistical how to change wallpaper on android concepts, it is helpful to first arrange the values of the individual “members” in ascending order (this is called a “cumulative distribution function”), which leads to the following representation. We see that each value is shown twice and the maximum value (occurs only once, see the graph above) is 26 mm:
Cumulative precipitation distribution of agb directory the 51 “members”. Source: MeteoSwiss
Cumulative precipitation distribution of the 51 “members”. Source: MeteoSwiss
Based on the exemplary precipitation distribution of the 51 “members” we now come to the most important statistical terms:
The mean (or average) is the simplest term. It is calculated by adding the value of all members and then dividing it by the number of members. It is therefore a single value whose representativeness in relation to the whole can vary greatly (cf. standard deviation). In the distribution above, the mean is 13 mm and is represented by member number 26 (in red).