Probability and Statistics in weather forecasting

                                                            

 We have all had days when we wished we could just accurately predict the weather, may it be for our dinner dates or even a long vacation. But alas, nature isn't that predictable. It is complex to predict how the weather will behave in the coming hours, days, weeks and months. The only one thing we can do to get the best and closest results is to calculate the probabilities of the prevalence of particular weather conditions. But the question is how? Lets understand the process-

We begin with gathering the observations from all around the world and then use these observations to set up a computer simulation of the atmosphere which represents what is happening in the world right now. The model that is developed predicts/ calculates how the atmosphere will evolve over the coming days. Unfortunately, there can be a presence of uncertainties in the forecast. 

Thus, many companies have developed sophisticated techniques that can understand these uncertainties, called ensemble forecasts. What is an ensemble forecast you ask, well, in the simplest words it just means the simulation is run multiple times instead of just once. The range of the different outcomes obtained gives us a measure of how confident or uncertain we should be in the overall forecast. 

Another way is doing a probability forecast which includes a numerical expression of uncertainty about the quantity or event being forecast. Even though much progress has been made in developing methods to create probabilistic forecasts, currently only a small fraction of the elements of weather, hydrologic, and climate forecasts are expressed probabilistically.

various concepts of probability forecasting include frequentist, subjective , climatological and conditional. Frequentist is the concept which reflects the relative frequency of occurrence of a weather event in past circumstances analogous to the situation being addressed. Subjective forecast reflects the degree of certainty a forecaster has that a weather event will occur or not. The Climatology method is a simple way of producing a forecast. It involves averaging weather statistics accumulated over many years to make the forecast. The modified version of climatologist probability which is formulated by focusing on the relative frequency with which a particular weather is associated with a given set of conditions.

One highly desirable property of any probability forecast is that it must be “reliable” or “well-calibrated”. But, to clearly interpret and communicate the results effectively, the definition of the event being forecasted must be clearly understood. 

Now, let's look at the statistical methods for predicting weather. These methods play a vital role because the atmosphere is a nonlinear dynamical system, and is not perfectly predictable in a deterministic sense. The classical statistical forecast methods do not operate into the fluid-dynamical NWP models but still are very useful at short lead times (hours in advance), or even in long lead times (weeks or more). The simplest method is Multiple Linear Regression where more than 1 predictor (independent) variable is needed in practical forecasts. Here, the regression procedure chooses the line that produces the least error for predictions of u based on x which is calculated by SPSS (Statistical Package for the Social Sciences) software. Later, various goodness of fit tests are performed. Finally, a resampling technique is carried out which is known as cross-validation where the available data is repeatedly divided into developmental and verification data subsets. 

Another method in statistical forecasting involves Analog Forecasting. This method is slightly more complicated, it involves examining today’s forecast scenario and remembering a day in the past when the weather scenario looked very similar. So, how is statistics involved here? Statistics can be used to search for analogs and rank historical cases for closeness to current and then take average outcomes of all the good analogs. 

In summary, weather forecasts are increasing in accuracy and are very useful, their benefits extend widely across the economy. The forecasting community is working to ensure that forecasts and warnings meet their specific needs and are also developing new technologies that can enhance the forecasting skills and can add value to the users of their services.

Source: 

https://blog.metoffice.gov.uk/2012/10/04/using-probabilities-in-weather-forecasting/  https://www.ametsoc.org/index.cfm/ams/about-ams/ams-statements/statements-of-the-ams-in-force/enhancing-weather-information-with-probability-forecasts/#:~:text=A%20probability%20forecast%20includes%20a,accurately%20quantifies%20the%20inherent%20uncertainty. 

http://udel.edu/~daria/Statistical_Weather_Forecasting_1.ppt