Imagine weather balloons that are regularly launched every day from various weather stations around the world: as they travel upwards, they record how pressure, temperature, speed and wind direction vary with altitude.
The number of stations present, however, is so small that, for example, in the state of Indiana there is an expanse of about 500 kilometers between the two nearest aerial observation stations in Wilmington, Ohio and Lincoln, Illinois. The collected data, therefore, can only approximate the behavior of weather variables between stations.
The numerical models that then elaborate such measurements, moreover, must face the so-called non-linear nature of the atmosphere and its complex interactions with the biosphere and the oceans. In particular, the first implies that its temporal evolution depends strongly on the initial conditions, that is, the observations (which, as we have just seen, can be very approximate).
These predictive models also apply their equations iteratively over time: in this way, the estimated future value for each meteorological magnitude is then used as the initial value for the next iteration. In doing so, the measurement errors propagate, that is, every new calculated value 'accumulates' in some way the uncertainties of the values used to calculate it: so that the errors grow and, because of the aforementioned non-linearity, This increase is already significant after a relatively small number of cycles.
Returning to the dependence on the initial conditions, we can say, in other words, that slight changes in the initial conditions can lead to very different predictions. During the 1979 Annual Meeting of the American Association for the Advancement of Science in Washington, D.C., Edward Lorenz described the phenomenon as a 'butterfly effect': To give an idea, he said that the flapping of a butterfly’s wings could cause a tornado to occur at great distances.
Therefore a technique known as 'ensemble predictions' (translatable as 'set predictions') is applied, which consists in slightly modifying the initial inputs (that is, the observations made by the meteorological stations) before executing a model. This is done a number of times, resulting in several possible future scenarios: thus, for a particular model, 10 percent chance of rain indicating 10 percent of the time the rain was predicted.
But it doesn’t stop there. The available models are numerous, each with its own strengths and weaknesses, depending on the way they treat small-scale processes: the behavior of water drops is the example of a process too small for the model to appreciate from direct measurements, therefore can only be approximated and each model does so in a unique way.
With experience, meteorologists also learn to recognize situations where a particular model is poorly effective: for example, when there is snow cover on the ground, some models overestimate the temperature because they do not know that there is a snow deposit. A meteorologist who works in a local office, however, is aware of this and knows that the Sun’s energy is partially used to melt snow - instead of heating the air - making temperatures rise more slowly.
These are some of the main reasons why weather apps often provide you with unreliable information even after just a few days.
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