## Deterministic vs Probabilistic Forecasting

### Deterministic Weather Forecasts

Determinism: every event is the inevitable result of antecedent causes. Cause and effect.

Entrenched preconceived notion held by forecasters is that a forecaster is not doing his or her job unless he or she can make a spot forecast...an actual temperature or precipitation amount, deterministically. Thus, unless one can say that on Saturday at 8AM the temperature WILL be 51F (say), the forecaster is not doing his or her job. It turns out that the further out from present time one attempts to make a forecast, the less such a deterministic forecast is possible. The further out from present time one goes, the more important it is that a forecaster integrates "probabilistic" language either into his actual forecast wording, or at least into the intellectual underpinning for his forecast. Not to do so is to not produce a state of the art forecast.

### Background

The world is governed by (or is under the sway of) determinism if and only if, given a specified way things are at a time t, the way things go thereafter is fixed as a matter of natural law.

 Observations + Correction Factor = Forecast Diagnosis Models Prognosis 1. Example: Pressure observations on map 2. Pressure Tendency Equation: Local pressure change at every spot at which (1) exist on map 3. Forecast Pressure Map Forecast is the result of the causes implicit in (2)

A perfect deterministic (or categorical) forecast can only be as good as (a) the meteorologist's skills in interpreting (3); (b) the degree to which we understand the forecast models (2) and how good these models are at estimating things (3); (c) the degree to which the original observations are accurate.

Assuming that meteorologists are trained perfectly (dubious), and that the models are excellent at what they do (not so dubious --the primitive equations), the "perfect forecast" problem reduces to the integrity of the original observations. However, there is a natural tendency for meteorologists to believe that unless a forecast is deterministic, it is not a good forecast. In short, there is the natural tendency for meteorologists to believe that they are not "doing their jobs" if they do not make a derministic forecast.

### Perspectives on Probabilistic Weather Forecasts

##### (taken from Doswell and Brooks 2001)

Probabilistic forecasting is a technique for weather forecasting that relies on different methods to establish an event occurrence/magnitude probability. This differs substantially from giving a definite information on the occurrence/magnitude (or not) of the same event, technique used in deterministic forecasting. Both techniques try to predict events but information on the uncertainty of the prediction is only present in the probabilistic forecast.

"...Think about how you do a forecast. The internal conversation you carry on with yourself as you look at weather maps is virtually always involves probabilistic concepts. It is quite natural to have uncertainty about what's going to happen. And uncertainty compounds itself. You find yourself saying things like "If that front moves here by such-and-such a time, and if the moisture of a certain value comes to be near that front, then an event of a certain character is more likely than if it those conditions don't occur." This brings up the notion of conditional probability. A conditional probability is defined as the probability of one event, given that some other event has occurred. We might think of the probability of measureable rain (the standard PoP), given that the surface dewpoint reaches 55F, or whatever...."

Figure 1. Schematic showing different types of uncertainty associated with forecasting some quantity, Q. The "categorical" forecast implies 100% probability of Q taking on a particular value, whereas the others illustrate varies kinds of probability distribution (from Doswell and Brooks 2001).

"....There are many different kinds of probability. The textbook example is derived from some inherent property of the system producing the event; an example is tossing a coin..."

"...This classic concept of probability arises inherently from the system being considered. It should be just as obvious that this does not apply to meteorological forecasting probabilities. We are not dealing with geometric idealizations when we look at real weather systems and processes...." (You can't look at a weather system and assign a definite probability that a certain temperature will occur, for example, a percentage of the time, and another temperature will occur the rest of the time)

"....Another form of probability is associated with the notion of the frequency of occurrence of events. We can return to the coin tossing example to illustrate this. If a real coin is tossed, we can collect data about such things as the frequency with which heads and tails occur, or the frequency of particular sequences of heads and tails...." (But weather systems are not analogs to coins, no matter how identical weather systems may appear)

"...Although we certainly make use of analogs in forecasting, each weather system is basically different to a greater or lesser extent from every other weather system. Is the weather along each cold front the same as the weather along every other cold front? Not likely! Therefore, if a weather system looks similar to another one we've experienced in the past, we might think that the weather would evolve similarly, but only to a point. It would be extremely unlikely that exactly the same weather would unfold, down to the tiniest detail. In fact, this uncertainty was instrumental in the development of the ideas of "chaos" by Ed Lorenz. No matter how similar two weather systems appear to be, eventually their evolutions diverge, due to small differences in their initial states, to the point where subsequent events are as dissimilar as if they had begun with completely different initial conditions. These ideas are at the very core of notions of "predictability"..."

"...This brings us to yet another type of probability, called subjective probability. It can be defined in a variety of ways, but the sort of definition that makes most sense in the context of weather forecasting is that the subjective probability of a particular weather event is associated with the forecaster's uncertainty that the event will occur...."

"...This subjective probability is just as legitimate as a probability derived from some other process, like the geometric- or frequency-derived probabilities just described. Obviously, two different forecasters might arrive at quite different subjective probabilities. Some might worry about whether their subjectively derived probabilities are right or wrong...."

"...The probability of a severe thunderstorm involves first having a thunderstorm. Given that there is a thunderstorm, we can estimate how confident we are that it would be severe. But the probability of a thunderstorm is itself conditioned by other factors[3] and those factors in turn are conditioned by still other factors. Somehow our minds are capable of integrating all these factors into a subjective estimate...."

"..The events we forecast are conditioned on a whole series of events occuring, none of which are absolute certainties the vast majority of the time...." (Gives rise to the concept of conditional probability)

"... We really need to accumulate an ensemble of forecasts before we can say much of value about our subjective probability estimates..." (We need not to guess about what type of weather might occur for a given event, but have some objective way of evaluating the range of possiblities. One way of determining this is termed ENSEMBLE FORECASTING)