Probabilistic and Deterministic Forecasting using Evolutionary Program Ensembles
Paul J. Roebber
UW Milwaukee
Noon August 11 in Room 2155
Abstract: Charles Darwin wrote: “Can it … be thought
improbable … that other variations useful in some way to each being in
the great and complex battle of life, should sometimes occur in the
course of thousands of generations? If such do occur, can we doubt …
that individuals having any advantage, however slight … would have the
best chance of surviving and of procreating their kind?” This is the
conceptual basis of evolutionary programming (EP), a process in which
simulated evolution is used to find solutions to problems as diverse as
the sorting of numbers and forecasting minimum temperature. Despite a
history in computer sciences dating back to the 1960s, the application
of this idea to meteorological studies is relatively new. Recently, EP
has been adapted to the weather domain in order to generate large
member ensemble forecasts for minimum temperature, maximum temperature,
wind power, and heavy rainfall (Roebber 2013; Roebber 2015abc). These
studies have shown that the method can provide greater probabilistic
and deterministic skill, particularly at the extremes, than
post-processed numerical weather prediction (NWP) ensembles. Further
research has shown that this skill advantage persists out to longer
ranges, where the forecast signal is presumably weaker.
The
method can be understood as follows. Suppose that we have a
well-defined problem with a clear measure of success (e.g.,
root-mean-square-error), and for which we can construct solutions by
performing various mathematical operations on a set of inputs. In this
case, it is possible to develop a single computer program that
generates algorithms which solve the defined problem by applying
various operators and coefficients to the inputs. The level of success
or "fitness" of a particular solution can then be measured. The idea of
fitness invokes evolutionary principles and suggests that if one starts
from a very large set of random initial algorithms and allows fit
algorithms to propagate some portion of their components to the next
generation, then it may be possible to produce improved algorithms over
time. This culling of the population in favor of stronger individuals
through maximizing fitness and the exchange of "genetic material"
between fit algorithms drives the progress towards improved solutions.
Since weather forecast problems are nonlinear with non-unique
solutions, evolved programs are a new means for generating a set of
skillful but independent solutions. The algorithms resemble multiple
linear or nonlinear regression equations, but with conditionals that
allow for special circumstances to be accounted for as a routine
outcome of the data search (e.g., the impact of snow cover on
temperature under conditions of clear skies and light winds; Roebber
2010).
In this talk, I will discuss the EP concept and its most
recent meteorological forms, including examples from various
applications of the method. Roebber (2015abc) modified the technique to
incorporate various forms of genetic exchange, disease, mutation, and
the training of solutions within ecological niches, and to produce an
adaptive form that can account for changing local conditions (such as
changing flow regimes) as well as improved forecast inputs – thus, once
initial training is completed, the ensemble will adapt automatically as
forecasts are produced. I will outline efforts to mitigate the tendency
for EP ensembles to exhibit under dispersion as with NWP ensembles and
the concept of balancing the minimization of root-mean-square error
with the maximization of ensemble diversity. I will then conclude with
a discussion of outstanding questions regarding the method and future
research directions.