Further Comments Demonstrating that Climate Prediction Is An Initial Value Problem

There is a paper

F. Giorgi, 2005 : Climate Change Prediction: Climatic Change (2005) 73: 239–265
DOI: 10.1007/s10584-005-6857-4

which provides information by a well respected climate scientist which can be used to show why climate prediction is an initial value problem.

He starts the article by defining the two types of prediction that Ian Rutherford also commented on in his testimony as discussed on Climate Science (see). The two types listed in the Giorgi article are

“In the late 1960s and mid 1970s the chaotic nature of the climate system was first recognized. Lorenz (1969, 1975) defined two types of predictability problems:

1) Predictability of the first kind, which is essentially the prediction of the evolution of the atmosphere, or more generally the climate system, given some knowledge of its initial state. Predictability of the first kind is therefore primarily an initial value problem, and numerical weather prediction is a typical example of it.

2) Predictability of the second kind, in which the objective is to predict the evolution of the statistical properties of the climate system in response to changes in external forcings. Predictability of the second kind is thus essentially a boundary value problem.”

In the text of this paper, Dr. Giorgi writes,

“….because of the long time scales involved in ocean, cryosphere and biosphere processes a first kind predictability component also arises. The slower components of the climate system (e.g. the ocean and biosphere) affect the statistics of climate variables (e.g. precipitation) and since they may feel the influence of their initial state at multi decadal time scales, it is possible that climate changes also depend on the initial state of the climate system (e.g. Collins, 2002; Pielke, 1998). For example, the evolution of the THC in response to GHG forcing can depend on the THC initial state, and this evolution will in general affect the full climate system. As a result, the climate change prediction problem has components of both first and second kind which are deeply intertwined.

This concept is illustrated in Figure 2, which shows two hypothetical future climate evolutions as simulated by a climate model. In each simulation the GHG concentration increases in the same way but starting from different times of the Control run, and thus different initial ocean, sea ice and land surface conditions. As illustrated, the two climate evolutions can potentially differ both in their mean and variability characteristics. The relevance of the first kind predictability aspect of climate change is that we do not know what the initial conditions of the climate system were at the beginning of the “industrialization experimentâ€? and this adds an element of uncertainty to the climate prediction.”

He also states that,

“To add difficulty to a prediction is the fact that the predictability of a system is strongly affected by non-linearities. A system that responds linearly to forcings is highly predictable, i.e. doubling of the forcing results in a doubling of the response. Non-linear behaviors are much less predictable and several factors increase the non-linearity of the climate system as a whole, thereby decreasing its predictability (e.g. Rial et al., 2004).”

Thus, if the climate system is both a boundary value and an initial value problem (which I agree with), it is an initial value problem!

I read the article as a transition in progress in the thinking, from the assumption that multi-decadal global climate model projections are a boundary value problem, to the recognition that the prediction of the evolution of the climate system is an initial value problem. Moreover, if the climate system is sufficiently nonlinear, as the observational evidence indicates that it is (see), then achieving skillful multi decadal climate predictions in response to the diversity of human and natural climate forcings is a daunting challenge, as has been emphasized on Climate Science.

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