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Abstract
One of the main challenges in climate research is the estimation of the climate response to external forcing. This challenge is often met by the use of climate models, which are known to show a wide spread of uncertainties. An alternative route has been proposed by Leith (1975) and has earned the name fluctuation-dissipation theorem (FDT). The promise of this method is in its ability to predict a response from observations of present climate. However, direct observations of the climate are known to be short, yet, the application of FDT to climate may only be achieved through high dimensional operators. The theory is also known to be applicable to climate in an approximate way, and the confidence in its applicability can only be achieved through simulations using models of different complexities and by subjecting it to a wide variety of forcings.
The aim of this thesis is to test the application of the theory using a sample size that approximates available observational record. FD operators are constructed using data produced from a global climate model (GCM) of intermediate complexity (namely Mk3L Phipps, 2006). These are based on one of: fixed-season boundary conditions, a fixed-season boundary conditions with interactive ocean or a full seasonal cycle. The set of forcing cases that are used to test these operators are all simulating long term steady state responses. These are divided into surface forcing cases, localized atmospheric forcing cases and global, carbon-dioxide, forcing cases.
The lower bound of the data needed to construct an operator was between 30 and 50 years of daily data. While the decrease in sample size was matched by a visible decrease in pattern correlations, gross features of the full response were clearly seen. Monotonic increase in skill was also observed when additional variables were added to the state representation. The prediction of quadratic functions of the state (e.g. clouds) showed that most of the skill was associated with variables such as high clouds, long-wave cloud radiative effect (CRE) and convective precipitation.
The addition of seasonality to the climate system adds to the data requirement. We focus on seasonal and annual predictions and propose operators based on two approximations: the first is based on a theoretical derivation that explicitly caters for the seasonal cycle while being more sensitive to small sample. The second approach is based on a single time-invariant probability density function (PDF) for each season. For the specific case of seasonal prediction, none of these approaches show superior skill. Both operators performed relatively well for tropical forcing cases and poorly for extra-tropical forcing cases.
We also study the prediction of long term responses to a change carbon-dioxide concentrations. In this case the forcing function is defined as the instantaneous heating rate, due to a change in carbon-dioxide concentrations. The FD operators are able to predict the long term cloud response. In particular, the operators are able to capture the direct effect of carbon-dioxide on clouds (i.e. Gregory and Webb, 2008). This provides a more physically plausible framework as well as a confirmation of FDT in the climate context.
One of the main challenges in applying FDT to climate is the need to resort to a reduced representation of the climate system. In this case, lack of skill arises from the choice of reduced representation as well as from the derivation of the theory. This gains further emphasis when the sample size is small. We show that it is possible to couple the representation of the state with the sample size using the concept of similarity between pairs of states. This approach scales to phase spaces that are arbitrarily large while providing a clean way to incorporate domain knowledge about the climate system by means of a kernel function.