Quantifying Information Gain from Dynamic Downscaling Experiments

Abstract:

Dynamic climate downscaling experiments are designed to produce information at higher spatial and temporal resolutions. Such additional information is generated from the low-resolution initial and boundary conditions via the predictive power of the physical laws. However, errors and uncertainties in the initial and boundary conditions can be propagated and even amplified to the downscaled simulations. Additionally, the limit of predictability in nonlinear dynamical systems will also damper the information gain, even if the initial and boundary conditions were error-free. Thus it is critical to quantitatively define and measure the amount of information increase from dynamic downscaling experiments, to better understand and appreciate their potentials and limitations.

We present a scheme to objectively measure the information gain from such experiments. The scheme is based on information theory, and we argue that if a downscaling experiment is to exhibit value, it has to produce more information than what can be simply inferred from information sources already available. These information sources include the initial and boundary conditions, the coarse resolution model in which the higher-resolution models are embedded, and the same set of physical laws. These existing information sources define an “information threshold” as a function of the spatial and temporal resolution, and this threshold serves as a benchmark to quantify the information gain from the downscaling experiments, or any other approaches. For a downscaling experiment to shown any value, the information has to be above this threshold. A recent NASA-supported downscaling experiment is used as an example to illustrate the application of this scheme.