تجزیه و تحلیل حساسیت برای یک مدل تکامل ورقه یخ قطب جنوب

The evolution of the Antarctic ice sheet for the last 200,000 years is simulated with a finite difference thermomechanical model based on the shallow ice approximation. The model depends on the surface temperature, the ice accumulation rate, the geothermal heat flux and the basal sliding coefficient, which are estimated with large uncertainty. A second-order approximation of the model in a neighborhood of the reference values for these parameters permits the computation of both local and variance-based sensitivity indices. The results show the dominant effect of the surface temperature on the model predictions.

The presence of water at the base of the Antarctic ice sheet has been revealed from several geophysical surveys [1] and requires that the temperature at the bedrock is close to the melting point. The melt rate is one of the terms of the mass balance of the Antarctic ice sheet, which is a huge reservoir of (frozen) fresh water, and therefore is an important parameter to assess the impacts of climate change on the Earth. Since environmental conditions prevent from acquiring direct information, the knowledge about the physical processes occurring at the base of the Antarctic ice sheet is still incomplete. Simulation models can be used to test different hypotheses and to plan field or remote sensing surveys. In this paper it is illustrated an example of a dynamical model of the ice sheets, which is applied to simulate the evolution of the Antarctic ice sheet during the last 200,000 years before present. Some of the input parameters might be affected by strong uncertainty, which reflects into the model outcomes. Moreover, the non-linearity of the physical processes makes it difficult to identify which parameters are the most important to obtain physically consistent results. Therefore the sensitivity analysis aims not only to quantify the reliability of the model predictions, but also to identify which parameters require a better estimate. A thorough review of the concepts of sensitivity analysis can be found in textbooks on this topic: see, e.g., [2] for a recently updated work. Here a very short discussion of few basic ideas related to the specific test presented in this paper is given. Local measures of uncertainty, which are essentially based on linear approximations of the model, can be easily computed even for very complex non-linear models. A more advanced approach to sensitivity analysis would require the computation of variance-based sensitivity indicators, which are more relevant for the above mentioned goals. However, such indices are difficult to be computed for complex non-linear numerical models which require not only great computing power, but also great care to avoid numerical instabilities when the code runs with inconsistent values of the input parameters. As a first step toward a thorough sensitivity analysis, in this paper the first-order sensitivity index is analytically computed with an approximated model. In particular, the model output is approximated in a neighborhood of some input parameters as a second-order function of the deviation from their reference values. In the next section the model characteristics are summarised and the results of its application are discussed. The third section is devoted to the application of the sensitivity analysis for this model. In the fourth section the results are illustrated and conclusive remarks are given.