Parameter sensitivity of climate models and climate driven ecological systems

Uncertainty in the outcome of numerical models of physical and biological processes, such as the climate and ecological systems, is widely recognized. One contributing factor is uncertainty in model parameters. Because of this uncertainty, a range of model outcomes is usually given. This might obstruct policy making for topics such as the reduction of climate change and nature conservation management. Part of the estimation of uncertainty is a parameter sensitivity analysis. It is important to verify how small changes in parameters can affect the model outcome. Especially extreme deviations are of interest to gain an understanding of the variability of the result. We therefore need to identify the parameter perturbations the model is most sensitive to. Since the atmospheric circulation behaves as a chaotic system quantities that characterise the climate have to be computed froman integrationover a large time interval. Perturbing a large set of parameters to analyse the variability of the outcome would require an enormous computing time. It would therefore be advantageous to select effective parameters a priori. In this thesis a method is described that selects these parameters in an efficient way. The short term behaviour of a nonlinear model is used to select parameter perturbations that are likely to cause a large change in the dynamics of the long term behaviour of the model. A short section of a reference orbit is calculated. Next the error growth from the parameter perturbation can be computed with the use of tangent linear equations. The adjoint of the model acts as a backward integration and can then be used to calculate the parameter perturbation that causes the largest error growth over this interval. This perturbation vector is more likely to be also an effective parameter perturbation for a long time integration simulating the climate than a randomly chosen one. More precisely, it turns out that not exactly at a point of the chaotic attractor with a large error growth but just a moment later when this growth has fallen back has to be selected. These points are found by analysing a succession of many short time intervals over each of which the tangent linear approximation holds.We apply this adjoint method to two climate models; the Lorenz 63 model and the atmospheric T21QG model, and a climate driven metapopulation model; the Rosenzweig-McArthur model coupled to the Lorenz 84 model. The success rate of drawing a parameter perturbation causing a large change should for the adjoint method be considerably higher than for a random search method. Climate change is defined in terms of changes in the occurrence and strength of different preferred atmospheric circulation patterns. In the contextof metapopulationmodels and conservation management, the goal is to find perturbations in the biological parameters that lower the risk of extinction of herbivore subpopulations. It is found that in the simple models, where only 5 parameters are varied (Lorenz 63 and the Rosenzweig-McArthur model forced by Lorenz 84), the adjoint method has a significantly higher success rate in drawing effective parameter perturbations than a random search method does. In the more complex T21QG model drawing an effective parameter perturbation appears to be a much more strenuous task due to the large number of 1449 parameters that are varied. However, although hampered by this large parameter set and the required long time integrationof thissystem with many degrees of freedom, the adjoint method comes much closer to selecting the parameter perturbation causing the largest climate change than the random method