Recent work by Forest et al. (2002) provides probability density functions (pdfs) for climate system properties (e.g., sensitivity of climate change to a doubling of CO$_2$ concentrations) that affect the global climate response to external forcings on decadal to century time-scales. These pdfs can be used in simulations of future climate change when uncertain emissions scenarios are also included to estimate the uncertainty by both scientific and economic contributions. We will explore the implications of these constraints on the climate changes in the polar region by examining the output of 250 simulations of the MIT Integrated Global System Model with emissions and scientific parameters randomly drawn using the Latin Hypercube Sampling method. These simulations cover the period 1860-2100 with historical climate forcings until 1995 and future scenarios thereafter. First, we will examine simulated temperature and sea-ice changes and compare the results with the observed records. Second, we will explore changes in temperature, precipitation, and sea-ice as well as identifying feedbacks on the carbon cycle and local ecosystems. For example, in the 60--90$^o$N region, we estimate the 2.5--97.5% range for temperature increase to be 2--12$^o$C and for the fractional precipitation increase to be 0.1--0.4. As a result, we will examine the potential effect on natural methane emissions as well as the carbon uptake by terrestrial ecosystems in these regions.