For computationally expensive climate models, Monte-Carlo approaches of exploring the input parameter space are often prohibitive due to slow convergence with respect to ensemble size. To alleviate this, we build inexpensive surrogates using uncertainty quantification (UQ) methods employing Polynomial Chaos (PC) expansions that approximate the input-output relationships using as few model evaluations as possible. However, when many uncertain input parameters are present, such UQ studies suffer from the curse of dimensionality. In particular, for 50-100 input parameters non-adaptive PC representations have infeasible numbers of basis terms. To this end, we develop and employ Weighted Iterative Bayesian Compressive Sensing to learn the most important input parameter relationships for efficient, sparse PC surrogate construction. The surrogates are employed for forward uncertainty propagation and variance-based sensitivity analysis, as well as to greatly accelerate statistical methods for parameter estimation, where one relies on observational data to estimate input parameters with quantified uncertainty. Steady state sensitivity analysis with respect to 55 input parameters and 15 output QoIs representing 10-year average steady state values are performed for the boreal evergreen forest AmeriFlux site Niwot Ridge and the temperate boreal evergreen forest at Campbell river, CA with ACME v0. A sparse adaptive surrogate model is constructed using 10000 model simulations, followed by variance-based decomposition to rank input parameters and their joint contributions to the total output uncertainty. Results from the sensitivity analysis indicate that, e.g. for the AmeriFlux site, key model outputs are most sensitive to parameters controlling leaf and fine root nitrogen concentrations, as well as fine root allocation, leaf longevity, denitrification, and the temperature sensitivity of autotrophic respiration.