In this thesis we investigate various inversion approaches for a general type of biogeochemical cycle model that describes the carbon sequestration mechanism of terrestrial ecosystem. We formulate the inverse problems in two approaches---a deterministic inverse approach and a probabilistic inverse approach. We first develop the deterministic inverse techniques by calculating the first and second derivatives of the cost functional. Algorithms that depend on the gradient information are proposed. Then, considering the stochasticity in the model, we introduce two stochastic optimization methods---genetic algorithm and simulated annealing, to estimate the model parameters. We further consider the inverse uncertainty of the problem and introduce the Bayesian paradigm to formulate a posterior probability density function that describes the inverse uncertainty. Function approximation approach and Markov Chain Monte Carlo technique are then used to study the probability density function to reveal the inversion result. To increase the simulation efficiency, we combine Hessian matrix information with the proposal probability density function in the Metropolis-Hastings algorithm for fast sampling. All the approaches are tested against a practical numerical model that describes forest ecosystem carbon sequestration. The thesis concludes by comparing the various approaches and by discussing further issues that needs to be studied.