The response of a grassland ecosystem to climate change is discussed within the context of a theoretical model.An optimization approach,a conditional nonlinear optimal perturbation related to parameter(CNOP-P) approach,was employed in this study.The CNOP-P,a perturbation of moisture index in the theoretical model,represents a nonlinear climate perturbation.Two kinds of linear climate perturbations were also used to study the response of the grassland ecosystem to different types of climate changes.The results show that the extent of grassland ecosystem variation caused by the CNOP-P-type climate change is greater than that caused by the two linear types of climate change.In addition,the grassland ecosystem affected by the CNOP-P-type climate change evolved into a desert ecosystem,and the two linear types of climate changes failed within a specific amplitude range when the moisture index recovered to its reference state.Therefore,the grassland ecosystem response to climate change was nonlinear.This study yielded similar results for a desert ecosystem seeded with both living and wilted biomass litter.The quantitative analysis performed in this study also accounted for the role of soil moisture in the root zone and the shading effect of wilted biomass on the grassland ecosystem through nonlinear interactions between soil and vegetation.The results of this study imply that the CNOP-P approach is a potentially effective tool for assessing the impact of nonlinear climate change on grassland ecosystems.
The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.
