The Application Of The CNOP Method In Uncertainty Of Simulation In Uncertainty Of Simulation With A Grassland Ecosystem Model

Based on a five-variable grassland ecosystem theoretical model and a conditional nonlinear optimal perturbation (CNOP) method, we discuss the issue of the uncertainties in a grassland ecosystem. The main points and conclusions are as follows:Firstly, sensitivity tests have been applied on the five-variable grassland ecosystem model, and the result implies that the model can clearly simulate some of the fundamental nonlinear features of the grassland ecosystem, such as multi-equilibria, bifurcation and abrupt changes. Based on these work, we establish a nonlinear optimization system to study the uncertainty of the simulation.Secondly, we discuss the issue of the uncertainties in a grassland ecosystem simulation caused by parameters uncertainties is explored. The parameters uncertainties may originate from uncertainties in observations and (or) descriptions of the physical process, and so on. In this paper,32model parameters with the physical meanings in the five-variable grassland ecosystem model are selected to implement numerical experiments. The results show that when the32model parameters have the same size of uncertainty, and the optimization time is given, a combination of CNOP-Ps that are optimized for each parameter is different from the CNOP-P that is simultaneously optimized for the32model parameters. We compare the grassland ecosystem simulations under the above two types of parameter errors and random parameter errors, whose size of uncertainty is same as that for the optimized parameters errors. A conclusion can be made that the CNOP-P for the32model parameters optimized at the same time leads to the maximum uncertainty in the grassland ecosystem simulation. The maximum uncertainty is that the grassland ecosystem is transformed into a desert ecosystem, or is transformed into another grassland ecosystem with more living biomass. The above results are independent of the size of parameters uncertainties and the optimization time.Furthermore, the paper studies the uncertainty of parameters that cause the grassland ecosystem maintenance or degradation and discuss the maximum extent of the grassland ecosystem’s maintenance or degradation. Maintenance of the grassland ecosystem means that compares with reference state, the amount of living biomass and wilted biomass remain unchanged or increase. Degradation of the grassland ecosystem means that compares with reference state, the amount of living biomass and wilted biomass decrease or translate into desert ecosystem. Compare the difference pattern between CNOP-P (local CNOP-P) result from multi-parameters optimization and error of given linear combination of the parameters, then discuss their influence on simulated result of five-variable grassland ecosystem model. Error of linear combination of the parameters is produced by combining parameters leading the grassland ecosystem to maintenance or degradation. The result of the experiment reveals that under the specified range of uncertainty and optimization time, the pattern of CNOP-P produced from multi-parameters optimization is same as the one result from error of linear combination of the parameter, their influence on the simulated result of the prairie ecosystem express they all lead the prairie ecosystem into maintenance. With the parameter uncertainty range increases, the pattern of CNOP-P produced from multi-parameters optimization become different from the one result from error of linear combination of the parameter, the difference represent the signs of some parameter error component are opposite; they have different effect on the prairie ecosystem, while they all maintain the system, but the CNOP-P show a stronger impact. For different uncertainty scopes decided by different parameters, the pattern of local CNOP-P produced by multi-parameter optimization is as same as the pattern relate to liner combination of every different parameter errors that lead to degradation, they all lead the prairie ecosystem into desert ecosystem. The conclusions above are independent of the choice of objective function. These numerical results indicate that as the increase of the uncertain region, the linear combination of the parameters which lead the ecosystem into maintenance is not the one lead the ecosystem to maximum extent, at the same time they reveal the pattern of parameter error is very important to the maintenance of the ecosystem.Finally, we investigate the uncertainty of simulation caused by the uncertainty of initial values and parameters. It shows that: at the initial moment, the results can be affected by both initial errors and parameter errors, but after a certain time, it is dominated by parameter errors, that is, the uncertainty of result of simulation derives from initial values only at the beginning of model integration, then, it mainly due to parameter values after a certain period of time. We can know form the result that: with the growth of the integration time, the errors of the model parameters become the primary source of uncertainly in simulation results.These numerical results reveal the pattern of parameter errors play a great role in the grassland ecosystem simulation, suggest us when study the uncertainty of grassland ecosystem, we could consider multi-parameter nonlinear interaction. At the meanwhile they also imply the CNOP method is considered to be a powerful tool to solve above problem.