Abstract
In this paper, we apply the approach of conditional nonlinear optimal perturbation related to the parameter (CNOP-P) to study parameter uncertainties that lead to the stability (maintenance or degradation) of a grassland ecosystem. The maintenance of the grassland ecosystem refers to the unchanged or increased quantity of living biomass and wilted biomass in the ecosystem, and the degradation of the grassland ecosystem refers to the reduction in the quantity of living biomass and wilted biomass or its transformation into a desert ecosystem. Based on a theoretical five-variable grassland ecosystem model, 32 physical model parameters are selected for numerical experiments. Two types of parameter uncertainties could be obtained. The first type of parameter uncertainty is the linear combination of each parameter uncertainty that is computed using the CNOP-P method. The second type is the parameter uncertainty from multi-parameter optimization using the CNOP-P method. The results show that for the 32 model parameters, at a given optimization time and with greater parameter uncertainty, the patterns of the two types of parameter uncertainties are different. The different patterns represent physical processes of soil wetness. This implies that the variations in soil wetness (surface layer and root zone) are the primary reasons for uncertainty in the maintenance or degradation of grassland ecosystems, especially for the soil moisture of the surface layer. The above results show that the CNOP-P method is a useful tool for discussing the abovementioned problems.
Similar content being viewed by others
References
Adams J M, Faure H, Faure-Denard L, McGlade J M, Woodward F I. 1990. Increases in terrestrial carbon storage from the Last Glacial Maximum to the present. Nature, 348: 711–714
Beven K, Binley A. 1992. The future of distributed models: Model calibration and uncertainty prediction. Hydrol Process, 6: 279–298
Byrd R H, Lu P, Nocedal J, Zhu C. 1995. A Limited memory algorithm for bound constrained optimization. SIAM J Sci Comput, 16: 1190–1208
Duan Q, Sorooshian S, Gupta V. 1992. Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour Res, 28: 1015–1031
Duan W, Zhang R. 2010. Is model parameter error related to a significant spring predictability barrier for El Niño events? Results from a theoretical model. Adv Atmos Sci, 27: 1003–1013
Fang J Y, Yang Y H, Ma W H, Mohammat A, Shen H H. 2010. Ecosystem carbon stocks and their changes in China’s grasslands. Sci China Life Sci, 53: 757–765
Klausmeier C A. 1999. Regular and irregular patterns in semiarid vegetation. Science, 284: 1826–1828
Li H Q, Guo W D, Sun G D, Zhang Y C. 2010. Using conditional nonlinear optimal perturbation method in parameter optimization of land surface processes model. Acta Phys Sin, 60: 019201
Li H Q, Guo W D, Sun G D, Zhang Y C, Fu C. 2011. A new approach for parameter optimization in land surface model. Adv Atmos Sci, 28: 1056–1066
Lu D R, Chen Z Z, Wang G C. 1997. Inner Mongoli semi-arid grassland soil-vegetation-atmosphere interaction (in Chinese). Clim Environ Res, 2: 199–209
Lu D R, Chen Z Z, Wang G C. 2002. Climate-ecology interaction in Inner Mongolia semi-arid grassland (2): Preliminary results of IMGRASS project (in Chinese). Earth Sci Front, 9: 307–320
Mu M, Duan W S, Wang B. 2003. Conditional nonlinear optimal perturbation and its applications. Nonlin Processes Geophys, 10: 493–501
Mu M, Duan W, Wang Q, Zhang R. 2010. An extension of conditional nonlinear optimal perturbation approach and its applications. Nonlin Processes Geophys, 17: 211–220
Mu M, Wang B. 2007. Nonlinear instability and sensitivity of a theoretical grassland ecosystem to finite-amplitude perturbations. Nonlin Processes Geophys, 14: 409–423
Spear R C, Grieb T M, Shang N. 1994. Parameter uncertainty and interaction in complex environmental models. Water Resour Res, 30: 3159–3169
Sun G, Mu M. 2009. Nonlinear feature of the abrupt transitions between multiple equilibria states of an ecosystem model. Adv Atmos Sci, 26: 293–304
Sun G, Mu M. 2011. Nonlinearly combined impacts of initial perturbation from human activities and parameter perturbation from climate change on the grassland ecosystem. Nonlin Processes Geophys, 18: 883–893
Sun G, Mu M. 2013. Understanding variations and seasonal characteristics of net primary production under two types of climate change scenarios in China using the LPJ model. Clim Change, 120: 755–769
Sun G, Mu M. 2014. The analyses of the net primary production due to regional and seasonal temperature differences in eastern China using the LPJ model. Ecol Model, 289: 66–76
Sun G, Mu M. 2016. A new approach to identify the sensitivity and importance of physical parameters combination within numerical models using the Lund-Potsdam-Jena (LPJ) model as an example. Theor Appl Climatol, 128: 587–601
Sun G, Mu M. 2017. Projections of soil carbon using the combination of the CNOP-P method and GCMs from CMIP5 under RCP4.5 in north-south transect of eastern China. Plant Soil, 413: 243–260
Vrugt J A, Gupta H V, Bouten W, Sorooshian S. 2003. A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters. Water Resour Res, 39: 1201
Vrugt J A, Ter Braak C J F, Clark M P, Hyman J M, Robinson B A. 2008. Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation. Water Resour Res, 44: W00B09
Wang Q, Mu M, Dijkstra H A. 2011. Application of the conditional nonlinear optimal perturbation method to the predictability study of the Kuroshio large meander. Adv Atmos Sci, 29: 118–134
Yu Y, Mu M, Duan W. 2012. Does model parameter error cause a significant “spring predictability barrier” for El Niño events in the Zebiak-Cane model? J Clim, 25: 1263–1277
Zeng X D, Shen S S P, Zeng X B, Dickinson R E. 2004. Multiple equilibrium states and the abrupt transitions in a dynamical system of soil water interacting with vegetation. Geophys Res Lett, 31: 5501
Zeng X D, Zeng X B, Shen S S P, Dickinson R E, Zeng Q C. 2005. Dynamics of resonantly interacting equatorial waves. Tellus-A, 58: 263–276
Zeng X D, Wang A H, Zeng Q C, Dickinson R E, Zeng X B, Shen S S P. 2006. Intermediately complex models for the hydrological interactions in the atmosphere-vegetation-soil system. Adv Atmos Sci, 23: 127–140
Zhu C, Byrd R H, Lu P, Nocedal J. 1997. Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization. ACM Trans Math Softw, 23: 550–560
Acknowledgements
This work was supported by the Foundation for Young University Key Teacher by the Educational Department of Henan Province (Grant No. 2014GGJS-021), and the National Natural Science Foundation of China (Grant Nos. 41375111, 41675104 & 41230420).
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Rights and permissions
About this article
Cite this article
Sun, G., Xie, D. A study of parameter uncertainties causing uncertainties in modeling a grassland ecosystem using the conditional nonlinear optimal perturbation method. Sci. China Earth Sci. 60, 1674–1684 (2017). https://doi.org/10.1007/s11430-016-9065-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11430-016-9065-9