Impulse response functions of terrestrial carbon cycle models: method and application

Matthew V Thompson,James T Randerson

doi:10.1046/j.1365-2486.1999.00235.x

Matthew V Thompson, James T Randerson

Open Access

https://doi.org/10.1046/j.1365-2486.1999.00235.x

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Abstract

AbstractTo provide a common currency for model comparison, validation and manipulation, we suggest and describe the use of impulse response functions, a concept well‐developed in other fields, but only partially developed for use in terrestrial carbon cycle modelling. In this paper, we describe the derivation of impulse response functions, and then examine (i) the dynamics of a simple five‐box biosphere carbon model; (ii) the dynamics of the CASA biosphere model, a spatially explicit NPP and soil carbon biogeochemistry model; and (iii) various diagnostics of the two models, including the latitudinal distribution of mean age, mean residence time and turnover time. We also (i) deconvolve the past history of terrestrial NPP from an estimate of past carbon sequestration using a derived impulse response function to test the performance of impulse response functions during periods of historical climate change; (ii) convolve impulse response functions from both the simple five‐box model and the CASA model against a historical record of atmospheric δ13C to estimate the size of the terrestrial 13C isotopic disequilibrium; and (iii) convolve the same impulse response functions against a historical record of atmospheric 14C to estimate the 14C content and isotopic disequilibrium of the terrestrial biosphere at the 1° × 1° scale. Given their utility in model comparison, and the fact that they facilitate a number of numerical calculations that are difficult to perform with the complex carbon turnover models from which they are derived, we strongly urge the inclusion of impulse response functions as a diagnostic of the perturbation response of terrestrial carbon cycle models.

Highlights

The global carbon budget has changed significantly due to anthropogenic increases in atmospheric carbon dioxide (Keeling et al 1989), and many suspect this increase may have wide-ranging effects on global climate as well as on basic terrestrial physiological and hydrological processes (Schimel et al 1995)
The change in slope of the log-y plots of Φ(τ) and Ψ(τ) (Fig. 5) shows that turnover rates varied with age: as the carbon shifted between different reservoirs, the slope was reduced
To test impulse response functions as surrogates for their parent models, as well as their ability to operate under periods of changing turnover dynamics, we repeated the analysis of Thompson et al (1996) using the global impulse response function determined in the previous section (Fig. 8), assuming steady-state conditions at and before the beginning of the simulation, as well as an initial global annual Net primary production (NPP) of 48.2 Pg C y–1 from Thompson et al (1996), using (19) and (20)

Summary

Introduction

The global carbon budget has changed significantly due to anthropogenic increases in atmospheric carbon dioxide (Keeling et al 1989), and many suspect this increase may have wide-ranging effects on global climate as well as on basic terrestrial physiological and hydrological processes (Schimel et al 1995). As well as the CASA-derived, global impulse response function, we repeated their analysis, using the same initial conditions (48.2 Pg C y–1 NPP and steady-state carbon storage at and before 1880) and the same estimate for the terrestrial carbon sink from the study of Houghton (1995).

Results

Conclusion