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


  • Matthew V. Thompson,

    1. Department of Organismic and Evolutionary Biology, Harvard University, 16 Divinity Avenue, Cambridge, MA, 02138, USA,
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  • James T. Randerson

    1. Carnegie Institution of Washington, Department of Plant Biology, 260 Panama Street and, Stanford University, Department of Biological Sciences, Stanford, CA, 94305, USA
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Matthew Thompson, tel + 1/617-496-3580, fax + 1/617-496-5854, e-mail


To 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.