The ICBM family of analytically solved models of soil carbon, nitrogen and microbial biomass dynamics — descriptions and application examples
Introduction
Carbon and nitrogen dynamics in the soil can be described by a number of approaches, usually involving simulation modelling (see e.g. Ågren et al., 1991, Chertov and Komarov, 1996, Powlson et al., 1996, Paustian et al., 1997, Fu et al., 2000). The analytical approach to soil carbon modelling, as opposed to simulation, is not new (Hénin and Dupuis, 1945, Hénin et al., 1959, Ågren and Bosatta, 1996), but recent interest in regional and global modelling (often GIS based) has spawned a number of efforts to use simple, analytically solved models.
Andrén and Kätterer (1997) presented the Introductory Carbon Balance Model (ICBM), originally designed to calculate soil carbon balances in a 30-year time perspective. The differential equations were solved analytically, and thus, parameter values could be estimated by using generally available non-linear regression routines, model properties could be mathematically derived, and the model could be used as well as optimised interactively in computer spreadsheet programs.
The objective of the work presented here was to expand the ICBM concept of analytically solved models to also include nitrogen and soil organism biomass dynamics. We give examples of how the ICBM family of models (Fig. 1) can be used to describe, analyse and predict C, N and organism biomass dynamics during short-, medium- and long-term decomposition of organic materials such as litter and older soil organic matter — including a constant input from plant production. We also show how driving variables such as daily temperature and soil moisture under certain assumptions can be used without simulation techniques, by transforming time into ‘optimum temperature and moisture time’ using any temperature and moisture response function. (See http://www.mv.slu.se/vaxtnaring/olle/ICBM.html for programs in Excel and SAS.)
For a number of reasons, the models are developed with simplicity as the main objective. In contrast to complex simulation models, analytically solved models can easily be surveyed and distributed and their outcome can be calculated using a pocket calculator. Less effort is needed to obtain estimates for parameter values. A simple model can also fairly easily be parameterised for large and incomplete data sets (Kätterer and Andrén, 1999), or be run with many parameter settings simultaneously, e.g. in a GIS grid (Andrén, In press), on an ordinary personal computer yielding almost instantaneous outputs.
The disadvantage of a simple model is that so much falls outside the model. We think that this in many cases can be turned into an advantage, since a step-by-step approach to a complex problem often can be the best one. For example, to estimate the annual amount and quality of carbon input to the soil is very hard — no simple, general methods exist. However, if we make our best estimates in this respect, we can easily use these as input to the simple and straightforward soil carbon model and see how they work. Alternatively, we can use the soil carbon model to calculate a probable input — in a sense modelling the unmeasurable (cf. Elliott et al., 1996, Magid et al., 1997).
In the first part of this paper, the ICBM family of models are presented. In the second part, examples are provided, showing how to use these models for analysing soil C and N dynamics at different time scales. A list of all symbols used in the model equations are given in Appendix A and exact analytical solutions to the model equations are provided in Appendix B.
Section snippets
ICBM
ICBM has two carbon pools (Fig. 1, Fig. 2, ‘ICBM’), a ‘Young’ (Y) and an ‘Old’ (O). Input to Y (from litter-fall and root death) is usually calculated as fraction of plant production. Outflows from the pools follow first-order kinetics (kY, kO). External (climate, soil type, cultivation etc.) factors are condensed into one parameter, re, which affects the decomposition rates of Y and O equally. The parameter re does not affect the ‘humification coefficient’ (h), i.e. the fraction of the outflux
Statistical analysis and optimisation techniques
The models were fitted to data using non-linear regression analysis (procedure NLIN in SAS (SAS, 1985, SAS Institute Inc., NC)) by the multivariate secant method (Ralston and Jennrich, 1979), which was used when optimising pre-selected parameter values to measured data.
Application of ICBM/N to a long-term field experiment
The ICBM/N model was fitted to the top-soil (0–23 cm) of the treatment of the Hoosfield Continuous Barley experiment (Jenkinson and Johnston, 1977), where farmyard manure (FYM) is added annually. Firstly, Eq. (A1) and Eq. (A2) were fit to the data for soil carbon stocks by optimising kY and kO simultaneously using non-linear regression (the unit for t was year). Thereafter, Eq. (A6) and Eq. (A7) were fitted to the data for soil nitrogen stocks by optimising eY. All other parameter values were
Conclusions
The models devised here, when presented as box-and-arrow diagrams, represent more or less the conventional wisdom of soil C and N modelling. They are similar to those implemented in many soil organic matter models and decomposition sub-model in complex ecosystem models, e.g. Van Dijk et al., 1985, Jenkinson et al., 1987, Johnsson et al., 1987, Parton et al., 1987, Hansen et al., 1991, Bradbury et al., 1993). First-order assumptions, the divisions into a number of pools, and subsequent
Acknowledgements
This work contributes to the GCTE Core Research Programme, Category 1, which is a part of the IGBP. Financial support was received from the Swedish Environmental Protection Agency.
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