Elsevier

Ecological Modelling

Volume 136, Issues 2–3, 20 January 2001, Pages 191-207
Ecological Modelling

The ICBM family of analytically solved models of soil carbon, nitrogen and microbial biomass dynamics — descriptions and application examples

https://doi.org/10.1016/S0304-3800(00)00420-8Get rights and content

Abstract

Based on the Introductory Carbon Balance Model, ICBM, we present a set of analytically solved models. The original ICBM comprises ‘Young’ and ‘Old’ soil C, two decay constants and parameters for litter input,'humification' and external influences — in all five parameters. The new models describe soil C (and N) balances more in detail, but they are built around the same core concepts such as first-order decomposition kinetics and a minimum number of soil C and N pools. More complex processes, such as plant growth and mortality as well as weather influence are not explicitly included. However, these processes are allowed to influence the model predictions by modifying model parameter values. These modifications may be based on ‘best guesses’, parameter optimisations to available data, or independent ‘front-end models’, e.g. calculations of temperature influence on decomposer activity. Listed according to increasing complexity, the models are: (1) ICBM/N, which is ICBM with nitrogen added. It calculates net N-mineralisation and adds parameters for C/N ratios and soil organisms as well as organism efficieny — nine parameters in all; (2) ICBM/2N, which gives a more precise description of the initial stages of decomposition by splitting the ‘Young’ pool into two. The nitrogen part of the model has parameters for the C/N ratios of ‘labile’ and ‘refractory’ input of organic material, organism biomass and humification and also microbial growth efficiency for ‘labile’ and ‘refractory’. The model has 13 parameters in all, but can be run as a pure C model (ICBM/2) with only seven parameters; (3) ICBM/2BN, where organism biomass C and N is explicitly modelled. This model is usually run with daily, weekly or monthly steps and adds parameters related to biomass — 18 parameters in total — and can be run as a pure C model (ICBM/2B) with 13 parameters or even as a model with only one ‘Young’ pool (ICBM/B). We give examples of model applications, both short- and long-term, and show that the models relatively easily can be applied to various, more or less incomplete, data sets. The models do not require simulation techniques and are easily programmed in, e.g. electronic spreadsheets such as Microsoft Excel. By transformation of the time steps even dynamic driving variables, e.g. weather-related, can be applied without simulation. Model equations and ready-to-run programs (Excel, SAS) can be found at http://www.mv.slu.se/vaxtnaring/olle/ICBM.html.

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.

References (39)

  • Andrén, O., Kätterer, T., In press. Basic principles for soil carbon sequestration and calculating dynamic...
  • A.K.M. Azmal et al.

    Mineralization and microbial biomass formation in upland soil amended with some tropical plant residues at different temperatures

    Soil Sci. Plant Nutr.

    (1996)
  • N.J. Bradbury et al.

    Modelling the fate of nitrogen in crop and soil in the years following application of 15N-labelled fertilizer to winter wheat

    J. Agric. Sci.

    (1993)
  • O.G. Chertov et al.

    SOMM: a model of soil organic matter dynamics

    Ecol. Model

    (1996)
  • E.T. Elliott et al.

    Modeling the measurable or measuring the modelable: a hierarchical approach to isolating meaningful soil organic matter fractionations

  • P.W. Flanagan et al.

    Decomposition models based on climatic variables, substrate variables, microbial respiration and production

  • Franko, U., Oelschlägel, B., Schenk, S., 1995. Modellierung von Bodenprozessen in Agrarlandschaften zur Untersuchung...
  • U. Franko et al.

    Simulation of temperature-, water-, and nitrogen-dynamics using the model CANDY

    Ecol. Model.

    (1996)
  • S. Hansen et al.

    Simulation of nitrogen dynamics and biomass production in winter wheat using the Danish simulation model DAISY

    Fert. Res.

    (1991)
  • Cited by (0)

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