Conceptual models in pedogenesis: Can soil-forming functions be solved?

Abstract Quantitative solutions of the univariant soil-forming functions are reviewed. Lithofunctions are essentially of a comparative nature. Numerical solutions are possible if a coding of the parent material or its properties is made. The number of solutions of topofunctions and climofunctions is already considerable, though too few generally valid equations have been derived. These are required for the further development of the general solutions. Numerical solutions of true biotic functions are likely to remain exceptional and the biotic attributes are best considered as a dependent variable and property of the soil-ecosystem, like any of the soil properties. Several chronofunctions have been obtained for the initial stages of soil formation, and good graphical summaries for long-term soil development functions have been constructed, but strict numerical chronofunctions are rare because the difficulties in isolating and dating properly controlled sites. Runge's energy model uses incongruous terms whilst it essentially follows the tenets of the factorial system, but neglects the parent material (capacity) factor. Chesworth's weathering trend line does not disprove the absence of the steady state and his inference from this and his criticism of the state factor equation are essentially invalid. Because the number of degrees of freedom in the solution of the general soil formation function is rather large, the best way for advancing the solution of the state equation is by increasing the solutions of the univariant functions. It is suggested that the next step should be the preparation of a family of topofunctions, graphically or numerically, showing their change with time and on different parent materials or under different macroclimates. Computerized simulation models of such multivariate functions can then be prepared and compared with real data for further refinement and for pinpointing univariant functions or equations which are needed for the improvement of the solutions already obtained. Whereas the relevance of the univariant and multivariant functions of the state factors is in deriving the significant or major causal relationships, and thus explain or predict the distribution of soils in space and time, the computer simulation strategy can advance the quantification of the process-oriented models of soil dynamics.