An explicit and computationally efficient method to initialise first-order-based soil organic matter models—The Geometric Series Solution (GSS)

• We derive a method for the spin-up of first-order-based soil organic matter models.
• The method explicitly relates soil organic matter pools with input data.
• The method is probably the most efficient method to solve the spin-up problem.

This paper derives an algebraic solution (the Geometric Series Solution; GSS) to replace iterative runs of soil organic matter (SOM) models for initialisation of SOM pools. The method requires steady-state/long-term-average series of plant input and soil climate driving data. It calculates the values of SOM pools as if SOM models are iterated for a large number of cycles. The method has a high computational efficiency because it is an explicit solution to the calculations used to initialise the model and so requires a single iteration of the SOM model. Under the premise that the iterative pool inputs can be derived analytically, the GSS equations are applicable for other first-order-based SOM models. To illustrate applicability the method is applied to the coupled JULES-ECOSSE model.