Appendix 7. Soil phosphorus dynamics.

In the Land Manager model, soil phosphorus is included explicitly as a dynamic variable, S:

St+1 = St + a1F1 - a2F2St - L2St exp[zt ς - (ς2/2)].

(A.7.1)

The proportions of farmers using phosphorus-intensive and phosphorus-conservative practices are F1 and F2, respectively. Phosphorus-intensive farmers add phosphorus to the soil at rate a1. Phosphorus-conservative farmers remove it from the soil at rate a2. Soil phosphorus is added to the lake at rate L2. The exponential term adds a stochastic disturbance due to effects of precipitation on erosion. Parameters of the disturbance are the same as in Appendix 1. Mean inputs to the lake (It of Appendix 1) are the sum of soil erosion plus direct inputs from phosphorus intensive farming:

It = L1F1 + L2St.

(A.7.2)

The input from phosphorus-intensive farming, L1, represents manure that is not incorporated into soil phosphorus, but runs off directly to surface water.