摘要
A biased coinflip Ansatz provides a stochastic regional scale land surface climate model of minimum complexity, which represents physical and stochastic properties of an ideal rainfall–runoff chain. The solution yields the empirically derived Schreiber formula as an Arrhenius-type equation of state W--em class="a-plus-plus">exp(?em class="a-plus-plus">D). It is associated with two thresholds and combines river runoff Ro, precipitation P and potential evaporation N as flux ratios, which represent water efficiency, W--em class="a-plus-plus">Ro/P, and vegetation states, D--em class="a-plus-plus">N/P. This stochastic rainfall–runoff chain is analyzed utilizing a global climate model (GCM) environment. The following results are obtained for present and future climate settings: (i) The climate mean rainfall-runoff chain is validated in terms of consistency and predictability, which demonstrate the stochastic rainfall–runoff chain to be a viable surrogate model for simulating means and variability of regional climates. (ii) Climate change is analyzed in terms of runoff sensitivity/elasticity and attribution measures.