A toy model of climatic variability with scaling behaviour

It is demonstrated that a simple deterministic model in discrete time can capture the scaling behaviour of hydroclimatic processes at time scales coarser than annual. This toy model is based on a generalized "chaotic tent map", which may be considered as the compound result of a positive and a negative feedback mechanism, and involves two degrees of freedom. The model is not a realistic representation of a climatic system, but rather a radical simplification of real climatic dynamics. However, its simplicity enables easy implementation, even on a spreadsheet environment, and convenient experimentation. Application of the toy model gives traces that can resemble historical time series of hydroclimatic variables, such as temperature, rainfall and runoff. In particular, such traces exhibit scaling behaviour with a Hurst exponent greater than 0.5 and density function similar to that of observed time series. Moreover, application demonstrates that large-scale synthetic "climatic" fluctuations (like upward or downward trends) can emerge without any specific reason and their evolution is unpredictable, even when they are generated by this simple fully deterministic model with only two degrees of freedom. Obviously, however, the fact that such a simple model can generate time series that are realistic surrogates of real climatic series does not mean that a real climatic system involves that simple dynamics.