On the importance of including vegetation dynamics in Budyko's hydrological model

The Budyko curve describes the patterns observed between between climate, evapotranspiration and run-off and has proven to be a useful model for predicting catchment energy and water balances. In this paper we review the Budyko curve's underlying framework and, based on the literature, present an argument for why it is important to include vegetation dynamics into the framework for some purposes. The Budyko framework assumes catchments are at steady-state and are driven by the macro-climate, two conditions dependent on the scales of application, such that the framework's reliability is greatest when applied using long-term averages (≫1 year) and to large catchments (> 10 000 km2). At these scales previous experience has shown that the hydrological role of vegetation does not need to be explicitly considered within the framework. By demonstrating how dynamics in the leaf area, photosynthetic capacity and rooting depth of vegetation affect not only annual and seasonal vegetation water use, but also steady-state conditions, we argue that it is necessary to explicitly include vegetation dynamics into the Budyko framework before it is applied at small scales. Such adaptations would extend the framework not only to applications at small timescales and/or small catchments but to operational activities relating to vegetation and water management

Stochastic energy-balance model with a moving ice line

In [SIAM J. Appl. Dyn. Sys., 12(4):2068--2092, 2013], Widiasih proposed and analyzed a deterministic one-dimensional Budyko-Sellers energy-balance model with a moving ice-line. In this paper, we extend this model to the stochastic setting and analyze it within the framework of stochastic slow-fast systems. We derive the dynamics for the ice line in the limit of a small parameter as a solution to a stochastic differential equation. The stochastic approach enables the study of co-existing (metastable) climate states as well as the transition dynamics between them.Comment: 32 pages, 1 figur

Entropy production and multiple equilibria: the case of the ice-albedo feedback

Nonlinear feedbacks in the Earth System provide mechanisms that can prove very useful in understanding complex dynamics with relatively simple concepts. For example, the temperature and the ice cover of the planet are linked in a positive feedback which gives birth to multiple equilibria for some values of the solar constant: fully ice-covered Earth, ice-free Earth and an intermediate unstable solution. In this study, we show an analogy between a classical dynamical system approach to this problem and a Maximum Entropy Production (MEP) principle view, and we suggest a glimpse on how to reconcile MEP with the time evolution of a variable. It enables us in particular to resolve the question of the stability of the entropy production maxima. We also compare the surface heat flux obtained with MEP and with the bulk-aerodynamic formula.Comment: 29 pages, 12 figure

Periodic Orbits for a Discontinuous Vector Field Arising from a Conceptual Model of Glacial Cycles

Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of nonsmooth dynamical systems. Here we discuss a conceptual model of glacial cycles consisting of a system of three ordinary differential equations defining a discontinuous vector field. We show that this system has a large periodic orbit crossing the discontinuity boundary. This orbit can be interpreted as an intrinsic cycling of the Earth's climate giving rise to alternating glaciations and deglaciations