## Energy Balance Models

ENERGY Balance Models represent the First Law of Thermodynamics applied to a system. In climatology, energy balance models are used for the Earth-atmosphere system. This is a closed thermo-dynamic system because it does not exchange matter with the surrounding environment, or space. Energy balance models can be applied to the Earth-atmosphere systems for different timescales such as a year, day, or hour. Depending on the timescale, the models would produce an annual, daily, or hourly temperature of the Earth-atmosphere system. Also, the energy transfer processes, the energy cycle, could be either steady-state or transient processes. For steady-state models, the energy input is equal to the energy output in the system, resulting in a steady temperature that does not change with time. This assumption is simple, and results in an energy balance model that can be easily solved. More complex models use transient assumptions and give more informative results, but their solution requires numerical simulations.

The simplest energy balance models assume that the incoming solar radiation, called the solar constant, is equal to the radiative energy lost by the Earth-atmosphere system over the period of one year. These simple balance models can calculate an average constant temperature, and cannot account for the climatic shift defined by the change of the Earth-atmosphere temperature. To study more realistic natural problems, these models can take into account more complicated energy-transfer processes, such as thermal storage of the energy in the upper layer of the ocean, which makes the model inherently transient. Another modeling improvement includes atmospheric energy transfer by convection and radiation. These models enable studies of the climatic shift by decoupling the incoming solar radiation, forcing, climatic shift, and response.

In terms of spatial distribution, the simplest are zero-dimensional models that assume the Earth-atmosphere system to be a single, uniform point. Dividing the Earth-atmosphere system into zones can refine this assumption. One-dimensional models divide the system into latitude zones to allow for latitude-dependent solar flux, albedo, and emissivity. Two-dimensional models create zones in both latitudinal and longitudinal directions.

Energy balance models can be coupled with mass balance models for the atmospheric air and species conservation models for particulate matter or CO2. These comprehensive models are called Global Climate Models (GCM). With GCMs, the calculations become much more numerically complex, and provide results for weather forecasting and climate change predictions.

sEE ALso: Climate Cycles; Climate Models; Computer Models.

bibliography. S. Amano, Thermal Engineering Aspects in Power Systems (Wit Pr/Computational Mechanics, 2008);

A. Kleidon and R.D. Lorenz, Non-equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond (Springer, 2004); Michael E. Schlesinger, et al., Human-Induced Climate Change: An Interdisciplinary Assessment (Cambridge University Press, 2007).

Jelena Srebric Pennsylvania State University

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