A Simple Lumped Model for the Prediction of Global Warming Due to Increasing Greenhouse Gas Concentrations

The objective of this study is to prove the hypothesis that the Earth's average equilibrium surface temperature increase with increasing greenhouse gas concentrations can be predicted with reasonable accuracy using a simple lumped energy balance model, provided the radiation transport component of the problem is modeled accurately. To accomplish this goal, spectral and total incoming and outgoing transmissivities of a multi-layer atmosphere are first computed using Line-by-Line calculations from the spectral absorption coefficients of carbon dioxide, water vapor and methane, which are computed using the HITRAN database under various atmospheric conditions (varying temperature, pressure, and concentrations). The total absorptivity and emissivity of the Earth's surface are also computed from high-resolution spectral reflectance data. These quantities are then incorporated into a model based on global energy balance of the Earth to predict its equilibrium average surface temperature. The effect of clouds and heat losses due to phase change and conduction/convection are treated semi-empirically. The model has just one calibrated parameter and predicts a rise of 1.28 degrees in the Earth's temperature when the carbon dioxide concentration is increased from 250 ppm to 400 ppm, which is consistent with observed changes. Addition of ~2 ppm methane to an atmosphere with 400 ppm carbon dioxide is found to have the same effect as the addition of 40 ppm of carbon dioxide (440 ppm total carbon dioxide): a rise of an additional 0.3 degree. The climate sensitivity is found to be ~2 degrees.