Energy Balance


Calculation of the global energy balance and meridional enthalpy transport

On an annual basis, the global energy balance is calculated for output data of Climate Models.This is done separately for each gridbox by considering the radiation fluxes and the heat fluxes.The balance is calculated at the top of the atmosphere and at the surface, the surface layer is further devided into the domains land and sea; values for the atmosphere given as difference of top of the atmosphere and surface values.

Some stastitics are done: global mean, NH mean, SH mean, zonal means, meridional transport of zonal means, maximum value of the transport for each hemisphere and its geographical location.

Further the bootstrap method is used to get an estimate of the variability.In the same way the latent heat balance can be calculated.As basis to this program package serves the work Francesco Ragone did as part of his MSc Thesis, used in Lucarini and Ragone, 2011.


To illustrate the results given by the introduced calculation, the energy balance was calculated for model data published with IPCC4. This example shows the result for the pre-industrial run of MPI-ECHAM5 (run1), last 100 years of dataset ...

Additionally an example for the comparison of model data is shown: the left plot shows a set of IPCC4 models (always the preindustrial control run), and the right one shows the comparison of two sets of models. In this case IPCC4 vs. IPCC5 ...



A program package for calculation and plotting is available together with a detailed description. Please be aware that it is a beta-version at the current state.

The package consists of tcsh scripts in which parameter are set to run the underlying matlab functions. It is tested with model data of IPCC4 and IPCC5 models, so for the already used model sets parameter files are also provided, which contain the necessary information about the data ( as name of the files, resolution etc).

The package includes programs:

  • to convert the land sea mask from netCDF to matlab Format (and to fract if given in percent), including a quick look plot
  • to convert the required input fields, calculate the balance and transport and plot the global energy balances, meridional enthalpy transport, meridional enthalpy transport max for NH and SH (one plot per model)
  • to plot a time series of one of the energy balance values
  • to plot balance and transport values as above, but for a set of models in one plot
  • to plot balance and transport values as above, but for a comparison of two sets of models in one plot

Please contact Silke Schubert.


  • input data in netCDF format, monthly timeseries of global fields of: hfls, hfss, rlds, rlus, rlut, rsds, rsdt, rsus, rsut and a land sea mask
  • Climate Data Operators (CDO's)
  • matlab (version R2013a was used)


Lucarini, V., and F. Ragone, 2011: Energetics of Climate Models: Net Energy Balance and Meridional Enthalpy Transport. Rev. Geophys., 49, RG1001, doi:10.1029/2009RG000323, PDF

Lucarini, V., et al., 2013: Mathematical and Physical Ideas for Climate Science, arXiv:1311.1190 []