Description

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A collection of tools to compute the Spectral Energy Budget of a dry hydrostatic
Atmosphere (SEBA). This package is developed for application to global numerical
simulations of General Circulation Models (GCMs). SEBA is implemented based on the
formalism developed by Augier and Lindborg (2013) and includes the Helmholtz decomposition
into the rotational and divergent kinetic energy contributions to the nonlinear energy
fluxes introduced by Li et al. (2023). The Spherical Harmonic Transforms are carried out
with the high-performance SHTns C library. The analysis supports data sampled on a
regular (equally spaced in longitude and latitude) or Gaussian (equally spaced in
longitude, latitudes located at roots of ordinary Legendre polynomial of degree nlat)
horizontal grids. The vertical grid can be arbitrary; if data is not sampled on
pressure levels, it is interpolated to isobaric levels before the analysis.
References:
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Augier, P., and E. Lindborg (2013), A new formulation of the spectral energy budget
of the atmosphere, with application to two high-resolution general circulation models,
J. Atmos. Sci., 70, 2293–2308, https://doi.org/10.1175/JAS-D-12-0281.1.
Li, Z., J. Peng, and L. Zhang, 2023: Spectral Budget of Rotational and Divergent Kinetic
Energy in Global Analyses. J. Atmos. Sci., 80, 813–831,
https://doi.org/10.1175/JAS-D-21-0332.1.
Schaeffer, N. (2013). Efficient spherical harmonic transforms aimed at pseudospectral
numerical simulations, Geochem. Geophys. Geosyst., 14, 751– 758,
https://doi.org/10.1002/ggge.20071.

Examples

This example demonstrates how to compute and visualize spectral energy diagnostics and nonlinear energy transfers using SEBA with reanalysis or model data.

1. Load atmospheric data

importxarrayasxrfromseba.sebaimportEnergyBudget# Define dataset path and modelmodel="ERA5"resolution="025deg"data_path="/path/to/simulations/"date_time="20200128"# Load atmospheric 3D fields and surface pressurefile_name="/path/to/simulations/data.nc"# Define external surface variables. Optional: read from input model data if available, override if specifiedsfc_pres=xr.open_dataset("/path/to/simulations/surface_data.nc")["sfc_pressure"]

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2. Create an energy budget object

# Create budget object from data path or directly from loaded xarray.Datasetbudget=EnergyBudget(file_name, truncation=511, ps=sfc_pres)

The truncation parameter sets the spectral resolution of the spherical harmonic transform used internally. Default None: truncation is based on Gaussian grid resolution, e.g., n512

---

3. Compute energy diagnostics

dataset_energy=budget.energy_diagnostics()

This computes Horizontal kinetic energy (HKE), Vertical kinetic energy (VKE), Rotational/Divergent kinetic energy ([R/D]KE), and Available potential energy (APE) spectra for each time and pressure level.

---

4. Visualize energy spectra

layers= {"Troposphere": [250e2, 450e2], "Stratosphere": [50e2, 250e2]}
dataset_energy.visualize_energy(model=model, layers=layers, fig_name=f"figures/energy_spectra.pdf")

This produces a subplot per layer of the energy spectra. Variables can be specified via the variables argument, e.g., variables=['hke', 'vke', 'ape'].

---

5. Compute and visualize nonlinear energy fluxes

dataset_fluxes=budget.cumulative_energy_fluxes()
layers= {
"Lower troposphere": [450e2, 850e2],
"Free troposphere": [250e2, 450e2],
"Stratosphere": [20e2, 250e2],
}
y_limits= {
"Stratosphere": [-0.6, 1.0],
"Free troposphere": [-0.6, 1.0],
"Lower troposphere": [-0.9, 1.5],
}
dataset_fluxes.visualize_fluxes(
model=model,
variables=["pi_hke+pi_ape", "pi_hke", "pi_ape"],
layers=layers, y_limits=y_limits,
fig_name=f"figures/energy_fluxes.pdf"
)

This generates layer-wise flux plots showing Cumulative nonlinear spectral energy transfers.

---

6. Cross-section visualization

dataset_fluxes.visualize_sections(
variables=["cad", "vfd_dke"],
y_limits=[1000., 98.],
fig_name=f"figures/fluxes_section.pdf"
)

Plots vertical cross-sections of specific HKE budget terms (e.g., conversion from APE to HKE, vertical flux divergence) as a function of pressure and horizontal wavenumber.