DOI: 10.5281/zenodo.15530699
title: Dataset of the globally computed terms of the Barotropic Vorticity (BV) budget, and THOR v2 neural network input fields
title: BV dataset used for the THOR method

description: This is a global ocean field dataset containing all the data used to extend the Tracking global Heating with Ocean Regimes (THOR) method (Sonnewald and Lguensat, 2021; Yik et al., 2023). In the THOR methodology, the Native Emergent Manifold Interrogation (NEMI) method (Sonnewald, 2023) was used to determine ocean regimes (clusters).

Specifically, this dataset includes the nine computed terms of the Barotropic Vorticity (BV) budget (see Equation 1), based on the depth-integrated Boussinesq-hydrostatic ocean primitive equations, which were used to determine the clustered fields. The calculation of these terms utilized 0.25º x 0.25º resolution outputs from the latest version of the numerical ocean model originating from the NOAA/GFDL coupled model simulation series CM4X.\begin{equation*}\beta \, {V} = \dfrac{1}{\rho_o}\cdot {J(p_b, H)} - f\cdot {\dfrac{Q_m}{\rho_o}} + f\cdot \partial_t\eta - \nabla \wedge \mathcal{U}_t + \dfrac{1}{\rho_o}\cdot \nabla \wedge \tau_s - \dfrac{1}{\rho_o}\cdot \nabla\wedge \tau_b + \nabla \wedge \mathcal{A} + \nabla \wedge \mathcal{B} \tag{1}\end{equation*}

The nine terms of this BV budget equation describe the ocean dynamics. Going in order from left to right in this equation, we have:







Meridional Coriolis gradient x depth-integrated meridional velocity (beta_V): $\beta \, {V}$ 




Bottom pressure torque term (BPT): $\dfrac{1}{\rho_o}\cdot {J(p_b, H)}$ 




Coriolis x surface mass flux / Boussinesq reference density (Mass_flux): $- f\cdot {\dfrac{Q_m}{\rho_o}}$ 




Coriolis x horizontal viscous friction term, also known as return dynamic viscosity (eta_dt): $f\cdot \partial_t\eta$




Curl of depth-integrated velocity tendency term (Curl_dudt): $- \nabla \wedge \mathcal{U}_t$




Curl of surface wind stress / Boussinesq reference density (Curl_taus): $\dfrac{1}{\rho_o}\cdot \nabla \wedge \tau_s$




Curl of bottom boundary stress / Boussinesq reference density (Curl_taub): $- \dfrac{1}{\rho_o}\cdot \nabla\wedge \tau_b$




Curl of depth-integrated meridional velocity advection (nonlinear) term (Curl_Adv): ${\nabla \wedge \mathcal{A}}$




Curl of depth-integrated horizontal viscous friction (diffusion) term (Curl_diff): ${\nabla \wedge \mathcal{B}}$




More details on how Equation 1 was derived can be seen in Appendix A of Khatri et al. (2024). The names of the data variables present in the dataset are highlighted in brackets after the description of each of the nine terms.

Additionally, from the same ocean model, this dataset also contains two clustered fields (nemi_6clusters and nemi_15clusters) resulted from NEMI with cluster numbers 6 and 15, and the following input fields that were used to train the THOR neural network ensemble:



Wind stress curl (curlTau)

Bathymetry – water column height (col_height)

Sea surface height above geoid (zos)

Coriolis parameter (f or Coriolis)

x-component of column height gradients (gradColHeight_x)

y-component of column height gradients (gradColHeight_y)

x-component of zos gradients (gradZos_x)

y-component of zos gradients (gradZos_y)

Horizontal mass transport (umo)

Vertical mass transport (vmo)