2. Ocean Bottom Pressure

2.1. Models

2.1.1. ECCO

Uses outputs from the NASA-JPL Estimating the Circulation and Climate of the Ocean (ECCO) model. For ECCO near real-time Kalman-filtered (kf080i) and Rauch-Tung-Striebel (RTS) smoother (dr080i) models, reads 12-hour ocean bottom pressure data (OBP) and calculates monthly averages. For ECCO version 4 models, reads monthly ocean bottom pressure potential anomalies and converts to estimates of absolute ocean bottom pressure (OBP). Near real-time models are downloaded using the jpl_ecco_sync.py program, monthly Cube92 models are calculated using the jpl_ecco_cube92_sync.py program, interpolated Version 4 models are downloaded using the jpl_ecco_v4_sync.py program, and monthly Version 4 and 5 models in LLC tile format are downloaded using the jpl_ecco_llc_sync.py program.

2.2. Background

Boussinesq-type models conserve volume rather than mass, and so the global area average of each monthly map is removed [7]. Monthly anomalies in ocean bottom pressure are calculated by removing a multi-annual mean (typically 2003 – 2007). Ocean bottom pressure anomalies are converted to spherical harmonics following Boy and Chao [2] [Equations 2.1 and 2.2].

(2.1)\[\begin{split} \left\{\begin{matrix}\tilde{C}_{lm}(t) \\ \tilde{S}_{lm}(t) \end{matrix} \right\} = \frac{3}{4\pi a\rho_{e}}\frac{1+k_l}{(2l+1)}\int \xi_l(\theta,\phi,t)~P_{lm}(\cos\theta) \left\{\begin{matrix}\cos{m\phi} \\ \sin{m\phi} \end{matrix} \right\}\,d\Omega\end{split}\]

(2.2)\[ \xi_l(\theta,\phi,t) = \left(\frac{a + N(\theta,\phi) - d(\theta,\phi)}{a}\right)^{l+2}\frac{p_{bot}(\theta,\phi,t)}{g(\theta,\phi)}\]

2.3. Framework

Figure 2.1: ECCO Spherical Harmonics Framework