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8.1 ECCO: model-data comparisons using gridded data sets

The functionalities implemented in pkg/ecco are: (1) output time-averaged model fields to compare with gridded data sets; (2) compute normalized model-data distances (i.e., cost functions); (3) compute averages and transports (i.e., integrals). The former is achieved as the model runs forwards in time whereas the others occur after time-integration has completed. Following Forget et al. [2015] the total cost function is formulated generically as


using symbols defined in table 8.1. Per Eq. (8.3) model counterparts ($ \vec{m}_i$ ) to observational data ($ \vec{o}_i$ ) derive from adjustable model parameters ($ \vec{v}$ ) through model dynamics integration ( $ \mathcal{M}$ ), diagnostic calculations ( $ \mathcal{D}$ ), and averaging in space and time ( $ \mathcal{S}$ ). Alternatively $ \mathcal{S}$ stands for subsampling in space and time (section 8.2). Plain model-data misfits ( $ \vec{m}_i-\vec{o}_i$ ) can be penalized directly in Eq. (8.1) but penalized misfits ($ \vec{d}_i$ ) more generally derive from $ \vec{m}_i-\vec{o}_i$ through the generic $ \mathcal{P}$ post-processor (Eq. (8.2)). Eqs. (8.4)-(8.5) pertain to model control parameter adjustment capabilities described in section 8.3.


Table 8.1: Symbol definitions for pkg/ecco and pkg/ctrl generic cost functions.
symbol definition
$ \vec{u}$ vector of nondimensional control variables
$ \vec{v}$ vector of dimensional control variables
$ \alpha_i, \beta_j$ misfit and control cost function multipliers (1 by default)
$ R_i$ data error covariance matrix ($ R_i^{-1}$ are weights)
$ \vec{d}_i$ a set of model-data differences
$ \vec{o}_i$ observational data vector
$ \vec{m}_i$ model counterpart to $ \vec{o}_i$
$ \mathcal{P}$ post-processing operator (e.g., a smoother)
$ \mathcal{M}$ forward model dynamics operator
$ \mathcal{D}$ diagnostic computation operator
$ \mathcal{S}$ averaging/subsampling operator
$ \mathcal{Q}$ Pre-processing operator
$ \mathcal{R}$ Pre-conditioning operator



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Next: 8.1.1 Generic Cost Function Up: 8. Ocean State Estimation Previous: 8. Ocean State Estimation   Contents
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