Affiliations: [a] Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, A. P. 55-534, C.P. 09340, D. F., México | [b] Instituto Tecnológico y de Estudios Superiores de Monterrey, C.P. 42080, Hidalgo, México | [c] Departamento de Matemáticas, Universidad Autónoma Metropolitana Iztapalapa, C.P. 09340
Abstract: Variational mass consistent models (MCM’s) provide a solenoidal field V in a region Ω by minimizing a metric ||V−V0||ΩS2 subject to ∇·V=0, where Sij=αi2δij is a symmetric and positive definite matrix. A least-squares approach suggests that S−1 can be estimated with a Gaussian statistics. This approach is not valid in general, instead, it is shown that MCM’s constitute a general scheme to get solenoidal fields V where the αi’s are distributed parameters that can be estimated by means regularization methods. The range of values of α2=α12/α32 considered in the literature is [10−12,∞). It is shown that V becomes singular as α2→0 or ∞ and this behavior together with the loss of regularity of λ on the boundary of Ω produce a spurious sensitivity of the residual divergence, which was proposed to estimate the optimal ratio α2. Several simulations with MCM’s use the boundary condition ∂λ/∂n=0 but it is not valid general. A deduction of MCM’s in terrain-following coordinates is given and it is shown that such coordinates may hide the use of inconsistent boundary conditions. Numerical examples illustrate significative changes in the field V when the condition ∂λ/∂n=0 is used.
Keywords: Atmospheric data assimilation, interpolation of solenoidal or nondivergent fields, particle image velocimetry
