BedSmoother compute_coefficients_on_proc0 m_C2 m_C2p0 m_C3 m_C3p0 m_C4 m_C4p0 m_config m_Glen_exponent m_grid m_maxtl m_maxtlp0 m_Nx m_Ny m_smoothing_range m_topgp0 m_topgsmooth m_topgsmoothp0 preprocess_bed preprocess_bed smooth_the_bed_on_proc0 smoothed_bed smoothed_thk theta ~BedSmoother

theta() void pism::stressbalance::BedSmoother::theta ( const array::Scalar &  usurf, array::Scalar &  result  ) const Implements the strategy for computing $\theta(h,x,y)$ from previously- stored coefficients, described on Bed roughness parameterization page and in [Schoofbasaltopg2003]. Specifically, $\theta = \omega^{-n}$ where $\omega$ is a local average of a rational function of surface elevation, approximated here by a Taylor polynomial: $$\omega = \fint \left(1 - \frac{\tilde b(x_1,x_2,\xi_1,\xi_2)}{H} \right)^{-(n+2)/n}\,d\xi_1\,d\xi_2 \approx 1 + C_2 H^{-2} + C_3 H^{-3} + C_4 H^{-4}$$ where $h =$ usurf, $H = h -$ topgsmooth and $\tilde b$ is the local bed topography, a function with mean zero. The coefficients $C_2,C_3,C_4$, which depend on $x,y$, are precomputed by preprocess_bed(). Ghosted values are updated directly and no communication occurs. In fact, we assume usurf and theta have stencil width at least equal to GHOSTS. We check whether topgsmooth, which has stencil width maxGHOSTS, has at least GHOSTS stencil width, and throw an error if not. Call preprocess_bed() first. Definition at line 350 of file BedSmoother.cc. References pism::ParallelSection::check(), pism::clip(), pism::ParallelSection::failed(), pism::RuntimeError::formatted(), m_C2, m_C3, m_C4, m_config, m_Glen_exponent, m_grid, m_maxtl, m_Nx, m_Ny, m_topgsmooth, PISM_ERROR_LOCATION, pism::array::Array::set(), and pism::array::Array::stencil_width(). Referenced by pism::stressbalance::SIAFD::compute_diffusivity().