A Linearized Prognostic Cloud Scheme in NASA’s Goddard Earth Observing System Data Assimilation Tools

Abstract

A linearized prognostic cloud scheme has been developed to accompany the linearized convection scheme recently implemented in NASA’s Goddard Earth Observing System data assimilation tools. The linearization, developed from the nonlinear cloud scheme, treats cloud variables prognostically so they are subject to linearized advection, diffusion, generation, and evaporation. Four linearized cloud variables are modeled, the ice and water phases of clouds generated by large-scale condensation and, separately, by detraining convection. For each species the scheme models their sources, sublimation, evaporation, and autoconversion. Large-scale, anvil and convective species of precipitation are modeled and evaporated. The cloud scheme exhibits linearity and realistic perturbation growth, except around the generation of clouds through large-scale condensation. Discontinuities and steep gradients are widely used here and severe problems occur in the calculation of cloud fraction. For data assimilation applications this poor behavior is controlled by replacing this part of the scheme with a perturbation model. For observation impacts, where efficiency is less of a concern, a filtering is developed that examines the Jacobian. The replacement scheme is only invoked if Jacobian elements or eigenvalues violate a series of tuned constants. The linearized prognostic cloud scheme is tested by comparing the linear and nonlinear perturbation trajectories for 6-, 12-, and 24-h forecast times. The tangent linear model performs well and perturbations of clouds are well captured for the lead times of interest.

Definition of the Moist-Air Exergy Norm: A Comparison with Existing “Moist Energy Norms”

“…The linearized version of GEOS has a complete tangent linear and adjoint of the FV3 dynamical core, as well as linearization of the Relaxed Arakawa-Schubert convection scheme (Holdaway et al, 2014, hereafter H14), single moment cloud scheme (Holdaway et al, 2015) and a simplified boundary layer scheme.…”

Implicit ensemble tangent linear models (IETLMs) for model differentiation

“…Yet another challenge is the development of useful TLMs and adjoints for the model's parametrisations of the effects of poorly resolved processes (Janisková et al ., 1999; Janiskov'a et al ., 2002; Tompkins and Janisková, 2004; Janiskov'a and Morcrette, 2005; Lopez, 2011; Janisková et al ., 2012; Janisková and Lopez, 2013; Holdaway et al ., 2014; Holdaway and Errico, 2014; Holdaway et al ., 2015). Janisková and Lopez (2013) outline four major steps within this development; the first of which involves developing a simplified version of the non‐linear model's parametrisations that are more suitable for linearisation than the original parametrisation scheme.…”

An idealized test case for assessing the linearization of tracer transport schemes in NWP models

“…Beyond representing the inherent nonlinear behaviour of the atmosphere, models often rely on the use of highly nonlinear numerics. This can be to achieve the modelling of discrete‐like behaviour, as in the moist physics (Holdaway et al , 2015), or to control something undesirable, such as the removal of negative tracer densities. Note that there are ongoing attempts to overcome some of the assumptions fundamental in current data assimilation, though computational efficiency remains a significant challenge (van Leeuwen, 2009).…”