Nonlinear Advection Algorithms Applied to Interrelated Tracers : Errors and Implications for Modeling Aerosol-Cloud Interactions

Monotonicity constraints and gradient-preserving flux corrections employed by many advection algorithms used in atmospheric models make these algorithms nonlinear. Consequently, any relations among model variables transported separately are not necessarily preserved in such models. These errors cann...

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Bibliographic Details
Published in:Monthly weather review 2009-02, Vol.137 (2), p.632-644
Main Authors: OVTCHINNIKOV, Mikhail, EASTER, Richard C
Format: Article
Language:English
Subjects:
Advection
Aerosol-cloud interactions
Aerosols
Algorithms
Atmospheric models
Atoms & subatomic particles
Cloud particles
Clouds
Constraint modelling
Corrections
Earth, ocean, space
Energy conservation
Errors
Exact sciences and technology
External geophysics
Flow velocity
Fluctuations
Meteorology
Mixing ratio
Modelling
Particle size distribution
Ratios
Scalars
Sums
Tracers
Variables
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Summary:Monotonicity constraints and gradient-preserving flux corrections employed by many advection algorithms used in atmospheric models make these algorithms nonlinear. Consequently, any relations among model variables transported separately are not necessarily preserved in such models. These errors cannot be revealed by traditional algorithm testing based on advection of a single tracer. New types of tests are developed and conducted to evaluate the monotonicity of a sum of several number mixing ratios advected independently of each other-as is the case, for example, in models using bin or sectional representations of aerosol or cloud particle size distributions. The tests show that when three tracers with an initially constant sum are advected separately in one-dimensional constant velocity flow, local errors in their sum can be on the order of 10%. When cloudlike interactions are allowed among the tracers in the idealized "cloud base" test, errors in the sum of three mixing ratios can reach 30%. Several approaches to eliminate the error are suggested, all based on advecting the sum as a separate variable and then using it to normalize the sum of the individual tracers' mixing ratios or fluxes. A simple scalar normalization ensures the monotonicity of the total number mixing ratio and positive definiteness of the variables, but the monotonicity of individual tracers is no longer maintained. More involved flux normalization procedures are developed for the flux-based advection algorithms to maintain the monotonicity for individual scalars and their sum. [PUBLICATION ABSTRACT]
ISSN:0027-0644
1520-0493
DOI:10.1175/2008mwr2626.1