Spatial Reduction Algorithm for Numerical Modeling of Atmospheric Pollutant Transport Yevgenii Rastigejev, Philippe LeSager Harvard University Michael P. Brenner, Daniel J. Jacob April, 2007

Motivation Problem: There is an urgent need to improve significantly computational performance of the existing GEOS-Chem code motivated by difficulties with numerical simulation of immerging applications Solution: To create a multi-scale numerical algorithm which provides a significant (order of magnitude) reduction in computational cost Slow Region Fast Region Our algorithm is inspired by the observation that atmospheric emissions have most of their fast reactants and their quickly decomposing reaction products localized near the emitter, typically on the ground. Far from the emitter, the fast reactants do not play a significant role.

Solution: Spatial Reduction In the Slow region For the algorithm to be efficient: size Slow Region >> size Fast Region comp. cost Slow Region << comp. cost Fast Region Fast Region – the species is fully accounted as a dependent variable in the system of transport equations Slow Region – the species concentration is found through extrapolation or Chemical source r Fast Slow D

Gradual Spatial Reduction Consider a two species reaction system, comprised of chemicals A and B The central idea of our algorithm is to track a series of chemical boundary layers (CBL) within which the gradual, continuous spatial reduction is employed from the domain where the full mechanism is needed to the domain where the most simplified mechanism is sufficient. Slow Fast Slow AB A,BA,B A B Domain partitioning for A and B 2 eqn 1 eqn

 Fast-Slow domain partitioning algorithm  Algorithms for Reduced Model construction  Matching procedure  Efficient methodology for adaptation in time Prerequisites for Spatial Reduction Numerical Method Fast Slow Fast if Slow otherwise Domain partitioning

Matching conditions matching procedure for concentration values and mass fluxes ensures good mass conservation and continuity properties of the numerical scheme Reduced model – exponential extrapolation into Slow region Fast Slow exp. decay rate distance exp. decaying concentration

Adaptive algorithm summary

Chemical model oxidation of a number of C3H6 in an OH oxidizing atmosphere, with NOx serving as catalyst through the cycling of HOx radicals 15 chemical species and 24 reactions chemical flux O3O3 OHHO 2 NO 2 NO O3O3 OHHO 2 NO 2 NO O3O3 OHHO 2 NO 2 NO

Fast Slow Fast – Slow domain partitioning for the atmosphere with horizontal shear layer flow at time Comparison of species distribution obtained by the spatial reduction algorithm (spheres and cubes) and conventional method (solid line) depicted in blue and red colors at and at correspondingly at time Max err = 2-3 % Average err = 0.5 %

Some preliminary conclusions  A gradual continuous spatial reduction computational method for Atmospheric chemistry has been developed.  Unlike conventional time-scale separation methods, the spatial reduction algorithm allows to speed up not only a "chemical solver" but also advection- diffusion numerical integration.  The method produced accurate results at 5-6 times lower computational cost for the 2-dimensional Atmospheric chemistry problems tested.  Currently we are working on the algorithm implementation into GEOS-Chem three-dimensional solver. To be continued with three-dimensional description …

G-C Implementation Old SOLVER (SMVGEAR) New SOLVER (DLSODES)

Criteria for CBLs [ n ] > Threshold Values OR Net Production > Max Value 54% of ODE solved averaged RMS error of 7.2% Run Time = 0.66 Full Resolution Case

Nb of Species

Short lived species : Max error in the outskirts of concentration peaks

Transported tracer: Max error further away from concentration peaks.

To be continued… 1) Better CBLs ( combining absolute/relative criteria, discriminating b/w species, fine tuning ) 2) Extrapolation mechanism will substantially reduce the error in the slow region noticeably reduce the size of the fast region 3)Full advantage of sparse structure substantial speed up