The composite-tendency Robert-Asselin-Williams (RAW) filter in semi-implicit integrations

Timediscretization in weatherandclimate modelsintroduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leap-frog integrations from first-order to fifth-order.This improvement is achieved by replacing the Robert–Asselin filter with the Robert–Asselin–Williams (RAW) filter and using a linear combination of unfiltered and filtered states to compute the tendency term. The purpose of the present article is to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model and yields substantial improvements in both cases. We conclude that the composite-tendency RAW-filtered leap-frog scheme is suitable for use in semi-implicit integrations.

University of Michigan Men's Basketball Team, 1998

Back Row: ?, ?, Travis Conlan, Brandon Smith, Darius Taylor, Robbie Reid, ?,

Front Row: Ron Oliver, Jerod Ward, Josh Asselin, Robert Traylor, Peter Vignier, Erik Szyndlar, Louis Bullock

University of Michigan Men's Basketball Team, 1998

L-R: Ron Oliver (25), Darius Taylor (10), Jerod Ward (32) Robbie Reid (3), Peter Vignier (55), Robert Traylor (54), Josh Asselin (25), Travis Conlan (21), Maceo Baston (30), Brandun Smith (34), Louis Bullock (11)

University of Michigan Men's Basketball Team, 1999

Back Row: asst. coach Scott Trost, asst. coach Kurtis Townsend, Leon Jones, Brandon Smith, Chris Young, Josh Asselin, Peter Vignier, Erik Szyndlar, Darius Taylor, coach Brian Ellerbe

Front Row: equip. mngr. Bob Bland, asst. coach Lorenzo Neely, Donte Scott, Robbie Reid, Louis Bullock, Ron Oliver, admin. assoc. Tom Sorboro, trainer Steve Stricker

University of Michigan Men's Basketball Team, 2000

Back Row: Assistant Tom Sorboro, Assistant Kurtis Townsend, Darius Taylor, Rotolu Adebiyi, Brandon Smith, Josh Asselin, Peter Vignier, Chris Young, Leland Anderson, LaVell Blanchard, Herb Gibson, Assistant Scott Trost, Assistant Lorenzo Neely.

Front Row: Trainer Steve Stricker, Mike Gotfredson, Gavin Groninger, Kevin Gaines, head coach Brian Ellerbe, Jamal Crawford, Leon Jones, Ramal Hunter, equip. mngr. Bob Bland.