A Data assimilation model for determining the mean state and - PowerPoint PPT Presentation

A Data assimilation model for determining the mean state and migrating tide structures in the mesosphere and lower thermosphere using satellite measurements of wind and temperature David Ortland NorthWest Research Associates (ortland@nwra.com) Contributions from: TIMED/TIDI and SABER science teams, University of Michigan, NCAR, Langely HRDI science team, University of Michigan Rolando Garcia, NCAR Ruth Lieberman, Co-RA

Introduction • Migrating tide and mean flow Analysis begins with separately components of the dynamic fields averaging all data from ascending u,v, and T are almost perfectly and descending nodes aliased in satellite measurements. Satellite sampling pattern of mean+tide • Although satellite precession 24 provides local time sampling, tide and mean flow variability over the 18 timer period required makes Time (hrs) harmonic analysis problematic. Ascending node 12 (Local midnight) • Information on tide and mean flow is contained in data binned by Descending node 6 track angle and altitude. This (Local noon) information can be extracted by 0 using u, v and T and the distinct 0 60 120 180 240 300 360 Longitude dynamical balance relations for At the equator diurnal, semi-diurnal and mean flow. 2

Basic Idea behind the assimilation method • Track-altitude cross section of either v in a single node or difference of T for ascending and descending nodes is mainly a superposition of the migrating diurnal and semi-diurnal tides. • Diurnal and semi-diurnal tides have distinct vertical and horizontal structural patterns that enable these two tides to be distinguished. • Once the tidal structures are known in one field they can be determined in the other fields and subtracted from the data to determine the zonal mean flow. • Sums and differences of ascending and descending node data in all three fields actually gives an over determined inverse problem and contributes to improved accuracy. • Almost enough information to solve the tide and mean separation problem is contained in the T field alone. Only an additional lower boundary condition is required. 3

SABER temperature and model fit (T ascending -T descending )/2 on 15-sep-2004 SABER asc-desc 15-Sep-2004 Model fit 60 3 6 4 36 24 2 12 12 110 110 0 40 0 0 12 -12 100 100 20 12 Alt (km) 0 12 0 K 90 90 -20 80 80 0 0 -40 0 0 0 0 0 70 70 -60 -80 -60 -40 -20 0 20 40 -80 -60 -40 -20 0 20 40 Diurnal asc-desc Semi-diurnal asc-desc 0 60 0 36 4 12 2 110 110 0 -12 40 0 0 0 100 100 20 1 2 Alt (km) 0 K 90 90 -20 0 80 80 0 -40 0 0 0 70 70 -60 -80 -60 -40 -20 0 20 40 -80 -60 -40 -20 0 20 40 Latitude Latitude 4

SABER temperature and model fit (T ascending+ T descending )/2 – T mean SABER-mean, asc+desc Diur+Sdiur asc+desc 0 10 0 -10 20 0 -10 0 0 40 110 110 1 20 10 0 0 1 10 20 100 100 Alt (km) 0 0 0 K 90 90 -20 0 80 80 -40 0 0 70 70 0 0 -80 -60 -40 -20 0 20 40 -80 -60 -40 -20 0 20 40 Latitude Diurnal asc+desc Semi-diurnal asc+desc 0 20 0 0 10 40 110 110 - 1 0 1 0 20 100 100 0 Alt (km) 0 0 0 K 90 90 -20 80 80 -40 0 70 0 70 0 -80 -60 -40 -20 0 20 40 -80 -60 -40 -20 0 20 40 Latitude Latitude 5

SABER temperature and model fit (T ascending+ T descending )/2 SABER asc+desc 15-Sep-2004 Model asc+desc 8 2 4 110 8 110 2 3 4 264 4 2 6 248 232 2 2 2 1 300 217 7 201 201 280 185 100 100 260 185 Alt (km) 185 240 90 90 K 201 201 220 200 80 80 180 217 217 160 70 70 -80 -60 -40 -20 0 20 40 -80 -60 -40 -20 0 20 40 SABER-diur-sdiur, asc-desc Zonal mean T 248 264 2 2 4 110 4 8 110 8 264 2 4 8 2 232 2 3 300 7 2 1 217 201 201 185 280 8 5 1 100 100 260 Alt (km) 240 90 90 K 2 0 1 201 220 200 80 80 180 217 217 160 70 70 -80 -60 -40 -20 0 20 40 -80 -60 -40 -20 0 20 40 Latitude Latitude 6

Assimilation model components • Tidal structures are determined using a time-dependent primitive equation model forced by heating at various altitude levels that has Hough function structure and run to steady state. • Both the diurnal and semi diurnal tides are represented as linear combinations of the mode-like responses determined in this way. • Tidal structure is also controlled by the background mean flow, dissipation mechanisms and interaction with gravity waves. The dissipation and GW effects are represented by a small number of parameters that are determined via an off-line nonlinear least-squares fitting. • The zonal mean u and T are represented in terms of a linear combination of geostrophic ‘modes’. • The assimilation is accomplished by fitting the coefficients of these linear expansions to the data. 7

Why GW forcing is necessary: Model simulations of the tide reproduce the observed vertical wavelength only if gravity waves are included HRDI v, March 94 at 12h TIDI v, March 04 at 12h 110 110 20 0 6 0 -40 0 -20 6 -60 - -80 60 0 60 TIDI 105 40 105 40 40 -40 HRDI 0 20 2 0 0 4 100 0 100 -20 - 0 Altitude (km) 0 - 2 -20 80 0 95 95 80 0 60 - 6 0 20 -40 40 -20 90 20 90 0 0 -20 85 85 0 -20 -60 0 20 -20 2 40 - 80 - 4 0 80 0 0 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 Model with no GW Model with GW 0 0 20 -40 4 0 0 -20 -20 Model GW force 0 20 105 105 diurnal tide included 100 100 Altitude (km) simulations: 0 6 60 - 40 -40 95 95 20 -20 80 0 60 -60 4 -40 0 90 90 -20 20 No GW 0 - 4 0 85 85 -40 -20 force 0 20 2 20 40 - 0 0 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 Latitude Latitude 8

Diurnal tide basis functions Generated with a linear tidal model, GW forcing, eddy, molecular diffusion; URAP March wind/temperature background; Forced in a thin layer by heating with a Hough function horizontal structure Temperature Zonal wind Meridional wind Forcing 110 110 110 100 100 100 Altitude 90 90 90 (1,1) 80 80 80 70 70 70 60 60 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 110 110 110 100 100 100 Altitude 90 90 90 (1,2) 80 80 80 70 70 70 60 60 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 110 110 110 100 100 100 Altitude 90 90 90 (1,3) 80 80 80 70 70 70 60 60 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 110 110 110 100 100 100 (1,-2) Altitude 90 90 90 80 80 80 70 70 70 60 60 60 9 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 Latitude Latitude Latitude

Semi-diurnal tide basis functions Tide patterns are distinct from each other and from the geostrophic modes (But maybe not distinct from terdiurnal tide?) Temperature Zonal wind Meridional wind Forcing 110 110 110 100 100 100 Altitude (2,1) 90 90 90 80 80 80 70 70 70 60 60 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 110 110 110 100 100 100 Altitude 90 90 90 (2,2) 80 80 80 70 70 70 60 60 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 110 110 110 100 100 100 Altitude 90 90 90 80 80 80 (2,3) 70 70 70 60 60 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 110 110 110 100 100 100 Altitude 90 90 90 (2,4) 80 80 80 70 70 70 60 60 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 Latitude Latitude Latitude 10

Construction of geostrophic modes used to represent zonal mean wind and temperatures Vertical structure Geopotental and U Zonal wind Horizontal structure of U 4 110 110 2 100 100 dH n ( θ ) V m (z) Altitude Altitude 0 90 90 -2 80 80 70 70 -4 -2 -1 0 1 2 3 -50 0 50 0 20 40 60 Latitude Latitude Φ = − d u nm ( θ ,z) =dH n ( θ) V m (z) Geopotential fu 110 d θ 100 Altitude 90 80 70 Φ = d RT T nm ( θ ,z) =H n ( θ) dV m (z) -50 0 50 Latitude dz H Horizontal structure Geopotential and T Temperature Vertical structure of T 3 110 110 2 1 100 100 Altitude Altitude dV m (z) H n ( θ ) 0 90 90 -1 80 80 -2 -3 70 70 0 20 40 60 -50 0 50 -0.4 -0.2 0.0 0.2 0.4 11 Latitude Latitude

Validation experiment: proof of concept • Use WACCM 1b run for the month of January to simulate a ‘real’ atmosphere sampled by TIMED TIDI and SABER tangent point locations. • Use Fourier analysis to determine WACCM tide, mean flow and planetary waves structures. • Individual structures can be removed from the WACCM fields to test the sensitivity of the assimilation method to their presence. 12