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Thermosphere-Ionosphere ����������� ��������������������������������� ����������� ������������� �������� ������ �� ����� ������� ������������������������������������������� ������������� �������� ������ ���������������������������������������� ������������������������������� ����� ������� ���� ��� ���� ��������������������������������������������������������������������� ��������������������������������������� ������� ����������� ����� �������������������������������������������� ������� ����������� ����� ����� ����� �������������������������������� �������� ���� ����� ���� ����� �������� �� ���������� ������������ �� �������� ������ ��� ����������� �������� ���� ����� ���� ����� �������� �� ���������� ������ ��������������������������������������������������������������������������� ����� ������� ����� ��� �������� ���� ��� ������������ �� ������������ ��������������������������������������������������������������������������� ����� ������� ����� ��� �������� ���� ��� ������������ �� ������������ Thermosphere-Ionosphere-Electrodynamics General Circulation Model TIEGCM Maura Hagan Jiuhou Lei, Gang Lu Ray Roble, Art Richmond, Stan Solomon Ben Foster, Astrid Maute, Liying Qian High Altitude Observatory National Center for Atmospheric Research Boulder, Colorado USA 12 May 2006 ICTP Space Weather School Maura Hagan - 1 - TIEGCM Objectives • Describe the chemistry, dynamics and electrodynamics of the Earth’s upper atmosphere within a mathematical framework • Diagnose the Earth’s upper atmosphere; develop understanding by comparing model results with observations • Predict future conditions of the Earth’s upper atmosphere (e.g., thermospheric cooling associated with increased CO2) • Strategies: – 1-D: column model (global mean) – 2-D: zonal averages (height & latitude) – 3-D: global 12 May 2006 ICTP Space Weather School Maura Hagan - 2 - Historical Development of TIEGCM • TGCM; an adaptation of the NCAR climate model (ca.1970) – 97 to 500 km (solar minimum) – solar EUV heating – thermospheric composition – molecular diffusion – parameterized ionosphere • TIGCM (ca. 1988) – added ionospheric chemistry and dynamics Ray Roble – parameterized electric fields • TIEGCM (ca. 1992) – added self-consistent low and middle latitude electrodynamics – parameterized high-latitude Art Richmond electrodynamics 12 May 2006 ICTP Space Weather School Maura Hagan - 3 - Thermosphere-Ionosphere-Electrodynamics General Circulation Model TIEGCM Part 1: Model Overview • functional description • references • select formulations and numerical schemes 12 May 2006 ICTP Space Weather School Maura Hagan - 4 - TIEGCM Functional Description • comprehensive, first-principles, three-dimensional, non-linear representation of the coupled thermosphere and ionosphere system, including a self-consistent solution of the middle and low- latitude dynamo field, • solves the 3-D momentum, energy and continuity equations for neutral and ion species at each time step (typically 120–180s), • employs a semi-implicit, fourth-order, centered finite difference scheme on each pressure surface in a staggered vertical grid, • runs in either serial or parallel mode on a variety of platforms, including Linux workstations and supercomputers. The standard low-resolution grid parameters are: • Latitude: -87.5° to 87.5° in 5° increments • Longitude: -180° to 180° in 5° increments • Altitude: 29 pressure levels from -7 to +6.5 in increments of 2 grid points per scale height • Lower boundary: ~97 km • Upper boundary: ~500–700 km depending on solar activity 12 May 2006 ICTP Space Weather School Maura Hagan - 5 - NCAR TIEGCM Development References: Dickinson, R. E., E. C. Ridley and R. G. Roble, A three-dimensional general circulation model of the thermosphere, J. Geophys. Res., 86, 1499-1512, 1981. Dickinson, R. E., E. C. Ridley and R. G. Roble, Thermospheric general circulation with coupled dynamics and composition, J. Atmos. Sci., 41, 205-219, 1984 . Richmond, A. D., E. C. Ridley and R. G. Roble, A Thermosphere/Ionosphere General Circulation Model with coupled electrodynamics, Geophys. Res. Lett., 19, 601-604, 1992. Roble, R. G., and E. C. Ridley, An auroral model for the NCAR thermospheric general circulation model (TGCM), Annales Geophys., 5A, 369-382, 1987. Roble, R. G., E. C. Ridley and R. E. Dickinson, On the global mean structure of the thermosphere, J. Geophys. Res., 92, 8745-8758, 1987. Roble, R. G., E. C. Ridley, A. D. Richmond and R. E. Dickinson, A coupled thermosphere/ionosphere general circulation model, Geophys. Res. Lett., 15, 1325- 1328, 1988. Roble, R. G., and E. C. Ridley, A thermosphere-ionosphere-mesosphere-electrodynamics general circulation model (time-GCM): equinox solar cycle minimum simulations (30- 500 km), Geophys. Res. Lett., 21, 417-420, 1994. Roble, R. G., Energetics of the mesosphere and thermosphere, AGU, Geophysical Monographs, eds. R. M. Johnson and T. L. Killeen, 87, 1-22, 1995. 12 May 2006 ICTP Space Weather School Maura Hagan - 6 - TThheerrmmooddyynnaammiicc eeqquuaattiioonn -- ggeenneerraall ffoorrmm "T "T (Q # L ) = #($ + )% #U & 'T + tot tot "t "Z C p diabatic adiabatic heating ! heating & cooling T temperature heat advection Γ atmospheric stability Z vertical coordinate ln(Po/P) ω vertical velocity = "Z "t U horizontal velocity vector Qtot total heating rate Ltot total cooling rate Cp specific heat per unit mass ! ! 12 May 2006 ICTP Space Weather School Maura Hagan - 7 - TTIIEEGGCCMM TThheerrmmooddyynnaammiicc eeqquuaattiioonn Z * $ '. "T ge " , KT "T 2 g 1 "T , = + + KE H Cp#& + )/ "t PoCp "Z -, H "Z % Cp H "Z (0, '& T RT * (Q " L) "U # $T "%) + , + &Z C m C ! ( p + p g gravitational acceleration -4 Po reference pressure; 5x10 µbar KT molecular thermal conductivity H scale h!eig ht KE eddy diffusion coefficient = eddy thermal conductivity ρ total mass density m mean molecular mass Q heating rate L total cooling rate 12 May 2006 ICTP Space Weather School Maura Hagan - 8 - ! TTIIEEGGCCMM TThheerrmmooddyynnaammiicc eeqquuaattiioonn diabatic heating • absorption of solar radiation - UV and EUV • absorption of energetic particles • chemical heating - exothermic reactions • ion - neutral collisions; Joule heating Schematic absorption diabatic cooling of • airglow UV and EUV…. • CO2 infrared cooling up next • nitric oxide (NO) infrared cooling 12 May 2006 ICTP Space Weather School Maura Hagan - 9 - Solar UV & EUV photoelectron heating photoionization O2 + hν O + O N2 + hν N + N electron ionosphere major minor and with O+ species species and Τε Σnn with O Σnn species Σnn Ion diffusion: diffusion diffusion T Σn 2 energy n O + N + NO+ i O O and N( D) 2 2 2 4 equation N+ in PCE* N N( S) 2 NO *photochemical equilibrium heating heating Ion/neutral neutral O chemistry gas recombination energy equation heating electron/ion/neutral collisions heating neutral-neutral chemistry 12 May 2006 ICTP Space Weather School Maura Hagan - 10 - CCoonnttiinnuuiittyy EEqquuaattiioonn -- ggeenneerraall ffoorrmm "#n + $ %(#nU) = CSn &CRn "t transport chemical production & loss ρn ! mass density of species, n U wind velocity vector CSn mass source of minor species, n CRn mass sink of minor species, n # " = n mass mixing ratio of species, n, for total mass density, ρ n # "# n +U $ %# = S & R "t n n n ! S source of minor species, n CS " CR n S " R = n n R sink of minor species, n n n n #n 12 May 2006 ICTP Space Weather School Maura Hagan - 11 - ! ! TIEGCM Minor Neutral Species Transport: "#n $Z " % " ( = $e Dn $ En #n + Sn $ Rn "t "Z &'" Z )* ( '%n + Z ' "Z ( ' 1 'm+ " V # $%n +& + e e KE (Z) + %n )* 'Z ,- 'Z )*' Z m 'Z ,- ! Ψn mass mixing ratio of minor species, n D molecular diffusion coefficient ! n En gravitational, thermal diffusion, and frictional interaction with the major species; $ mn 1 #m' 1 #T &1 " " ) "*n + F+n % m m #Z ( T #Z mn mass of the minor species, n m average mass of the major species ! 12 May 2006 ICTP Space Weather School Maura Hagan - 12 - ! TTIIEEGGCCMM SSoolluuttiioonn -- CCoonnttiinnuuiittyy EEqquuaattiioonnss -- 11 derivatives become finite differences at model grid points – for each specie, i – at every grid point, x grid spacing, Δx – at every time, t time step, Δt Chemistry "# i = S $ R "t i i Sufficiently small time step - explicit: m+1 m t S t , m R t , m "i =!" i + # $[ i ( m "i ) % i ( m "i )] Otherwise - implicit: m+1 m t S t , m+1 R t , m+1 "i = "i + # $[ i ( m+1 "i ) % i ( m+1 "i )] ! ! 12 May 2006 ICTP Space Weather School Maura Hagan - 13 - TTIIEEGGCCMM SSoolluuttiioonn -- CCoonnttiinnuuiittyy EEqquuaattiioonnss -- 22 derivatives become finite differences at model grid points – for each specie, i – at every grid point; grid spacing, Δx – at every time step, Δt Eulerian Transport "#i "Fi + = 0 for flux, Fi = c"i "t "x leap-frog method: ! m+1 m#1 $t m m ! "i, j = "i, j # %[Fi , j+1 # Fi , j#1 ] $x "t if c #1 (CFL stability condition) "x ! ! 12 May 2006 ICTP Space Weather School Maura Hagan - 14 - TTIIEEGGCCMM SSoolluuttiioonn -- CCoonnttiinnuuiittyy EEqquuaattiioonnss -- 33 derivatives become finite differences at model grid points – for each specie, i – at every grid point; grid spacing, Δx – at every time step, Δt Diffusion "# " $ "# ' i = & K i ) for diffusion coefficient, K > 0 "t "x % "x ( explicit: m+1 m ! "i, j # "i, j K m m m "t ! = " # 2" + " stable if 2K 2 #1 $t ($x) 2 ( i , j+1 i , j i, j#1 ) ("x) implicit: m+1 m " # " K m+1 m+1 m#1 i, j i, j = " # 2" + " ! $t ($x) 2 ( i , j+1 i , j i , j+1 ) ! 12 May 2006 ICTP Space Weather School Maura Hagan - 15 - ! EEqquuaattiioonnss ooff NNeeuuttrraall MMoottiioonn ( + . 1 " U# " U% " " g " U% " p " U# = $ U# $ U#
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