thermodynamics occurs in the form of the pressure gradient

force.

The foundation of the CMAQ’s multiscale capability is the

use of a consistent governing set of equations for

meteorological and air quality modeling applications as

proposed by Byun [28]. We can relate the generalized

meteorological curvilinear coordinates (

xˆ 1,xˆ 2 ,xˆ 3 ,tˆ ) in aconformal map projection to the rotated earth-tangential

coordinates (

x,y,z,t) as:

xˆ 1 =mx

xˆ 2 =my

xˆ 3 =s

tˆ =t

x=m−1xˆ 1

y=m−1xˆ 2

z=h(xˆ 1,xˆ 2,xˆ 3,tˆ ) =hAGL(xˆ 1,xˆ 2,xˆ 3,tˆ ) +zsfc(xˆ 1,xˆ 2 )

t=tˆwhere

mis the map scale factor,sis the generalizedmeteorological vertical coordinate,

zsfcis the topographicheight,

his the geometric height, andhAGLrepresents heightabove the ground level (AGL). Here,

sis a symbol for thegeneralized vertical coordinate and

zis a specific Cartesiancoordinate representing vertical displacement, i.e., height.

In the generalized coordinate system, the contravariant and

covariant wind components are represented with

vˆjandvˆk.The square root of the determinant of the metric (Jacobian)

where V

z= Vˆs/mis the horizontal wind vector representedin the Cartesian coordinate system, and

F3 is the forcingterm for the

w-component. The contravariant verticalvelocity component is related to the Cartesian vertical

velocity with:

With the ideal gas law, the thermodynamic variables (i.e.,

temperature, entropy, pressure gradients, and density) are

diagnostically related (Byun [28]). The entropy per unit

volume (entropy density), ζ is defined as

where

Tis temperature,Cvdis the specific heat capacity fordry air at constant volume, and

Rdis the dry air gasconstant.

Toois temperature of the reference atmosphere atthe reference pressure

poo= 105 Pascal. The atmosphericpressure is treated as a thermodynamic variable that is fully

defined by the density and entropy of the atmosphere. The

conservation equations for air density, entropy density, and

tracer concentrations are:

n1001 - n1002 - n1003 - n1004 - n1005 - n1006 - n1007 - n1008 - n1009 - n1010 - n1011 - n1012 - n1013 - n1014 - n1015 - n1016 - n1017 - n1018 - n1019 - n1020 - n1021 - n1022 - n1023 - n1024 - n1025 - n1026 - n1027 - n1028 - n1029 - n1030 - n1031 - n1032 - n1033 - n1034 - n1035 - n1036 - n1037 - n1038 - n1039 - n1040 - n1041 - n1042 - n1043 - n1044 - n1045 - n1046 - n1047 - n1048 - n1049 - n1050

castellano: DISPER CUSTIC DESCAR RADIA italiano:

castellano: DIS CUS DES RAD english: DIS CUS DES RAD

português: DIS CUS DES RAD italiano: DIS CUS DES RAD