21
Atms 4320 / 7320 Atms 4320 / 7320 Lab Lab On the use of isentropic On the use of isentropic maps in weather analysis maps in weather analysis and forecasting. and forecasting.

Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

  • View
    220

  • Download
    1

Embed Size (px)

Citation preview

Page 1: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

Atms 4320 / 7320 LabAtms 4320 / 7320 Lab

On the use of isentropic On the use of isentropic maps in weather analysis maps in weather analysis

and forecasting.and forecasting.

Page 2: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►Concept of potential Vorticity Concept of potential Vorticity (Pedlosky pp34 ff):(Pedlosky pp34 ff):

►Start with the N-S equation (x,y,z,t Start with the N-S equation (x,y,z,t coords):coords):

F

gVpdt

Vd

2

13

3

Page 3: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►Take the Take the curl curl of the momentum of the momentum equation to get the 3-dimensional equation to get the 3-dimensional vorticity equation:vorticity equation:

► (A)(A) (B)(B) (C) (C) (D)(D)

►a in this case is the 3-dimentional a in this case is the 3-dimentional vorticity: vorticity:

Fp

VVdtd

aa

2

Page 4: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►a in this case is the 3-dimentional a in this case is the 3-dimentional vorticityvorticity

kjiaˆˆˆ

Page 5: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

► term (A) is vortex tilting term -- variation of term (A) is vortex tilting term -- variation of velocity v perpendicular to the vorticity velocity v perpendicular to the vorticity filamentsfilaments

► term (b) vortex stretching termterm (b) vortex stretching term

► term (c) baroclinic production term (source of term (c) baroclinic production term (source of vorticity)vorticity)

► term (d) diffusive effects of Frictionterm (d) diffusive effects of Friction

Page 6: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►Use Continuity equation to combine Use Continuity equation to combine terms (a and b) to get:terms (a and b) to get:

►Consider a scalar that has this form:Consider a scalar that has this form:

233

Fp

Vdtd a

0, dtd

dtd

Page 7: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►Now dot vorticity equation with ( )Now dot vorticity equation with ( )

►to get a potential vorticity equation:to get a potential vorticity equation:

Fp

dtd aa

3

Page 8: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►Now Now potential vorticitypotential vorticity is is conserved if:conserved if:

► is conserved for each(adiabatic is conserved for each(adiabatic process)process)

►frictional force is negligiblefrictional force is negligible

►the fluid is barotropic, or the fluid is barotropic, or ((,p):,p):

a

Page 9: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►Potential Vorticity, given the proper Potential Vorticity, given the proper balance conditions, can be inverted to balance conditions, can be inverted to recover the “balanced” height field, recover the “balanced” height field, wind field, temperature field, etc. wind field, temperature field, etc. (Hoskins, 1985 QJRMS) (Hoskins, 1985 QJRMS)

►Potential Vorticity in Pressure Coords Potential Vorticity in Pressure Coords (No longer conserved!)(No longer conserved!)

Page 10: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►The expression (see Lupo and Bosart, The expression (see Lupo and Bosart, 1999)1999)

►How good an assumption is this? See How good an assumption is this? See Bosart and Lackmann (1995, MWR,) Bosart and Lackmann (1995, MWR,) Bosart and Lupo (1999, QJRMS), Bosart and Lupo (1999, QJRMS), Burkhardt and Lupo (2005, JAS).Burkhardt and Lupo (2005, JAS).

ppV

kgPV a

ˆ

Page 11: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

► PV maps: Usually we interpolate data to the PV maps: Usually we interpolate data to the x,y,x,y, coordinate system. Then we can coordinate system. Then we can examine PV on surfaces of Kelvin (potential examine PV on surfaces of Kelvin (potential temperature). Most commonly choose, 315 temperature). Most commonly choose, 315 K, 300 K, 280 K, etc.K, 300 K, 280 K, etc.

► Also, Eady postulated (1957), that surface Also, Eady postulated (1957), that surface disturbances grow and decay due to disturbances grow and decay due to disturbances on the upper “lid” disturbances on the upper “lid” (tropopause). (tropopause).

Page 12: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►This is the idea behind defining a This is the idea behind defining a tropopause based on Potential tropopause based on Potential Vorticity values. (Dynamic tropopause) Vorticity values. (Dynamic tropopause) (as the 2 PVU surface typically), and (as the 2 PVU surface typically), and examining quantities on that. examining quantities on that.

►This is as opposed to a This is as opposed to a “thermodynamic tropopuase” defined “thermodynamic tropopuase” defined as an isothermal layer by the WMO.as an isothermal layer by the WMO.

Page 13: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►Modern isentropic analysis involves Modern isentropic analysis involves examining Pressure, potential temperature, examining Pressure, potential temperature, on a potential vorticity surface (Lupo and on a potential vorticity surface (Lupo and Bosart, 1999 chose the 2 PVU surface). Read Bosart, 1999 chose the 2 PVU surface). Read Nielsen-Gammon and Lefevre (1996, JAS). Nielsen-Gammon and Lefevre (1996, JAS). Read Hoskins (1985, QJRMS)Read Hoskins (1985, QJRMS)

► I’ll pass out Morgan, M, and Nielsen-Gammon, I’ll pass out Morgan, M, and Nielsen-Gammon, J.W., (1998). This is a comprehensive guide J.W., (1998). This is a comprehensive guide for the use of these maps in the NH. In the for the use of these maps in the NH. In the SH, see Lupo et al. (2001, MWR). SH, see Lupo et al. (2001, MWR).

Page 14: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►The mapsThe maps

Page 15: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►Maps!Maps!

Page 16: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►Low pressure and trough regions tend Low pressure and trough regions tend to show up as areas of high to show up as areas of high tropopause pressure and “cold” tropopause pressure and “cold” potential temperatures.potential temperatures.

Page 17: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

High pressure and ridges tend to show High pressure and ridges tend to show up as areas of low tropopause up as areas of low tropopause pressure and “warm” potential pressure and “warm” potential temperatures. temperatures.

Page 18: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►At the surface, the opposite is true.At the surface, the opposite is true.

► Jet maxima tend to show up where the Jet maxima tend to show up where the isotherms, or isobars are “packed” isotherms, or isobars are “packed”

►Visit: Visit: www.atmos.albany.edu/deas/nwp.htmlwww.atmos.albany.edu/deas/nwp.html

Page 19: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

►The End!The End!

Page 20: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.

Page 21: Atms 4320 / 7320 Lab On the use of isentropic maps in weather analysis and forecasting

On the use of isentropic maps in On the use of isentropic maps in weather analysis and forecasting.weather analysis and forecasting.