Teddie Keller Rich Rotunno Matthias Steiner Bob Sharman Orographic Precipitation and Climate Change Workshop NCAR Boulder CO 14 Mar 2012 Miglietta M M R Rotunno 2005 Simulations of Moist Nearly Neutral Flow over a Ridge J Atmos Sci 62 14101427 ID: 262098
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Slide1
Upstream propagating wave modes in moist and dry flow over topography
Teddie Keller
Rich Rotunno, Matthias Steiner, Bob Sharman
Orographic Precipitation and Climate Change Workshop
NCAR, Boulder, CO 14 Mar 2012 Slide2
*Miglietta, M. M., R. Rotunno, 2005: Simulations of Moist Nearly Neutral Flow over a Ridge. J. Atmos. Sci., 62, 1410-1427
Background flow:
2 layer troposphere-stratosphere profile. Moist nearly neutral flow troposphere. Constant wind.
Vertical velocity contours at 5
hrs
Note W cells 100 km upstream of mountain
W perturbation fills depth of troposphere
Associated with W cells is a midlevel zone of
desaturated
air extending upstream
Cloud water content (white q
c
< .01 g kg-1).
5 hr
W
q
c
Miglietta
and
Rotunno
- investigated saturated, moist nearly neutral flow over topography*
Motivation
- n
early
moist neutral
flow
soundings observed during
Mesoscale
Alpine Program. May be important to non-convective flood producing events.
Slide3
Expanding on
Miglietta
and
Rotunno
Steiner et al.* conducted a series of 2-D idealized simulations of both moist and dry flow over topography
Similar background flow conditions – 2-layer stability, constant windVaried wind speed, stability, mountain height and half-width
WRF version 1.3Initially focused on comparing long-time solutions for moist and dry flow
Investigation of temporal evolution of flow revealed similar upstream propagating mode as MR2005*Steiner, M, R.
Rotunno, and W. C. Skamarock, 2005: Examining the moisture effects on idealized flow past 2D hills. 11th Conference on Mesoscale
Processes, 24-29 October 2005, Albuquerque, NM.Slide4
Example - W and RH for saturated flow
Vertical velocity (lines)
Relative humidity (color)
Animation
from 2 to 9 hours
Desaturated zone associated with upstream propagating mode
Background flow: Initially saturated Trop N
m = .002 s-1 U = 10 ms-1 Isothermal stratosphere
Witch of Agnesi mountain height 500 m half-width 20 kmRH:
W cont .02 ms-1Nh/U = .1Slide5
But – dry simulations also show upstream propagating mode
Vertical velocity contours (color)
Animation
from 3 to 23.5 hours
Background flow:
U = 10 ms-1 Tropospheric stability .004 s
-1 Isothermal stratosphere Witch of Agnesi
mountain height 500 m half-width 20 kmNh
/U = .2W cont .01 ms-1Slide6
Upstream propagating wave and desaturated region in moist flow
Is this related to upstream propagating waves in dry flow?
Are modes partially trapped by stability jump at tropopause?
Linear or nonlinear phenomena?
Use simplified models to investigate upstream wave modes
Linear, hydrostatic analytic solution
Nonhydrostatic
, nonlinear gravity wave numerical model Slide7
Single layer analytic solution
Time-dependent, linear analytic solution based on
Engevik
*
Troposphere only - constant U, N
Rigid lid replaces tropopauseAssume hydrostatic wave motionRotunno
derived and coded solution for W
*Engevik, L, 1971: On the Flow of Stratified Fluid over a Barrier. J. Engin. Math., 5, 81-88Slide8
Steady state wave
Left moving transient modes
Right moving transient modes
Steady state solution plus sums over left and right moving transient modes
n
Solution depends on
K
(=
N
Z
t
/ πU0 ), i.e., depends on background wind and stability as well as the layer depth
Transient wave
speed c
± =
U0(
1 ±
K/n)
Upstream modes traveling faster than the background wind penetrate upwind (i.e., c
-
/U0 < 0)
Number and speed of modes penetrating upwind depends on K
Time-dependent analytic solution
Mountain profile
η
(x)Slide9
Time-dependent analytic solutions for W
Vary K by changing N and Z
t
0-20 hrs
One mode propagating upstream
K (=
NZ
t
/ πU0
) = 1.15U=10ms
-1, N=.0036s-1, Z=10km
Two modes propagating upstream
W*50 ms-1
W*50 ms
-1
K (=
NZ
t
/ πU
0) = 2.3
U=10ms-1
, N=.006s-1, Z=12km
Mountain profile η(x)=h0
/(1+(x/a)
2
); h=10m, a=20kmSlide10
Only transient modes with c
-
/U
0
< 0 actually
appear
upwind
Thus for a given
K
will see only
nk modes upstream, where nk is the largest integer less than
K (i.e., nk < K < (n
k +1) )Speed of a particular mode penetrating upwind depends on KWave speed vs K for modes propagating faster than background wind
C
-
/
U
0= 1
- K/n
Wave speed
vs
K for c
-/U
< 0Slide11
Numerical simulations – gravity wave model*
Use to simulate both rigid lid and linear/nonlinear 2-layer troposphere-stratosphere stability profile
Time-dependent, nonhydrostatic
Boussinesq
Option for either linear or nonlinear advection termsNo coordinate transformation – mountain introduced by specifying w (=
Udh/dx) at lower boundaryMountain can be raised slowly
*Sharman
, R.D. and Wurtele, M.G., 1983: Ship Waves and Lee Waves. J. Atmos. Sci., 40, 396-427Slide12
Same upstream waves in rigid lid and troposphere-stratosphere simulations
U = 10 m/s, N = .0045/s, Z = 12 km, K = 1.7
time 0 - 5.5 hrs
Mountain half-width 20 km height
a-b)10 m, c) 1.5 km. W cont
.
int
.05
m s
-1
, W multiplied by
50 in a), 100 in b)
Nonlinear troposphere-stratosphere
Linear troposphere-stratosphere
Linear – rigid lid replaces tropopause
W*50 (ms
-1
)
W*100 (ms
-1
)
W (ms
-1)Nh
/U = .68Slide13
Upstream propagating waves
Fundamental feature of both linear and nonlinear dry numerical simulations
In both WRF and G.W. models
Similar to transient modes seen in analytic solution for single tropospheric layer capped by rigid lid
Similar behavior of upstream modes for moist flowSlide14
WRF - upstream
modes saturated flow –
vary background wind speed
For stronger background wind speed (U=20 ms
-1
) all modes are swept downstream
As with dry case, 1
st mode able to penetrate upwind as K increases (K10 > K
20)Similar to dry simulations, except can’t substitute moist stability in Km (=N
mZt/πU
0)
U = 20
U = 10N=.002s-1, Z=11.5km
.37, .73Slide15
W (lines) and RH (color) at 5 hr
Speed of wave and desaturated region increases with increasing N
m
(i.e. increasing K)
But - can
’
t simply use N
m
to calculate K
N
m = .002
Nm = .004WRF saturated simulations- upstream mode 1 speed increases with increasing K
(K=NmZt/πU0; .73 and 1.46)Slide16
Saturated background flow
Transient upstream modes similar to dry flow
Region of desaturation extends upwind with wave
What if background flow is
subsaturated
?Slide17
Background flow 70% relative humidity
W (lines) and RH (color)
Simulation time 2 hours
Upstream mode associated with region of
increased
relative humidity upwind of mountainCould transient upstream propagating wave modes influence precipitation upwind of mountain?
Slide18
Summary -
Analytic solution shows transient upstream propagating waves a feature of linear, hydrostatic dry flow over topography
Same modes appear in dry troposphere-stratosphere numerical simulations
Propagation speed depends on tropospheric wind, stability and
tropopause
depth Speed of upstream propagating wave and desaturated region in saturated moist flow follows similar trend
For subsaturated flow – upstream mode may increase RHSlide19
Are these transient modes important for orographic precipitation?
Maybe…
Numerical simulations contain transients
Transients can alter moisture content of air impinging on mountain
When upstream wave speed only slightly greater than U
0
the transient wave modes may dominate upwind for hoursMay influence spatial distribution of precipitation upwind of mountainsImportant to be aware of this possibility when scrutinizing numerical simulations
Could play a role when background atmospheric conditions rapidly changing?