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Upstream propagating wave modes in moist and dry flow over Upstream propagating wave modes in moist and dry flow over

Upstream propagating wave modes in moist and dry flow over - PowerPoint Presentation

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Upstream propagating wave modes in moist and dry flow over - PPT Presentation

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

upstream flow wave modes flow upstream modes wave background speed propagating dry moist simulations mountain transient solution mode troposphere

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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?