Upstream propagating wave modes in moist and dry flow over topography

1. 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

2. W 5 hr qc Miglietta and Rotunno - investigated saturated, moist nearly neutral flow over topography* Vertical velocity contours at 5 hrs Note W cells 100 km upstream of mountain W perturbation fills depth of troposphere Motivation- nearly moist neutral flow soundings observed during Mesoscale Alpine Program. May be important to non-convective flood producing events. Associated with W cells is a midlevel zone of desaturated air extending upstream Cloud water content (white qc < .01 g kg-1). Background flow: 2 layer troposphere-stratosphere profile. Moist nearly neutral flow troposphere. Constant wind. *Miglietta, M. M., R. Rotunno, 2005: Simulations of Moist Nearly Neutral Flow over a Ridge. J. Atmos. Sci., 62, 1410-1427

3. 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 wind • Varied wind speed, stability, mountain height and half-width • WRF version 1.3 • Initially 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.

4. 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 Nm = .002 s-1 • U = 10 ms-1 • Isothermal stratosphere • Witch of Agnesi mountain • height 500 m • half-width 20 km RH: W cont .02 ms-1 Nh/U = .1

5. 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 km W cont .01 ms-1 Nh/U = .2

6. 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

7. Single layer analytic solution Time-dependent, linear analytic solution based on Engevik* Troposphere only - constant U, N Rigid lid replaces tropopause Assume hydrostatic wave motion Rotunno derived and coded solution for W *Engevik, L, 1971: On the Flow of Stratified Fluid over a Barrier. J. Engin. Math., 5, 81-88

8. Time-dependent analytic solution Left moving transient modes Right moving transient modes Steady state wave • Steady state solution plus sums over left and right moving transient modes n • Solution depends on K (= N Zt/ 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 Mountain profile η(x)

9. W*50 ms-1 W*50 ms-1 Time-dependent analytic solutions for WVary K by changing N and Zt 0-20 hrs One mode propagating upstream Two modes propagating upstream K (= NZt/ πU0) = 1.15 U=10ms-1, N=.0036s-1, Z=10km K (= NZt/ πU0) = 2.3 U=10ms-1, N=.006s-1, Z=12km Mountain profile η(x)=h0/(1+(x/a)2); h=10m, a=20km

10. Wave speed vs K for c-/U < 0 Wave speed vs K for modes propagating faster than background wind C- /U0= 1 - K/n • Only transient modes with c- /U0 < 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 < (nk +1) ) • Speed of a particular mode penetrating upwind depends on K

11. 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 terms • No coordinate transformation – mountain introduced by specifying w (= Udh/dx) at lower boundary • Mountain can be raised slowly *Sharman, R.D. and Wurtele, M.G., 1983: Ship Waves and Lee Waves. J. Atmos. Sci., 40, 396-427

12. Linear – rigid lid replaces tropopause Linear troposphere-stratosphere Nonlinear troposphere-stratosphere W*50 (ms-1) W*100 (ms-1) W (ms-1) Same upstream waves in rigid lid and troposphere-stratosphere simulations time 0 - 5.5 hrs Nh/U = .68 U = 10 m/s, N = .0045/s, Z = 12 km, K = 1.7 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)

13. 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 flow

14. For stronger background wind speed (U=20 ms-1) all modes are swept downstream As with dry case, 1st mode able to penetrate upwind as K increases (K10 > K20) Similar to dry simulations, except can’t substitute moist stability in Km (=NmZt/πU0) WRF - upstream modes saturated flow –vary background wind speed U = 20 U = 10 N=.002s-1, Z=11.5km .37, .73

15. WRF saturated simulations- upstream mode 1 speed increases with increasing K • W (lines) and RH (color) at 5 hr • Speed of wave and desaturated region increases with increasing Nm (i.e. increasing K) • But - can’t simply use Nm to calculate K Nm = .002 Nm = .004 (K=NmZt/πU0; .73 and 1.46)

16. Saturated background flow • Transient upstream modes similar to dry flow • Region of desaturation extends upwind with wave • What if background flow is subsaturated?

17. W (lines) and RH (color) Simulation time 2 hours Upstream mode associated with region of increased relative humidity upwind of mountain Could transient upstream propagating wave modes influence precipitation upwind of mountain? Background flow 70% relative humidity

18. 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 tropopausedepth • Speed of upstream propagating wave and desaturated region in saturated moist flow follows similar trend • For subsaturated flow – upstream mode may increase RH

19. 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 U0 the transient wave modes may dominate upwind for hours • May influence spatial distribution of precipitation upwind of mountains • Important to be aware of this possibility when scrutinizing numerical simulations • Could play a role when background atmospheric conditions rapidly changing?