Dynamics and Thermodynamics Demonstration Model (DTDM) Robert Fovell University of California, Los Angeles rfovell@ucla.edu

DTDM home page http://www.atmos.ucla.edu/~fovell/DTDM/ or http://tinyurl.com/nhoj6 Files: DTDM_package.tar [< 1 MB] DTDM_examples.tar.gz [600 MB, expands to 1 GB] Extract: tar -xvf DTDM_package.tar tar -zxvf DTDM_examples.tar.gz

DTDM is… A very simple, 2D compressible model Free, portable: Fortran 77 (g77) and GrADS Demonstrates gravity waves, sea-breeze circulations, convective rolls, KHI, etc. Options for including heat and momentum sources, surface fluxes, cold pools, etc. Input script driven… may not need to modify code

What DTDM is not… Not a sophisticated model Not guaranteed bug-free Second-order numerics, primitive physics Crude boundary conditions Not guaranteed bug-free Not always physically accurate or realistic Some parameters, processes may be exaggerated for demonstration purposes and/or computational efficiency Not complete or research-quality

DTDM features Model prognostic variables: Environmental settings Wind components: u, w, v (when Coriolis active) Potential temperature:  Nondimensional pressure:  Environmental settings Brunt-Vaisala frequency of boundary layer, free troposphere and stratosphere Up to 3 layers for vertical shear Latitude (for Coriolis parameter) Numerical settings Horizontal and vertical diffusion Temporal diffusion Wave speed for open lateral boundaries Speed of sound

DTDM features Source terms Momentum source, configurable as single or repeated, steady or oscillatory Heat source, steady or oscillatory Surface heat flux Sea-breeze-specific heat source Lower tropospheric cooling zone and/or impulsive cold block Impulsive thermal Creates GrADS output

DTDM rationale and use Demonstrate physical and thermodynamical phenomena with simple simulations Stills, animations, decomposing forcing fields, etc. Provide a hands-on package suitable for homeworks, labs Easily runs on Unix and Unix-like systems (Linux, Mac OS X, Suns, etc.) Next generation Java or C++? Web-based? Implement using WRF? Namelist input (done as of July 2006 version)

DTDM package DTDM_package.tar DTDM_model.f ~ program storage.txt ~ defines arrays Makefile If storage.txt modifed, touch DTDM_model.f and make again Model input scripts (input_*.txt) GrADS plotting scripts (*.gs)

storage.txt nxm, nzm are max values of horizontal dimensions nx and nz c max array dimensions parameter(nxm=503,nzm=122,ny=1) ! requires nx <= nxm, nz <= nzm nxm, nzm are max values of horizontal dimensions nx and nz

Makefile # Mac OS X (PPC) with IBM xlf #FC = xlf #FCFLAGS = -O3 -C -Wl,-stack_size,10000000,-stack_addr,0xc0000000 # Linux with Intel compiler #FC = ifort #FCFLAGS = -O3 -convert big_endian # Linux with Portland Group compiler FC = pgf77 FCFLAGS = -O3 -byteswapio SOURCES=src/DTDM_model.f src/blktri.f OBJS= $(SOURCES:.f=.o) dtdm: $(OBJS) $(FC) $(FCFLAGS) -o $@ $(OBJS)

How to run Edit Makefile - make sure correct lines are uncommented Execute ./make (executable is dtdm) Edit input.txt file (many examples included) First line specifies name of GrADS output ./dtdm < input.txt Output are GrADS control (.ctl) and data (.dat) files Do NOT use “>” symbol by accident!

New for July, 2006, version Namelist input replaces previous input scripts Anelastic model option installed Warning: not all combinations of model physics switches and parameters have been tried; bugs may remain Many input scripts set up with sound speed csnd = 50 m/s, which is far, far too small In many cases, this permits much faster integration without fundamentally altering results

Statospheric gravity waves produced by obstacles (convective cells) Reference: Fovell, Durran and Holton (1992, J. Atmos. Sci.)** **references to my papers illustrate my interest in these phenomena

input_strfcn_isolated_nowind.txt c=================================================================== c c The experiment namelist sets the casename for naming the c GrADS output. Max 72 characters and avoid using underscores. c Enter filename within single quotes (e.g., 'test.number.1') &experiment casename = 'strfcn.isolated.1200sec.nowind', $ First namelist section sets experiment name (casename) Names used for GrADS files limited to 76 characters; avoid underscores with GrADS

input_strfcn_isolated_nowind.txt c=================================================================== c c The grid_run namelist specifies model dimensions, integration c length, and plotting output interval c nx - number of horizontal grid points - max NXM in storage.txt c default is 101 c nz - number of vertical grid points - max NZM in storage.txt c default is 84 c dx - horizontal grid spacing (m; default = 1000.) c dz - vertical grid spacing (m; default = 250.) c dt - time step (s; default = 1.0) c timend - integration stop time (s; default = 7200.) c plot - plotting interval (s; default = 300.) c * if interval < 60 sec, GrADS will report time incorrectly &grid_run nx = 101, nz = 122, dx = 1000., dz = 250., dt = 1.0, timend = 7200., plot = 60., $

input_strfcn_isolated_nowind.txt &environ section c The environ namelist sets up the model initial state c bvpbl - PBL tropospheric BV freq (1$s; default = 0.01) c pbld - PBL depth (m; default = 2000.) c bvtropo - free tropospheric BV freq (1$s; default = 0.01) c tropo - tropopause height (m; default = 12000.) c bvstrat - stratospheric BV freq (1$s; default = 0.02) c psurf - surface pressure (mb; default = 965.) c usurf - surface wind speed (m$s; default = 0.) c shear1 - vertical shear for first layer (1$s; default = 0.) c depth1 - thickness of first layer (m; default = 3000.) c shear2 - vertical shear for second layer (1$s; default = 0.) c depth2 - thickness of second layer (m; default = 1500.) c shear3 - vertical shear above second layer (1$s; default = 0.) c * this layer extends to model top

input_strfcn_isolated_nowind.txt &environ section bvpbl = 0.002, pbld = 2000., bvtropo = 0.01, tropo = 12000., bvstrat = 0.02, psurf = 965., usurf = 0., shear1 = 0., sdepth1 = 3000., shear2 = 0., sdepth2 = 1500., shear3 = 0., $

input_strfcn_isolated_nowind.txt &streamfunction section c The streamfunction namelist sets up a momentum source used c to excite gravity waves. The source may be isolated or repeated, c oscillatory or steady c istrfcn (1 = turn streamfunction forcing on; default is 0) c s_repeat(1 for repeated source, 0 for single source; default 0) c s_ampl - amplitude of momentum source (kg$m/s/s; default = 40.) c s_naught - height of source center (m; default = 6000.) c s_hwavel - horizontal wavelength of source (m; default = 40000.) c s_vwavel - vertical wavelength of source (m; default = 18000.) c s_period - oscillation period (s; default = 1200.) &streamfunction istrfcn = 1, s_repeat = 0, s_ampl = 40., s_znaught = 6000., s_hwavel = 10000., s_vwavel = 18000., s_period = 1200., $ dtdm < input_strfcn_isolated_nowind.txt

Streamfunction 

Initial conditions Note: aspect ratio not 1:1

Animation (strfcn_isolated_movie.gs) s_period = 1200 sec For this run: bvpbl = .01 (only part of model depth shown) Note: aspect ratio not 1:1

Invoking GrADS “-l” requests landscape-oriented window gradsnc -l “-l” requests landscape-oriented window Opens a GrADS graphics window GrADS prompt is “ga->” ga-> open strfcn.isolated.1200sec.nowind Tab completion works! ga-> strfcn_isolated_movie.gs Executes a GrADS script (gs)

Varying oscillation period (strfcn_isolated.gs) Only part of domain is shown Note: aspect ratio not 1:1

Inside a GrADS script (strfcn_isolated.gs) 'set mproj off' 'set display color white' * changes aspect ratio of plot 'set vpage 0.5 11.0 0.5 5' 'clear' 'set grads off' 'set lev 10 16' 'set lon 24 74 ' 'run rgbset.gs’ Continues… 'set gxout shaded' 'set xaxis 34 64 4' 'set yaxis 10 16 2' 'set clevs -2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5' 'set ccols 49 47 45 43 41 0 61 62 63 65 67 69' 'd thp' 'cbarn 1.0 0 6.0' 'set gxout contour' 'set cmax 2.4' 'set cmin -2.4' 'set cint 0.4' 'd w'

Executing this GrADS script gradsnc -l ga-> open strfcn.isolated.1200sec.nowind ga-> q file File 1 : DTDM demo simulation Descriptor: strfcn.isolated.1200sec.nowind.ctl Binary: strfcn.isolated.1200sec.nowind.dat Type = Gridded Xsize = 99 Ysize = 1 Zsize = 120 Tsize = 121 Number of Variables = 9 u 120 0 horizontal velocity up 120 0 pert horizontal velocity w 120 0 vertical velocity th 120 0 potential temperature thp 120 0 pert potential temperature pi 120 0 ndim pressure pip 120 0 pert ndim pressure ppmb 120 0 pert pressure in millibars str 120 0 streamfunction ga-> set t 115 ga-> strfcn_isolated

Gravity waves Period and frequency Intrinsic frequency & mean flow Wavelength and wavenumber Dispersion relation

Tilt angle from vertical Gravity waves Dispersion relation Tilt angle from vertical Longer period -> Smaller omega -> smaller cos(alpha) -> larger alpha -> greater tilt from vertical

Adding flow relative to momentum source input_strfcn_isolated_up4.txt &environ bvpbl = 0.01, pbld = 2000., bvtropo = 0.01, tropo = 12000., bvstrat = 0.02, psurf = 965., usurf = 0., shear1 = 0., sdepth1 = 8000., shear2 = 0.002, sdepth2 = 2000., shear3 = 0., $ Shear = 0.002 over 2000 m = ∆U = 4 m/s Shear = 0.004 yields ∆U = 8 m/s dtdm < input_strfcn_isolated_up4.txt

Flow relative to obstacle Height z Wind U

Flow relative to obstacle (period = 1200 sec) U = 0 U = 4 m/s U = 8 m/s Mean flow: add U>0… on upwind side (k negative) omega larger (-Uk >0), less tilt from vertical on downwind side (k positive) omega smaller, more tilt from vertical Note: aspect ratio not 1:1

Further exploration Measure phase angles, compare to theory Perhaps alter plot aspect ratio to 1:1 Vary source frequency, amplitude, width Vary environmental stability, wind and wind shear

Obstacle-effect gravity waves above convective rolls Reference: Fovell (2004, Mon. Wea. Rev.)

input_strfcn_rolls.txt &environ section usurf = 0., shear1 = 0., sdepth1 = 1800., shear2 = -0.0036, sdepth2 = 2500., shear3 = 0., Zero shear below 1.8 km -9 m/s of wind speed difference between 1.8 and 4.3 km

input_strfcn_rolls.txt s_repeat= 1 for repeated source &streamfunction istrfcn = 1, s_repeat = 1, s_ampl = .40, s_znaught = 1000., s_hwavel = 10000., s_vwavel = 6000., s_period = 0., $ s_repeat= 1 for repeated source s_period=0 for steady momentum source

Initial conditions dtdm < input_strfcn_rolls.txt

Varying flow above obstacle (strfcn_rolls.gs) u = -3 m/s u = -6 m/s u = -9 m/s Standing waves, so omega = 0, and intrinsic omegahat=-Uk. k is specified by roll spacing. As U larger in magnitude, omegahat mag larger, less tilt from vertical m^2 = (N^2/U^2)-k^2. For k small, as U larger -> m smaller -> vert wavelength larger Note: aspect ratio not 1:1

Gravity waves excited by heat sources References: Fovell (2002, QJRMS), Fovell, Mullendore and Kim (2006, Mon. Wea. Rev.) Nicholls et al. (1991, J. Atmos. Sci.) Mapes (1993, J. Atmos. Sci.)

input_hsrc.txt &experiment &environ casename = 'hsrc.2mode.no.oscil', $ &grid_run nx = 101, nz = 84, dx = 1000., dz = 250., dt = 2.0, timend = 6000., plot = 60., &environ bvpbl = 0.00, pbld = 1500., bvtropo = 0.01, tropo = 12000., bvstrat = 0.02, psurf = 965., usurf = 0., shear1 = 0., sdepth1 = 1800., shear2 = 0., sdepth2 = 2500., shear3 = 0., $

input_hsrc.txt c=================================================================== c c The atmos_heat_source namelist sets up a free tropospheric heat source c used to excite gravity waves. The source may be oscillatory or steady c ihsrc (1 = turn tropospheric heat source on; default is 0) c h_ampl - amplitude of heat source (K$s; default = 0.075) c h_radius_x - horizontal radius of heat source (m; default = 3000.) c h_radius_z - vertical radius of heat source (m; default = 3000.) c h_center_z - height of heat source center (m; default = 3000.) c h_freq - frequency for heat source oscillation (1$s; default = 0.005) c h_modes - number of vertical modes (ndim, max 2; default = 2) &atmos_heat_source ihsrc = 1, h_ampl = 0.025, h_radius_x = 3000., h_radius_z = 3000., h_center_z = 3000., h_freq = 0.000, h_modes = 2, $

Heating profiles For heat source depth H 1st mode H = 6000 m (2 x h_radius_z) 2nd mode H = 3000 m

Results (hsrc.gs)

Animations (hsrc_movie.gs)

Phase speed… Deeper H - faster speeds.. Cx rel to source. Even faster rel to ground…

Animation h_freq = 0.005 [~ 21 min]

A simple sea-breeze circulation Reference: Dailey and Fovell (1999, Mon. Wea. Rev.)

Simple sea-breeze strategy Add a surface heat flux for part of domain (“land”) Large vertical diffusion as proxy for boundary layer mixing One use: to investigate effect of offshore or onshore wind on lifting and propagation of sea-breeze front

input_sbf_no_rolls.txt &experiment Coarse resolution casename = 'sbf.noroll.nowind', $ &grid_run nx = 301, nz = 26, dx = 1000., dz = 400., dt = 1.0, timend = 18000., plot = 300., &framework csnd = 50., &numerics cstar = 100., dkx = 1500., dkz = 100., Coarse resolution large diffusion suppresses noise and mixes surface heating vertically

input_sbf_no_rolls.txt c=================================================================== c c The surface_flux namelist sets up at least part of a domain c to represent a heated surface, to heat atmosphere from below c ishflux (1 = turn surface heat flux on; default is 0) c tdelt - initial ground-air T difference (K; default = 12) c icoast - gridpt location of coastline (0 for all land; default = 30) c cdh - effective heat flux coefficient (ndim; default = 7.2e-3) c irand - (1 = impose randomness on surface heat flux; default is 0) &surface_flux ishflux = 1, tdelt = 12., icoast = 90, cdh = 7.2e-3, irand = 0, $ Coastline 90 grid points from left side (of 301 total) Large cdh reflects unstable conditions; No imposed random perturbations (irand=0)

Surface wind speed = -3, 0 and +3 m/s Cases Surface wind speed = -3, 0 and +3 m/s

Offshore case animation (sbf_movie.gs) Colored: vertical velocity Contoured: perturbation horizontal velocity

Mean flow effect on sea-breeze (sbf_noroll.gs) 3 m/s offshore No mean flow 3 m/s onshore Perturbation u (contoured) and w (shaded); Aspect ratio not 1:1

Sea-breeze with “rolls” irand = 1 superimposes random perturbations on surface heat flux Encourages 2D pseudo-roll circulations In reality, rolls are 3D organized by along-roll shear Two-dimensionality provides an (overpowering) organization mechanism input_sbf_with_rolls.txt * Integration can be lengthy

Vertical velocity (sbfhcr.gs) set t 20 sbfhcr.gs

Added horizontal velocity set ccolor 1 set cthick 6 d up

Added airflow vectors set ccolor 1 d u;w

Animation (sbfhcr_movie.gs)

Effect of Coriolis on the sea-breeze circulation Reference: Rotunno (1983, J. Atmos. Sci.)

Long-term sea-breeze strategy Add a lower tropospheric heat source (Rotunno 1983), mimicking effect of surface heating + vertical mixing Reduce vertical diffusion Simulations start at sunrise One use: to investigate effect of latitude and/or linearity on onshore flow, timing and circulation strength

input_seabreeze.txt &rotunno_seabreeze section c The rotunno_seabreeze namelist implements a lower tropospheric c heat source following Rotunno (1983), useful for long-term c integrations of the sea-land-breeze circulation c iseabreeze (1 = turn Rotunno heat source on; default is 0) c sb_ampl - amplitude of heat source (K$s; default = 0.000175) c sb_x0 - controls heat source shape at coastline (m; default = 1000.) c sb_z0 - controls heat source shape at coastline (m; default = 1000.) c sb_period - period of heating, in days (default = 1.0) c sb_latitude - latitude for experiment (degrees; default = 60.) c sb_linear (1 = linearize model; default = 1) * Integration can be lengthy

input_seabreeze.txt &rotunno_seabreeze section iseabreeze = 1, sb_ampl = 0.000175, sb_x0 = 1000., sb_z0 = 1000., sb_period = 1.0, sb_latitude = 30., sb_linear = 1, $ * Integration can be lengthy sb_latitude ≠ 0 activates Coriolis sb_linear = 1 linearizes the model Other settings include: dx = 2000 m, dz = 250 m, dt = 1 sec dkx = dkz = 5 m2/s (since linear)

Cross-shore near-surface wind at coastline (linear model) Equator - no offshore flow 30N strongest offshore flow Aperiodicity in 24h indicates need run model longer for it to settle

Time series using GrADS > open seabreeze.rotunno.00deg > set t 1 289 > set z 1 > set x 100 > set vrange -25 25 > set xaxis 0 24 3 > d u > open seabreeze.rotunno.60deg > d u.2 > open seabreeze.rotunno.30deg > d u.3

Cross-shore flow and vertical motion at noon Shaded: vertical velocity; contoured: cross-shore velocity (seabreeze.gs)

Cross-shore flow and vertical motion at sunset Set t 144

Cross-shore flow and vertical motion at midnight

Hovmoller diagrams (seabreeze_hov.gs) Note lack of propagation

Further exploration Make model nonlinear Add mean flow and wind shear Explain latitudinal dependence Compare to actual data

Fun with cold pools Reference: Fovell and Tan (2000, QJRMS) Droegemeier and Wilhelmson (1987, J. Atmos. Sci.)

Cold pool options ICOOLZONE has two options ICOOLZONE = 1 for “storm-adaptive” cold pool… maintained and stays aligned with gust front ICOOLZONE = 2 gives model impulsive block of cold air Lower resolution - look at lifting Higher resolution - Kelvin-Helmholtz instability Either - compare buoyancy and dynamic components of pressure field

Kelvin-Helmholtz Instability (KHI) input_coldpool_hires.txt nx=501, nz=101, dx=dz=50 m, dt=0.125 sec, plotting interval 20 sec GrADS ctl file will misreport plot interval as 1 min ICOOLZONE=2, cz_width=4000 m, cz_depth=2000 m coldpool.hires.ctl, coldpool.hires.dat Simulation takes a very long time

Animation (khi_movie.gs)

Perturbation potential temperature (khi.gs)

Vertical velocity

Horizontal velocity

Airflow vectors

Perturbation pressure (p’)

Perturbation buoyancy pressure (p’byc) ipressure = 1 Enables calculation of buoyancy and dynamic pressure components of perturbation pressure

Perturbation dynamic pressure (p’dyn)

Pressure decomposition equations operation

Pressure decomposition yields (if density constant) where and because pressure perturbation is separable Solve for buoyancy and dynamic pressure perturbations; dimensionalize to millibars

Comparing ppmb and ptot pbyc+pdyn ppmb Small differences owing to anelastic, missing diffusion, etc.

ICOOLZONE = 1 (input_coolzone.txt & coolzone_movie.gs)

Contact info: help, bug reports, suggestions Robert Fovell Atmospheric and Oceanic Sciences University of California, Los Angeles 405 Hilgard Ave Los Angeles, CA 90095-1565 rfovell@ucla.edu (310) 206-9956