1. Dynamics and Thermodynamics Demonstration Model (DTDM)
Robert Fovell
University of California, Los Angeles

2. DTDM home page http://www.atmos.ucla.edu/~fovell/DTDM/ or
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

3. 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

4. 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

5. 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

6. 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

7. 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)

8. 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)

9. 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

10. Makefile # Mac OS X (PPC) with IBM xlf #FC = xlf
#FCFLAGS = -O3 -C -Wl,-stack_size, ,-stack_addr,0xc
# 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)

11. 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!

12. 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

13. 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

14. 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

15. 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., $

16. 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 = )
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

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

18. 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 = )
c s_vwavel - vertical wavelength of source (m; default = )
c s_period - oscillation period (s; default = 1200.)
&streamfunction
istrfcn = 1,
s_repeat = 0,
s_ampl = 40.,
s_znaught = 6000.,
s_hwavel = ,
s_vwavel = ,
s_period = 1200., $
dtdm < input_strfcn_isolated_nowind.txt

19. Streamfunction 

20. Initial conditions
Note: aspect ratio not 1:1

21. 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

22. 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)

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

24. Inside a GrADS script (strfcn_isolated.gs)
'set mproj off'
'set display color white'
* changes aspect ratio of plot
'set vpage '
'clear'
'set grads off'
'set lev 10 16'
'set lon '
'run rgbset.gs’
Continues…
'set gxout shaded'
'set xaxis '
'set yaxis '
'set clevs '
'set ccols '
'd thp'
'cbarn '
'set gxout contour'
'set cmax 2.4'
'set cmin -2.4'
'set cint 0.4'
'd w'

25. 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 horizontal velocity
up pert horizontal velocity
w vertical velocity
th potential temperature
thp pert potential temperature
pi ndim pressure
pip pert ndim pressure
ppmb pert pressure in millibars
str streamfunction
ga-> set t 115
ga-> strfcn_isolated

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

27. 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

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

29. Flow relative to obstacle
Height z
Wind U

30. 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

31. 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

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

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

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

35. Initial conditions
dtdm < input_strfcn_rolls.txt

36. 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

37. 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.)

38. 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 = ,
bvstrat = 0.02,
psurf = 965.,
usurf = 0.,
shear1 = 0.,
sdepth1 = 1800.,
shear2 = 0.,
sdepth2 = 2500.,
shear3 = 0., $

39. 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, $

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

41. Results (hsrc.gs)

42. Animations (hsrc_movie.gs)

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

44. Animation h_freq = 0.005 [~ 21 min]

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

46. 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

47. 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 = ,
plot = 300.,
&framework
csnd = 50.,
&numerics
cstar = 100.,
dkx = 1500.,
dkz = 100.,
Coarse resolution
large diffusion suppresses noise and
mixes surface heating vertically

48. 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)

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

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

51. 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

52. 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

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

54. Added horizontal velocity
set ccolor 1
set cthick 6
d up

55. Added airflow vectors
set ccolor 1
d u;w

56. Animation (sbfhcr_movie.gs)

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

58. 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

59. 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 = )
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

60. input_seabreeze.txt &rotunno_seabreeze section
iseabreeze = 1,
sb_ampl = ,
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)

61. 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

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

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

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

65. Cross-shore flow and vertical motion at midnight

66. Hovmoller diagrams
(seabreeze_hov.gs)
Note lack of propagation

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

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

69. 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

70. 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

71. Animation (khi_movie.gs)

72. Perturbation potential temperature (khi.gs)

73. Vertical velocity

74. Horizontal velocity

75. Airflow vectors

76. Perturbation pressure (p’)

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

78. Perturbation dynamic pressure (p’dyn)

79. Pressure decomposition
equations
operation

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

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

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

83. Contact info: help, bug reports, suggestions
Robert Fovell
Atmospheric and Oceanic Sciences
University of California, Los Angeles
405 Hilgard Ave
Los Angeles, CA
(310)