Isentropic Diagnostic Assessments and Modeling

1
Isentropic Diagnostic Assessments and Modeling
Strategies Appropriate to the Development
of Weather and Climate Models
Donald R. Johnson
Emeritus Professor
University of
Wisconsin
and NCEP
Special Project Scientist
National Centers for Environmental Prediction

2
Acknowledgements
Todd Schaack, Allen Lenzen and Tom Zapotocny
University of
Wisconsin Hua-Lu Pan, Robert
Kistler, Shrinivas Moorthi,
Mark Iredell, Suru Saha and others
National Centers for Environmental Prediction

3
As far as JNWP or should I say NCEP, there has
been long standing interests in isentropic
modeling of atmospheric circulation even before
Louis Uccellini arrived on the scene. Note in a
study entitled Numerical Experiments with the
Primitive Equations that Fred Shuman (1962)
proposed to integrate the atmospheric
equations utilizing the quasi-Lagrangian
coordinate system proposed by Starr
(1945). Shuman comments that one would
intuitively expect the finite difference
analogues to the quasi-Lagrangian equations to
behave better that the finite difference
equations analogues of equations of higher
degree and therefore greater mathematical
complexity. Furthermore, he notes that
isentropic surfaces would be the natural choice
for coordinates surfaces in the middle
stratosphere and higher
4

See Shuman, F. G., 1962 Numerical Experiments
with the Primitive Equations. Proceedings of
the International Symposium on Numerical
Weather Prediction in Tokyo,
Nov. 7-13, l960 pp. 85-107. Fred you were
right, except you were too conservative!
5
(No Transcript)
6
292 K Specific Humidity
Specific Humidity
Superimposed on the
292K Pressure Topography
7
(No Transcript)
8
Extrusion at Day Two
9
Danielsens 1967 Schematic of Stratospheric -
Tropospheric Exchange
10
Scatter diagrams of IPV versus trace of IPV at
Day 10 at all grid points witin the global
domains of the UW theta-eta model and CCM 3
11
Conservation of Proxy Ozone
12
Fig. 11. Fifteen month record of Anomaly
Correlation from the UW ??? model and NCEPs
Global Forecast System (GFS).
13
Day 5 UW ?-? (solid) and NCEP GFS (dashed) 500
hPa 5 AC scores Apr. 2002 Feb. 2003 UW ?-?
0.7 deg., 28 layers (0.77) GFS
T170L42 or T254L64 (0.80)

T170 to T254
14
B
A
Fig 12. The UW hybrid model forms the global
component of the RAQMS data assimilation system.
Figure B shows tropospheric ozone burden (DU) for
June-July 1999 from the RAQMS assimilation while
Fig. A is the satellite observed estimate.
15
(No Transcript)
16
Modeling and diagnostic strategies employed in
the development and employment of the UW Hybrid
Isentropic Model including some which have been
utilized at NCEP will be briefly reviewed. Within
an emphasis on the importance of long range
transport and ensuring reversibility, results
will be presented which illustrate the relevance
of these considerations. The aim of the review
and results presented, however, will be 1) to
raise key issues faced in advancing accuracies in
the simulation of weather and climate and, 2) to
foster discussion on strategies to isolate the
strengths and current limitations of weather and
climate models within a unified modeling endeavor
envisaged as a key component of the Earth System
Modeling Framework.
17
For those who focus on the capabilities of global
models to simulate monsoons, regional climate
and medium range weather prediction and those
who recognize the fundamental importance of
water, moist thermodynamic processes, cloudiness
and its related impact of radiation and surface
energy exchange, there should be common
agreement that the scientific challenges in
modeling weather and climate are one and the
same.
18
While the focus on carbon and global warming lies
somewhat outside of the focus on medium range
weather and seasonalclimate forecasts, there is
the emerging relevance of aerosols, the biosphere
and related biogeochemical processes, diurnally
varying land and surface boundary conditions and
other processes being brought to the forefront
that links all. As such, advancing accuracies in
the simulation of weather and climate in the
coming decade must be viewed as common challenge,
particularly as attention is given to
implementing an environmental forecasting
capability that serves the nations larger
interests.
19
What is Reversibility and How Relevant is
Ensuring Reversibility in the Simulation of
Atmsopheric Hydrologic and Chemical Processes
20
An NCAR Reviewers Comment
It is doubtful that strict global conservation of
energy and entropy by a numerical scheme plays a
significant role in weather prediction. The
advantage of center difference schemes like
Arakawa and Lamb (1977) in conserving energy and
entropy are often over-stated while its
shortcomings (e.g., numerical instability near
poles degradation in vorticity advection in
divergent flows which results in poor correlation
between potential vorticity and passive tracers)
being ignored. All models need sub-grid
damping mechanisms. How this can be achieved
can be very different among models. It should
be noted that even the Arakawa and Lamb scheme
needs artificial smoothing/filtering (in time
and in space) renders all GCMs effectively
non-energy conserving and irreversible. In
standard CCM3 the total energy is nearly
conserved because, 1) the lost kinetic energy
due to hyper-viscosity is added back to the
thermodynamic equation and also due in part, 2) a
lucky cancel- lation between the energy
conserving errors in dynamics and physics.
21
(No Transcript)
22
A Comparison and Discussion of Meridional
Model Coordinate Representations of the
Isentropic Structure of the Atmosphere
along 104º E Longitude
23
Fig. 1 Meridional cross section between the
earths surface and 50 hPa of UW model
quasi-horizontal surfaces (black), and potential
temperature (dashed red) along 104 E longitude
for day 235 (early August) of a 14 year climate
simulation. Model coordinates at and above 336 K
are isentropic surfaces. Potential temperatures
are plotted at 10 K resolution.
24
UW Hybrid ?-?
Model
25
UW Hybrid ?-? Model
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
UW ?-? Model ?? ? vs t((T?(1000/p?)?) (dry)
Table 1   day I II
III IV V VI
VII   0.0 0.003 0.054 0.055 0.234
0.016 0.126 0.073 0.271 -0.126 344.651
0.000 2.5 0.856 0.925 0.097 0.311
0.006 0.080 0.959 0.979 0.080 344.669
0.017 5.0 1.124 1.060 0.168 0.410
0.095 0.308 1.387 1.178 0.308 344.688
0.037 7.5 1.184 1.088 0.238 0.488
0.249 0.499 1.671 1.293 0.499 344.706
0.055 10.0 1.162 1.078 0.300 0.548
0.409 0.640 1.872 1.368 0.640 344.723
0.072
UW ? Model ?? ? vs t((T?(1000/p?)?) (dry)
Table 1   day I II
III IV V VI
VII   0.0 0.011 0.104 0.048 0.219
0.014 0.120 0.073 0.270 -0.120 342.748
0.000 2.5 12.025 3.468 9.521 3.086
0.334 0.578 21.880 4.678 0.578 342.798
0.050 5.0 16.556 4.069 17.692 4.206
1.469 1.212 35.717 5.976 1.212 342.850
0.102 7.5 17.638 4.200 25.360 5.036
3.205 1.790 46.204 6.797 1.790 342.901
0.153 10.0 17.706 4.208 35.288 5.940
5.123 2.263 58.117 7.623 2.263 342.951
0.203
30
UW ? Model ?? ? vs t((T?(1000/p?)?) (dry)
Table_2   I II III IV
V VI VII VIII
IX X   10 10 10
5 10 10 10 0 10-0  
1 701.86 179.25 881.11 -4.6867
13.3886 .1536 1014.8 1108.6 -93.87 1.0 5.0
2 308.47 28.9084
40.8186 .1536 716.7 674.7 42.02 2.2 20.8
3 39.75 6.30 9.71 3.12 49.45 7.03 1.4541
3.1159 .1536 512.0 513.6 -1.57 2.9 45.9
4 22.10 4.70 0.48 0.69 22.58 4.75 -0.0940
0.6943 .1536 430.9 430.8 0.06 3.1 75.5
5 12.30 3.51 0.00 0.01 12.30 3.51 -0.5110
0.0102 .1536 391.6 391.1 0.45 2.7 104.1
6 5.68 2.38 4.34 2.08 10.02 3.16 1.2339
2.0826 .1536 375.4 375.1 0.32 1.9 126.8
7 3.46 1.86 5.28 2.30 8.73 2.96 1.2028
2.2972 .1536 366.5 366.2 0.23 1.7 144.5
8 3.61 1.90 4.26 2.06 7.88 2.81 1.0186
2.0641 .1536 360.3 360.2 0.13 1.3 159.3
9 4.01 2.00 3.86 1.96 7.87 2.80 0.9424
1.9639 .1536 355.5 355.3 0.25 1.4
172.6 10 4.19 2.05 3.63 1.91 7.82 2.80
0.9530 1.9065 .1536 350.8 350.2 0.60
1.7 187.9 11 4.26 2.06 3.38 1.84 7.63 2.76
0.9624 1.8372 .1536 345.9 344.7 1.24
2.1 206.6 12 3.93 1.98 3.20 1.79 7.13 2.67
0.9611 1.7894 .1536 341.4 339.9 1.52
2.3 228.3 13 3.63 1.91 2.90 1.70 6.53 2.56
0.9178 1.7029 .1536 337.4 335.4 1.98
2.3 251.0 14 3.37 1.84 2.84 1.69 6.21 2.49
0.9264 1.6861 .1536 334.2 332.3 1.85
2.4 274.1 15 2.86 1.69 2.92 1.71 5.79 2.41
0.9448 1.7099 .1536 330.0 328.4 1.62
5.1 311.1 16 2.36 1.54 2.88 1.70 5.24 2.29
0.9859 1.6984 .1536 325.0 323.7 1.29
6.0 365.8 17 1.96 1.40 2.51 1.59 4.47 2.11
0.9331 1.5852 .1536 320.2 319.5 0.74
6.7 428.4 18 1.84 1.36 2.23 1.49 4.07 2.02
0.7996 1.4931 .1536 315.6 315.2 0.40
7.3 497.4 19 1.54 1.24 1.81 1.35 3.36 1.83
0.7031 1.3471 .1536 311.2 310.8 0.41
7.4 569.9 20 1.32 1.15 1.30 1.14 2.61 1.62
0.6060 1.1388 .1536 307.1 306.6 0.46
7.1 641.3 21 1.16 1.08 1.02 1.01 2.18 1.48
0.4988 1.0100 .1536 303.2 302.6 0.55
6.7 709.4 22 0.92 0.96 0.76 0.87 1.68 1.30
0.4264 0.8729 .1536 299.6 299.0 0.56
6.1 772.5 23 0.81 0.90 0.51 0.71 1.32 1.15
0.3710 0.7150 .1536 296.2 295.6 0.56
5.4 829.1 24 0.77 0.88 0.29 0.54 1.06 1.03
0.2936 0.5403 .1536 292.9 293.0 -0.13
4.3 876.9 25 0.80 0.90 0.17 0.41 0.97 0.99
0.1750 0.4100 .1536 290.0 291.6 -1.59
3.2 913.9 26 0.80 0.90 0.09 0.30 0.89 0.94
0.1092 0.2993 .1536 287.3 290.7 -3.39
2.5 942.0 27 0.86 0.93 0.06 0.25 0.92 0.96
0.0995 0.2509 .1536 284.9 290.0 -5.08
1.9 963.7 28 0.95 0.98 0.01 0.12 0.97 0.98
-0.0150 0.1188 .1536 282.3 289.5 -7.18
1.3 979.5
31
UW ?-? Model- ?? ? vs t((T?(1000/p?)?) (dry)
Table_2   I II III IV
V VI VII VIII
IX X   10 10 10
5 10 10 10 0 10-0  
1 9.00 3.00 3.07 1.75 12.07 3.47 -2.0703
-1.7522 .1473 1414.3 1414.3 0.00 0.4 2.2
2 2.85 1.69 0.75 0.87 3.60 1.90 -1.0903
-0.8675 .1452 950.0 950.0 0.00 0.8 8.2
3 1.05 1.03 0.32 0.56 1.37 1.17 -0.6852
-0.5638 .1454 675.0 675.0 0.00 2.6 24.7
4 1.01 1.01 0.04 0.19 1.05 1.02 -0.3791
-0.1946 .1419 505.0 505.0 0.00 2.6 50.5
5 0.73 0.86 0.01 0.08 0.74 0.86 -0.2519
-0.0755 .1436 435.0 435.0 0.00 2.7 76.9
6 0.65 0.80 0.00 0.04 0.65 0.81 -0.1400
0.0440 .1471 395.0 395.0 0.00 2.7 103.9
7 0.95 0.97 0.02 0.15 0.97 0.98 -0.0464
0.1495 .1547 374.0 374.0 0.00 1.6 125.3
8 0.97 0.99 0.03 0.17 1.00 1.00 0.0144
0.1688 .1787 362.0 362.0 0.00 2.6 146.3
9 0.27 0.52 0.01 0.07 0.28 0.53 -0.0287
0.0727 .2561 354.0 354.0 0.00 1.6
167.3 10 0.19 0.44 0.00 0.06 0.19 0.44
-0.0375 0.0615 .2802 350.0 350.0 0.00
2.2 186.1 11 0.42 0.65 0.01 0.11 0.43 0.66
-0.0022 0.1112 .3012 346.5 346.5 0.00
2.1 207.2 12 0.68 0.83 0.05 0.22 0.73 0.86
0.0723 0.2236 .2979 343.5 343.5 0.00
2.3 228.9 13 1.05 1.02 0.11 0.34 1.16 1.08
0.1510 0.3356 .2694 340.5 340.5 0.00
2.3 251.8 14 1.00 1.00 0.17 0.41 1.17 1.08
0.1977 0.4133 .2504 337.5 337.5 0.00
2.4 275.3 15 1.17 1.08 0.11 0.33 1.29 1.13
0.1824 0.3349 .1497 330.7 330.3 0.45
5.1 312.5 16 1.48 1.22 1.32 1.15 2.80 1.67
0.6679 1.1491 .1497 324.1 323.0 1.11
6.0 367.2 17 1.83 1.35 1.74 1.32 3.57 1.89
0.8389 1.3181 .1497 319.1 318.1 0.93
6.8 430.1 18 1.67 1.29 1.71 1.31 3.38 1.84
0.7718 1.3073 .1497 314.5 313.9 0.58
7.3 499.5 19 1.55 1.24 1.47 1.21 3.02 1.74
0.6577 1.2125 .1497 310.1 309.7 0.42
7.5 572.5 20 1.35 1.16 1.16 1.08 2.51 1.58
0.5776 1.0765 .1497 306.1 305.6 0.51
7.1 644.5 21 1.06 1.03 0.96 0.98 2.02 1.42
0.4735 0.9779 .1497 302.3 301.6 0.61
6.8 713.0 22 0.98 0.99 0.70 0.83 1.68 1.30
0.4219 0.8348 .1497 298.7 298.0 0.65
6.1 776.5 23 0.79 0.89 0.45 0.67 1.24 1.11
0.3601 0.6685 .1497 295.1 294.6 0.56
5.4 833.4 24 0.82 0.91 0.25 0.50 1.07 1.04
0.2731 0.5019 .1497 291.9 291.9 -0.04
4.1 880.2 25 0.76 0.87 0.16 0.40 0.92 0.96
0.2301 0.4027 .1497 289.1 290.5 -1.47
3.0 915.1 26 0.79 0.89 0.09 0.30 0.88 0.94
0.1142 0.3039 .1497 286.7 289.6 -2.98
2.4 941.5 27 0.89 0.94 0.12 0.35 1.01 1.00
0.2496 0.3461 .1497 284.3 288.9 -4.62
2.0 962.9 28 0.94 0.97 0.01 0.10 0.95 0.98
-0.0364 0.1011 .1535 282.3 289.5 -7.14
1.3 979.3
32
Bivariate Scatter Distributions -Day 10
Less Horizontal Diffusion
33
Day 10 - Dry Experiment
UW ?
UW ?-?
t(s) vs cp ln(t(T)(1000/t(p))?)
34
Day 10 Moist convection Large scale
condensation and radiation Source/sink of ?e
used in trace equation
35
Day 10 Moist convection Large scale
condensation and radiation Source/sink of ?e
used in trace equation
36
(No Transcript)
37
Fig. 3 Meridional cross section between the
earths surface and 50 hPa of the potential
temperature distribution between the earths
surface and 50 hPa along 104 E longitude for day
235 (early August) of a 14 year climate
simulation of potential temperature simulated by
CCM3, which utilizes a hybrid sigma isobaric
coordinate system. The isentropes are dashed
red, and hybrid sigma isobaric coordinate
surfaces are solid turquoise.
38
Assessment of Numerical Accuracies for CCM2 and
CCM3 Scatter Diagrams for Equivalent Potential
Temperature and its trace at Day 10 Empirical
Probability Density Functions at Days 2.5, 5.0,
7.5 and 10.0 for Pure Error Differences of
Equivalent Potential Temperature and its
Trace Vertical Profiles of Global Areally
Averages of Pure Error Differences of Equivalent
Potential Temperatue and its Trace
39
NCAR CCM3
40
(No Transcript)
41
(No Transcript)
42
A Statement of Principle Concerning Model
Diversity and Diagnostics in Relation to the
Earth System Modeling Framework (ESMF)
Within the context of an umbrella for model
diagnostics and validation, lets us strive to
develop an assessment strategy and capability for
advancing global models and the underlying
science that is independent of the vested
interests and developers of model, whether they
be in the government, academic or private
sectors. At the same time, the effort should
also ensure the mutual interests and activities
of the major centers and their scientists in a
community effort that isolates deficiencies and
shortcomings of global models while advancing
modeling accuracies and understanding of global
and regional modeling of weather and climate.
43
Several Underlying Considerations Concerning
NOAA's involvement in the ESMF The
following are several underlying considerations
aimed to facilitate NOAAs development of weather
and climate models under the unified modeling
effort envisaged within the ESMF as prepared by
Donald R. Johnson, NCEP Special Project Scientist
in response to Louis Uccellini's request as the
Director of NCEP The agreement that model
diversity within a community framework is
required for progress in both weather and climate
models is predicated on the premise that no
single model or approach to modeling the weather
climate state at this time or in the foreseeable
future has achieved the level of accuracy needed
for weather and climate prediction.
44

45
The Greatest Obstacle To Scientific Advances
Is Scientific Consensus