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

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

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 equationsutilizing 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 behavebetter 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”

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!

292 K Specific Humidity

Specific Humidity Superimposed on the292K Pressure Topography

Extrusion at Day Two

Danielsen’s 1967 Schematic of Stratospheric - Tropospheric Exchange

Scatter diagrams of IPV versus trace of IPV at Day 10 at all grid pointswitin the global domains of the UW theta-eta modeland CCM 3

Conservation of Proxy Ozone

Fig. 11. Fifteen month record of Anomaly Correlation from the UW model and NCEP’s Global Forecast System (GFS).

Day 5UW - (solid) and NCEP GFS (dashed)500 hPa 5 AC scoresApr. 2002 – Feb. 2003

UW - 0.7 deg., 28 layers (0.77)GFS T170L42 or T254L64 (0.80)

T170 to T254

Regional Air Quality Modeling System (RAQMS)Collaboration - NASA Langley and the University of Wisconsin - Madison

UW Hybrid - ModelGlobal model

UW - NMSRegional non-hydrostatic model

NASA Langley Impact ModelChemical Module

Multi-scale (global/regional) chemical modeling and data assimilation system

'Observed' RAQMS Assimilation

Tropospheric Ozone Residual (TOR) Estimate of tropospheric ozone burden

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.

BA

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.

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.

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 nation’s larger interests.

What is Reversibility and How Relevant is Ensuring

Reversibility in the Simulation of Atmsopheric Hydrologic and

Chemical Processes

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.

A Comparison and Discussion of

Meridional Model Coordinate

Representations of the Isentropic

Structure of the Atmosphere

along 104º E Longitude

Fig. 1 Meridional cross section between the earth’s 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.

UW Hybrid - Model

UW Hybrid - Model

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

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 1.4 172.610 4.19 2.05 3.63 1.91 7.82 2.80 0.9530 1.9065 .1536 350.8 350.2 0.60 1.7 187.911 4.26 2.06 3.38 1.84 7.63 2.76 0.9624 1.8372 .1536 345.9 344.7 1.24 2.1 206.612 3.93 1.98 3.20 1.79 7.13 2.67 0.9611 1.7894 .1536 341.4 339.9 1.52 2.3 228.313 3.63 1.91 2.90 1.70 6.53 2.56 0.9178 1.7029 .1536 337.4 335.4 1.98 2.3 251.014 3.37 1.84 2.84 1.69 6.21 2.49 0.9264 1.6861 .1536 334.2 332.3 1.85 2.4 274.115 2.86 1.69 2.92 1.71 5.79 2.41 0.9448 1.7099 .1536 330.0 328.4 1.62 5.1 311.116 2.36 1.54 2.88 1.70 5.24 2.29 0.9859 1.6984 .1536 325.0 323.7 1.29 6.0 365.817 1.96 1.40 2.51 1.59 4.47 2.11 0.9331 1.5852 .1536 320.2 319.5 0.74 6.7 428.418 1.84 1.36 2.23 1.49 4.07 2.02 0.7996 1.4931 .1536 315.6 315.2 0.40 7.3 497.419 1.54 1.24 1.81 1.35 3.36 1.83 0.7031 1.3471 .1536 311.2 310.8 0.41 7.4 569.920 1.32 1.15 1.30 1.14 2.61 1.62 0.6060 1.1388 .1536 307.1 306.6 0.46 7.1 641.321 1.16 1.08 1.02 1.01 2.18 1.48 0.4988 1.0100 .1536 303.2 302.6 0.55 6.7 709.422 0.92 0.96 0.76 0.87 1.68 1.30 0.4264 0.8729 .1536 299.6 299.0 0.56 6.1 772.523 0.81 0.90 0.51 0.71 1.32 1.15 0.3710 0.7150 .1536 296.2 295.6 0.56 5.4 829.124 0.77 0.88 0.29 0.54 1.06 1.03 0.2936 0.5403 .1536 292.9 293.0 -0.13 4.3 876.925 0.80 0.90 0.17 0.41 0.97 0.99 0.1750 0.4100 .1536 290.0 291.6 -1.59 3.2 913.926 0.80 0.90 0.09 0.30 0.89 0.94 0.1092 0.2993 .1536 287.3 290.7 -3.39 2.5 942.027 0.86 0.93 0.06 0.25 0.92 0.96 0.0995 0.2509 .1536 284.9 290.0 -5.08 1.9 963.728 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

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 1.6 167.310 0.19 0.44 0.00 0.06 0.19 0.44 -0.0375 0.0615 .2802 350.0 350.0 0.00 2.2 186.111 0.42 0.65 0.01 0.11 0.43 0.66 -0.0022 0.1112 .3012 346.5 346.5 0.00 2.1 207.212 0.68 0.83 0.05 0.22 0.73 0.86 0.0723 0.2236 .2979 343.5 343.5 0.00 2.3 228.913 1.05 1.02 0.11 0.34 1.16 1.08 0.1510 0.3356 .2694 340.5 340.5 0.00 2.3 251.814 1.00 1.00 0.17 0.41 1.17 1.08 0.1977 0.4133 .2504 337.5 337.5 0.00 2.4 275.315 1.17 1.08 0.11 0.33 1.29 1.13 0.1824 0.3349 .1497 330.7 330.3 0.45 5.1 312.516 1.48 1.22 1.32 1.15 2.80 1.67 0.6679 1.1491 .1497 324.1 323.0 1.11 6.0 367.217 1.83 1.35 1.74 1.32 3.57 1.89 0.8389 1.3181 .1497 319.1 318.1 0.93 6.8 430.118 1.67 1.29 1.71 1.31 3.38 1.84 0.7718 1.3073 .1497 314.5 313.9 0.58 7.3 499.519 1.55 1.24 1.47 1.21 3.02 1.74 0.6577 1.2125 .1497 310.1 309.7 0.42 7.5 572.520 1.35 1.16 1.16 1.08 2.51 1.58 0.5776 1.0765 .1497 306.1 305.6 0.51 7.1 644.521 1.06 1.03 0.96 0.98 2.02 1.42 0.4735 0.9779 .1497 302.3 301.6 0.61 6.8 713.022 0.98 0.99 0.70 0.83 1.68 1.30 0.4219 0.8348 .1497 298.7 298.0 0.65 6.1 776.523 0.79 0.89 0.45 0.67 1.24 1.11 0.3601 0.6685 .1497 295.1 294.6 0.56 5.4 833.424 0.82 0.91 0.25 0.50 1.07 1.04 0.2731 0.5019 .1497 291.9 291.9 -0.04 4.1 880.225 0.76 0.87 0.16 0.40 0.92 0.96 0.2301 0.4027 .1497 289.1 290.5 -1.47 3.0 915.126 0.79 0.89 0.09 0.30 0.88 0.94 0.1142 0.3039 .1497 286.7 289.6 -2.98 2.4 941.527 0.89 0.94 0.12 0.35 1.01 1.00 0.2496 0.3461 .1497 284.3 288.9 -4.62 2.0 962.928 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

Less Horizontal Diffusion

Bivariate Scatter Distributions -Day 10

Day 10 - Dry Experiment

UW - UW

t(s) vs cp ln(t(T)*(1000/t(p)))

Day 10

Moist convectionLarge scale condensation andradiation

Source/sink of e

used in trace equation

Day 10

Moist convectionLarge scale condensation andradiation

Source/sink of e

used in trace equation

Fig. 3 Meridional cross section between the earth’s surface and 50 hPa of the potential temperature distribution between the earth’s 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.

Assessment of Numerical Accuracies for CCM2 and CCM3

Scatter Diagrams for EquivalentPotential Temperature and its traceat Day 10

Empirical Probability Density Functions at Days 2.5, 5.0, 7.5 and10.0 for Pure Error Differences of Equivalent Potential Temperature and its Trace

Vertical Profiles of Global Areally Averages of Pure Error Differencesof Equivalent Potential Temperatueand its Trace

NCAR CCM3

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”.

Several Underlying Considerations Concerning NOAA's involvement in the ESMFThe following are several underlying considerations aimed to facilitate NOAA’s 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.

Strategies should focus on ascertaining the strengths and weaknesses of models inrelation to advancing NOAA’s capabilities for weather and climate predictionbroadly defined. The underlying issue is how through collaborative utilization of the ESMF andworking partnerships can NOAA and the larger scientific community advanceunderstanding and accuracies for weather and climate prediction. Advancing understanding and prediction of weather and of climate arecomplementary to each other in implementing an environmental forecastingcapability in NOAA that serves the nation’s larger interests. Within the effort to advance weather and climate prediction for their ownpurposes and also to mutually complement each other in implementing anenvironmental forecasting capability, there must be recognition on the part of thescience community, theoreticians, modelers, diagnosticians, and operationalforecasters that all have a stake and need to contribute to this effort. The challenge then is how to ensure the active engagement of not only thosewithin NOAA including ESMF partners, but also the larger scientific community.

The Greatest Obstacle To

Scientific Advances Is

Scientific Consensus