# Presentation: 237128

## 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 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”

## Fred you were right, except you were too conservative!

-                                              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.

## 292 K Specific Humidity

- Specific Humidity

- Superimposed on the

- 292K Pressure Topography

## Slide 7

- Extrusion at Day Two

## Danielsen’s 1967 Schematic of Stratospheric - Tropospheric Exchange

## Scatter diagrams of IPV 

- 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

## Conservation of Proxy Ozone

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

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

## 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

## B

- 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.

- A

## Slide 15

## 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.

## Slide 21

## A Comparison and Discussion of 

-    Meridional Model Coordinate
- Representations of the Isentropic
-    Structure of the Atmosphere
-       along 104o E  Longitude

## 336 K are isentropic surfaces.  Potential temperatures are plotted at 10 K resolution. 

- 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 Hybrid - Model

- UW Hybrid - Model

## Slide 26

## Slide 27

## Slide 28

## 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   1.4 172.6
- 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

## 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

## Bivariate Scatter Distributions -Day 10

- Less Horizontal Diffusion

## Day 10 - Dry Experiment

- UW -

- UW 

- t(s)  vs  cp ln(t(T)*(1000/t(p)))

## Day 10 

- Day 10
- Moist convection
- Large scale
- condensation and
- radiation
- Source/sink of e
-  used in trace
- equation

## Day 10 

- Day 10
- Moist convection
- Large scale
- condensation and
- radiation
- Source/sink of e
-  used in trace
- equation

## Slide 36

## 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 

- 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

## NCAR CCM3

## Slide 41

## “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”. 

- “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 ESMF

- The 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.

## Slide 44

## The Greatest Obstacle To Scientific Advances Is Scientific Consensus