Sensitivity tests are
presented which demonstrate how global climate models (GCMs) respond
to longwave radiation input. This input is established by the
inclusion in the GCM of a longwave radiation heating algorithm,
and a number of such algorithms are tested in the NCAR/CCM2.

Climate model dynamics
are driven by forcing and the primary forces affecting the thermal
field are long wave radiative heating (LWR), short wave radiative
heating (SWR), and convection (cumulus, etc.). These forcing
effects are cycled through the thermal field to the motion field
by nonlinear transfer. The model dependent variables, in particular
temperature (T), moisture (Q) and especially clouds, evolve in
time in a GCM and determine the subsequent forcing. If the dependent
variables are not accurately calculated in space and time, the
predicted forcing functions will be adversely affected. As integration
time proceeds, such inaccuracies will lead to systematic errors
in the prediction of climate. Although the effects of all these
forces need evaluation to understand their impact on climate,
we focus here on one of the primary forces, the long wave radiative
heating.

This forcing is determined
in GCMs by a LWR heating algorithm. Such algorithms compute vertical
heating rate (HR) profiles from profiles of T, Q, clouds, and
minor constituents. The HRs thus depend on the vertical structure
of the input variables plus internal physics. To test the sensitivity
to input variables of various algorithms taken from global climate
models, we intercompared the heating rate profiles produced by
six GCM algorithms each receiving identical input conditions from
two distinct weather situations. One had clear skies and the
other had deep clouds. The algorithms proved to be extremely
sensitive to clouds, yielding remarkably different heating rates
for identical input conditions. For more details, see Baer, et
al., 1996.

Noting this sensitivity,
we must determine how global climate models (GCMs) respond to
the HRs generated by the LWR algorithms. The LWR algorithms calculate
vertical profiles of HRs periodically at each point in a GCM generating
3-dimensional fields; these HR fields represent the LWR forcing
which determines the temperature-tendencies. The temperature
field predicted from these tendencies modifies the wind field
tendencies by nonlinear interaction in space. The predicted wind
field then subsequently modifies the temperature tendencies by
nonlinear advection. Thus the impact of the HRs is spread in
time and space to all the variables (T, Q, clouds), and these
modified variables are then used to recalculate new Hrs. For
details on modeling climate see Washington and Parkinson, 1986.

We choose to present the model output in spectral statistics as well as in physical space. This is provoked because climate model statistics in physical space generally require many realizations and computer time is very limited. Thus if we can reduce the number of realizations from which we can derive meaningful statistics, we will be able to achieve more experiments. Spectral statistics provide scaling information and allow for separation of amplitude from phase. The variability in phase seems much more pronounced than that in amplitude. If so, perhaps only a few realizations may yield a good representation of the amplitude. We tested this hypothesis with data from a long run with a two level baroclinic model given 80 realizations, and indications from this experiment showed that amplitudes did indeed vary considerably less than phase, thus suggesting that even an individual realization may provide useful information.

Three dimensional fields
from model output archives were utilized to demonstrate sensitivity
of GCMs to longwave radiative heating. Model output of LWR HRs
and other fields at each archived time were averaged over 60 day
wintertime (Jan-Feb.) periods to develop climate statistics.
The model archives available for analysis included;

- NCAR CCM1: R15, T42; 12 levels; SST climatology
- NCAR CCM2: R15, T42, T106; 18 levels; SST climatology
- NCAR CCM2: T42; 18 levels; AMIP SSTs
- CSU: 4x5x10 levels ; AMIP SSTs
- NASA GEOS-1: 4x5x20 levels ; AMIP SSTs

Unfortunately, no observations
are available for comparison. We therefore used a model to generate
clouds from observed (T, Q) data, and used those clouds to generate
HRs in the model. We introduced the observed data into the CCM2
as initial conditions for each day of the AMIP period (J-F, 1987)
and ran the model for 36 hours. For information on AMIP, see
Gates, 1992. We used the HR fields which the model developed
at that time and defined them as "pseudo-observations"
to compare with the output from various AMIP model runs. For
comparison, we repeated the above calculation with the CCM2 but
substituted the ECMWF LWRM algorithm (see Morcrette,
1990).

The results of the intercomparisons of model output showed the following sensitivities.

*Model truncation*-- Analysis of both the CCM1 and CCM2 climatology archived data showed that HRs are much more dependent on model truncation in the CCM1 than the CCM2.*Model changes*, including changes to the incorporated LWR algorithm-- HRs are strongly dependent on model changes as observed when comparing output from the CCM1 and CCM2 climatology runs and also from comparison of archived AMIP data from the CCM2, CSU and GEOS-1 GCM runs.*Surface forcing*in the form of sea-surface temperature (SST)-- This forcing appears to have a significant effect on the evolution of the model variables as seen when comparing two CCM2 AMIP periods (J-F, 87 and J-F, 83) and the winter months from the CCM2 climatology run .*Control integrations/ pseudo-observations*-- When comparing a CCM2 AMIP winter with our pseudo-observations using both the CCM and ECMWF algorithms, the model output fields of the pseudo- observations calculation compare more favorably to one another than to the AMIP run output. This indicates strong dependence on the initial data entering the LWR algorithm.

To test the effect of
longwave radiative forcing with other GCM features held fixed,
we ran the CCM2 with two different LWRM algorithms, the NCAR version
native to the model and the ECMWF (Morcrette) algorithm implanted.
Both integrations are for two months of the AMIP period, Jan.-Feb./87,
with identical initial conditions. From averaged heating rates
for this experiment on the 250hPa surface compared to the corresponding
pseudo- observation maps, we note differences on the order of
10 percent, which is a significant difference, and the ECMWF algorithm
yields stronger cooling. To determine if these differences are
due to the algorithms or to climate variability, we must establish
the GCMs inherent variability.

Any one realization of
climate statistics may not reflect the climate for that period.
To determine the effect of climatic variability, we have run
ten realizations of the CCM2 with only slight variations in the
initial states. We began the runs at the beginning of October
1986, allowed two months for equilibrium, and took model output
statistics from the subsequent three months of DJF. The ten runs
used the NCAR radiation algorithm (see Kiehl et al., 1994). Means
of the heating rates from the ten realizations and their standard
deviations were taken from the integrations and 200 and 500hPa
maps were created. These maps showed substantial variability
in the runs with standard deviations at many locations in excess
of ten percent. Similar results were found in the fields of clouds
and temperature.

To determine if the variability between model runs with different heating algorithms exceeds the climate variability of a model with no algorithm change (results just described), we ran three realizations with the CCM2 including the ECMWF algorithm and then repeated the same test using the NCEP algorithm. Testing for climate variability with three realizations appears realistic. Comparing averages of the three realizations with the averages of the ten CCM realizations, we are able to demonstrate the impact of algorithm change. On Figure 1 we show the difference maps of the average temperature at both 200 and 500hPa, comparing the ten CCM runs with the three runs each using the ECMWF, NCEP and CCM algorithms. All three runs for each case were for the same initial conditions. The two right panels used the same algorithm; thus their difference reflects model climate variability. The other panels reflect variability dependent on algorithm choice. It is evident that the climate statistics for the runs with different algorithms show much larger variability from one another than is seen for the model climate variability. This effect is also evident if a scale dependent diagram for heating rates is developed.

Figure 1. Model output statistics of temperature fields averaged over DJF (1986-87) using different algorithms in the CCM2. Data from 3 realizations of each run using the 3 algorithms (CCM, ECMWF, NMC) were compared by differencing to the CCM2 output for 10 realizations.

Figure 2. Temperature fields
at 200hPa averaged over DJF (1986-87) using different algorithms
in the CCM2 and averaged over 3 realizations. Output using all
3 algorithms is presented as well as differences between the 3
maps.

Having established the
significance of climate statistics for runs with different LWR
algorithms, we now compare integrations using the CCM, ECMWF and
NCEP algorithms. Since we have only three realizations using
the ECMWF and NCEP algorithms, we compare the average fields from
those three realizations with the same three realizations using
the CCM algorithm. We have considered the 500hPa mean fields
of heating rates for the three experiments together with their
absolute differences. The same analysis has been performed for
temperature on the 200hPa surface and is presented on Figure 2.
One can see immediately from this figure that the CCM and ECMWF
runs compare more favorably to one another than to the NCEP(NMC)
run. Additionally, the differences on all maps exceed ten percent
in many locations on the globe, differences which are far above
the climate variability of the model.

Using different LWRM algorithms
in the CCM2 results in notable differences of model output when
the integration proceeds for 60 days. This contrasts to the similarities
found from integrations after 36 hours. From climate validation
studies as discussed, the impact of HR algorithms in a GCM shows
significant climate variability. The climate statistics developed
using three different LWR algorithms in a GCM (the CCM2) when
compared show much greater variability than the climate variability
of the GCM itself. Of the three algorithms tested, the NCEP algorithm
showed greater differences from the other two, the NCAR and ECMWF
algorithms. Further tests are needed with different models.
Plans are underway to perform the same experiment described here
with the ECMWF, NCEP and NASA GCM models.

Baer, F., N. Arsky, J.
J. Charney, and R. G. Ellingson, 1996: Intercomparison of heating
rates generated by global climate model longwave radiation codes.
*J. Geophys. Res.*, accepted for publication.

Gates, W.L., 1992: AMIP:
The Atmospheric Model Intercomparison Project. *Bull. Amer.
Meteor. Soc.*, **73**, 1962-1970.

Kiehl, J.T., J.J. Hack,
and B.P. Briegleb, 1994: Simulated Earth radiation budget of the
National Center for Atmospheric Research Community Climate Model
2 and comparisons with the ERB experiment. *J. Geophys. Res*.,
**99**, 20815-20827.

Morcrette,
J.-J., 1990: Impact of changes to the radiation transfer parameterizations
plus cloud optical properties in the ECMWF model. *Mon. Weather
Rev.*, **118**, 847-873.

Washington, W.M., and C.L.
Parkinson, 1986:* An Introduction to Three-Dimensional Climate
Modeling*, 422 pp., Univ. Sci. Books, Mill Valley, Calif.