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On the validation of RCMs in terms of reproducing the annual cycle
Tomas Halenka, Petr Skalak and Michal Belda
Department of Meteorology and Environment Protection, Charles University; tomas.halenka@mff.cuni.cz
1. Climate models and annual cycle
There are many aspects of the validation of climate models.
In addition to standard statistical characteristics a more indepth
analysis of annual cycle performance can provide
more information on ability of the models to reproduce
properly the physical processes which strongly affect the
behavior of climate parameters during the year. Global
Circulation Models (GCMs) can reproduce climate features
on large scales, but their accuracy decreases when
proceeding from continental to regional and local scales
because of the lack of resolution and thus on the regional
scale they are very often rather poor in reproducing the
annual cycle. The more detail analysis of 15 RCMs used in
EC FP6 IP ENSEMBLES in ERA 40 driven experiment on
25 km resolution for the period of 1961-2000 in different
PRUDENCE regions presents the comparison of the models
and their validation in terms of annual cycle reproduction.
While for the temperature the performance of the models is
mostly very good and quite consistent, there are some
models with rather significant problems in some regions in
reproducing annual cycle of precipitation.
2. ENSEMBLES RCMs assessment in terms of
annual cycle
The quality of reproducing the annual course in the model
simulations is believed to be good indication of quality of
different atmospheric processes description which affects
the overall model performance. However, to compare the
annual course patterns with those based on observational
data is not simple and unambiguous task, for the purpose of
the use in the weighting methods in ENSEMBLES project
some objective method is required. The problem of the
annual course analysis is that we cannot use just one simple
characteristic as bias, basically at least three patters are of
importance, i.e. in addition to the bias it is the amplitude and
shift in period, either as a whole or partly in some seasons.
Taylor (2001) presented so called Taylor diagram, which is
used for presenting the data in terms of RMS error, standard
deviation and correlation and show just the analysis of
models simulations with emphasis on annual cycle.
Actually, although these characteristics are not completely
independent, we can see the analogue between the bias and
RMS error, as well as in between amplitude and standard
deviation, correlation being good representation of the shifts
in the annual course. For purpose of the weighting we
propose to use the score index
where R 0 is the maximum correlation attainable. For
simplicity we used maximum value R 0 =1. Parameter R is the
correlation coefficient with respect to the observation dataset
used for comparison, m is standard deviation of the
model results m normalized by standard deviation of the
observational dataset used for validation . We have made
calculations both for first degree formulation as above and
fourth degree one discussed in Taylor (2001), which reads
Additionally, we have tested the second degree
formulation as well, basically the higher degree penalizes
the lower correlation, for computations in this analysis
seems to be usefull to use the 4 th order formulation for
temperature to resolve the differences between otherwise
very high scores, for precipitation the scores are not so
high anyway and the first degree is enough to resolve the
performance of the individual models. All the calculations
were performed for individual PRUDENCE regions, quite
significant differences appears between the models for
some regions. To compare these score annual cycles for
temperature and precipitation are presented in Fig. 1 and
2, respectively, using ENSEMBLES gridded data (E-obs,
Haylock et al., 2008). Original CRU databases are shown
for comparison as well, although for precipitation there are
some differences between the climatologies the resulting
scores are not so significantly affected.
It should be mentioned that this method is validating the
general performance of the models anyway, for
temperature, where the variance of the complete monthly
data is usually nearly of order higher than interannual
variance (year by year) of data for individual months, this
performance well correspond with the performance of
annual cycle. The results for precipitation are not so clear,
the variance of all the time series is basically the similar as
the interannual variability of individual monthly data so
that the overall performance and quality of annual cycle
cannot be well resolved by this method. Proper choice of
R 0 for precipitation could be of great importance for
further application of the method.
Annual courses of temperature as well as precipitation will
be presented for individual models and regions. Taylor’s
diagrams will show the models validation against E-Obs.
Acknowledgements
This work is supported in framework of EC FP6 IP
ENSEMBLES. Some contributions to the tasks are
supported from local sources as well under Research Plan
of MSMT, No. MSM 0021620860. We acknowledge the
E-Obs dataset from the EU-FP6 project ENSEMBLES
(http://www.ensembles-eu.org) and the data providers in
the ECA&D project (http://eca.knmi.nl).
References
Haylock, M.R., N. Hofstra, A.M.G. Klein Tank, E.J. Klok,
P.D. Jones, M. New, A European daily high-resolution
gridded dataset of surface temperature and
precipitation. J. Geophys. Res (Atmospheres), 113,
D20119, doi:10.1029/2008JD10201, 2008.
Taylor, Karl E., Summarizing multiple aspects of model
performance in single diagram, J. Geophys. Res., 106,
D7, 7183--7192, 2001.