Various ways of using Empirical Orthogonal Functions for Climate Model evaluation
Abstract. We present a framework for evaluating multi-model ensembles based on common empirical orthogonal functions ('common EOFs') that emphasise salient features connected to spatio-temporal covariance structures embedded in large climate data volumes. In other words, this framework enables the extraction of the most pronounced spatial patterns of coherent variability within the joint data set and provides a set of weights for each model in terms of principal components which refer to exactly the same set of spatial patterns of covariance. In other words, common EOFs provide a means for extracting information from large volumes of data. Moreover, they can provide an objective basis for evaluation that can be used to accentuate ensembles more than traditional methods for evaluation, which tend to focus on individual models. Our demonstration of the capability of common EOFs reveals a statistically significant improvement of the sixth generation of the World Climate Research Programme (WCRP) Climate Model Intercomparison Project (CMIP6) simulations over the previous generation (CMIP5) in terms of their ability to reproduce the mean seasonal cycle in air surface temperature, precipitation, and mean sea-level pressure over the Nordic countries. The leading common EOF principal component for annually/seasonally aggregated temperature, precipitation and pressure statistics suggest that their simulated interannual variability is generally consistent with that seen in the ERA5 reanalysis. We also demonstrate how common EOFs can be used to analyse whether CMIP ensembles reproduce the observed historical trends over the historical period 1959–2021, and the results suggest that the trend statistics provided by both CMIP5 RCP4.5 and CMIP6 SSP245 are consistent with observed trends. An interesting finding is also that the leading common EOF principal component for annually/seasonally aggregated statistics seems to be approximately normally distributed, which is useful information about the multi-model ensemble data.
Rasmus E. Benestad et al.
Status: open (until 13 Apr 2023)
RC1: 'Comment on egusphere-2022-1385', Abdel Hannachi, 05 Mar 2023
- AC1: 'Reply on RC1', Rasmus Benestad, 22 Mar 2023 reply
RC2: 'Comment on egusphere-2022-1385', Anonymous Referee #2, 23 Mar 2023
- CC1: 'Reply on RC2', Rasmus Benestad, 30 Mar 2023 reply
- CC2: 'Reply on RC2', Rasmus Benestad, 30 Mar 2023 reply
Rasmus E. Benestad et al.
common EOFs for evaluation of geophysical data and global climate models. https://www.youtube.com/watch?v=32mtHHAoq6k
A brief presentation of common EOFs in R-studio https://www.youtube.com/watch?v=E01hthVL9pY
Rasmus E. Benestad et al.
Viewed (geographical distribution)
Review of "Various ways of using empirical orthogonal functions
for climate model evaluation" by Benestad et al., submitted to
Geoscientific Model Development.
The paper discusses a particular version of common EOFs with
application to a large number (75) of GCMs runs from CMIP5 and
CMIP6 simulations. The paper highlights the benefits of applying
common EOFs in model evaluation, and points to its use in related
topics such as empirical-statistical downscaling. The authors show
in particular that all the models capture the mean seasonal cycle
and interannual variability of precipitation, sea-level pressure
and surface air temperature reasonably well and that CMIP6 shows
some improvement over CMIP5.
The authors are to be congratulated for this huge effort to apply
common EOFs to a large data base of CMIP5 and CMIP6 simulations.
I support its publication in Geoscientific Model Development
subject to some minor changes.
The SVD-based common EOFs method used in the paper is akin to the
combined EOFs (e.g., Navarra and Simoricini 2010) where the
different datasets are packed in one single large array, which is
then analysed via SVD. Of course the difference is in the way the
data bloc matrices are arranged in the large array. The result is
a set of individual eigenelements (i.e. EOF in S-mode as in
Barnett (1998) and also here, or PC in T-mode as in combined PCA,
see, e.g. Jolliffe (2002)) associated with corresponding
The original common EOFs method as presented first by Flury
(1984, 1986), see also Hannachi (2021) for earlier literature,
analyses different covariance matrices, for which one common EOF
has different explained variances depending on the data (or model
run). Clearly this version gives more degrees-of-freedom to the
common EOFs compared to the one defined by Barnett (1998) or here
where one common EOF has one single explained variance for all the
models' simulations. One benefit of the former is that these
eigenvalues --for one given common EOF-- can be made useful to
weigh the different models, and can be used in various other ways,
e.g., to get the models' climatology. In addition, it overcomes the
issue of scaling in the different datasets.
Of course I must say though that the SVD-based common EOFs
(Barnett 1998 and the present manuscript) is computationally much
faster and is convenient for application with large number of GCMs
runs as in this paper. I think these points, with the above
references highlighting the historical context of common EOF/PCs
should be included in the revised version.
In Hannachi et al. (2022) the references we mentioned there are
more related to climate research. Some other references (e.g.,
Barnett 1999) were missing because the search engine did not find
them as they do not mention common EOFs/PCs in the title. In any
case, the first time common EOF/PCs was mentioned was in Flury
Pg 3 - Please change TAS to SAT (surface air temperature) and PSL
to SLP (sea level pressure) in page 3 and elsewhere.
Pg 3, l71: 'vector' --> 'value'
Pg 6, near l171, l175 - repetition.
Pg 5, top panel: y-axis label: add "Relative (or scaled) rank".
Pg 8, l240 - ensemble spread cannot be normal - could be truncated
Fig. 8, I presume there is one value per model, right? Is it global
mean of the climatology?
Fig. 9, top left and bottom panels, units: oC/yr
Flury B.N., Common principal components in k groups. J. Am. Stat.
Flury B.N., and W. Gutchi: An algorithm for simultaneous orthogonal
transformation of several positive definite symmetric matrices to
nearly diagonal form. SIAM J. Sci. Stat. Comput., 1986.
Hannachi, A., Pattern Identification and Data Mining in Weather and
Climate, Springer Nature, 2021.
Jolliffe I.T., Principal Component Analysis, Second Edition, Springer
Navarra, A., and V. Simoncini, A Guide to Empirical Orthogonal
Functions for Climate Data Analysis. Springer, 2010.