Monday, April 30, 2012


date: Thu, 02 Jan 2003 10:04:43 -0500
from: "Michael E. Mann" <>
subject: Gil-Alana manuscript

Dear Keith,
First off, happy new year!
Sorry I haven't gotten back to you sooner on this manuscript. It has been sitting in my
inbox in Charlottesville while I was on sabbatical this fall, so I just found it the other
Hopefully not too late. Here is my quick review based on admittedly only skimming the
paper. I hope it is still helpful!
best regards,
Review of manuscript "A Global Warming in the Temperatures in the Northern Hemisphere Using
Fractionally Integrated Techniques",
author: L.A. Gil-Alana
This manuscript describes some interesting statistical modeling experiments with the CRU
instrumental 'Northern hemisphere mean temperature' series of 1854-1989, building on
previous work by Bloomfield and others.
The primary problem with this, and other similar past papers of this kind, however, is that
the wrong null hypothesis is assumed, creating somewhat of a 'straw man' for the argument
in favor of a long-range dependent noise process. The null hypothesis invoked is that the
observed NH mean temperature series is a realization of a stationary noise process, and
that null hypothesis is subsequently rejected in favor of a non-stationary noise process
(i.e., a fractionally-integrated noise process). The null hypothesis thusly assumed is
inappropriate however, leading to false conclusions regarding the statistical character of
the series. It is very likely that at least 50% of the low-frequency variability in the
series in question is externally forced (by volcanic, solar, and in particular in the 20th
century, anthropogenic radiative forcing). See e.g.:
Crowley, T.J., Causes of Climate Change Over the Past 1000 Years, Science, 289 (14 July),
270-277, 2000.
The non-stationary (ie., the 20th century trends) in the series in large part arises from
the linear response of the climate to these forcings, and much of the apparent
'non-stationarity' is simply a result of the non-stationary nature of the forcings, not the
non-stationarity of the noise term. Moreover, this associated temporal dependence structure
is almost certain to change over time, as the emerging anthropogenic forcing increases the
relative importance of the forced vs. internal (noise) component of variance. See e.g.:
Wigley, T.M.L., R.L. .Smith, and B.D. Santer, Anthropogenic Influence on the
Autocorrelation Structure of Hemispheric-Mean Temperatures, Science, 282, 1676-1680, 1998.
The appropriate null hypothesis (and a challenging one to beat, in my opinion) would be
that the observed temperature series is the sum of an externally-forced component as
modeled e.g. by Crowley (the data is available here: plus a simple autocorrelated AR(1)
internal noise process. This is the most physically-plausible model for the observed NH
mean temperature variations, so the fractionally-integrated process must at the very least
do better (in a statistical sense) than this model...
There are a number of other minor problems:
1) No account is taken of the obvious change in variance (and presumably, the temporal
dependence structure as well) back in time with increased sampling uncertainty (and
potentially, bias due to limited spatial representation in the underlying data network) in
the sparser early observations. For some purposes that isn't a problem. However, in this
study, where it is precisely the variance and temporal dependence structure of the series
that is being analyzed, I believe this is a problem.
2) It looks as if an unnecessarily outdated version of the CRU NH series has been used. A
revised, and updated version through 2001 is available online here:
The author should also reference more recent work:
Jones, P.D., M. New, D.E. Parker, S. Martin, and J.G. Rigor, Surface Air Temperature and
its Changes over the Past 150 Years, Reviews of Geophysics, 37 (2), 173-199, 1999.
see also the additional references and information in the website indicated above.
3) It seems to me that a number of other papers on long-range dependence in surface
temperature series have been published over the past 5 years (e.g. Smith, Nychka, others),
and the author needs to do a far more thorough literature review. The reviewers literature
review looks, on the average, to be about 5 years or so out of date...
I would thus suggest that the authors resubmit the paper for consideration after
appropriately dealing with the issues outlined above.

Professor Michael E. Mann
Department of Environmental Sciences, Clark Hall
University of Virginia
Charlottesville, VA 22903
e-mail: Phone: (434) 924-7770 FAX: (434) 982-2137

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