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Hugues Goosse et al.

hundreds of proxy records are available for the past millennium, mainly localized

on the mid-latitude continents. Secondly, analysis in weather forecasting is

performed several times a day, typically every 6 hours. By contrast, proxy data

provide at best seasonal resolution. It is therefore not possible to constrain the

day-to-day variability of the climate system. Thirdly, proxy data contain climatic as

well as nonclimatic signals and the variables measured, such as tree-ring width,

wood density or varve thickness, are usually not a simple function of climate.

Determining precisely the form of the observation operator H is thus a difﬁcult

task. Finally, sophisticated data assimilation techniques are expensive, in particular

if they have to be applied on relatively long periods such as the past millennium.

The central processing unit (CPU) time requirements could be a limiting factor for

the AOGCMs, and the technique developed for data assimilation exercises cover-

ing the past 20 to 50 years for the atmosphere and the ocean cannot be transferred

to the analysis of climate variations during the past millennium without signiﬁcant

adaptation.

Because of the difﬁculties, only a few attempts of data assimilation have been

published for the past millennium (von Storch et al. 2000; Jones and Widmann

2003; van der Schrier and Barkmeijer 2005, Goosse et al. 2006). The ﬁrst technique

proposed was called DATUN, for Data Assimilation Through Upscaling and

Nudging (von Storch et al. 2000). In this technique, the ﬁrst step, upscaling, is to

derive from proxy data the intensity of some large-scale patterns, for instance the

one of the Northern Annular Mode (also known as the Arctic Oscillation and is

linked to the NAO, see previous section). The goal is to increase the signal-to-noise

ratio, as proxy data are usually more suitable for reconstructing large-scale ﬁelds

than small-scale ones. In the second step, a simple nudging technique is applied to

force the model to remain close to the pattern obtained by upscaling. In DATUN,

the nudging is performed directly on the pattern space.

The goal of van der Schrier and Barkmeijer (2005) is also to bring model results

close to a pattern deduced from observations. In the example they studied, the tar-

get for the model surface atmospheric circulation in winter is a reconstruction for

the period 1790–1820. This is not achieved through nudging as in DATUN, but by

adding small perturbations to model variables that optimally lead the atmospheric

model to the target pattern. These perturbations are called “forcing singular vec-

tors” and are computed using the adjoint of the atmospheric model. To apply this

technique, the adjoint model must be available, which induces a limitation of the

applications. As the forcing singular vectors have small amplitudes, they affect

only the large-scale variability while the synoptic variability evolves freely. Van der

Schrier and Barkmeijer (2005) argue that this provides an advantage compared

with nudging techniques, which tend to suppress the variability in the nudged pat-

tern. Unfortunately, no systematic comparison of the two techniques is presently

available.

In the technique described by Goosse et al. (2006), it is not necessary to obtain

ﬁrst a large-scale pattern from observations. The proxy data are directly compared

with model results of an ensemble of simulations, using a simple quadratic law to

compute a cost function CF:

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Climate of the past millennium

181

(t) = (2)

where CF

(t) is the value of the cost function for the experiment k – a member of

the ensemble – for a particular period t, and n is the number of reconstructions or

proxy data used in the model–data comparison. F

obs

is the reconstruction of a

variable F, based on observations, in a particular location for the period t. F

obs

the value of the corresponding variable F simulated in experiment k in the model

and w

is a weight factor characterizing the statistics and reliability of proxy data.

For the technique of Goosse et al. (2006), a relatively large number of simula-

tions (i.e. at least 30) is required. CF

(t) is ﬁrst evaluated for all the simulations and

all the time periods. The minimum for each t over all k experiments is then selected

and the corresponding experiment corresponds to the “best” one for this period.

Such a “best” model estimate for the whole millennium is obtained by grouping

the best simulations for all the periods t, obtaining what is called the best pseudo-

simulation. The technique selects among the ensemble of simulations the one that

is the closest to the available reconstructions, with the cost function measuring the

misﬁt between model results and proxy records. From this cost function, it is then

also possible to assess the quality of the reconstruction for all the periods investig-

ated. An example of the application of this technique is illustrated in Figure 7.9,

showing that it is possible to ﬁnd, for nearly all the periods, an element of the

ensemble that is close to all the available proxies, at least in the case tested by

Goosse et al. (2006) using only a few temperature-sensitive proxies that covered

(nearly) the whole past millennium. We must be aware, however, that this tech-

nique implicitly assumes that the ensemble members cover a sufﬁciently wide

range of internal variability compared with the observed one, in order to ﬁnd a

good analog of the observed situations among the simulations. Problems could

thus occur in regions where this assumption is not valid.

wF t F t

(() ())

modobs

−

∑

1100 1200 1300 1400 1500 17001600 1800 1900

Time (years)

1.0

1.5

2.0

2.5

3.0

Normalized temperature

0.0

0.5

–2.0

–1.5

–1.0

–0.5

Figure 7.9 Anomaly of

summer mean temperature in

Fennoscandia. The average

over an ensemble of 125

simulations performed with

ECBILT–CLIO–VECODE is

in black. The reconstruction

of Briffa et al. (1992) is in

green. The red line is the best

pseudo-simulation obtained

by using 12 proxy records in

the Northern Hemisphere

extratropics (Goosse et al.

2006). The time series are

grouped by 10-year average

and divided by their standard

deviation. The reference

period is 1500–1850.

9781405159050_4_007.qxd 6/3/08 4:44 PM Page 181

182

Hugues Goosse et al.

A main goal of the data assimilation techniques is to provide a reconstruction of

the state of the climate system that is consistent with proxy records, the physical

laws described by the model, and forcing reconstructions. These techniques can

be considered as a physically based way to interpolate the information provided

by data that have an incomplete spatial and temporal coverage. This reconstruc-

tion of past climate variations includes the forced response of the system as well as

the random variations associated with internal variability. As mentioned before,

models alone could not estimate the history of the latter component if model

evolution is not constrained by observations.

Although observations provide only regional- and seasonal-scale constraints,

the estimates obtained by these techniques could be used to analyze high-

frequency changes. For instance, van der Schrier and Barkmeijer (2005) analyze, in

their model, the inﬂuence of the assimilation of a pattern of winter-mean sea-level

pressure corresponding to the period 1790–1820 on the number of cyclones in the

Atlantic and found an enhanced cyclonic activity both south and north of

the modern storm track position. The model results also include information on

variables that are not assimilated, such as oceanic currents. This has allowed van

der Schrier and Barkmeijer (2005) to show that changes in oceanic surface circula-

tion and temperature in the North Atlantic have played a role during the coldest

periods observed in Europe in winter. This kind of information on variables that

are not directly accessible using proxy records provides a very powerful tool to

analyze past climate variations. Indeed, it is possible to propose mechanisms that

are consistent with proxy evidence as well as with the physics governing the atmo-

sphere, the ocean, and sea ice. In a following step, the proposed hypotheses could

be tested using new data or the results of the data assimilation exercise could be

used to select data locations that would give essential information and a strong

constraint on the mechanisms involved.

Conclusions

In this chapter, we have discussed some recent developments that aim to optimize

the combination of proxy data and climate model results, with a focus on the

climate of the past millennium.

One development is to evaluate temperature reconstructions based on proxy

records by using independent “pseudo-proxy records” that are derived from

model experiments. An important application of this method is the validation of

the reliability of the statistical CFR method that has been used for several tempera-

ture reconstructions of the past millennium and improved since its introduction.

Another recent development is to run climate models to compute the climatic

“ﬁngerprint” associated with a particular forcing, and subsequently to apply multi-

ple regression to ﬁnd the combination of ﬁngerprints that gives the best match

with proxy-based temperature reconstructions. This technique has provided a

detailed analysis of the impact of different forcings on the climate of the past

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Climate of the past millennium

183

millennium, including the important effect of anthropogenic forcings on the late

20th century climate. Model and proxy data could also be used to constrain model

parameters as well as important characteristics of the climate system.

Progress is also made by the application of data assimilation techniques that

use both proxy data and models’ results in order to obtain a climate state that is

consistent with the proxy records and model physics. Once such a climate state is

obtained, aspects of this state that are not registered in proxies can be analyzed

in detail, thus providing additional information on the climate of the past millen-

nium. In addition, this climate state can be used to ﬁnd key locations for data

collection. At the moment, the number of suitable proxy data and the computation

time involved still limit the application of data assimilation methods for the past

millennium.

The examples displayed here have shown that the combined analysis of proxy

and model results is certainly an interesting way to improve our understanding of

past climate changes. The examples also show that several difﬁculties remain that

need intense collaboration between scientists from different backgrounds to solve

them. Any improvement in the representation of past changes by models or in the

number and quality of proxy records would certainly be very beneﬁcial. The

method used to combine proxy data and models, however, needs also to be reﬁned

and different methods could be required if one is interested in reconstructions

of past changes or in understanding the causes of those changes. In particular,

estimating precisely the impact on the results of the analysis of the various

hypotheses or prior assumptions involved in the method, sometimes hidden in

complex formulations that could be assessed by only a few specialists, is certainly

an important task.

Acknowledgments

We would like to thank all the scientists who sent us or made available their data-

sets and results. H. Renssen is sponsored by the Netherlands Organization for

Scientiﬁc Research (NWO). M.E. Mann gratefully acknowledges support from

the ATM program of the National Science Foundation (Grant ATM-0542356).

H. Goosse is a Research Associate with the Fonds National de la Recherche

Scientiﬁque (Belgium) and is supported by the Belgian Federal Science Policy

Ofﬁce.

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Latitudinal linkages in late

Holocene moisture-balance

variation

Dirk Verschuren and Dan J. Charman

Keywords

Africa, dendroclimatology, Europe, Holocene, Indian Ocean monsoon, lake-level records,

Little Ice Age, Medieval Warm Period, PEPIII transect, paleohydrology, peat surface-wetness

records, rainfall and drought, speleothem records

Introduction

Projected changes in the amount and distribution of global precipitation over the

next century will almost certainly have greater impacts on the quality of human life

and natural ecosystem functioning than temperature change (IPCC 2007). Most

paleoclimate research to date, however, has concentrated on global and regional

histories of temperature change. This is partly because most high-quality con-

tinental climate-proxy archives are located in regions with positive water balance

and above-average temperature sensitivity. More fundamentally, reconstructing

past precipitation variation independent of coincident temperature changes is a

difﬁcult task. Although temperature and precipitation co-vary on large spatial and

long time-scales (Trenberth and Shea 2005), breakdown of this co-variation at

smaller spatial and shorter time-scales is often a key to understanding the climate

mechanisms involved. Improving our understanding of regional climate and

hydrologic variability at decade to century time-scales thus represents a signiﬁcant

challenge for both the paleoclimate data and paleoclimate modeling communities.

External climate forcing at this time-scale (solar variability, volcanic eruptions) is

relatively modest and expressed through both direct and cumulative effects, there-

fore delays in the response of individual climate-system components and their

associated climate archives to this forcing become more important than they are

over longer time-scales. Consequently, uncertainty exists over the extent to which

observed decadal to century-scale changes truly reﬂect abrupt events or result from

the cumulative effect of interannual variation. A satisfactory answer to this ques-

tion is critical to evaluate the exact relationship between climate variability and

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