Efforts to improve the understanding of past climatic or hydrologic variability have received a great deal of attention in various fields of geosciences such as glaciology, dendrochronology, sedimentology and hydrology. Based on different proxies, each research community produces different kinds of climatic or hydrologic reanalyses at different spatio-temporal scales and resolutions. When considering climate or hydrology, many studies have been devoted to characterising variability, trends or breaks using observed time series representing different regions or climates of the world. However, in hydrology, these studies have usually been limited to short temporal scales (mainly a few decades and more rarely a century) because they require observed time series (which suffer from a limited spatio-temporal density).

This paper introduces ANATEM, a method that combines local observations
and large-scale climatic information (such as the 20CR Reanalysis) to build
long-term probabilistic air temperature and precipitation time series with a high
spatio-temporal resolution (1 day and a few km

Multi-decadal variations of climate variables, intrinsically arising from the
chaotic and non-linear nature of the climate system, have long been observed for
a number of large as well as local-scale climate features

In a non-stationary climate, multi-decadal variations can remain
substantially above or below the long-term trend. In climate projections for
the coming decades, they often lead to large uncertainties

Unfortunately, most climate change impact studies still fail to account for
them. For example, projected climatic and hydrological scenarios for a given
future lead time are classically compared to a so-called reference period
(around 30 years of data) expected to be representative of the recent climate
context. As shown by

Today, characterising the multi-scale variability of climate variables would
appear to be important (if not mandatory) in order to put future climate
projections into perspective. Numerous studies worldwide have investigated
past variability of climate and related variables. In hydrology for instance,
the following studies could be considered as representative for France

Characterising the low-frequency variability of climate and related variables
from observations is therefore seldom possible. An alternative is to
reconstruct the past temporal variations of the variable of interest.
A number of reconstruction approaches have been presented for numerous fields
of geosciences. They use environmental markers such as tree rings

Local meteorological data can alternatively be reconstructed from past
climate variations. The recent release of two major atmospheric reanalyses
covering the entire 20th century (from 1871 for the NOAA 20CR,

Schemes of the three reconstruction models: local model (LM – top scheme), analogue model (ANA – middle scheme), combined local+analogue model (ANATEM – bottom scheme). Predictors are either (1) local-scale meteorological predictors (LM model), (2) mesoscale atmospheric predictors (ANA model) or both (1) + (2) (ANATEM model). Local-scale predictors are daily observations of the variable at one (possibly several) neighbouring precipitation or temperature station (for the present work, Gap rain gauge, Marseille temperature station for precipitation/temperature reconstruction respectively). Mesoscale predictors are fields of atmospheric variables (700 and 1000 hPa geopotential heights over a mesoscale European domain). Local and mesoscale predictors cover the whole period (observation + reconstruction). The three reconstruction models are first developed and evaluated based on their reconstruction skill for the observation period where concomitant observations of the target variable are available (dots of series 3 in the scheme, period 1948–2010 in the present work). Models are next applied for the reconstruction of each day of the reconstruction period (period 1883–2010 in the present work). Note: the reconstruction period can also include the observation period (this is the case in the present work).

This study compares three different statistical approaches for the reconstruction
of high-resolution precipitation and temperature data. Reconstructions are
respectively obtained from observations available at a neighbouring station,
from large-scale (mesoscale) atmospheric variables extracted from the 20CR
reanalysis and from a combination of both. Although the first two approaches
have already been applied in similar studies, the last is an original
approach in that it makes use of both local observations and large-scale
atmospheric information. The principle of reconstructions obtained with the three
approaches is illustrated in Fig.

The Upper Durance River basin as well as the meteorological and atmospheric
data are presented in Sect.

Map of the study area with the 22 selected watersheds.

The three methods have been applied for the reconstruction of mean areal
temperature and precipitations of 22 sub-basins of the Durance River basin,
a mesoscale Alpine watershed located in southeastern France
(Fig.

Main characteristics of the 22 selected watersheds. The numbers in the first
column correspond to those indicated in Fig.

Bounded in the north by the Écrins mountain range of the Alps and in the south by the Mediterranean Sea, the various subcatchments display very different climates. Upstream hydrological regimes are dominated by snow with high snowmelt flows in late spring and early summer. When moving downstream, they become more Mediterranean with additional autumn floods due to large rainfall amounts in that period.

For each watershed, daily mean areal air temperature and precipitation data
over the 1948–2010 period have been taken from the SPAZM meteorological
analysis produced by

To reconstruct the mean areal air temperatures and precipitation of the 22
watersheds, it was first necessary to search for the longest observed series
on or near the Durance watershed. In a technical report published in 1892,

For a qualitative assessment of the reconstructed series, five monthly time
series from the HISTALP project database (monthly series,

Large-scale atmospheric data (describing mesoscale circulation) were
extracted from the “20th Century Reanalysis” (“20CR”,

In climatology and hydrology, the reconstruction of past climatic data is usually necessary to estimate missing values, assess data quality or build long-term climatic reanalyses. Different methods are classically used to reconstruct climatic observations. Some of them are solely based on the series being reconstructed (long-term average or regime methods, temporal interpolation techniques …), others are based on external data (proxy data) used to calibrate and run a reconstruction model. For climatic reconstructions, proxy data could be either observations of the same variable as the one to be reconstructed or observations of different variables assumed to be linked to it.

In the following section, the three methods used for the reconstruction are presented. The first one uses local neighbour observations of a similar proxy (respectively, air temperature or precipitation observation). The second is basically a downscaling approach using regional large-scale information of a different proxy (geopotential fields). The third approach uses both proxies.

As in most reconstruction works, these methods rely on a period over which
both data at the reconstruction point and proxy information are available
(see Fig.

A classical method used for climatic reconstructions is based on regression-like models, where predictors should be well correlated with the data to be reconstructed. This model is calibrated against observations during the observation period.

In the following, the principle of the local model (LM) is to reconstruct the target series (referred to as Tg) from a local neighbour series (referred to as Ne) using a classical linear regression model.

For air temperature reconstruction, the LM model classically uses an additive correction, assumed to be constant over time and mainly influenced by the altitude difference between the target and neighbour series. However, even when the target and neighbour series are very well correlated, residuals of such a model usually exhibit a strong seasonal pattern. In this case, the LM model can be slightly improved by applying an additive correction that varies over time. In the present case, it is represented by a daily harmonic function, calibrated on the inter-annual mean monthly residuals of the differences between the target series and the neighbour series.

The local model for air temperature reconstruction can thus be written as

In the present study this model has been used in a deterministic way, that is
without considering the residual term. Uncertainty is accounted for in the
mixed model as explained in Sect.

For precipitation reconstruction, the LM model classically uses
a multiplicative correction, assumed to be constant over time. This
multiplicative correction is compatible with the asymmetrical distribution of
precipitation values (never negative). The correction factor is taken to be
constant throughout the year. The improvement obtained by using a variable
correction has been assessed and shown to be negligible

The local model used for precipitation reconstruction reads

The second reconstruction model is based on the analogue method introduced by

The analogue method is based on the fact that local meteorological variables
are strongly influenced by the state of the atmosphere and its mesoscale
circulation. Provided that a sufficiently long archive with concomitant local
and large-scale observations is available, it is therefore possible to
produce local meteorological scenarios for any other day for which the
required large-scale atmospheric predictors are available. For this, the

In the present case, the archive is the SPAZM meteorological analysis

The analogue method has some parameters to be set such as the type and level
of predictors, the number of analogue days selected for the prediction, the
spatial domain used to compute the similarity criterion or the similarity
criterion itself. Numerous variations of the analogue method have been
developed. In the present work, the analogue model (ANA) presented
by

Both local and large-scale predictors are available for the 1870–2010 period. The local model (LM) and the analogue model (ANA) can therefore be used to produce two different reconstructions of precipitation or air temperature for this period, one based on local observed data (another station with available data), the other from large-scale atmospheric information (mesoscale variables). The originality and strength of the ANATEM model introduced here lies in an approach that combines the two previous models. In this way, it can take advantage of both local and large-scale information and produce an original representation of uncertainties, conditioned by atmospheric circulation patterns.

The principle of ANATEM is the following: for any target day, the analogue
model allows the identification of

The probabilistic air temperature prediction from the ANATEM model for day

Representation of the ANATEM formulation for air temperature reconstruction
of a given day

In this expression,

The statistical dressing of the LM prediction for the target day

For the example shown in Fig.

Representation of the additive and multiplicative formulation for
precipitation reconstruction from a local model and 50 analogue days for a
given day

Although the ANATEM model uses the same basic principle for precipitation reconstruction, a somewhat different formulation is proposed to account for the specific features of precipitation (asymmetric distribution and many zero values).

The additive correction formulation used for the probabilistic reconstruction
of temperature (Eq.

An alternative formulation uses a multiplicative correction for each analogue
date. The probabilistic reconstruction is here defined by the following
expression:

In the following, the probabilistic reconstruction of precipitation has
therefore been built with a correction model intended to have
a multiplicative behaviour for low values of

Two conditions have been set to define the parameters:

the slope of the tangent to the curve at

when

These two conditions lead to the following expressions for the parameters:

More detailed calculations of the asymptotic behaviour when

Representation of the ANATEM formulation for precipitation reconstruction for
a given day

The probabilistic reconstruction obtained with ANATEM for precipitation
finally reads

In the case of very different values of

if

if

For the example day shown in Fig.

The data presented in Sect.

The evaluation is based on three criteria. The ratio

In the following sections, the performance of the three models for an
illustrative watershed (Ubaye River at Barcelonnette) is first presented. The
evaluation relies (1) on the graphical comparison of the observed and
reconstructed annual series for the 1948–2010 period and (2) on the
distributions obtained for

Annual time series of air temperature reconstructions for the Ubaye River at Barcelonnette watershed by the analogue (ANA), local (LM) and ANATEM models.

Daily, monthly and annual performance criteria of air temperature reconstructions for the Ubaye River at Barcelonnette watershed by the analogue (ANA), local (LM) and ANATEM models. For the annual time step, ANA results are smaller than 0.75; they therefore do not appear in the figure.

Figure

ANA shows a limited mean bias (

LM and ANATEM show very good temporal correlations (mean

Annual time series of precipitation reconstructions for the Ubaye River at Barcelonnette watershed by the analogue (ANA), local (LM) and ANATEM models.

Figure

Daily, monthly and annual performance criteria of precipitation reconstructions for the Ubaye River at Barcelonnette watershed by the analogue (ANA), local (LM) and ANATEM models.

The distributions of criteria at the annual time step
(Fig.

ANA shows a moderate correlation (mean

LM shows no mean bias (by construction), while ANA and ANATEM show a moderate mean bias (less than 0.05);

ANA shows a noticeable variability bias (up to 0.15), while LM and ANATEM show a limited variability bias (around 0.03).

For the sake of readability, only one time series is considered for each
model. ANA and ANATEM probabilistic reconstructions are represented by the
mean time series derived from the ensemble (the daily reconstructed value for
a given day is the mean of the 50 probabilistic reconstructions for this
day). For the sake of simplicity, these mean time series will be referred to
as the reconstructed time series in the following. As will be illustrated
later, note that these ensemble mean time series logically present a much
lower temporal variability than each individual component of the
reconstruction ensemble. In the following, the performance of a given model
will be presented with the distributions of

Daily, monthly and annual performance criteria of air temperature mean reconstructions for 22 watersheds by the analogue (ANA), local (LM) and ANATEM models. For the annual time step, ANA results are smaller than 0.6; they therefore do not appear in the figure.

The main results obtained for air temperature reconstruction are
(Fig.

At daily and monthly time steps, the ANA model suffers from a limited
positive mean bias (mean

At all the different time steps, the LM model provides very satisfactory
results. It shows no mean bias (by construction) and a moderate to limited
variability bias (mean

At all the different time steps, the ANATEM model provides very
satisfactory results. It shows a moderate mean negative bias (mean

Daily, monthly and annual performance criteria of precipitation mean reconstructions for 22 watersheds by the analogue (ANA), local (LM) and ANATEM models.

The three models present slightly different results for precipitation
reconstruction (Fig.

At a daily time step, ANA suffers from a very moderate mean negative
mean bias (mean

At all the different time steps, the LM model shows very satisfactory
results. It shows no mean bias (by construction) and a limited variability
bias (mean

At all the different time steps, the ANATEM model shows very satisfactory
results. It shows a limited negative mean bias (mean

In the present section, the spatial patterns of performance (in terms of correlation, at a daily time step) of the three models and the spatial patterns of the gain in performance obtained with ANATEM reconstructions when either compared to ANA or LM alternatives will be discussed.

Regional correlation patterns of air temperature mean reconstructions by the

For temperature reconstructions, the spatial patterns of model performance
are presented in Fig.

The contribution of the LM (resp. ANA) model to the performance of the ANATEM
model is presented in Fig.

Regional correlation patterns of precipitation mean reconstructions by the

The spatial patterns of model performance obtained for precipitation are
slightly different than those obtained for temperature
(Fig.

ANATEM slightly increases the overall reconstruction performance but at the
same time notably smoothes local contrasts. The contribution of LM to the
performance of ANATEM is generally higher than that of ANA, but decreases as
the distance from Gap increases, ranging from 0.22 to 0.02
(Fig.

Figure

The ANATEM reconstructions have been qualitatively compared to five series of air temperature anomalies obtained from homogenised series of the HISTALP project (University of Genoa, Milan-Brera, Montpellier, Nice airport and Nîmes airport).

The ANATEM model reproduces fairly well the annual and low-frequency
variability of air temperature anomalies from the HISTALP stations (the mean
correlation between ANATEM and HISTALP annual series is close to 0.8).
However, the warming trend in the HISTALP series is stronger than in the
ANATEM reconstructions, HISTALP temperatures being significantly lower than
ANATEM temperatures before 1900 and significantly higher after 1980. ANATEM
reconstructions and HISTALP time series are obviously sensitive to the
reference time series (i.e. Marseille for ANATEM) and the homogenisation
process applied to the observations (for both Marseille and HISTALP
stations). Further research is required to explore the sensitivity of the
ANATEM reconstructions to these key features (partly tested in

Figure

The dispersion between the 22 ANATEM reconstructed time series is relatively low. It is actually similar to the dispersion obtained between the time series of observations available for the same 22 watersheds over the 1960–2010 period (not shown here). The dispersion observed between the five HISTALP series is comparatively much higher. This may be partly explained by the fact that the ANATEM series are reconstructed for all watersheds based on a same reference series (Gap). The main reason is however probably that the HISTALP series cover a much wider spatial domain with a high spatial variability of atmospheric influences and thus precipitation regimes and times series.

The smoothed time series from ANATEM reconstructions is highly correlated with the smoothed time series from HISTALP data. The ANATEM reconstruction is therefore able to reproduce the low-frequency variability of precipitation resulting from climate variability. Some differences can be observed, for example between 1920 and 1930 or between 1970 and 1980. They may be due again to the large spatial variability of precipitation which would also correspond to different precipitation indices, as long as they are estimated from different stations. As already noted for air temperature reconstructions, these differences could also be due to the reference series used in ANATEM and to the homogenisation process for the HISTALP series. Additional work should be considered to explore the importance of such issues.

Mean annual air temperature additive anomaly for the 22 watersheds (ANATEM) and five stations (HISTALP). The additive anomaly for a given year has been computed as the difference between the annual temperature for this year and the 1883–2010 mean.

Mean annual precipitation multiplicative anomaly for the 22 watersheds (ANATEM) and five stations (HISTALP). The multiplicative anomaly for a given year has been computed as the ratio between the annual precipitation for this year and the 1883–2010 mean.

Reconstructing local-scale meteorological variables over long periods is a challenging but necessary task in order to obtain a better understanding of the low-frequency variability of regional climate and climate-driven variables. Three models are compared in the present work, using different types of data for the reconstruction: the regression-based local model (LM) uses local observations of the variable from neighbouring stations as a predictor; the analogue model (ANA), a so-called downscaling model, uses large-scale information concerning atmospheric circulation and the ANATEM model uses a mix of both local and large-scale atmospheric information by combining the local and analogue models.

The three models have been developed and applied to the reconstruction of mean air temperature and precipitation time series for a sample of 22 watersheds situated in the Durance Basin, in the south-east of France. This sample of watersheds represents a wide range of climatic conditions, from highly mountainous to Mediterranean. The local observations used for the reconstruction are respectively Marseille air temperature, Gap precipitation historical time series and geopotential height fields from the 20CR reanalysis.

The multi-criteria and multi-scale performance assessment highlights that the
best reconstructions are obtained when local information is used. The ANA
model is clearly less efficient than the two other models, particularly
concerning low-frequency (annual) air temperature variability or
high-frequency (daily) precipitation variability. On the other hand, the
regression-based model and the ANATEM model provide very satisfactory results
for all criteria. ANATEM offers a slight advantage and the spatial patterns
of the reconstruction skills show that it benefits from the qualities of both
underlying models. Hence, the ANATEM model can be used to reconstruct
adequate air temperature and precipitation series at a high temporal
resolution (daily) and different spatial scales (from 4 to 3500 km

Time series of air temperatures reconstructed for the 1883–2010 period exhibit the well-known warming experienced since the middle of last century, with a higher rate since the 1980s. Reconstructed precipitation time series highlight the large inter-annual variability of annual precipitation for the Durance region. Long-term climatic reanalyses exhibit some particular periods with rather strong rainfall anomalies, such as the wet periods at the beginning of the 1910s and mid-1930s (known for flood events), or relatively dry periods such as the 1940s and 1970s (known for drought events).

The potential for improving the method is considerable. The ANA method used
here was first developed for precipitation forecasts

Another possibility for improvement concerns the combined formulation used
for the ANATEM model. The formulation presented in this paper has been
applied in a straightforward fashion. However, the authors are convinced that
further statistical developments concerning the way the two models are
combined (e.g. forecast combination methods as in

The choice of the reference series used for the local model also presents a challenging issue. It has been shown that the good performance of the models largely depends on this local information. A thorough analysis of the sensitivity to the choice of the reference time series should be carried out. Considering the importance of local information, an extension of the method should also consider the possibility of making use of other historical stations, if available, in the neighbourhood of the region of reconstruction. Cases with multiple historical stations available would open the door to other alternative reconstruction approaches (as stated in the Introduction). Of course, historical local-scale data covering long historical periods are very scarce and sparse. The results also show that the reconstruction skill decreases as the distance from the reference station increases. The region considered in the present study is relatively small. The importance of the reference station would be expected to decrease for reconstructions concerning larger regions. At the same time, in such cases, the contribution of the large-scale information would be expected to be higher. Additional work is definitively required to assess the relative interest of both components of the ANATEM model in this context.

Because of the numerous scientific and operational stakes associated with the
characterisation of long-term variability, the authors are confident that all
of these questions will be tackled by the scientific community in the coming
years. A major application of such reconstructions will obviously be the
reconstruction of long-term variations for a number of climate-driven
variables. For example, the long-term climatic time series produced in the
present work have been used to reconstruct long-term hydrological time series
at multiple hydrometric stations of the Durance Basin

The authors are grateful to Meteo-France and the HISTALP project (Historical Instrumental Climatological Surface Time Series Of The Greater Alpine Region) for providing long-term climatic data, as well as to NOAA for the Twentieth Century Reanalysis Project data set. The authors also wish to thank warmly Vazken Andréassian, Anne-Catherine Favre and Cristian Perret for their support and their helpful comments during different phases of this work. Last but not least, the authors are very grateful to Bettina Schaefli and the three anonymous reviewers for their positive, encouraging and demanding comments that significantly contributed to the improvement of this paper. Edited by: B. Schaefli