We analyse the variability of the probability distribution of daily wind speed in wintertime over Northern and Central Europe in a series of global and regional climate simulations covering the last centuries, and in reanalysis products covering approximately the last 60 years. The focus of the study lies on identifying the link of the variations in the wind speed distribution to the regional near-surface temperature, to the meridional temperature gradient and to the North Atlantic Oscillation.
Our main result is that the link between the daily wind distribution and the regional climate drivers is strongly model dependent. The global models tend to behave similarly, although they show some discrepancies. The two regional models also tend to behave similarly to each other, but surprisingly the results derived from each regional model strongly deviates from the results derived from its driving global model. In addition, considering multi-centennial timescales, we find in two global simulations a long-term tendency for the probability distribution of daily wind speed to widen through the last centuries. The cause for this widening is likely the effect of the deforestation prescribed in these simulations.
We conclude that no clear systematic relationship between the mean temperature, the temperature gradient and/or the North Atlantic Oscillation, with the daily wind speed statistics can be inferred from these simulations. The understanding of past and future changes in the distribution of wind speeds, and thus of wind speed extremes, will require a detailed analysis of the representation of the interaction between large-scale and small-scale dynamics.
Anthropogenic climate change is expected to cause an increase of various
types of extreme events, such as heatwaves, but its effects on extreme winds
is less clear. Section 3 of the Intergovernmental Panel on Climate Change
(IPCC) special report “Managing the Risks of Extreme Events and Disasters
to Advance Climate Change Adaptation” states that there is only low
confidence in projections of changes in extreme winds
The hypotheses put forward to explain changes in storminess are related to
the general physical consideration that warmer periods provide more humidity
and consequently more (latent) energy for possible storms. However, warmer
periods are generally characterized by a weaker meridional temperature
gradient due to the stronger warming of the high latitudes with respect to
the tropics, and thus a weaker baroclinicity, which should lead to weaker or
less storms
Thus, for Northern Europe, from the dynamical point of view it is not clear
how the distribution of wind speed would respond to changes in temperature.
The analysis of long-term trends in wind extremes and storminess in the
observational record has so far yielded inconclusive results, probably due to
the difficulty of constructing homogeneous series of wind speed, because of
e.g. station relocation or changing measuring techniques. Furthermore, the
covered period might be too short to realistically demonstrate trends in the
rarely occurring extreme wind events. On the other hand, reanalysis products
covering long periods
The analysis of the climate of the past centuries can shed light on the
question of whether external climate forcing has an effect on the intensity
or frequency of wind extremes and whether or not the temperature variability
is linked to variability in statistics of wind speeds. Unfortunately,
proxy-based climate reconstructions in general still do not provide
information about extreme wind statistics in the past, except for intense
tropical cyclones
The evolution of temperatures of the past millennium in this region, as
reconstructed from proxy and long-instrumental records, exhibits a generally
warm period in the early centuries (the Medieval Warm Period) and generally
colder centuries around 1700 AD (the Little Ice Age), with the subsequent
warming leading to the current warm period
Climate simulations had been previously used to address the connection
between winds and temperatures in the past
Overview of the analysed simulations/reanalysis and their simulation acronyms, underlying atmosphere and ocean models, boundary forcings (only for regional data sets) as well as the spatial resolution of the atmosphere models and time periods, as used for the analysis.
The spatial resolution of
global climate models may not be adequate to realistically represent extreme
events, especially over regions with complex coastlines. In this respect,
regional climate models, driven by the fields simulated by global climate
models, should provide a better representation of small-scale processes,
topographic influences and of the land-sea contrasts
In this study we present an analysis of the variability of daily wind speed statistics over Northern Europe over the past centuries as simulated by different regional and global climate models. We mainly focus on the consistency among the different models in simulating the relationship between large-scale drivers and the statistics of daily wind speed with the goal of identifying robust patterns across models that can be later tested with proxy reconstructions. These results are also compared to a similar analysis of reanalysis data sets. Although these data sets cover a shorter period and, therefore, they cannot properly capture the decadal and multidecadal variability, they at least offer a possibility to ground truth the results obtained from free-running climate simulations.
This paper is structured as follows: Sect. 2 describes the analysed data sets separated into climate simulations of global circulation models, regional circulation models and reanalysis products. Section 3 defines our area of interest and outlines the applied methods and definitions. Section 4 presents the analysis of the relationship of large-scale drivers and wind speed variance, as well as the comparison of the evolution of the wind speed variance in the millennium simulations. A discussion of the results and conclusions closes the manuscript.
Land-Sea-Masks of the analysed simulations. Figures regarding global data sets (ECHAM5, ECHOG, ECHAM6, NCEP) only show the investigation area. Figures concerning regional data sets (CCLM, MM5, coastDat2) include the Land-Sea-Mask for the whole simulation domain and the investigation area is shown with a red triangle.
Our study focuses on the statistical relationship between spatial and
temporal mean temperature/pressure and daily wind statistics. We use monthly
mean 2 m temperature (T2M) values, monthly mean values of mean sea
level pressure (MSLP) and daily mean 10 m wind speed (WS) for our
analysis. These values are taken from a set of five simulations performed
with five different models, with different spatial and temporal resolution.
These models include global as well as regional models. Additionally, we
analyse one global reanalysis and one regional reanalysis. Table
The NAO pattern exemplarily shown for ECHAM6 as the 1. EOF of mean-sea-level-pressure (MSLP). The corresponding principal components are used as the NAO index.
The coupled GCM ECHAM4-HOPE-G, also denoted in previous literature as ECHO-G
The coupled GCM ECHAM5/MPI-OM consists of the atmospheric component ECHAM5
We also include a climate simulation with the model MPI-ESM with the P
configuration
We outlined above the key-properties of the analysed global simulations.
However, the differences in the external forcings used to drive the
simulations play a crucial role in our analysis. Hence, we additionally
provide a comparison of these differences. An overview can be found in Table
While all three simulations include total solar irradiance (TSI), greenhouse
gas (GHG) and volcanic forcing as external forcings, only ECHAM5 and ECHAM6
incorporate also anthropogenic aerosols and land use changes. There are
various estimations of past TSI, which can be broadly divided into a strong
(S;
Note that for the RCM simulations the same external forcings were applied as for their driving global simulations.
Overview of the GCM forcings. The forcings are abbreviated as
follows: S – strong solar forcing (
The RCM MM5 model consists of a slight modification of the non-hydrostatic
Fifth-generation Pennsylvania-State University-National Center for
Atmospheric Research Mesoscale Model. Such modification allows this
meteorological model to perform long climate simulations. This setup has been
used to conduct a long high-resolution climate simulation of the European
climate during the last millennium, driven at the domain boundaries by the
coupled GCM ECHO-G
A second regional simulation was carried out with the non-hydrostatic
operational weather prediction model COSMO in CLimate Mode (CCLM)
The NCEP/NCAR reanalysis covers the period from 1948-present and is available
at 6-hourly intervals
All wind speed data were daily averaged to proceed with the analysis.
Our analysis concentrates on the distribution of daily wind speed in
wintertime (December, January, February – DJF) over Central and Northern
Europe. The area of investigation has approximately the same extension from
Time correlation coefficients between the following parameters of
the probability distribution of daily mean wind speed: standard deviation of
wind speed (SD), the 50th, 95th and 99th percentile (P50, P95, P99) and the
differences between P95-P50 (diffM) and P99-P95 (diffE) and some large-scale
drivers: spatially averaged December-February air temperature (mTemp), the
spatial air temperature gradient (tGrad) and the North Atlantic Oscillation
index (NAO). The parameters of the probability distributions have been
computed in 30-year sliding windows for the simulations and in 5-year sliding
windows for the reanalysis products. The time series of the drivers have been
smoothed with a running mean filter. Significant (
The statistics of daily wind speed were evaluated over gliding time windows for the different simulation periods. These wind speed statistics include the standard deviation (SD) of the distribution, its 50th, 95th and 99th percentiles (P50, P95, P99) and the differences P95 minus P50 (diffM) and P99 minus P95 (diffE) as a measure of the width of the distribution in the high wind ranges. The analysis of several percentiles and their differences allows the determination of basic changes in the characteristics of wind speed distributions, hence it is possible to investigate if it shifts with time with unchanged shape and/or whether its width changes. Thus, we can discriminate between a change in the mean and/or in the extreme of the wind speed distribution. In our case “extreme” means the tail of the distribution, which includes values above the 95th percentile. For instance, increasing diffM and diffE values would show a broadening of the distribution which means higher extreme wind speeds. The three climate parameters analysed regarding their influence on wind speed are (1) mean seasonal near-surface air temperature (mTemp), (2) mean seasonal meridional temperature gradient (tGrad) and (3) the North Atlantic Oscillation index (NAO). Table 3 presents a summary of these statistical relationships derived from the different model simulations analysed. The presented time correlation coefficients are obtained by calculating the parameters of the daily wind probability distribution at grid-cell scale, followed by averaging over the whole spatial domain.
The temperature gradient is calculated as the absolute value of the
difference between the northern (N) and the southern (S) half of the
investigation area tGrad
The North Atlantic Oscillation (NAO) index is defined as the leading pattern
resulting from principal component analysis (PCA) of the winter mean
sea-level pressure (MSLP) field. This dominant pattern of variability is
characterized by a low pressure system over Iceland and a high pressure
system over the Azores (exemplarily shown for ECHAM6 in Fig.
Because we are interested in the relationship between the slowly changing
mean climate and the variability of the distribution of daily wind speed, the
wind statistics are calculated considering gliding time windows over the
respective time series for each model simulation before they are correlated
with the running mean values of the atmospheric drivers. The climate
parameters analysed are considered as means over the respective time windows
and for Figs.
A random-phase bootstrap method
In the following, we first present the general findings for each of the climate drivers analysed (mTemp, tGrad, NAO) by comparing all considered model simulations and reanalysis products. This is followed by a more detailed presentation of the results with a focus on (a) the regional model simulations and their corresponding driving global models (b) the simulation with the global model ECHAM6/MPI-OM and (c) the reanalysis products. In addition, (d) we compare the results for the overlapping time periods without reanalysis (1655–1990 AD) and with reanalysis (1948–1990 AD) data and (e) for some of the long simulations a comparison of time slices is presented.
Correlation between field mean temperature and 50th percentile of
wind speed for seven different data sets:
A common characteristic shared by all analysed simulations is the negative
correlation between the mean winter temperature (mTemp) and the mean
meridional temperature gradient (tGrad). Hence, in warmer decades the
northern regions warm more strongly than the southern regions, and in colder
decades the northern regions also cool more strongly than the southern
regions. This “high-latitude amplification” is also found in climate
simulations for future scenarios. In those simulations, it is caused by
several positive feedbacks that operate more strongly at high latitudes, such
as ice-snow-albedo feedback
A positive link between these two variables would support the idea that in a warmer atmosphere, holding more humidity and being more energetic in general, stronger winds are more probable. In fact, the relationship between the mTemp and the median winds (P50) is positive in all analysed simulations and reanalysis products, but with the exception of the regional simulation with MM5. However, the correlations, taken individually, are not always statistically significant at the 5 % level.
Warmer air temperatures are also strongly linked to larger values of the high percentiles of the distribution of daily wind, P95 and P99, for most of the simulations. Again, the exceptions relate to the regional model simulations MM5 and CCLM. MM5 presents a negative correlation and CCLM a weak positive correlation.
Variations in the width of the daily wind distribution are described by the differences between the high percentiles, P95 or P99, and the median wind P50. The correlations between mean temperature and these measures of the distribution widths tend to be small for all simulations with the exceptions of the regional models MM5 and CCLM. For these two regional models the correlations are strongly negative, and more strongly so for the MM5 model, indicating that in periods with warmer air temperatures the wind distribution gets narrower at the same time that it shifts to lower values of wind speed, as indicated by the negative correlation with P50.
Briefly summarized, the relationship between winds and mean regional temperature in the global models does support the idea that warmer temperatures are associated with a shift of the distribution of daily winds as a whole. However, this link is not very strong and is contradicted by the regional models.
The temperature gradient should modulate the atmospheric baroclinicity, which should be reflected in the distribution of wind speed. The correlation coefficients between the distribution of wind speeds and tGrad are summarized in the third block of Table 3. In general, the correlations tend to be weak, with some exceptions. In the MM5 simulations they are stronger and positive, whereas in the ECHAM6 simulation they are somewhat weaker but negative. In the NCEP reanalysis the correlations between tGrad and the median wind P50 or the higher percentile winds P95 and P99 are negative and statistically significant. Therefore, this analysis does not support the idea of a relationship between stronger temperature gradient should cause stronger mean winds or more frequent extremes.
The NAO is a large-scale winter circulation pattern that describes the mean strength of the seasonal mean westerly winds in the North Atlantic-European sector and therefore it is plausible that it is also related to the distribution of the daily wind speed in Northern Europe. The correlations between the NAO index across the different simulations yield, however, an incoherent picture. Most simulations do display a positive and relatively strong correlation between the NAO index and the spatially averaged P50, but again with the exception of the two regional models, MM5 and CCLM.
Thus, the regional models behave differently to their respective driving GCMs. In the case of MM5 the correlation between the NAO index and P50 is strikingly negative whereas in the case of CCLM the correlation is weakly positive. A positive phase of the NAO is linked to stronger westerly winds over Northern Europe and hence a negative or weakly negative correlation of the NAO with P50 is surprising. We show later that the negative sign of this correlation in the regional simulations can be explained by the behaviour of the regional models over land areas, whereas the sign of the correlation between NAO and wind over the ocean is the expected one.
The correlation between the NAO index and the width of the distribution (SD) of wind speed averaged over the study region tends to be also positive for most simulations, indicating that stronger mean westerlies tend to concur with a wider distribution of daily wind speed. However, there are exceptions. Again, the regional model simulation MM5 displays a strong negative correlation and the regional model simulation CCLM shows a positive but weak correlation. These negative (MM5) or positive but weak (CCLM) correlations also contrast with the link between the NAO index and the width of the wind speed distribution in their parent global models, ECHO-G and ECHAM5, respectively, both of which display positive and statistically significant correlations. Similarly to the global models, in both reanalysis products the NAO index is strongly and positively correlated with the width of the wind speed distribution.
Briefly stated, the global models display the expected link between the NAO and the median winds over the ocean, but this link is distorted over land. The regional models, with a domain mostly located over land, now show the expected relationship between NAO and wind speed.
It is well known that the winter NAO index is positively correlated with air
temperatures in Northern Europe. The link between the parameters of the wind
speed distribution on one side, and the NAO or the mean air temperature on
the other side may thus be just a reflection of the same physical
relationship. This is also supported by paying attention to how the
correlations with the NAO and with the mean temperature vary across
simulations (third line in Table
The results of this section can be summarized in two main points. All models reproduce the link between mean temperature and temperature gradient, and therefore the regional analysis seems to be physically consistent regarding the thermal variables. The link between these thermal variables and the distribution of wind speed is much weaker and very much model dependent, with regional models deviating from their respective global models.
In the following subsections we investigate in more detail the links between
the large-scale atmospheric drivers and the distributions of daily wind at a
grid-cell level, which allows us to better understand the spatially
aggregated correlations included in Table
In the CCLM simulation (1655–1999 AD) the relationship between P50 wind speed
and mTemp (Fig.
Concerning the link between mTemp and the width of the distribution (SD) the
regional simulations and ECHAM5 the SD correlates negatively with the mean
temperature (Fig.
The ECHO-G simulation (used to drive MM5) displays, in contrast, positive
correlations in a region along the North and South Baltic Sea, straddled by
regions of zero or negative correlations in Scandinavia and central Europe
(Fig.
We assume that the results showing colder periods correlating with stronger
winds may be induced by a stronger meridional temperature gradient (tGrad;
see Sect.
Correlation between field mean temperature and standard deviation of
wind
speed for seven different data sets:
Correlation between NAO index and 50th percentile of wind speed for
seven different data
sets:
Correlation between NAO index and standard deviation of wind speed
for seven
different data sets:
We additionally investigate the relationship between the mean NAO index and
the distribution of wind speeds. The correlation coefficient between the NAO
index (Sect.
The spatially averaged correlation between the NAO and SD is very low in the
CCLM simulation (0.12), but much stronger and negative in the MM5 simulation
(
As already known by the scientific community NAO and mTemp are correlated, hence it is not surprising that in most simulations both show comparable relations to the wind speed distribution. Nevertheless, due to internal model variability and different resolutions the global and regional models show different spatial fingerprints for the correlation maps.
In general the correlation patterns between the large-scale drivers and the parameters of the distribution of wind speed resemble those obtained with ECHAM5 and ECHO-G (ECHAM4/HOPE-G), but some clear differences exist. The higher spatial resolution of ECHAM6 does not, however, lead to correlation patterns that resemble those derived from the regional model simulations CCLM and MM5, pointing towards changes in the physical parametrization (i.e. PBL – Planetary Boundary Layer – scheme) as the main factor explaining the differences in the simulations.
The correlation patterns between the median wind speed P50 and the mean
temperature or the NAO index in ECHAM6 are indeed similar to the ones derived
from ECHAM5 and ECHO-G, displaying generally positive, albeit weak,
correlations between the median winds and temperature
(Fig.
Physically, the relationship between mTemp and median wind is positive (but
statistically not significant) in the ECHAM6 simulation. This indicates that
warmer temperatures are accompanied by a shift towards higher wind speeds and
by a slight tendency to a broader wind speed distribution (see also Fig.
We present the link between the large-scale drivers and the wind speed distribution for the two reanalysis products NCEP and coastDat2. It can be argued that these two reanalysis data sets should be closer to the real climate, because they both incorporate information based on meteorological observations. On the other hand, the reanalysis models are integrated over a relatively short period of time of about 60 years. Therefore the decadal-scale links between the large-scale climate drivers and the probability distribution of wind speed derived from these data sets is most likely afflicted with a higher degree of uncertainty. The correlation patterns derived from NCEP and coastDat2 are based on gliding 5-year windows, instead of 30-year windows as for the longer simulations described before. In addition, this period has witnessed external climate forcings that are quite different from the natural forcings of the previous centuries. Nevertheless, the links between temperature and wind speed distribution should be independent of the radiative forcings that drive the surface temperatures.
Correlation between field mean Temperature and 50th percentile of
wind speed for seven different data sets in the overlapping time period from 1948 to 1990:
The correlation between mTemp and the parameters of the wind speed
distribution for coastDat2 and NCEP shows generally significant positive
values with P50, SD, P95 and P99, but no significant correlation for diffM
and diffE. The spatially resolved correlation between mTemp and P50 (Fig.
The relationship between tGrad and mTemp is negative (
The correlation between tGrad and the distribution of wind speed is found to be predominantly weak in the coastDat2 data, with the only mentionable value (0.34) for the correlation tGrad-diffM. This result means that higher temperature differences between North and South are slightly correlated with a broader wind speed distribution. In contrast, for the NCEP reanalysis, the link is strong but opposite: weaker meridional gradients are linked to stronger median winds and wider wind speed distributions. Regarding the link to the NAO, both reanalysis data sets display a consistent picture, with a positive NAO closely linked to stronger median winds and wider distributions (SD) in most of the domain. This link is stronger over the northern regions and becomes smaller and even negative over the southern fringes of the domain. Again, this spatial structure resembles more closely the structure provided by the global models and differs from the pattern provided by the regional models.
Correlation between field mean Temperature and SD of wind speed for
seven different data sets in the overlapping time period from 1948 to 1990:
This section is dedicated to the comparison of the above explained results
with results for the overlapping time periods without (1655–1990 AD, 30-year
running mean) and with reanalysis data (1948–1990 AD, 5-year running mean).
Regarding the overlapping period 1655 to 1990 the main conclusions remain the
same for both, Table
Regarding the overlapping period 1948 to 1990 the values and patterns change.
Nevertheless, each model simulation still shows different results, and they
do not become more similar to the reanalysis data
(Figs.
Time series of 30-year running mean values of mean temperature (blue) and the
standard deviation (SD) of the wind speed (green) for the GCMs ECHAM6
In the previous sections we analysed the links between large-scale
atmospheric drivers and the distribution of wind speed at decadal and
multidecadal timescales. The time series of the width of the wind speed
distribution over the past millennium indicate, however, that the slowly
changing soil boundary conditions may also have a strong influence on the
long-term evolution of the variability of wind speed in Northern Europe.
Figure
The spatial pattern of changes in SD between the beginning and end of the
ECHAM6 and ECHAM5 simulation suggests that the increase in the width of the
wind speed distribution may be related to surface-boundary processes. This
suggestion is supported by the changes in forest cover in the course of the
last millennium as reconstructed by
This is supported by the analysis of a third time period from 1571 to 1690 AD
(P3) which also shows a strong agreement for the SD ratio (P3
This is also visible for the time series in Fig.
Therefore, at multi-centennial timescales the correlation between the wind speed distribution and temperature that was explored in the previous sections, for ECHAM5 and ECHAM6, could have been indirectly caused by land-use changes. At these timescales, anthropogenic deforestation and mean temperature exhibit a positive trend. Thus the expansion of the wind speed distribution and the increase of temperature in these decades might be induced by physically different factors, leading to positive correlations in our analysis.
Figure
The correlations between mean temperature and the width of the wind
distribution does show a difference in the correlation. For TP1 of ECHAM6
mTemp-diffM is around 0 and mTemp-diffE
This study investigates and compares different simulation data sets and reanalysis products, on timescales covering the last decades to the past millennium, regarding the probability distribution of the daily wind speed in winter time over Northern Europe. Our investigation is aimed at identifying the large-scale factors that drive changes in this probability distribution. The study is based on correlations between different parameters of the wind speed distribution and different climatic indices related to mean temperature, meridional temperature gradient, and the North Atlantic Oscillation. The overlaying question is whether and how the wind speed distribution may change during varying climate conditions and hence whether these conditions may provoke more and/or stronger wind speed extremes.
One prominent result is that the link between the thermal indices and the
North Atlantic Oscillation appears physically consistent in all data sets, and
thus all models are consistent in this regard. The relationship between the
NAO and mean temperature over Europe is a well-known effect
A second important result is that the correlation
between the large-scale indices and the parameters of the wind speed
distribution exhibit markedly different results among the data sets analysed
and it is difficult to derive general conclusions on the effect of these
large-scale drivers on the distribution of daily wind. Comparable
difficulties are reported by
The striking result is that the regional models do not seem to inherit the
dynamical properties of their respective global models, but produce instead
different correlation patterns between the large-scale drivers and the wind
speed distributions. It is plausible that the higher resolution and the
different parametrization schemes of the boundary layer shape the link
between the large-scale dynamics and turbulent processes that modulate the
width of the daily wind distribution. As
Another indicator for the influence of the spatial resolution on our results might be the fact that only the regional simulations MM5 and CCLM show strong negative correlations between mean temperature and the width of the probability distribution as measured by diffM/diffE. These correlations suggest that colder periods are connected with stronger wind speed extremes. In contrast, the GCM data show no clear correlations between these parameters. This study does not allow us to provide a comprehensive dynamical explanation for the different behaviour of wind speeds in changing temperature or pressure conditions: the models show different results although each model seems to be dynamical consistent in itself. Therefore, a detailed analysis of each of the simulations, and maybe of the physical parameterization and computer codes, becomes necessary to understand how the different correlation patterns arise.
On centennial timescales, we identified land-use changes as a very important
factor modulating near-surface wind in the simulations. Note that
anthropogenic changes in land-use are prescribed only in the ECHAM5 and
ECHAM6 simulations, whereas for ECHO-G land-use is kept constant during the
whole simulation. The analysis of the ECHAM5 and ECHAM6 millennium
simulations reveals a strong increase of the standard deviation of wind speed
for the last decades since the industrialization, and in areas that coincide
with larger deforestation along the last centuries. The impact of land-use
changes on wind conditions was also shown by
The main conclusion that can be drawn from this study is that the link between large-scale climate drivers and the distribution of daily wind speeds in wintertime in this region is complex and not fully constrained by currently available simulations. All models analysed here have been individually profusely used in climate simulations and the data sets have been used in a number of other previous studies, and no gross deficiencies have been pointed out so far. We conclude that, although climate models may be dynamically sound in the large-scale contest, the impact of climate change on variables like near-surface wind speed distribution possibly depends more strongly on the details of the physical parametrization and changes in surface forcing, like deforestation, than on the large-scale dynamical drivers, such as large-scale temperature or sea-level-pressure changes.
This work is a contribution to the Helmholtz Climate Initiative REKLIM (Regional Climate Change), a joint research project of the Helmholtz Association of German Research Centres (HGF). The MM5 simulation was carried within the SPEQTRES project (Spanish Ministry of Economy and Competitiveness, ref. CGL2011-29672-C02-02). The work benefited from the Cluster of Excellence “CliSAP” (EXC177), Universität Hamburg, funded through the German Research Foundation (DFG).The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: P. Braconnot