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In alpine environments, the growing season is severely constrained by low temperature and snow. Here, we aim at determining the climatic factors that best explain the interannual variation in spring growth onset of alpine plants, and at examining whether photoperiod might limit their phe- nological response during exceptionally warm springs and early snowmelts. We analysed 17 years of data (1998–2014) from 35 automatic weather stations located in subalpine and alpine zones ranging from 1560 to 2450 m asl in the Swiss Alps. These stations are equipped with ultrasonic sensors for snow depth measurements that are also able to detect plant growth in spring and summer, giving a unique opportunity to analyse snow and climate effects on alpine plant phenology. Our analysis showed high phenological variation among years, with one exceptionally early and late spring, namely 2011 and 2013. Overall, the timing of snowmelt and the beginning of plant growth were tightly linked irrespective of the elevation of the station. Snowmelt date was the best predictor of plant growth onset with air temperature after snowmelt modulating the plants’ development rate. This multiple series of alpine plant phenology suggests that currently alpine plants are directly tracking climate change with no major photoperiod limitation.
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ORIGINAL PAPER
Hearingalpine plants growing after snowmelt: ultrasonic snow
sensors provide long-term series of alpine plant phenology
Ya n n Vi t a s s e
1,2,3
&Martine Rebetez
1,2
&Gianluca Filippa
4
&Edoardo Cremonese
4
&
Geoffrey Klein
1,2
&Christian Rixen
3
Received: 9 March 2016 /Revised: 1 June 2016 /Accepted: 15 July 2016 /Published online: 18 August 2016
#ISB 2016
Abstract In alpine environments, the growing season is se-
verely constrained by low temperature and snow. Here, we
aim at determining the climatic factors that best explain the
interannual variation in spring growth onset of alpine plants,
and at examining whether photoperiod might limit their phe-
nological response during exceptionally warm springs and
early snowmelts. We analysed 17 years of data (19982014)
from 35 automatic weather stations located in subalpine and
alpine zones ranging from 1560 to 2450 m asl in the Swiss
Alps. These stations are equipped with ultrasonic sensors for
snow depth measurements that are also able to detect plant
growth in spring and summer, giving a unique opportunity
to analyse snow and climate effects on alpine plant phenology.
Our analysis showed high phenological variation among
years, with one exceptionally early and late spring, namely
2011 and 2013. Overall, the timing of snowmelt and the be-
ginning of plant growth were tightly linked irrespective of the
elevation of the station. Snowmelt date was the best predictor
of plant growth onset with air temperature after snowmelt
modulating the plantsdevelopment rate. This multiple series
of alpine plant phenology suggests that currently alpine plants
are directly tracking climate change with no major photoperi-
od limitation.
Keywords Phenology .Snowmelt .Alpine vegetation .
Climate warming .Growth onset .Photoperiod .Thermal
time .Ultrasonic sensor
Introduction
The shift in the timing of seasonal events in plant and animal
taxa is one of the most visible effects of global warming on
ecosystems in temperate and boreal areas (Parmesan 2006;
Reid et al. 2016; Walther 2003). Motivated by the wish to
quantify the effects of climate warming on terrestrial ecosys-
tems, phenology of temperate and boreal trees has been ex-
tensively documented over the last decades, and numerous
phenological networks were established worldwide to collect
long-term series of observations. The analysis of these series
together with recent experimental studies manipulating tem-
perature and photoperiod have considerably advanced knowl-
edge about the interactions between the main environmental
cues that drive spring phenology in temperate and boreal trees,
namely chilling and forcing temperatures in winter and early
spring, and photoperiod (e.g., Basler and Körner 2012;Clark
et al. 2014;Fuetal.2015a;Fuetal.2015b;Fuetal.2014;
Gallinat et al. 2015; Laube et al. 2014; Zohner and Renner
2015), though the actual physiological processes are still not
well accurately represented in current phenological models
(Basler 2016; Clark et al. 2014).
No such long-term series of phenological data have been
collected in herbaceous plants, especially in alpine plants, for
which phenology remains poorly documented (but see a few
Electronic supplementary material The online version of this article
(doi:10.1007/s00484-016-1216-x) contains supplementary material,
which is available to authorized users.
*Yann Vitasse
yann.vitasse@wsl.ch
1
Institute of Geography, University of Neuchatel,
Neuchatel, Switzerland
2
WSL Swiss Federal Institute for Forest, Snow and Landscape
Research, Neuchatel, Switzerland
3
WSL Institute for Snow and Avalanche Research SLF, Group
Mountain Ecosystems, Davos, Switzerland
4
Environmental Protection Agency of Aosta Valley, ARPAVdA,
Climate Change Unit, Aosta, Italy
Int J Biometeorol (2017) 61:349361
DOI 10.1007/s00484-016-1216-x
long-term series of alpine plant flowering dates in, e.g.,
CaraDonna and Inouye 2015;Inouye2008; Wielgolaski and
Inouye 2013). Yet, global warming has been particularly in-
tense in Arctic and alpine regions over the last decades and is
expected to be more pronounced than on a global or northern
hemisphere average during the next decades (Gobiet et al.
2014). In the Swiss Alps, the annual temperature warming
observed during the last three decades was twice as high com-
pared with what is reported at larger scale in the northern
hemisphere (Böhm et al. 2001; Meehl et al. 2007;Rebetez
and Reinhard 2008). In addition to higher trends on the re-
gional scale, the warming process might be enhanced at higher
elevations in the European Alps due to rapid modifications of
numerous climatic, biological and physical parameters such as
the snow albedo, water vapour changes and latent heat release
or aerosols (Hernández-Henríquez et al. 2015;Mountain
Research Initiative 2015). Alpine regions are therefore partic-
ularly inclined to undergo intense modifications including up-
slope migration of plant species together with modification in
the composition of plant communities (Gottfried et al. 2012;
Grabherr et al. 1994; Parolo and Rossi 2008; Pauli et al. 2012).
The presence of a long-lasting snow cover, insulating
plants from air temperature, complicates phenological studies
conducted in the alpine or arctic tundra. Hence, in such eco-
systems, snow depth data and temperatures recorded at the
plant site are essential for understanding the relationship be-
tween alpine plant phenology and climatic parameters (Wipf
and Rixen 2010). The timing of snowmelt in combination
with temperature and photoperiod is often seen as the main
driver of alpine and Arctic plant phenology (Hülber et al.
2010; Keller and Körner 2003;Wipfetal.2009), and a tight
link between the date of snowmelt and the beginning of plant
growth has been documented in Arctic and alpine ecosystems
(e.g., Bjorkman et al. 2015;Chenetal.2015; Cornelius et al.
2013; Ernakovich et al. 2014; Filippa et al. 2015; Jonas et al.
2008). While in the Arctic, the phenology of plants is expected
to advance in relation to earlier snowmelt and warmer air
temperature (Bjorkman et al. 2015), the phenological shift
may be more moderate in alpine areas because of a possible
limitation by the photoperiod (Ernakovich et al. 2014; Iler
et al. 2013). In fact, an experimental study using 33 alpine
plant species in the Central Alps revealed that about half of
them could be under strong control of photoperiod in their
spring phenology (Keller and Körner 2003). The control of
phenology by photoperiod is supposed to be more moderate in
plant species inhabiting snowbed conditions, for which the
timing of snowmelt would constitute the main driver com-
pared to species growing in wind-exposed habitats with earlier
and stochastic snowmelt (Hülber et al. 2010). However, only
very few long-term series of phenology have been yet
analysed in alpine regions to assess their phenological sensi-
tivity to temperature, snowmelt timing and photoperiod (but
see Anderson et al. 2012;Ileretal.2013).
In the European Alps, warmer winter temperatures have
affected snow cover up to the elevation of 1500 to 2000 m
asl (Laternser and Schneebeli 2003; Scherrer and Appenzeller
2006). At higher elevations, the impact of warmer tempera-
tures on snow pack is usually less pronounced because most
of the winter temperatures at these elevations ranged below
the melting point (Serquet et al. 2011; Serquet et al. 2013).
However, snowpack and snowfall data at higher elevations
and after the month of April were usually too sparse to provide
robust results, but preliminary analysis of several long-term
series of snow data in the Swiss Alps shows evidence for
earlier snowmelt and thinner snowpack irrespective of eleva-
tions from 1139 to 2540 m asl (Klein et al., in revision). A
longer growing season induced by earlier snowmelt is not
necessarily an advantage for plant fitness because it generally
induces a higher exposure of plants to potentially damaging
freezing temperatures or to early development in sub-optimal
climatic conditions, as shown in alpine dwarf shrubs (Wheeler
et al. 2014) and in herbaceous plants (Galvagno et al. 2013;
Inouye 2008).Interestingly, based on fitness-related traits, ear-
lier snowmelt was shown to decrease the overall performance
of Salix herbacea in the Swiss Alps, in spite of the increase of
the growing season length (Sedlacek et al. 2016; Sedlacek
et al. 2015; Wheeler et al. 2016). Yet, some plant species that
are adapted to thin snow (e.g., Loiseleuria procumbens)may
be more advantaged by earlier snowmelt than plants that gen-
erally develop in snowbeds (Wipf et al. 2009). A major
change in the timing of snowmelt is therefore expected to lead
to dramatic changes in plant community composition (Wahren
et al. 2005). As a matter of fact, the heterogeneity of snowmelt
in alpine habitats largely reflects the difference in plant com-
munity composition with some species more adapted to long-
lasting cover and others to more wind-exposed conditions
(Julitta et al. 2014; Walker et al. 1993). However, experimen-
tal snow removal has shown only little advance in the repro-
ductive phenology in alpine species inhabiting snowbed con-
ditions (Petraglia et al. 2014). Long-term observations of veg-
etation onset in alpine plants would help to clarify whether the
photoperiod may become a limiting factor under exceptionally
early snowmelt years but are to date clearly lacking (but see
Bjorkman et al. 2015;Ileretal.2013).
Here, we used a unique dataset, recorded in the Swiss Alps at
elevations ranging from 1560 to 2450 m asl, that combines cli-
matic parameters such as snow depth, air and soil temperature
along with phenological parameters derived from the ultrasonic
sensors mounted at each weather station over the period 1998
2014. We tested two hypotheses. First, we hypothesised that soil
and surface temperatures as well as the date of snowmelt, rather
than mean air temperature, are the best predictors for alpine
spring phenology. Second, we expected to observe a longer time
lag between snowmelt and vegetation onset during warm springs
with early snowmelt as a consequence of lower temperatures
following early snowmelt (compared to later snowmelt), slowing
350 Int J Biometeorol (2017) 61:349361
down plant development, rather than as a consequence of a
photoperiodic limitation.
Materials and methods
Study sites
All climatic and phenological parameters were extracted from
automatic weather stations that belong to the IMIS network
setup by the Swiss Federal Institute for Snow and Avalanche
Research (SLF) in the 1990s. These automatic meteorological
stations monitor and relay to a server every 30 min several
parameters such as snow depth, air temperature, soil surface
temperature, ground temperature recorded just above the soil
but covered by rocks, and solar radiation. Most of the sites are
meadows moderately grazed by cattle, a common type of eco-
system for the Swiss Alps. The ultrasonic sensor (SR50,
Campbell Scientific, USA) mounted on each weather station
for measuring snow depth was also shown to track vegetation
growth accurately after snowmelt (Jonas et al. 2008). In fact,
the ultrasonic sensors were sensitive to plants within a radius of
75 cm below the aiming point for a sensor situated 6 m above
ground. The sensor picks up the reflection of leaves or flowers
if they occupied a minimum horizontal surface of 4 % of the
sensor footprint, and its accuracy is about 2 cm. Note that the
sensor was set up to respond to the nearest target (i.e., for the
purpose of this study, the tallest plants). Hence, the data from
the IMIS network provide a unique opportunity to analyse
snow and climate effects on timing and growth of alpine veg-
etation over a long time period. As the stations were originally
installed to record snow depth and climatic parameters, many
of them are located in rocky terrain with no or very short plants
growing below the ultrasonic sensor. Therefore, among the 123
weather stations that belong to this network, we selected 35
stations for which a clear signal of vegetation was detected by
the ultrasonic sensor (localisation of the weather stations on
Fig. 1). All the 35 sites are in open and flat remote areas,
ranging from 1560 to 2450 m asl and generally not exposed
to wind. Vegetation surveys, conducted in summer 2015 on the
surface covered by the ultrasonic sensors, indicate that
graminoid species are largely dominant at most of the stations,
especially above 2000 m (in which they are dominant in ~85 %
of the selected stations), whereas the proportion of forbs in-
creases towards lower elevations (Table S1). Number of species
growing below the ultrasonic sensors varied between three and
35 depending on the station, with an average of 16 species per
station (Table S1). At the time of the vegetation survey, the
tallest species covering more than 4 % of sampled surface
(i.e., likely to be tracked by the ultrasonic sensor) were always
represented by graminoid species (e.g., Festuca rubra aggr.,
Poa alpina or Carex sempervirens) at the 15 highest selected
stations, whereas forbs were the tallest species in six of the ten
lowest stations (e.g., Rumex alpestris, Rumex alpinus or
Ranunculus aconitifolius, Ta bl e S1).
Data analysis
Extraction of the phenological parameters
We used snow depth data recorded every 30 min by the ultra-
sonic sensors to derive the dates of snowmelt. Figure 2shows
the expected signal of snow and vegetation height detected
from the ultrasonic sensors. We define the snowmelt date after
the end of the meteorological winter (1st of March), as the first
snow-free day after the last snow cover sequence during at
least 1 month. Snowmelt dates correspond to the period when
soil temperature becomes positive and starts varying signifi-
cantly. Height recorded by the ultrasonic sensor after snow-
melt was daily aggregated and used to estimate vegetation
height. Daily median vegetation height time series were pre-
treated as following: we first deleted the data occurring 5 days
earlier than the snowmelt dateand after the day 250 of the year
(7th of September) to avoid inclusion of snow depth data from
the following winter season. We then computed the minimum
vegetation height of the first 6 days after snowmelt and shift
the following data by this number. This step was needed to
account for potentially uncalibrated snow-depth sensors.
Phenological parameters were extracted from a growth curve
fitted to the observed data. To improve fitting accuracy, we
generated an artificial baseline with 30 data points of 0 cm
vegetation height before snowmelt and an artificial plateau
replicating maximum observed vegetation height after the
maximum height detected by a spline function. This was par-
ticularly useful for the maximum plateau because vegetation
growing below the ultrasonic sensors was often grazed during
the growing season (as shown in Fig. 3). To mimic a credible
noise to the data, the random plateau was generated using the
mean and the standard deviations of the five daily vegetation
height values occurring after the maximum height determined
by the spline fitting. After this pre-treatment, we then applied a
statistical method to extract the phenological parameters using
the logistic (Eq. 1), the Gompertz (Eq. 2) and the modified
Gompertz models (Eq. 3), allowing a second increase after the
function enters a first saturation plateau.
ytðÞ¼ A
1þexp 4μ
AλtðÞþ2
 ð1Þ
ytðÞ¼Aexp exp μexp 1ðÞ
AλtðÞþ1

ð2Þ
ytðÞ¼Aexp exp μexp 1ðÞ
AλtðÞþ1

þAexp αttshift
ðÞðÞ ð3Þ
Int J Biometeorol (2017) 61:349361 351
where Aisthe maximum vegetation height (cm), μis the
maximum growth rate (cm/day), λis the start of growth based
on the inflexion point of the fitted curve (day of the year), t
shift
and the scaling factor αcontrol the location (time) and the
strength (slope) of the second increase in the modified
Gompertz model.
Models were optimized by non-linear least squares
methods using the R-package grofit. For each year and site,
the best model was selected according to Akaike Information
Criterion (AIC) values. Confidence intervals for all parame-
ters are estimated by using a non-parametric bootstrap method
(Efron and Tibshirani 1994).
As the focus of the present paper is the beginning of veg-
etation in relation to climatic parameters and snowmelt dates,
we present only the start of growth (λ) and the time lag be-
tween snowmelt and the start of growth (Δ) and disregarded
the other parameters (Fig. 2). After parameter estimation, fil-
tering procedures were applied to remove unreliable values
and inaccuracies. We discarded all data for which: Awas lower
than 4 cm because it would be too close to the accuracy res-
olution of the sensor (15 discarded site-years), Δwas negative
(four discarded site-years), λwas found later than 1st of
August to avoid inclusion of early snowfall (five discarded
site-years), and finally when the standard error of λwas higher
than 3 days, allowing us to keep only robust extracted pheno-
logical parameters (35 discarded site-years). In addition, visu-
al inspection revealed inaccurate site-years that had to be re-
moved manually, mostly because the vegetation signal was
mixed up with late snowfall events (23 site-years). The select-
ed 35 stations provided 322 site-years of phenological records,
covering 17 winter/spring seasons during the period 1998
2014. These data were then used in all further analyses.
Among these 35 sites, 43 % (15) had data of 3 to 7 years,
31 % (11) 8 to 12 years and 26 % (9) more than 12. These last
nine stations were examined in more detail to test a possible
photoperiodic limitation during the warmest springs over the
study period. The earliest vegetation onset dates occurred dur-
ingthewarmestspringin2011andthelatestduringthe
coldest spring in 2013. These 2 years are shown with red
squares and blue triangles, respectively in all graphs, in order
Fig. 2 Conceptual diagram showing the expected theoretical signal of
snow and vegetation detected by the ultrasonic sensors
Fig. 1 Localization and elevation of the 35 weather stations used in the analyses to extract phenological and meteorological data
352 Int J Biometeorol (2017) 61:349361
to visualize the effect of extreme warm and cold years on
alpine plant phenology. Figure 3shows examples of the fitting
procedure that allow us to extract phenological parameters for
a low- and a high-elevation station during three contrasting
years (warm spring: 2011, intermediate: 2009 and cold spring:
2013).
Thermal time required for vegetation onset
For each site and year, we computed thermal time above 0 °C
required from the date of snowmelt to the vegetation onset
using daily mean air temperature data (Eq. 4)
TT i¼d1
d0Ti;dTb

IT
i;d>Tb
 ð4Þ
where TT
i
is the thermal time requirement to initiate vegeta-
tion onset, which occurs for a given station ion day of the year
d
1
.Ti,d is the mean temperature for a given station ion day d,
T
b
is the temperature threshold required to accumulate forcing
temperatures, and I() is an indicator equal to 1 when its argu-
ment is true and 0 otherwise. Thermal time counting begins on
day d
0
which is the day of the year corresponding to the
snowmelt date for a given station i.
As alpine plants may be photosynthetically active during
periods with low temperature (Kimball et al. 1973), we used a
threshold temperature value (T
b
) of 0 °C. Calculations using
other threshold temperatures (from 2 °C to 5 °C) led to similar
results, and thus are not shown.
Statistical analysis
To test which climatic parameters are the best predictors
of vegetation onset dates across stations and years, we
applied a linear mixed effect model accounting for the
variation among stations as a random effect (as different
plant communities with potentially different thermal re-
quirements for vegetation onset can grow at the different
study stations) and the tested climatic parameter as a fixed
effect. We then plotted the predicted values from these
models against the observed values and compared the ac-
curacy of the predictions based on the root mean square
errors (RMSE) and the R
2
of the linear regressions be-
tween predicted and observed values. Residuals were vi-
sually checked for normality and homoscedasticity and
were found to respect model assumptions for any climatic
parameter. We did not combine several climatic parame-
ters as fixed effects in the model because they were col-
linear and we aimed to compare the predictive power of
each factor separately. We selected the following
Fig. 3 Example of the fitting procedure applied to obtain the vegetation
growth parameters for a low- and high-elevation station (GLA2, 1630 m
asl and VAL2, 2270 m asl) for a warm (2011), intermediate (2009) and
cold spring (2013). Lambda is the vegetation onset (day of the year) and
has been determined based on the inflexion point of the logistic,
Gompertz or modified Gomperts models that fitted the best to the data.
The Gompertz model was used to fit the vegetation height in the station
GLA2 in 2013, whereas logistic models were used for all the other five
examples
Int J Biometeorol (2017) 61:349361 353
explanatory variables as fixed effects in the models across
stations and years: mean spring air temperature from
March to May (temperature sensor at 7 m height), mean
monthly(MarchtoJune)airtemperature,meanmonthly
(March to June) soil surface and ground temperature and
the snowmelt dates.
Within individual stations, simple linear regressions be-
tween above-mentioned climatic parameters and vegetation
onset dates were fitted: the explanatory power of each climatic
parameter was evaluated using coefficients of determination.
To test the hypothesis of a photoperiodic limitation
over spring phenology and whether plant development is
slower after early snowmelt, we used an exponential mod-
el to test or evaluate the influence of the date of snowmelt
on the lag between snowmelt and vegetation onset. A
significant relationship can be the result of two non-
exclusive explanations: (i) a genuine photoperiodic limi-
tation, or (ii) a non-proportional effect between the tem-
perature course in spring and the course of plant phenol-
ogy, that is, temperatures following the snowmelt are
colder during years with very early snowmelt than during
years with intermediate and late snowmelt. The apparent
relationship may reflect the different sensitivity of the
different vegetation communities to snowmelt and temper-
atures. The vegetation found at low-elevation sites, having
usually early snowmelt, may require higher thermal time
or longer time lag after snowmelt to start their growth. To
test these two hypotheses, we first calculated the mean air
temperature during a 15-day period after the snowmelt
dates for each site and year (15 days correspond to the
mean time lag between snowmelt and vegetation onset
across stations and years). We then equally separated the
site-years into early, intermediate and late snowmelt dates
to check whether temperatures following early snowmelt
are also colder, potentially explaining the longer time lag
for vegetation onset. Second, we tested whether we do
have a relationship between the thermal time to grow
and the snowmelt dates over the years for stations having
the most available data (nine stations with more than
12 years available) and finally for all stations (Table 1).
A photoperiod limitation would extent the lag between
snowmelt and vegetation onset and increase the thermal
time to trigger vegetation onset during exceptionally early
snowmelt, whereas a pure thermal effect is expected if the
thermal time remains unchanged irrespective of the lag
between snowmelt and vegetation onset. We used linear
regressions rather than exponential relationships because
the linear model performed better than the exponential
model in the cases when a significant linear relationship
was detected. The higher performance of linear models is
likely due to the limited number of data (maximum 17 for
a given station) and we expected individual stationsre-
sults to be either in the increasing part of the non-linear
relationship or in the plateau of the exponential model
that includes all the nine stations.
All data analyses were performed using Rstudio version
0.99.489 (R Core Team 2015).
Results
Climatic and phenological variability
While mean spring temperatures, snowmelt and vegeta-
tion onset showed no significant temporal trends over
the study period (19982014), a high interannual variabil-
ity was detected (Fig. 4). During the study period, mean
spring (MarchAprilMay) temperature ranged between
0.1 and 3.6 °C with a rather homogeneous period from
1998 to 2003 (02 °C) and higher variation afterwards.
Remarkably, the two most extreme years in terms of
spring temperatures occurred in a period of 3 years
(20112013), 2011 being the warmest and 2013 the
coldest. The date of snowmelt and vegetation onset
followed the same general pattern as spring temperature.
The earliest dates of snowmelt and vegetation onset de-
tected over the study period were in 2011 (snowmelt
2011: DOY 119, i.e., about a month earlier than the aver-
age of the other years; vegetation onset 2011: DOY 141,
i.e., about 3 weeks earlier than the average of the other
years), whereas the coldest spring occurred in 2013
(0.02 °C) and coincided with the latest snowmelt and
vegetation onset (DOY 164 and DOY 177, respectively,
Fig. 4). On average, the greatest difference of the date of
vegetation onset for an individual station across years was
about 38 days, reaching up to more than 50 days in a few
stations (data not shown).
Best climatic predictors of alpine spring phenology
While air temperature in April or May explains on average
less than 40 % of the variation of the vegetation onset dates
within stations, soil surface and ground surface temperature
in May explain 57 and 61 % of the variation (Table S2). The
best predictor of vegetation onset for individual stations over
the years is snowmelt dates (R
2
=0.72,TableS2). Using the
linear mixed effect model accounting for the variability
among stations, we found that more than 75 % of the total
variation of the timing of the vegetation onset can be ex-
plained by the following parameters: the snowmelt dates
(R
2
= 0.85, RMSE = 5.9 days, overall the mean time lag
between snowmelt dates and vegetation onset across stations
and years was 15.2 days), the mean soil temperature in May
(R
2
= 0.76, RMSE = 7.7 days) and the mean surface tem-
perature in May (R
2
= 0.75, RMSE = 8.0 days, Fig. 5). The
mixed effect model using spring air temperature as fixed
354 Int J Biometeorol (2017) 61:349361
variable explained less of the variation (66 %, RMSE = 9.0,
Fig. 5). Every degree increase advanced the vegetation onset
by about 4 days using soil surface and ground temperature
in May and by 6.3 days using spring air temperature, where-
as a delay of 10 days in snowmelt delayed the vegetation
onset by 7.5 days. Unexpectedly, the strength of the relation-
ship between the snowmelt dates and the vegetation onset
does not decline or increase, neither with elevation nor with
mean spring temperatures across years of the corresponding
stations (data not shown). Snowmelt is hence an excellent
proxy to predict vegetation onset irrespective of the
elevation.
Little evidence for photoperiod limitation
Across stations and years, the time lag between snowmelt
and the vegetation onset increased exponentially towards
earlier snowmelt (i.e., at low-elevation sites or during the
warmest springs), potentially suggesting a photoperiod
limitation (Fig. 6). However, the mean temperature
Tabl e 1 Linear relationships
between (1) the time lag snow-
melt date-vegetation onset (Δ)
and snowmelt dates, (2) between
the thermal time >0 °C accumu-
lated from snowmelt to vegetation
onset and snowmelt dates.
ID Elevation
(m asl)
nR
2
Δ
vs. snowmelt
Pvalue R
2
Thermal time
vs. snowmelt
Pvalue
SLF2 1560 14 0.45 0.008 0.00 0.991
GLA2 1630 13 0.77 <0.001 0.48 0.008
YBR2 1701 5 0.68 0.087 0.09 0.628
ALI2 1716 10 0.62 0.007 0.74 0.001
JAU2 1716 9 0.64 0.010 0.04 0.603
SCB2 1770 13 0.19 0.136 0.00 0.855
STH2 1780 12 0.68 0.001 0.77 <0.001
ROA4 1838 3 0.14 0.751 0.82 0.281
ROA2 1870 17 0.26 0.038 0.03 0.527
FAE2 1970 17 0.52 0.001 0.07 0.294
LAU2 1970 12 0.23 0.111 0.04 0.531
GRA2 1984 4 0.29 0.462 0.02 0.861
ILI2 2020 9 0.34 0.098 0.09 0.440
SCA2 2030 11 0.01 0.813 0.07 0.419
ELM2 2050 5 0.00 0.923 0.03 0.777
DTR2 2060 8 0.08 0.492 0.10 0.449
VLS2 2070 10 0.17 0.242 0.09 0.391
FIR2 2110 7 0.21 0.306 0.01 0.837
OBM2 2110 5 0.02 0.816 0.21 0.444
HTR2 2150 11 0.32 0.072 0.00 0.844
FIS2 2160 11 0.00 0.866 0.00 0.903
LHO2 2166 5 0.00 0.979 0.25 0.389
TAM3 2170 4 0.18 0.571 0.00 0.988
URS2 2170 14 0.24 0.079 0.00 0.999
PUZ2 2195 5 0.37 0.276 0.14 0.532
TUM2 2195 4 0.22 0.528 0.65 0.196
OBW3 2200 11 0.20 0.166 0.00 0.937
MEI2 2210 4 0.28 0.473 0.02 0.859
CHA2 2220 14 0.26 0.064 0.00 0.835
TUJ3 2220 7 0.02 0.742 0.19 0.325
TUJ2 2270 15 0.11 0.236 0.03 0.549
VAL2 2270 16 0.11 0.204 0.00 0.969
LAG3 2300 7 0.32 0.190 0.22 0.287
LUM2 2388 6 0.47 0.131 0.31 0.247
DAV3 2450 4 0.29 0.465 0.06 0.758
All significant linear relationships at P0.1 are highlighted in bold. For the relationship 1, this was found
significant in 11 stations, mainly at lower elevations, whereas in the lrelationship 2, this was significant in only
three stations
Int J Biometeorol (2017) 61:349361 355
occurring during 15 days following the snowmelt was
also substantially colder in early snowmelt years than in
intermediate or late snowmelt years (Fig. 7), so that the
plants required more time to accumulate the same amount
of heat during early snowmelt years.
At the individual station scale, we detected a significant linear
increase in the time lag from snowmelt to vegetation onset (Δ)
when snowmelt dates occurred earlier in six out of the nine
stations having more than 12 years of available data (at
p< 0.10), mostly at lower elevations (Fig. 8). Across the 35
stations, this relationship was significant for 31 % of the stations
(11 out of the 35 stations), especially at lower elevations
(Table 1). However, when taking into account the temperature
course in spring by using the thermal time above 0 °C from
snowmelt to vegetation onset, only one of the nine stations hav-
ing more than 12 years of data presented a significant linear
relationship (Fig. 8), and three out of 35 stations (8.5 %).
These three stations were located at the lowest elevations within
our dataset (below 1800 m, Table 1). This result indicates the
absence of a strong photoperiodic limitation in recent climatic
conditions, but rather supports the non-proportional increase of
temperature over the course of phenology in spring (i.e., slower
and faster accumulation of the same amount of heat in early- and
late-melting years, respectively, Fig. 7). Thus, at the majority of
the stations, the time lag between snowmelt and vegetation onset
increases with earlier snowmelt as a result of the non-
proportional increase of temperature over the course of spring,
while at a few stations (8.5 %) the vegetation might be limited by
a too-short photoperiod during warm springs (early snowmelt).
Discussion
The network of weather stations analysed here was initially set
up to monitor the snow cover in the Swiss Alps. Our results show
that it also provides a unique long-term and continuous dataset
for tracking the spring phenology of alpine plants. Overall, in
contrast to spring air temperature, the timing of snowmelt is an
excellent proxy to predict the beginning of vegetation growth, as
it explained 85 % of the total variation observed across years and
sites with an accuracy of less than 6 days. No significant shift of
alpine plant phenology was detected over the last 18 years, which
is in fact consistent with climatic data showing no major trends in
spring air temperature and snowmelt over the study period (Reid
et al. 2016). In fact, the study period was too short to detect
robust temporal trends, and it occurred after the major regime
shift (1980s) observed for Earths major biophysical phenomena
including temperature and phenology (Reid et al. 2016).
Unexpectedly, we found that, at the majority of the study sites,
photoperiod did not play a significant role in triggering vegeta-
tion onset over the last two decades, as no significant increase in
heat accumulation required for vegetation onset was detected
during early snowmelt years (warmer springs).
The observed advance of spring onset in response to climate
warming is slowing down in temperate trees, likely as a conse-
quence of a lack of chilling for dormancy release and photope-
riod constrains (Fu et al. 2015b). In contrast, the effect of global
change on alpine plant phenology is expected to be stronger as
alpine plants are beneath snow cover during winter, providing a
long duration of chilling temperature. We could indeed reason-
ably assume that the endodormancy of alpine plants is released
well before snowmelt, so that alpine plants are directly respon-
sive to warm air temperature once snow has melted. In support of
that assumption, we found that the date of snowmelt is the best
proxy for predicting the beginning of the vegetation growth,
while the temperature after the snowmelt modulates the time
lag before growth initiation. This is in line with a recent study
conducted on the alpine vegetation of the Qinghai-Tibetan
Plateau (Chen et al. 2015) and a recent experimental study ma-
nipulating both snow cover and temperature in the Arctic
(Livensperger et al. 2016). Yet, physiologically, the temperature
surrounding the plant meristem tissues is most important. After
snowmelt, the local temperature around the plant changes dra-
matically as the plant tissues become coupled with surface air
temperature. It is then not surprising to obtain higher correlations
when using soil or surface temperature over a short period before
vegetation onset, rather than standard mean spring air
Fig. 4 Spring temperature, snowmelt and the timing of vegetation onset
over the study period. The box-plots show median, first and third quartiles
and extremes values (open circles) of the considered parameter. Filled
circles indicate the mean. Different letters means significant differences
as tested by an ANOVA following by Tukeys honestly significant dif-
ference (HSD) tests
356 Int J Biometeorol (2017) 61:349361
temperature, because the former two capture both snow condi-
tions (temperature around zero under snowpack) and variation in
air temperature once snow has melted. For instance, the
correlation between soil or surface ground temperature in May
and vegetation onset was much higher than if using air temper-
ature of the same month (Table S2).
Within similar elevation ranges, temperatures in alpine ter-
rain can widely vary over very short distances due to rapid
change in the microtopography (slopes, ridges, depressions,
rocks, cracks, etc.), leading to a mosaic of life conditions for
Fig. 5 a. Relationships between the best explanatory variables and the
vegetation onset using the linear mixed effect model. The mean slope
value of the model is reported at the bottom of each graph. b.
Comparison of predicted vegetation onset using the linear mixed effect
model versus observedvegetation onset (extracted from the ultrasonic
sensor) using the best explanatory variables. Spring air temperature is the
mean of daily mean temperature from 1 March to 31 May. The identity
line is reported together with the R
2
,thePvalue of the linear regression
and the RMSE. The year 2011 is represented in red and the year 2013 in
blue to visualize better the effect of extreme warm and cold springs. For
black and white print: The year 2011 is represented with squares and the
year 2013 is represented with triangles
Fig. 6 Time lag between snowmelt and vegetation onset in relation to the
timing of snowmelt. Only data of the nine stations having more than
12 years are plotted. A nonlinear model was fitted between the time lag
snowmelt-vegetation onset and the timing of snowmelt (y = a * exp.(m*
x) + b), with parameters for the exponential model: a = 428 ± 457
(P=0.35);b=7.1±3.8(P=0.06);m=0.029±0.011(P=0.013).
The year 2011 is represented in red and the year 2013 is represented in
blue. For blackand white print: The year 2011 is representedwith squares
and the year 2013 is represented with triangles
Fig. 7 Mean air temperature 15 days after the snowmelt (corresponding
to the mean delay between snowmelt and vegetation across all stations
and years) by clustering years by early, intermediate and late snowmelt
using the quantile 33 and 66 %
Int J Biometeorol (2017) 61:349361 357
alpine plants (e.g., Körner 2003; Scherrer and Körner 2010).
Even when temperature is directly measured at a study site in
standard conditions (i.e., 2 m height under shelter), it can
substantially vary from the actual temperature that is experi-
enced by short-stature alpine plants. Hence, it is largely as-
sumed that standard weather stations do not reflect well the
temperature that prevails at plant height, especially minimum
temperatures (Kollas et al. 2014; Körner 2003). Ground and
plant temperature can also be much colder than air tempera-
ture during clear nights, due to radiative cooling (Inouye
2000) and much warmer during sunny days. In this study,
temperature sums were calculated using air temperatures re-
corded at a 7 m height which might deviate from temperatures
a few centimetres above the ground. However, all the weather
stations used in this study were built to detect the snow cover
and were therefore mounted in flat terrains preventing an im-
portant mismatch between surface ground and air temperature
due to variations in the microtopography.
Alpine plant phenology under global warming; is there
a photoperiod limitation?
A longer time lag was detected between snowmelt and vegeta-
tion onset when snowmelt occurred earlier (i.e., at low-
elevation sites or during warmer springs). The increasing time
required for the vegetation onset with earlier snowmelt could be
the result of two causes: (i) a photoperiodic limitation
preventing the plants from frost damage and (ii) a non-
proportional increase of temperature over time, that is, late veg-
etation onset is likely to occur when temperatures are warmer
than temperatures that occur earlier in the season at lower ele-
vations. Overall, our results support mainly the second hypoth-
esis since no significant increase of growing degree days re-
quired for vegetation onset was detected towards earlier dates
of snowmelt. This is true in 95 % of the study sites, even during
exceptionally warm springs such as those that occurred in 2007
and 2011. Hence, spring phenology of alpine plants is tracking
snowmelt patterns and temperature irrespective of elevation
and the degree of warming. This suggests that, at the commu-
nity level, alpine plants could be fully able to utilize periods of
earlier snowmelt induced by global warming without a pro-
nounced limitation induced by shorter daylength at the time
of snowmelt. However, an increase of the thermal time with
the advance of snowmelt was found in three sites located at low
elevations (below 1800 m). The vegetation tracked by the ul-
trasonic sensors at these sites may be responding to photoperiod
to initiate its development in spring and may therefore be less
sensitive to climate warming. Interestingly, the same dominant
species occur in two of these three sites: Rumex alpinus (Alpine
dock, station ALI2 and GLA2), whereas at the third station
(STH2) the dominant species is represented by Ranunculus
aconitifolius (Buttercup, Table S2).Further investigation would
be necessary to test whether the phenology of these two species
is controlled by photoperiod. Our study may have
underestimated the proportion of species for which photoperiod
is an important factor to initiate their growth because the signals
detected by the ultrasonic sensors may correspond to tall and
fast-growing species only, which are the ones expected to be the
most sensitive to warming and the least responsive to photope-
riod. In contrast, slow-growing plant species that might not
have been detected by the ultrasonic sensors may have a lower
sensitivity with regards to temperature and snowmelt change
and a higher control by photoperiod. Besides, all the weather
Fig. 8 Linear relationships between (1) the time lag from snowmelt date
to vegetation onset (Δ) and snowmelt dates, (2) between the thermal time
>0 °C accumulated from snowmelt to vegetation onset and snowmelt
dates for the nine individual stations having the most available data.
Only stations having more than 12 years of phenology data are represent-
ed. Stations are sorted by their elevation as a photoperiod effect is more
expected in low-elevation stations with early snowmelt. Note that Table 1
shows statistics of the linear regressions for all stations. The year 2011 is
represented in red and the year 2013 is represented in blue. For black and
white print: The year 2011 is represented with squares and the year 2013
with triangles
358 Int J Biometeorol (2017) 61:349361
stations analysed in this study are located in flat terrain, in
which snowbed plant species are expected to occur, while the
effect of photoperiod has been shown to be more significant for
species inhabiting wind-exposed areas, usually convex or steep
terrains with less and irregular snow patterns (Hülber et al.
2010; Keller and Körner 2003). Hence, at current conditions
in flat areas above 1800 m asl, photoperiod seems to not be a
limiting factor in plant development even under unusually
warm springs associated to early snowmelt conditions such as
occurred in 2011. Furthermore, it is likely that, currently, the
beginning of vegetation growth occurs late enough not to be
limited by a photoperiod constraint. Most of alpine plants start
their development only a few days before the maximum
daylength, that is, the summer solstice on 21st of June. For
instance, the average date of vegetation onset found here across
all sites and years was on the day 161 (i.e., 10th of June).
However, extreme early snowmelt together with warmer air
temperature, as is expected by the end of the century, could
expose the plants to a time window for which photoperiod
may become inadequate. As a result, a nonlinear change in
phenology may be expected in response to earlier snowmelt
and temperature rise in the longer term under continued climate
warming (Iler et al. 2013), as currently observed in temperate
and boreal trees (Fu et al. 2015b). For a better understanding of
how climate warming is going to affect plant fitness, we en-
courage further investigations focused on the effect of warmer
temperatures on the timing of flowering and seed production, in
relation to warmer temperatures (Iler and Inouye 2013). For
instance, Scheepens and Stöcklin (2013) showed for
Campanula thyrsoides that, when transplanted towards lower
elevations, the beginning of growth started well earlier, in line
with our results, but also produced substantially fewer flowers
and so likely reduced their fitness.
Our analysis also revealed that the heat required to trigger
vegetation growth substantially varies among the sites, likely
reflecting species-specific heat requirement for growth with
no apparent correlation to elevation. We attribute the differ-
ence in heat requirement among sites to different composi-
tions of the local vegetation (Table S2).
Conclusion
This study shows that, under current climatic conditions, al-
pine plants respond quickly and directly to earlier snowmelt
and increasing temperature in a linear way without a signifi-
cant control of photoperiod over the timing of vegetation onset
in the vast majority of the study sites above 1800 m asl. Any
change in the snowmelt timing has a strong impact on the
surrounding air temperature experienced by alpine plants
and therefore dramatically impacts their spring phenology,
confirming earlier results conducted by Hülber et al. (2010)
in the Austrian Alps at ~2650 m asl. Alpine vegetation will
therefore undergo earlier exposure to warm temperatures be-
cause snowmelt is expected to occur earlier under climate
change, which would enhance the sole effect of warmer tem-
peratures. This is why alpine vegetation might respond more
to climate warming than lowland vegetation. Consequently,
the phenology of alpine vegetation is likely to respond rapidly
at sites with warmer temperatures and earlier snowmelt due to
climate change, especially in snowbed habitats. Finally, the
method developed here to extract the sensorsdetection of
vegetation growth could be extended to other meteorological
networks using ultrasonic sensors all over the globe, opening
promising avenues to explore how alpine or arctic vegetation
will respond to global warming worldwide.
Acknowledgments We are grateful to Marcel Schoch and Christoph
Marty for their assistance in providing climate parameters from the IMIS
weather stations and to Andreas Scharl and André Fichtner for their field
assistance with the vegetation surveys at the weather stations. We thank
Andreas Stoffel for drawing the map of the selected stations shown in
Fig. 1. We are grateful to David Inouye for his valuable comments on the
manuscript and William Doehler for his editorial improvements of the
manuscript. The research leading to these results has been funded by the
Swiss National Science Foundation (grant number 200021-152954).
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... Therefore, our findings challenge the widely assumed rise in future productivity as the thermal growing season prolongs due to climate warming. A close correlation between snowmelt and the onset of leaf greening and elongation has previously been observed in alpine [26][27][28] and arctic vegetation 29,30 . While climatic conditions for arctic and alpine plants differ in important aspects such as solar angle, photoperiod, precipitation and frost regime, they also share important similarities such as the short GSL 31 . ...
... We observed normal growth rates with a day-length of 14.5 h (1-1.5 months ahead of the natural season start) and previously even initiated typical spring growth using an 11.5 h-photoperiod for the same vegetation type (unpublished data). A study across ca. 25 alpine sites and 17 years found no indication that photoperiod influenced leaf elongation after snowmelt 28 . Beside its signalling effect, a short photoperiod also encompasses lower levels of photon fluxes, possibly limiting carbon uptake. ...
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... We then calculated for each species and each observation site growing degree-days (GDD) defined as the sum of positive daily mean temperature from January 1 st to the median date of budburst observed over the 2007-2014 observation period. GDD was calculated with two different temperature thresholds: the more commonly-used 5°C (hereafter designated as GDD5) and 0°C (hereafter designated as GDD0) because daily mean temperatures between 0°C and 5°C may contribute to trigger budburst events in plants growing in mountainous environments (Körner 1999;Vitasse et al. 2016). We chose Jan 1 st as the starting date of accumulation because the ecodormancy phase can begin as early as January for some species and because the climatic conditions at the beginning of this phase vary a lot between species, years, and sites along elevation and latitudinal gradient (Asse et al., 2018). ...
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Inter-annual variation in climate is reflected by changes in the timing of phenology. Over the last decades a considerable number of models have been developed in order to explain the inter-annual variation of spring phenology in trees. Contrary to empirical models, "process-based" models aim at simulating physiological processes in order to yield more realistic predictions of growing season onset dates. Despite the increasing knowledge on the environmental controls of seasonal dormancy in trees, the detailed action and interaction of the involved environmental drivers (chilling, photoperiod and warm temperature) remains to be elucidated. This study aims at a uniform comparison of a wide range of existing models (and new recombinations), on a multitude of long-term observation series in six tree species across central Europe, using extensive cross-validation. Even though the assessed models differ in the phases of dormancy and environmental drivers accounted for, they yielded a surprisingly similar quality of prediction of leaf unfolding dates. Depending on the species, the lowest average prediction errors for leaf unfolding (RMSE) ranged from 7 to 9 days for the dataset pooled across sites and years and from 4 to 6 days for site-specific predictions, in absence of any obvious geographical pattern. Simple models, that feature ecodormancy release only, performed similar or better than more complex models, which additionally include endodormancy release through chilling temperatures. Model parameterisation tended to converge towards similar behaviour and models with many parameters tended to overfit on the 40 year time-series of leaf unfolding. Additionally, all models tended to underestimate the inter-annual variation of leaf unfolding and failed to predict very early or late dates of leaf unfolding in certain years. The transfer of site-specific parameters to other sites was associated with an almost doubling of the average prediction error, independent of distance and climatic similarity between the calibration and validation sites. The findings challenge the accurate implementation of the physiological processes controlling spring phenology in the models and highlight shortcomings associated with model parameterisation on observational time-series only.
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Despite evidence from a number of Earth systems that abrupt temporal changes known as regime shifts are important, their nature, scale and mechanisms remain poorly documented and understood. Applying principal component analysis, change-point analysis and a sequential t-test analysis of regime shifts to 72 time series, we confirm that the 1980s regime shift represented a major change in the Earth's biophysical systems from the upper atmosphere to the depths of the ocean and from the Arctic to the Antarctic, and occurred at slightly different times around the world. Using historical climate model simulations from the Coupled Model Intercomparison Project Phase 5 (CMIP5) and statistical modelling of historical temperatures, we then demonstrate that this event was triggered by rapid global warming from anthropogenic plus natural forcing, the latter associated with the recovery from the El Chichón volcanic eruption. The shift in temperature that occurred at this time is hypothesized as the main forcing for a cascade of abrupt environmental changes. Within the context of the last century or more, the 1980s event was unique in terms of its global scope and scale; our observed consequences imply that if unavoidable natural events such as major volcanic eruptions interact with anthropogenic warming unforeseen multiplier effects may occur.
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Earlier spring leaf unfolding is a frequently observed response of plants to climate warming. Many deciduous tree species require chilling for dormancy release, and warming-related reductions in chilling may counteract the advance of leaf unfolding in response to warming. Empirical evidence for this, however, is limited to saplings or twigs in climate-controlled chambers. Using long-term in situ observations of leaf unfolding for seven dominant European tree species at 1,245 sites, here we show that the apparent response of leaf unfolding to climate warming (ST, expressed in days advance of leaf unfolding per °C warming) has significantly decreased from 1980 to 2013 in all monitored tree species. Averaged across all species and sites, ST decreased by 40% from 4.0 ± 1.8 days °C(-1) during 1980-1994 to 2.3 ± 1.6 days °C(-1) during 1999-2013. The declining ST was also simulated by chilling-based phenology models, albeit with a weaker decline (24-30%) than observed in situ. The reduction in ST is likely to be partly attributable to reduced chilling. Nonetheless, other mechanisms may also have a role, such as 'photoperiod limitation' mechanisms that may become ultimately limiting when leaf unfolding dates occur too early in the season. Our results provide empirical evidence for a declining ST, but also suggest that the predicted strong winter warming in the future may further reduce ST and therefore result in a slowdown in the advance of tree spring phenology.
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Despite evidence from a number of Earth systems that abrupt temporal changes known as regime shifts are important, their nature, scale and mechanisms remain poorly documented and understood. Applying principal component analysis, change-point analysis and a sequential t-test analysis of regime shifts to 72 time series, we confirm that the 1980s regime shift represented a major change in the Earth's biophysical systems from the upper atmosphere to the depths of the ocean and from the Arctic to the Antarctic, and occurred at slightly different times around the world. Using historical climate model simulations from the Coupled Model Intercomparison Project Phase 5 (CMIP5) and statistical modelling of historical temperatures, we then demonstrate that this event was triggered by rapid global warming from anthropogenic plus natural forcing, the latter associated with the recovery from the El Chichón volcanic eruption. The shift in temperature that occurred at this time is hypothesized as the main forcing for a cascade of abrupt environmental changes. Within the context of the last century or more, the 1980s event was unique in terms of its global scope and scale; our observed consequences imply that if unavoidable natural events such as major volcanic eruptions interact with anthropogenic warming unforeseen multiplier effects may occur.
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Plant communities in the European Alps are assumed to be highly affected by climate change, as the temperature rise in this region is above the global average. It is predicted that higher temperatures will lead to advanced snowmelt dates and that the number of extreme weather events will increase. The aims of this study were to determine the impacts of extreme climatic events on flower phenology and to assess whether those impacts differed between lower and higher altitudes. In 2010, an experiment simulating advanced and delayed snowmelt as well as a drought event was conducted along an altitudinal transect approximately every 250 m (600–2000 m above sea level) in the Berchtesgaden National Park, Germany. The study showed that flower phenology was strongly affected by altitude; however, there were few effects of the manipulative treatments on flowering. The effects of advanced snowmelt were significantly greater at higher than at lower sites, but no significant difference was found between both altitudinal bands for the other treatments. The response of flower phenology to temperature declined through the season and the length of flowering duration was not significantly influenced by treatments. The stronger effect of advanced snowmelt at higher altitudes may be a response to differences in treatment intensity across the gradient. Consequently, shifts in the date of snowmelt due to global warming may affect species more at higher than at lower altitudes, as changes may be more pronounced at higher altitudes. These data indicate a rather low risk of drought events on flowering phenology in the Bavarian Alps.
Chapter
Phenology, mainly on plants, in the Northern Hemisphere north of 60°N in the Old World and of 50°N in the New World is described in the present chapter, both historically and in modern times. Experiments, field work and satellite data are discussed. Phenological observations related to recent climate change at high latitudes are discussed in detail, and they are generally found to be good indicators of such changes during long-term studies. However, various organisms in the food chain, or sometimes even different individuals of the same species, do not react in exactly the same way on climate change. The response may also vary with the continentality of a region and with the time of the year. An increasing mismatch may be seen between production and consumption at various trophic levels both in terrestrial and aquatic ecosystems. © 2013 Springer Science+Business Media B.V. All rights are reserved.