Electronic Supplementary Information for the paper “Climatic factors controlling plant
sensitivity to warming” by Andrei Lapenis1,2, Hugh Henry3, Mathias Vuille1, James Mower2
1 Department of Atmospheric and Environmental Sciences
2 Department of Geography
University at Albany, SUNY
1400 Washington Ave.
Albany, NY 12222
3 Department of Biology
University of Western Ontario, London, ON, Canada
CORRESPONDING AUTHOR: Andrei Lapenis, tel: 518-442-4191, fax: 518-442-4742, e-mail:
andreil@albany.edu
MATERIALS AND METHODS.
Files FFD_supplemental.xls and FLD_supplemental.xls provide details regarding the clusters of
the PEP 725 sites, from which the plant sensitivity values were estimated. Each file contains a
table with average values for each cluster of Mean Annual Temperature (MAT), Seasonal
Temperature Range (STR), Latitude (LAT) and Longitude (LONG), number of original records
(NUM), average number of years of observations (YEARS), and the observed estimate of plant
sensitivity to warming averaged over species (BETA). The latter variable was obtained as an
average for the corresponding sites from the Electronic Supplemental Information in Wolkovich
and colleagues (2012).
Model of plant sensitivity to warming based on the concept of the Thermal Growing Season.
Model description.
In some hypothetical model (Fig.1 main text), the extension of the growing season due
to warming is symmetrical around the seasonal temperature maximum. However, observations
indicate a weaker fall temperature trend relative to the spring warming (Barichivich et al.
2013). This delay of fall warming can be described as an additional shift in the phase of
seasonal temperature changes or a shift in the time lag between some arbitrary day, and the
day of minimum or maximum annual temperature.
The propagation of the temperature signal in soil with time (t) and depth (z) can be
described as a diffusion process (de Vries, 1963):
(1)
, where K is the thermal diffusivity coefficient or the ratio between thermal conductivity and
the volumetric heat capacity of the soil. The fundamental periodic solution of the heat
diffusion equation above can be used to link seasonal changes in temperature at any depth (T)
with MAT and STR at the surface (Kasuda and Archenbach 1965; Hillel 1982; Peixoto and Oort
1992):
(2)
, where is the phase shift of seasonal temperature changes, D is the dimensionless damping
coefficient or the decline of the seasonal temperature range at some depth z, compared to the
surface value of STR (
, and where d =
). This solution was obtained
under the assumption that MAT in soil at some infinite depth is the same as at the surface, and
K is constant (Hillel 1982). The solution demonstrates that the seasonal temperature range
should decline exponentially with soil depth. Parameter D depends on the value of the thermal
diffusivity coefficient. The value of K, in turn, varies with the moisture and mineral composition
of the soil (Kasuda and Archenbach 1965). Overall, in different types of soil under various
moisture conditions, K could change from ~10-7 to ~1.5*10-6 [m2 s–1] (Kasuda and Archenbach
1965). At 0.5 m depth, where the TGS is calculated, this rather large range of changes in K
causes D to change from 0.6 to 0.9. The decline of STR with depth means that the sensitivity of
TGS to 1 oC of MAT warming, measured at some depth in the soil, should always be greater
than the sensitivity defined via surface temperature (see Fig. 1b in main text for illustration).
Eq. 2 can be solved to find the day (t1) of the year (counting from 1 January) when
temperature at 0.5 m is equal to Biological Zero (T= 5 oC, at 0.5 m). For a rather broad range of
MAT and STR values, and under condition that both D and STR are greater than 0, we can
obtain an analytical solution for eq. 2:
(3)
There is, of course, the second solution of eq. 2 for the last day of the year with soil
temperature above the Biological Zero temperature. The second solution, however, was not
used in the analysis, because of the definition of  as the first day of leafing and flowering. As
expected, this first day (t1) depends on MAT and STR, as well as on the phase  and the soil
thermal diffusivity coefficient K (eq. 3).
We can present changes in MAT and STR as their original, pre-warming values plus some
change due to warming: MAT= MAT0 + x, and STR= STR0 + y. During the last four decades,
warming over continents in the winter months was about twice as strong as summer warming
(Lugina et al. 2007; Stine et al. 2009; IPCC, 2007). Therefore, greater MAT caused some decline
in STR, which means that during the last few decades the “x” was overall positive, while the “y”
was typically negative.
These new variables, “x” and “y”, can be linked with each other. If we suggest an
increase in summer temperature of “q” degrees, then the increase in winter should be nq,
where n is the amplification coefficient for winter warming or the ratio between departures
due to the warming of average winter temperature to the departures of temperature in the
summer months. For the case of winter warming being twice as strong as summer warming, for
example, this coefficient equals 2. Here we suggest that the average of summer and winter
warming equals the increase in the mean annual temperature:
(4)
The amplitude of the seasonal temperature range is altered by the uneven distribution
of the seasonal warming signal. The STR should increase, for example, due to summer warming,
but the warming in winter decreases the seasonal temperature range (Fig. 1 in the main text).
Therefore, changes in the STR, or the half amplitude of seasonal temperature changes, can be
calculated as:
(5)
We can use eq. 4 to express q via x and n, and then put this expression in eq. 5 to link y
with x and n:
(6)
The response of t1 (first day of flowering or leafing) to warming depends not only on the
absolute values of MAT and STR, but on the phase shift of STR (parameter  in eq.3). In other
words, we should consider the impact of potential changes in  as well as changes in MAT (x)
and STR (y) on t1. An additional shift of the phase towards winter causes a move of the seasonal
temperature minimum and maximum towards the first day of the year. This process should
decrease the value of t1 (eq.4). During 1954-2007,  declined by about 1.7 days (Stine et al.
2009). Over the same period, the average MAT increased by 1.30 oC (Lugina et al., 2007; Stine
et al. 2009), thus the STR phase shifted by about 1.35 days per 1 oC MAT change. Therefore,
changes in can be linked to the same variable x we introduced above. Due to the increase of
MAT by x oC, the phase should move forward by - m , where m = 1.35 days/1 oC MAT.
Now, suggesting that changes in the MAT (x) as well as pre-warming values of MAT do
not depend on depth, we can reduce eq. 3 to a new expression with a single characteristic of
the warming signal x and three parameters: K, n and m:
(7)
, where, MAT0, STR0 and  are pre-warming values of these variables.
An estimate of observed  via the correlation coefficient between FFD/FDL and MAT
records (Wolkovich, et al. 2012), geometrically, represents an estimate of the slope of changes
in the first flowering/leafing days to the changes in MAT. We can derive an analogue of , called
modeled sensitivity or m, as the full derivative of changes in the first day of the TGS (t1) due to
changes in MAT (x): . The dimension of this derivative is the same as : number of days per 1
oC
MAT. Under conditions of a very small disturbance (x->0), we can obtain the final estimate of
possible changes in the flowering and leafing days due to warming:
(8)
As we can see from eq.8, the modeled sensitivity m does not depend on the pre-warming shift
of the phase of seasonal temperature changes (0). It does depend, however, on the additional
shift in the phase caused by warming (m), as well as on the coefficient of winter warming
amplification (n), soil thermal diffusivity (K) and the pre-warming values of MAT0 and STR0.
Model of interseasonal variability of  at any single geographic location.
The amplification of the warming signal in the winter and spring months relative to
summer and early fall is an important feature of recent climate warming. In our model, the
amplification of warming in winter was described by the variable “y” (above). Another
significant parameter in the seasonal propagation of warming signal is “m” or the phase shift in
the seasonal temperature range. The latter parameter describes the shift of summer maximum
and winter minimum temperature towards the beginning of the calendar year.
Mathematically, the seasonal warming pattern can be described using a slight
modification of eq. 3 described above. First, we introduced the new variable “s”, defined as the
shift in the day of year with respect to a specific daily temperature due to the MAT change. This
new variable is used to link the post warming date (t) with the pre-warming Day of Year via a
specific temperature value in:
(9)
Combining eq. 2 and 9, we express the mean daily temperature via s and DoY:
(10)
Now, we solve eq. 10 for “s” at any given DoY with a threshold temperature (TDoY)
(11)
The two solutions (s1,2) correspond to the two sides of the seasonal temperature range: before
the summer maximum (s1) and after the summer maximum (s2). Finally, we can calculate the
derivative of s by x to estimate the potential shift in the day of year when a specific
temperature can be reached after an increase in the MAT of 1 oC :
(12)
Here, s1,2 (seasonal sensitivity before the summer maximum (s1) and after (s2) ) has the same
dimension as m eq. 8). MAT0, STR0 and 0 are the pre-warming values of these parameters. The
difference between eq. 13 and eq. 9, however, is that eq. 8 is related to changes in the timing
of the TGS (the average growth limiting thermal conditions for entire year), whereas eq. 12
allows shifts in the timing of any period due to a 1 oC MAT increase to be calculated in the
context of a specific temperature (TDaY). Thus, if a specific TDoY value was observed during the
pre-warming conditions on the spring day DoY, after the increase in MAT of 1 oC, the same
temperature will be observed at DoY minus s1.
FIGURES.
Figure 1S. Geographic distribution of MAT (a) and the full amplitude of seasonal temperature
range (2 x STR) (b) at the central coordinates of the clusters of the PEP 725 sites. The size of
each cluster was 0.5 degree of latitude by 0.5 degrees of longitude. All original PEP 725 records
within a single cluster were averaged to obtain average values of plant sensitivity to warming
(see Fig. 2S), as well as other variables shown in the attached MS Excel files (above). As
expected, the geographic distribution of MAT values increased towards southern Europe, while
for 2xSTR, the lowest values occurred along the coasts of the North Sea and the Baltic Sea,
which have maritime climates, and these values increased towards the continental interior of
eastern Europe. Both MAT and STR showed significant spatial clustering. The Moran’s
coefficient for the MAT map was 0.24 with a Z-score of 70 (p<0.001), and the Moran’s
coefficient for the STR distribution was 0.34 with a Z-score of 122 (p<0.001). This clustering was
caused by the aforementioned features of their geographic distributions, such as the increase in
MAT towards southern Europe, and the increase in STR values towards the continental interior
of eastern Europe.
Figure 2S. Geographic distribution of the observed values of plant sensitivity to warming () in
days per 1 oC MAT from FFD (a) and FLD–based (b) estimates (above). The geographic
distribution of  demonstrated features of both the MAT and STR distributions. More
specifically, it increased in absolute value towards coastal regions, and increased somewhat
towards southern Europe. These features were consistent with the suggestion in this paper that
plant sensitivity to warming is controlled by climate (see Fig. 1 in the main text).
Fig. 1Sa
Fig. 1Sb.
Fig. 2Sa.
Fig. 2Sb.
RESULTS.
Figure 3S. Sensitivity of m to the parameter n in “cold” (MAT=0) (a) and “warm” (MAT=10) (b)
midlatitude climatic regions with various values of the thermal diffusivity coefficient (K). Both
figures were derived at a constant STR of 10 oC, which is typical for the climate of central
Europe (Peixoto and Oort 1992). Contour lines on this figure represent m of -8, -9, -10 etc.
days per 1 oC MAT. m demonstrated little dependence on the winter warming amplification
coefficient n (horizontal axis). Overall, departures of n of 50% from the modern average (n=2),
caused less than 10% variation in m. m increased visibly, however, with decreases in K [m2/s].
See the main text for description of calibration approach we used to find optimum K value of
2 10-7 [m2/s] for average climatic conditions of central Europe.
Figure 4S. Estimates of Pearson’s Correlation Coefficient between  and m for a wide range of
the parameter K (thermal diffusivity of soil). The best agreement of the observations and
modeled estimates (highest PCC) is obtained at a value of K of about 2 * 10-7 [m2/s].
Figure 5S. The relationship between plant sensitivity to warming (vertical axis) and the mean
annual temperature (MAT), and the amplitude of the seasonal temperature range (2 STR)
(horizontal axis). Blue diamonds - average observational values of  red squares - estimates of
 via the multiple regression model; green triangles - estimates of  via the deterministic model
(m). The (a) and (b) panels illustrate these relationships for the FFD data, while the (c) and (d)
panels do so for the the FLD data. For each panel, the line represents the best fit obtained
from the corresponding linear regression model. The slopes of these lines differ from the slopes
derived from the two dimentional multiple linear regression analysis shown in Table 1 (main
text). However, the absolute values of the observed and modeled estimates of plant sensitivity
to warming increase with MAT and decline with STR. Overall, the deterministic model showed
a better agreement with the observations than the results of the multiple linear regression (see
the main text for details).
Fig. 3a
Fig. 3b
Fig. 4S.
Fig. 5Sa.
Fig. 5Sb.
Fig. 5Sc.
Fig. 5Sd.
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