Ecosystems are open systems that exchange matter and energy with their
environment. They differ in their efficiency in doing so as a result of their
location on Earth, structure and disturbance, including anthropogenic legacy.
Entropy has been proposed to be an effective metric to describe these
differences as it relates energy use efficiencies of ecosystems to their
thermodynamic environment (i.e., temperature) but has rarely been studied to
understand how ecosystems with different disturbance legacies respond when
confronted with environmental variability. We studied three sites in a
longleaf pine ecosystem with varying levels of anthropogenic legacy and plant
functional diversity, all of which were exposed to extreme drought. We
quantified radiative (effrad), metabolic and overall entropy
changes – as well as changes in exported to imported entropy
(effflux) in response to drought disturbance and environmental
variability using 24 total years of eddy covariance data (8 years per site).
We show that structural and functional characteristics contribute to
differences in energy use efficiencies at the three study sites. Our results
demonstrate that ecosystem function during drought is modulated by decreased
absorbed solar energy and variation in the partitioning of energy and entropy
exports owing to differences in site enhanced vegetation index and/or soil
water content. Low effrad and metabolic entropy as well as slow
adjustment of effflux at the anthropogenically altered site
prolonged its recovery from drought by approximately 1 year. In contrast,
stands with greater plant functional diversity (i.e., the ones that included
both C3 and C4 species) adjusted their entropy exports when faced
with drought, which accelerated their recovery. Our study provides a path
forward for using entropy to determine ecosystem function across different
global ecosystems.
Introduction
Ecosystems utilize resources, such as solar radiation, nutrients and water,
to maintain a state far from thermodynamic equilibrium
(Amthor, 2010; Beer et al., 2009; Finzi et al., 2007; Thomas et al., 2016). Understanding ecosystem resource
use efficiency is crucial, as anthropogenic and climate-induced changes
around the globe continue to alter ecosystem structure and function
(Haddeland et al., 2014; Porter et al., 2012;
Reinmann and Hutyra, 2016; Thom et al., 2017).
Ecosystems are open and dynamic systems that exchange matter and energy with
their surroundings as described by the ecosystem energy balance:
Rn=Rs,in-Rs,out+Rl,in-Rl,out=LE+H+G+M,
where Rn is net radiation, Rs,in and
Rs,out are incident and upwelling shortwave radiation, and
Rl,in and Rl,out are incoming and upwelling longwave
radiation, respectively. The terms LE, H and G represent energy exports
through latent heat, sensible heat and ground heat fluxes, respectively; and
M is an energy storage term comprised of changes in biomass accumulation
through metabolic processes (Holdaway et al., 2010). M is often neglected
due to the assumption of a steady state over longer periods and because M
is much smaller in magnitude compared to other fluxes. However, M imposes a
control on energy fluxes, like Rn, LE and H, through changes in
leaf area and reflective properties, as well as through active biotic control
in response to changes in environmental variables (i.e., stomata opening and
closing due to water availability, Hammerle et al., 2008).
From Eq. (1), ecosystem energy exchange is a function of its thermodynamic
environment – the heat transfer of a system with its surroundings – which
differs based on the different mechanisms by which heat is transported:
conduction, convection and radiation. Complicating our understanding of
ecosystem energy dynamics is the fact that more frequent fluctuations in
environmental variables are expected as a result of global climate change,
including extreme events like droughts, which will alter the resource
efficiency of ecosystems across the globe and with it their resilience
(Franklin et al., 2016; Woodward et al., 2010).
It is hypothesized that ecosystems aim to optimize their energy use and thus
maximize their balance of entropy production and entropy exports to avoid
thermodynamic equilibrium (Schneider and Kay, 1994; Schymanski et al.,
2010). The magnitude of entropy production and entropy fluxes in ecosystems
depends on thermodynamic gradients (i.e., thermal gradients, chemical
gradients, etc.) between organisms and their surroundings (Kleidon,
2010). Ecosystems invest energy to build more complex structures
(i.e., self-sustainability; Müller and Kroll, 2011; Virgo and
Harvey, 2007), which can enhance their entropy export and therefore keep the
ecosystem far from thermodynamic equilibrium (Odum, 1988;
Schneider and Kay, 1994; Holdaway et al., 2010; Skene, 2015). For example,
forest stands with more vertical structure were found to be more efficient
in harvesting available light, which consequently increased their
productivity (Bohn and Huth, 2017; Hardiman et al., 2011).
Productive sites with greater leaf area can maintain higher LE fluxes, which
increases their entropy export (Meysman and Bruers, 2010; Brunsell
et al., 2011); LE fluxes also maintain lower ecosystem surface temperatures
and thereby greater entropy production. On the contrary, large values of H
caused by surface temperatures that are greater than air temperatures
result in lower entropy production (LeMone et al., 2007). This has
been shown in deforested landscapes (Bonan, 2008; Khanna et al., 2017), as
well as comparative studies of different vegetation types, and in ecosystems
with heterogeneity in their vegetation distribution (Holdaway et al., 2010;
Brunsell et al., 2011; Kuricheva et al., 2017).
Here, we evaluate how efficiently ecosystems use energy by assessing
ecosystem entropy production as well as by quantifying the ratios in entropy
imports and exports (effflux and dS/dt) in three study ecosystems that
represent an edaphic and management gradient. We do so by measuring their
structural complexity over an 8-year period via the enhanced vegetation
index (EVI) and variation in annual understory biomass, as well as in relation to
the energy and entropy partitioning of incoming energy from solar radiation.
We build upon the techniques proposed by Holdaway et al. (2010), Brunsell
et al. (2011) and Stoy et al. (2014), by calculating entropy production
and entropy fluxes within longleaf pine (Pinus palustris Mill.) ecosystems. The sites
differed in ecosystem structure (i.e., basal area, Table 1) and plant
functional diversity due in part to differences in soil water holding
capacity, as well as different levels of anthropogenic legacy. The sites
experienced severe drought in the beginning of this study, which we used to
quantify entropy exchanges in response to the disturbance. First, we compare
and contrast differences in ecosystem energy fluxes (i.e., Rn; LE;
H; G; and the net ecosystem exchange of carbon dioxide, NEE) and entropy fluxes
(JLE; JH; JG; metabolic entropy, Sm; and radiative
entropy production, σ) in response to changes in structural and
environmental variables (EVI; soil water content, SWC; vapor pressure
deficit, VPD; and precipitation). Next, we quantify how entropy exports and
entropy production at the different sites adjust to changes in incoming
entropy when exposed to drought. We do so by estimating radiative efficiency
(effrad), the ratio of entropy production to an empirical maximum
entropy production (MEP), and ratios of daily imported and exported entropy
fluxes (effflux), as well as through the overall change in entropy
(dS/ dt) at the sites. We hypothesize that (1) the xeric site will have a
higher entropy flux from JH and JG but lower Sm due to its
lower EVI and lower basal area, which will result in more variable dS/ dt
compared to the other sites; (2) the mesic site will maintain higher
effrad due to its greater structural complexity (i.e., plant functional
diversity and basal area) and thus greater absorptive capacity for solar
radiation compared to the other sites; and (3) the intermediate site will have
lower effrad and effflux compared to the mesic and xeric sites, as
a result of its lower plant functional diversity (i.e., low abundance of
C4
species) and structural complexity, causing lower absorption of solar
radiation and export of entropy through LE.
Stand characteristics at the mesic, intermediate and xeric sites at
the Joseph W. Jones Ecological Research Center, Newton, GA, USA.
CharacteristicMesicIntermediateXericMean DBH (cm)25.942.522.5BAP. palustris (m2 ha-1)17.714.68.9BA all tree spp. (m2 ha-1)19.015.711.0Proportion of oak overstory trees (%)6.87.019.1LAI (m-2 m-2)1.0*unknown0.69*Wiregrass in the understory (%)28524Woody species in the understory (%)121510Prescribed fireEarly spring of 2009,Early spring of 2009,Early spring of 2009,2011, 2013, 20152011, 2013, 20152011, 2013, 2015
* Wright et al. (2012).
Materials and methodsSite description
This study was conducted at the Joseph W. Jones Ecological Research Center
in southwestern Georgia, USA (31.2201∘ N, 84.4792∘ W), from
January 2009 to December 2016. The three sites are maintained by frequent
low-intensity fire on a 2-year return interval and were last burned in
2015 (Starr et al., 2016). The climate is humid subtropical with a mean
annual precipitation of 1310 mm (Kirkman et al., 2001). Mean temperature
extremes range from 3 to 16 ∘C in winter and 22 to 33 ∘C in summer (NCDC, 2011).
The three sites differ based on soil moisture availability as a result of
differences in soil drainage. The mesic site lies on somewhat poorly drained
sandy loam over sandy clay loam and clay textured soils (Goebel et
al., 1997, 2001). Soils at the intermediate site are well drained and have a
depth to the argillic horizon of ∼165 cm (Goebel et
al., 1997). The xeric site lies on well-drained deep sandy soils with no
argillic horizon (Goebel et al., 1997). All sites are situated within
10 km of each other and have average elevations of 165, 155 and 160 m for
the mesic, intermediate and xeric sites, respectively.
Ninety-five-year-old longleaf pine trees (Pinus palustris Mill.) dominate the overstory of
all sites, and overall basal area (BA) and diameter at breast height
(DBH) varied by site (Table 1). The overstories of each site also contain a
small proportion of oak trees; the xeric site has the highest proportion
with 22 %, versus 8 % and 7.7 % at the mesic and intermediate
sites, respectively. The understory at the mesic and xeric sites is largely
covered with perennial C4 grass species, such as wiregrass (Aristida beyrichiana [Trin.]),
whereas woody species dominate the intermediate site. Composition and
abundance of other plant species varies by site (Kirkman et al., 2001,
2016). Soil perturbation at the intermediate site affected species richness,
so that wiregrass is almost absent.
We acquired EVI for 2009 through 2016 for all three sites from the online
data pool at https://lpdaac.usgs.gov/products/mod13q1v006/ and https://lpdaac.usgs.gov/products/myd13q1v006/ via the NASA
Land Processes Distributed Active Archive Center (LP DAAC) and the USGS Earth
Resources Observation and Science Center (EROS), using MODIS Aqua and Terra
data products (MYD13Q1 and MOD13Q1; Didan, 2015a, b) to quantify
changes in ecosystem structure from disturbance. EVI products for the sites
were available on a 16 d basis and linearly interpolated to obtain daily
estimates. We also acquired the Palmer Drought Severity Index (PDSI) for
southwest Georgia from the National Oceanic and Atmospheric Administration
data archive for 2009 to 2016 to identify the months of drought disturbance
(Dai et al., 2004).
Understory composition and biomass was estimated annually from 2009 through
2013. Thereafter, the collection frequency became biannual, so that 2014 and
2016 were missing in the data collection. Understory biomass was estimated
using 0.75 m2 clip plots, which were randomly located by tossing a plot
frame from preinstalled litter trap positions (n=20 per site; see
Wiesner et al., 2018). All live and dead vegetation
smaller than 1 m in height was clipped and analyzed in our laboratory. Vegetation was classified
by plant life form (here, forbs, ferns, legumes, wiregrass, other grasses,
and woody plants), and each sample was dried to constant weight.
Net ecosystem exchange of CO2 measurements
Net ecosystem exchange (NEE) was measured continuously at 10 Hz at all three
sites from January 2009 to December 2016 using open-path eddy covariance (EC)
techniques (Whelan et al., 2013). Data were stored on CR-5000 dataloggers
(Campbell Scientific, Logan, UT). CO2 and water vapor concentration
were measured with an open-path infrared gas analyzer (IRGA, LI-7500, LI-COR
Inc., Lincoln, NE) and wind velocity and sonic temperature were measured with
a three-dimensional sonic anemometer (CSAT3, Campbell Scientific, Logan, UT).
These sensors were installed ∼4 m above mean canopy height at each
site (34.5, 37.5 and 34.9 m for the mesic, intermediate and xeric sites,
respectively), ∼0.2 m apart to minimize flow distortion between the
two instruments and vertically aligned to match the sampling volume of both
instruments.
Sensible and latent heat flux measurements
Net energy fluxes of LE and H were estimated in W m-2 using temperature
and wind velocity measurements from the sonic anemometer, as well as water
vapor density measurements from the IRGA:
2LE=λρaw′q′‾,3H=ρacpw′Ts′‾-0.000321Tsw′q′‾,
where λ is the latent heat of vaporization (J kg-1),
ρa is the density of air (kg m-3),
cp is the specific heat of air (kJ kg-1 K-1),
w′ is the instantaneous deviation of vertical wind speed (w,
m s-1) from the mean, and q′ and Ts′ are the
instantaneous deviations of water vapor concentration (kg kg-1) and
sonic temperature (Kaimal and Gaynor, 1991) from their respective means. The
overbars in Eqs. (2) and (3) signify the time-averaged covariance. Missing
H and LE were gap-filled on a monthly basis using simple linear models as a
function of Rn.
In cases where energy balance closure was not achieved, energy fluxes of H
and LE were corrected using the Bowen method following Twine et al. (2000),
where fluxes are adjusted using residual energy, and the
estimated Bowen ratio (β=H/LE), which assumes that
β was correctly measured by the EC system:
4LE=11+βRn-G,5H=β×LE.
Closing the energy balance is important to quantify differences in energy
and entropy fluxes by site, as according to the first law of thermodynamics
energy is always conserved. To quantify differences in environmental drivers
and site variation between energy and entropy fluxes, we established models
of average daily energy fluxes (described in Sect. 2.7)
Meteorological instrumentation
Meteorological data above the canopy were also collected and stored on the
CR-5000 dataloggers (Campbell Scientific, Logan, UT). Meteorological data
measured on the towers included photosynthetically active radiation (PAR;
LI-190, LI-COR Inc., Lincoln, NE), global radiation (LI-200SZ, LI-COR Inc.,
Lincoln, NE), incident and outgoing shortwave and longwave radiation to
calculate Rn (NR01, Hukseflux Thermal Sensors, Delft, the
Netherlands), precipitation (TE525 Tipping Bucket Rain Gauge, Texas
Electronics, Dallas, TX), wind direction and velocity (model 05103-5, R.M.
Young, Traverse City, MI), air temperature (Tair) and relative humidity
(RH; HMP45C, Campbell Scientific, Logan, UT), and barometric pressure
(PTB110, Vaisala, Helsinki, Finland).
Soil temperature (Tsoil), volumetric water content of the soil (SWC)
and soil heat flux (G) were measured in one location near the base of each
tower at each site every 15 s and averaged every 30 min on an
independently powered CR10X datalogger. Tsoil was measured at depths of
4 and 8 cm with insulated thermocouples (type T, Omega Engineering, INC.,
Stamford, CT), and G was measured at a depth of 10 cm with soil heat flux
plates (HFP01, Hukseflux, Delft, the Netherlands). SWC was measured within
the top 20 cm of the soil surface using a water content reflectometer probe
(CS616, Campbell Scientific, Logan, UT).
Data processing
Raw EC data were processed using EdiRe (v.1.4.3.1184; Clement, 1999),
which carried out a two-dimensional coordinate rotation of the horizontal
wind velocities to obtain turbulence statistics perpendicular to the local
streamline. Fluxes were calculated for half-hour intervals and then
corrected for mass transfer resulting from changes in density not accounted
for by the IRGA. Barometric pressure data were used to correct fluxes to
standard atmospheric pressure. Flux data screening was applied to eliminate
30 min fluxes of NEE, H and LE, resulting from systematic errors as
described in Whelan et al. (2013) and Starr et al. (2016). Such
errors encompassed (amongst other things) rain, poor coupling of the canopy
and the atmosphere (defined by the friction velocity, ustar), and excessive
variation from half-hourly means.
Gross ecosystem exchange (GEE) and ecosystem respiration (Reco) were
estimated from eddy covariance measurements of net ecosystem exchange of
CO2 (NEE; µmol m-2 s-1) at a time resolution of half an
hour, from which GEE and Reco can be estimated as follows:
GEE=-NEE+Reco.
Missing half-hourly data were gap-filled as described in Whelan et al. (2013)
and Starr et al. (2016). Daytime and nighttime data were estimated utilizing
a Michaelis–Menten approach for
(PAR >10µmol m-2 s-1) and a
modification of the Lloyd and Taylor (1994) model (PAR ≤10µmol m-2 s-1), respectively. Monthly equations were used to
gap-fill data; however, where too few observations were available to produce
stable and biologically reasonable parameter estimates, annual equations were
used. NEE partitioning to estimate daytime Reco was performed by
using the nighttime gap-filling equation and then utilizing Eq. (6) to
estimate GEE. Nighttime GEE was assumed to be zero.
Entropy production calculations
Half-hourly GEE and Reco were converted to W m-2 (GEEe and
Recoe), using the assumption that 1 µmol of CO2 stores
approximately 0.506 J, where 1 J m-2 s-1 equals 1 W m-2
(Nikolov et al., 1995), which is then released during respiration.
For entropy production and fluxes of shortwave (Rs) and longwave
radiation (Rl) we followed established approaches of Brunsell et
al. (2011), Holdaway et al. (2010) and Stoy et al. (2014). The half-hourly
entropy flux produced through absorption of Rs emitted by the
surface of the sun (JRs,
W m-2 K-1) was calculated as
JRs=Rs,netTsun,
where sun surface temperature (Tsun) was assumed to be 5780 K, with
Rs,net defined as the difference of incident and upwelling Rs. The
entropy flux of Rl (JRl, W m-2 K-1) was calculated as
JRl=Rl,inTsky-Rl,outTsrf,
where Rl,in/Tsky is the entropy flux of Rl,in as incoming
Rl (JRl,in), and Rl,out/Tsrf is the entropy flux of
Rl,out as outgoing Rl (JRl,out). Surface temperature
(Tsrf; K) was calculated from upwelling Rl (Rl,out):
Tsrf=Rl,out/A×esrf×kB1/4,
with emissivity of the surface calculated as esrf=0.99–0.16α (Juang et al., 2007); the view factor A was assumed to
be unity, and the Stefan–Boltzmann constant kB=5.67×10-8 W m-2 K-4. The shortwave albedo (α) was
calculated as the daily average of noontime outgoing Rs
(Rs,out) divided by Rs,in. The sky temperature,
Tsky (K), was calculated from Rlin using the Stefan–Boltzmann equation:
Tsky=Rl,in/A×eatm×kB1/4,
where the emissivity of the atmosphere (eatm) was assumed to be 0.85,
following Campbell and Norman (1998).
All other ecosystem entropy fluxes JLE, JH, JG, and JGEE
and JReco (W m-2 K-1) were calculated by dividing the energy
fluxes by temperature as
Jx=xTy,
where x represents LE, H, G, and GEEe and
Recoe; and Ty was assumed to be Tair (for JLE, JH,
JGEE and JReco; K) or Tsoil (for
JG, in K).
We also calculated entropy produced from evaporation associated with mixing
of saturated air from the canopy with the fraction of air in the atmosphere
that has RH below 100 % (JLEmix), following Holdaway et al. (2010):
JLEmix=ET×Rv×lnRH,
where the evapotranspiration rate is calculated as ET =LE/λ (kg m-2 s-1) and Rv
is the gas constant of water vapor (0.461 kJ kg-1 K-1 for moist air).
The sum of entropy of ecosystem fluxes (J, W m-2 K-1) for each
half-hour was then calculated by adding all entropy fluxes between the
surface and atmosphere:
J=JRl+JRs+JLE+JH+JG+JGEE+JReco+JLEmix.
The conversion of low entropy Rs and Rl to high entropy heat at
the surface through absorption of Rs and Rl, respectively, was
calculated as
14σRs=Rs,net1Tsrf-1Tsun,15σRl=Rl,in1Tsrf-1Tsky,
where Tsrf is the radiometric surface temperature (Eq. 9) and
σRs and σRl are in
W m-2 K-1.
The overall half-hourly entropy production (σ, W m-2 K-1)
was then calculated as the sum of the entropy productions of Rs and
Rl:
σ=σRl+σRs.
We excluded the factor 4/3, which is associated with the transfer of
momentum exerted by electromagnetic radiation on a surface (Wu et al., 2008),
in our calculations of σ and J for entropy production and entropy
fluxes because we assumed that radiation pressure at the sites would be
negligible (see Ozawa et al., 2003; Kleidon and Lorenz, 2005; Fraedrich and
Lunkeit, 2008; Kleidon, 2009; Pascale et al., 2012).
To account for the difference in absorbed radiation on leaf and
non-vegetated surfaces, we partitioned σ using EVI as an
approximation for fractional vegetation cover. Accordingly, σ of
non-vegetated surfaces (σland) was estimated as
σland=(1-EVI)×σ.
Entropy production on leaf surfaces (σleaf, Eq. 18) was
calculated as the sum of entropy production (σPAR Eq. 19)
from absorbed photosynthetic active radiation (FPAR in W m-2, Eq. 20);
entropy production from the remainder of
Rs- PAR (σRs,leaf, Eq. 21), assuming
all was absorbed and converted into heat on leaf surfaces; and entropy
production from absorbed longwave radiation on leaf surfaces (Eq. 22).
σleaf=σPAR+σRs,leaf+σRl,leaf,
where
19σPAR=FPAR1Tair-1Tsun,20FPAR=EVI×PAR,21σRs,leaf=(Rs-PAR)1Tair-1Tsun×EVI,22σRl,leaf=σRl×EVI.
We assumed Tair was close to leaf temperature. While this formulation
may introduce assumptions about the absorptive behavior of leaves, it helps
us to estimate entropy production from the metabolic processes of
photosynthesis and respiration (Sm) as follows:
Sm=σleaf+JGEE+JReco.
Finally, we estimated half-hourly change in entropy production (S) over time
(t) in W m-2 K-1 of the ecosystem by adding entropy flux of
imports (JRs,net, RRl,in) and exports
(i.e., JLE, JH, JG, JGEE, JReco, JRl,up, JLEmix) and entropy
production of vegetated and non-vegetated surfaces:
dS/dt=J+σland+σleaf.
Note that this approach does not account for entropy production due to
frictional dissipation of entropy from rainfall or subsurface water flow, as
these would be of even smaller magnitude than entropy production from
metabolic activity of the ecosystem (Brunsell et al., 2011). Here negative
dS/ dt represents the export of entropy of the ecosystem to its surroundings.
Ecosystem entropy models for radiation and ecosystem fluxes
We estimated half-hourly MEP of the radiation budget (MEPrad)
in W m-2 K-1, to compare site differences in radiation energy use and
entropy dissipation.
Empirical MEP (MEPrad) was determined following Stoy et al. (2014),
by estimating the MEP of half-hourly Rs (MEPRs) and Rl
(MEPRl):
25MEPRs=Rs,in1Tsrf-1Tsun,26MEPRl=Rl,net1Tsrf-1Tair,27MEPrad=MEPRs+MEPRl.
This method offers a means to compare different sites with respect to their
reflective and absorptive capacities versus a reference ecosystem that absorbs and
dissipates all incident solar energy. Note that MEPRl is often of lower
magnitude than MEPRs because here we assume that an efficient ecosystem
would dissipate less energy through sensible heat, such that Tsrf would
approach Tair.
The half-hourly entropy ratio of radiation is then calculated using σland and σleaf as follows:
effrad=σland+σleafMEPrad.
We refer to this ratio as an efficiency to describe differences in the
absorptive characteristics at the sites, where a ratio closer to 1 would
indicate high radiation absorption. Furthermore, sites that maintain lower
surface temperatures through greater LE fluxes would also increase their
entropy production, thus linking ecosystem functional efficiency with
radiative entropy production. We then estimated the variable effflux as
the ratio of incoming radiation entropy (JRs and JRl,in) and the
sum of exported entropy fluxes (JLE, JH, JG, JGEE,
JReco and JRl,up) to assess how entropy was partitioned into
entropy production and entropy fluxes over the different study years.
Statistical analyses
We estimated average daily values for all response variables to decrease
autocorrelation for statistical analysis. We first tested for significant
differences in environmental and structural variables among the three sites
prior to the entropy analysis. We estimated simple general linear mixed
models (GLMMs) using the R package nmle to look at differences among sites for
rain, SWC, vapor pressure deficit (VPD), EVI, Tsrf, Tair,
Tsky and Tsoil, as well as Rs,in, Rs,out, Rl,in and
Rl,out. All response variables were daily means. For rainfall we
calculated monthly sums to estimate differences among the sites. We included
a random effect for day of measurement to account for repeated
measurements, as well as an AR(1) structure to account for temporal
autocorrelation among measurements. The model of rainfall only included year
and site as independent variables and no random effects. Independent
variables for the other models were month, year and site, as well as their
interactions.
Subsequently, we estimated GLMMs of daily energy (Rn, LE, H, G and
NEEe) and entropy fluxes (JLE, JH, JG and Sm),
entropy production (σ), entropy ratios (effrad and
effflux) and overall entropy (dS/ dt) to quantify their differences by
environmental and structural variables by site. For all models we included
random effects and an AR(1) autoregressive correlation structure to account
for repeated daily measurements. All models initially included independent
variables for site, year and month, mean EVI, SWC, VPD and daily rainfall
sums. We also included interactions of environmental variables with site,
site with year and site with month to determine changes in the energy
efficiency over the study period among sites. Independent variables and
their interactions were deemed significant when p<0.05. We used a
Tukey adjustment to test for significant differences among sites. GLMM
analyses were performed via the R packages nlme, lsmeans and car (Fox and
Weisberg, 2011; Lenth, 2016; Pinheiro et al., 2014).
ResultsDifferences in environmental, radiative and temperature variables among
sites
All three sites experienced a severe drought from mid-2010 through mid-2012
(Fig. S1 in the Supplement). There was no significant difference
between the mesic and xeric sites in rainfall sums, but the intermediate
site had lower rainfall sums (∼20 mm per month) compared to
the other sites (Supplement Table S1). SWC was significantly lower at the xeric
(<19 %) compared to mesic and intermediate sites
(∼20 %) for all years of this study (Fig. 1a and b, Table S2).
SWC and EVI decreased during the drought at all sites but only
significantly so at the mesic site. VPD significantly increased at all sites
during the drought. For all years, EVI was significantly lower (0.02–0.04)
at the xeric site compared to the other two sites (Fig. 1e and f), while the
intermediate site had a significantly higher EVI compared to the mesic site,
except in 2010.
Least squares mean predicted values from mixed models of
environmental and structural variables for the years 2009–2016 at the mesic,
intermediate and xeric sites, with average annual (a, c, e) and monthly (b, d, f)
means of (a, b) soil water content (SWC), (c, d) vapor
pressure deficit (VPD) and (e, f) enhanced vegetation index (EVI). Error
bars represent standard errors (SE).
Daily Tsrf at the mesic site was significantly higher than the xeric
site for all years except 2012, 2014 and 2016 (Fig. 2a). From 2012 to 2016
the intermediate site had higher Tsrf compared to the other two sites.
Tair was significantly lower at the mesic site compared to the
intermediate and xeric sites for all years, except in 2012 and in 2014,
when the xeric site had higher Tair compared to the intermediate
(Fig. 2a). Tsoil was significantly lower at the mesic site compared to the
other sites, except in 2013, when there was no significant difference
between the mesic and xeric sites. For all years, daily Tsoil was
significantly higher at the xeric site compared to the intermediate site
except for 2011 and 2012, when the intermediate site was significantly
higher.
Least squares mean predicted values from mixed models of annual sky
temperature (Tsky), air temperature (Tair), surface temperature
(Tsrf), and soil temperature (Tsoil) at the mesic, intermediate
and xeric sites. Error bars represent SE.
Rs,out was significantly higher at the xeric site compared to the other
sites, except for 2014, where we found no significant difference between the
intermediate and xeric sites. Daily Rs,out was also significantly lower
at the mesic site, compared to the intermediate site, except in 2009.
Average daily Rl,out was significantly lower at the mesic site compared
to the intermediate site during all years, except for 2011 and 2012, and
compared to the xeric site for all years, except for 2011. The intermediate
site had significantly higher Rl,out compared to the xeric site during
2013, 2014 and 2016. As a consequence of these component fluxes, Rn was
significantly higher at the xeric site compared to the intermediate site for
all years except 2009 and 2014 (Fig. S2a, Table S3). Average Rn was
significantly lower at the mesic site compared to the xeric site in 2013 and
2016 and was significantly higher compared to the xeric site from 2009 to
2011. Average daily Rn significantly increased at the intermediate and
xeric sites but showed no change at the mesic site with an increase in EVI
(Fig. S3a).
Environmental, radiative and temperature variables also tended to be
significantly different among months within site and in many instances
among sites by month. Differences followed seasonal patterns, as noted in
Fig. S2 and Table S2.
Least squares mean predicted values from mixed models of annual
average radiation at the mesic, intermediate and xeric sites for the years
2009–2016: (a) annual incoming and outgoing shortwave radiation
(Rs,in and Rs,out) and (b) annual incoming
and outgoing longwave radiation (Rl,in and Rl,out).
Error bars represent SE.
Understory wiregrass and woody abundance at the sites
Wiregrass was virtually absent at the intermediate site for all years of
this study (Fig. 4a), whereas woody species were more abundant compared to
the others. The mesic and xeric sites both had higher proportions of
wiregrass in the understory (∼25 % versus 5 % at the
intermediate site), which slightly decreased during 2011 (Fig. 4a). In
addition, woody biomass increased to ∼75 g m-2 at the
xeric site during 2011 but not at the mesic site. In 2012, woody biomass
decreased to ∼40 g m-2 at the xeric and intermediate
sites and remained low during the following years at the xeric site but
increased at the intermediate site (>100 g m-2, Fig. 4b).
(a) Wiregrass and (b) woody understory biomass from 2009 through
2015 at the mesic, intermediate and xeric sites. Note that the sampling
protocol changed to a 2-year measurements cycle in 2013, such that
measurements were not made in 2014 and 2016.
Energy fluxes of H, LE and G
LE was significantly lower at the intermediate site compared to the mesic
site for all years, except 2011, and compared to the xeric site for all
years, except for 2015. We found no significant difference between the mesic
and xeric sites in 2009, 2010, 2014 and 2016, but for the other years of
this study the xeric site had significantly higher LE. LE significantly
increased at all sites with higher EVI, with a greater increase at the
intermediate and a smaller increase at the xeric site, compared to the mesic
site (Fig. S3g). LE significantly increased at all sites with an increase
in SWC and VPD (Fig. S3e and f). LE at the intermediate site was
significantly lower compared to the other sites for all levels of VPD (Fig. S3g).
LE was significantly lower with higher rainfall, with no
significant differences among sites (Fig. S3h).
There was no significant difference in H between the mesic and intermediate
sites, except in 2011 and 2013, when the mesic site was higher than the
intermediate site, and in 2015 and 2016, when the reverse occurred. H was
significantly lower at the xeric site compared to the mesic site for all
years except for 2014 and 2016 and compared to the intermediate site for
all years except 2011 and 2013. Average H was significantly higher at the
mesic site compared to the xeric site during the months of May through
October (Fig. S2b). The intermediate site had significantly lower H
compared to the other two sites for the months of January through March, and
the xeric site had significantly lower H for June through October. Compared
to the other two sites, average H was significantly lower at the
intermediate site when EVI was greater than 0.4 and significantly higher at
the xeric site for EVI >0.5 (Fig. S3i). Average H
significantly decreased at all sites with an increase in SWC (Fig. S3j).
Average daily H significantly increased at all sites with an increase in
VPD, with a lower decrease at the intermediate site (Fig. S3k).
G was significantly lower at the intermediate site during 2016 (negative),
compared to 2009 through 2011 and 2014. Average daily G was positive during
summer months and negative during winter months (October through March) at
all sites (Fig. S2b). Average daily G significantly decreased with an
increase in EVI at the mesic and intermediate site but had no significant
change at the xeric site (Fig. S3m). G was significantly less positive at
the xeric site compared to the other sites for EVI < 0.3 but was
significantly more negative at the intermediate site compared to the mesic
and xeric sites when EVI was above 0.4. Average G significantly decreased
(to negative) with an increase in SWC (Fig. S3n) and significantly
increased (to positive) with an increase in VPD but only at the
intermediate and xeric sites (Fig. S3o). Daily rainfall did not
significantly alter G at the sites, but the intermediate site had
significantly more negative G compared to the other two sites
(2–10 W m-2) when daily rainfall was positive (Fig. S3p).
Entropy production and fluxes of JH, JLE and
JG
For all years, average daily σ (as the sum of σland and
σleaf) was significantly higher at the mesic site compared to
the intermediate site (by >0.01–0.036 W m-2 K-1;
Fig. 5a, Table S4), while σ was not significantly different between
the mesic and xeric sites for almost all years (Fig. 5a). Average daily
σ significantly increased with EVI, independent of site (Fig. 6a),
and also significantly increased with SWC and VPD, with a greater slope at
the xeric site (Fig. 6b and c). Average daily σ significantly
decreased at all sites with an increase in rainfall (noting that entropy
production from rainfall itself is not considered here and assumed to be
approximately equal among ecosystems), and σ was significantly lower
at the intermediate site during rainy periods compared to the other two
sites (Fig. 6d). There was no significant difference in σ at the
mesic and xeric sites for all levels of rain.
Least squares mean predicted values from mixed models of annual (a)
and monthly (b) average entropy production (σ) and entropy fluxes of
latent energy (JLE), sensible heat (JH) and ground heat (JG)
at the mesic, intermediate and xeric sites. Error bars represent SE.
The xeric site had significantly higher average daily JLE, ranging from
∼0.22 to 0.28 W m-2 K-1, versus the intermediate
site with ∼0.18–0.25 W m-2 K-1 (Fig. 5a, Table S4)
for all years, except 2015. JLE at the xeric site was also higher
than the mesic site in 2011 through 2013 and in 2015, ranging from 0.2 to
0.26 W m-2 K-1. The mesic site had ∼0.01–0.06 W m-2 K-1 higher
JLE compared to the intermediate site, except
in 2011. JLE significantly increased with greater EVI and SWC (Fig. 6e
and f). JLE was significantly higher at the xeric site compared to the
other sites for EVI <0.4. JLE was significantly higher at the
xeric site compared to the other sites when SWC was above 19 %, similar to
the model of LE. JLE significantly increased with VPD and
significantly decreased with rainfall (Fig. 6g and h). Unlike the model
results for LE, the effects of VPD were not significantly different by site.
Least squares mean predicted values from mixed models of
(a–d) entropy production (σ) and entropy fluxes of (e–h) latent energy
(JLE), (i–l) sensible heat (JH), and (m–p) ground heat (JG)
by site and (a, e, i, m) enhanced vegetation index (EVI), (b, f, j, n) soil
water content (SWC), (c, g, k, o) vapor pressure deficit (VPD) and (d, h, l, p) rain. For (g), (h) and (o) the interaction with site was not
significant, as signified by a single black line. Error bars represent SE.
Models of H and JH were similar, except that JH in the mesic and
xeric sites was not significantly different in 2015 (Fig. 5a, Table S4).
Average daily JH was significantly higher at the mesic site in 2011 and
2012 (∼0.2–0.24 W m-2 K-1) compared to the
intermediate (∼0.19 W m-2 K-1; Fig. 5a) and xeric
sites (∼0.16–0.20 W m-2 K-1). In 2009, 2010 and
2012, the xeric site had significantly lower JH compared to the other
sites (by ∼0.02 W m-2 K-1). JH decreased only
at the mesic and intermediate sites with increasing EVI (Fig. 6i) such that
the intermediate site had significantly lower JH compared to the other
sites when EVI was above 0.4. JH decreased with increased SWC at all
sites, and the xeric site had significantly lower JH compared to the
other sites when SWC was above 19 % (Fig. 6j). VPD significantly
increased JH at all three sites, with a greater increase at the xeric
site (Fig. 6k). JH significantly decreased at all sites with increased
rainfall, where the intermediate site had significantly lower JH
compared to the mesic and xeric sites when rainfall was greater than 40 mm
per day (Fig. 6l).
Average daily JG was not significantly different among the years
2009–2014 and 2016 at the mesic site but significantly increased during
2015 (Fig. 5a, Table S4), similar to the model results for G. Similarly,
JG was significantly lower at the intermediate site during 2016
(negative). JG at the xeric site was not significantly different by
year. Average daily JG was positive during summer months and negative
during winter months at all sites (Fig. 5b). Average daily JG
significantly decreased from positive to negative at the mesic and
intermediate sites with an increase in EVI, with no significant change at
the xeric site (Fig. 6m), similar to the model of G. JG was
significantly more negative at the intermediate site compared to the other
sites for EVI >0.4. Average JG only significantly decreased
at the intermediate and xeric sites (to negative), such that JG was
significantly more negative at the two sites when SWC was above 18 % (Fig. 6n).
JG significantly increased with greater VPD, independent of site
(Fig. 6o). Similar to the model of G, daily rainfall did not significantly
alter the magnitude of JG at the sites. However, the intermediate site had
significantly more negative JG compared to the other two sites when
daily rainfall increased (Fig. 6p).
Metabolic energy and entropy
Metabolic energy was consistently more negative (more energy uptake) at the
mesic site, compared to the other sites for all years in this study (Fig. 7a,
Table S5). The intermediate and xeric sites exported metabolic energy from
2009 through 2011, which was greater at the intermediate site for 2010.
NEEe significantly increased to more negative at all sites during May
and significantly decreased during August through October, which resulted in
positive NEEe at the intermediate site (Fig. 7b). NEEe
significantly decreased at all sites with an increase in EVI, which was
greater at the xeric site (Fig. 7c). An increase in SWC resulted in
decreasing NEEe, independent of site (Fig. 7d). An increase in VPD
significantly decreased NEEe to more negative at all sites, with a
greater decrease at the intermediate site (Fig. 7e). Increases in rainfall
significantly increased NEEe to positive at all sites, where the
intermediate site had a greater increase compared to the other sites (Fig. 7f).
Least squares mean predictive values from mixed model of (a–f) the
metabolic energy flux (NEEe) and (g, l) metabolic entropy fluxes of
(Sm) by site and (a, g) year, (b, h) month, (c, i) enhanced
vegetation index (EVI), (d, j) soil water content (SWC), (e, k) vapor
pressure deficit (VPD) and (f, l) rain. For (d) and (i) the interaction
with site was not significant, as indicated by a single solid black line.
Error bars represent SE.
Results of the model of Sm indicated that the mesic site had
significantly greater metabolic entropy production compared to the
intermediate site for all years but 2009 and 2013. The xeric site had
significantly greater Sm compared to the mesic site in 2012 through
2014 and in 2016 and compared to the intermediate site for all years (Fig. 7g).
Sm was greater during summer months at all sites with no
significant differences between the mesic and xeric sites from February
through August but significantly lower at the intermediate site compared to
the xeric site for all months (Fig. 7h, Table S5). Metabolic entropy
production was significantly lower at the intermediate site compared to the
mesic site for most months except January, April, October and December.
Values of Sm significantly increased with an increase in EVI,
independent of site (Fig. 7i). SWC significantly increased Sm at all
sites, with a greater slope at the xeric site (Fig. 7j). Higher VPD
significantly increased Sm similar to the model of NEEe; however
slopes were more similar among the sites (Fig. 7k). Rainfall significantly
decreased Sm to ∼0 with a greater slope at the
intermediate site, similar to the model of NEEe (Fig. 7l).
Entropy models
From 2011 through 2016, effrad was significantly higher at the mesic
site (0.89–0.93), compared to the intermediate (0.88–0.91) and xeric
(0.88–0.92) sites, which were not significantly different (Fig. 8a). Average
effrad did not significantly change with EVI or SWC. Higher VPD
significantly decreased values of effrad at all sites (Fig. 8c). The
mesic site had significantly higher values of effrad compared to the
other two sites for all levels of VPD (Fig. 8c). Rainfall significantly
increased values of effrad at all sites, with a greater increase at the
intermediate site (Fig. 8d, Table S6).
Least squares mean predicted values from mixed models of average
daily half-hourly radiative entropy efficiencies (effrad) at the mesic,
intermediate and xeric sites by (a) year, (b) month, (c) vapor pressure
deficit (VPD) and (d) rain. Soil water content and the enhanced vegetation
index were not significant in the model. Error bars represent SE.
Daily average effflux was significantly greater at the mesic site for
most of the measurement period (Fig. 9a, Table S6). effflux was
significantly higher at the xeric site compared to the intermediate site for
the years 2009, 2011, and 2013 through 2015. For 2012 and 2016 the
intermediate site had significantly greater effflux compared to the
xeric site. Greater EVI only significantly increased effflux at the
mesic site, which had higher effflux compared to the other sites for
all levels of EVI (Fig. 9c). The intermediate site had significantly lower
effflux compared to the xeric site when EVI was above 0.3. An increase
in SWC significantly decreased values of effflux only at the
intermediate and xeric sites, with a greater decrease at the xeric site
(Fig. 9d). Higher VPD significantly decreased effflux at all sites,
with a greater decrease at the intermediate site (Fig. 9e). Rainfall
significantly increased effflux at all sites, where the intermediate
site showed the highest increase (Fig. 9f).
Least squares mean predicted values from mixed models of average
daily half-hourly flux entropy efficiencies (effflux) at the mesic,
intermediate and xeric sites by (a) year, (b) month, (c) enhanced vegetation
index (EVI), (d) soil water content (SWC), (e) vapor pressure deficit
(VPD) and (f) rain. Error bars represent SE.
There was no significant difference in dS/ dt among sites for all years and
months, except in 2014, where the intermediate site had significantly higher
dS/ dt compared to the other sites (Fig. 10a, Table S6). In addition, the
xeric site accumulated dS/ dt during 2012 such that it was significantly
different from the other sites. An increase in VPD resulted in a significant
increase in dS/ dt (more entropy export), independent of site (Fig. 10c).
EVI, SWC and rainfall were not significant in the model of dS/ dt. The
diurnal variation in dS/ dt was greater at the mesic and xeric sites during
the drought years 2010, 2011 and 2012, compared to the intermediate site,
specifically during nighttime (Fig. S4). At the intermediate site dS/ dt
varied more during the years 2014 and 2016, as seen by greater entropy
accumulation during nighttime hours and greater export during daytime hours
for the year 2014.
Least squares mean predicted values from mixed models of average
daily entropy at the mesic, intermediate and xeric sites by
(a) year, (b) month
and (c) vapor pressure deficit (VPD). Soil water content and rain, as
well as the interactions with site, were not significant in the model. Error
bars represent SE.
Discussion
Here we describe differences in energy use efficiencies of sites with varying
structural complexities (i.e., understory composition, basal area, DBH) using
metrics of energy and entropy. Different from our expectations, environmental
and structural effects on energy and entropy fluxes were not different with
the exception of NEEe and Sm. These results suggest
that differences in the thermodynamic environment among sites (i.e., air and
surface temperatures) did not contribute to changes in entropy export in
response to environmental variables. Metabolic entropy (Sm)
decreased during the drought at all sites but not significantly so (Fig. 7),
whereas NEEe showed significant change at the mesic site. The
different results were a function of SWC, which decreased during the summer
of 2011, thus lowering the flux of Sm (Fig. 7). Furthermore,
greater Rs,out during the drought indicated lower available
energy to drive photosynthetic processes. The decreases in Sm and
NEEe suggest that metabolic activity was affected by low
rainfall, increasing VPD and changes in temperature, demonstrating lower
physiological activity of plant species during drought (Barron-Gafford et
al., 2013). This decrease in metabolic efficiency supports a previous study
at the mesic and xeric sites, which found lower electron transport and
carboxylation capacity during drought (Wright et al., 2012).
Differences in the underlying reflective capacities at the sites
significantly altered their entropy production and resulted in variation in
entropy exchanges (Stoy et al., 2014). The more structurally complex
mesic site had greater metabolic entropy production (Sm) compared with
the intermediate site. Greater Sm at the mesic site translates to
greater energy accumulation, in addition to greater radiation entropy and
export efficiencies (effrad, effflux), compared to the intermediate
site, which had greater land use legacy and was structurally similar but
lower in plant functional diversity. Although the radiation entropy ratio
(effrad) indicated that both the intermediate and xeric sites were
equally energy efficient in terms of absorbing radiation, effflux and
Sm showed prolonged recovery of energy efficiency from drought by
1 year at the intermediate site. Entropy change over time (dS/ dt) did not
significantly vary at the mesic site but was more variable at the xeric and
intermediate sites following the drought.
We hypothesized that the xeric site would have higher H and JH, due to
its open canopy and sandy soils, and therefore lower volumetric heat
capacity. In contrast to our first hypothesis, the mesic and intermediate
sites and not the xeric site had a more pronounced increase in H and JH
when EVI decreased during drought (Fig. 1). Lower H and JH at the xeric
site was a consequence of greater energy partitioning into LE, enabled by
greater transpiration rates of plant functional types present at the site
(deciduous and evergreen oaks in the understory, midstory and overstory;
Klein et al., 2013; Renninger et al., 2015;
Stoy et al., 2006). This result was confirmed, as JH fluxes did not
significantly change with an increase in EVI, whereas JLE increased,
suggesting that evapotranspiration and the cooling of leaf and soil surfaces
had greater influence on the partitioning of available energy. In contrast,
JH increased more at the mesic and xeric sites with increasing VPD,
suggesting that drier air increased the sensible heat flux from the surface
to the atmosphere (Massmann et al., 2018). Similarly, as VPD increased so
did σ at all sites. This response was also observed in Kuricheva et
al. (2017), where drier summers resulted in greater entropy production,
likely because an increase in VPD correlated with greater absorption of
solar radiation and partitioning to H (Fig. 3a). Even though plant abundance
was lower at the xeric site, its species composition was better adapted to
drought conditions, which allowed for higher JLE compared to the other
sites (Roman et al., 2015). Furthermore, an increase in EVI during summer
months at the xeric site increased JLE, demonstrating that greater leaf
area enhanced ecosystem function (Peng et al., 2017; Zhu et al.,
2016). Interestingly, JLE did not vary significantly by site with
changes in VPD, which supported the findings of Whelan et al. (2013) that
all sites had similar stomatal regulation to increases in VPD. Overall, the
xeric site had higher JLE compared to the other sites for
EVI < 0.5, even though the site basal area was almost half that of the mesic and
intermediate sites (Table 1). An overstory composed of more oak species at
the xeric site (∼20 %) along with the C4 understory
resulted in higher transpiration during spring and summer, compared to
stands containing just pine trees (Klein et
al., 2013; Renninger et al., 2015; Stoy et al., 2006). Additionally, C4
grasses and oak species at the xeric site were better adapted to drought
(i.e., anisohydric response; Osborne and Sack, 2012; Roman
et al., 2015), which may enable higher entropy production and lower
variability in the structural integrity (i.e., lower decreases in EVI; Fig. 1e).
This suggests that the understory plays a crucial role in the structure
and function of more open canopy ecosystems (Aoki, 2012; Lin,
2015), in addition to more productive overstory trees during summer. This
led to similar entropy export efficiencies at all sites as evidenced by all
sites having comparable dS/ dt. Nevertheless, as σ increased with
greater absorption of radiation due to an increase in EVI, JH decreased
as a result of higher SWC, resulting in temporary entropy accumulation at
the xeric site during the end of 2012 (Fig. 4), which may have
contributed to higher Tair compared to the other sites (Fig. 2).
In contrast, the mesic site was affected by the interaction of biological
and radiative forces, as JLE and effrad decreased more severely
with decreasing plant leaf area compared to the xeric site (lower EVI; Fig. 1e).
As a consequence of lower LE and JLE during the drought, more
energy was partitioned into H in 2011 (Fig. 6), as air, soil and surface
temperatures increased due to lower leaf area (Figs. 1 and 2), indicating a
shift of ecosystem function (Ban-Weiss et al., 2011) towards lower-quality
energy degradation (Kuricheva et al., 2017). This initially
depleted soil moisture storage at the mesic site (Fig. 1) and further
decreased LE and JLE (Kim and Wang, 2012; Lauri et al., 2014).
Nevertheless, the shift in energy partitioning at the mesic site allowed for
the maintenance of dS/ dt during drought, by export of entropy which had
accumulated during nighttime hours (Fig. S4), demonstrating an adaptation
of the site to changes in resource availability (Basu et al.,
2016; Brodribb et al., 2014). In contrast, the xeric and intermediate sites
showed greater variability in annual dS/ dt following the drought when
rainfall returned to pre-drought levels and SWC increased (Fig. 10a).
Nevertheless, the rapid increase in JLE in 2012 at the mesic and xeric
sites indicated an increase in ecosystem function through greater
evapotranspiration. This provides evidence of recovery following the
drought, because JLE is of higher-quality entropy dissipation
(Kuricheva et al., 2017), coupling both mass and heat dynamics
(Brunsell et al., 2011), whereas JH is a function of the thermal
gradient (Kleidon, 2010; LeMone et al., 2007). In general,
plant species at the mesic site were better adapted to higher soil water
conditions, as entropy and energy fluxes did not change as drastically with
increasing SWC compared to the other sites.
This recovery of EVI following drought also allowed for greater effrad
at the sites. But effrad was higher at the mesic site despite lower EVI
compared to the intermediate site. This finding supports our second
hypothesis, that sites with greater plant functional diversity maintain
greater radiative entropy production. The mesic site efficiently used
available energy from incoming solar radiation (Fig. 2) through lower
reflection of Rs and by emitting less longwave radiation (Lin,
2015). Effrad decreased during the initial drought year because all
sites reflected more Rs, likely a consequence of a change in EVI, as
well as leaf angle from a decrease in SWC and altered plant hydraulics.
Higher effrad and effflux at the mesic site are consistent with
enhanced function due to greater plant diversity in the understory (Fig. 4a).
For example, wiregrass, a C4 species, can maintain photosynthetic
rates under high temperatures (Osborne and Sack,
2012; Ward et al., 1999), which allows for greater energy storage during
unfavorable environmental conditions (Brunsell et al., 2011). Despite higher
wiregrass biomass in the understory, the xeric site was less efficient in
using available radiation energy, indicated by high Rs,out and
Rl,out (Brunsell et al., 2011). Structural limitations of the canopy
(i.e., lower basal area) impeded the efficient absorption of available
radiation, therefore lowering effrad (Norris et al.,
2011). Furthermore, larger proportions of deciduous oak trees at the xeric
site (Table 1), which typically shed their leaves during the winter, lowered
the capacity of the system to acquire radiation (Baldocchi et al.,
2004: Fig. 8b). Nevertheless, this inefficiency was not confirmed by model
results for Sm, which, in contrast to NEEe, revealed higher
metabolic function at the xeric site relative to the mesic and intermediate
sites, reflecting greater metabolic performance despite differences in basal
area and site EVI. Overall our results demonstrate that the mesic site was
better adapted to changes in resource availability by way of altering its
reflective properties, where energy partitioning adjusted to maintain steady
entropy exports relative to incoming entropy (Gunawardena
et al., 2017; Otto et al., 2014; Taha et al., 1988).
Nevertheless, metabolic activity decreased during rainy periods
(Sm∼0), demonstrating an inefficiency in maintaining
optimal function when environmental pressure was imposed on the system. High
metabolic function at the mesic site resulted in more rapid increases in the
structural complexity as indicated by a decrease in Rs,out
following the drought when compared to the intermediate site (Brunsell et
al., 2011; Holdaway et al., 2010). Metabolic activity (in energy terms) at
the intermediate site was largely dependent on EVI (i.e., leaf area),
demonstrating lower biological control of individual plant species (i.e.,
stomatal control; Urban et al., 2017) but a strong influence of total leaf
area on metabolic function and the export of entropy (Brunsell et al., 2011;
Figs. 4 and 6). This was further illustrated at the intermediate site through
less negative metabolic energy (NEEe) when EVI was ∼0.25
(Fig. 7c). Even though EVI in 2012 was greater at the intermediate site this
did not correspond to higher JLE (Fig. 5a), which was also shown
by a lack of significant change in entropy exports with changes in EVI
(effflux, Fig. 9c). The result of lower metabolic function at the
intermediate site is intriguing as the mesic and intermediate sites were
structurally similar, based on similar BA, mean DBH and overstory
tree composition (Table 1). The inefficiency appears to be a consequence of
anthropogenic modification, which homogenized the ecosystem, leading to a
decrease in understory plant functional types (Table 1; Fig. 3), thereby
reducing values of effrad, effflux and
Sm. This result provides evidence that the intermediate site was
less efficient in absorbing energy and dissipating entropy compared to the
mesic site, resulting in slower adaptation to drought. Similar results were
shown in Lin et al. (2015), where disturbed sites had predominantly lower
entropy production rates, as well as in Lin et al. (2018), where greater
surface temperature led to decreased σ, which we also observed at the
intermediate site. Our third hypothesis was therefore supported, as the
intermediate site had lower effflux relative to the mesic and
xeric sites. Lower plant functional diversity, specifically the lack of
wiregrass, due to soil perturbations that took place prior to stand
establishment (>95 years ago), likely lowered metabolic
function, which in turn affected entropy exports at the intermediate site and
its recovery from drought. For example, a negative JG at the
intermediate site was observed with increasing SWC, suggesting poor soil
water drainage, which is also likely a consequence of agricultural legacy
(Kozlowski, 1999). A prolonged increase in effflux compared to
the other sites showed that the intermediate site did not adapt its entropy
exports, in addition to greater reflection of Rs during drought
recovery. This result indicates that differences in soil conditions and lower
plant functional diversity at the intermediate site reduced entropy exports
compared to the other sites (Meysman and Bruers, 2010), such that plant
functional types present at the site could not rescue the ecosystem's
function during disturbance (Elmqvist et al., 2003). Furthermore, while the
intermediate site showed no change in dS/ dt during the drought,
following the drought the export of entropy significantly increased,
resulting in more unstable conditions (Fig. 10a). The increase in entropy
export corresponded to high annual rainfall and soil moisture conditions
(Figs. 1 and S1), once more suggesting that soil characteristics were altered
due to its agricultural legacy. The lower ability to adapt to changes in
resource availability at the intermediate site could induce its degradation
if environmental fluctuations become more frequent and severe with climate
change (Mori, 2011; Siteur et al., 2016). This could further exacerbate
instabilities for nearby sites, as changes in the reflective properties of
degraded sites can alter microclimate and weather patterns across whole
ecosystems (Norris et al., 2011).
We conclude that the analysis of entropy dynamics in relation to structural
and environmental variables gives valuable insights into the functional
complexity of ecosystems and their ability to adapt to drought. A
combination of entropy fluxes and entropy ratios revealed how differences in
structural and/or functional characteristics affect energy efficiencies in
longleaf pine ecosystems. Our results show that all sites demonstrated
adaptive capacity to extreme drought, as indicated by a lack of significant
change in dS/ dt, except for greater variations at the xeric and intermediate
sites following the drought. We show that overall low entropy exports at the
site with greater land use legacy had the potential to decrease ecosystem
function (Meysman and Bruers, 2010), especially during high
rainfall events. Changes in climate and natural and human-induced
disturbances are becoming more frequent and severe (IPCC, 2014),
demanding more predictive power about how changes in ecosystem structure and
function will alter resilience to disturbances. Future policy, conservation
or restoration applications depend on reliable measures such as the metrics
presented here to monitor ecosystem function following disturbances
(Haddeland et al., 2014; Porter et al., 2012;
Reinmann and Hutyra, 2016; Thom et al., 2017). This is especially critical
for anthropogenically modified systems, as their land use history can affect
changes in energy use efficiency and thus alter their ability to recover
from disturbances (Bürgi et al., 2016; Foster et al., 2003).
The application of entropy metrics could improve our understanding of the
interaction of structure, function and legacy on energy use efficiency
across a variety of global ecosystems.
Data availability
Data used in this paper have been archived with the
AmeriFlux Data Management Project
(https://ameriflux.lbl.gov/sites/siteinfo/US-LL1, Starr and Brantley,
2019a; https://ameriflux.lbl.gov/sites/siteinfo/US-LL2, Starr and
Brantley, 2019b; https://ameriflux.lbl.gov/sites/siteinfo/US-LL3, Starr
and Brantley, 2019c). Interested parties can access the data through their
own account, which can be created on the AmeriFlux Management Project
website. Enhanced vegetation index (EVI) estimates were obtained from MODIS
Aqua (MYD13Q1) and Terra (MOD13Q1) vegetation indices products 16-Day L3
Global 250 m SIN Grid via the NASA Land Processes Distributed Active Archive
Center (LP DAAC) and the USGS Earth Resources Observation and Science Center
(EROS) at https://lpdaac.usgs.gov/products/mod13q1v006/ (Didan, 2015a)
and https://lpdaac.usgs.gov/products/myd13q1v006/ (Didan, 2015b).
The supplement related to this article is available online at: https://doi.org/10.5194/bg-16-1845-2019-supplement.
Author contributions
GS and LRB designed and acquired funding for the research. SW and CS
analyzed the data. PCS aided SW with the theories of entropy and energy
density. All authors contributed to the writing of the manuscript.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
The authors thank the Forest Ecology laboratories personnel, with special
thanks to Tanner Warren, Andres Baron-Lopez and Scott Taylor for data
collection and provision during the study at the Joseph W. Jones Ecological
Research Center. Christina L. Staudhammer and Gregory Starr acknowledge
support from the US National Science Foundation (DEB EF-1241881).
Paul C. Stoy acknowledges support from the US National Science Foundation
(DEB 1552976 and 1702029) and the USDA National Institute of Food and
Agriculture (Hatch project 228396).
Review statement
This paper was edited by Christopher Still and reviewed by Axel Kleidon
and one anonymous referee.
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