In this study, the Penman–Monteith equation [
71] is used to estimate the actual evapotranspiration of the vegetated areas under study. These evapotranspiration estimates will be used to validate the daily transpiration rate estimates at the plot scale. The Penman–Monteith equation estimates the actual evapotranspiration of vegetated surfaces by accounting for all the micrometeorological factors that influence evapotranspiration as well as the influence of the canopy conductance and aerodynamic resistance in the rates of vegetation transpiration:
where
is the latent heat of evapotranspiration
is the slope of the saturation vapor pressure curve (
C
),
is the latent heat of actual evapotranspiration (
),
is the net solar radiation, and
is the soil heat flux (all these terms in units of
). The air density,
is in (
);
is the specific heat of air at constant pressure (i.e.,
C
). The term
is the vapor pressure deficit (
) calculated by the difference between the saturation vapor pressure (
,
)) and the actual vapor pressure (
,
)). The psychrometric constant,
, is in units of (
C
). The aerodynamic terms,
and
are the aerodynamic resistance to vapor and heat transfer, and the bulk canopy resistance (both expressed in
). The following paragraphs explain in detail the calculation of each Penman–Monteith equation’s parameter. To convert the latent heat of evapotranspiration to actual evapotranspiration (
), use
in units of
.
Appendix A.1.1. Aerodynamic Parameters
To calculate the
term in the Penman–Monteith equation, the saturation vapor pressure was initially calculated using two different equations:
and
In both equations,
is the air temperature (°C, field weather station measurements). The first equation is the resultant of a Chebyshev fitting procedure used by [
72]. The polynomial coefficients (i.e.,
to
) are reported in Lowe’s paper [
72] and
is calculated in
units. The latter equation calculates
in
was derived by [
73] and its estimates are considered of high reliability [
64]. The average difference between
values calculated with both equations was of
. Thus, for further estimations, Equation (A3) is applied. The actual vapor pressure is calculated using the estimated
and the relative humidity (
, (%)) that was measured in the field [
74]:
The air density,
, can be derived from [
64]:
where
is the daily mean atmospheric pressure calculated with the field measurements (barometer, units of
),
is the specific gas constant (
).
is the virtual temperature in degrees Kelvin, calculated as [
64]:
where
and
are taken as the daily average of
and
respectively. A sensitivity analysis was performed to observe how
values affect
or the evapotranspiration estimates. There were no significant changes in the values. Thus,
was used in the equation. This analysis was performed since [
64] did not specify if an average temperature or temperature at each hourly time-step value should be used.
The psychrometric constant can be expressed as [
75]:
where
is given in units of
C
,
is entered as
, P is in
. The water vapor ratio molecular weight (
) is a constant value equal to
, and
is calculated using the following equation [
64]:
where
is given in units of
(i.e., multiply by 1000 to match units of
).
The slope of the saturation vapor pressure curve (
) is derived from the following equation:
The aerodynamic resistance to vapor and heat flux,
, is estimated with the following equation [
64,
76]:
where
is von Karman’s constant (0.40),
is the height (
) at which the wind speed
(
) has been recorded (
in this particular case),
is the zero-plane displacement (
) that is assumed as 67% of the canopy height (i.e.,
) for vegetation with
. Here, the average canopy height is
, which is the same height used in previous estimations. The parameters
and
are the roughness lengths for the momentum and heat transfer, respectively. Allen et al. [
64] suggested applying
. In this study, the fact that
varies with cover has been taken into account; thus,
is calculated differently for the Deciduous and the Coniferous sites. For the Deciduous sites, whose vegetation is considered dense and homogeneous, the equation suggested by [
76] is applied:
For the Coniferous sites, the equation suggested by [
64] is applied:
where
is an empirical factor that is independent of vegetation height [
77]. Based on their calculated values of
and
for conifers, [
77] determined
.
Table 1 lists the constant terms of the aerodynamic resistance equation. The ratio
calculated for Coniferous sites concurs with the mean value reported by [
64] for this ratio. The Deciduous’ sites
value is between the range of values listed for deciduous trees by [
64].
Table A1.
Steady parameters in the calculation of the aerodynamic resistance to heat and vapor transfer, . All parameters are reported in meters, with exception of , which is unitless.
Table A1.
Steady parameters in the calculation of the aerodynamic resistance to heat and vapor transfer, . All parameters are reported in meters, with exception of , which is unitless.
Parameter | Coniferous Sites | Deciduous Sites |
---|
| 15 | 15 |
| 0.22 | 0.37 |
| 10.05 | 10.05 |
| 1.089 | 1.82 |
| 0.1089 | 0.1821 |
The canopy resistance is more complicated to estimate since it varies along the day and it is a function of several atmospheric parameters [
78]:
This equation implies that the canopy conductance (
) is a function of the environmental parameters:
,
(
),
(
),
(°C), and volumetric soil moisture (
, in
). The parameter that reaches its minimum at a specific time (
), drives the canopy conductance. The lower the value of the environmental parameter reduction function, the lower the value of
, therefore the higher the
. Each parameter is represented by a reduction function that computes the value of the function between zero and one (i.e.,
). Different authors have developed and calibrated reduction functions for calculating each one of the parameters in Equation (A13). Allen et al. [
64] suggested that these equations can be replaced in the function above. Here, a set of equations was chosen and presented below. Most of the equations and empirical factors are taken from [
79]; otherwise, the author is cited. Stewart [
79] developed and calibrated these functions for Scots pine. This is the closest species to the species studied in this work with reported functions. In the case of the Deciduous site, the empirical factors were adjusted according to the response of
or
to the environmental parameters. This task was performed based on previous results and results that were obtained in this study.
The
is the reciprocal of the minimum canopy or surface resistance (
). Typical values reported for coniferous forests
range from
to
[
64]. Here, an average value of the reported ranges was taken for the Coniferous site (i.e.,
). Ref. [
80] reported maximum values of canopy conductance for Trembling aspen (
) and it is the one applied here for the Deciduous site. To compute
:
where
is the maximum LAI Along the year. Since data collection occurred during the peak of the summer (July and August), it is assumed that
for both the Coniferous and the Deciduous sites. The
is calculated with
where
is in
and
is an empirical factor that was set up as
.
The VPD function is established based on the two following equations:
and
with
. The
is called the “threshold vapor pressure deficit” and is set up as
for the Coniferous site. For the Deciduous site, [
52] reported the sap flow trend of four hardwood species in relation to
. One of the species studied is from the genus
Populus. For that result, it was reported that the
Populus sap flow did not significantly vary when
was greater than
, unless the soil moisture content was limiting. The results presented by [
52] perfectly concur with our study results. Thus, the threshold for the Deciduous site was assumed as
. Since a
factor was not found in the literature, its value was determined by using previously reported trends of
versus
. Thus, the value was assumed as
initially. This decision was somehow conservative and based on the fact that deciduous
reported values have reached
[
64]. Therefore,
was set up to make the reciprocal of
to quasi match
to
when
is greater than
and becomes the driving environmental parameter of
. Using graphs by [
80] of half-hourly changes in
and
, it was observed that
can change from
to
as
reaches values greater than
. In this case, a second run for
was performed assuming
, to make
when
. Values of
obtained with both parameters are presented here.
For calculating
, a maximum and a minimum temperature (
and
, in °C) is required that constrain the stomas process, plus another empirical factor,
(called the “optimum conductance temperature”):
where
and
is
°C for the Coniferous site. In the case of the Deciduous site, reported half-hour Trembling aspen
and temperature values [
80] were used to estimate the optimum conductance temperature for Trembling aspen
. An average optimum temperature of
°C was obtained.
Finally, to estimate the
, a function reported by [
64], which is a slightly modified version of the one suggested by [
79], was used:
where
(
is the empirical factor used to calculate
; and
is the fraction available for transpiration, also called the “effective fraction of available soil moisture” [
64]:
where
is the volumetric soil moisture (field measurements,
),
is the soil wilting point and
is the soil field capacity. The values of
and
are obtained based on the soil texture. Direct studies of the soil type and texture in the area of Kananaskis [
81,
82,
83,
84] were used to define the soil texture in the Coniferous and Deciduous sites. The soil texture, generally defined as fine sandy loam (for both areas), drew a soil field capacity ranging between 0.16 and 0.22, while the soil wilting point was estimated as 0.07 (all values in volumetric fraction).
Appendix A.1.2. Energy Parameters
The soil heat flux is calculated using a “universal relationship” developed by [
85]:
has the units of
. The net solar radiation is derived from the following equation [
64]:
where
is the shortwave solar radiation (measured in the field with a pyranometer),
is the net outgoing longwave solar radiation, and
is the surface’s albedo value. The term
helps to calculate the fraction of incident net shortwave solar radiation that is absorbed by a specific surface. For coniferous forests, mean
values are in the range of 0.09–0.15 [
66,
76], and deciduous forests are in the range of 0.15–0.25 [
76]. Monthly albedo values for mid-latitude forests are of 0.14 during the months of July and August [
86,
87,
88]. The net longwave solar radiation is calculated based on the emissivity values of four different surfaces and the air temperature,
[
47]:
where
is the Stefan–Boltzmann constant (
),
is the air temperature (units of K).
and
are the Leaf Area indices of the overstory and understory respectively;
and
are the clumping indices of the overstory and understory;
and
are estimations of the transmission of diffuse radiant energy through the understory and overstory. The emissivity of the overstory, the ground, the understory, and the atmosphere are respectively represented by
,
,
, and
. Emissivity values for the first three surfaces are assigned from [
47,
89] as 0.98, 0.95 and 0.98, respectively. These emissivity values concur with values reported by [
64]. Emissivity from the atmosphere is calculated with the following equation [
76]:
where
is in [
] and
is in degrees Kelvin. The transmission of diffuse radiant energy through the understory and overstory is given by the following two equations that were derived by [
47]:
was measured for every coniferous and deciduous site (i.e.,
);
is more complex to measure directly and it was derived from previous reports of understory NDVI and
values. Buerman et al. [
90] used the reflectance values to estimate the understory NDVI and calculate
indices based on understory NDVI-
scatterplots developed by [
91]. The
values reported by [
90] range between 0.6 and 1.0 (being the largest values for Black spruce and the smallest for Jack Pine). Conifers understory NDVI (NDVI
u) values reported by [
90] were compared with the studied Coniferous sites NDVI
u calculated from the understory spectral reflectance that was recorded in the 2003 field campaign at two Coniferous and two Deciduous sites [
92]. For both Coniferous and Deciduous sites, the average NDVI
u is 0.8, which is 0.3 larger than the values reported by [
90] in 2002 (their NDVI
u range is 0.35–0.50). Using information reported by [
91], ref. [
90] established that an NDVI
u of 0.5 corresponded to an
of 1.0. On the other hand, ref. [
92] established a standard
value of 0.5 for broadleaf and needle-leaf forests.
Therefore, based on these previous results,
for the Coniferous sites in Kananaskis is assumed 1.0, and for Deciduous sites, 0.6. The latter value is also in the
range reported by [
69] for deciduous stands in a boreal forest.
Figure A1 is the typical understory spectral response at a Coniferous and a Deciduous site in Kananaskis Field Station. It is convenient to stress the fact that these
values are approximate; however, the main objective is to acknowledge the importance of understory in the overall evapotranspiration estimates. Thus, as [
47] thought, it is convenient to somehow include the understory evapotranspiration based on assumptions about its
.
Figure A1.
Typical understory spectral reflectance in Kananaskis Field Station study sites during the summer of 2003.
Figure A1.
Typical understory spectral reflectance in Kananaskis Field Station study sites during the summer of 2003.
The understory clumping index
, was derived by modifying the former Chen’s equation:
where
in vascular vegetation [
93]. Thus, for understory vegetation
does not have to be partitioned into fractions that account for the shoot effect. At the same time, the
value is zero since there is no fraction of wood to account for in the understory vegetation present at the study sites. Thus,
As
is known,
can be approximated as 50% of
as suggested by [
94] for grasses (the closest that can be found to a forest understory). Hence,