# Canopy Resistance and Estimation of Evapotranspiration above a Humid Cypress Forest

Authors: Bau-Show Lin; Huimin Lei; Ming-Che Hu; Supattra Visessri; Cheng-I Hsieh
Journal: Advances in Meteorology
 (2020)

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## Abstract

This study presented a two-year data set of sensible heat and water vapor fluxes above a humid subtropical montane Cypress forest, located at 1650 m a.s.l. in northeastern Taiwan. The focuses of this study were to investigate (1) the diurnal and seasonal variations of canopy resistance and fluxes of sensible heat and water vapor above this forest; and (2) the mechanism of why a fixed canopy resistance could work when implementing the Penman–Monteith equation for diurnal hourly evapotranspiration estimation. Our results showed distinct seasonal variations in canopy resistance and water vapor flux, but on the contrary, the sensible heat flux did not change as much as the water vapor flux did with seasons. The seasonal variation patterns of the canopy resistance and water vapor flux were highly coupled with the meteorological factors. Also, the results demonstrated that a constant (fixed) canopy resistance was good enough for estimating the diurnal variation of evapotranspiration using Penman–Monteith equation. We observed a canopy resistance around 190 (s/m) for both the two warm seasons; and canopy resistances were around 670 and 320 (s/m) for the two cool seasons, respectively. In addition, our analytical analyses demonstrated that when the average canopy resistance is higher than 200 (s/m), the Penman–Monteith equation is less sensitive to the change of canopy resistance; hence, a fixed canopy resistance is suitable for the diurnal hourly evapotranspiration estimation. However, this is not the case when the average canopy resistance is less than 100 (s/m), and variable canopy resistances are needed. These two constraints (200 and 100) were obtained based on purely analytical analyses under a moderate meteorological condition (Rn = 600 W·m−2, RH = 60%, Ta = 20°C, U = 2 m·s−1) and a measurement height around two times of the canopy height.


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## Body

## 1. Introduction

Evapotranspiration (ET) and sensible heat have significant impacts on regional and global meteorology. In order to better understand heat, water vapor, and carbon dioxide fluxes between the vegetation and atmosphere, numerous measurements have been conducted on various terrestrial land surfaces (e.g., FLUXNET; see [1]). Based on these monitoring results, researchers have found that there is visible variability in heat, water vapor, and CO2 fluxes between the seasons and sometimes between years. Sensible and latent heat fluxes were large in summer and relatively low during winter, and CO2 assimilations were stronger in summer than in winter. However, the seasonal variations in sensible heat fluxes were stronger compared with both latent heat and CO2 fluxes [2–4]. Therefore, the surface energy partitioning and the ratio of sensible heat flux (H) to latent heat flux (LE) also varied with seasons.Because ET is a key process in the water cycle and in the surface energy budget, attention was paid to ET quantification methods (e.g., see review by [5]). The Penman–Monteith (P–M) equation, a method based on energy conservation and aerodynamic and surface (or canopy) resistances, is recommended worldwide [6] because of its standardization and universality in reference potential evapotranspiration estimation [7]. However, the difficulty in implementing P–M equation comes from parameterizing the resistance inputs, particularly the canopy (stomatal) resistance [8–10], which controls water vapor passing in and out of the plant. High priced instruments (e.g., the photosynthesis systems) can be used to directly measure the canopy resistance; however, indirect parameterizing of this resistance is adopted more widely. Thus, models that deal with parameterizing the canopy resistance from meteorological data (i.e., net radiation, air temperature, wind speed, humidity, and soil water content) were proposed by many researchers [11–15].Katerji and Rana [16] investigated the ET of six irrigated crops under the Mediterranean climate. Their results showed that adopting variable canopy resistance (calculated from meteorological data) to estimate evapotranspiration by the P–M equation has a significant advantage over constant (fixed) canopy resistance. Perez et al. [17] compared different methods for estimating canopy resistance under semiarid conditions in river valley with uniform grass. They showed that the constant canopy resistance (=70 s/m) might underestimate/overestimate evapotranspiration during summer/winter. Pauwels and Samson [18] pointed out that using the monthly averaged surface (canopy) resistance would lead to a better estimation of evapotranspiration at a seasonal time scale.Above two semiarid grass sites, Lecina et al. [19] found that a fixed canopy resistance (70 s/m) could result in a good estimation of the daily reference evapotranspiration; but for the estimation of hourly reference evapotranspiration, variable canopy resistance values were needed. Kosugi et al. [20] reported a constant canopy resistance of 149 (s/m) for a temperate Japanese Cypress forest. Also, Hsieh et al. [21] used a constant canopy resistance for a year round estimation of hourly ET from grassland and found good agreement with the measurements. In short, a fixed constant canopy resistance may work for estimating ET rather than using variable canopy resistance, but the mechanism of why this works is still unsolved.Among Earth surfaces, forests are one of the important ecosystems that affect our water resources and climate. Forests return large portions of precipitation water to the atmosphere through evapotranspiration, which greatly affect the hydrological cycle and relate to carbon fixation [22–24]. Montane cloud forests are one of the world’s most endangered ecosystems because of their sensitivity to changes in unique ecological conditions [25, 26]. Understanding ET from montane cloud forests continues to be an active research topic [27, 28]. In Taiwan, the Chamaecyparis (Cypress) forest grows across the whole island, varying in species composition and habitat conditions [29]. This study investigated the ET of a humid montane Cypress forest with a relatively homogeneous slope topography in northern Taiwan from a two-year eddy-covariance measurement data set. The purposes of this research are to (1) reveal the diurnal and seasonal variations and patterns of canopy resistance, sensible heat flux, and evapotranspiration above a mountain forest, (2) investigate the mechanism of why a constant (fixed) canopy resistance may work when implementing Penman–Monteith equation for ET estimation, (3) examine the performance of Penman–Monteith equation on estimating evapotranspiration in different seasons, (4) investigate the relationship between net radiation, sensible heat, and latent heat fluxes, and their influences on meteorological conditions above the forest.


## 2. Experiment

### 2.1. Site Description and Experimental Setup

Meteorological and surface flux measurements were made from May 1, 2005, to April 30, 2007, above a homogeneous Cypress forest at 1,650 m a.s.l. in northeastern Taiwan (24°35′27.4″N, 121°29′56.3″E). The site is at Chi-Lan Mountain and close to the Yuan Yang Lake ecosystem, which is declared a nature preserve in order to protect it against anthropogenic disturbances. The topography of this site is a relatively homogeneous slope of 14 degrees facing the southeastern direction and extending for 2 km and the Cypress forest covers an altitude range from 1,650 to 2,432 m a.s.l. Frequently covered by fog and cloud, the site received relatively less solar radiation and featured a temperate heavy moist climate. From previous record, the average annual air temperature was 13°C, and annual precipitation was around 4,000 mm. In this Cypress forest,Chamaecyparis obtusa var. formosana and Chamaecyparis formosensis are the predominant species; the understory is mainly comprised by Rhododendron formosanum [30]. Due to frequent precipitation, the soil water content at 30 cm was about 0.3–0.4 (m3/m3) and relatively steady annually [27]. Soil water status has no or minor influence on the daily ET and, thus, plays an unimportant role in regulating the water use of this Cypress forest [27]. Previous studies at Chi-Lan Mountain cloud forest in Taiwan indicated that the endemic tree species—yellow Cypress (Chamaecyparis obtusa var. formosana)—is well adapted to conditions of moist atmosphere and lower incident radiation [31–33]. The ecosystem CO2 uptake was found to be only marginally reduced, and small evapotranspiration still occurred during the fog periods [33, 34]. At this site, the canopy was closed and uniform with a leaf area index (LAI) of 6.3 m2/m2 [35], and hence the soil heat flux was small all year round. More details about the site can be found in the work by Chang et al. [35] and Chu et al. [27].The eddy-covariance method was applied to determine surface fluxes over this subtropical evergreen coniferous forest. The monitoring instruments were attached to a 23.4 m height walkup tower, where the average canopy height was 10.3 m. Around the tower site, the plantation exhibits a relatively narrow age range; trees were planted between 1961 and 1978 [30]. The tower was located in the north-westerly end of the plantation. The terrain around the tower site was relatively flat.The net radiation was measured with a CNR1 radiometer (Kipp & Zonen, Delft, The Netherlands), which separates the upward and downward short wave and long wave radiation components. The air temperature and humidity were measured with a HMP45A sensor (Vaisala, Helsinki, Finland). The radiometer and temperature/humidity sensors were installed at 22.5 and 23.5 m above the ground, respectively. Net radiation (Rn), air temperature (Ta) and relative humidity (RH) were all recorded on a data logger and averaged for a 30 min period. The eddy-covariance system was installed at 24 m above the ground. The three-dimensional wind velocity and virtual potential temperature were measured with an ultrasonic anemometer (R. M. Young 81000, Traverse City, Michigan, USA). The water vapor concentration was measured with a LI-7500 open path infrared gas analyzer (LI-COR, Lincoln, Nebraska, USA). Wind velocity, water vapor concentration, and virtual potential temperature were collected on a portable laptop at 10 Hz and the averaging period was half an hour. All instruments were powered by a series of 12 VDC batteries.


### 2.2. Data Processing

For the flux calculation, the general FLUXNET standard process (e.g., [36, 37]) including detrending, despiking, and spectral correction were applied. Detrending was done by removing the linear trend of the raw data. Spikes outside the ±3 standard deviation were replaced with the interpolated values. If the number of spikes exceeded 1% of the total number of each measurement run, then this run was abandoned. The spectral correction (frequency filtering) was done following Moore [38]. Time lags between measured scalars and vertical velocity were removed, and the planar fit method was applied to rotate the three velocity components into the mean streamline coordinate system [39]. The Webb–Pearman–Leuning correction was applied to correct the fluctuation of air density [40]. The data was collected during the period from May 2005 to April 2007.The 30 min data were then divided into two seasons: warm (May to October) and cool seasons (November to April). Missing data (due to weather conditions, instruments maintenance, etc.,) were excluded from the analysis. The data available rates for the warm and cool seasons of 2005 and 2006 were 34.42, 36.03, 47.78, and 70.11%, respectively (also listed in Table1). In each season, data were averaged to get a seasonal mean of diurnal variation. Due to instruments maintenance and weather condition, the data of March, 2006, was discarded. The average air temperature, relative humidity, wind speed, and vapor pressure deficit diurnal variations for the period of May 2015–April 2017 are shown in Figures 1(a)–1(d). The time zone of this site is UTC + 8 hours. In warm seasons, the temperature varied between 18 and 20°C and in cool seasons it ranged between 11 and 14°C (Figure 1(a)). For both warm and cool seasons, the humidity patterns were different from our normal experience in this foggy montane forest site. The humidity remained roughly constant (around 85–93%) from 00:00 to 06:00, then increased linearly to around 100% from 07:00 to 16:00 (fog started forming around 15:00), and then dropped linearly to around 90% from 17:00 to 24:00 (Figure 1(b)). For the wind field, the obvious valley-mountain wind diurnal cycles for all seasons were noticed, as shown in Figure 1(c), and the wind speed ranged between 1 and 2 (m/s). As to the vapor pressure deficit diurnal patterns (Figure 1(d)), they were inversely related to the patterns of relative humidity. Also, the precipitation in 2005 warm and cool seasons and 2006 warm and cool seasons were 4061, 1232, 2760, and 1086 mm, respectively (Figure 1(e)). At this site, the typhoon period is within the warm season; hence the warm seasons generally have higher precipitation than the cool seasons.Table 1
Summary of energy partition for LE andH Bowen ratio, energy closure ratio, direct energy transfer coefficient, and data available rate.
Season
Energy partition LE
Energy partitionH
Bowen ratio
Energy closure ratio
Averagedtc
Data available rate (%)
2005 warm
0.35
0.50
1.28
0.85
0.35
34.42
2005 cool
0.11
0.63
4.20
0.74
0.12
36.03
2006 warm
0.31
0.53
1.39
0.84
0.32
47.78
2006 cool
0.20
0.56
2.15
0.76
0.20
70.11
t
c: direct energy transfer coefficient, defined in equation (1).Figure 1
Averaged diurnal variations of (a) air temperature, (b) relative humidity, (c) wind speed, and (d) vapor pressure deficit for the warm (May to Oct.) and cool (Nov. to April) seasons of 2005–2006. The vertical bars indicate the standard deviations. (e) Precipitation for each season.
(a)
(b)
(c)
(d)
(e)


## 2.1. Site Description and Experimental Setup

Meteorological and surface flux measurements were made from May 1, 2005, to April 30, 2007, above a homogeneous Cypress forest at 1,650 m a.s.l. in northeastern Taiwan (24°35′27.4″N, 121°29′56.3″E). The site is at Chi-Lan Mountain and close to the Yuan Yang Lake ecosystem, which is declared a nature preserve in order to protect it against anthropogenic disturbances. The topography of this site is a relatively homogeneous slope of 14 degrees facing the southeastern direction and extending for 2 km and the Cypress forest covers an altitude range from 1,650 to 2,432 m a.s.l. Frequently covered by fog and cloud, the site received relatively less solar radiation and featured a temperate heavy moist climate. From previous record, the average annual air temperature was 13°C, and annual precipitation was around 4,000 mm. In this Cypress forest,Chamaecyparis obtusa var. formosana and Chamaecyparis formosensis are the predominant species; the understory is mainly comprised by Rhododendron formosanum [30]. Due to frequent precipitation, the soil water content at 30 cm was about 0.3–0.4 (m3/m3) and relatively steady annually [27]. Soil water status has no or minor influence on the daily ET and, thus, plays an unimportant role in regulating the water use of this Cypress forest [27]. Previous studies at Chi-Lan Mountain cloud forest in Taiwan indicated that the endemic tree species—yellow Cypress (Chamaecyparis obtusa var. formosana)—is well adapted to conditions of moist atmosphere and lower incident radiation [31–33]. The ecosystem CO2 uptake was found to be only marginally reduced, and small evapotranspiration still occurred during the fog periods [33, 34]. At this site, the canopy was closed and uniform with a leaf area index (LAI) of 6.3 m2/m2 [35], and hence the soil heat flux was small all year round. More details about the site can be found in the work by Chang et al. [35] and Chu et al. [27].The eddy-covariance method was applied to determine surface fluxes over this subtropical evergreen coniferous forest. The monitoring instruments were attached to a 23.4 m height walkup tower, where the average canopy height was 10.3 m. Around the tower site, the plantation exhibits a relatively narrow age range; trees were planted between 1961 and 1978 [30]. The tower was located in the north-westerly end of the plantation. The terrain around the tower site was relatively flat.The net radiation was measured with a CNR1 radiometer (Kipp & Zonen, Delft, The Netherlands), which separates the upward and downward short wave and long wave radiation components. The air temperature and humidity were measured with a HMP45A sensor (Vaisala, Helsinki, Finland). The radiometer and temperature/humidity sensors were installed at 22.5 and 23.5 m above the ground, respectively. Net radiation (Rn), air temperature (Ta) and relative humidity (RH) were all recorded on a data logger and averaged for a 30 min period. The eddy-covariance system was installed at 24 m above the ground. The three-dimensional wind velocity and virtual potential temperature were measured with an ultrasonic anemometer (R. M. Young 81000, Traverse City, Michigan, USA). The water vapor concentration was measured with a LI-7500 open path infrared gas analyzer (LI-COR, Lincoln, Nebraska, USA). Wind velocity, water vapor concentration, and virtual potential temperature were collected on a portable laptop at 10 Hz and the averaging period was half an hour. All instruments were powered by a series of 12 VDC batteries.


## 2.2. Data Processing

For the flux calculation, the general FLUXNET standard process (e.g., [36, 37]) including detrending, despiking, and spectral correction were applied. Detrending was done by removing the linear trend of the raw data. Spikes outside the ±3 standard deviation were replaced with the interpolated values. If the number of spikes exceeded 1% of the total number of each measurement run, then this run was abandoned. The spectral correction (frequency filtering) was done following Moore [38]. Time lags between measured scalars and vertical velocity were removed, and the planar fit method was applied to rotate the three velocity components into the mean streamline coordinate system [39]. The Webb–Pearman–Leuning correction was applied to correct the fluctuation of air density [40]. The data was collected during the period from May 2005 to April 2007.The 30 min data were then divided into two seasons: warm (May to October) and cool seasons (November to April). Missing data (due to weather conditions, instruments maintenance, etc.,) were excluded from the analysis. The data available rates for the warm and cool seasons of 2005 and 2006 were 34.42, 36.03, 47.78, and 70.11%, respectively (also listed in Table1). In each season, data were averaged to get a seasonal mean of diurnal variation. Due to instruments maintenance and weather condition, the data of March, 2006, was discarded. The average air temperature, relative humidity, wind speed, and vapor pressure deficit diurnal variations for the period of May 2015–April 2017 are shown in Figures 1(a)–1(d). The time zone of this site is UTC + 8 hours. In warm seasons, the temperature varied between 18 and 20°C and in cool seasons it ranged between 11 and 14°C (Figure 1(a)). For both warm and cool seasons, the humidity patterns were different from our normal experience in this foggy montane forest site. The humidity remained roughly constant (around 85–93%) from 00:00 to 06:00, then increased linearly to around 100% from 07:00 to 16:00 (fog started forming around 15:00), and then dropped linearly to around 90% from 17:00 to 24:00 (Figure 1(b)). For the wind field, the obvious valley-mountain wind diurnal cycles for all seasons were noticed, as shown in Figure 1(c), and the wind speed ranged between 1 and 2 (m/s). As to the vapor pressure deficit diurnal patterns (Figure 1(d)), they were inversely related to the patterns of relative humidity. Also, the precipitation in 2005 warm and cool seasons and 2006 warm and cool seasons were 4061, 1232, 2760, and 1086 mm, respectively (Figure 1(e)). At this site, the typhoon period is within the warm season; hence the warm seasons generally have higher precipitation than the cool seasons.Table 1
Summary of energy partition for LE andH Bowen ratio, energy closure ratio, direct energy transfer coefficient, and data available rate.
Season
Energy partition LE
Energy partitionH
Bowen ratio
Energy closure ratio
Averagedtc
Data available rate (%)
2005 warm
0.35
0.50
1.28
0.85
0.35
34.42
2005 cool
0.11
0.63
4.20
0.74
0.12
36.03
2006 warm
0.31
0.53
1.39
0.84
0.32
47.78
2006 cool
0.20
0.56
2.15
0.76
0.20
70.11
t
c: direct energy transfer coefficient, defined in equation (1).Figure 1
Averaged diurnal variations of (a) air temperature, (b) relative humidity, (c) wind speed, and (d) vapor pressure deficit for the warm (May to Oct.) and cool (Nov. to April) seasons of 2005–2006. The vertical bars indicate the standard deviations. (e) Precipitation for each season.
(a)
(b)
(c)
(d)
(e)


## 3. Methods

In this section, the Penman–Monteith equation (used for estimating ET) was first described and the role of canopy resistance was then discussed.


### 3.1. Penman–Monteith Equation

The Penman–Monteith equation for calculating latent heat flux, LE (W·m−2), can be expressed as follows [6]:(1)LE=ΔQnΔ+γ1+rc/ra+ρcpD/raΔ+γ1+rc/ra,where Δ is the slope of the saturation vapor pressure-temperature curve calculated at the air temperature Ta, γ (=Pcp/0.622Lv) is the psychrometric constant, P is the air pressure, ρ (≈1.2 kg·m−3) is the mean air density, cp (=1005 J·kg−1·K−1) is the specific heat for air, Lv (=2.46 × 106 J·kg−1) is the latent heat of vaporization, Qn (=Rn − G) is the available energy, G is the soil heat flux, D is the vapor pressure deficit, ra is the aerodynamic resistance of water vapor (s·m−1), and rc is the canopy resistance (s·m−1). The first term on the right hand side in (1) is generally called as the energy term (LE_eq) and represents the contribution from available energy; and we can define a direct energy transfer coefficient (tc)(2)tc=ΔΔ+γ1+rc/ra,which describes how much available energy (Qn) would be transferred into LE directly. The second term on the right hand side is called the atmospheric demand term (LE_vpd) and describes the ET demanding from the atmosphere. Now, equation (1) can be rewritten as(3)LE=tc∗Qn+LE_vpd.If a linear relationship exists betweenQn and LE, that is, LE = a ∗ Qn + b. Then the regression slope a should be close to tc, and LE_vpd is close to the intercept b and relatively constant. In (1), ra can be calculated by(4)ra=lnz/zolnz/zovk2U=lnz/zovku∗,where k (=0.4) is the von Karman constant, u∗ is the friction velocity (m·s−1), z is the measurement height, zo is the surface roughness (≅0.1h, h is the average canopy height) for momentum, zov is the surface roughness (≅0.01h) for water vapor, and U is the mean wind speed at measurement height z.Whenrc approaches zero, then (1) becomes the Penman equation:(5)LE=ΔQn+ρcpD/raΔ+γ,for calculating the potential evapotranspiration (PET). Also, when the vapor pressure deficit, D, approaches zero, (1) reduces to(6)LE=ΔQnΔ+γ1+rc/ra.Equation (6) is the so-called equilibrium evapotranspiration (LE_eq), and ET is mainly driven by the available energy under this condition.Following McNaughton and Jarvis [41], (1) can also be expressed as(7)LE=ΩΔQnΔ+γ+1−ΩρCpDγrc,where the decoupling coefficient Ω is defined as(8)Ω=Δ/γ+1Δ/γ+1+rc/ra=Δ+γ/γΔ+γ/γ+rc/ra.The decoupling coefficient indicates the relative importance of the energy term in (1). When rc approaches 0, Ω becomes unity; this represents the daytime condition with a wet canopy surface where the role of rc is ignored. When rc approaches infinite, Ω becomes zero; this represents the night time condition in which the ET portion from the energy term (LE_eq) is zero. Jarvis and McNaughton [42] showed that forests generally have smaller decoupling coefficient than short grass and crops. This implies that forests are very closely coupled to the atmosphere above and that the evapotranspiration rate is thus dominated by the atmospheric demand term.


### 3.2. Sensitivity of P–M Equation on Canopy Resistance

As stated in the Introduction section, an interesting phenomenon in implementing P–M equation is that some research concluded that a fixed constantrc is good enough (e.g., [19]) but some others suggested variable rc (e.g., [12]) is needed. To investigate the sensitivity of LE estimation to a change of the canopy resistance, we consider the following:(9)∂LE∂rc=−γΔQn+ρCpD/raraΔ+γ1+rc/ra2.Equation (9) represents the sensitivity of the P–M equation with respect to rc and describes how LE estimation would be varied by a unit increase of rc. Now substitute ra with equation (4), we then have(10)∂LE∂rc=−γΔQn+ρCpDk2U/lnz/z0lnz/zovlnz/z0lnz/zov/k2UΔ+γ1+rck2U/lnz/z0lnz/zov2.Equation (10) explicitly describes that the ratio of ∂LE/∂rc is also a function of wind speed in addition to the other three meteorological parameters: net radiation, temperature, and vapor pressure deficit. Using equation (4) and setting the measurement height z as two times of the canopy height (z = 2h), one obtains ra = 99/U, and equation (10) reduces to(11)∂LE∂rc=−γΔQn+ρCpDU/9999/UΔ+γ1+rcU/992.Also, in this study, with the measured LE and rearranging equation (1), the measured rc was calculated by the following:(12)rc=ΔγQn−LELE−1ra+ρCpγDLE.


## 3.1. Penman–Monteith Equation

The Penman–Monteith equation for calculating latent heat flux, LE (W·m−2), can be expressed as follows [6]:(1)LE=ΔQnΔ+γ1+rc/ra+ρcpD/raΔ+γ1+rc/ra,where Δ is the slope of the saturation vapor pressure-temperature curve calculated at the air temperature Ta, γ (=Pcp/0.622Lv) is the psychrometric constant, P is the air pressure, ρ (≈1.2 kg·m−3) is the mean air density, cp (=1005 J·kg−1·K−1) is the specific heat for air, Lv (=2.46 × 106 J·kg−1) is the latent heat of vaporization, Qn (=Rn − G) is the available energy, G is the soil heat flux, D is the vapor pressure deficit, ra is the aerodynamic resistance of water vapor (s·m−1), and rc is the canopy resistance (s·m−1). The first term on the right hand side in (1) is generally called as the energy term (LE_eq) and represents the contribution from available energy; and we can define a direct energy transfer coefficient (tc)(2)tc=ΔΔ+γ1+rc/ra,which describes how much available energy (Qn) would be transferred into LE directly. The second term on the right hand side is called the atmospheric demand term (LE_vpd) and describes the ET demanding from the atmosphere. Now, equation (1) can be rewritten as(3)LE=tc∗Qn+LE_vpd.If a linear relationship exists betweenQn and LE, that is, LE = a ∗ Qn + b. Then the regression slope a should be close to tc, and LE_vpd is close to the intercept b and relatively constant. In (1), ra can be calculated by(4)ra=lnz/zolnz/zovk2U=lnz/zovku∗,where k (=0.4) is the von Karman constant, u∗ is the friction velocity (m·s−1), z is the measurement height, zo is the surface roughness (≅0.1h, h is the average canopy height) for momentum, zov is the surface roughness (≅0.01h) for water vapor, and U is the mean wind speed at measurement height z.Whenrc approaches zero, then (1) becomes the Penman equation:(5)LE=ΔQn+ρcpD/raΔ+γ,for calculating the potential evapotranspiration (PET). Also, when the vapor pressure deficit, D, approaches zero, (1) reduces to(6)LE=ΔQnΔ+γ1+rc/ra.Equation (6) is the so-called equilibrium evapotranspiration (LE_eq), and ET is mainly driven by the available energy under this condition.Following McNaughton and Jarvis [41], (1) can also be expressed as(7)LE=ΩΔQnΔ+γ+1−ΩρCpDγrc,where the decoupling coefficient Ω is defined as(8)Ω=Δ/γ+1Δ/γ+1+rc/ra=Δ+γ/γΔ+γ/γ+rc/ra.The decoupling coefficient indicates the relative importance of the energy term in (1). When rc approaches 0, Ω becomes unity; this represents the daytime condition with a wet canopy surface where the role of rc is ignored. When rc approaches infinite, Ω becomes zero; this represents the night time condition in which the ET portion from the energy term (LE_eq) is zero. Jarvis and McNaughton [42] showed that forests generally have smaller decoupling coefficient than short grass and crops. This implies that forests are very closely coupled to the atmosphere above and that the evapotranspiration rate is thus dominated by the atmospheric demand term.


## 3.2. Sensitivity of P–M Equation on Canopy Resistance

As stated in the Introduction section, an interesting phenomenon in implementing P–M equation is that some research concluded that a fixed constantrc is good enough (e.g., [19]) but some others suggested variable rc (e.g., [12]) is needed. To investigate the sensitivity of LE estimation to a change of the canopy resistance, we consider the following:(9)∂LE∂rc=−γΔQn+ρCpD/raraΔ+γ1+rc/ra2.Equation (9) represents the sensitivity of the P–M equation with respect to rc and describes how LE estimation would be varied by a unit increase of rc. Now substitute ra with equation (4), we then have(10)∂LE∂rc=−γΔQn+ρCpDk2U/lnz/z0lnz/zovlnz/z0lnz/zov/k2UΔ+γ1+rck2U/lnz/z0lnz/zov2.Equation (10) explicitly describes that the ratio of ∂LE/∂rc is also a function of wind speed in addition to the other three meteorological parameters: net radiation, temperature, and vapor pressure deficit. Using equation (4) and setting the measurement height z as two times of the canopy height (z = 2h), one obtains ra = 99/U, and equation (10) reduces to(11)∂LE∂rc=−γΔQn+ρCpDU/9999/UΔ+γ1+rcU/992.Also, in this study, with the measured LE and rearranging equation (1), the measured rc was calculated by the following:(12)rc=ΔγQn−LELE−1ra+ρCpγDLE.


## 4. Results and Discussion

In this section, we first present the temporal variation ofRn, H, LE, and G, the characteristics of ET, and energy partition for the warm and cool seasons of the year 2005-2006 at this humid montane forest. Then we discuss the performance of P–M equation, the role of canopy resistance, the decoupling coefficient, and the direct energy transfer rate.


### 4.1. Energy Partition

The averaged diurnal variations ofG, Rn, H, and LE in warm and cool seasons during the year 2005-2006 are plotted in Figure 2. Since at this site the canopy was closed, the soil heat fluxes (G) for the warm and cool seasons were all very small (Figure 2(a)). In Figure 2(a), the maximum and minimum soil heat fluxes are 8 and −4 (W/m2), respectively; and the soil heat flux measurements were not available in 2006 cool season due to the soil heat flux plate maintenance. For Rn, as expected, warm seasons received more net radiation than cool seasons did (Figure 2(b)); the maximum Rn for warm and cool seasons were around 514 and 437 (W·m−2), respectively. For H, there was no major tendency between warm and cool seasons (Figure 2(c)); the maximum H varied between 257 and 311 (W·m−2). As to LE, in both warm seasons the LE peak value could be as large as 175 W·m−2, but the peak values were only 50 and 100 (W·m−2) for 2005 and 2006 cool seasons, respectively (Figure 2(d)). Why the 2006 cool season had a higher LE than the 2005 cool season? This was because the relative humidity was lower during day time in 2006 cool season (Figure 1(b)) and resulted in a lower canopy resistance [12, 43]. This relatively low RH also created a relatively higher atmospheric demand for ET in the cool season of the year 2006. It was noticed that, as shown in Figure 2(b), the cool season 2005 received less Rn than the warm season 2005, but the cool season 2005 had a higher H than the warm season 2005 had. This was due to the low LE in the cool season of 2005 and the major portion of Rn was distributed into H. This revealed that the meteorological condition was coupled with the biological condition (i.e., rc). In other words, low air temperature and high relative humidity caused a higher canopy resistance and then resulted in a lower LE and then produced a higher sensible heat, which would later on warm the air more. This also demonstrated how vegetation could change the micrometeorology.Figure 2
Averaged diurnal variations of (a)G, (b) Rn, (c) H, and (d) LE for the warm (May to Oct.) and cool (Nov. to April) seasons of 2005–2006. The vertical bars indicate the standard deviations.
(a)
(b)
(c)
(d)To check the energy partition of this site, the scatter plots ofH v.s. Rn and LE v.s. Rn for each season are shown in Figure 3. In the warm seasons of 2005 and 2006, half of the Rn was transferred into H and around 35% of Rn was transferred into LE. For cool season 2005, only 0.11Rn was transferred into LE and 0.63Rn was distributed into H. As for the cool season of 2006, LE was about 0.2Rn and H was around 0.56Rn. In short, Figure 3 shows that in cool seasons, ET was smaller and resulted in a higher percentage of Rn distributing into H. Figures 2 and 3 indicate that the ET phenomenon controlled the micrometeorology on this site. Also, from Figures 2 and 3, there is a hysteresis between Rn and ET. Both biotic factors (e.g., canopy resistance, root water potential) and abiotic factors (e.g., soil water status, boundary layer processes) contribute to the LE hysteresis [44]. In our site, due to frequent precipitation, the soil water content at 30 cm was about 0.3–0.4 (m3/m3) and relatively steady annually; so soil water status has no or minor influence on the daily ET. Hence, the hysteresis of LE in this site is attributed to the canopy resistance and boundary layer process.Figure 3
Scatter plots ofH and LE as a function of Rn for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006. H LE and Rn are in (W·m−2).
(a)
(b)
(c)
(d)These energy partition results, Bowen ratios (H/LE), and energy closure ratio for these four seasons were also summarized in Table 1. For warm seasons, the energy closure was about 85%; for cool seasons, it was around 75%. These energy closure ratios are normal compared with the literature.


### 4.2. Estimation of Latent Heat Flux

For estimating LE, we adopted Penman–Monteith equation (equation1) in conjunction with a constant canopy resistance. The comparisons between the seasonal averages of half-hourly measured and predicted LE for each season are shown in Figure 4. The regression analyses for Figure 4 are also summarized in Table 2. In Figure 4, the fixed constant canopy resistance adopted in each season was the average canopy resistance between 10:00 and 14:00 (the period when the canopy surface was dry). The canopy resistance values were calculated by equation (12) with the measured LE and Rn. The average and maximum canopy resistances for each season were also listed in Table 2. For complete purpose, we also provided the comparisons between all the half-hourly (not averaged) measured and predicted LE for each season in the Appendix.Figure 4
Comparisons between measured and predicted LE (W·m−2) for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006.
(a)
(b)
(c)
(d)Table 2
Summary of regression analysis between measured and predicted LE (W·m−2). Y = aX + b; Y is measured LE; X is predicted LE.
Season
a
b (W·m−2)
R
2
Averagerc (s/m)
Maximumrc (s/m)
2005 warm
0.98
11.55
0.98
185
226
2005 cool
1.00
3.63
0.93
673
831
2006 warm
0.95
16.51
0.97
201
229
2006 cool
0.98
10.07
0.91
320
418From Figure4 and Table 2, it is clear that P–M method could predict LE well (R2 ranged from 0.91–0.98) with a fixed constant rc. The average canopy resistances for warm and cool seasons of 2005 and 2006 were 185, 673, 201, and 320 (s/m), respectively. It is noticed that the average canopy resistances for warm seasons were around 190 (s/m), but the average canopy resistances for cool seasons were much higher (more than 320). This difference of canopy resistance between the warm and cool seasons was attributed to the air temperature (Figure 1(a)), since low temperature resulted in high canopy resistance [12].To further examine the variation ofrc during day time (07:00–17:00), we plotted the diurnal course of rc in Figure 5. Notice that no matter in warm or cool season, rc had its lowest value around 07:00 in the morning and then increased linearly to its highest value around 12:00 then remained constant till around 1500 and then dropped. This diurnal variation of rc could be explained by the following: in the early morning ET occurred under wet surface condition (fog water remained on the leaf surface), so rc was small (and this should close to PET, shown in Figure 6); then rc was increased due to a drier canopy surface, and around 15:00 the fog started forming and caused a wet canopy surface and resulted in a reduction of rc. It is noticed that this drop of rc would not happen for a forest (or other vegetation) with dry canopy surface in the late afternoon (e.g., [45, 46]).Figure 5
Diurnal variations of canopy resistance (s/m) for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006.
(a)
(b)
(c)
(d)Figure 6
Comparisons between potential evapotranspiration (PET), predicted LE by PM equation (LE_PM), and measured LE (LE_measured) for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006. The yellow box highlights the region where LE_measured is close to PET. The vertical bars indicate the standard deviations.
(a)
(b)
(c)
(d)Using equation (5), we presented the calculated PET and measured LE in Figure 6 for each season. Figure 6 shows that in the early morning (06:00–07:00) and late afternoon (17:00–18:00) the ET was close to PET for all the seasons. This again confirms that in the early morning and late afternoon, the canopy surface was wet and created a relatively high ET. Also, recalling from the P–M equation, there are two sources for LE, one is the energy term (LE_eq) and the other is the atmospheric demand term (LE_vpd). To quantify the relative magnitude of these two terms, Figure 7 shows the diurnal variation of these two terms as well as measured and predicted LE. It is obvious that the energy term was much bigger than the LE_vpd term. The LE_vpd term was very small at this humid montane forest.Figure 7
Diurnal variations of measured LE (LE_measured), LE predictions by PM equation (LE_PM), LE at equilibrium (LE_eq), and the LE contribution by vpd (LE_vpd) for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006. The vertical bars indicate the standard deviations.
(a)
(b)
(c)
(d)


### 4.3. The Role of Canopy Resistance

From Figures4 and 5 and Table 2, it is noticed that though rc varied with time, a constant rc could still provide good estimations of LE for the whole diurnal period. To explore the sensitivity of the P–M equation estimated LE to rc, we considered equation (11), which describes how much of the estimated LE is increased with a unit increase of rc. Equation (11) reveals that the ratio of ∂LE/∂rc is a function of rc and four meteorological parameters: U, Rn, Ta, and RH. To explicitly determine the variation of ∂LE/∂rc with respect to rc under different meteorological conditions, the following steps were taken. Firstly, a moderate meteorological condition was selected as the baseline, where Rn = 600 (W/m2), U = 2 (m/s), RH = 0.6, and Ta = 20 (°C). Secondly, we varied one of the four meteorological parameters (i.e., Rn, Ta, U, or RH) each time, and the other three parameters remained constant as the baseline values.Now, given the baseline condition:U = 2 m/s, RH = 0.6, and Ta = 20°C, we plotted the variations of ∂LE/∂rc with respect to rc for Rn from 50 to 800 (W/m2) in Figure 8(a). From Figure 8(a), we noticed that (1) when rc is large (say greater than 500 s/m), ∂LE/∂rc is small (<−0.2) irrelevant to the magnitude of Rn; (2) when rc = 200 (s/m), a unit increase of rc would cause only 0.2 to 0.8 unit decrease on LE estimation; (3) however, if rc = 100 (s/m), then ∂LE/∂rc could reach 1.4 when Rn is 600 (W·m−2); and (4) when Rn is smaller, ∂LE/∂rc is smaller for the same rc. Figure 8(b) is the same as Figure 8(a), but for different wind speeds (U ranged from 0.05 to 6 m/s with Rn = 600 W·m−2, RH = 0.6, and Ta = 20°C). Figure 8(b) has the similar pattern as in Figure 8(a) and shows that (1) if U is small (≤0.05 m/s), then the ratio of ∂LE/∂rc is around −0.08 and does not change with rc much; (2) for the cases where U is larger than 2 (m/s), the curves of ∂LE/∂rc are quite close; (3) when rc = 200 (s/m), a unit increase of rc would cause only 0.6 unit decrease on LE estimation.Figure 8
∂LE/∂rc as a function of rc (m/s) under different meteorological conditions (a) U = 2 (m/s), Ta = 20 (°C), RH = 60%; (b) Rn = 600 (W·m−2), Ta = 20 (°C), RH = 60%, (c) Rn = 600 (W·m−2), U = 2 (m/s), Ta = 20 (°C), and (d) Rn = 600 (W·m−2), U = 2 (m/s), RH = 60%.
(a)
(b)
(c)
(d)We also plotted∂LE/∂rc as a function of rc under different relative humidity conditions (RH varied from 30 to 90% with Rn = 600 W·m−2, U = 2 m/s, and Ta = 20°C) in Figure 8(c). Similar to Figure 8(c), ∂LE/∂rc with respect to rc for different temperature (Ta varied from 5 to 40°C given Rn = 600 W·m−2, U = 2 m/s, and RH = 0.6) are presented in Figure 8(d). Figures 8(c) and 8(d) also have similar patterns as Figure 8(a), and it can be seen that at rc = 200 (s/m), ∂LE/∂rc ranges from −0.77 to −0.53 in Figure 8(c) and ranges from −0.86 to −0.37 in Figure 8(d).In summary, under a general moderate meteorological condition whereRn = 600 (W/m2), U = 2 (m/s), RH = 0.6, and Ta = 20 (°C), if rc is larger than 200 (s/m), ∂LE/∂rc is less than 0.65; This implies that the predicted LE is not sensitive to the value of rc used, when the average rc is larger than 200. It is also important to note that Figures 8(a)–8(d) show that when rc is small (<100 s/m), a unit increase of rc could result in 1.34 units decrease on predicted LE. If this is the case of the site, then a variable rc is needed. This provides an explanation for Lecina et al.’s [19] results where they found that a fixed canopy resistance (70 s/m) could provide good daily reference evapotranspiration estimation, but for the estimation of hourly reference evapotranspiration, variable canopy resistance values were needed; since their average canopy resistance was small (only 70 m/s). The values of ∂LE/∂rc with respect to some certain rc under Rn = 600 (W/m2), RH = 0.6, U = 2 (m/s) at two different temperatures [Ta = 20 and 10 (°C)] are also listed in Table 3.Table 3
Values of∂LE/∂rc with different rc under Rn = 600 (W/m2), RH = 0.6, U = 2 (m/s) at two different temperatures [Ta = 20 and 10 (°C)].
r
c (s/m)
∂
LE
/
∂
r
c [Ta = 20 (°C)]
∂
LE
/
∂
r
c [Ta = 10 (°C)]
70
−1.78
−1.52
100
−1.34
−1.07
200
−0.65
−0.46
400
−0.25
−0.16From Figures8(a)–8(d), it is clear that under the conditions of low Rn, U, Ta, or vapor pressure deficit (i.e., high RH), the ratio of ∂LE/∂rc is smaller. In other words, under a low wind speed, low temperature, small radiation, or low vapor pressure deficit condition, different rc values will result in a relatively similar LE prediction. Hence, it does not matter much which rc value is adopted. Also, from Table 3, it can be seen that when rc is around 200 (s/m), a 100 units (s/m) increase of rc only causes a 46–65 unit (W·m−2) decrease on LE. These explained why a fixed constant rc worked well for estimating diurnal LE while, in fact, rc varied with time.We also applied the measured data to equation (11). Figure 9 plots ∂LE/∂rc as a function of time with measured Rn, Ta, U, and RH. In Figure 9, ∂LE/∂rc varied in consistence with Rn; hence, at this site, Rn was the major (primary regulator) parameter controlling ∂LE/∂rc. The ratio of ∂LE/∂rc was the lowest in the early morning and reached its maximum around 11:00, and then started to decrease in the afternoon. This diurnal trend is caused by the response of rc to the increase of radiation, temperature, and other micrometeorological variables with time. Notice that the maximum values of ∂LE/∂rc were only −0.5, −0.065, −0.5, and −0.2, respectively, for the warm and cool seasons of 2005 and 2006. This also indicated that a constant rc was good enough for the whole diurnal LE estimation.Figure 9
Diurnal variations of∂LE/∂rc and Rn for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006.
(a)
(b)
(c)
(d)


### 4.4. Energy Transfer Rate from Available Energy to LE

To explore the direct energy transfer rate (tc) from available energy, Qn, (here Qn ≡ Rn) to LE, we plotted the diurnal pattern of averaged decoupling factor and energy transfer rate (equation (2)) in Figure 10. At the beginning of the morning, the decoupling coefficient was large due to the small value of rc (Figure 5); and then following an increasing rc, the decoupling coefficient then decreased to its lowest value around 10:00, then remained constant till around 14:00, and then increased again. In Figure 10, the direct energy transfer coefficient and the decoupling coefficient varied with the same pattern.Figure 10
Diurnal variations of decoupling coefficient and energy transfer coefficient for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006.
(a)
(b)
(c)
(d)Also, it is noticed that on the basis of the linear relation betweenRn and LE (shown in Figure 3) and equation (3), the slope of the regression between Rn and LE should be about the same as the averaged tc in equation (3). We calculated the averaged tc for the period of 10:00–14:00 when the canopy surface was dry. We found the averaged direct energy transfer rate for the warm and cool seasons of 2005 and 2006 were 0.35, 0.12, 0.32, and 0.20, respectively, and were about the same as the slope in that season shown in Figure 3 (these values were also listed in Table 1). Figure 10 and Table 1 demonstrated that the P–M equation was able to capture the energy transfer rate from Qn to LE.


## 4.1. Energy Partition

The averaged diurnal variations ofG, Rn, H, and LE in warm and cool seasons during the year 2005-2006 are plotted in Figure 2. Since at this site the canopy was closed, the soil heat fluxes (G) for the warm and cool seasons were all very small (Figure 2(a)). In Figure 2(a), the maximum and minimum soil heat fluxes are 8 and −4 (W/m2), respectively; and the soil heat flux measurements were not available in 2006 cool season due to the soil heat flux plate maintenance. For Rn, as expected, warm seasons received more net radiation than cool seasons did (Figure 2(b)); the maximum Rn for warm and cool seasons were around 514 and 437 (W·m−2), respectively. For H, there was no major tendency between warm and cool seasons (Figure 2(c)); the maximum H varied between 257 and 311 (W·m−2). As to LE, in both warm seasons the LE peak value could be as large as 175 W·m−2, but the peak values were only 50 and 100 (W·m−2) for 2005 and 2006 cool seasons, respectively (Figure 2(d)). Why the 2006 cool season had a higher LE than the 2005 cool season? This was because the relative humidity was lower during day time in 2006 cool season (Figure 1(b)) and resulted in a lower canopy resistance [12, 43]. This relatively low RH also created a relatively higher atmospheric demand for ET in the cool season of the year 2006. It was noticed that, as shown in Figure 2(b), the cool season 2005 received less Rn than the warm season 2005, but the cool season 2005 had a higher H than the warm season 2005 had. This was due to the low LE in the cool season of 2005 and the major portion of Rn was distributed into H. This revealed that the meteorological condition was coupled with the biological condition (i.e., rc). In other words, low air temperature and high relative humidity caused a higher canopy resistance and then resulted in a lower LE and then produced a higher sensible heat, which would later on warm the air more. This also demonstrated how vegetation could change the micrometeorology.Figure 2
Averaged diurnal variations of (a)G, (b) Rn, (c) H, and (d) LE for the warm (May to Oct.) and cool (Nov. to April) seasons of 2005–2006. The vertical bars indicate the standard deviations.
(a)
(b)
(c)
(d)To check the energy partition of this site, the scatter plots ofH v.s. Rn and LE v.s. Rn for each season are shown in Figure 3. In the warm seasons of 2005 and 2006, half of the Rn was transferred into H and around 35% of Rn was transferred into LE. For cool season 2005, only 0.11Rn was transferred into LE and 0.63Rn was distributed into H. As for the cool season of 2006, LE was about 0.2Rn and H was around 0.56Rn. In short, Figure 3 shows that in cool seasons, ET was smaller and resulted in a higher percentage of Rn distributing into H. Figures 2 and 3 indicate that the ET phenomenon controlled the micrometeorology on this site. Also, from Figures 2 and 3, there is a hysteresis between Rn and ET. Both biotic factors (e.g., canopy resistance, root water potential) and abiotic factors (e.g., soil water status, boundary layer processes) contribute to the LE hysteresis [44]. In our site, due to frequent precipitation, the soil water content at 30 cm was about 0.3–0.4 (m3/m3) and relatively steady annually; so soil water status has no or minor influence on the daily ET. Hence, the hysteresis of LE in this site is attributed to the canopy resistance and boundary layer process.Figure 3
Scatter plots ofH and LE as a function of Rn for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006. H LE and Rn are in (W·m−2).
(a)
(b)
(c)
(d)These energy partition results, Bowen ratios (H/LE), and energy closure ratio for these four seasons were also summarized in Table 1. For warm seasons, the energy closure was about 85%; for cool seasons, it was around 75%. These energy closure ratios are normal compared with the literature.


## 4.2. Estimation of Latent Heat Flux

For estimating LE, we adopted Penman–Monteith equation (equation1) in conjunction with a constant canopy resistance. The comparisons between the seasonal averages of half-hourly measured and predicted LE for each season are shown in Figure 4. The regression analyses for Figure 4 are also summarized in Table 2. In Figure 4, the fixed constant canopy resistance adopted in each season was the average canopy resistance between 10:00 and 14:00 (the period when the canopy surface was dry). The canopy resistance values were calculated by equation (12) with the measured LE and Rn. The average and maximum canopy resistances for each season were also listed in Table 2. For complete purpose, we also provided the comparisons between all the half-hourly (not averaged) measured and predicted LE for each season in the Appendix.Figure 4
Comparisons between measured and predicted LE (W·m−2) for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006.
(a)
(b)
(c)
(d)Table 2
Summary of regression analysis between measured and predicted LE (W·m−2). Y = aX + b; Y is measured LE; X is predicted LE.
Season
a
b (W·m−2)
R
2
Averagerc (s/m)
Maximumrc (s/m)
2005 warm
0.98
11.55
0.98
185
226
2005 cool
1.00
3.63
0.93
673
831
2006 warm
0.95
16.51
0.97
201
229
2006 cool
0.98
10.07
0.91
320
418From Figure4 and Table 2, it is clear that P–M method could predict LE well (R2 ranged from 0.91–0.98) with a fixed constant rc. The average canopy resistances for warm and cool seasons of 2005 and 2006 were 185, 673, 201, and 320 (s/m), respectively. It is noticed that the average canopy resistances for warm seasons were around 190 (s/m), but the average canopy resistances for cool seasons were much higher (more than 320). This difference of canopy resistance between the warm and cool seasons was attributed to the air temperature (Figure 1(a)), since low temperature resulted in high canopy resistance [12].To further examine the variation ofrc during day time (07:00–17:00), we plotted the diurnal course of rc in Figure 5. Notice that no matter in warm or cool season, rc had its lowest value around 07:00 in the morning and then increased linearly to its highest value around 12:00 then remained constant till around 1500 and then dropped. This diurnal variation of rc could be explained by the following: in the early morning ET occurred under wet surface condition (fog water remained on the leaf surface), so rc was small (and this should close to PET, shown in Figure 6); then rc was increased due to a drier canopy surface, and around 15:00 the fog started forming and caused a wet canopy surface and resulted in a reduction of rc. It is noticed that this drop of rc would not happen for a forest (or other vegetation) with dry canopy surface in the late afternoon (e.g., [45, 46]).Figure 5
Diurnal variations of canopy resistance (s/m) for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006.
(a)
(b)
(c)
(d)Figure 6
Comparisons between potential evapotranspiration (PET), predicted LE by PM equation (LE_PM), and measured LE (LE_measured) for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006. The yellow box highlights the region where LE_measured is close to PET. The vertical bars indicate the standard deviations.
(a)
(b)
(c)
(d)Using equation (5), we presented the calculated PET and measured LE in Figure 6 for each season. Figure 6 shows that in the early morning (06:00–07:00) and late afternoon (17:00–18:00) the ET was close to PET for all the seasons. This again confirms that in the early morning and late afternoon, the canopy surface was wet and created a relatively high ET. Also, recalling from the P–M equation, there are two sources for LE, one is the energy term (LE_eq) and the other is the atmospheric demand term (LE_vpd). To quantify the relative magnitude of these two terms, Figure 7 shows the diurnal variation of these two terms as well as measured and predicted LE. It is obvious that the energy term was much bigger than the LE_vpd term. The LE_vpd term was very small at this humid montane forest.Figure 7
Diurnal variations of measured LE (LE_measured), LE predictions by PM equation (LE_PM), LE at equilibrium (LE_eq), and the LE contribution by vpd (LE_vpd) for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006. The vertical bars indicate the standard deviations.
(a)
(b)
(c)
(d)


## 4.3. The Role of Canopy Resistance

From Figures4 and 5 and Table 2, it is noticed that though rc varied with time, a constant rc could still provide good estimations of LE for the whole diurnal period. To explore the sensitivity of the P–M equation estimated LE to rc, we considered equation (11), which describes how much of the estimated LE is increased with a unit increase of rc. Equation (11) reveals that the ratio of ∂LE/∂rc is a function of rc and four meteorological parameters: U, Rn, Ta, and RH. To explicitly determine the variation of ∂LE/∂rc with respect to rc under different meteorological conditions, the following steps were taken. Firstly, a moderate meteorological condition was selected as the baseline, where Rn = 600 (W/m2), U = 2 (m/s), RH = 0.6, and Ta = 20 (°C). Secondly, we varied one of the four meteorological parameters (i.e., Rn, Ta, U, or RH) each time, and the other three parameters remained constant as the baseline values.Now, given the baseline condition:U = 2 m/s, RH = 0.6, and Ta = 20°C, we plotted the variations of ∂LE/∂rc with respect to rc for Rn from 50 to 800 (W/m2) in Figure 8(a). From Figure 8(a), we noticed that (1) when rc is large (say greater than 500 s/m), ∂LE/∂rc is small (<−0.2) irrelevant to the magnitude of Rn; (2) when rc = 200 (s/m), a unit increase of rc would cause only 0.2 to 0.8 unit decrease on LE estimation; (3) however, if rc = 100 (s/m), then ∂LE/∂rc could reach 1.4 when Rn is 600 (W·m−2); and (4) when Rn is smaller, ∂LE/∂rc is smaller for the same rc. Figure 8(b) is the same as Figure 8(a), but for different wind speeds (U ranged from 0.05 to 6 m/s with Rn = 600 W·m−2, RH = 0.6, and Ta = 20°C). Figure 8(b) has the similar pattern as in Figure 8(a) and shows that (1) if U is small (≤0.05 m/s), then the ratio of ∂LE/∂rc is around −0.08 and does not change with rc much; (2) for the cases where U is larger than 2 (m/s), the curves of ∂LE/∂rc are quite close; (3) when rc = 200 (s/m), a unit increase of rc would cause only 0.6 unit decrease on LE estimation.Figure 8
∂LE/∂rc as a function of rc (m/s) under different meteorological conditions (a) U = 2 (m/s), Ta = 20 (°C), RH = 60%; (b) Rn = 600 (W·m−2), Ta = 20 (°C), RH = 60%, (c) Rn = 600 (W·m−2), U = 2 (m/s), Ta = 20 (°C), and (d) Rn = 600 (W·m−2), U = 2 (m/s), RH = 60%.
(a)
(b)
(c)
(d)We also plotted∂LE/∂rc as a function of rc under different relative humidity conditions (RH varied from 30 to 90% with Rn = 600 W·m−2, U = 2 m/s, and Ta = 20°C) in Figure 8(c). Similar to Figure 8(c), ∂LE/∂rc with respect to rc for different temperature (Ta varied from 5 to 40°C given Rn = 600 W·m−2, U = 2 m/s, and RH = 0.6) are presented in Figure 8(d). Figures 8(c) and 8(d) also have similar patterns as Figure 8(a), and it can be seen that at rc = 200 (s/m), ∂LE/∂rc ranges from −0.77 to −0.53 in Figure 8(c) and ranges from −0.86 to −0.37 in Figure 8(d).In summary, under a general moderate meteorological condition whereRn = 600 (W/m2), U = 2 (m/s), RH = 0.6, and Ta = 20 (°C), if rc is larger than 200 (s/m), ∂LE/∂rc is less than 0.65; This implies that the predicted LE is not sensitive to the value of rc used, when the average rc is larger than 200. It is also important to note that Figures 8(a)–8(d) show that when rc is small (<100 s/m), a unit increase of rc could result in 1.34 units decrease on predicted LE. If this is the case of the site, then a variable rc is needed. This provides an explanation for Lecina et al.’s [19] results where they found that a fixed canopy resistance (70 s/m) could provide good daily reference evapotranspiration estimation, but for the estimation of hourly reference evapotranspiration, variable canopy resistance values were needed; since their average canopy resistance was small (only 70 m/s). The values of ∂LE/∂rc with respect to some certain rc under Rn = 600 (W/m2), RH = 0.6, U = 2 (m/s) at two different temperatures [Ta = 20 and 10 (°C)] are also listed in Table 3.Table 3
Values of∂LE/∂rc with different rc under Rn = 600 (W/m2), RH = 0.6, U = 2 (m/s) at two different temperatures [Ta = 20 and 10 (°C)].
r
c (s/m)
∂
LE
/
∂
r
c [Ta = 20 (°C)]
∂
LE
/
∂
r
c [Ta = 10 (°C)]
70
−1.78
−1.52
100
−1.34
−1.07
200
−0.65
−0.46
400
−0.25
−0.16From Figures8(a)–8(d), it is clear that under the conditions of low Rn, U, Ta, or vapor pressure deficit (i.e., high RH), the ratio of ∂LE/∂rc is smaller. In other words, under a low wind speed, low temperature, small radiation, or low vapor pressure deficit condition, different rc values will result in a relatively similar LE prediction. Hence, it does not matter much which rc value is adopted. Also, from Table 3, it can be seen that when rc is around 200 (s/m), a 100 units (s/m) increase of rc only causes a 46–65 unit (W·m−2) decrease on LE. These explained why a fixed constant rc worked well for estimating diurnal LE while, in fact, rc varied with time.We also applied the measured data to equation (11). Figure 9 plots ∂LE/∂rc as a function of time with measured Rn, Ta, U, and RH. In Figure 9, ∂LE/∂rc varied in consistence with Rn; hence, at this site, Rn was the major (primary regulator) parameter controlling ∂LE/∂rc. The ratio of ∂LE/∂rc was the lowest in the early morning and reached its maximum around 11:00, and then started to decrease in the afternoon. This diurnal trend is caused by the response of rc to the increase of radiation, temperature, and other micrometeorological variables with time. Notice that the maximum values of ∂LE/∂rc were only −0.5, −0.065, −0.5, and −0.2, respectively, for the warm and cool seasons of 2005 and 2006. This also indicated that a constant rc was good enough for the whole diurnal LE estimation.Figure 9
Diurnal variations of∂LE/∂rc and Rn for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006.
(a)
(b)
(c)
(d)


## 4.4. Energy Transfer Rate from Available Energy to LE

To explore the direct energy transfer rate (tc) from available energy, Qn, (here Qn ≡ Rn) to LE, we plotted the diurnal pattern of averaged decoupling factor and energy transfer rate (equation (2)) in Figure 10. At the beginning of the morning, the decoupling coefficient was large due to the small value of rc (Figure 5); and then following an increasing rc, the decoupling coefficient then decreased to its lowest value around 10:00, then remained constant till around 14:00, and then increased again. In Figure 10, the direct energy transfer coefficient and the decoupling coefficient varied with the same pattern.Figure 10
Diurnal variations of decoupling coefficient and energy transfer coefficient for the season of (a) warm 2005, (b) cool 2005, (c) warm 2006, and (d) cool 2006.
(a)
(b)
(c)
(d)Also, it is noticed that on the basis of the linear relation betweenRn and LE (shown in Figure 3) and equation (3), the slope of the regression between Rn and LE should be about the same as the averaged tc in equation (3). We calculated the averaged tc for the period of 10:00–14:00 when the canopy surface was dry. We found the averaged direct energy transfer rate for the warm and cool seasons of 2005 and 2006 were 0.35, 0.12, 0.32, and 0.20, respectively, and were about the same as the slope in that season shown in Figure 3 (these values were also listed in Table 1). Figure 10 and Table 1 demonstrated that the P–M equation was able to capture the energy transfer rate from Qn to LE.


## 5. Conclusions

This study analyzed the two-year eddy-covariance flux measurements of sensible and latent heat above a humid montane Cypress forest in Taiwan and focused on the characteristics and estimation of evapotranspiration using the Penman–Monteith equation and the role of canopy resistance. Our results demonstrated the following:(1)
The evapotranspiration phenomenon controlled the micrometeorology on this site. In cool seasons, evapotranspiration was small and resulted in a higher percentage of net radiation distributing into sensible heat.(2)
Evapotranspiration above this site was mainly driven by the radiation energy and approached to the equilibrium status. And this is different from Jarvis and McNaughton [42] where they showed that forest generally has a smaller decoupling coefficient and the evapotranspiration rate is thus dominated by the atmospheric demand term.(3)
A fixed constantrc is suitable for estimating the diurnal variation of ET for this site, but rc should be varied with season. This also implies that the P–M equation is a good method for ET gap-filling if the canopy resistance is known a priori.(4)
When the average canopy resistance is higher than 200 (s/m),∂LE/∂rc is less than 0.65 under a general meteorological condition: Rn = 600 (W/m2), U = 2 (m/s), Ta = 20 (°C), RH = 0.6; hence, a fixed canopy resistance is good enough for diurnal evapotranspiration estimation. However, when the average canopy resistance is less than 100 (s/m), ∂LE/∂rc is bigger than 1.34 and variable canopy resistance are needed. These two constraints (200 and 100) were obtained based on purely analytical analyses and a measurement height around two times of the canopy height.



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*Source: 4232138-2020-01-04.xml*