Hydrological Sciences Journal

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Water and energy balance of canopy interception
as evidence of splash droplet evaporation
hypothesis
Shigeki Murakami
To cite this article: Shigeki Murakami (2021): Water and energy balance of canopy interception
as evidence of splash droplet evaporation hypothesis, Hydrological Sciences Journal, DOI:
10.1080/02626667.2021.1924378
To link to this article: https://doi.org/10.1080/02626667.2021.1924378

Accepted author version posted online: 04
May 2021.

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Publisher: Taylor & Francis & IAHS
Journal: Hydrological Sciences Journal
DOI: 10.1080/02626667.2021.1924378

Water and energy balance of canopy interception as evidence of splash
droplet evaporation hypothesis
Shigeki Murakami
Kyushu Research Center, Forestry and Forest Products Research Institute, Kumamoto,Japan
Kyushu Research Center, Forestry and Forest Products Research Institute, 4-11-16
Kurokami, Chuo, Kumamoto, 860-0862, Japan
E-mail: smura@affrc.go.jp

1Water and energy balance of canopy interception as evidence of splash
droplet evaporation hypothesis
Canopy interception I can be divided into three processes: evaporation during
rainfall IR, during storm break time ISbt, and after cessation of rainfall. Thosevalues were measured using plastic Christmas tree stands, and it was found that IR
was much larger than ISbt. Though it is commonly accepted that wet canopy
evaporation is major process of I, if so, ISbt must be greater than IR because ofhigher potential evaporation during storm break time. It was also demonstrated
that measured IR was greater than calculated IR using the Penman–Monteith (PM)equation that assumes wet surface evaporation. Splash droplet evaporation(SDE), described as splash droplets generated by a raindrop hitting the canopy
evaporate, was alternative mechanism of I. SDE can elucidate ISbt << IR; forlarger rainfall amount, the number of splash droplets becomes higher. Calculated
IR was smaller than measured because the PM equation does not include SDE.
Keywords: Penman–Monteith equation; wet canopy evaporation; splash droplet
evaporation

1. Introduction
Forest is the land surface with the greatest evapotranspiration on earth, because of large
values of canopy interception I that amount to 11% to 48% of rainfall (Hörmann et al.
1996). I is dependent not only on rainfall amount but also on types of rainfall and tree
structures. Hall (2003) simulated the effect of rainfall intensity which affects raindrop
size on I using stochastic model. It was concluded that I is insensitive to the types ofrainfall, contrary to some studies that showed rise in I with rainfall intensity mentioned
later in this section. Hall (2003) also revealed that predicted I was not necessarily
greater for trees with larger leaf area index, because leaves with waxy needles havesmall storage capacity. In Hall's paper the evaporation component was calculated using
Rutter model (Rutter et al. 1971) which is a physically based method to estimate I
considering micrometeorological factors, e.g. air temperature, relative humidity, wind2

speed and radiation. Rutter et al. is based on the Penman–Monteith (PM) equation(Monteith 1965) that has been believed to be able to successfully reproduce measured
values. Gash (1979) also used the equation in a different mathematical approach fromthat of Rutter et al. to estimate I, confirming the reproducibility. Both models, i.e.
Rutter et al. and Gash, are based on the accuracy of the PM equation that calculates
evaporation rate from wet canopy surface.
However, there are many papers that claim that the PM equation or equivalentheat balance equation underestimated I in comparison with I measured by the water
budget method, and some of those works indicated that the underestimation is greaterthan one order of magnitude (Schellekens et al. 1999, van der Tol et al. 2003,
Murakami 2007, Wallace and McJannet 2008, Ghimire et al. 2012, Hashino et al. 2010,
Saito et al. 2013, Ghimire et al. 2017). The discrepancy between the PM equation basedmodels and the measured data often occurred at the time of heavy rainfall.
Though Gash model (Gash 1979) along with the revised one (Gash et al. 1995)
used the PM equation to calculate evaporation rate from the wet canopy surface, both
Gash models can calculate the evaporation rate without applying the equation. That is tosay, the evaporation rate is obtained analytically using gross precipitation PG,
throughfall and stemflow. Applying this method, many studies calculated evaporation
rate from the wet canopy surface. The maximum values were typically around 0.5 mm/h
to 1 mm/h (Schellekens et al. 1999, Carlyle-Moses and Price 1999, Park et al. 2000,
Price and Carlyle-Moses 2003, Deguchi et al. 2006, Wallace and McJannet 2008).
Evaporation of 1 mm/h requires latent heat of vaporization of 694 W/m2, which is 51%of the solar constant. Such a large amount of energy and evaporation is impossible toreproduce by the models using measured meteorological data.
Another aspect of contradiction on I is that I is proportional to rainfall amount,3

while the PM equation, i.e. calculation of wet surface evaporation, does not include any
parameter on rainfall amount. The fact implies the PM equation cannot predict I. In caseof the model in Hall (2003), rainfall intensity was included to calculate water storage on
canopy. A possible alternative mechanism of I is splash droplet evaporation (SDE,
Dunin et al. 1988, Murakami 2006, Dunkerley 2009). Micro droplets produced by araindrop impacting on canopy surface evaporate in a moment even under high relative
humidity RH due to a combined huge surface area. SDE cannot be calculated by the PM
equation, since SDE is not evaporation from the wet surface and not considered in theequation. SDE can explain the proportional relationship between the amount of I and PG
expressed in mm, because the larger the rainfall amount is the more the number ofdroplets generated becomes.
In recent years increasing number of researches showed the data that support thevalidity of SDE hypothesis (Zabret and Šraj 2019, Zhang et al. 2019, Jeong et al. 2019,
Liu and Zhao 2020, Jiménez-Rodríguez et al. 2021) and required detailed process of
SDE (Allen et al. 2017, Fan et al. 2019, Levia et al. 2019). Nonetheless, SDE has not
yet been proved directly and the details are unknown. Murakami and Toba (2013) usedwater balance approach with a measurement of single tree weight that enabled obtaining
I with high temporal resolution. They measured I in artificial Christmas tree stands thatmade it easy to measure the single tree weight and that enabled to separate I into threecomponents, during rainfall IR, during the storm break time ISbt, and after the cessationof rainfall IAft. They showed that the major part of I was IR, with ISbt almost zero and IAftcontributing a small percentage, which suggests SDE is the major process of I. As ageneral trend, potential evaporation during rainfall is smaller than during storm breaktime because of lower RH, higher solar radiation and air temperature at the time of4

storm break time. If wet surface evaporation would have been the main mechanism of I,
IR had been smaller than ISbt, but in actuality, the result was opposite.
In the present study, a full analysis of the data collected by Murakami and Toba
(2013) was made, which was a preliminary study, using the PM equation to confirm thevalidity of the equation and to evaluate the degree of contribution of SDE. Specifically,
the objective of this paper is 1) to analyse IR and ISbt with higher temporal resolution
than Murakami and Toba (2013) to evaluate the diurnal change and the response to
micrometeorology, namely, meteorological factors in the vicinity of the site, 2) toevaluate the amount of SDE, and 3) to discuss the validity and limitations of the PM
equation, the physics of small droplet evaporation and the heat source of latent heat ofvaporization from a SDE's point of view.

2. Material and methods
2.1 Site and trays with trees
The experiment was conducted at Tohkamachi Experimental Station of the Forestry andForest Products Research Institute, Tohkamachi, Japan, 37°07'53"N 138°46'00"E.
Artificial Christmas trees made of polyvinyl chloride (PVC) and iron lines were placedon three trays outside, exposed to natural weather conditions (Fig. 1). Canopy
diameters, the degree of canopy closure, and plant area index are shown in Table 1,along with tree height and stand density for each tray. Trees of original height 65 cm(small) and 150 cm (large) were used. Both Tray 1 and Tray 2 had the outer dimensionof a 180-cm square. They were made of plywood with a waterproof coating and set at
an average height of 120 cm above ground level. Forty-one small trees were set on bothtrays, but on Tray 2 the tree height was extended to 110 cm using plastic rods of 1.2-cm
5diameter. The catchment area of the two trays was reduced to a 122.4-cm square,
smaller than the outer dimension. Because rainwater near the edge of the tray might
escape and thus caused error (i.e., the “edge effect”), we avoided collecting rainwaterfrom the outermost row of trees. Tray 3 was a lysimeter consisting of wood plates and aplastic sheet placed on the ground, with the catchment area of a 360-cm square. The
same number of large trees as Trays 1 and 2 was used on Tray 3. Tree height on Tray 3
was extended to 240 cm by iron pipes of 2.8-cm outer diameter. Additional trees wereplaced along the outer edge of Tray 3 to avoid the edge effect. The arrangement of trees
on trays was schematically shown in Murakami and Toba (2013). Each tray drained
rainwater to a tipping bucket flow meter (see next section) and discharge from the tray
was defined as net precipitation PN that comprised both throughfall and stemflow. The
measurement began on June 24, 2012. Murakami and Toba (2013) began to measure on
May 24, 2012; however, we used data from June 24 because that was whenmeasurement of single tree weight began. On August 23, in the middle of the start andthe end of the experiment, the number of trees on Trays 2 and 3 was reduced to 25; i.e.,
those stands were thinned. However, Tray 1 remained unthinned because it was thecontrol. The experiment ended on October 26, 2012.

2.2 Instrumentation
PG was measured using three rain gauges. These were a storage-type gauge (home-madeof copper alloy, 22.7 cm in diameter) and two tipping-bucket gauges, one with 0.5 mm
per tip (B-071-02-00, Yokokawa Denshi Co., Ltd., Tokyo) and the other 0.1 mm per tip(CTKF-0.1, Climatec Inc., Tokyo). Though the 0.1-mm gauge could measure theamount of rainfall, it was used to determine the temporal distribution of rainfall, e.g.,
the start and end of a rain event, because this gauge tended to underestimate rainfall
6amount relative to the 0.5-mm gauge. Rainfall measured by the 0.1-mm gauge wascorrected using either the storage-type or the 0.5-mm gauge, and analysed at a 5-minuteinterval (Appendix A gives a detailed description of the method).
Three tipping-bucket type flow meters, two with 500-ml per tip (UIZ-TB500,
Uizin Co., Ltd., Tokyo, for Tray 1; J-271-01-00, Yokogawa Co., Ltd., Tokyo, for Tray2) and the other 2000-ml per tip (UIZ-TB2000, Uizin Co., Ltd., Tokyo, for Tray 3),
were used with a measurement interval of 5 minutes. The resolution of PN for Trays 1
and 2 was 0.333 mm, and that of Tray 3 was 0.154 mm. Weight of a single tree on
Trays 1 and 3 was measured every minute using an electric balance (UX4200S,
Shimadzu Corporation, Kyoto, Japan) and a digital push-pull gauge (RX-20, Aikoh
Engineering Co., Ltd., Osaka, Japan), respectively, to monitor the influence of gusts onwater storage. Actually, the data fluctuated due to wind and a 5-minute average wasused to calculate water balance. Tree weight on Tray 2 was assumed to be the same asthat on Tray 1. Measurement resolution of tree weight was some 0.01 mm waterequivalent on Trays 1 and 2, and around 0.1 mm on Tray 3, respectively, considering
the influence of wind. Net radiation Rn (Q*7, Radiation and Energy Balance Systems,
Seattle, Washington, USA), air temperature Ta with RH (Sato Keiryoki Mfg. Co., Ltd.,Tokyo, No. 7435-00 Hygro-station SK-5RAD-SP), and wind speed u (Ikeda Keiki Co.,
Ltd., Tokyo, WM-30P) were measured above Tray 2. Rn, Ta with RH, and u were
measured at 2.7 m, 2.5 m and 4.0 m above ground, respectively. The type of instrument
for Ta and RH was an aspirated psychrometer with a platinum resistance thermometerfor the dry and wet bulb sensors. The accuracy of Ta and RH was ±0.1 °C and ±1%,respectively. The interval of measurement for Rn, Ta, RH and u was 1 minute, but 5minute average data were used for analysis.

72.3 Separation of rainfall into rain and sub-rain events
Rainfall is intermittent, and a rain event was defined if rainfall stopped for a certain
period of time or more. The time duration to separate rainfall into each independent rain
event was defined as separation time Spt, which was set at 6 hours. In other words, if itstopped raining for 6 hours or longer rainfall was divided into two independent rain
events. During the rain event there may be a time when rainfall ceases temporarily,
which was defined as the storm break time(s) Sbt (s). The rain event was divided into
two or more sub-rain events with Sbt. In the present study Sbt was set at 20 minutes.
The time of the start and the end of i-th sub-rain event (i-th storm break) was defined astRsi and tRei (tBsi and tBei), respectively. Spt and Sbt satisfy the relationship 20 minutes ≤Sbt < 6 hours ≤ Spt. There appear many acronyms, abbreviations and symbols hereafter,
and they are listed in Table B1 in Appendix B.
A shorter Sbt is better in terms of temporal resolution. However, a too-short Sbt
causes large error, because it takes some time for rainwater in the tray to reach the flow
meter. Just after the end of a sub-rain event with high rainfall intensity, changes indrainage were too rapid and too large to measure correctly within such a short Sbt. A
20-minute Sbt was found to be optimal by trial and error.

2.4 Water balance on a rain event and a sub-rain event bases
On a rain-event basis, PG, PN and I have a simple relationship:
=

−

(1)

When a rain event consists of n sub-rain events, i.e. n-1 storm break time, with total
amount of PG, it is expressed as

8

=

=

=

+

+

+

+∆

(2)

where PGi is PG for the i-th sub-rain event, R is rainfall rate, D is drainage rate from thetray, E is evaporation rate. ΔS is the difference in water storage S between tRen and tRs1.
It was assumed that S became zero at the end of Spt (= tRen + 6 hours), which meant thatthe canopy dried out before the next rain event. Under the assumption ΔS is zero in Eq.
(2) S does not appear in Eq. (1).
I during a sub-rain event IR is given by

=

=

=

−

− ∆
(3)

where IRi is IR for the i-th sub-rain event and ΔSRi is the difference in S between tRei andtRsi. Considering that R = 0 during Sbt, Eq. (2) gives I during Sbt (ISbt).
=0

=1
(4)

=

=

=

−

− ∆
(5)

9

≥2

where ISbti is ISbt for the i-th Sbt, and ΔSBi (≤ 0) is the difference in S between tBei
and tBsi.
ΔS in Eq. (2) is partitioned into drainage and evaporation after the cessation of
rainfall. Hence, I after the cessation of rainfall is written as

=∆ −
(6)

On a rain event basis, I is calculated using PG and PN (Eq. (1)), but Eqs. (3)–(6)can also yield canopy interception, which is defined as I'.
=

+

+

(7)

Theoretically, Eqs. (1) and (7) yield the same result. However, they are notnecessarily the same, because Eq. (1) is the difference between PG and PN, whereas Eq.
(7) is calculated using PG, PN and S. S includes some errors that is independent of PG
and PN, which can make a difference between I and I'.
Murakami and Toba (2013) analysed rain events with PG ≥ 0.1 mm. In thepresent study, rain events with PG ≥ 0.5 mm were considered because PN = 0 for PG <0.5 mm. If data were missing at one tray or more, data for the period were not analysed,
though Murakami and Toba used such data.

2.5 Wet canopy evaporation model using the PM equation for IR and ISbt
Wet canopy evaporation model using the PM equation was applied that has the samestructure as that of Saito et al. (2013), except for water storage calculation. In thepresent study, S was directly measured. However, Saito et al. estimated S using water
10

storage capacity and rainfall intensity. I was calculated for each sub-rain event and Sbt.
IAft was not estimated using the model, but obtained using Eq. (6).

=

_

_

=
(8)

_

=0

=1
(9)

_

=

_

=

≥2
(10)

=

>

∙∆
(11)

=

/∆

≤

∙∆
(12)

The subscript “PM” represents calculation using the PM equation, and “i” does
the i-th sub-rain event or Sbt. The calculation was done at a 5-minute interval (Δt = 5min), corresponding to the measurement interval of PG and PN. EPM is the evaporation
rate for a wet canopy surface, estimated by the PM equation:=∆((∆ + )− )+( ( ) − ( ))(∆ + )(13)11

where Δ is slope of the saturated specific humidity versus temperature curve, Rn is net
radiation, G is ground heat flux (assumed to be zero), ρ is air density, CP is the specificheat of air, qS(Ta) and q(Ta) are saturated specific humidity and specific humidity at air
temperature Ta, respectively, λ is latent heat of vaporization, γ (= CP/λ) is thepsychrometric constant, and ra is aerodynamic resistance.

=

1

−

(14)

where k is the von Karman constant (0.4). z is the reference height (4.0 m above theground, where the anemometer was placed), d is zero plane distance, and z0 is roughness
height length. d and z0 were assumed to be 0.78 times and 0.08 times the tree height,
respectively (Hattori 1985).

2.6 Estimation of SDE
Canopy interception during rainfall IR comprises wet surface evaporation and SDE. IR isderived from water balance using Eq. (3), while wet surface evaporation during rainfall
is calculated using Eq. (8) as IR_PM. Therefore, SDE can be estimated as the difference
between IR and IR_PM. Namely, Eq. (15) calculates a component of canopy interception
caused by SDE, ISDE.
=

−

(15)

_

3. Results
3.1 PG and PN for each TrayAll PG and PN analysed are shown in Table 2 on a rain event basis. Monthly total
12

rainfall and average air temperature at the site were, respectively, 191.5 mm and 24.6°C
in July, 49.0 mm and 26.5°C in August, 215.5 mm and 23.0°C in September and 131.5mm and 14.8°C in October. As mentioned in the section 2.4 some rain events were notanalysed and not included in Table 2.

3.2 I, IR, ISbt and IAft on a rain event basis
All panels in Fig. 2 show a clear linear relationship between PG and IR, with large
determination coefficients r2 ≥ 0.795. IjR denotes IR for Tray j (j = 1, 2, and 3), with thesame convention for ISbt and IAft. Data shown in Fig. 2 are almost the same with those in
Murakami and Toba (2013). However, the period of data used (cf. the section 2.1) andthe size of the minimum rain event analysed (cf. the section 2.4) were slightly different.
ISbt in each tray was nearly zero and tended to have negative values, which werecaused by measurement error. This error was caused by the drainage term in Eq. (5) due
to time lag. The details are described in Appendix C.
For PG ≥ about 5 mm, IAft reached a plateau around 1 mm, 1 mm and 2 mm
before thinning for Trays 1, 2 and 3, respectively (Fig. 2a to c). After thinning, thesevalues were around 1, 0.5 and 1 mm (Fig. 2d to f), corresponding to the reduction in tree
density for Trays 2 and 3. However, Tray 1, the control, maintained the same value.
As shown in Table 3 the difference between I and I’ between trays was 7.5% orless that was within the measurement error. I/PG changed from 10.8% to 21.7%
throughout the experiment, which was comparable with that in actual forests, though theexperiments were conducted using plastic trees. IR was the major constituent of I, i.e.
IR/I ranged from 67.3% to 93.8%, while IAft was minor. Considering the error of theflow meters (Section 2.2), ISbt was reasonably measured and was close to zero.

13

3.3 Comparison of IR and IR_PM, ISbt and ISbt_PM on a rain event basis with ISDE
Observed values (IR and ISbt) and calculated ones (IR_PM and ISbt_PM) are shown in Fig. 3.
Before the thinning period, most IR_PM were nearly zero, though there were a few
exceptions, i.e. some values of IR_PM are around 2 mm (Fig. 3a–c). ISbt_PM fit to ISbt, i.e.,
close to zero, except for two rain events with PG of 5.0 mm and 110.2 mm (named as"Rain Event 1" in the next section) that had ISbt_PM between 8.1 mm and 11.3 mm. The
cause of the large ISbt_PM for those two rain events is unsuitable parameterization for theperiods with larger positive Rn than the others as discussed in the section 3.5. Each tray
had a similar trend of reproducibility for IR_PM and ISbt_PM, implying that not forest
parameters but meteorological conditions mainly determined the calculated results.
After the thinning period, estimated values of IR_PM were greatly improved, even thoughmany still underestimated IR (Table 3, Fig. 3d–f). The reason why the reproducibility of
IR_PM got better the after-thinning period is described in the section 4.2. Reproducibilityof ISbt_PM was much worse than that of the before-thinning period, with large scatter. In
the after-thinning period, each tray had the same trend of reproducibility. The cause ofpoorer estimation of ISbt_PM, i.e., overestimation, after thinning was also attributed tolarge Rn with inappropriate parameterization discussed in the section 3.5.
In the before-thinning period ISDE for each Tray was predominant process of I as
ISDE /I ranged from 52.0 to 58.3% (Table 3). In the after-thinning period ISDE /I showedsmaller values 26.0% in Trays 1 and 15.9% in Tray 3 (the cause is discussed in thesections 4.2 and 4.6). ISDE was major process only in Tray 2 with I/ISDE of 60.9% in theafter-thinning period.

14

3.4 PG, IR, IR_PM and ISDE for four heavy rain events
As a general trend, the longer the rainfall duration is the more the number of sub-rain
events becomes. Kondo et al. (1992) and Návar (2020) found that the rainfall duration
tends to become longer with increasing rainfall amount, though the correlation between
the two variables were not very high. As a consequence, the number of sub-rain events
is expected to increase with the rainfall amount. A rain event with many sub-rain events
tends to include larger variation in meteorological conditions than with less sub-rain
events. Analysing such a rain event is an effective approach to investigate the responseof canopy interception on meteorological factors. The two heaviest rain events wereselected in the before-thinning and after-thinning periods, respectively (Table 2), andconducted a detailed analysis of PG, IR, IR_PM and ISDE. The before-thinning period hadrain events with PG of 110.2 mm (Rain Event 1 with 22 sub-rain events) and 31.0 mm(Rain Event 2 with 6 sub-rain events) as shown in Table 4. The two rain events
accounted for 69.1% of total rainfall in the before-thinning period (Table 3). In theafter-thinning period, we selected one with PG of 36.4 mm (Rain Event 3 with 14 subrain events) and another with 84.9 mm (Rain Event 4 with 8 sub-rain events). The tworain events occupied 41.6% of total rainfall in the after-thinning period (Table 3). In
Table 4 values of I/I' are 90.9% to 108.1%, which were within the range ofmeasurement error, except for an outlier of 81.0% in Tray 3 for Rain Event 1 that might
be concerned with the clogging up of the drain. Some of values of IR/I and ISDE/I wereover 100% due to measurement errors. IR was major component of I. ISDE was also
predominant process of I, though in Tray 3 ISDE/I for Rain Events 3 and 4 were 13.3%
and 33.5%, respectively, which were much smaller than the others (Table 4). It isestimated that wet surface evaporation was the major evaporation process in Tray 3 forRain Events 3 and 4. During Rain Event 2 the values of ISDE/I were larger than IR/I in all

15

trays, while for all the other events that was not the case. ISDE was calculated as theresidual between IR and IR_PM as shown in Eq. (15). In all trays IR_PM for Rain Event 2
were -0.2 (< 0) that meant water vapour condensed on trees in calculation. Negativevalues of IR_PM seemingly boosted ISDE whether actual SDE increased or not, which was
the cause of ISDE/I > IR/I during Rain Event 2.
Fig. 4a–d, corresponding to Rain Events 1–4, respectively, indicate therelationship between PGi and IjRi where IjRi is IR for Tray j (i = 1, 2 and 3) for the i-th
sub-rain event. Solid and open symbols represent IjRi with Rn ≥ 0 and Rn < 0,respectively. Regression lines shown in Fig. 4a–d were calculated irrespective of thesign of Rn. Eleven regression lines were calculated, all of which showed r2 ≥ 0.5 (range
0.574–0.999). In Tray 3 before thinning, the regression line for Rain Event 1 (Fig. 4a)
was unavailable because of missing data. The largest I3Ri in Fig. 4b for Tray 3 was 2.2mm, but the value in Murakami and Toba (2013) was mistakenly presented as 4.1 mm.
The inclination of the regression line for a certain tray was not necessarily constant ineach period, i.e. the before-thinning or the after-thinning period. At the same timechange in the inclination between rain events was different depending on the tray. For
instance in Tray 2 the inclination between Rain Events 3 and 4 are almost the same (redbroken lines in Fig. 4c and d), while in Tray 3 it drastically declines (black long dasheddotted lines in Fig. 4c and d). Fig. 4e–h, respectively, corresponding to Rain Events 1–
4, show the relationship between IjR_PMi and IjRi for each tray. Regression lines were
calculated for IjRi with Rn ≥ 0, and are shown if r2 ≥ 0.5. Four out of nine regression
lines indicated r2 ≥ 0.5. All regression lines that were calculated combining IjRi withboth Rn ≥ 0 and Rn < 0 resulted in r2 < 0.5. Regression lines derived from IjRi with Rn < 0gave r2 < 0.5. The results in Fig. 4 imply that IjR_PMi can estimate IjRi only when Rn ≥ 0;
however, the estimation using PGi on a sub-rain event basis (Fig. 4a–d) is much better

16than that of IjR_PMi (Fig. 4e–h). All IjR_PMi with Rn < 0 were negative, but only a small
number of data for IjRi with Rn < 0 were negative.

3.5 PG, ISbt and ISbt_PM for four heavy rain events
Fig. 5a–d, respectively, corresponding to Rain Events 1–4, show measured andcalculated I during Sbt on a storm break time basis in Tray j, i.e., IjSbti and IjSbt_PMi,
respectively. Though measured ISbt on a rain event basis tended to show negative values,
e.g. typically -1mm, due to measurement errors (Fig. 2), those of ISbt on a storm breaktime basis were much smaller because they were divided into each storm break time.
Specifically, IjSbti with Rn < 0 ranged from −0.402 to 0.343 mm that was comparablewith the measurement resolution of PN in Trays 1 and 2 (0.333mm). All IjSbt_PMi with Rn< 0 had negative values, with a minimum of −0.219 mm. Data of IjSbti with Rn ≥ 0 were
within −0.735 to 0.428 mm. Nevertheless, IjSbt_PMi with Rn ≥ 0 seriously overestimated
IjSbti, except for Rain Event 2 (Fig. 5b) that had only one IjSbti with Rn ≥ 0. Thisoverestimation was attributed to inappropriate parameterization.
As stated in the section 3.2 and Table 3, ISbt was nearly zero on a rain event basis
both in before and after thinning periods. Unsuitable parameterization for the periods
with Rn ≥ 0 was the cause of overestimation originated from capillary water in trees.
The details are described in Appendix D.

3.6 Time course of IR, IR_PM, ISbt and ISbt_PM
A couple of time series for measured and/or calculated components, PG, S, ∑
∑

_

,∑

,∑

_

,

(hereafter the last four are denoted as ΣIjRi,

ΣIjR_PMi, ΣIjSbti and ΣIjSbt_PMi for simplicity) potential evaporation EPM calculated by the17PM equation, and micrometeorological data Rn, RH, Ta and u are shown in Figs. 6 and7, which correspond to Rain Events 1 and 4, respectively. "Nighttime" in Figures
represents from sunset to sunrise. The time course of ΣIjRi and ΣIjSbti are shown stepwise
because they were calculated on a sub-rain event basis and on a Sbt basis, respectively,
based on water balance. That means it took some time for rainwater on the tray and in
the tube to reach the flowmeter, and 5 minutes was too short in many cases. Note that
IjRi and IjSbti are the difference between ΣIjRi and ΣIjRi-1, and ΣIjSbti and ΣIjSbti-1 for i ≥ 2,
respectively, and ΣIjR1 = IjR1 and ΣIjSbt1 = IjSbt1 for i =1. Other data including ΣIjR_PMi andΣIjSbt_PMi are plotted every 5 minutes.
Rain Event 1 (Fig. 6) began at 13:45 on July 6, 2012 Japan Standard Time.
Water storage in Trays 1 and 3 (S1 and S3, respectively) increased or decreased with
rainfall. As mentioned in the section 2.2, S2 in Tray 2 was assumed the same as in Tray
1. For Tray 3, ΣI3Ri, ΣI3R_PMi, ΣI3Sbti and ΣI3Sbt_PMi are shown through 17:15 on July 6,
because the drain of the tray clogged (the caption in Fig. 2). In Trays 1 and 2, ΣIjRi
increased with PG throughout Rain Event 1, except for three sub-rain events (total
decreases were 0.24 and 0.21 mm for Trays 1 and 2, respectively, but difficult to readfrom Fig. 6c because of small changes), which was caused by measurement errors. At
the end of Rain Event 1, ΣI1Ri and ΣI2Ri, i.e. I1R and I2R, respectively, were 8.8 and 9.2mm, but ΣI1R_PMi and ΣI2R_PMi, i.e. I1R_PM and I2R_PM, respectively, were only 1.6 and 2.2
mm (Fig. 6c–d, Table 4). The underestimation of ΣIjR_PMi was attributed to negative
EPM, reflecting Rn < 0 during nighttime (Fig. 6g). During nighttime on July 7 throughon July 8 ΣIjR_PMi decreased (again difficult to read in Fig. 6d) that meant condensation
not evaporation occurred. Condensation was also occurred during nighttime on
September 30 through on October 1 (Fig. 7d).

18

The greatest discrepancy between IR and IR_PM during nighttime is shown in Fig.
4h and Fig. 7 (for i=2, 17:55 on September 30 through 0:00 on October 1). For the subrain event with PG2 = 59.6 mm, I1R2, I2R2 and I3R2 were 4.2, 11.6 and 1.7 mm (opensquare on the middle left, circle on the upper left and triangle on the lower left in Fig.
4h that correspond to Fig. 7c for i=2), respectively, while changes in I1R_PM, I2R_PM and
I3R_PM between i=2 and i=1 were −0.1, −0.2 and −0.2 mm (in Fig. 7d).The PM equation
did not function at all as a predictive method.
Obviously, IjRi was controlled by PGi instead of IjR_PMi that is EPM, as seen in Fig.
4 a–d. Meteorological factors RH, Ta and u (except for Rn during daytime) do notnecessarily correlate with EPM but with Rn (Figs. 6 and 7). IjR_PMi was valid only whenRn ≥ 0, but Rn was independent of PGi. PGi controlled IjRi and ΣIjRi, regardless of the signof Rn.
ΣIjSbti in Figs. 6e and 7e are nearly equal to zero corresponding to those in Fig.
5a and 5d, respectively. However, in Figs. 6f and 7f ΣIjSbt_PMi rise on daytime when EPM
shows high value due to large Rn that caused overestimation in combine with capillarywater in the trees as mentioned in the previous section.

4. Discussion
4.1 Increase in I after thinning
There are some studies that showed I declined after thinning (Teklehaimanot et al.
1991, Sun et al. 2015, Shinohara et al. 2015) or diminished with decreasing standdensity (Komatsu et al. 2008), but no study demonstrated rise in I after thinning.
Unexpectedly, I in Tray 2 increased after thinning (Table 3, Fig. 2b and e, Fig. 3b ande). The increase in I was observed on a rain event basis and was proportional to the19rainfall amount for each rain event. That held true on a sub-rain event basis as shown in
Fig. 4a−d. The largest rain event after thinning was Rain Event 4 and the time course isshown in Fig. 7. The water storage on Tray 2 (red circles in Fig. 7b) was the smallest
among the three trays. That meant Tray 2 was the least evaporative with the smallest
wet surface area. The values of ra for Tray 2 before and after thinning were assumed
identical, because the two stands had the same tree heights (Eq. (14)). Considering thesmallest water storage and the values of ra for Tray 2 IR_PM and ISbt_PM after thinningmust decrease in terms of wet canopy evaporation. After all, there is no prospect that theincrease in I can be elucidated by the PM equation, i.e., wet surface evaporation. It is
presumed that thinning in Tray 2 promoted production of splash droplets and/or
ventilation, though it still has to be supported by additional measurements, analysis andstudies.

4.2 Validity and limitations of the PM equation
During nighttime, almost all IjR_PMi for Rain Events 1–4 was negative, reflecting Rn < 0,meaning that water vapour condensed on the canopy surface instead of evaporation(Fig. 4e–h). In contrast, the measurement showed that IjRi with Rn < 0 had positive
values (Fig. 4e−h, Figs. 6 and 7) except for some sub-rain events in Fig. 6, which wascaused by measurement error (the section 3.6). The discrepancy between IjR_PMi and IjRi
was very large, and it was obvious that the PM equation did not work at night when Rn< 0 (the section 3.6). The aerodynamic term (second term on the right side of Eq. (13))
was small during the sub-rain event because of high RH, especially when the wind was
weak. In that case, the radiation term (first term on the right side of Eq. (13)) controlled
EPM. At night, Rn was negative and as a consequence, EPM during the sub-rain event20became negative during nighttime (Figs. 6 and 7). In daytime, the aerodynamic term
remained small during the sub-rain event, but more often than not, Rn became positive,
resulting in EPM ≥ 0. The observation indicated that IjSbti was nearly zero and that IjRi
accounted for the major part of I, irrespective of the sign of Rn, i.e. regardless ofdaytime or nighttime (Tables 3 and 4, Figs. 6 and 7). IjR_PMi with Rn ≥ 0 could reproduce
IjRi (Figs. 4e–h), but estimation using PG was better than the model (Figs. 4a–d). The
reproducibility of IR_PM got better the after-thinning period (the section 3.3 and Fig. 3),
because there were more rain events with Rn ≥ 0 during rainfall after thinning than
before thinning.
Tsukamoto et al. (1988) conducted a water balance experiment using a single
Japanese cedar tree placed in the stand. They measured PG, PN and tree weight undernatural rainfall on an hourly basis, showing that IR was proportional to PG for a sub-rain
event with ISbt nearly zero. They also indicated that ISbt and/or IAft were close to zero if
solar radiation was nil, but the values increased with increasing radiation. Although weused artificial Christmas trees, the results were the same as those of Tsukamoto et al.
(1988). Ours and the study of Tsukamoto et al. are consistent with the observational factthat IR is independent of the radiative energy received by the canopy. Similarly, Pearce
et al. (1980) found that hourly evaporation rates during daytime and nighttime were thesame. Thus, we conclude that the PM-based model contradicts the measurements,
though it can work when Rn > 0.
ISDE is calculated using Eq. (15) as the difference between IR and IR_PM, whichmeans ISDE declines with increasing positive Rn as IR_PM is boosted by Rn. However, if
SDE actually reduces with Rn or not remains a problem to be solved because in thepresent study ISDE was not measured directly but the residual between measured IR andcalculated IR_PM.

21

4.3 Do splash droplets drift or evaporate?
Some studies assert that small droplets are transported somewhere by turbulence insteadof being eliminated by evaporation (Hashino et al. 2010, Saito et al. 2013). The
foundation of such studies was that terminal velocities of droplets with diameters 10, 20
and 50 µm are, respectively, 0.3, 1.2 and 7.6 cm/s. This means that the droplets areeasily transported by weak wind and do not fall on the ground, because they areaerosols. Nonetheless, airborne droplets are captured by canopy again and observed asfog precipitation. This results in a contradiction, because the precipitation increases PN
and reduces I. For example, in tropical montane cloud forests fog precipitation accounts
for between 2% and 45% of incident annual rainfall (Bruijnzeel et al. 2011). In Japan itis reported that cloud water deposition was more than 100% of annual rainfall(Kobayashi et al. 2001; Igawa et al. 2002). Apart from the transport of small droplets,
first and foremost, it is impossible for such droplets to survive in the air without
evaporation, even under high RH. They can survive stably only when the air is insaturation or supersaturation with respect to liquid water. Though EPM is a function ofsome meteorological variables, evaporation of a small droplet is a function of Ta and
RH in addition to the initial diameter (Holterman 2003). That means SDE must be
calculated independent of the PM equation. The big difference between wet surface
evaporation and SDE is that the surface evaporation rate saturates if the surface iscompletely wet but the SDE rate increases with increasing the number of droplets anddecreasing the diameter of the droplets. It implies a slight change in the splash droplet
size distribution, which is dictated by the raindrop size distribution and tree structures,can make a significant difference in the amount of SDE.
Life time of a small droplet under RH of 95% and 99% is shown in Fig. 8. It isstrongly dependent on RH and the initial diameter. Fig. 8 was calculated based on

22Holterman (2003) that was developed to evaluate spray drift on agricultural chemicals.
Another approach to calculate evaporation of a small droplet is the theory of cloudphysics. Murakami (2006) estimated life time of a small droplet using the cloudphysical approach (Beard and Pruppacher 1971) that included much more complicatedmathematical processes. For the droplet of 50 μm in diameter with RH of 95% theestimated life times in Fig. 8 and Murakami (2006) were, respectively, 58 s and 73 s at
10°C, 48 s and 61 s at 15°C, and 13 s and 47 s at 25°C. Unfortunately, the discrepancy
between the two methods was 362% at 25°C. Assuming RH of 96% instead of 95%, life
times in Fig. 8 got longer and almost the same with those of Murakami (2006): 72 s at
10°C, 60 s at 15°C and 45 s at 25°C. Considering the measurement accuracy of RH, i.e.
±1% at best, both estimations are within the measurement error range.
As shown in Fig. 8 and Murakami (2006) splash droplets do not drift andsurvive in the air but evaporate and disappear during rainfall. If the splash droplet size
distribution along with the production rate are measured, it is possible to calculate SDE.
Splash droplet size distribution may be measured using an aerosol spectrometer. It ischallenging but required for the development of forest hydrology.

4.4 Heat source of latent heat of vaporization
Stewart (1977) showed that in a pine forest when the canopy was wet, flux of the latent
heat of vaporization exceeded net radiation, and they presumed that sensible heatoriginated upwind and was advected to the forest. Pearce et al. (1980) also concluded
that not net radiation but advected energy drives evaporation of a wet canopy. However,it seems unlikely that the latent heat continues to advect during a long-lasting rainfall
event, and if the advection had been the energy source, the PM equation that takes in23

situ meteorological factors into consideration could have successfully predicted I. There
must be alternative mechanism and source.
Latent heat of vaporization for I2R2 in Fig. 7 (for i=2, 17:55 September 30 to
0:00 October 1) was 1294 W/m2, as large as the solar constant (1370 W/m2). JiménezRodríguez et al. (2021) pointed out that during rainfall the temperature difference
between the forest floor and the air in forest makes atmosphere unstable that causes
vertical mixing. This mechanism transports water vapour upward. However, it isdifficult for soil to exchange heat with the atmosphere due to nearly zero wind speed at
the ground surface. Clouds where condensation occurs constantly is the only possible
heat source. There are four possible mechanisms for transport of energy from the baseof the cloud to the canopy, and at the same time it works as removal mechanism ofwater vapour above the canopy. First, the original air mass at the ground surface issqueezed upward by falling raindrops and the ambient air dragged downward by those
drops (Dunin et al., 1988). Second, an updraft driven by the difference of molar weight
between water and dry air transports the vapour together with energy, called“evaporative force” (Makarieva and Gorshkov, 2007). Decrease in air volume caused by
the removal of water vapour near the ground is essentially compensated by thedowndraft. Third, an updraft is caused by a reduction of air volume in cloud due towater vapour condensation (Makarieva et al., 2013). Like the second processes, thedowndraft occurs automatically to compensate for the updraft. Fourth, evaporation ofwater itself boosts air pressure around the canopy and makes updraft because it is anabrupt expansion: phase change from liquid to gas. That is the opposite process of thethird one and is proposed in the present study for the first time. The four processes have
not received much attention and have not been widely accepted. None of them has been
proved by measurements and they are still hypotheses, however, those processes can24elucidate the enigmatic problems: the removal mechanism of water vapour from thecanopy during rainfall, the heat source (i.e., latent heat released in the cloud uponcondensation of water vapour), and the supply of sensible heat from the cloud(Murakami 2006). Vertical mixing of air between the ground surface and the cloud baseprovides a simple answer for the heat source enigma. Because water vapour and energy
are always balanced by rapid vertical mixing, variation in Ta and RH caused by theexchange between the cloud and the ground surface are seemingly not observed.

4.5. Rainfall intensity, types of rainfall and traits of vegetation
As mentioned in Introduction, simulation using the PM equation revealed that I wasinsensitive to rainfall intensity (Hall 2003). However, many studies including thispresent one showed that I increases with increasing rainfall amount or intensity, because
actual evaporation process includes both wet surface evaporation and SDE, while Hall
(2003) considered only wet surface evaporation.
Change in the inclination of the regression lines between rain events wasdifferent depending on the tray (Fig. 4a−d, the section 3.4). That would be caused by
the difference in rainfall intensity. In the after-thinning period ISDE/I was 26.0% in Tray
1 and 15.9% in Tray 3 (Table 3), but in the same period on a rain event basis it was
56.4% (Rain Event 3) and 69.5% (Rain event 4) in Tray 1 and 33.5% (Ran Event 4) inTray 3 (Table 4). The difference in ISDE/I on the period basis in Table 3 and on the rain
event basis in Table 4 was more than double that would also be caused by the change inrainfall intensity. Larger ISDE/I would be the result of higher rainfall intensity that can
produce more splash droplets. Actually, ISDE/I in Rian Event 4 (rainfall intensity derived
from Table 2 was 3.7 mm/hour) was greater than that in Rain Event 3 (2.0 mm/hour) in
all trays (Table 4).
25

The influence of rainfall intensity on rainwater partitioning including I isdependent on vegetation types. Janeau et al. (2015) showed that throughfall changes not
only with rainfall intensity but also with vegetation types. In low rainfall intensity
vegetation with flexible leaves had high interception ability and yielded much stemflow,
but in high rainfall intensity it showed less interception ability due to flexibility ofleaves falling rain water down. Contrary, vegetation with rigid leaves had highinterception ability in both low and high rainfall intensities because of resistance against
raindrop impact. In some vegetation shape of leaf is more important than leaf amount.
Liu and Zhao (2020) pointed out that Artemisia sacrorum Ledeb (less leaf amount,canopy cover and leaf area but a fragmented leaf) showed less throughfall incomparison with Spiraea pubescens Turcz (larger leaf amount, canopy cover and leaf
area but a compact leaf) probably due to effective splash droplets production.
Considering above-mentioned facts, the amount of I is dependent on bothcharacteristics of trees and types of rainfall, e.g. drizzle, widespread rain andthunderstorm, because types of rainfall is relevant to raindrop size distribution (Seela etal. 2018). However, there are few studies focusing on the relationship between traits oftrees, types of rainfall and I. To deal with the issue SDE is a key process that should betaken into account as SDE is dictated by those factors.

5. Conclusions
When net radiation Rn was positive, the PM equation could predict measured canopy
interception during rainfall IR, though the accuracy was not high enough. However, theequation could not do so during nighttime and when Rn was zero or negative. In manycases IR was much larger than the predicted canopy interception using the PM equation
IR_PM, which proved wet canopy evaporation is the minor process and SDE dictates
canopy interception. Specifically, the ratio of SDE to total canopy interception, ISDE/I,
26

accounted for 52.0% to 58.3% and 15.9% to 60.9% in the before-thinning and the afterthinning periods, respectively, and on a rain event basis for nine out of eleven rain
events ISDE/I was over 56.4%.
The best predictor of IR (and I also) was gross rainfall PG. IR and PG had a
proportional relationship that implied that rainfall itself is the driver of IR. SDE could
elucidate the proportional relationship between IR and PG, which is another evidence of
SDE hypothesis. Calculation indicated that splash droplets do not drift and survive
during rainfall but evaporate and disappear in a short time even under high relative
humidity, e.g. 99%.
Considering the latent heat of vaporization required, clouds are the only possible
heat source. Vertical mixing of air between the ground surface and the cloud basecaused by the difference in molar weight of gases, falling raindrops, condensation in theclouds and evaporation of canopy interception can be the driving force. However, there
is little theoretical and observational knowledge of the transport mechanism during
rainfall, so this knowledge should be pursued.
I depends not only on PG or rainfall intensity but also on rainfall types and tree
characteristics, though the relationship between I and types of rainfall and/or tree
properties is little known. Those unknown part of canopy interception processes arestrongly associated with SDE.

Acknowledgements
I am grateful to two anonymous reviewers for useful and instructive comments. This study was
financially supported by JSPS KAKENHI Grant Number 23580216.

Disclosure statement
The author has no conflicts of interest relevant to this article.

27

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Appendix A
Modification of rainfall amount measured by the 0.1-mm rain gauge
The 0.1-mm rain gauge underestimated rainfall amount in comparison with that of thestorage-type and the 0.5-mm gauge, but the degree of underestimation varied dependingon the rain event. For example, for one rain event that started on July 6 the rainfall
amount measured by the storage-type, the 0.5-mm and the 0.1-mm gauge was 110.2mm, 110.5 mm and 104.3 mm (94.6% of the storage-type gauge), respectively, while
for another rain event on September 6 the amount of rainfall measured by the storagetype, the 0.5-mm and the 0.1-mm gauge was 27.0 mm, 27.0 mm and 24.4 mm (90.4%of the storage-type gauge), respectively (cf. Table 2). Thus, either the storage-type or
the 0.5-mm gauge was used to measure the rainfall amount. Rainfall of the storage
gauge was measured manually at least every few days on weekdays but omitted on a
day off. Rainfall amount measured by the 0.1-mm gauge was modified based on that of
the storage-type gauge on a rain event basis, but was corrected based on data measured
by the 0.5-mm gauge when storage gauge data were missing. PG was analysed at a 5minute interval.

33

Appendix C
Cause of negative values of ISbt in Fig. 2
Ideally, rainwater stored on the stand S at the end of a sub-rain event would have been
the only drainage source during the subsequent Sbt. However, in actuality, at the end of
the sub-rain event, rainwater that would have drained during that sub-rain event fromthe trees prior to the Sbt of interest remained on the tray and in the tube leading to theflow meters. The remaining rainwater was supplied as runoff D in Eq. (5), resulting in
negative ISbt. The storage term in Eq. (5), ∆SBi, is always negative or zero, i.e., −∆SBi ≥0. Normally, the error caused by ∆SBi is smaller than that of the drainage term, because
S measured by weighing devices has no delay time like drainage from trays, as well as a
resolution higher than that of the drainage measurement (the section 2.2.).

34

Appendix D
Cause of overestimation of ISbt_PM
According to Eqs. 8–12, evaporation rate ECal = EPM for S > E_PM·∆t; otherwise, Ecal =S/∆t. Assuming that EPM is sufficiently large for a wet canopy surface to dry out during
Sbt and S = 0 is reached, ECal = S/∆t= 0 at the end of Sbt. However, the trees did notalways dry out (S ≠ 0), even when EPM maintained a large value over a long period. Thiswas because under certain conditions, rainwater was not on the surface of the canopy
but existed as capillary water. The trees were made of PVC imitation leaves that wereinserted in twisted iron lines. Rainwater was stored in the spaces of the twisted ironlines and PVC leaves as capillary water, which was difficult to evaporate. In otherwords, the actual ra was much larger than that calculated by Eq. (14). Because theobjective of the present study was not to reproduce ISbt but to evaluate the amount of
SDE and the validity and limitations of the PM equation, optimization of ra for IjSbt_PMiwith Rn ≥ 0 was not carried out.

35

Table 1 Stand structure of each tray before and after thinning.
Tray number

1

2

3

Tree height

(cm)

65

110

240

Tree height from the ground

(cm)

185

230

240

Canopy diameter

(cm)

30

30

75

Number of trees(trees/tray)

41

41

41

2

Jun. 24 to Aug. 23, 2012
Before thinning

Plant area index*(m /m )

5.1

5.1

5.9

Canopy closure

(%)

96

96

94

Water storage capacity Smax**

(mm)

2.0

2.0

3.8

Number of trees(trees/tray)

41

25

25

Plant area index*(m2/m2)

5.1

1.8

2.9

Canopy closure

(%)

96

58

79

Water storage capacity Smax**

(mm)

2.0

1.2

2.3

2

Aug. 24 to Oct. 26, 2012
After thinning* Measured by LAI-2000 (LI-COR, NE, USA)** Measured by weighing a tree one minute after pouring water over the tree

36

Table 2 Gross rainfall PG and net rainfall PN for each tray on a rain event basis.
Start of rain event

Duration

PG

PN

PN

PN

Tray 1

Tray 2

Tray 3(hours)

(mm)

(mm)

(mm)

(mm)

2012/7/1

16:00

10.3

4.5

3.3

3.0

2.6

2012/7/2

8:35

0.2

0.5

0.3

0.0

0.2

2012/7/6

13:45

52.2

110.2

101.3

101.6

98.5

2012/7/12

0:15

16.7

5.0

3.0

2.0

2.3

2012/7/13

2:45

0.3

0.5

0.3

0.3

0.0

2012/7/14

0:30

8.6

13.0

12.3

12.0

11.4

2012/7/15

5:05

3.9

0.5

0.0

0.0

0.0

2012/7/20

22:10

10.7

24.0

22.7

21.3

20.8

2012/7/21

20:25

0.6

0.5

0.0

0.0

0.0

2012/7/22

15:45

0.3

0.5

0.0

0.0

0.0

2012/8/5

23:50

0.9

0.5

0.0

0.0

0.0

2012/8/12

3:00

1.1

8.5

7.7
0.3

6.9
2.0

2012/8/13

13:25

0.3

3.5

8.0
2.3

2012/8/13

20:20

11.3

31.0

28.3

27.3

26.1

2012/8/15

19:10

7.0

0.5

0.0

0.0

0.0

2012/8/17

22:00

1.3

1.0

0.3

0.3

0.0

204.2

182.3

175.9

170.9

Total for before-thinning period

Rain Event
numberRain Event 1

Rain Event 2

Thinned on August 23
2012/8/24

17:35

2.0

0.5

0.0

0.3

0.2

2012/8/27

17:10

0.9

3.0

2.0

1.0

1.5

2012/8/30

7:30

0.8

0.6

0.3

0.3

0.3

2012/8/30

20:00

5.3

0.5

0.0

0.3

0.3

2012/9/1

16:25

1.8

5.5

4.3

3.7

3.9

2012/9/4

12:05

2.7

6.8

5.7

5.3

5.6

2012/9/6

8:20

3.5

27.0

24.7

22.0

23.7

2012/9/11

9:35

13.8

18.2

16.3

14.3

15.3

2012/9/12

16:40

0.7

5.3

4.7

4.3

4.8

2012/9/15

22:50

3.3

1.5

1.0

1.0

0.6

2012/9/23

4:05

13.7

14.8

13.0

12.3

13.0

2012/9/24

1:10

18.2

36.4

32.0

30.0

31.9

2012/9/25

9:05

0.1

0.5

0.0

0.0

0.0

2012/9/30

17:10

23.1

84.9

77.3

67.6

79.0

2012/10/2

0:55

5.7

2.0

1.7

1.7

1.7

2012/10/2

22:50

3.3

1.4

0.7

1.0

0.8

2012/10/5

2:55

0.4

2.0

1.7

1.7

1.4

2012/10/6

20:15

6.8

4.5

3.7

3.3

3.4

2012/10/11

17:35

10.4

10.8

9.3

8.7

9.1

2012/10/13

6:00

2.2

1.5

1.0

1.3

0.9

2012/10/15

11:05

0.8

2.0

1.3

1.3

1.4

2012/10/17

15:00

26.9

33.0

29.3

26.7

29.0

2012/10/23

7:30

26.3

28.0

24.3

19.7

24.1

2012/10/25

21:45

6.8

Total for after-thinning period

0.7

0.3

0.3

0.2

291.5

254.6

228.2

251.8

37

Rain Event 3
Rain Event 4

Table 3 Amount of rainfall and canopy interception before and after thinning for each tray.

PG

Numberof raineventsTraynumberI

I'

I / I'

I/PG

IR

IR_PM

ISDE

ISbt

ISbt_PM

IAft

IR/ I

ISDE / I

(mm)

(mm)

(%)

(%)

(mm)

(mm)

(mm)

(mm)

(mm)

(mm)

(%)

(%)

1

22.0

23.5

93.6

10.8

14.8

3.4

11.4

-0.8

17.0

9.5

67.3

52.0

2

28.3

29.8

95.0

13.9

21.2

4.7

16.5

-1.5

21.7

10.1

74.9

58.3

3*

33.4

36.1

92.5

16.3

24.3

4.9

19.4

-2.1

22.6

13.9

72.8

58.0

1

37.0

36.3

101.9

12.7

26.1

16.5

9.6

-1.7

11.1

11.9

70.5

26.0

2

63.3

63.2

100.2

21.7

59.4

20.9

38.5

-2.0

14.3

5.8

93.8

60.9

3

39.7

38.1

104.2

13.6

28.7

22.4

6.3

-0.9

15.0

10.3

72.3

15.9

(mm)
Before thinning

After thinning

204.2

291.5

16

24

* In the rain event on July 6 (Rain Event 1) in Table 2 IR and ISbt were not obtained independently due to clogging up of the drain, but the total value of IR +ISbt was measured. In the event it was assumed that ISbt = 0 based on the results as shown in Figure 2 and that IR + ISbt = IR.

38

Table 4 Amount of rainfall and canopy interception during four heavy rain events.
Each value represents the total amount, although the sum operator is omitted.
Rain
Event

PG

Number of
sub-rain
eventsTraynumberI

I'

I / I'

I/PG

IR

IR_PM

ISDE

ISbt

IAft

IR/ I

ISDE / I

(mm)

(mm)

(%)

(%)

(mm)

(mm)

(mm)

(mm)

(mm)

(%)

(%)

1

8.9

9.5

94.4

8.1

8.8

1.6

7.2

-0.5

1.1

98.3

80.5

2

8.6

9.5

90.9

7.8

9.2

2.2

7.0

-1.2

1.5

106.8

81.2

3*

11.7

14.5

81.0

9.6

−

2.3

−

−

2.2

−

−

1

2.7

2.6

102.6

8.6

2.5

-0.2

2.7

-0.6

0.7

93.4

100.8

2

3.7

3.6

101.9

11.9

3.5

-0.2

3.7

-0.6

0.7

95.2

100.6

3

4.9

5.0

99.2

15.9

3.4

-0.2

3.6

-0.3

1.8

69.1

73.1

1

4.4

4.1

108.1

12.2

5.4

2.9

2.5

-1.2

-0.1

121.7

56.4

2

6.4

6.4

100.0

17.7

6.9

3.2

3.7

-0.2

-0.2

107.2

57.5

3

4.5

4.5

100.5

12.4

4.6

4.0

0.6

-0.4

0.2

102.1

13.3

1

7.6

7.6

100.0

9.0

7.0

1.7

5.3

0.1

0.5

91.9

69.5

2

17.3

17.3

100.0

20.4

16.3

2.2

14.1

0.4

0.6

94.3

81.6

3

6.0

5.8

103.6

7.0

4.4

2.4

2.0

0.3

1.0

73.7

33.5

(mm)
Before thinning1

2

After thinning

3

4

110.2

31.0

36.4

84.9

22

6

14

8

* IR and ISbt were not obtained due to clogging up of the drain, and ISDE was not calculated.

39

Appendix B
Table B1 List of acronyms, abbreviations and symbols.
SymbolUnit

Description

-1

γ

K

Δ

K-1

ΔS

mm

Psychrometric constant
Slope of the saturated specific humidity versus
temperature curve
Difference in water storage between tRen and tRe1

ΔSBi

mm

Difference in water storage between tBei and tBsi

ΔSRi

mm

Difference in water storage between tRei and tRsi

Δt

h

λ
ρ

J kg

Time interval (5 minutes)-1

Latent heat of vaporization

-3

kg m

-1

Air density-1CP

J kg K

D

mm h

-1

d

m

Specific heat of air
Drainage rate from the tray
Zero plane distance

mm h

-1

Evaporation rate during rain event

Ecal

mm h

-1

EPM

mm h-1

G

W m-2

Calculated evaporation rate
Calculated evaporation rate using the Penman–
Monteith equation
Ground heat flux

I

mm

Canopy interception

i

–

I'

mm

IAft

mm

IjAft

mm

IjR

mm

IjRi

mm

IjR_PMi

mm

IjSbt

mm

IjSbtimm

E

Ordinal number for the sub-rain event or the storm
break time: i = 1, 2, • • • , n
Canopy interception calculated as the sum of IR, ISbt
and IAft
Canopy interception after cessation of rainfall
Canopy interception after cessation of rainfall for Trayj
Canopy interception during rainfall for Tray j
Canopy interception during rainfall for Tray j for the ith sub rain event
Canopy interception during rainfall for Tray j for the ith sub rain event calculated using the Penman–
Monteith equation
Canopy interception during storm break time for Trayj
Canopy interception during storm break time for Trayj for the i-th storm break time40

IjSbt_PMi

mm

IR

mm

IRi

mm

IR_PM

mm

IR_PMi

mm

ISbt

mm

ISbti

mm

ISbt_PMmm

ISbt_PMi

mm

ISDE

mm

j
k
n
PG
PGi
PM
PN
PVC
q
qs
R
r2
ra
RH
Rn
S
Sj
Sbt
SDE

–
–
–
mm
mm
–
mm
–
kg kg-1
kg kg-1
mm h-1
–
s m-1
%
W m-2
mm
mm
h
–

Spt

h

Canopy interception during storm break time for Trayj for the i-th storm break time calculated using thePenman–Monteith equation
Canopy interception during rainfall
Canopy interception during rainfall for the i-th sub
rain event
Canopy interception during rainfall calculated using
the Penman–Monteith equation
Canopy interception during rainfall for the i-th sub
rain event calculated using the Penman–Monteithequation
Canopy interception during storm break time
Canopy interception during storm break time for the ith sub rain event
Canopy interception during storm break time
calculated using the Penman–Monteith equation
Canopy interception during storm break time for the ith storm break time calculated using the Penman–
Monteith equation
Canopy interception during rainfall caused by splash
droplet evaporation
Ordinal number for the tray: j = 1, 2 and 3
von Karman constant
Number of sur-rain events
Gross rainfall
Gross rainfall for the i-th sub-rain event
Penman–Monteith (equation)
Net rainfall
Polyvinyl chrodride
Specific humidity
Saturated specific humidity
Rainfall rate
Determination coefficient
Aerodynamic resistance
Relative humidity
Net radiation
Water storage
Water storage for Tray j
Storm break time
Splash droplet evaporation
Separation time to divide rainfall into two independent
rain events
41

Ta
tBei
tBsi
tRei
tRsi
u
z
z0

ºC
h
h
h
h
m s-1
m
m

Air temperature
Time of the end of the i-th storm breakTime of the start of the i-th storm breakTime of the end of the i-th sub-rain event
Time of the start of the i-th sub-rain event
Wind speed
Reference height
Roughness height length42Figure captions
Figure 1. Arrangement of Trays 1, 2 and 3 before thinning. Note that Tray 1 and Tray 2
were inclined so rainwater drained. In Trays 1 and 2, the height difference between thefront right corner and far left corner where the drains were made was ~10 cm.
Figure 2. Relationship between gross rainfall PG and observed canopy interception
during rainfall IR, during storm break time ISbt, and after cessation of rainfall IAft, on arain event basis. (a) Tray 1 (control), (b) Tray 2 before thinning, (c) Tray 3 before
thinning; (d) Tray 1 (control); (e) Tray 2 after thinning, (f) Tray 3 after thinning. In thepanel (c) for the largest PG of 110.2 mm, the sum of I3R and I3Sbt is shown due to theclogged drain.
Figure 3. Observed and calculated canopy interception during rainfall (respectively, IR
and IR_PM) and during storm break time (respectively, ISbt and ISbt_PM), against gross
rainfall PG. (a) Tray 1 (control), (b) Tray 2 before thinning, (c) Tray 3 before thinning;(d) Tray 1 (control), (e) Tray 2 after thinning, (f) Tray 3 after thinning. Observed values
and regression lines are the same as those in Fig. 2.
Figure 4. (a)–(d): Gross rainfall for the i-th sub-rain event PGi and observed canopy
interception during rainfall for the sub-rain event IjRi in Tray j for four heavy rain
events. (e)–(h): Calculated canopy interception during rainfall for i-th sub-rain event
IjR_PMi and that of observed IjRi for four heavy rain events in Tray j. (a) and (e): Rain
Event 1 with total gross rainfall (PG) of 110.2 mm before thinning period; (b) and (f):Rain Event 2 with PG of 31.0 mm before thinning period; (c) and (g): Rain Event 3 with
PG of 36.4 mm after thinning period; (d) and (h): Rain Event 4 with PG of 84.9 mm afterthinning period.
Figure 5. Observed canopy interception during storm break time IjSbti and calculated
IjSbt_PMi on a storm break time basis in Tray j. (a) Rain Event 1 before thinning period;(b) Rain Event 2 before thinning period; (c) Rain Event 3 after thinning period; (d) Rain
Event 4 after thinning period.
Figure 6. Time series of water budget, canopy interception and meteorological elements
for Rain Event 1 with total gross rainfall PG of 110.2 mm, before thinning: (a) PG; (b)canopy storage S; (c) observed cumulative IjRi; (d) calculated cumulative IjR_PMi; (e)43observed cumulative IjSbti; (f) calculated cumulative IjSbt_PMi; (g) calculated potential
evaporation EPM; (h) net radiation Rn; (i) relative humidity RH; (j) air temperature Ta;(k) wind speed u. Unit of ordinates is mm unless otherwise indicated.
Figure 7. Time series of water budget, evaporation and meteorological elements forRain Event 4 with total gross rainfall PG of 84.9 mm, after thinning; details on eachpanel are the same as in Fig. 6.
Figure 8. Dependence of lifetime for small droplets on relative humidity RH and airtemperature. (a) RH=95%; (b) RH=99%.

44

45

46

47

48

49

50

51

52