Forest floor evaporation in a dense Douglas fir stand

Journal of Hydrology 193 (1997) 97–113

Forest floor evaporation in a dense Douglas fir stand M.G. Schaap*, W. Bouten Landscape and Environmental Research Group, University of Amsterdam, Nieuwe Prinsengracht 130, 1018 VZ Amsterdam, The Netherlands Received 26 January 1996; accepted 15 May 1996

Abstract Forest floor evaporation was measured with an accurate weighing lysimeter during 44 days in early spring and summer. The Penman–Monteith approach was used to model the evaporation rates as well as the temperature difference between forest floor surface and air at 1 m height. Values of resistance parameters were slightly different when the Penman–Monteith model was optimized for measured evaporation rates or for measured temperature differences. These discrepancies were partly due to field variability in forest floor water contents but also because our approach considered the forest floor to be isothermal. With the appropriate parameter sets, the model was able to predict measured hourly forest floor evaporation rates and surface temperature dynamics satisfactorily. We show that in the forest discussed in this paper the Penman–Monteith ventilation term dominates over the available energy term. As a result the evaporation flux is matched by an almost equal, sensible heat flux but in opposite direction. Forest floor water content dynamics have a strong control over the evaporation flux. Spatial variability in forest floor water contents cause the 44-day average forest floor evaporation to range from 0.19 mm d −1 in a dry part of the forest to 0.3 mm d −1 in a wet part with 0.23 mm d −1 as a site representative value. q 1997 Elsevier Science B.V.

1. Introduction Presently, a great deal of forest hydrological research focuses on SVAT (Soil Vegetation Atmosphere) processes. Rainfall interception and transpiration by tree canopies are responsible for most of the transfer of water and energy. Smaller, but still significant, roles are played by forest floor evaporation and understorey evapotranspiration

* Corresponding author present address: US Salinity Laboratory, ARS-USDA, 450 Big Springs Road, Riverside, CA 92507, USA. E-mail: [email protected] 0022-1694/97/$17.00 q 1997– Elsevier Science B.V. All rights reserved PII S00 22-1694(96)032 01-5

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(Roberts, 1983; Kelliher et al., 1993). In extreme cases half or more of the total forest evapotranspiration originates from these processes (Roberts et al., 1980; Black and Kelliher, 1989). To some degree, forest floor (FF) evaporation and understorey evapotranspiration are complementary: if abundant understorey vegetation is present FF evaporation is negligible (Black and Kelliher, 1989). In stands without an understorey FF evaporation may range between 3 and 21% of the total forest evapotranspiration (Kelliher et al., 1993). Black and Kelliher (1989) showed that below canopy available energy and turbulence regimes control understorey transpiration and FF evaporation. Because these have high spatial and temporal variabilities, FF evaporation may also vary considerably in space and time (Black and Kelliher, 1989; Lee and Black, 1993). Additionally, Kelliher et al. (1986) found a strong relationship between root zone water contents and the surface resistance to vapor transport. Since soil water contents in forests are also spatially very variable (Bouten et al., 1993) this may increase the spatial variability of FF evaporation. Forest floor evaporation is a SVAT process about which relatively little is known. Most estimates of forest floor evaporation are based on short measurement periods (Black and Kelliher, 1989). Longer time series covering different seasons are hardly available. The aim of this study is to present measurements of 44 days of forest floor evaporation and other micrometereological data and to calibrate the Penman–Monteith equation (Monteith, 1965). With this approach, we wish to find out which variables control FF evaporation and to estimate the influence of FF floor water contents on FF evaporation in a dense Douglas fir forest without understorey vegetation.

2. Theory Defining all upward fluxes and an increase in heat storage as positive, the energy balance of a forest floor (shown in Fig. 1) is written as: A = − R n + G − S = lE + H

(1) −2

All these variable are energy fluxes in W m . Forest floor evaporation (the latent heat flux, lE) and the sensible heat flux (H) are balanced by the available energy (A). If evaporation takes place from the surface the available energy is written as the sum of net radiation (R n) and the soil heat flux (G). In this paper we adopt a somewhat different definition because

Fig. 1. Schematic diagram of the forest floor energy balance. See text and list of symbols (Section 6) for an explanation.

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Kelliher et al. (1986) showed that forest floor evaporation may take place from within the forest floor. Because evaporation requires energy, we must include FF heat storage dynamics (S) into the available energy term. To maintain the FF energy balance, the soil heat flux must now be located at the interface of FF and mineral soil rather than at the FF surface (see Fig. 1). Forest floor evaporation and sensible heat fluxes can be expressed as: lE =

rCp (e (T ) − eair )=(ra + rs ) g s 0

H = rCp (T0 − Tair )=ra

(2) (3)

where r is the density of air, C p the specific heat of air, g the psychrometer constant, e s(T 0) − e air the vapor pressure difference between the FF surface and air, and T 0 − T air is the temperature difference between the FF surface and air. These equations assume that the air at the FF surface is saturated with water and that the FF is isothermal. The aerodynamic resistance to heat and vapor transport is represented by r a. The surface resistance r s is a combination of the resistance to vapor release from the organic FF material and the subsequent diffusive resistance to the FF surface. The well-known Penman–Monteith equation (Monteith, 1965) implicitly incorporates the surface energy balance and has the soil surface temperature, which is usually not measured, conveniently eliminated: lE =

sv A + rCp D=ra g(1 + rs =ra ) + sv

(4)

The first term in the numerator is the contribution of the available energy to evaporation. The second term is the contribution of ventilation (the ‘‘drying power’’) where D is the vapor pressure deficit (e s(T air) − e air). Using a combination of Eqs. (1), (3) and (4) it is possible to rewrite the Penman– Monteith equation to yield the temperature difference between FF and air: T0 − Tair =

[g=(rCp )](ra + rs )A − D g(1 + rs =ra ) + sv

(5)

r a and r s can be expressed in other variables. Assuming the air below the canopy to have a neutral stability, we express r a by an aerodynamic parameter (c a) and the wind speed (u): ra =

1 ca u

(6)

We assume that r s is a simple empirical function of the FF water content (v FF) and a parameter vector C with a minimum value of 0 s m −1: rs = max{0, f (vFF , C)}

(7)

The two versions of the Penman–Monteith equation (called models) essentially describe the same energy balance of the forest floor. The first model (the lE model) is a combination of Eqs. (4), (6) and (7) which are fitted to measured forest floor evaporation data, yielding a parameter set {c a, C}. The second model (the T 0 model) is a combination of

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Eqs. (5)–(7) which are fitted to measured T 0 − T air values, thus yielding a similar parameter set as the lE model. If the Penman–Monteith concept applies to forest floor evaporation and if the data set is consistent, fitting these models should yield similar parameter values. The degree of agreement between the parameter sets can thus give an idea of how well we can model the FF energy balance.

3. Materials and methods 3.1. Research site The experimental site is a 2.5 ha Douglas fir stand in the central Netherlands (52.18N and 5.48E) at an altitude of 50 m above sea level. The stand was planted in 1962 and is surrounded by a heterogeneous forest of approximately 50 km 2 with the nearest edge at 1.5 km distance. Average tree height is 21 m; stem density is 992 trees ha −1, with a basal area of 33.4 m 2 ha −1. Living branches above 8 m form a dense canopy with a single sided leaf area index (LAI) ranging from 8 m 2 m −2 in spring to 11 m 2 m −2 in early summer. Because forest management remove dead branches, a relatively open space was present between 0 and 3 m causing a wind speed maximum at about 1 m above the FF. Because of the dense canopy there is no understorey vegetation. The FF is 5 cm thick with a standard deviation of 2 cm (Tiktak and Bouten, 1990). It consists mainly of partly decomposed Douglas fir needles and a small quantity of branches. Maximum FF water storage is 10 mm (Tiktak and Bouten, 1990). The mineral soil is a well-drained Typic Dystrocrept on heterogeneous glacier-pushed loamy river sands. The water table is at a depth greater than 40 m. The 30 year mean annual rainfall is 834 mm, and the 30 year mean annual potential evapotranspiration is 712 mm (Tiktak and Bouten, 1994). 3.2. Experimental equipment We measured FF evaporation (lE) with a weighing lysimeter consisting of a soil container and a balance (Fig. 2). The diameter of the soil column was 30 cm and its depth was 35 cm. These dimensions allowed a realistic representation of the forest soil heat balance while still allowing the container to be handled by two persons. An undisturbed sample was obtained by removing the bottom of the container and pressing the container into the soil until the FF reached the upper edge. A 4 cm layer of synthetic water repellant foam in the sides and bottom of the container minimized heat exchange with the surroundings. The container was placed on a symmetrical balance with an arm length of 0.8 m and total dimensions of 2.5 × 0.6 × 1.0 m (length, width, height). Approximately 95% of the container weight was counterbalanced at the other balance arm; the remaining weight was counterbalanced by a load cell (a Ho¨ttinger–Baldwin HBM Z6-2 with a 5 kg range) (Darmstadt, Germany). Because the counterbalance weight was also insulated it had the same thermal properties as the lysimeter, thus minimizing the effects of dew formation on the measurements. We placed the balance in a pit on a 400 kg cast concrete plate. The

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Fig. 2. Schematic diagram of the lysimeter equipment.

column surface was leveled with respect to the surrounding FF; the remaining pit opening was covered with plywood coated with disturbed FF material. To minimize wind influence and to enhance the measurement resolution, the load cell signal was sampled every second with a CR10 datalogger and was subsequently averaged to 15 min values. The first derivative of the measured weight provided the evaporation flux; further data reduction provided hourly estimates of FF evaporation. The resolution was 0.035 mm which is only slightly worse than that obtained with much larger weighing lysimeters (Howell et al., 1985; Perttu et al., 1980). We carried out measurements on 50 days in July–August 1992, March–April 1993, and June–July 1993. Long periods of rain disturbed the measurements on six days, reducing the data set to 44 days. Sometimes these days have missing hourly values owing to short periods of rain or maintenance. Micrometeorological measurements were carried out every 10 s at 15 m from the lysimeter. Data reduction provided hourly values; typical values for the three periods are shown in Table 1. Vapor pressures (e air) and air temperatures (T air) were measured at 1 and 4 m height with ventilated psychrometers (Model WVU with 2KA39 thermistors, Delta-T Devices, Berwell, UK) having a specified accuracy of 0.06 K. The measurements at these heights were almost identical. Net radiation (R n) was measured at 1 m height with a Fritschen type net radiometer (Model Q* 6.1, REBS, Seattle, Oregon, USA) with hard shields. Because the canopy was closed we assumed that there was little spatial variability in R n. Wind speeds (u) were measured at 1 m above the FF in the below canopy wind speed maximum. An anemometer with a six-cup rotor and 13 pulses per revolution (Models R60 and A101M respectively, Vector Instruments, Rhyl, UK) indicated a starting wind speed of about 0.15 m s −1. Inspection of the data showed that measured wind speeds below 0.20 m s −1 were unreliable. With missing lysimeter values this reduced the 44 day data set from 1056 to 725 hourly values. We measured soil temperatures with 32 thermistors at different soil depths near the meteorological equipment. The thermistors were installed at 5 cm (FF surface), at 2.5 cm (middle of FF) and at 0 cm (between FF and mineral soil). In the mineral soil the

10 1.2 Min. 6.9 12.4 − 3.4 − 12.0 − 26.8 − 13.8 , 0.20 a 35 0.05 − 4.1

Length (d) Rainfall (mm) Variable T air (8C) T 0 (8C) − R n (W m −2) S (W m −2) G (W m −2) A (W m −2) u (m s −1) D (Pa) v FF (cm 3 cm −3) lE (W m −2)

19.1 18.4 5.0 0.0 − 3.7 1.3 0.47 673 0.10 8.5

Avg. 30.6 28.1 28.4 14.0 10.7 12.3 1.1 2401 0.16 51.7 b

Max.

Avg. 5.7 5.5 2.5 0.1 4.5 6.9 0.47 223 0.16 6.7

Min. − 4.1 − 1.5 − 5.1 − 13.7 − 9.2 − 8.0 , 0.20 a 0 0.14 − 5.7

14 19.4

March 1993

14.9 12.4 15.0 20.7 17.9 29.5 1.5 1003 0.18 35.7

Max. 6.9 8.4 − 3.6 − 15.4 − 16.5 − 9.9 , 0.20 a 14 0.10 − 10.9

Min.

20 30.4

June 1993

15.2 14.7 4.5 0.0 0.4 4.9 0.38 393 0.16 6.7

Avg.

24.9 23.0 21.8 17.6 14.6 17.5 0.92 1651 0.21 36.7

Max.

b

Minimum reliable windspeed. Measured at a high vapor pressure deficit after a few raindrops. T air: Air temperatures (at 1 m height); T 0: FF surface temperatures; R n: net radiation at the FF; S: FF heat storage change; G: soil heat flux; A: Available energy; u: windspeed; D: vapor pressure deficit; vFF : forest floor water contents; lE: measured FF evaporation.

a

August 1992

Period

Table 1 Some general micrometeorological characteristics of the three measurement campaigns

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measurement depths were 5, 10, 20, 30, 40, 50, 60, 80 and 100 cm. To correct instrumental differences between soil and air temperatures, we installed one thermistor of the system near the psychrometer at 1 m height. The accuracy of the soil temperatures is approximately 0.168C; surface temperatures were checked with an infrared radiometer (Heimann KT15.82 with a K6 lens having a wavelength range from 8 to 14 mm). The soil heat flux (G) was calculated using the temperature gradient (DT) between 0 and 5 cm (DZ) in the mineral soil using: G= −K

DT DZ

(8)

The thermal conductivity of the mineral soil (K) was determined to be 1.0 W m −1 K −1 using an inverse simulation with a soil temperature dynamics model (Bouma, 1991) and half a year of soil temperature data. The inverse simulation showed that K was almost constant in the observed range of mineral soil water contents. We calculated the heat storage change in the FF (S) by multiplying the derivative of the 2.5 cm FF temperatures with the composite heat capacity of FF. This value was obtained from the FF bulk density and the FF water content. We used a dry bulk density of 0.1 × 10 3 kg m −3 and a heat capacity of 1800 J kg −1 K −1 for dry organic material. FF water contents were measured 2 to 8 times a day at depths between 1.5 and 7.6 cm using an automated TDR system with 30 sensors (Heimovaara and Bouten, 1990). These measurements were carried out at 100 m distance from the meteorological site. Because this area was relatively ‘‘wet’’ (Schaap, 1996), we installed 18 additional TDR sensors near the meteorological equipment where hydrological conditions were more representative for the forest. Furthermore, we installed 12 TDR sensors at a particularly ‘‘dry’’ area in the forest. These sensors were read manually every week. Schaap (1996) provided empirical transfer functions to translate the wet site FF water content dynamics to the meteorological and dry site. 3.3. Approach and presentation of results We fitted the T 0 and lE model to the T 0 − T air or FF evaporation data to obtain two {c a, C} parameter sets. Prior to presenting results our first task is to find a simple empirical formula for Eq. (7). With two optimizations we demonstrate that a linear formula, similar to that used by Kelliher et al. (1986), is adequate. In the first optimization we optimize the c a and C parameters simultaneously for the whole data set, thus yielding a parameterized form of Eq. (7). The validity of this equation is checked with the second optimization where we keep c a at the same value as found in the first optimization and fit r s values (rather than the C vector) for each day in the data set. Here we use the fact that FF water contents change only slowly during a (dry) day causing the r s values to remain approximately constant. The resulting 44 daily r s values can be plotted versus f FF and should have a similar trend as the expression used for Eq. (7). Fitting was carried out with the simplex or amoeba algorithm (Nelder and Mead, 1965; Press et al., 1988, p. 305); parameter uncertainty was obtained by means of the Jackknife method (Efron and Tibshirani, 1993). The fitting procedure minimized root mean square residuals (RMSR) between observed and modeled T 0 and lE values. These RMSR values

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also provide us the model accuracy in absolute terms. Coefficients of determination (R 2) between measured and modeled values give an idea about the ability of the models to predict the T 0 − T air and lE dynamics. Subsequently, we deal with similarities and differences between the T 0 and lE model parameters sets. To find out if the FF energy balance is described well, we use the T 0 and lE model parameter sets in cross validations. This means that the T 0 model parameter set is used to predict lE dynamics and vice versa for the lE model parameter set. To find out which variables control FF evaporation, we investigate the contribution of the ventilation and radiation terms in Eq. (6) as well as the importance of r a and r s. Lastly, we evaluate the effect of the variability of forest floor moisture contents on FF evaporation rates.

4. Results and discussion 4.1. Cross-validation Table 2 shows the values of the parameters of the lE and T 0 parameter sets as well as RMSRs and R 2 values. After trying some alternatives we found that Eq. (7) can best be expressed as: rs = max{0, c1 (vFF − vtr )}

(9)

Where c 1 and v tr are the elements of the parameter vector C, v tr is the threshold water content above which r s is zero, and c 1 is the slope of the relation at FF water contents below v tr. The lE and T 0 datasets did not allow the simultaneous optimization of c a, c 1 and v tr. To end up with identifiable c a and c 1 parameters we had to fix v tr at the listed values, and so no uncertainty estimates are available. The difference in v tr values is considerable (0.021 cm 3 cm −3) and may be explained by spatial variability of forest floor water contents, since FF evaporation (lE model) was measured at 15 m distance from the FF temperature measurements (T 0 model). At a similar spatial scale, TDR measurements at the automated TDR site show a variability of about 0.05 cm 3 cm −3 (Schaap, 1996). Fig. 3 demonstrates that Eq. (9) is indeed an appropriate expression for r s. This figure shows Eq. (9) (further denoted as r s(v FF)) for both models as lines as well as optimized daily r s values for each day in the 44 day data set as symbols. The distributions of the symbols show that the r s(v FF) relation is approximately linear in the measured range of FF Table 2 Results of the parameter optimizations for the lE and the T 0 models. Parameter uncertainties, model errors and coefficients of determinations (R 2) are also given. Forest floor threshold water contents (v tr) were not optimized but fixed at their listed values. The R 2 value of the T 0 model is based on T 0−T air data

3

−3

v tr (cm cm ) ca c 1 (s m −1) RMSR R2

lE model

T 0 model

0.199 0.0100(60.0009) −1.29 × 10 4(60.09 × 10 4) 4.93 W m −2 0.57

0.178 0.0154(60.0004) −1.61 × 10 4(60.05 × 10 4) 0.50 K 0.85

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Fig. 3. Surface resistance versus FF water content. The lines show the optimized relations of the 44 day data set for the T 0 and lE data sets. The intersection with the x-axis represents the threshold FF water content. The circles represent optimized daily values with the c a values fixed at their optimized values. The relation of Kelliher et al. (1986) is also shown: in this case the x-axis represents root zone water contents. The four circles near this relation are our (deviating) data, not those of Kelliher et al. (1986).

water contents. In the ideal case, the symbols should be distributed around the lines, but in particular some lE-model r s points at the wet end of the graph deviate from the general trend and show much higher r s values than predicted by the r s(v FF) relation. Although these points clearly deviate from the trend there was no good reason to exclude them from the data set. If these points had been excluded, the values of the c 1 parameters in Table 2 (representing the slopes of the r s(v FF) relations) would have been the same. The intersection of the r s(v FF) relations with the vertical axis (2.9 × 10 3 and 2.6 × 10 3 s m −1 for the T 0 model and lE model respectively) provides an estimate of the surface resistance of a completely dry FF. Assuming that diffusion of water vapor through the FF is responsible for r s, a theoretical estimate would be: z (10) rs = Q(vFF )Dw Where z is the diffusion distance, D w is the Fickian diffusion coefficient of water vapor in the absence of a porous medium (2.2 10 −5 m 2 s −1 at 208C), Q(v FF) is a porous medium specific function that reduces D w according to the water content (Freijer, 1994). In the case of a completely dry Douglas fir forest floor Q(v FF) is equal to 0.45 (Freijer, 1994) and with a FF thickness of 0.05 m this results in a theoretical r s of 5.1 × 10 3 s m −1. Although this value is almost twice as high as the intersection values it gives us an indication that the r s(v FF) relations have at least some physical background. Note that some of the r s points at the dry end of Fig. 3 seem to indicate higher intersection values than were calculated with the (linear) r s(v FF) relations.

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Fig. 3 also shows the Kelliher et al. (1986) r s(v FF) relation for a Douglas fir site in Canada. Our values of v tr agree well with the threshold water content found by Kelliher et al. (0.185 cm 3 cm −3). At water contents above v tr we find r s values of 0 s m −1 while Kelliher et al. found a minimum r s of 800 s m −1. However, their relation is based on a limited number of data points and may not be very reliable. The Kelliher et al. (1986) relation is much steeper than ours because they related root zone water contents to r s values. Root zone water contents react much more slowly to evaporation than FF water contents causing r s to react much more strongly to decreasing water contents in the Kelliher relation than in our results. Table 2 shows that R 2 and the c a parameter values of the lE and T 0 models differ significantly. The low R 2 of the lE model may be explained by wind causing a slight movement of the lysimeter container thereby introducing noise into the lysimeter signal. Additionally, to obtain evaporation rates the first derivative of the lysimeter signal must be calculated, thus causing the noise to increase further. Three causes may be responsible for the difference in c a values: spatial variability of meteorological variables, differences in the optimization criteria and an oversimplified model. It is unlikely that spatial variability in meteorological variables can explain the difference. Measurements showed that wind speeds near the lysimeter were almost identical with the wind speeds at the meteorological site. Furthermore, sensitivity analyses showed that even unrealistic increases and decreases in measured forest floor temperatures or energy balance components (R n, G and S) could not account for the inconsistent c a values. Because the lE and T 0 models are fitted using different optimization criteria, the T 0 model attributes other ‘‘weights’’ to specific data points than does the lE model. However, model residuals show no clear systematic relation with the lE fluxes and T 0 − T air values. Therefore, the effects of differences in optimization criteria are random and cannot influence the parameter values too much. A more likely explanation of the difference in c a values may be that our description of the FF energy balance is too simplified a view of reality. Fig. 1 shows that while sensible heat is exchanged at the surface, water vapor is generated somewhere inside the FF and escapes to the surface by means of molecular diffusion. In the Penman–Monteith approach to leaf transpiration (Monteith, 1965), the resistance to heat transport between leaf surface and location of transpiration can be neglected. In our model, we followed the same approach by assuming the FF is isothermal. However, to allow FF evaporation to take place, there must be a supply of energy and therefore a temperature gradient must exist within the FF. The thermal diffusion coefficient may pose as an extra resistance to FF evaporation, allowing the difference in the c a values to be explained. Like Kelliher et al. (1986), we think that modeling heat transport and diffusion of vapor inside the FF will yield more precise results. Such an approach is beyond the scope of this paper because it requires dynamic simulation models and additional data. Although the two c a values are somewhat inconsistent we will demonstrate that the Penman–Monteith approach still describes FF evaporation fluxes and surface temperatures with reasonable accuracy. Figs 4 and 5 show the cross-validations time series of two parameter sets for a moist period in spring and a dry period in summer. Usable data (wind speeds above 0.2 m s −1) are represented by a black bar above the x-axis. Because the c a parameter value of the T 0 model is higher than that of the lE model, the T 0 model overestimates the latent energy flux in March (Fig. 4(a)). Conversely, the lE optimization underestimates the daytime T 0 − T air

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Fig. 4. Cross-validations of the lE and T 0 parameters for (a) latent heat and (b) T 0 − T air for moist spring situations. Measured data are represented by the dots. The black bar represents wind speeds greater than 0.2 m s −1.

dynamics (Fig. 4(b)). The T 0 parameters do not capture the daytime T 0 − T air values very well on days 80 and 81. The predicted nighttime dynamics are often much larger than measured; this, however, involves low wind speed conditions that were not used in the optimizations. Apparently, nighttime c a values are smaller than as extrapolated by the models. This may indicate that nighttime instability of the air above the FF caused free convection to occur as found by Jacobs et al. (1994). Since measured nighttime evaporation did not contribute significantly to the total FF evaporation we did not consider this process further.

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Fig. 5. Cross-validations of the lE and T 0 parameters for (a) latent heat and (b) T 0 − T air for dry summer situations. Measured data are represented by the dots. The black bar represents wind speeds greater than 0.2 m s −1.

In summer (Fig. 5(a)), the T 0 parameters still overestimate the lE values somewhat, but the agreement is better than in the March period. Both parameter sets capture the T 0 − T air dynamics well in this period (Fig. 5(b)). Apparently, the difference in c a parameters is not important here. Note that both parameter sets are unable to model the negative lE fluxes in some nights of the June 1993 period. Fig. 5(b) shows that dew formation on the FF was impossible because nighttime T 0 − T air values are positive. A possible explanation is that condensation

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on the lysimeter container and the counterweight did not balance out. Another explanation is that dew formation might have taken place in the canopy and dripped back to the FF thus causing the lysimeter to measure negative lE. 4.2. Micrometeorological and surface control over forest floor evaporation A correlation of the Penman–Monteith ventilation term (Eq. (6)) with measured FF evaporation data yields a R 2 of 0.54; correlation of the available energy term with evaporation

Fig. 6. (a) Energy partitioning of the lE model in Penman–Monteith ventilation and available energy terms. Measured data are represented by the dots. (b) Corresponding time series of surface resistance (r s), aerodynamic resistance (r a) and vapor pressure deficits (D).

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data yields a R of only 0.01. It is clear that the Penman–Monteith ventilation term controls FF evaporation whereas the available energy term apparently contributes very little. Fig. 6(a) shows the partition of both terms during three days of the wet and dry periods; Fig. 6(b) provides information about r a, r s, and the vapor pressure deficit. The available energy term is continuously very low, caused by cancelation of the R n, S and G terms. As a result, Eq. (1) requires that lE (the latent heat flux) is matched by an almost equal, but negative, sensible heat flux. Because of the high LAI of this forest and the low net radiation, the partitioning of energy is probably not representative of other more ‘‘open’’ forests. Black and Kelliher (1989) presented cases where higher net radiation levels did control FF evaporation. As defined in Eq. (2), the evaporation flux is dependent on the sum of r a and r s. The ratio of r s and (r a + r s) gives the amount of surface control over FF evaporation in relation to the total resistance. This ratio is shown in Fig. 7 for the lE model in summer 1993 period showing a dry period followed by a few rainstorms after day 186. On days 170 and 171, the water content is above the threshold value and r s is thus 0 causing the FF evaporation dynamics to be controlled only by the aerodynamic resistance. After day 171, the water content decreases further and the r s and r s/(r a + r s) values increase. In these circumstances, the FF water content strongly influences evaporation. The extremely dry period of August 1992 reached levels of 0.90; the moist March 1993 period usually had ratios around 0.5. 4.3. Influence of v FF on forest floor evaporation Fig. 8 shows the cumulative FF evaporations (in mm) for the three periods with lysimeter data and lE and T 0 model parameter sets for the lysimeter site. The evaporation

Fig. 7. The fraction of the surface resistance in the total resistance for a drying FF in June–July 1993. Only data points with wind speeds greater than 0.20 m s −1 are shown. The water content and hourly throughfall amounts are also shown.

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Fig. 8. Measured FF evaporations and T 0 and lE model predictions of the lysimeter site for the three periods and lE model predictions for the ‘‘wet’’ and ‘‘dry’’ areas in the same forest. In the case of the March period the days are not consecutive.

rates are almost constant in the three periods; no clear seasonal effects occur. In March 1993, lower vapor pressure deficits (with a maximum of approximately 500 Pa, Fig. 6(b)) are compensated by lower r s values (approximately 400 s m −1). In summer, high r s values (1000 s m −1) compensate high vapor pressure deficits (1000 Pa). Since the lE model is optimized on lysimeter data, the agreement between these two is excellent, both yielding an average flux of 0.23 mm d −1. The T 0 parameter set predicts higher FF evaporation rates (0.32 mm d −1), because its c a parameter value is higher. We also applied the lE model to the ‘‘wet’’ and ‘‘dry’’ areas in the same forest with the assumption that the spatial variability in micrometeorological variables was negligible. The only variable that differs is the FF water content which causes differences in r s values among lysimeter, wet, and dry areas. At the wet area, water contents are almost always above or near the threshold values resulting in r s values close to zero. In these circumstances, FF evaporation is only dependent on the aerodynamic resistance and the average flux reaches a maximum 0.38 mm d −1. Conversely, the water contents at the dry site are usually lower than the threshold values, causing r s to play a much more important role. At this area, average fluxes are 0.19 mm d −1.

5. Conclusion We have measured forest floor evaporation with an accurate weighing lysimeter. Evaporation rates and temperature differences between surface and air could be modeled with the Penman–Monteith equation. This resulted into two parameter sets which showed some

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inconsistencies that may be explained by spatial variability in forest floor water contents and too simplified an approach to the forest floor energy balance. Because of the dense canopy the available energy was small. Consequently, ventilation and forest floor water contents dominated the forest floor evaporation causing the latent heat flux to be matched by an almost equal negative sensible heat flux. Because forest floor water contents are spatially variable, FF evaporation rates also vary in space. The 44 day average evaporation showed a spatial range of 0.19 to 0.38 mm d −1 within a homogeneous site with 0.23 mm d −1 as a site representative value. The forest described in this paper has a high canopy density and model results cannot be extrapolated directly to all other stands. Forests with a lower LAI may have larger net radiation levels and higher wind speeds than the forest in this study. Consequently, we expect that forest floor evaporation rates may be higher in these forests. However, feedback mechanisms also exist since higher evaporation rates tend to dry the FF more quickly thus causing a more rapid increase in the surface resistance and a decrease in FF evaporation. On the basis of the FF evaporation levels found in this dense forest we believe that additional studies in forests with different canopy properties and forest floors are warranted. 6. List of symbols A C Cp ca c1 D Dw e air e s(T 0) G H K Q(v FF) Rn ra rs sv S T0 T air g v FF v tr lE r

Available energy Parameter vector (c 1, v tr) Specific heat of air Aerodynamic parameter Slope of the r s(v FF) relation Vapor pressure deficit (e s(T air) − e air) Fickian free air diffusion coefficient for water vapor Vapor pressure of the air Saturated vapor pressure at surface temperature T 0 Soil heat flux Sensible heat flux Soil heat conductivity Porous medium specific reduction function for D w Net radiation Aerodynamic resistance to heat transport Surface resistance to vapor exchange Slope of the saturated vapor pressure curve Heat storage change in the forest floor Surface temperature Air temperature Psychrometer constant Forest floor water content Threshold forest floor water content Latent heat flux Density of air

[W m −2] [s m −1, cm 3 cm −3] 1005 [J kg −1 K −1] [–] [s m −1] [Pa] 2.2 × 10 −5 [m 2 s −1] [Pa] [Pa] [W m −2] [W m −2] [W m −1 K −1] [–] [W m −2] [s m −1] [s m −1] [Pa K −1] [W m −2] [K] [K] 63 [Pa K −1] [cm 3 cm −3] [cm 3 cm −3] [W m −2] 1.225 [kg m −3]

Acknowledgements We are grateful to Hans Brugman and Tjerk van Goudoever for constructing and installing the lysimeter. We would like to thank Remco van Ek, Leo Huijsen and Wiro

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Keijer for field assistance. John van Boxel is thanked for lending out the psychrometers and anemometers and for commenting on the manuscript for which we also thank Jan Freijer, Pieter Musters and Koos Verstraten. Gerard Heuvelink helped us with the Jackknife uncertainty estimates. We are grateful to Fred Bosveld of the Royal Dutch Meteorological Institute for discussions and for supplying data. We also thank the Dutch program on Global Air Pollution and Climate Change (NOP) for their financial support (Project No. 850010). Two anonymous reviewers are thanked for their useful suggestions. References Black, D.T. and Kelliher, F.M., 1989. Processes controlling understorey evapotranspiration. Phil. Trans. R. Soc. Lond. B, 324: 207–231. Bouma, N., 1991. Simulation of heat dynamics in a soil profile: a deterministic temperature model. Masters thesis, Laboratory of Physical Geography and Soil Science, University of Amsterdam, The Netherlands. Bouten, W., Heimovaara, T.J. and Tiktak, A., 1993. Spatial patterns of throughfall and soil water dynamics in a Douglas fir stand. Water Resour. Res., 28: 3227–3234. Efron, B. and Tibshirani, R.J., 1993. An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability. Chapman and Hall, New York, 436 pp. Freijer, J.I., 1994. Calibration of jointed tube model for the gas diffusion coefficient in soils. Soil Sci. Am. J., 58: 1067–1076. Heimovaara, T.J. and Bouten, W., 1990. A computer-controlled 36-channel time domain reflectometry system for monitoring soil water contents. Water Resour. Res., 26: 2311–2316. Howell, T.A., McCormick, R.L. and Phene, C.L., 1985. Design and installation of large weighing lysimeters. Transactions of the ASAE, 28: 106–117. Jacobs, A.F.G., van Boxel, J.H. and El-Kilani, R.M.M., 1994. Nighttime free convection characteristics within a plant canopy. Boundary Layer Meteorology, 71: 375–391. Kelliher, F.M., Black, T.A. and Price, D.T., 1986. Estimating the effects of understorey removal from a Douglas fir forest using a two-layer canopy evapotranspiration model. Water Resour. Res., 22: 1891–1899. Kelliher, F.M., Leuning, R. and Schulze, E.-D., 1993. Evaporation and canopy characteristics of coniferous forests and grasslands. Oecologia, 95: 153–163. Lee, X. and Black, T.A., 1993. Atmospheric turbulence within and above a Douglas-fir stand, Part II: eddy fluxes of sensible heat and water vapour. Boundary-Layer Meteorology, 64: 369–390. Monteith, J.L., 1965. Evaporation and environment. In: G.E. Fogg (ed), The State and Movement of Water in Living Organisms, 19th Symp. Soc. Exp. Biol., Cambridge University Press, London, pp. 205–235,. Nelder, J.A. and Mead, R., 1965. A simplex method for function minimization. Computer J., 7: 308–313. ˚ ., Lindroth, A. and Nore´n, B., 1980. MicrometeorPerttu, K., Bischof, W., Grip, H., Jansson, P-E., Lindgren, A ology and hydrology of pine forest ecosystems. I. Field Studies. In: Persson T. (ed), Structure and function of northern coniferous forests – An ecosystem study. Ecol. Bull. (Stockholm), 32: 75–121. Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T., 1988, Numerical Recipes in C. Cambridge University Press, Cambridge, UK. Roberts, J., Pymar, C.F., Wallace, J.S. and Pitman, R.M., 1980. Seasonal changes in leaf area, stomatal conductances and transpiration from bracken below a forest canopy. J. Appl. Ecol., 17: 409–422. Roberts, J., 1983. Forest transpiration: a conservative hydrological process? J. Hydrol., 66: 133–141. Schaap, M.G., 1996. The role of soil organic matter in the hydrology of forests on dry sandy soils. PhD Thesis, University of Amsterdam, Amsterdam, The Netherlands. Tiktak, A. and Bouten, W., 1990. Soil hydrological system characterisation of the two Aciforn stands using monitoring data and the soil hydrological model ‘‘SWIF’’. Dutch priority programme on acidification report No. 102.2-01, RIVM, Bilthoven, The Netherlands. Tiktak, A. and Bouten, W., 1994. Soil Water dynamics and long-term water balances of a Douglas fir stand in the Netherlands. J. Hydrol., 156: 265–283.