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  • View in gallery

    Location of the Waldstein site in the Fichtelgebirge Mountains in Germany.

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    Schematic diagram of the processes of heat and water exchanges in vegetation and atmospheric submodels in SOLVEG.

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    The calculated curves of capture efficiency plotted against Stokes number Stk and horizontal wind speed |U| with the droplet diameter of 15 μm, for (a) needle leaves and (b) broad leaves, respectively.

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    (a) Change of mean droplet diameter of cloud water dependence on total liquid cloud water content for the observations (open circles), this study (solid line), Joslin et al. (1990) (open squares), McFarlane et al. (1992) (dashed line), and Sävijarvi and Räisänen (1998) (dot–dashed line). (b) Change of liquid water content in each bin according to the droplet diameter of the bin at the Waldstein site during September 2001.

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    Temporal changes of (a) net radiation Rnet, (b) sensible heat flux H, and (c) latent heat flux lE over the canopy at the Waldstein site during September 2000 (solid lines: calculations by this model; open circles: observations).

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    Time series of (a) turbulent and (b) gravitational cloud water fluxes over the canopy at the Waldstein site in October 2001 (solid lines and open circles indicate computations and observations, respectively).

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    Comparisons of calculated and measured values for (a) turbulent and (b) gravitational cloud water fluxes over the canopy over the model test period.

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    (a) Deposition velocity measurements. Deposition velocity calculations by (b) mod-SOLVEG, (c) the Lovett model, (d) original SOLVEG, (e) original SOLVEG plus capture efficiency calculations, and (f) original SOLVEG plus capture efficiency and cloud DSD calculations based on horizontal wind speed over the canopy. Linear regressions are shown as solid lines. Note that for the Lovett model calculations only data from September–December 2000 were used because of a lack of data in 2001.

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    Deposition velocity of cloud water on (a) needle leaves and (b) broad leaves plotted against horizontal wind speed over the canopy. In (b), linear regression curves in the cases of characteristic leaf length dleaf of 10 (thin solid line), 30 (thick solid line), and 50 (dot–dashed line) mm calculated with the mod-SOLVEG model as well as the curve derived from field experiments (dashed line) are also shown.

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    Deposition velocity Vdep (circles) and aerodynamic (r−1a) (triangles) and canopy (r−1c) (plus signs) conductances of cloud water transfer for coniferous trees with a height of 10 m and varying LAI plotted against horizontal wind speed over the canopy. Solid lines are linear regression lines for Vdep.

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    (a) Changes of the slope of deposition velocity of cloud water A with change in total LAD. Values are also given for experiments done at various forests: Waldstein (star), Holwerda et al. (2006) (large open circle), Lovett (1984) (large open square), Kowalski and Vong (1999) (large open diamond), and Dasch (1988) (large open triangle). The smaller symbols in (a) represent the heights of canopies. (b) As in (a), but for LAD > 0.2 for this study.

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Development of a Land Surface Model Including Cloud Water Deposition on Vegetation

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  • 1 Japan Atomic Energy Agency, Tokai, Ibaraki, Japan
  • | 2 University of Münster, Münster, Germany
  • | 3 ETH Zürich, Zurich, Switzerland
  • | 4 University of Bern, Bern, Switzerland
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Abstract

A land surface model including cloud (fog) water deposition on vegetation was developed to better predict the heat and water exchanges between the biosphere and atmosphere. A new scheme to calculate cloud water deposition on vegetation was implemented in this model. High performance of the model was confirmed by comparison of calculated heat and cloud water flux over a forest with measurements. The new model provided a better prediction of measured turbulent and gravitational fluxes of cloud water over the canopy than the commonly used cloud water deposition model. In addition, simple linear relationships between wind speed over the canopy (|U|) and deposition velocity of cloud water (Vdep) were found both in measurements and in the calculations. Numerical experiments using the model were performed to study the influences of two types of leaves (needle and broad leaves) and canopy structure parameters (total leaf area index and canopy height) on Vdep. When the size of broad leaves is small, they can capture larger amounts of cloud water than needle leaves with the same canopy structure. The relationship between aerodynamic and canopy conductances for cloud water at a given total leaf area density (LAD) strongly influenced Vdep. From this, it was found that trees whose LAD ≈ 0.1 m2 m−3 are the most efficient structures for cloud water deposition. A simple expression for the slope of Vdep plotted against LAD obtained from the experiments can be useful for predicting total cloud water deposition to forests on large spatial scales.

Corresponding author address: Genki Katata, Japan Atomic Energy Agency, 2-4 Shirakata-shirane, Tokai, Ibaraki 319-1195, Japan. Email: katata.genki@jaea.go.jp

Abstract

A land surface model including cloud (fog) water deposition on vegetation was developed to better predict the heat and water exchanges between the biosphere and atmosphere. A new scheme to calculate cloud water deposition on vegetation was implemented in this model. High performance of the model was confirmed by comparison of calculated heat and cloud water flux over a forest with measurements. The new model provided a better prediction of measured turbulent and gravitational fluxes of cloud water over the canopy than the commonly used cloud water deposition model. In addition, simple linear relationships between wind speed over the canopy (|U|) and deposition velocity of cloud water (Vdep) were found both in measurements and in the calculations. Numerical experiments using the model were performed to study the influences of two types of leaves (needle and broad leaves) and canopy structure parameters (total leaf area index and canopy height) on Vdep. When the size of broad leaves is small, they can capture larger amounts of cloud water than needle leaves with the same canopy structure. The relationship between aerodynamic and canopy conductances for cloud water at a given total leaf area density (LAD) strongly influenced Vdep. From this, it was found that trees whose LAD ≈ 0.1 m2 m−3 are the most efficient structures for cloud water deposition. A simple expression for the slope of Vdep plotted against LAD obtained from the experiments can be useful for predicting total cloud water deposition to forests on large spatial scales.

Corresponding author address: Genki Katata, Japan Atomic Energy Agency, 2-4 Shirakata-shirane, Tokai, Ibaraki 319-1195, Japan. Email: katata.genki@jaea.go.jp

1. Introduction

Cloud water (or fog) deposition has long been recognized to be an important factor in the water balance of mountainous vegetation, especially in arid and semiarid regions. Under temperate climates, water for vegetation is supplied sufficiently by rainfall: more than 800–1000 mm yr−1 in most locations. In contrast, vegetation surviving in arid and semiarid areas generally has to cope with insufficient precipitation. Fog may be an important water resource in such regions. Fog occurring at the surface boundary layer is transported downward by turbulence generated by the strong wind shears at terrestrial surfaces such as plant canopies and is captured by these canopies. If the cloud water captured on foliar and woody surfaces of plants does not exceed the storage capacity of the canopy during a cloud water deposition episode, the water is later lost from the canopy to the atmosphere through surface evaporation (Juvik and Nullet 1995) or is absorbed by the wetted leaves (Burgess and Dawson 2004). If the intercepted water increases above the storage capacity, the water on the plant surfaces drips to the soil by means of throughfall and stemflow. This phenomenon is also known as fog precipitation (Hutley et al. 1997; Dawson 1998). Dripped water is finally absorbed by the root systems of plants or could potentially contribute to runoff. Moreover, several studies using stable isotope tracers have shown that fog precipitation can be used as a resource of groundwater recharge at certain locations (Ingraham and Matthews 1988, 1995; Scholl et al. 2002).

Past investigations have shown that fog precipitation accounts for a significant fraction of the total precipitation, which is the sum of rainfall and fog precipitation. On the west coast of South Africa, where annual rainfall rarely exceeds 250 mm, approximately 90% of total precipitation is fog precipitation; rainfall contributes the remaining 10% (Olivier 2002). In Oman, where annual rainfall ranges between 10 and 100 mm, fog precipitation collected by the artificial fog collectors is about 5 times the rainfall (Schemenauer and Cereceda 1994). Cereceda et al. (2002) report that fog precipitation collected by two artificial collectors for 3 half-years averaged 8.5 mm day−1, which is equivalent to more than 3000 mm year−1, on the coastal area in northern Chile. These and many more studies around the world have suggested that fog precipitation can be a valuable water resource in some arid and semiarid environments (Schemenauer and Cereceda 1991).

Several other studies have demonstrated that the uptake of the water from fog precipitation can be an important water resource also for vegetation. For example, Dawson (1998) has shown that 34% of the annual total precipitation was from fog precipitation at the coastal redwood forests in northern California. At a mountainous forest in Germany, the contribution of fog precipitation to total water input was about 9% (Klemm and Wrzesinsky 2007). Cavelier and Goldstein (1989) have found that 48% of total annual precipitation (796 mm yr−1) to the forest floor was from fog precipitation in a Colombian cloud forest. During the dry season, fog precipitation contributed 19% of total precipitation to the cloud forest in Guatemala (Holder 2006). Data collected from various cloud forests around the world show that fog precipitation can account for up to 14–28% and 15–100% of total precipitation during the wet and dry seasons, respectively (Bruijnzeel and Proctor 1993). These studies indicate that fog precipitation is probably more important for the vegetation than rainfall in arid and semiarid coastal areas.

Many numerical models have been proposed to estimate the cloud water deposition on the canopy. These models have been based on the cloud water deposition model formulated by Lovett (1984), hereinafter referred to as the Lovett model. The Lovett model is a multilayer model for atmosphere–vegetation interaction that contains equations for turbulent transfer of horizontal wind speed and cloud water content. The Lovett model has been widely used to estimate cloud water deposition because of its simple formulation (e.g., Lovett 1984; Joslin et al. 1990; Mueller et al. 1991; Miller et al. 1993; Herckes et al. 2002; Baumgardner et al. 2003). Direct comparisons of model calculations with measurements, however, have been limited until now. A recent study by Klemm et al. (2005) has indicated that calculations of cloud water flux over the forest canopy by the Lovett model overestimated measurements by the eddy covariance method by up to 32%. This overestimation most likely causes significant errors that hinder accurate prediction of cloud deposition on the forest. A more detailed model including the process of cloud water deposition is, therefore, necessary to evaluate the contribution of cloud water deposition on total precipitation in forests.

Therefore, a detailed one-dimensional vertical model called “SOLVEG” for atmosphere–vegetation–soil interaction (Yamazawa and Nagai 1997; Nagai and Yamazawa 1999) that has the potential to predict cloud water fluxes more accurately was used in this study. This model is unique in that it solves the equations of turbulent transfer of liquid water in air (fog), momentum, heat, and water vapor. However, the performance of SOLVEG has only been examined for heat and water vapor exchanges of short vegetation and semiarid bare soil areas (Nagai 2002, 2003, 2005; Katata et al. 2007); it has never been tested for cloud water deposition on high vegetation until now. The objective of this study is to validate the functions to calculate cloud water deposition on vegetation in SOLVEG. Model calculations of net radiation, sensible and latent heat, and cloud water fluxes over the canopy were compared with flux measurements carried out at the Waldstein site in Germany (Burkard et al. 2001a, b, 2002). Necessary modifications of existing processes in and addition of new processes to the original SOLVEG code were done prior to this comparison. Numerical experiments using the modified SOLVEG (hereinafter called mod-SOLVEG) were also performed to evaluate the dependence of cloud water deposition on plant leaf characteristics and structure.

2. Observational data

Data from a study at the Waldstein site in Germany (Burkard et al. 2001a, b, 2002; Klemm and Wrzesinsky 2007) were used for model validation. That study focused on the relevance of rain and cloud (fog) water deposition processes on the pollutant and nutrient cycles of this ecosystem. The Waldstein site is located in the Fichtelgebirge mountain range in northeastern Bavaria (50°08′32″N, 11°52′04″E, 775 m above sea level), shown in Fig. 1. Micrometeorological and cloud water data were observed from September to December in 2000 and from May in 2001 to March in 2002. The forest is a Norway spruce [Picea abies (L.) Karst.] monoculture. Detailed site and observational descriptions can be found in Klemm et al. (2005).

Meteorological observations of radiation (upward and downward fluxes of shortwave and longwave radiation), wind speed and direction, air temperature and humidity, and precipitation throughout the entire period were conducted at the site. The data were measured every 10 s, and 10-min mean values were stored using a datalogger. Sensible and latent heat fluxes over the canopy were measured by the eddy covariance method (Rebmann et al. 2004). The eddy covariance measuring system consists of a sonic anemometer (Solent R2 from Gill Instruments, Ltd.) and a closed path analyzer (LI6262 from Li-Cor, Inc.) for high-frequency measurements of wind components, air temperature, and water vapor. The data were recorded with a frequency of 20.8 Hz in a computer, and the sensible and latent heat fluxes were calculated as 30-min mean values. The quality of measured fluxes was checked with the procedures described in Foken and Wichura (1996).

Cloud water fluxes over the canopy resulting from atmospheric turbulent mixing and from gravitational settlement were measured separately. Turbulent cloud water flux was quantified with a three-dimensional sonic anemometer (R.M. Young Co. 81000) in combination with an active high-speed FM-100 cloud particle spectrometer (Droplet Measurement Technologies, Inc.). Both instruments were placed on a rotating platform on a tower rising 31 m above the ground and were pointed into the wind to establish isoaxial sampling conditions. Raw data were recorded at 12.5 Hz and were averaged every 30 min. This direct flux measurement method can be sufficiently accurate to obtain reliable data on cloud water deposition (Eugster et al. 2001). Cloud water content was observed by the FM-100, which counts all droplets with diameters from 2 to 50 μm and categorizes them into 40 particle size bins (Thalmann et al. 2002). Liquid water content was then computed using the geometric mean volumes of each size bin multiplied by the respective droplet counts. Gravitational flux was calculated with Stokes’s settling velocity for each size class and integrated over the full size range.

3. Model structure and modifications

SOLVEG consists of one-dimensional multilayer submodels for atmosphere, soil, and vegetation with a radiation transfer scheme for calculating the transmission of solar and longwave radiation fluxes in the canopy layer. The variables from the bottom of soil layer to the top of air layer were integrated numerically using an implicit finite-difference method and a Gaussian elimination method. In this study, the atmosphere and vegetation components of SOLVEG were modified to model the cloud water deposition process more precisely. A detailed description of SOLVEG can be found in Nagai (2004). Basic equations for atmosphere and vegetation submodels and the newly incorporated processes are described here.

a. Basic equations for atmosphere and vegetation submodels

In the atmospheric submodel, there is a one-dimensional diffusion equation for cloud liquid water content in the atmosphere wf (kg kg−1):
i1558-8432-47-8-2129-e1
where t is the time (s), z is the height in the atmosphere (m), Kz is the vertical turbulence diffusivity for wf calculated by the turbulence closure model (Yamada 1981) (m2 s−1), Fsed is the gravitational flux of cloud water (kg m−2 s−1), a is the leaf area density at each canopy layer (m−2 m−3), Ecap is the capture rate of cloud water by leaves (kg m−2 s−1), Ef is the evaporation or condensation rate of cloud water (kg m−3 s−1), Ecol and Epr are the capture rate of cloud water by rain droplets and the evaporation rate of rain droplets (kg m−3 s−1), respectively, and ρ is the density of air (kg m−3).
The vegetation submodel calculates the leaf surface water for each canopy layer wd (kg m−2), the vertical liquid water flux in the canopy Pr (kg m−2 s−1), and the leaf temperature Tc (K). The value of wd is determined by the following equation:
i1558-8432-47-8-2129-e2
where Eint is the water exchange resulting from the interception of precipitation by leaves (kg m−2 s−1), Ed is the evaporation rate of leaf surface water (kg m−2 s−1), and Pd is the drip from leaves (kg m−2 s−1). Flux Pr is calculated by the following equation:
i1558-8432-47-8-2129-e3
and Tc is calculated by solving the leaf surface heat budget equation
i1558-8432-47-8-2129-e4
where Rc, Hc, Es, and Hp are the net radiation, sensible heat flux (W m−2), transpiration rate (kg m−2 s−1), and cooling by precipitation (W m−2), respectively, and l is the latent heat of vaporization (J kg−1). Each of these terms is determined by the leaf temperature and variables from the atmospheric and radiation submodels. Figure 2 summarizes the above processes of heat and water exchange in the atmospheric and vegetation submodels.

b. Capture efficiency of cloud water droplets

In mod-SOLVEG, cloud water deposition on the canopy Ecap is expressed by the following equations:
i1558-8432-47-8-2129-e5
i1558-8432-47-8-2129-e6
where ε is the capture efficiency of leaves for cloud water (unitless), Ff is the shielding coefficient for cloud water in horizontal direction (unitless), |u| is the wind speed (m s−1), kp is the averaged projection coefficient of an individual leaf for cloud water (unitless), and Δz is the thickness of the canopy layer at height z (m), respectively. The average projection coefficient of radiation flux on an individual leaf was introduced in the original SOLVEG (Nagai 2003). In the current study, we applied this coefficient of radiation flux to cloud water kp, with the result that Ff incorporates the decrease of effective leaf surface area intercepting cloud water below the total leaf area because of the inclination of leaf surface and the overlap of leaves. The original SOLVEG is based on the assumption that all cloud water droplet trajectories are perpendicular to the leaves and that the droplets are all captured (i.e., ε = 1). However, ε is usually less than 1 because the droplets moving toward the leaf surfaces travel along curved streamlines that lead beyond the leaf, and only by loss of the inertia of the droplets are they intercepted by leaves, according to a theory of droplet impaction (Chamberlain 1975). In the current study, ε is calculated with the following empirical function of the Stokes number Stk (unitless) (Peters and Eiden 1992):
i1558-8432-47-8-2129-e7
i1558-8432-47-8-2129-e8
where α, β, and γ are unitless fitting parameters, ρw is the density of water (kg m−3), dp is the droplet diameter of cloud water (μm), ν is the viscosity coefficient of air (kg m−1 s−1), and dleaf is the characteristic leaf length (m). The curves of ε computed for needle and broad leaves with a dp of 15 μm are shown in Fig. 3. A summary of the parameters used in (7) is given in Table 1. The curve of ε for needle leaves begins to rise at higher Stk than for broad leaves, but both approach unity with increasing Stk and wind speed. This is similar to an older study that showed that ε for a disk (representing a broad leaf) is larger than that for a cylinder (representing a needle leaf) for the same Stk (May and Clifford 1967).

c. Gravitational flux of cloud water

Total cloud water flux over the canopy is the sum of the turbulent flux, caused by atmospheric turbulent mixing, and the gravitational flux [Fsed in (1)], which cannot be neglected when cloud droplets are large or wind speed is low (Lovett 1984). According to Stokes’s law, Fsed for each cloud water droplet is given as
i1558-8432-47-8-2129-e9
i1558-8432-47-8-2129-e10
where υs is the sedimentation velocity of cloud water droplets (m s−1), g is the gravitational acceleration (m s−2), and μ is the viscosity of air (m2 s−1). In considering Fsed, Ecap for each cloud water droplet calculated by (5) can be expressed as
i1558-8432-47-8-2129-e11
where Fυ is the shielding coefficient for cloud water in the vertical direction (unitless) and is assumed to be equal to Ff .

d. Droplet size distribution of cloud water

Because Ecap varies with the droplet diameter of cloud water dp, the droplet size distribution (DSD) is required for the calculation of ε for all cloud droplets. Although the DSD is generally a site-specific parameter and varies greatly with studies (Klemm et al. 2005), the following modified gamma distribution (Deirmendjian 1969) has been applied to describe the DSD:
i1558-8432-47-8-2129-e12
i1558-8432-47-8-2129-e13
where f (dp) is the probability density (unitless) for cloud water droplets with diameter dp; a, p, and q are constants; and b is a function of dmod, which is the mode diameter of the droplet (μm). Note that dmod is approximately equal to mean droplet diameter [dmean (μm)], which in the Waldstein data is
i1558-8432-47-8-2129-e14
Figure 4 shows the change of dmean with change in liquid water content and compares measured and calculated DSD. Equation (14) has a better correlation with observations (R2 = 0.818) than do other equations and correlates well with the data from other experimental studies as well (Fig. 4a). Because the calculations with (12) were in good agreement with measured DSD (Fig. 4b), (12) can be used to predict the change of the DSD with change in liquid water content.
By considering the DSD, total capture of cloud water by leaves is represented by
i1558-8432-47-8-2129-e15
where dpmax and dpmin are the maximum and minimum diameters among cloud water in all present cloud droplets (μm), set to 5dmean and 0 μm, respectively. In mod-SOLVEG, 100 bins from dpmin to dpmax, each with an increment of 1 μm, are integrated.

e. Phase change processes for cloud water

To describe evaporation and condensation processes of cloud water, the following mass transfer submodel was introduced in mod-SOLVEG. The evaporation or condensation rate of cloud water droplets with dp [Ef(dp)] is determined by
i1558-8432-47-8-2129-e16
where kf(dp) is the mass transfer coefficient for cloud droplets (m s−1), Af(dp) is the liquid vapor interfacial area per weight of cloud water droplets (m2 m−3), and qsat and qa are the saturated and air specific humidity (kg kg−1), respectively. By assuming that all cloud water droplets are of spherical shape, kf(dp) is calculated as follows:
i1558-8432-47-8-2129-e17
where a value of 2 represents the Sherwood number of liquid water droplet at rest (Ranz and Marshall 1952) and Dυ is the diffusion coefficient of water vapor (m2 s−1). Using the volume [(4/3)π(dp/2)3] and surface area [4π(dp/2)2] of a cloud droplet, Af(dp) can be described as
i1558-8432-47-8-2129-e18
where the second term on the middle of (18) is the number density of cloud water droplets with dp (m−3). Last, total evaporation/condensation of cloud water Ef in (1), expressed as Ef(dp), is integrated from dpmin to dpmax by using (17) and (18), as in the case of the Ecap calculation.

f. Evaporation and condensation process on the leaf surface

The water vapor flux from leaf surface to the atmosphere is divided into two components: transpiration Es and evaporation from leaf surface water Ed in (2), expressed as
i1558-8432-47-8-2129-e19
i1558-8432-47-8-2129-e20
where R′ = (rars + rard + rsrd) and ra, rd, and rs are evaporation resistances of the laminar leaf boundary layer, the leaf surface water, and the stomata of the leaves, respectively. Resistance ra and the total of rd and rs are in series, but rd and rs are in parallel because evaporation from leaf surface water and evaporation from transpiration only occur from leaf surface water and stomata, respectively. The value of rs used in the model is that given by Nagai (2004). Resistance ra is expressed using a generic transfer coefficient that accounts for the influence of wind speed and object shape and size estimated by mass transport theory (Magarey et al. 2005) as
i1558-8432-47-8-2129-e21
i1558-8432-47-8-2129-e22
where wdw is the leaf surface water amount where there is maximum evaporation (Deardorff 1978) (kg m−3) and cw and cd are the vapor exchange coefficients between leaf and canopy air for wet and dry leaf surfaces, respectively (m0.5 s−0.5). The value of c varies from cw to cd with a change of leaf wetness fraction (wd/wdw). The values of cw and cd were determined from experiments that investigated the drying of water droplets on an artificial leaf surface representing a typical hydrophobic leaf surface; the best estimates were 2.582 × 10−2 and 1.123 × 10−1 m0.5 s−0.5, respectively (Magarey et al. 2005). The SOLVEG model uses the formulation of rd expressed as
i1558-8432-47-8-2129-e23
When water partially exists on the leaf, the balance of Es and Ed is controlled by total resistance of rd and rs connected in parallel. When the leaf is completely dry, rd has the value of infinity because xd, representing leaf wetness fraction, is zero; this results in Ed = 0 by (20). In contrast, when leaf surface is covered with water sufficiently (wd > wdw), rd = 0 because of the fact that xd = 1. As a result, Es = 0 as calculated by (19).

Evaporation (or condensation) on the leaf surface affects the energy balance at the plant–atmosphere interface: as such, it should be taken into account whenever exchange processes within the canopy are being analyzed. Condensation appears to be a major sink for available energy in the early morning and appears to affect the actual canopy temperature, as reported by Agam and Berliner (2006).

g. Comparison with the Lovett model

To evaluate the performance of mod-SOLVEG, comparisons with the widely used cloud water deposition model formulated by Lovett (1984) were performed. In the Lovett model, total deposition flux of cloud water on the vegetation Ftot (kg m−2 s−1) is predicted from the following equations:
i1558-8432-47-8-2129-e24
i1558-8432-47-8-2129-e25
where r−1tot is the total conductance of cloud water transfer, which is equal to the deposition velocity Vdep (m s−1), ra and rc are the aerodynamic and canopy resistances to cloud water transfer at each atmosphere and canopy layer, respectively (s m−1), i is the number of atmosphere and canopy layers (unitless), and zh and zr are the heights of the canopy and of the top boundary of the atmospheric submodel, respectively (m). Resistance rtot is computed from the integrated values of ra and rc throughout all atmospheric and canopy layers.

The Lovell model does not predict air temperature and humidity in the canopy; it follows that evapotranspiration and evaporation from wet leaf surfaces cannot be calculated. Moreover, turbulent diffusivities of momentum and cloud water are calculated from a simple exponential equation using wind speed and liquid water content at the upper boundary and cumulative surface area density. In contrast, mod-SOLVEG models both the processes of evapotranspiration and evaporation from wet leaf surfaces, and turbulent diffusivities can be calculated with the SOLVEG model, which uses a high-order closure approach, resulting in accurate predictions of profiles of wind speed, air temperature, humidity, and liquid water content.

h. Model parameters and simulation conditions

Values of parameters and grids for atmospheric, soil, and vegetation submodels are provided in Table 1. The forest is divided into layers of 1-m depth each. Among the upper boundary conditions between the vegetation canopy and atmosphere that were set, the incoming shortwave and longwave radiation, precipitation, air temperature, wind speed, and specific humidity at the 31-m level were set, and liquid water content at the 32-m level above the ground surface was set. The initial and lower boundary conditions of soil temperature and volumetric soil water content were set to constant values (12.5°C and 0.2 m3 m−3, respectively; see Table 1). The parameters and simulation conditions for the Lovett model have been summarized by Klemm et al. (2005).

4. Performance tests

Simulations by mod-SOLVEG using measured data from the Waldstein site were carried out. The results were compared with measurements from September to December 2000 and from May to November 2001. Measurements of turbulent and gravitational fluxes of cloud water over the canopy were compared with the model calculations throughout the period. In 2000, predicted net radiation and sensible and latent heat fluxes were also compared with measurements. Note that coordinated universal time (UTC) was used for the simulation.

Temporal changes in calculated and measured net radiation and sensible and latent heat fluxes are shown in Fig. 5. Only the calculations of mod-SOLVEG are depicted in this figure because the Lovett model does not predict heat fluxes over the canopy. Diurnal changes of the sensible and latent heat fluxes over the canopy calculated with mod-SOLVEG agreed very well with measurements. These results show that mod-SOLVEG is capable of predicting the process of turbulent diffusion of heat and water vapor.

The time series of the turbulent and gravitational cloud water fluxes over the canopy are shown in Fig. 6. This shows that mod-SOLVEG can reproduce the dynamical behavior of turbulent and gravitational cloud water fluxes in measurements very well. Figure 7 summarizes comparisons of mod-SOLVEG results with the observations of turbulent and gravitational cloud water fluxes over the canopy during the whole simulation period. The root-mean-square error (RMSE) and the average difference (AD) of the scatterplot of calculations versus observations for both fluxes have a very small value (RMSE = 3.8 and 0.1 and AD = −0.7 and −0.0034 mg m−2 s−1 for turbulent and gravitational fluxes, respectively). These results indicate that mod-SOLVEG can provide accurate predictions of the cloud water deposition over the coniferous forest, even at half-hourly temporal resolution.

Figure 8 depicts the deposition velocity Vdep (m s−1), obtained from the total cloud water flux Ftot divided by cloud water content over the canopy, plotted against absolute value of horizontal wind speed at the height of the top boundary |U| (m s−1). Only measurements and calculations when cloud water content over the canopy was around 120 mg m−3 are plotted. In comparing Figs. 8a and 8b, it is seen that the slope of the Vdep curve in mod-SOLVEG (0.248) agrees well with that of the measurements (0.242). This result indicates that the following linear relationship between |U| and Vdep can be used to predict cloud water deposition:
i1558-8432-47-8-2129-e26
where A is a constant that depends on vegetation characteristics. Such simple formulations have been made in previously reported experimental and numerical studies (Ruijgrok et al. 1997; Zhang et al. 2001; Holwerda et al. 2006). Total cloud water deposition during the whole simulation period was 61.0 mm in measurements, 67.5 mm for mod-SOLVEG in calculations, and 69.7 mm in calculations using (26): that is, a simple linear formulation predicted the amount of cloud water deposition with an error of 13%. This accuracy is at least clearly better than the error of 32% from the calculation by the Lovett model (Klemm et al. 2005). The linear expression can therefore provide a good estimation of the amount of cloud water deposition on a yearly basis. We found that meteorological variables other than horizontal wind speed do not have a large effect on A. For the DSD of cloud water, it is found that Vdep increases with the size of cloud water droplets. This effect is, however, much smaller than that of the linear relationship represented in (26). From a practical point of view (i.e., avoiding complicated formulation if possible), the simple formulation of Vdep using the slope A and wind speed can provide an adequate estimation of cloud water deposition. If (26) is adapted to express Vdep for all types of vegetation, we can easily estimate cloud water deposition using the slope A determined by mod-SOLVEG calculations, and the only data needed are wind speed and liquid water content over the canopy. The impact of vegetation characteristics on the slope A is discussed later.

Comparison between mod-SOLVEG and the original SOLVEG (Figs. 8b and 8d, respectively) shows that the newly incorporated processes of mod-SOLVEG clearly improved the prediction of Vdep. In particular, the incorporation of a calculation function of capture efficiency ε reduced cloud water deposition considerably (cf. Figs. 8d and 8e). The decrease depends on |U|, which ranged between 0 and 7 m s−1 (0 < Stk < 10; Fig. 3a) and thus yielded ε in the range from 0 to 0.63 at this site. Values of Vdep are further reduced by considering the DSD of cloud water, resulting in an additional improvement of the model performance in reproducing the measurements (cf. Figs. 8f and 8a). The difference in the slope A of Figs. 8b and 8f indicates that the gravitational cloud water flux Fsed contributes 10.9% of total cloud water flux and is only significant at low wind speeds. This result is similar to prior reported numerical analyses (Lovett 1984). Note that Ef did not affect Vdep in the tests because of its small amount (not shown).

In Fig. 8c, the Lovett model yielded a value of A that was 1.73 times that of the measurements. Such an overestimation by the computations of the Lovett model on a monthly basis has also been reported by Klemm et al. (2005). Here, the superiority of the calculations of cloud water deposition by mod-SOLVEG is clear (Fig. 8b).

5. Influence of vegetation features on deposition velocity

To determine the dependence of Vdep on vegetation characteristics and to validate (26), we used mod-SOLVEG to carry out a set of numerical experiments. First, the experiments for two vegetation types, with needle leaves and broad leaves of varying dleaf, were performed to evaluate the influence of leaf shapes and sizes on Vdep. Second, the sensitivity of Vdep on coniferous trees to various combinations of total leaf area index (LAI) and canopy height was tested. All combinations of canopy heights of 4, 6, 10, 14, 18, 22, 26, 30, and 34 m with LAIs of 0.1, 0.5, 1, 2, 3, 4, 5, 6, 7, and 8 m2 m−2 were used for this test. All experiments were performed using the same simulation conditions as those for the performance tests, except that meteorological data from September of 2000 at the Waldstein site were used as the boundary condition 10 m above the top of the canopy. Note that the LAI divided by canopy height is defined as the total leaf area density (LAD) here.

a. Effect of leaf shape and sizes

Calculated Vdep for the trees with needle leaves and broad leaves as a function of horizontal wind speed over the canopy are shown in Fig. 9. LAI and canopy height for both types of tree were set to 2.1 m2 m−2 and 3.0 m, respectively. The slope of Vdep for broad-leaved trees agreed with turbulence measurements collected by Holwerda et al. (2006) in a broad-leaved forest whose LAI and canopy height are the same as these calculations (Fig. 9b). It is clear that Vdep of both trees linearly increases with wind speed and, under the same LAI and canopy height, a coniferous tree can capture a larger amount of cloud water than can a broad-leaved tree with 30- and 50-mm dleaf. This difference is due to the fact that dleaf of a broad leaf, which is 30 or 50 times that of a needle leaf, exhibits considerable decreases of ε at a certain |U| (Fig. 3). Similar results were found in a past investigation that showed that conifers are more efficient fog catchers than are broad-leaved trees (Went 1955).

However, when the dleaf of a broad leaf is 10 mm, the above relation between the Vdep of trees with needle leaves and broad leaves reverses; that is, Vdep for broad leaf is greater than Vdep for needle leaf, corresponding to their ε ratio, given the same Stk (Fig. 3). It is thus considered that, when the characteristic length of a broad leaf is small, the broad-leaved tree captures the same or larger amounts of cloud water as a coniferous tree with the same canopy height and LAI. Results indicate that cloud water deposition is significantly affected by differences of leaf shapes and sizes.

b. Impact of canopy height and leaf area index

To investigate the factors determining the |U| dependence of Vdep, we considered aerodynamic, canopy, and total resistances to cloud water transfer as introduced by the Lovett model. Similar to the Lovett model, components of rtot are calculated with (25) except for Fsed/(ρwf), whose contribution to rtot is smaller than those of ra and rc. Resistances ra(zi) and rc(zi) in (25) are expressed as follows:
i1558-8432-47-8-2129-e27
i1558-8432-47-8-2129-e28
where cw0 is the bulk coefficient for cloud water at the ground surface (unitless). Note that rc differs from stomatal resistance rs in (20)—that is, rc represents the resistance to cloud water deposition on vegetation as shown in (28). Figure 10 shows total (r−1tot; i.e., Vdep), aerodynamic (r−1a) and canopy conductances (r−1c) for coniferous trees with a height of 10 m and varying LAI. When LAI is small, rc dominates rtot. With an increase of LAI, rc is not as important for rtot (Figs. 10a–c) because a larger amount of cloud water can be captured by trees with higher LAI. In contrast, when LAI > 3, ra contributes more to rtot than does rc, especially in the range of high wind speeds (|U| > 3–4 m s−1 in Figs. 10d–f); that is, ra becomes an important limiting factor to control Vdep at high wind speeds. As a result, Vdep decreases with an increase of LAI in the range of high LAI. Results indicate that the |U| dependence of Vdep is determined by the balance of aerodynamics and canopy resistances at a given LAI.

To summarize the above discussion, dependence of the slope A on LAD is shown in Fig. 11a. Selected measurements of A from other studies are also plotted in the figure. The general trend of total cloud water deposition was almost the same as A (not shown). When LAD is small, A also has small values because rc inhibits increase of cloud water deposition velocity. This limitation gradually disappears with an increase in LAD, meaning an increase of leaf surface areas where cloud water can be captured. The optimum is reached at LAD ≈ 0.1 m2 m−3. Further increases in LAD decrease A because ra begins to control Vdep; in other words, cloud water in the air penetrates less through the canopy. As a result, high LAD blocks the air and reduces total cloud water deposition. It can be seen that trees whose LAD ≈ 0.1 m2 m−3 are the most efficient for cloud water deposition to the canopy.

In section 4, the linear regression curve provided a good estimation of total cloud water deposition at the Waldstein forest. This suggests that a linear expression of Vdep can still be useful to predict total cloud water deposition on the forests with high LAI and LAD. For LAD > 0.2 m2 m−3, the following simple expression for A with good correlation (R2 = 0.928) was obtained from our numerical experiments (Fig. 11b):
i1558-8432-47-8-2129-e29
where m is the unit meters. Because many cloud forests have a large LAD (LAD > 0.2 m2 m−3) as shown in Fig. 11a, it is considered that (29) can be widely used to predict cloud water deposition in these forests.

6. Conclusions

This paper addressed cloud water deposition processes on vegetation. A detailed one-dimensional vegetation model including these processes was developed. Simulations by mod-SOLVEG were carried out to examine its ability to predict net radiation, sensible and latent heat, and cloud water fluxes in the spruce forest at the Waldstein site. Calculations of mod-SOLVEG were compared with those of the widely used cloud water deposition model formulated by Lovett (1984) (the Lovett model): mod-SOLVEG predicted turbulent and gravitational fluxes of cloud water over the canopy accurately, whereas the Lovett model overestimated these measurements. There was clear improvement in the calculations of cloud water deposition by mod-SOLVEG throughout the simulation periods over the original SOLVEG and the Lovett model. Moreover, simple linear relationships between wind speed over the canopy |U| and deposition velocity of cloud water Vdep were found both in measurements and calculations. The overall performance of mod-SOLVEG for predicting heat flux and cloud water deposition over the canopy was validated.

Numerical experiments using mod-SOLVEG were performed to study the impact of vegetation characteristics on the cloud water deposition process. First, the difference in cloud water deposition on trees with needle leaves and broad leaves was tested. With the same LAI and canopy height, needle leaves can capture larger amounts of cloud water than can broad leaves with large characteristic leaf lengths dleaf. In contrast, when dleaf of broad leaves is small, broad-leaved trees can capture the same or larger amounts of cloud water than can coniferous trees. Second, numerical experiments of Vdep on coniferous trees under various combinations of total leaf area index and canopy height were carried out. The inverse relationship between aerodynamic and canopy resistances to cloud water as a function of wind speed at a given total leaf area density strongly influenced Vdep. From this, we found that trees whose LAD was approximately 0.1 m2 m−3 are the most efficient structures for cloud water deposition.

A simple function for the slope of Vdep against LAD was obtained from numerical experiments. This function should become a useful tool for studying cloud water deposition in forests on regional to global scales; it can be used to estimate monthly or yearly cloud water deposition solely from atmosphere liquid water content (which often can be estimated by visibility) and |U| above the canopy. Continuous observations of these variables are frequently performed in long-term studies (e.g., Klemm et al. 2005). With the modifications made in mod-SOLVEG as presented here, this model is now suited for application on larger spatial scales.

Acknowledgments

The authors are grateful to Drs. H. Ueda, T. Foken, H. Yamazawa, H. Ishikawa, F. Griessbaum, A. Held, M. Kajino, and M. Yamada for their helpful discussion and criticism. This study was supported by the Research Revolution Plan 2002 (RR 2002) of the Ministry of Education, Culture, Sports, Science, and Technology.

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Fig. 1.
Fig. 1.

Location of the Waldstein site in the Fichtelgebirge Mountains in Germany.

Citation: Journal of Applied Meteorology and Climatology 47, 8; 10.1175/2008JAMC1758.1

Fig. 2.
Fig. 2.

Schematic diagram of the processes of heat and water exchanges in vegetation and atmospheric submodels in SOLVEG.

Citation: Journal of Applied Meteorology and Climatology 47, 8; 10.1175/2008JAMC1758.1

Fig. 3.
Fig. 3.

The calculated curves of capture efficiency plotted against Stokes number Stk and horizontal wind speed |U| with the droplet diameter of 15 μm, for (a) needle leaves and (b) broad leaves, respectively.

Citation: Journal of Applied Meteorology and Climatology 47, 8; 10.1175/2008JAMC1758.1

Fig. 4.
Fig. 4.

(a) Change of mean droplet diameter of cloud water dependence on total liquid cloud water content for the observations (open circles), this study (solid line), Joslin et al. (1990) (open squares), McFarlane et al. (1992) (dashed line), and Sävijarvi and Räisänen (1998) (dot–dashed line). (b) Change of liquid water content in each bin according to the droplet diameter of the bin at the Waldstein site during September 2001.

Citation: Journal of Applied Meteorology and Climatology 47, 8; 10.1175/2008JAMC1758.1

Fig. 5.
Fig. 5.

Temporal changes of (a) net radiation Rnet, (b) sensible heat flux H, and (c) latent heat flux lE over the canopy at the Waldstein site during September 2000 (solid lines: calculations by this model; open circles: observations).

Citation: Journal of Applied Meteorology and Climatology 47, 8; 10.1175/2008JAMC1758.1

Fig. 6.
Fig. 6.

Time series of (a) turbulent and (b) gravitational cloud water fluxes over the canopy at the Waldstein site in October 2001 (solid lines and open circles indicate computations and observations, respectively).

Citation: Journal of Applied Meteorology and Climatology 47, 8; 10.1175/2008JAMC1758.1

Fig. 7.
Fig. 7.

Comparisons of calculated and measured values for (a) turbulent and (b) gravitational cloud water fluxes over the canopy over the model test period.

Citation: Journal of Applied Meteorology and Climatology 47, 8; 10.1175/2008JAMC1758.1

Fig. 8.
Fig. 8.

(a) Deposition velocity measurements. Deposition velocity calculations by (b) mod-SOLVEG, (c) the Lovett model, (d) original SOLVEG, (e) original SOLVEG plus capture efficiency calculations, and (f) original SOLVEG plus capture efficiency and cloud DSD calculations based on horizontal wind speed over the canopy. Linear regressions are shown as solid lines. Note that for the Lovett model calculations only data from September–December 2000 were used because of a lack of data in 2001.

Citation: Journal of Applied Meteorology and Climatology 47, 8; 10.1175/2008JAMC1758.1

Fig. 9.
Fig. 9.

Deposition velocity of cloud water on (a) needle leaves and (b) broad leaves plotted against horizontal wind speed over the canopy. In (b), linear regression curves in the cases of characteristic leaf length dleaf of 10 (thin solid line), 30 (thick solid line), and 50 (dot–dashed line) mm calculated with the mod-SOLVEG model as well as the curve derived from field experiments (dashed line) are also shown.

Citation: Journal of Applied Meteorology and Climatology 47, 8; 10.1175/2008JAMC1758.1

Fig. 10.
Fig. 10.

Deposition velocity Vdep (circles) and aerodynamic (r−1a) (triangles) and canopy (r−1c) (plus signs) conductances of cloud water transfer for coniferous trees with a height of 10 m and varying LAI plotted against horizontal wind speed over the canopy. Solid lines are linear regression lines for Vdep.

Citation: Journal of Applied Meteorology and Climatology 47, 8; 10.1175/2008JAMC1758.1

Fig. 11.
Fig. 11.

(a) Changes of the slope of deposition velocity of cloud water A with change in total LAD. Values are also given for experiments done at various forests: Waldstein (star), Holwerda et al. (2006) (large open circle), Lovett (1984) (large open square), Kowalski and Vong (1999) (large open diamond), and Dasch (1988) (large open triangle). The smaller symbols in (a) represent the heights of canopies. (b) As in (a), but for LAD > 0.2 for this study.

Citation: Journal of Applied Meteorology and Climatology 47, 8; 10.1175/2008JAMC1758.1

Table 1.

Model grids and vegetation parameters used in the calculations.

Table 1.
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