Estimating cloud water deposition to subalpine spruce-fir forests—I. Modifications to an existing model

Atmospheric Environment Vol. 25A, No. 5/6, pp. 1093-1104, 1991. Printed in Great Britain.

0004-6981/91 $3.00+0.00 Pergamon Press plc

ESTIMATING CLOUD WATER DEPOSITION TO SUBALPINE SPRUCE-FIR FORESTS--I. MODIFICATIONS TO AN EXISTING MODEL STEPHEN F. MUELLER Tennessee Valley Authority, Muscle Shoals, AL 35660, U.S.A.

(First received 16 March 1990 and in final form 19 September 1990) Abstraet--A previously published steady*state model for computing cloud water deposition to a subalpine balsam fir (Abies balsamea) forest was modified for more generalized application to spruce-fir forests. One modification provided options for describing the cloud droplet size spectrum using observed relationships, in the vicinity of high elevation forests, between cloud liquid water content and the distribution of droplet size. Another modification implemented an optional experimental droplet collection efficiency parameterization scheme. This scheme computes collection efficiencyfor the most dense portion of a tree by treating it as a bulk collector rather than a multi-component (stems, branches, etc.) structure for which collection efficiencyis determined by the individual collection efficienciesof its components. A study of model sensitivity to various physical parameterizations revealed that computations of gross cloud water flux to a canopy are most sensitive to canopy inhomogeneity, the relationship between cloud liquid water content and droplet size spectrum, and droplet collection effÉciency.As expected, sensitivitytest results also indicated that computed evaporation (and hence, the computed net cloud water flux) of intercepted cloud water from a canopy is strongly dependent on net radiation. The model modificationsand sensitivity studies described here are the prelude to a test of the model described in a companion paper.

Key word index: Acid deposition, cloud or occult deposition, deposition model, spruce or fir forest, forest meteorology. 1. INTRODUCTION Cloud water deposition is believed to have a major role in determining the chemical deposition and hydrologic budgets for some high elevation forests (see, for example, Nagel, 1956; Kerfoot, 1968; Vogelmann, 1973; Falconer and Falconer, 1980; Schemenauer, 1986). The Mountain Cloud Chemistry Project* (MCCP) has monitored conditions in high elevation spruce-fir forests (Sisterson et al., 1990) to determine the relative importance of the three deposition mechanisms (dry, precipitation and cloud) for various chemical species that are capable of affecting forest health and vitality. Mueller and Weatherford (1988) recently concluded, based on deposition models and high elevation MCCP measurements, that cloud inputs of important chemical species such as sulfate and nitrate probably constitute a large portion of the overall chemical deposition budget for some high elevation forest stands. Difficulty was encountered in extending this analysis to longer time periods and more sites. Specifically, model estimates of the contribution of cloud water to the total water input to the forests appeared to be too high when compared with similar estimates based on canopy throughfall data. It became apparent that a closer examination was

* MCCP research is supported by the U.S. Environmental Protection Agency and the U.S. Forest Service as part of the Forest Response Program of the National Acid Precipitation Assessment Program.

needed of the performance of the cloud water deposition model. A description of the model, with recent modifications, and the results of an analysis of model output sensitivity to physical parameterizations are presented here.

2. CHANGESTO THE ORIGINALCLOUD DEPOSITION MOD~L The cloud deposition model (CDM) used by the MCCP to estimate cloud water flux to a spruce-fir canopy is a modified version of the model that Lovett (1984) developed for a balsam fir (Abies balsamea) canopy on Mt. Moosilauke, New Hampshire. Lovett's model represents an extension of the earlier concepts of Shuttleworth (1979), who developed a single-layer, steady-state model of cloud deposition to vegetation canopies. The Appendix briefly describes the original Lovett model, but the reader should refer to Lovett's 1984 paper for a more complete description. Several substantive changes were made in Lovett's original model to make it applicable to different canopies on different mountains. An option was also added for a modified droplet collection efficiency parameterization scheme. These changes are described here in detail. Lovett built his model around a balsam fir canopy that he had studied in great detail, measuring many of its characteristics. The canopy structure was characterized by nine component types such as twigs and

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STEPHEN F. MUELLER

boles. Surface area indices (described in the Appendix) were determined by multiple-regression equations that related surface area of each component type at any height to dimensions of the bole and crown (Lovett, 1981). This type of canopy detail is generally not available for MCCP research sites. 2.1. Simulating different canopy structures The approach used to generalize the model was to allow the user to input canopy height, projected leaf surface area index and the ratio of total leaf area to the total surface area of all components. Canopy height is a required input, whereas the other two inputs are optional. Fortunately, the general morphologies of spruce and fir trees are very similar, with both growing to similar heights (spruce are longer lived and may grow somewhat taller). Thus, it is not unreasonable, as a first estimate, to use the component distribution by height of Lovett's Mt. Moosilauke balsam fir canopy to represent fir and spruce canopies at other locations. The CDM was given an option that uses the input canopy height to scale the vertical canopy structure. This autoscaling option divides the canopy into nominal 1-m deep layers above 1.37 m (this is the height at the bottom of the layers in Lovett's model and was selected because it represents the standard "breast height" at which foresters measure bole diameter). The alternative to this option is to input site-specific canopy structure data directly into the model. Lovett's canopy was 10.6 m tall. For canopies shorter than this, the autoscaling option shortens the relatively barren section of bole below the crown while keeping the full length of the crown. For the shortest canopies (the smallest canopy height the model will accept is about 5.5 m), the vertical surface area profile is identical to that of the crown. Surface area for canopies taller than that at Mt. Moosilauke is computed by adding a sufficient number of layers of relatively barren bole (i.e. as in Lovett's lowest canopy layer) to the total surface area of the Mt. Moosilauke canopy. Thus, bole layers are simply added or removed (the crown raised or lowered) to approximate the vertical surface area profile in the canopy of interest. This approach appears to produce satisfactory results for the test canopy simulations described in the companion paper (Mueller et al., 1991). The ratio (r) of total leaf area to total surface area can vary considerably from site to site. Leaf surface is the most important of all component surfaces because it generally composes the greatest fraction of the total surface area (as opposed to branches or boles) and because the droplet collection efficiency is greatest for the leaf (needle) component. For example, the Mt. Moosilauke canopy had an r value of about 0.8 (the default value in the model). The C D M user can adjust the model canopy surface area distribution by selecting a value for r different from the model default value. The model also accepts input of a specific leaf area index (leaf surface area divided by ground area). Input

of this index along with r allows a user to specify directly the leaf and total surface area index of a canopy to be modeled.

2.2. Generalizing canopy micrometeorology The CDM user must select a value for the wind speed extinction coefficient (~t) to determine the incanopy wind speed profile. Lovett found ~t= 0.27 for his Mt. Moosilauke canopy. The extinction coefficient determines, along with the profile of surface area, the vertical positioning and magnitude of the wind shear in the top portion of the canopy. The relationship, expressed by (A.2) in the Appendix, between the wind speed and surface area profiles is consistent with the findings of other investigators, such as Kinerson and Fritschen (1971). Use of ct=0.27 and the Mt. Moosilauke surface area profile produces a wind speed profile in the crown space that is not inconsistent with profiles measured by Kinerson and Fritschen in a Douglas fir (Pseudotsuga menziesii) forest and Oliver (1971) in a mixed pine forest. Another significant change from Lovett's original model is in the manner the model determines the zero plane displacement (d) and the roughness length (Zo) in the canopy in the absence of values for direct input. These parameters are needed for estimating eddy diffusivity and vertical cloud droplet transport. Originally, the values were fixed because they had been determined directly for the Mt. Moosilauke canopy. Later, Lovett and Reiners (1986) applied a technique based on the work of Thom (1971) to estimate d and Zo from information on the vertical surface area and wind speed profiles over a fiat surface. The method determines d as the mean level of momentum absorption within the canopy, and is described by Lovett and Reiners (1986) who used it to study the effect of changing canopy structure on cloud water deposition rates. The value of d is computed as au(z) 1 a(z) z dz

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where Zbi and Za are the heights of the bottom and top of layer i, respectively. In addition, z o is computed using Zo = Cd (H -- d) A a, (2) which was derived from a formula suggested by Lettau (1969). Here Ca is the average drag coefficient for individual needles and branches above a height of d,

Estimating cloud water deposition--l. and A d is the total surface area index for the portion of the canopy above d. Lovett and Reiners used 0.1 as the value of Cd. Equations (1) and (2) are used in the model without regard to terrain slope. The significance of this practice for the accuracy of CDM deposition estimates depends on the importance of turbulent droplet transport estimates. The assumption that vertical turbulent diffusion controls droplet flux into the canopy is fundamental to the CDM. The diffusion process is parameterized in the model using gradient transport t h e o r y - - G T T (see Appendix for details)--and requires knowledge of the vertical profile of eddy diffusivity (K) for vertical droplet diffusion. Corrsin's (1974) guidelines on the limitations of GTT indicate that the theory is not applicable to droplet diffusion unless the length scale of turbulence is much less than the length scale determined by the curvature of the scalar profile (e.g. of momentum or mass) associated with the property being transported. Studies of turbulence in tall canopies such as forests have found that G T T is not consistent with observations of momentum flux (see, for example, Baldocchi and Meyers, 1988). Thus, it is possible that Lovett's use of eddy diffusivity (Lovett assumes the droplet and momentum diffusivities, K a and Kin, are equal) for controlling the vertical rate of droplet transport will not adequately simulate the diffusion of cloud water into a forest. Another possibility, with the surface area available for collecting droplets usually being concentrated in the top few meters of a spruce-fir forest along with the highest wind speeds and concentrations of liquid water, is that the exact shape of the liquid water content (W) profile (and hence, the applicability of GTT) is fairly irrelevant because the largest proportion of water is deposited in the canopy top. Tests are needed to determine the extent to which nonconformity to GTT restrictions affects CDM results. The vertical profile of droplet eddy diffusivity (Kd) in the CDM was modified to be consistent with Thorn (1971). Therefore, all model runs assume K d is constant with height from H down to H/3, and then decreases linearly to zero below H/3. Other K d profiles were tested, including the original profile represented by (A.2) with ct=0.14. However, model sensitivity to the K d profile was quite small (Table 1) and is disregarded hereafter. 2.3. Simulatino differences in cloud microphysics

The original model used predetermined values of the droplet terminal fall speed, vt. The CDM computes vt for different droplet size classes and for canopies at different elevations. Thus, Lovett's model was modified to compute the average vt for each droplet size class using Stokes' Law and the root-mean-square droplet diameter of the class (the rms diameter was used because vt varies by the droplet diameter squared). This approach is valid for droplets up to about 80/~m diameter (Rogers, 1976).

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Fig. 1. Locations of the MCCP research sites: Howland, Maine; Mt. Moosilauke, New Hampshire; Whiteface Mt., New York; Shenandoah National Park, Virginia; Whitetop Mt., Virginia; Mt. Mitchell, North Carolina.

The droplet size spectrum used by Lovett was replaced by spectra derived from data collected during cloud events at the summits of Whiteface Mountain, New York (elevation 1483 m) and Whitetop Mountain, Virginia (elevation 1686 m). The locations of these and other MCCP sites are illustrated in Fig. 1. The summer 1982 Whiteface and autumn 1987 Whitetop droplet spectra were obtained using a forward scattering spectrometer probe (FSSP). An FSSP counts the number of droplets in several size bins by sensing the light scattered by each droplet as it passes through a red laser beam. For experimental purposes the CDM was modified to either allow use of a fixed droplet size spectrum or to let the spectrum be selected by the model depending on the cloud liquid water content (14/) that is input by the user. Lovett (1984) got reasonably good results with the model using a fixed droplet size spectrum. However, cloud physics theory suggests--as supported by the Whiteface and Whitetop FSSP d a t a - - t h a t there is a relationship between the droplet size spectrum and the value of W. Examples of the Whiteface and Whitetop size spectra are plotted in Fig. 2. The change in shape of the droplet size spectrum with W is consistent with the hypothesis that higher liquid water contents are usually associated with cloud parcels having longer lifetimes (i.e. lower cloud bases relative to the height of the canopy of interest). Lower relative cloud bases imply a greater depth of cloud, a greater amount of water condensation within the cloud at mountaintop, and greater opportunity for droplet growth to produce relatively large droplets with diameters in excess of 10-20 #m.

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DropletDiameter(pro) Fig. 2. Relative cloud droplet size spectra determined from data collected at (a) Whiteface Mt. and (b) Whitetop Mt. and (c) used by Lovett for Mt. Moosilauke. Spectra for three values of liquid water content (IT')are shown. Droplet concentrations have been divided by the maximum modal droplet concentration to get relative concentration.

Lovett (1984) assumed a modal droplet diameter of 10 #m, based on the work of Grunow (1960) in fog, when he tested his model. Data from Whitetop indicated that the mean modal diameter varied from 7 to 9 pm over three intervals of W covering the range of 0.01--0.4 g m-3. By contrast, Whiteface data showed a much larger range in W(values greater than 1.0 g m - 3 were not uncommon) with mean modal droplet dia-

meter varying between about 2 and 16 #m. In addition, Whiteface spectra suggested a slower decline in droplet number concentration with increasing diameter than at Whitetop for W>0.3 g m -3. This can significantly affect the magnitude of computed sedimentation and gross cloud water deposition flux (F,). Distributions of W for all MCCP sites indicated that Whiteface clouds were unique relative to the

Estimating cloud water deposition--I. other sites. Thus, use of site-specific droplet spectra is preferred, especially when testing the CDM against onsite data. 2.4. Handling inhomogeneity effects The existence of canopy inhomogeneity (clearings; abrupt changes in canopy structure) and sloping terrain can lead to localized increases in cloud deposition relative to a fiat, homogeneous canopy. At a canopy edge, horizontal (defined as parallel to the ground) cloud water advection is expected to be the predominant mechanism, rather than vertical turbulent transport, for transporting water into a canopy. The vertical profiles of wind speed and liquid water content at an edge would be different from those profiles within a canopy far from an edge. Terrain slope can also affect airflow through the canopy by aiding the formation of large, persistent eddies or by streamline compression (confluence). These effects could enhance deposition by creating droplet-laden airflows (streamlines) that enter the canopy from above at rates exceeding those due to turbulence over a fiat canopy. The Lovett model does not simulate these conditions. Lovett's model was modified to allow a simulation of the upper limit to cloud water collection at a canopy edge or in the presence of streamlines entering a canopy. The changes involved use of a different vertical wind speed profile and the elimination of turbulence as the factor controlling the vertical distribution of cloud water. For an edge situation d is assumed to be zero, making the wind speed profile logarithmic from a height of z o. This is most likely to be valid for the near-neutral conditions believed prevalent during cloud impaction events. The model treatment of liquid water content was also modified to force W to be the same at all canopy levels. This was also done in simulations by Lovett and Reiners (1986). Such an approach obviously represents an unlikely extreme, and is used here only to put an upper bound on the deposition estimate. A clearing may not have sufficient fetch to allow the wind speed profile to adjust completely to the theoretical shape for neutral conditions, and the clearing surface may be more complex than is implied by assuming d = 0. The exact effect of slopeinduced eddies on in-canopy wind speed and liquid water profiles is unknown, but may cause some increase in wind speed and turbulence in at least the top portion of forest. 2.5. Droplet collection efficiency options Lovett (1984) estimated droplet collection efficiency (e) for all tree component classes using an empirical relationship, developed in a wind tunnel study by Thorne et al. (1982), between e and the dimensionless Stokes number (S): S = Pd Op2 u

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where Pa and p, are the droplet and air densities, Dp is droplet diameter, u is the free stream air speed, v is the kinematic viscosity of air and Dc is the effective length scale of the tree component. Lovett's model computes S at each model level for each combination of droplet size class and tree component type. The mathematical expression (A.1) used in the model relates In(e.) to a third-degree polynomial of In (S). However, by determining e in this manner Lovett assumed that each twig and branch at a given height level was exposed to the same wind speed and population of droplets. Observations of Whitetop Mountain trees exposed to cloud reveal that the downwind portion of a tree is typically relatively dry while the upwind portion collects many water droplets. It is possible that, for the denser tree crowns, so many favorably-sized cloud droplets are scavenged from the airstream at the leading (upwind) edge of the tree that little deposition can occur on the lee side. In addition, the density of foliage in a tree crown is such that the air speed upstream from the crown is unlikely to be representative of the mean air speed (u) within the crown. Grant (1983) studied the characteristics of airflow near spruce twigs and found that the u within the downwind wake of a twig was decreased relative to the upwind free-stream speed by 20-90% when the free-stream speed was 2.5 m s-1. This reduction extended to about 0.4 m beyond the twig. Thus, many of the tree components in a crown lie within the wakes of upwind components. Collection efficiency calculations that rely on canopy wind speed profile d a t a - typically collected in spaces between tree crowns--are likely to overestimate e because of the expected draginduced reduction of air speed within each crown. Joslin et al. (1991) recently investigated the cloud water collection efficiency of 'whole' trees (including a Norway spruce--Picea abies) on Whitetop. They found that, for long ( > 10 h) cloud immersion events having relatively few periods of intermittent cloud, collection efficiency (e) for the spruce varied approximately linearly with In (u W). The slope of e vs In (u W) linear regressions were nearly the same as that computed by Lovett's (1984) scheme, but e values computed by Joslin et al. (1991) were substantially lower (Fig. 3). The average e--ln (u W) relationship during the long cloud events can be expressed as e= 0.1056 In (uW) + 0.0133.

(4)

This expression is valid only for uW>0.285 g m - 2 s - 1. Although based on 63 h of data, (4) must be considered experimental at this stage because it is based on data for only one tree. In addition, (4) is only applicable to the most dense portions of a t r e e - portions in which leaf area composes at least 90% of the total surface area. Figure 3 illustrates the differences between e computed by (4) and e computed by the Lovett model for the top 3 m of a typical forest with 0
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Where r ~<0.85, only the individual component values are used. This experimental parameterization scheme for e is not expected to be precise; it is somewhat arbitrary in its choice of layers for application (for example, using r=0.85 as the lower cutoff limit for adjustments of individual tree component values of ~) and in its degree of adjustment. It is not meant to represent a final solution to the problem. Instead, it is illustrative of the importance of developing a better understanding of the t r e e , d r o p l e t collection efficiency phenomenon. A more refined study of the relationship between e and tree morphology is needed.

3. MODEL SENSITIVITYTO VARIOUSPHYSICAL PARAMETERIZATIONS

3.1. M e t h o d o l o o y Table 1. Model response ranked by decreasing sensitivity to some selected parameterizations Parameterization Canopy homogeneity Droplet size spectra Droplet capture efficiency Evaporation1" SAI§ profile-wind profile Turbulence (Ka) profile

Response* (%) 300-400 200 100 50:~ 50 20

* Variation in gross and net cloud water deposition flux relative to the base case scenario described in the text. t Affects net flux only. :~Difference between no evaporation and effect of maximum probable evaporation. § Surface area index.

g m - 3 . The top of the forest canopy (according to Lovett's Mt. Moosilauke tree component data) represents that part of the canopy most similar in foliage density to the tree used in the Joslin et al. study. The computed values of e decrease at higher wind speeds because of an observed decline in e when S > 1 0 (Thorne et al., 1982). At its maximum difference, the Lovett model value of e is almost a factor of 3 greater than the whole tree value. This is consistent with expectations arising from the foliar clustering effects previously mentioned, and represents a potentially large bias in computed cloud water flux values. The CDM was modified to include an option for an experimental droplet collection efficiency parameterization. The experimental scheme attempts to include the effects of the denser foliar clustering in the top portions of a forest canopy crown. The scheme models cloud water flux in the topmost model layer with derived from J oslin et a l. (1991 ) if r - - t h e ratio of leaf to total surface area--is at least 0.9 (the r value of the studied spruce). The value of e in underlying layers having r>0.85 is computed as the average of the individual component (Lovett) and whole tree values.

The CDM was examined to determine the relative importance of various parameterizations to model output values. However, this sensitivity study was not meant to be a detailed examination of all parameters (both input and internal) in the model. The model response to input parameters such as wind speed and surface area index has been previously described (Lovett, 1984; Lovett and Reiners, 1986). Instead, this study was aimed at discovering model sensitivity to parameterizations, such as droplet size distribution and the vertical surface area profile, that are sources of substantial uncertainty because of the desire to apply the model at locations other than that for which it was originally designed. The relative importance of each parameterization examined here is given in Table I. The values in the response column illustrate the approximate upper limit to the sensitivity of computed flux for nominal conditions. These conditions are those that are typical (not necessarily average) at an M C C P site when substantial cloud deposition is expected. The canopy structure used for this sensitivity study was very similar to that used by Lovett (1984) for his Mt. Moosilauke site. The differences between his study and this work were that the canopy height used here was greater (12 m vs 10.6 m), the leaf-to-total surface area ratio was smaller (0.6 vs 0.8), and the total surface area index was larger (9.6 vs 7.6). Lovett's original collection efficiency parameterization was used for all sensitivity tests except when directly examining effects of the ~ parameterization. The 'base case' wind speed extinction coefficient equalled Lovett's value of 0.27. The 'nominal' meteorological conditions (defining the base case) were: canopy top wind speed (uH) of 4 m s-1, canopy top cloud liquid water content of 0.4gin -3, air temperature of 10°C, air pressure of 83.5 kPa, relative humidity of 100%, zero net radiation, d=9.3 m and z o = 0.6 m. Using Whiteface droplet size spectra (allowed to vary with water content by interpolating droplet number concentration in each size class ttsing spectra at fixed reference values of

Estimating cloud water deposition--I. W), these conditions resulted in a computed gross cloud deposition flux, Fj (and F , because evaporation was 0), to a homogeneous canopy of 0.77 mm h - 1 The procedure followed to determine model sensitivity was to run the model while varying one particular parameterization over a realistic range of conditions whenever possible. For example, in examining the effect of the Lovett droplet collection efficiency scheme, e values were varied over a range representing the degree of uncertainty in the empirical collection efficiency formulation caused by the scatter in the experimental data. A much larger range of values could have been selected, but would not have furthered the goals of this analysis. 3.2. Canopy homooeneity Figure 4 illustrates the effect of the edge enhancement parameterization on computed flux using both Whiteface and Whitetop droplet size distributions. Computed flux was less than 1.0 mm h-1 over most of the range of 0 ~
between these key values, with the spectra remaining fixed for W<0.05 gm -3 and W>0.85 g m -3. Droplet size affects the droplet collection efficiency (e) of the canopy surfaces because e is an empirical function of Stokes' number, S, as defined in (3). The morphological differences between spruce and fir needles (spruce needles are nearly cylindrical whereas fir needles are more flattened) and not believed to be significant given the experimental uncertainty in the wind tunnel data (Thorne et al., 1982). Thorne et al. believed that their experimental results may possibly be generalized to a broader range of coniferous canopy components. Their data indicated that e reached a maximum of about 0.5 for S = 10 and decreased for larger values of S, possibly because of droplet blowoff. The experimental data do not provide information on e for S > 60; for S > 60 Lovett's original model uses the value of e at S = 60. Droplet size also affects the droplet sedimentation rate. The relative magnitude of turbulent deposition to sedimentation for different values of W, and hence, different size spectra, is given in Table 2. Using Whiteface spectra, turbulent deposition was found to be 10 times larger than sedimentation (in the model base case) for very small values of W, but was about

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The shape of the optional droplet size spectra (Fig. 2) was the second most influential parameterization. Five different Whiteface spectra (not all are illustrated in Fig. 2) are used to represent five values of liquid water content: 0.05, 0.2, 0.4, 0.6 and 0.85 g m -3. Smooth transitions in the spectra are computed for W

Fig. 4. Variation of computed cloud water deposition flux with canopy-top wind speed for the homogeneous (closed canopy) and inhomogeneous model parameterizations. Model response differences, due to the different Whiteface and Whitetop droplet size spectra, are illustrated.

Table 2. Ratio of computed turbulent flux to sedimentation flux for selected values of liquid water content (un = 4 m s- 1). Droplet size spectra

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1100

STEPHEN F . MUELLER

equal to sedimentation for W>0.3 g m -a. This dramatic shift in the importance of sedimentation flux did not occur using Whitetop size spectra because of the smaller variations in spectral characteristics. The overall differences in Fg, resulting from use of different droplet spectra, are illustrated in Fig. 5. The Whiteface spectra, with their relatively large concentrations of large (diameter > 10 pm) droplets, caused a rapid increase in sedimentation and total flux for W>0.2 g m - 3 . The Lovett (1984) and Whitetop spectra produced results that were similar to each other and distinctly different from results based on Whiteface spectra. 3.4. Vertical canopy structure The earlier description of the method used to estimate zero plane displacement (d) and roughness length (Zo) hinted at the intimate relationship between

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canopy micrometeorology and structure. The vertical distribution of canopy surface area strongly influences wind speed and the intensity of shear-induced turbulence. The model default vertical surface area profile (based on Lovett's balsam fir canopy data) and two other profiles were used in a simulation of surface area profile effects on computed canopy d and Zo. The three profiles are illustrated in Fig. 6a for a canopy of 12 m high. The model default profile peaked at about 3 m below the canopy top. A slightly modified profile had its peak shifted downward an additional 3 m, while the third profile represented a completely inverted form of the default profile. Total surface area index was the same for each profile. The effect of the profile shape on d, z 0, and Fg is illustrated in Fig. 6b. Note that d/H increased continuously for increasing H using the 'normal' (default) and modified profiles, and decreased continuously with increasing H using the inverted profile. The behaviour of zo/H and F s was equally complex. The normal profile appeared to produce the smallest flux estimates for most values of H, although the magnitudes of F s for the three profiles were fairly similar. The inverted profile was used to investigate the model's properties only, and is not expected to be very common for spruce-fir canopies. The modified profile could be representative of a spruce-fir canopy containing trees of mixed heights, but would probably not represent an undisturbed mature spruce-fir canopy having trees of fairly uniform height. The computed water fluxes associated with the modified and inverted profiles are mostly larger than those for the normal profile because of the usually larger computed values of Zo and Kd for the modified and inverted profiles.

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0.2 t4

He~ ofCaaop/Top(m)

Fig. 6. (a) Illustration of the three test canopy surface area vertical profiles, expressed as surface area index per model layer, and (b) comparison of model responses to the three test profiles for canopies of different heights.

Estimating cloud water deposition--I. 3.5. Vertical wind speed structure Computed flux can also be affected by varying the in-canopy wind speed profile (done here by varying the wind speed extinction coefficient, ~t). Different speed profiles affect estimates of d, z 0, and diffusivity (Kd). Figure 7 illustrates the effect of ct for two different droplet size spectra. The model appeared to be only slightly sensitive when ct > 0.2. Lovett's value for ct falls between the extremes in sensitivity. Hence, if ~=0.27 is incorrectly assumed for a given situation, then the error could lead to a slight overestimate or a moderate-to-large underestimate of F~. 3.6. Droplet collection efficiency Uncertainty as to the appropriate choice of a droplet collection efficiency (e) parameterization can have a significant influence on model-based estimates of cloud water flux. The responses of the CDM to the two parameterizations previously described were somewhat different. In this series of model test runs, the leaf area index was held constant as the value of r was varied from 0.6 to 0.9. Thus, as r increased, the total surface area index decreased. The effect was to decrease the computed values of F s with increasing r. The smallest difference was found--using both sets of droplet size spectra--between the original Lovett collection efficiency scheme and the modified scheme for r = 0.6. In these cases, the layer-specific leaf area density was less than 0.85 (the threshold for triggering adjustments to e in the modified scheme) for all but one model layer. The discrepancy in model response increased as r increased to 0.9 and more layers exceeded the threshold. For this upper end of the range in r, the maximum difference in F~ computed using the Whiteface droplet spectra occurred at a wind speed of about 6 m s - 1. Smaller differences occurred at higher speeds because of the previously described empirical dependence of e on the Stokes number and wind speed in the Lovett scheme. In general, the CDM sensitivity to the e parameterization was greater for the Whitetop droplet spectra (Fig. 8). The smaller droplets of these

2o]

1101

spectra were less likely to trigger the e decline (see Fig. 3) characteristic of the Lovett scheme. Hence, the computed values of F~ for the two parameterizations diverged continuously with increasing wind speed. The maximum uncertainty in computed Fg due to the choice of ~ parameterization--for the examined range of r, wind speed and droplet spectra was about 40%. However, the correct form of the parameterization is unknown, so that the actual uncertainty may be larger. It is interesting to note that, for the Lovett scheme parameterization, the computational uncertainty in F~ attributable to experimental uncertainty in ~ is quite large. The maximum CDM response (Fg computational uncertainty about 100%) to the uncertainty in e exceeds the maximum response to uncertainty due to the choice of parameterization scheme. The effect of the noise in the ~ experimental data was determined by placing upper and lower bounds on the published, experimentally-derived estimates of e (Thorne et al., 1982). The largest computational uncertainty in Fg introduced by experimental noise in ~ occurs when liquid water content is low and wind speed is high. 3.7. Net radiation profile Computed F . was found to be relatively insensitive to the in-canopy profile of net radiation (R,). The Lovett profile produced a ground estimate of R,, for the base case canopy, that was 1% of the canopy-top value. Values of F . were not very sensitive to changes in the R, extinction coefficient. The sharp-gradient R. profile measured by Lovett (1984) is consistent with the findings of other studies of coniferous and deciduous canopies [several examples are cited by Munn (1966), Kinerson (1973)].

Lovett scheme (r=06} n 0 Lovett scheme (r=0.9) JA E×peri~ental scheme (r=06) B - - - - - . B ~I.0 Experimental scheme (r=O 9) h-. . . . A £

,~

//~ //,~ ~1///

"c" \

[ \"\ _o 00.2

0.5

'

oo

W',,,dS~ (m/s)

0.o

o.o

oT,

oT=

oT,

oT,

oT,

o.

a

Fig. 7. Variation of computed cloud water flux with wind speed extinction coefficient (ct)for two droplet size spectra (W=0.4 gm-3).

Fig. 8. Variation of computed cloud water flux with canopy-top wind speed for two values of leaf-to-total surface area ratio (r) and two alternative droplet collection efficiency schemes (Whitetop droplet size spectra only).

1102

STEPHEN F. MUELLER

3.8. Evaporation The sensitivity of F n to evaporation (E) was determined by examing F , over the range of uncertainty (as determined by data from Whitetop) in relative humidity (96-100%) and a realistic range (5th to 95th percentile values based on Whitetop observations) of canopy-top R n values (10-200 W m - 2 ) during cloud impaction events. As shown in Table 3, computed F . is more sensitive to Rn than to relative humidity, with the relative uncertainty in Fn decreasing as liquid water content increases. F o r example, at 98% relative humidity and W=0.4 g m -3, if Rn is unknown then assuming R n = 100 W m -2 can result in an error in computed F . of as large as _ 25%. The potential error grows to +__467% when W = 0 , 2 g m -3. Conversely, assuming a relative humidity of 98% when W =0.4 g m -3 yields a potential error of + 12% at R~ = 1 0 0 W m -2 which grows to +200% when W =0.2 g m -3. With 7 ~-;ng more sensitive to Rn, it is fortunate that R, can Je determined with greater accuracy over its typical range of values than can humidity over the range of 96-100%. 3.9. Other aspects of model sensitivity The model sensitivity results presented here are primarily of interest when one considers using the model at different sites where little or no detailed site characterization has been done. Other work, such as conducted by Lovett (1984) and Lovett and Reiners (1986), has demonstrated the importance of accurately knowing canopy-top wind speed and liquid water content, and the impact of canopy height and surface area index, even when the other internal parameterizations are nearly 'perfect'. The companion paper (Mueller et al., 1991) describes the influence of uncertainty in various model inputs on computed cloud water flux.

4. SUMMARYAND CONCLUSIONS The original Lovett cloud water deposition model was modified to enable a more generalized application

of the model to subalpine spruce-fir forests. The most significant changes involved adding options to enable the model user to customize the model for application to a particular site. These options allow the user to: • compute d and Zo rather than inputting observed values; • modify the built-in canopy structure data or replace them completely with site-specific data; • select various cloud droplet size spectra, some of which are varied with liquid water content; • choose between two different droplet collection efficiency parameterizations; • compute an upper limit to cloud deposition flux to non-homogeneous ot sloping canopies. As previously found by Lovett and Reiners (1986), computed estimates of the maximum deposition enhancement at a canopy edge are many times larger than computed deposition to a homogeneous canopy. Also, use of site-specific relationships between the droplet size spectrum and liquid water content can lead to large differences in computed cloud water deposition flux. Computed flux is slightly sensitive to changes in vertical canopy structure, but more sensitive to differences in the wind speed profile. The model is sensitive to uncertainty in droplet collection efficiency (E). Modest variations (relative to the base case) in canopy component mix (leaf-to-total surface area ratio, r) and total surface area index produce only small effects on deposition flux when the original Lovett e parameterization is used. The model is more sensitive to r when the experimental e parameterization is selected. Canopy-top net radiation is needed for realistic estimates of net water deposition flux. There is an obvious need to test the CDM against 'real-world' data. A companion paper describes such a test using canopy throughfall data from the MCCP Whitetop Mountain site (operated by the Tennessee Valley Authority, a member of the MCCP research consortium).

Acknowledgements--Thisproject has required the cooperation and efforts of many individuals. The author is indebted

Table 3. Uncertainty in computed net cloud water flux (F,) due to uncertainty in net radiation (Rn) and relative humidity (r.h.)

R.h. (Wgm -3) 96 98 100

0.2 0.4 0.2 0.4 0.2 0.4

Relative uncertainty (%) in F. due to R. being unknown* +483 + 28 +467 + 25 4-161 __+ 22

R,(Wm -2) 0 100 200

(Wgm -a)

Relative uncertainty (%) in F. due to r.h. uncertaintyt

0.2 0.4 0.2 0.4 0.2 0.4

_ 38 + 9 +200 4- 12 + 59 4- 14

* Ninety per cent confidence interval for R~ in clouds is about 0-200 W m- 2 (Whitetop data). Uncertainty magnitude computed relative to value of Fn when R. = 100 Wm -2. t Humidity sensor not accurate for r.h. I>96%. Uncertainty magnitude computed relative to value of F, when r.h. =98%.

Estimating cloud water deposition--I. to Gary Lovett (Institute of Ecosystem Studies) for providing his original model and for the many enlightening conversations dealing with various aspects of cloud deposition to forest canopies. I am also grateful to Michael Meyer and Garland Lala (Atmospheric Science Research Center-ASRC, State University of New York) for loaning an FSSP to measure Whitetop cloud droplet spectra, to Scott Dorris (Tennessee Valley Authority--TVA) for operating the FSSP, and to Ralph Valente (TVA) for providing an analysis of the data. Volker Mohnen (ASRC) is to be thanked for facilitating the loan of the FSSP for use at Whitetop, and for providing information on droplet size spectra at Whiteface. This research was co-funded by the following organizations: the Northeastern Forest Experiment Station, SpruceFir Research Cooperative within the joint U.S. Environmental Protection Agency (EPA)--USDA Forest Service Forest Response Program (a part of the National Acid Precipitation Assessment Program--NAPAP); a cooperative agreement with the EPA (813-934010) as part of the Mountain Cloud Chemistry Project (Volker Mohnen, Principal Investigator); TVA appropriations from the NAPAP; the TVA Office of Power. This material has not been subject to EPA, Forest Service, or TVA policy review and should not be construed to represent the policies of any of these agencies.

REFERENCES

Baldocchi D. D. and Meyers T. P. (1988) Spectral and lag correlation analysis of turbulence in a deciduous forest canopy. Boundary-Layer Met. 45, 31-58. Best A. C. (1951) Drop-size distribution in cloud and fog. Q. Jl R. met. Soc. 77, 418-426. Corrsin S. (1974) Limitations of gradient transport models in random walks and in turbulence. Adv. Geophys. 18A, 25-60. Falconer R. E. and Falconer P. D. (1980) Determination of cloud water acidity at a mountaintop observatory in the Adirondack Mountains of New York State. J. geophys. Res. 85, 7465-7470. Grunow J. (1960) The productiveness of fog precipitation in relation to the cloud droplet spectrum. In Physics of Precipitation (edited by H. Weickmann), pp. 110-117. Geophysical Monograph No. 5; American Geophysical Union, Washington, D.C. Joslin J. D., Mueller S. F. and Wolfe M. H. (1991) The use of artificial and living collectors in the testing of models of cloud water deposition to forest canopies. Atmospheric Environment (in press). Kerfoot O. (1968) Mist precipitation on vegetation. For. Abstr. 29, 8-20. Kinerson R. S. (1973) Fluxes of visible and net radiation within a forest canopy. J. appl. Ecol. 10, 657-660. Kinerson R., Jr and Fritschen L. J. (1971) Modeling a coniferous forest'canopy. Agricult. Met. 8, 439-445. Lettau H. (1969) Note on aerodynamic roughness-parameter estimation on the basis of roughness-element description. J. appl. Met. 8, 828-832. Lovett G. M. (1981) Forest structure and atmospheric interactions: predictive models for subalpine balsam fir forests. Ph.D. thesis, Dartmouth College, Hanover, New Hampshire. Lovett G. M. (1984) Rates and mechanisms of cloud water deposition to a subalpine balsam fir forest. Atmospheric Environment 18, 361-371. Lovett G. M. and Reiners W. A. (1986) Canopy structure and cloud water deposition in subalpine coniferous forests. Tellus 38B, 319-327. MueUer S. F., Joslin J. D. and Wolfe M. H. (1991) Estimating cloud water deposition to subalpine spruce-fir forests-II: model testing. Atmospheric Environment 25A, 1105-1122. AE(A)

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Mueller S. F. and Weatherford F. P. (1988) Chemical deposition to a high elevation red spruce forest. Wat. Air Soil Pollut. 38, 345-363. Munn R. E. (1966) Descriptive Micrometeorology, pp. 155-157. Academic Press, New York. Nagel J. F. (1956) Fog precipitation on Table Mountain. Q. Jl R. met. Soc. 82, 452-460. Oliver H. R. (1971) Wind profiles in and above a forest canopy. Q. Jl R. met. Soc. 97, 548-553. Rogers R. R. (1976) A Short Course in Cloud Physics, p. 90. Pergamon Press, Oxford. Schemenauer R. S. (1986) Acidic deposition to forests: the 1985 Chemistry of High Elevation Fog (CHEF) Project. Atmosphere-Ocean 24, 303-328. Shuttleworth W. J. (1977) The exchange of wind-driven fog and mist between vegetation and the atmosphere. Boundary-Layer Met. 12, 463-489. Sisterson D. L., Bowersox V. C., Olsen A. R., Meyers T. P. and Vong R. L. (1990) Deposition Monitoring: Methods and Results--State-of-the Science~Technology Report 6. National Acid Precipitation Assessment Program, Washington, D.C. Thorn A. S. (1971) Momentum absorption by vegetation. Q. Jl R. met. Soc. 97, 414--428. Thorne P. G., Lovett G. M. and Reiners W. A. (1982) Experimental determination of droplet impaction on canopy components of balsam fir. J. appl. Met. 21, 14131416. Vogelmann H. W. (1973) Fog precipitation in the cloud forests of eastern Mexico. Bio. Sci. 23, 96-100. Waggoner P. E., Furnival G. M. and Reifsnyder W. E. (1969) Simulation of the microclimate in a forest. For. Sci. 15, 37-45.

APPENDIX

DESCRIPTION OF THE ORIGINAL MODEL In his original cloud water deposition model, Lovett (1984) assumes steady-state conditions in a horizontally homogeneous canopy. Although developed for studying cloud impaction on a mountain forest, the model does not explicitly treat the effects of complex terrain or canopy inhomogeneities on deposition. Lovett's model uses a multilayer scheme in which the interception of cloud water is computed for the canopy surfaces in each layer. The horizontal canopy dimension is assumed to be sufficiently large so that the addition of cloud water to each layer is due totally to vertical turbulent transport and drop sedimentation, with cloud water advection rates into and out of a given location being equal. Lovett defines nine canopy component types, the principal ones being foliated twigs of various ages and stages of needle loss (other types include boles, various sizes of bare twigs, and tree lichens). Canopy structure information input to the model is in the form of surface area indices (ratios of canopy surface area to ground area) for each model layer and canopy component type. Droplet collection efficiency (~) was determined empirically as a function of the Stokes number [defined by (3) in the main text], S: = exp [ - 1.84 + 0.90(In S)-0.11 (In S)2 - 0.04(In S)3]. (A.1) This relationship is based on collection efficiency data obtained for balsam fir tree components in a wind tunnel (Thorne et al., 1982). The model also varies droplet fall speed with droplet size. The droplet size spectrum used originally by Lovett is based on a size distribution function described by Best (1951). The model computes vertical in-canopy profiles of wind speed, vertical droplet diffusivity, and net radiation. Each

1104

STEPHEN F. MUELLER

parameter is computed as an exponentially decreasing function of the downward cumulative surface area index at level i, Ic~, using the relation

tween canopy surfaces of layers i and i - 1 (a total of n layers) is computed as (Lovett, 1984)

xi = xR e- ~m.

Pi = ri Fi + Ri ~ Fk -- ri- 1 Fi- 1,

(A.2)

In (A.2), x~ and Xa represents a meteorological parameter at levels i and H (canopy top), respectively, and ,, is the extinction coefficient for parameter x. The vertical diffusivity for cloud droplets, Ka, is assumed by Lovett to equal that for momentum (Kin). This assumption is probably reasonable for very small droplets, but would be expected to be less valid for categories of large droplets whose fall speeds are relatively large. The value for Kd is computed assuming a neutral atmosphere. This assumption is reasonable for deposition events involving thick (radiatively blocking) clouds, but may not hold true in the more transparent clouds. K d at canopy top is computed from the well-known relationship for a neutral boundary layer K d = k u, ( H - d) where k is yon Karman's constant, H is the canopy height, d is the zero plane displacement, and u, is the canopy-top friction velocity computed as u, = ku/ln [(H-d)/Zo].

(A.3)

In (A.3), z o is the aerodynamic roughness length. The rate of vertical turbulent droplet transport between model layers i and i - 1 is controlled by an aerodynamic resistence, R~, computed as

/Az,

R~=0.5[--+ \Kd,

Azz- 1 "~ /

K~,_, ,]'

where Az is the layer thickness. Within the ith layer, the rate of transfer of droplets from the air to canopy surfaces (N types) is controlled by a resultant surface resistance, r~, computed as F N [Iij'%-I-a

where r~sis the surface resistance of tree component j and lis is the surface area index of component j, both in layer i. This modeling approach is an extension of the work of Shuttleworth (1977). The potential cloud water gradient (Pl) be-

(A.4)

k=l

where Pi = Wi - Wi_ 1 and subscripted F is the total turbulent droplet flux to canopy surfaces in specific layers. The values of Fi in the model layers are the unknown quantities in this equation, and arc computed by solving a simultaneous set of equations represented by (A.4) and rewritten in matrix notation as EF] = EP] Ell] -

1,

where [ F ] is the droplet flux vector, Eli]- 1 is the inverse of the resistance matrix, and [ P ] is the liquid water potential vector. Direct sedimentation may be relatively significant for some large cloud droplets. This is especially true when wind speed is low. Lovett computes the sedimentation flux in each layer, S i,

as

where vt is the droplet fall speed, Ip,j is the horizontal projected area index of thejth component in layer i, and lp,o is the 'open space area index' (the fraction of ground area not covered by foliage) in layer i. The gross cloud water flux (Fs) to the forest canopy is the sum, over all layers, of F i and Si. An estimate of F~ is all that is needed for computing chemical deposition to a forest canopy. However, a correction for evaporation (E) or condensation (negative evaporation) must be applied if model results are to be used for comparison with canopy throughfall data. Lovett computes a net cloud water flux, F,, which is Fg -- E. The evaporation module uses net radiation at canopy top, air temperature and relative humidity in an approach previously used by Waggoner et al. (1969). The net radiation within the canopy is balanced by the energy flow in sensible and Jatent heat exchange. The evaporation process is treated in a manner that is very similar to that used to compute cloud water flux, with evaporation and sensible heat resistance computed for the various canopy components. The reader is referred to Waggoner et al. (1969) and Lovett (1984) for more details.