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Physiology and Development |
2Department of Biological Sciences, Union College, Schenectady, New York 12308 USA 3Department of Mechanical Engineering, Union College, Schenectady, New York 12308 USA
Received for publication October 31, 2000. Accepted for publication February 20, 2001.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Key Words: boundary layer • bryophyte • evaporation • fractal dimension • growth form • particle image velocimetry (PIV) • surface roughness
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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; Fitzjarrald and Moore, 1992, 1994
; Williams and Flanagan, 1996
). However, with the exception of a few measurements on excised cushions (Proctor, 1980
), little is known about the range of variation in or about the underlying mechanisms that govern water loss in bryophytes. In addition, there is no model that would allow one to predict canopy–atmosphere interactions in bryophytes based on knowledge of their canopy properties. Such a model would not only serve as a basis for understanding the contribution of bryophytes to ecosystem water flux, but would also be useful in interpreting the ecological significance of growth forms in bryophytes.
Unlike vascular plants that control water loss by the opening and closing of stomata, most bryophytes, which lack similarly organized leaves, have no short-term mechanism to limit water loss. Consequently, the ecological distribution of many bryophytes is highly sensitive to factors that affect plant water status (Gimingham and Smith, 1971
; Proctor, 1981, 1982, 1984
). However, many bryophyte species have evolved morphological structures or architectural properties that enhance water uptake, water storage, and/or limit water loss from branch and leaf surfaces (Gimingham and Birse, 1957
; Proctor, 1979, 1980
; Schofield, 1981
). Such features allow these species to avoid water loss and exploit drier habitats. In mosses in the genus Sphagnum, for example, species that persist in dry hummock environments have a dense cushion surface that limits water loss compared to species that thrive in wetter environments (Hayward and Clymo, 1983
; Titus and Wagner, 1984
).
Once on the plant surface, water lost from bryophyte leaves (i.e., microphylls) and branches diffuses through boundary layers that surround plant surfaces and the thickness of these layers governs the rate of water loss. Boundary layers can be considered regions of reduced wind velocity or still air caused by surface friction. Within this layer, water moves via molecular diffusion and not by convective flow (Gates, 1980
; Nobel, 1991
; Jones, 1992
; Schuepp, 1993
; Campbell and Norman, 1998
). The thickness of these unstirred layers provides the primary resistance to water loss in bryophytes.
Wind-tunnel measurements performed by Proctor (1980)
demonstrated that morphological differences like the presence or absence of hair points cause variation in boundary layer thickness. Architectural features of bryophyte canopies also influence plant–atmosphere exchange. Using 9 cm and smaller cushions, Proctor (1980)
found significant variation in evaporation rates among species, but there was no attempt to quantify the surface characteristics of his samples. Canopies with an open, loosely branching architecture may enhance boundary layer transfer by causing laminar flows adjacent to cushions to break up and become turbulent at high wind speeds. This phenomenon has been described for submillimeter to >10 m scale rough surfaces that include natural soil surfaces, lichens, vascular plant branches, grasslands, herbaceous wetlands, and whole-forest canopies in addition to artificial surfaces (Landsberg and Thom, 1971
; Mulhern, 1978
; Schuepp, 1982, 1984
; Fazu and Schwerdtfeger, 1989
; McNaughton, 1989
; Gurevitch and Schuepp, 1990
; Raupach, Antonia, and Rajagopalan, 1991
; Fitzjarrald and Moore, 1992, 1994
). Surface roughness, however, does not always increase mass transfer. As the density of roughness elements increases, sheltering within the flow can occur, causing a decrease in rates of mass transfer (Landsberg and Thom, 1971
; Schuepp, 1989
; Gurevitch and Schuepp, 1990
; Raupach, Antonia, and Rajagopalan, 1991
; Rice and Schuepp, 1995
). Presently there is little understanding of how exchange elements the size and structure of bryophyte canopies influence evaporation even though features of the roughness of the surface are clearly related to plant performance (Hayward and Clymo, 1983
).
In the realms of micrometeorology and fluid mechanics, investigators have grappled with ways to account for the effect of surface roughness on mass transfer. In field studies of vascular plant canopies, the depth of eddy currents that penetrate the canopy is an essential model parameter (Raupach, Antonia, and Rajagopalan, 1991
; Jones, 1992
). This value, referred to as the roughness length, together with estimates of the frontal density of roughness elements (estimated from leaf area indices) are used to model mass and heat transfer. However, given their small size, lack of a discrete substrate, and spatial heterogeneity, bryophyte canopies are difficult to assess for these features.
Bryophyte canopies are closer in scale to the rough walls studied by fluid engineers. For rough-walled surfaces, measures of the depth of the roughness elements (usually constant and known) and their spacing correlate well with wind-speed profiles and mass transfer (reviewed in Raupach, Antonia, and Rajagopalan, 1991
). Similar estimates can be obtained from bryophytes that are based on average canopy depth measurements using a contact probe. However, these measures will be sensitive to sampling scale (e.g., canopy depth measures taken at 0.5 and 1.0 cm sampling scales will give different average values if the canopy has periodic fluctuations at 1.0 cm). To date, there has been no evaluation of what an appropriate sample scale would be that would parameterize a mass transfer model for bryophytes.
Also, average canopy depth measurements will not fully characterize architectural differences among canopy types. For example, a smoothly undulating cushion and an irregularly varying one may have similar average canopy depths at a given sample scale. However, the irregular one may have greater surface area or generate turbulence more readily thereby enhancing canopy exchange. Therefore, we characterize these differences in surface pattern using techniques borrowed from the field of geostatistics. These techniques allow us to quantify the height of the roughness elements, the scale of these elements, and their surface texture (i.e., fine-scale "smoothness" of the profile). Techniques based on similar analyses have been employed successfully to describe the patterns of irregularity in plant community composition, the complexities of leaf shapes, and aspects of roughness on chemical exchange surfaces (Gibbs and Bishop, 1995
; Iannaccone and Khokha, 1996
; Dale, 1999
).
Together, estimates of the magnitude of canopy height variation (i.e., roughness height, Lr), the scale of that variation (Sr), and the fine-scale texture of the canopy (indicated by D, the fractal dimension) will provide three structural parameters that can be used to develop a predictive model that describes the exchange properties of bryophyte canopies. There is presently no quantitative model that relates canopy exchange properties of bryophyte canopies to their architecture. Such a model would be useful to estimate community plant–atmosphere exchange where water loss from bryophytes contributes significantly to ecosystem flux (e.g., boreal forests, bog and fen ecosystems). In addition, such a model would further our understanding of how growth form affects the ecological distribution of bryophytes and will aid in predicting how local environmental changes that alter the evaporative environments (i.e., change humidity or temperature such as tree fall, logging, altering hydrology) will influence bryophyte survival.
The goal of this study is to explore the relationship between evaporative and structural properties of bryophyte canopies using wind-tunnel and morphometric analyses. Unlike many vascular plant canopies, intact bryophyte cushions can be evaluated meaningfully in the laboratory. In addition, cushions are small enough in size to allow quantitative wind-tunnel studies that employ particle image velocimetry (PIV) to make full field measurements of the instantaneous velocities around the cushion. In addition to qualitatively evaluating flow over surfaces, this technique allows quantitative assessments of boundary layer properties like thickness and turbulence intensity. To accomplish our goal, we performed the following: (1) evaluated mass transfer properties for 12 bryophyte populations (11 species) that differ in structural features—these properties were assessed using evaporation and PIV techniques in a wind-tunnel; (2) characterized canopy structure in these species by analyzing canopy profile patterns for surface roughness, scale of roughness elements, and fine-scale surface texture; and (3) combined mass transfer and canopy features to develop an empirical model that predicts functional properties of bryophyte cushions.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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for mosses and Stotler and Crandall-Stotler (1977)
for liverworts. Two samples of Callicladium haldanianum were used that were collected from distinct populations. These differed in canopy morphology and were treated as independent samples in the analysis. Specimens were collected in pure samples when possible, but the following mixtures occurred: Dicranella heteromalla contained C. haldanianum; C. haldanianum [B] contained Hypnum imponens; Thuidium delicatulum contained Bartramia pomiformis and Plagiothecium laetum; and Nowellia curvifolia contained Jamesoniella autumnalis, Harpanthus drummondii, and Hypnum pallescens.
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Mass transfer measurements
Each specimen was prepared prior to measurement by trimming its container to expose the plant canopy above the rim of the container. The exposed canopy corresponded with the photosynthetic portion of the plant and ranged in depth from 1 to 3 cm. Boundary layer properties were assessed using an evaporation technique (Jones, 1992
) in a variable speed, laminar-flow wind tunnel with the exception that ethanol evaporation was used instead of water. The use of ethanol allowed briefer exposure times (20–60 s), and the results do not depend on relative humidity that can vary during longer measurements. The wind tunnel used was 122 cm long with an 18 x 18 cm cross section. Specimens were sunken into the floor of the tunnel with the canopy emerging. They were placed 70 cm from the intake, which was fitted with a flow conditioner. Free-stream turbulence intensities were 
5–8% as measured by PIV (see below). Wind speed was measured using a Pitot probe and micromanometer (Dwyer Instruments, Michigan City, Idaho, USA) and was evaluated 2 cm above the surface of the specimen. Wind speeds ranged from 0.6 to 4.2 m/s. These are similar to those found within forest and stream-side environments in our region (S. Robinson, Union College). The rate of ethanol evaporation was measured gravimetrically at 6–8 different wind speeds for each sample. To do so, the surface of each specimen was sprayed with 100% ethanol. Evaporative loss was measured by calculating the difference in mass (to nearest 0.01 g) of each specimen before and after being placed in the wind tunnel. Trials ranged from 20 to 60 s depending upon the rate of mass loss, which was held under 2 g. Evaporation rates were measured twice at each wind speed. For plants with obvious morphological anisotropy (e.g., H. splendens), samples were initially placed with branch tips oriented downstream. For the second trial, plants were rotated 90°. Analyses are based on the average of these two trials, which generally did not differ by >5%.
To account for the cooling effects of evaporation, surface temperatures of one specimen of each species were measured across the range of wind speeds. Given the difficulty of measuring surface temperatures directly on bryophyte leaves, we constructed artificial branches to estimate surface temperatures. Filter paper was tied to each of three 0.5 mm thermocouples (temperature to nearest 0.1°C; Physitemp Instruments, Clifton, New Jersey, USA). These were attached to individual branches within the bryophyte canopy. Following this preparation, two evaporation trials as outlined above were followed with temperatures recorded at 70% of sampling time (e.g., at 42 s for a 1-min trial). Surface temperatures ranged from 5° to 13°C. The linear relationships between evaporation rate and temperature depression were estimated using regression analysis. Results from these regressions were used to estimate surface temperatures during evaporation trials of other samples within the same species.
Conductance (ga, in millimeters per second) of ethanol across the boundary layer is directly related to evaporation rates and was calculated following procedures described in Jones (1992)
with changes that account for the molar mass and vapor pressure of ethanol.
Mass transfer across the boundary layer of the bryophyte canopies was evaluated using Reynolds and Sherwood numbers to characterize the flow environment and mass transfer in dimensionless values. The Reynolds number (Re = u L/
; where u = flow velocity, L = characteristic dimension, and = kinematic viscosity) represents the flow environment. Morphological features vary at different spatial scales (e.g., leaves, branches, fronds) and each of these could represent a length dimension (i.e., L) that affects boundary layer properties. In his studies of bryophyte cushions, Proctor (1980)
used the average diameter of the sample cushion as L. That allowed a convenient comparison of his results to flat plates and has been a common practice in studies of leaves of vascular plants (see Gates, 1980
; Nobel, 1991
; Campbell and Norman, 1998
). However, that measure of L does not take the length of surface roughness elements into account. Along rough surfaces, these elements dramatically influence conductance and can be described by a roughness length. In vascular plant canopies, this roughness length is measured empirically by observing wind profiles. However, we can neither define a substrate nor measure wind penetration accurately within the canopy. Therefore, we use the average height of canopy roughness elements (Lr) to distinguish different surfaces. This length has the advantage that it is measured easily from morphological features and was estimated from the morphological analysis described below. The Reynolds number derived using Lr is called the roughness Re number (Rer). For comparison with previous data, we assessed boundary layer properties using average cushion diameters (denoted L), but rely principally on Lr because it takes into account variation in surface features of the type that differ among bryophytes.
The Sherwood number (Sh = ga L/D; ga = conductance, D = diffusivity) provides a measure of mass transfer, and the Schmidt number (Sc = /D) represents a property of a fluid. When the Sherwood and Schmidt numbers are multiplied (ShSc–0.33) they characterize conductance in dimensionless form. Again, the characteristic dimension was evaluated using the average cushion diameter (L) and the roughness length (Lr). The relationship between ShSc–0.33 and Re is log linear under ecologically meaningful conditions and assumes the following form: ShSc–0.33 = cRen. When log transformed, n, the scaling factor, describes the slope and log c is the y intercept. These parameters characterize boundary transfer across a range of fluid environments (Proctor, 1980
; Schuepp, 1993
; Rice and Schuepp, 1995
). For flat plates in laminar flow, theoretical and empirical results indicate that n = 0.5 and c = 0.66 (the Pohlhausen relationship). Within turbulent boundary layers, n = 0.8 and c increases by a factor between 1.08 and 2.5 (Schuepp, 1993
). Two experimental controls were constructed to evaluate our measurement conditions. One was made out of a flat plate with the same diameter as the cushions and covered with filter paper. This plate was supported within the center of the wind tunnel. A second control was a sponge covered with filter paper and placed in the same position as the bryophyte cushions. This control projected 1 cm above the tunnel wall. Evaporation and temperature measurements for these controls were performed as described above.
Within species, homogeneity of slopes of the ShSc–0.33–Re relationships among trials was evaluated by using Re as a covariate and testing for an interaction effect. When slopes were parallel (11 out of 12 samples), data from trials were combined for analyses of regression parameters. Among species, variation in slopes was evaluated similarly. Statistical procedures were carried out using STATISTICA version 5.1 (1998)
software.
Characteristics of flow over two species that differed in canopy properties (S. uncinata and C. haldanianum [A]) were assessed using particle image velocimetry (PIV), a full-field velocity measurement technique. In PIV, the field of interest is seeded with particles, and the system measures velocity by determining particle displacement over time using a double-pulsed laser/camera setup. The system used in this study consisted of a dual mini Nd:YAG laser (30 mJ/pulse at 532 nm; Big Sky Laser, Bozeman, Montana, USA), a computer-controlled synchronizer, a TSI PIVCAM 10–30 digital CCD camera (TSI, St. Paul, Minnesota, USA), with cross/auto correlation, which records 1K x 1K pixels and captures at a rate of 30 frames per second (yielding a data rate of 15 hz), and TSI image analysis software. The flow upstream of each moss cushion was seeded with smoke particles using a Rosco 1600 fog machine (Rosco Laboratories, Stamford, Connecticut, USA). The laser sheet was aligned to illuminate the flow field above the moss cushion and the camera was aligned normal to the light sheet. The two laser pulses were synchronized with the camera to acquire data at a rate of 15 hz. A set of 225 image pairs was acquired for each measurement. The velocity was computed by cross-correlation techniques in 32 x 32 pixel size interrogation regions. All 225 sets of vectors were averaged to calculate the mean velocity and the standard deviation in the mean in each 32 x 32 pixel region. Turbulence intensity was calculated by dividing the standard deviation of the local velocity by the approach flow velocity. For the flow conditions studied, it is estimated that the uncertainty in the mean velocity measurement ranged from 2 to 8% over the 4–1 m/s velocity range. The uncertainty in the turbulence intensity is calculated based on a chi-square distribution to be 8%. See Adrian (1991)
for more details on the PIV technique.
Canopy structure
Analysis of canopy structure was based on canopy depth measurements across sampling scales from 0.8 to 92.5 mm. However, given that the sample sizes decrease at coarse spatial scales, such analyses are usually undertaken at scales less than half of the total sample width (Dale, 1999
); we have restricted our analyses accordingly. Canopy depth was measured using a contact probe attached to a sliding scale. On each specimen, two parallel profile transects were established 1 cm apart near the center of the cushion. In anisotropic specimens these followed the direction of branch axes. For one transect, canopy depth was measured at 1.6-mm intervals along the 92.5-mm transect. For the middle 32 mm, sampling occurred every 0.8 mm. Along the parallel transect, measurements were made at 3.2-mm intervals. At each sample point, depth (to nearest 0.5 mm) to the canopy was measured using a 0.5 mm diameter wire probe. Two identical transects were measured orthogonal to the first pair. Overall, 186 points were measured on each canopy.
Using these data, three structural features of the canopy were assessed: height of the main roughness elements (Lr), spacing between these elements (Sr; i.e., scale of Lr), and fine-scale surface texture (D). In a previous study of bryophytes, the first was characterized by calculating the variance in canopy depth along surface profiles (Hayward and Clymo, 1983
). In that study, the variance in depth at a sampling scale of 8 mm was calculated to estimate the height of roughness elements. However, using such an estimate assumes that variation at other scales is irrelevant. Given that bryophytes are organized in a modular fashion and that they contain functional units at spatial scales across three orders of magnitude (e.g., leaves and small branches at 0.1 mm; branches and stems with displayed leaves at 0.1–10 mm; frondose branches at up to 30 mm), we chose a sampling scale that was based on intrinsic properties of each cushion to calculate an average height of roughness elements (Lr). To do this, we employed a spatial pattern analysis based on a geostatistical technique using the semivariance statistic. The semivariance characterizes the average squared differences in canopy depths at a given distance apart, called the lag. The semivariance is defined as: 
(
) = [1/2N()
(z(i) – z(i + )]2, where N() is the number of pair measurements separated by distance , and z(i) is the canopy depth at location i (Landini, 1996
). When the semivariance is graphed as a function of lag (i.e., sampling scale), the semivariance generally increases with lag to a maximum value and then remains constant. When transformed to length units (in centimeters) by doubling the square root of (), the maximum semivariance represents the average height of the roughness elements. This was employed as a measure of roughness length (Lr). Gibbs and Bishop (1995)
used the semivariance itself to estimate surface roughness properties of a submillimeter rough scale exchange surface. However, our analysis requires Lr to be in centimeters instead of centimeters squared. The scale of the roughness elements was calculated from twice the lag where the semivariance reaches a maximum value. This was made dimensionless by dividing by Lr. Thus, the scale (Sr) represents the average spacing between roughness elements as a proportion of the height of these elements. Semivariance was calculated using VESPER software (Minasny, McBratney, and Whelan, 1999
), and the maximum semivariance was estimated using the "linear fit with sill" algorithm.
We use the term "canopy texture" to refer to the fine-scale roughness (range of 0.8–8 mm) of the canopy profile that is independent of the coarse-scale roughness elements. Such fine-scale roughness may generate turbulence, increase the surface area, and enhance mass transfer from surfaces (Raupach, Antonia, and Rajagopalan, 1991
; Mills, 1992
). Canopy texture was characterized by calculating the fractal dimension (D) of the canopy profile. The fractal dimension has been used in a number of biological applications to characterize the degree of irregularity in time series and transect data (Palmer, 1988
; Iannaccone and Khokha, 1996
). In effect, D characterizes the self-similarity of a series of measurements; objects with minimal change with increasing scale (i.e., smooth) have low D and as texture increases, there is less similarity from one sample point to the next and D increases. In profile measurements, D varies from one (dimension of a line) to two (dimension of a plane). The fractal dimension was calculated using the semivariogram method. The initial slope of the ()—lag plot is related to the fractal dimension in the following way: log () 
2 (2 – D) log() – log a, where a is constant and the lag (Landini, 1996
). The slope (2 – D) for this relationship was determined using all points in the linearly increasing phase of the semivariance-lag plot. ANOVA and Tukey's honestly significant difference test were used to evaluate differences among species in these morphological features. Both Lr and Sr showed a correlation between group variances and magnitude and were log transformed prior to analyses. This did not qualitatively change any of the results presented.
Relationship between canopy structure and mass transfer
The influence of canopy structure on mass transfer was explored by developing an empirical model using a multiple regression approach. The canopy features of roughness scale (Sr) and canopy texture (D) are both dimensionless and were used together with the Rer as predictor variables in a linear multiple-regression model. Given that sample points are not independent (e.g., points within a sample are at different wind speeds), bootstrapping was employed to determine confidence intervals for the regression coefficients. To accomplish this, one datum point from each trial (N = 35) was randomly sampled and used in a multiple regression analysis to estimate parameters. This process was repeated 100 times, and the mean parameter values were used as bootstrap estimates of the regression coefficients. Confidence intervals (95%) around these coefficients were generated using the percentage method (Efron and Tibshirani, 1993
). These coefficients did not differ significantly from those generated using a multiple regression analysis on all sample points.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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) except for the two trials for N. curvifolia. Among species, the scaling factor, which is the same for either choice of L, differed significantly (P < 0.01, MS effect = 0.52, F = 0.15; Table 1). Nowellia. curvifolia had the lowest average slope (1.01), which differed significantly (P < 0.02) from C. haldanianum [B], B. trilobata, and P. cavifolium (slope 
1.50). Values for other species were intermediate between these extremes.
Particle image Velocimetry (PIV) for two species that differed in evaporative properties (S. uncinata and C. haldanianum [A]) was conducted within the range of wind speeds used for evaporation studies (1–4 m/s). Mean flow velocity and turbulence intensity plots were generated based on 225 sample intervals at two orientations perpendicular to one another. For all cases, the results show that the C. haldanianum [A] cushion had little interaction with the boundary layer that occurs near the plant surface (Fig. 2a, approach velocity of 3 m/s). The almost parallel streamlines indicate that the cushion causes only a slight disruption to the mean flow. In contrast, the S. uncinata cushion shows a much stronger interaction with the boundary layer at the same approach velocity (Fig. 2b). In this case the mean flow clearly bypasses (flows around) the cushion due to a blockage effect of the cushion itself, which protrudes into the flow field. This bypass effect raises the local velocity (from 3.3 to 5.0 m/s). In addition, the flow streamlines are no longer parallel to the cushion.
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Canopy structure
Variation in canopy depth as indicated by the semivariance analyses changed with sampling scale (lag). In all samples, semivariance increased with lag from the minimum at 0.8 mm lag to a maximum value that varied between 4.8 and 38 mm. Roughness length (Lr) was estimated at this maximum value and ranged from 1.7 to 14 mm. Species differed significantly in mean Lr (P < 0.0001, MS effect = 0.15, F = 6.83; Table 1). The relative spacing of these roughness elements (Sr) also varied from 0.74 to 12.7 and differed significantly among species (P < 0.0001, MS effect = 32.8, F = 17.2; Table 1). Variation in Lr and the scale of the roughness elements (Sr) was significantly negatively correlated (r = –0.83, P << 0.001).
Slopes of the semivariance–lag relationship were determined to the sill and were used to calculate the fractal dimension (D) of the canopy surface. Average fractal dimensions varied between 1.50 and 1.91. Mean D values differed significantly among species (P < 0.0001, MS effect = 0.058, F = 8.13; Table 1). Using either all trials or species means, D was uncorrelated with Lr (r = 0.10, P = 0.56, using species means), but was negatively correlated with Sr (r = –0.39, p = 0.02). Thus, D and Lr characterize two independent features of bryophyte canopies and Sr varies with each to some degree.
Relationship between canopy structure and mass transfer
Incorporating Lr based on average canopy depth measurements into the mass transfer model linearizes the ShrSc–0.33–Rer results from all samples (Fig. 3). A linear model
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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; Schuepp, 1993
) or from a control flat cushion (scaling factor of 0.91). The observed patterns of mass transfer are characteristic of those within turbulent boundary layers where surface features generate eddy currents that facilitate evaporation (Raupach, Antonia, and Rajagopalan, 1991
; Schuepp, 1993
). Within the wind tunnel, the experimental cushions were placed along the lower wall, similar to an ecological position along the ground. Even under controlled conditions, the cushion edge together with drag associated with the wall surface causes turbulence (Raupach, Antonia, and Rajagopalan, 1991
). Thus, the high exchange rates observed for all bryophyte cushions are in part due to their position at the surface–air interface.
The scaling factor in the present study, however, is as great as 1.79. This is greater than the maximal scaling factor of 1.3 observed in previous studies of mass transfer in bryophytes under controlled conditions (Proctor, 1980
, results derived from his fig. 12.2). The higher variation in the present study is likely due to the broader range of canopy morphologies represented (35 vs. 6). In addition, in 34 of 35 samples the scaling factor was >1.10 indicating a dramatic proportional increase in mass transfer at higher wind speeds. Turbulence generated from wall friction and edge effects only led to a scaling factor of 0.91 in controls and cannot account for such high values. Consequently, such high mass transfer rates must be generated by the morphology of the cushion. As surface roughness increases, not only does the generation of convective eddies increase, but so does their depth of penetration into the surface (Black and Kelliher, 1989
; Fazu and Schwerdtfeger, 1989
; Raupach, Antonia, and Rajagopalan, 1991
; Jones, 1992
; Campbell and Norman, 1998
). Effectively, this increases the amount of surface area exposed to wind and enhances mass transfer. Particle image velocimetry analyses demonstrate that singular roughness elements clearly influence flow patterns within the bryophyte canopy, especially within canopies with high surface roughness. The streamlines for the "rougher" canopies such as S. uncinata clearly have a greater effect on the mean flow than the "smoother" canopies such as C. haldanianum. Although the mean flow is primarily horizontal, the instantaneous vector fields show upflow regions that manifest themselves in elevated turbulence levels.
In addition to generating turbulence that increases the vertical movement of water vapor within the canopy, bryophyte canopies are potentially porous surfaces that may experience greater throughflow at higher wind speeds, particularly at exposed edges. At low flow rates (comparable to the lowest in the present study), lichens (Schuepp, 1984
) and finely dissected leaves of Achillea lanulosa (Gurevitch and Schuepp, 1990
) do not show enhanced mass transfer due to throughflow. However, at higher velocities, roughness elements impede flow less and cushions become porous. As this occurs, sheltering of branches and leaves within the canopy will be reduced and the effective surface area of exposure will be increased. The PIV analysis clearly shows horizontal movement of wind within the canopy. But, as employed, the technique is limited in its ability to track flow within the three-dimensional canopy; i.e., it is difficult to discern what is upstream for most of the flow vectors because of eclipsing of reflected light by visually closer portions of the canopy.
The large value of the scaling factor indicates that there is potentially a strong physiological cost to increases in canopy depth. Values greater than one (34 of 35 samples) define conditions where unit increases in canopy depth will be associated with exponential losses through evaporation. It is likely that these costs would be offset by physiological gains in light penetration and/or by the evolution of desiccation tolerance mechanisms that minimize the ecological cost of water loss. In addition, given that most bryophytes transport both water and nutrients within the same evaporation stream, it is possible that a loosely branched canopy morphology that leads to increased water loss might be beneficial in terms of nutrient uptake. However, the physiological association of these two traits remains to be investigated.
The influence of surface roughness features on mass transfer is emphasized by employing the roughness length (Lr) in calculations of dimensionless conductance and flow (i.e., ShrSc–0.33 and Rer, respectively). Using Lr derived from semivariance analysis linearized the ShSc–0.33–Re relationships from all samples (Figs. 1, 3). Thus Lr,which corresponds in scale to individual stems or fronds (2–12 mm), exerts a primary influence on mass transfer. However, this length scale is comparable with measures of canopy height but not with roughness length in studies of larger-scale plant canopies. In those systems, roughness length is derived empirically from the depth of wind penetration into the canopy and is usually 0.1–0.01 of the canopy height (Raupach, Antonia, and Rajagopalan, 1991
; Jones, 1992
; Campbell and Norman, 1998
). Unfortunately, there is no reason to suspect that this roughness length is a constant fraction of canopy depth, but it is likely to depend on its magnitude and on the density of roughness elements within the canopy, a feature that varies by an order of magnitude.
By itself Lr does not fully characterize the differences observed in mass transfer among samples. Lengths at fine (e.g., leaves, branches; indicated by D), medium (e.g., fronds, branch systems, indicated by Sr) and coarser scales (e.g., irregularities associated with substrate and microclimate, no data obtained) influence patterns of mass transfer and contributed to the observed differences in the scaling factor. Using the semivariance method to calculate D restricts the calculation of this to fine scales less than the scale of the roughness elements. In effect, D describes the degree of self-similarity (using proportional values) with increasing spatial scale without regard to size. As such, it characterizes the fine-scale roughness in dimensionless terms or more intuitively, the fine-scale texture. Measurements of D are positively associated with variation in the scaling factor that defines mass transfer from bryophyte canopies (R2 = 0.33, P = 0.04). As with coarser-scale roughness, such fine-scale surfaces may enhance mass transfer by generating turbulence (Raupach, Antonia, and Rajagopalan, 1991
; Mills, 1992). Analysis using PIV at the scale of whole cushions (9.3 cm) did not detect the influence of these patterns, but further work observing flow at finer resolutions is possible and might resolve the nature of this effect.
When used to parameterize a mass transfer model, the canopy features of Lr, the scale of those roughness elements (Sr), and the fine-scale surface texture (D) account for 91% of variation in mass transfer (Equation 2). Unlike studies of conductance that utilize only length measurements that describe the surface footprint (e.g., diameter in Proctor, 1980
), the roughness features employed in the present study have ecological meaning and can be measured readily in the field. However, these features require that measures be taken at nested spatial scales and present a substantial time investment. A simpler approach is to define a sample scale that maximizes the number of samples in a given area without sacrificing information about roughness features. Hayward and Clymo (1984) employed a sample scale of 0.8 cm because this is roughly the scale of the average canopy depth of the Sphagnum cushions in their study. Although the average distance between roughness elements (used to calculate Sr, see MATERIALS AND METHODS) varied between 0.5 and 3.7 cm in the present study, a scale of 0.8 cm corresponds with approximately half the median distance in this study (actually 0.9 cm). Intuitively, this value represents the median distance between high and low portions of the canopy and reflects a potentially meaningful sampling scale. Using correlation analysis to explore the relationship between average canopy depth at each sample interval (as indicated by the semivariance) and conductance at a given wind speed reveals that variation in canopy depth is maximally correlated (r = 0.87) with evaporation rates at a spatial scale of 0.8 cm (results not shown). For surfaces with variation in features like bryophyte canopies, this sampling interval will maximize the number of samples within a cushion and provide the most efficient sampling to estimate exchange properties. Thus, this sampling scale can be used to estimate average canopy depth and that value used as Lr in future field studies.
Surface features of roughness height, scale of roughness, and texture calculated from canopy depth profiles are all significant length scales that correlate with variation in evaporative exchange from bryophyte cushions. However, as a singular parameter, the roughness height, together with environmental information, accounts for 86% of variation in mass transfer rates. These results most directly apply to bryophyte cushions on smooth substrates like a forest floor, rock or exposed soil, common habitats for bryophytes. Similar mass transfer regimes would be expected for bryophytes supported on branches and trunks of similar diameter (i.e., 9.3 cm). However, many bryophytes persist in contiguous mats on tree trunks, logs, soil, and other substrates. Under these conditions, larger length scales will influence the local flow environment. In general, these would likely decrease evaporation by reducing the relative amount of edge exposure, limiting porous flow, and thickening average boundary layers. More information will be necessary to evaluate the relative influence of these factors on evaporative loss from bryophytes in those conditions.
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FOOTNOTES |
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4 Author for reprint requests (email: rices{at}union.edu
).
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LITERATURE CITED |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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