Leaves in the lowest and highest winds: temperature, force and shape


Author for correspondence:
Steven Vogel
Tel:+1 919 684-3791
Email: svogel@duke.edu



  • Summary 13

  • I. Introduction 13
  • II. Very low but steady wind 14
  • III. Very low and fluctuating wind 17
  • IV. Very high winds 20
  • V. Leaf form as adaptation 23
  • Acknowledgements 24

  • References 24


Climatic extremes can be as significant as averages in setting the conditions for successful organismal function and in determining the distribution of different forms. For lightweight, flexible structures such as leaves, even extremes lasting a few seconds can matter. The present review considers two extreme situations that may pose existential risks. Broad leaves heat rapidly when ambient air flows drop below c. 0.5 m s−1. Devices implicated in minimizing heating include: reduction in size, lobing, and adjustments of orientation to improve convective cooling; low near-infrared absorptivity; and thickening for short-term heat storage. Different features become relevant when storm gusts threaten to tear leaves and uproot trees with leaf-level winds of 20 m s−1 or more. Both individual leaves and clusters may curl into low-drag, stable cones and cylinders, facilitated by particular blade shapes, petioles that twist readily, and sufficient low-speed instability to initiate reconfiguration. While such factors may have implications in many areas, remarkably little relevant experimental work has addressed them.

I. Introduction

A considerable literature links plant functioning and distribution with habitat windiness. No doubt exists that plants respond to differences in the speeds of steady or averaged air flows (Grace, 1977; Coutts & Grace, 1995) with altered rates of photosynthesis, water loss, and other critical variables, and such responses correlate with both crop yields and wild plant distributions. But most attention has focused on time-averaged air movements rather than short-term lulls and peaks. The present review looks at the latter, attempting to evaluate their general importance and the specific parameters of concern. Its context is the general case made by Gaines & Denny (1993) that extremes are commonly critical determinants in physiological, ecological and evolutionary scenarios.

The review will consider two extremes, the lowest and highest rates of air movement, and within these the consequences of the unsteadiness of these air movements. It will focus on leaves rather than on whole plants or their larger components, and thus it will not deal with such matters as arrangements for effective light interception or structural failure in windthrow. In addition, it will consider just two factors, excessive heating and excessive drag, arguing that these can present immediate existential risks. For such hazards, extremes should have greater relevance than averages; the significance of an extreme, though, will depend on the time scales of both the environmental event and the plant's response.

II. Very low but steady wind

Ordinary anemometers rarely deliver reliable data for winds much less than 0.5 m s−1, which is coincidentally about the threshold of human perception, and thus winds below this speed are at least casually considered to be still. But a leaf in full sunlight within air moving at 0.5 m s−1 experiences a substantially different climate from one within air moving at 0.1 m s−1 or less. Attention was first drawn to such imperceptible winds by Gates in the 1960s (see, in particular, Gates, 1962), and its significance is now noted in textbooks (Nobel, 2005; Monteith & Unsworth, 2008). Using formulas from heat transfer engineering and persuasive Schlieren photographs taken in the field, Gates and his co-workers showed convective patterns consistent with very low rates of air movement. Images and direct measurements of leaf temperature showed that, under relatively ordinary conditions, leaves could reach temperatures sufficiently high to put their enzymes as serious risk of denaturation.

Not only can leaves get hot, they can do so with a rapidity quite out of the personal experience of bulky organisms such as ourselves. Consider a leaf with a heat capacity equivalent to a layer of water 0.1 mm thick, which approximates to the situation of a sun leaf of white oak (Quercus alba; Vogel, 1984a; Fig. 1a). Assume that it absorbs 500 W m−2 of sunlight (mainly as photosynthetically active radiation (PAR)), that it has no additional radiative sink, and that it neither expends water for evaporative cooling nor disposes of it by convection. Despite the high volumetric heat capacity of liquid water, c. 4 × 106 J m−3 K−1, the leaf should heat at 1.25 K s−1 and reach an extreme temperature before reradiation becomes sufficient to prevent a further rise. (With varying assumptions, Gates (1962) estimated a value of 1.9 K s−1; Monteith (1981) calculated a thermal time constant of c. 1 s and Nobel (2005) one of c. 10 s. For the relatively thick leaf of Eucalyptus pauciflora or snow gum, Leigh et al. (2006) measured a time constant for cooling of 17 s.)

Figure 1.

(a) Sun leaf and (b) shade leaf of white oak (Quercus alba). (c, d) Center-heated copper models used in Vogel (1970). Heat dissipation from (c) was unusually insensitive to orientation; when the model was held horizontally in free convection, heated air passed upward through its sinuses rather than building up underneath and thus reducing contact between the model and the surrounding cool air. Model (d), the most leaf-like tested, had the same orientation independence but was superior in overall heat dissipation.

1. The role of convection

Relaxing this worst case to permit free (thermally driven rather than wind-driven) convection still suggests an intolerable hazard. Monteith (1981) cites a semi-empirical expression for convective resistance (in s m−1),

image(Eqn 1)

where ΔT is the difference between air and leaf surface temperatures, assuming the latter to be uniform. For net steady-state absorption of radiant energy (Rn) he gives the following:

image(Eqn 2)

ρ and c are, respectively, the density (1.2 kg m−3) and specific heat (1000 J kg−1 K−1) of air. Inserting values, including the 500 W m−2 used above, gives a temperature difference between leaf and air of 70°C for net radiative input to be balanced by free convection. Because that assumes a leaf surface at constant temperature and free convection does not affect the entire surface equally, some parts would experience still higher temperatures. In short, free convection is so ineffective and broad leaves have such short thermal time constants that a leaf should find full sunlight exposure tolerable for, at most, 10 or 20 s.

Forced convection will improve convective heat loss; at what wind speed will it become significant? The ratio of two dimensionless numbers, the Grashof number, Gr (for free convection), and the square of the Reynolds number, Re (for forced convection), provides a rough indicator of the transition zone:

image(Eqn 3)

g is gravitational acceleration, β the thermal expansion coefficient of air (c. 1/K), l a characteristic linear dimension of the leaf, and v air speed. Below a value of the ratio of 0.1, forced convection predominates (> 90%); above a value of 10, free convection predominates (> 90%; Schuepp, 1993). (Other sources give slightly different ratios, but the index provides only a rough estimate.) For a surface temperature 20°C above ambient and a dimension of 5 cm, a ratio of 10 corresponds to an air speed of c. 0.06 m s−1. Free convection should remain significant to c. 0.6 m s−1, although the results of Roth-Nebelsink (2001) suggest a slightly lower limit. (Nobel (2005) gives 0.1 m s−1 but for a less extreme ΔT of 5°C.) In effect, when air movement becomes perceptible, free convection no longer matters much. One should note that the two kinds of convection do not add in any simple manner because forced convection normally consists of lateral air movement while free convection generates upward flows. Furthermore, an individual leaf will experience the free convection of nearby leaves as upward forced convection.

One can similarly estimate how hot a leaf might get at that minimal speed for predominantly forced convection (ignoring the residual effect of free convection as well as any evaporative cooling). From Monteith (1981),

image(Eqn 4)

For l = 0.05 m and v = 0.6 m s−1, r = 44 s m−1; from Eqn 2, ΔT = 18°C. Thus even modest air movement can prevent lethal heating.

2. Reducing peak temperatures: steady air flow

What temperatures do broad leaves reach when exposed to full sunlight? Peak temperatures of up to 20°C above ambient, but rarely higher, have been commonly reported (see, for instance, Gates et al., 1965; Loomis, 1965; Schuepp, 1993; Roth-Nebelsick, 2001; Leigh et al., 2006; Monteith & Unsworth, 2008). This implies a serious (although managed) physiological challenge for leaves in warm and windless places. Taken together with our earlier calculations, such data should focus attention on devices with which leaves keep overheating within this evidently tolerable range. At least four devices are likely to diminish the effect of very low air movement.

(1) Smaller or narrower leaves will reach lower peak surface temperatures than will larger ones as a result of thinner boundary layers and thus improved convective dissipation, something recognized long ago (see, for instance, Gates, 1965; Sinclair, 1970). For instance, in apparently still air, Gates et al. (1965) found that, while broad leaves reached 20°C above ambient temperature, conifers (pine, spruce and fir) reached only 10°C.

(2) Leaf shape also matters. Local temperature increases roughly with the square root of the distance from an edge (in parallel with boundary layer thickness). Being lobed, pinnate or narrow as well as being small decreases distance from an edge. The so-called sun leaves and shade leaves of several species of large oaks such as Quercus falcata (southern red oak), Quercus velutina (black oak), and Quercus alba (white oak) (Fig. 1a,b) provide a good experimental system. Sun leaves, which grow near the top and on the southern sides of trees, are smaller, thicker, have deeper sinuses between narrower lobes, and have more stomata per unit area. Shade leaves, opposite in each respect, grow beneath the tops and on the northern sides of trees (in the Northern Hemisphere), rarely exposed to direct sunlight. In effect, these two extremes of a continuum inhabit different thermal climates. One experiences temperatures from below ambient on clear, still nights to well above ambient in sunlight with minimal air movement. The other follows the less variable ambient air temperature itself.

In air moving at both < 0.01 and 0.1 m s−1 and several levels of illumination, nontranspiring sun leaves remained c. 20% closer to ambient temperature than did shade leaves (Vogel, 1968). Heated models differing only in shape showed sun leaves to be much more effective convective heat dissipaters (Fig. 2a). Heated leaf-shaped and more abstract models subjected to the same input (Fig. 1c,d) showed that lobing not only improved heat transfer (up to 30% above values for circular discs) but notably reduced its dependence on orientation, with horizontally held models dissipating heat nearly as well as vertical ones. By contrast, in unlobed models and simple circular discs, horizontal orientation proved as much as 20% less effective (Vogel, 1970). de Soyza & Kincaid (1991) reported similar results using posterboard models of sassafras (Sassafras albidum) leaves. Winn (1999) obtained similar results in field comparisons of mesophyll temperatures of highly dissected and cordate leaves of Viola septemloba, with dissected leaves remaining substantially cooler. During the summer, 73% of leaves took the lobed form, while only 12% of leaves were lobed in midwinter.

Figure 2.

(a) Horizontally held models of sun leaf and shade leaf made of liquid crystal sheet with a temperature range of 30°C (black) to 35°C (blue) (http://www.edmundscientific.com) glued to posterboard; the two models have been subjected to the same mild radiant heating from above with negligible air flow at an ambient temperature of 21°C. (b) Rectangles of the same liquid crystal sheet on copper plate (above) and posterboard (below); note the greater temperature uniformity of copper.

Other size- and shape-based devices besides deep lobing may also reduce leaf temperatures. Royer et al. (2008) note that leaves of red maple (Acer rubrum) in North America are larger in the north and smaller in the south. Lewis (1969) found more extensively dissected Geranium sanguineum leaves in drier habitats. Balding & Cunningham (1976) tested models at speeds down to 0.5 m s−1 and found that pinnately compound leaves dissipate heat more effectively than simple ones, concomitant with their prevalence in dry habitats. A wider survey, by Stowe & Brown (1981), found that North American trees with compound leaves were especially prevalent in places with high summer temperature maxima and places with limited water supplies.

Whether toothed leaves do better than leaves with straight margins remains uncertain. Gottschlich & Smith (1982) argued that they do, but they tested at an unrealistically high wind speed of 4.2 m s−1. They used area-heated copper models (see following page) whose high lateral conductivity should enable the improved contact of serrated edges with free stream air to improve heat transfer. With a model having a more appropriate center-to-edge temperature gradient, I found no effect of tooth-like serrations (previously unreported result). It is likely that a function for leaf teeth will be found elsewhere; see, for instance, Wilson et al. (1991).

(3) Effects of orientation appear in two guises, both evident mainly in unlobed leaves. Avoiding near-horizontal orientation reduces incident radiation during the parts of the day when it is most intense as well as improving convective coupling between leaf blade and surrounding air. This may be a permanent feature, as in the blackjack oak, Quercus marilandica, a ragged-looking tree almost all of whose large, unlobed leaves tilt > 20° from the horizontal. Another strategy is that leaves can orient so that they intercept least light at midday. Thus mangrove leaves in sunlight oriented close to vertical while those in shade were nearly horizontal (Ball et al., 1988). Silphium terebinthinaceum leaves with surfaces oriented north–south remained cooler than leaves oriented east–west (Smith & Ullberg, 1989). More commonly, unlobed leaves stressed by a shortage of water wilt down from a skyward, near-horizontal orientation to something close to vertical. Alternatively, the leaflets of a pinnately compound leaf may rotate about their midribs to reorient vertically as in a variety of shrubs as well as the silktree, Albizzia julibrissin (Fig. 3; Vogel, 2005a).

Figure 3.

Three postures of Alibizzia (julibrissin) leaves. (a) Leaf in full sunlight, with flat plate below to show the shadow it casts. (b) Leaf from shade moved into sunlight just before photography, again showing shadow area. (c) Leaves photographed at night.

(4) Yet another tactic consists of reducing incident radiation by reducing absorptivity. Nobel (2005) draws attention to the 20% absorbance reduction in silvery or shiny leaves. Either waxy coatings or pubescence can yield a substantial reduction in absorption of photosynthetically effective radiation, although with much less effect on near-infrared absorptivity (Sinclair & Thomas, 1970; Slaton et al., 2001). Pubescence can even reduce absorbance of leaves in full noon sunlight to levels below photosynthetic saturation, almost certainly responding to loss of effectiveness at high leaf temperatures (Ehleringer & Mooney, 1978). Increasing long-wavelength emissivity, though, produces only a modest reduction of net radiation absorbed, as all leaves have values well in excess of 90%. Gossypium (cotton) and Geranium leaves emit > 99%, slightly better than is typical (Monteith & Unsworth, 2008).

3. Is conduction significant?

Conduction from hotter mid-blade areas to cooler edges might reduce peak surface temperatures. But, while conduction plays a major role in the metallic heat sinks used in electronic devices, its effect should be insignificant for ordinary mesophytic broad leaves, because their lateral conductivity is three orders of magnitude below the conductivity of metals (Vogel, 1984a). Even for small, thick, xeromorphic leaves, lateral heat transfer from midrib to edge remains hypothetical (Vogel, 2005a).

The insignificance of lateral heat transfer implies that heat dissipation by leaves should not be modeled by a uniformly illuminated metal sheet, as has often been done (Martin, 1943; Tibbals et al., 1964; Parkhurst et al., 1968; Sinclair, 1970; Pearman et al., 1972; Parkhurst & Pearman, 1974; Balding & Cunningham, 1976; Gottschlich & Smith, 1982; Brenner & Jarvis, 1995; Grantz & Vaughn, 1999). (A notable exception, Stokes et al. (2006), used leaves of Mylar sheet.) As pointed out by Parlange et al. (1971), Perrier et al. (1973) and Wigley & Clark (1974) and as evident in Fig. 2(b), such models approximate constant temperature rather than constant heat flux. Leaves behave like the latter, with heat leaving at nearly the same place it entered. For average leaf temperature the error may not be great, as noted by Cowan (1972) and Parkhurst & Pearman (1974). But peak temperatures near midribs may be severely underestimated with such models or with engineering formulas, which typically assume constant temperature (see, for instance, Wigley & Clark, 1974; Roth-Nebelsink, 2001).

Metallic ‘leaves’ can model convective cooling, but they need to be heated near their centers with metal thickness chosen to match normal midrib-to-edge temperature gradients (Vogel, 1970). Alternatively, temperatures of metal models can be converted to (although slightly underestimating) local temperatures of nonmetallic ones by assuming that temperature increases in proportion to the square root of the distance from the closest edge. (This presumes that a laminar boundary layer is present, which is likely to be the case. Grace (1978) puts the transition Reynolds number at between 4000 and 23 000. If l = 0.05 m and v = 0.5 m s−1, the Reynolds number will be below 2000.) Thus peak temperatures near midribs will be at least 1.5 times those of area-heated metal models or calculated assuming constant temperature rather than constant heat flux.

III. Very low and fluctuating wind

The picture just presented, though, may be inadequate. First, we remain in woeful ignorance of wind speeds in nature under conditions ordinarily considered still air. Secondly, it presumes steady air flow, of uncertain relevance to these imperceptible flows. The difficulty may be glimpsed with a look at some preliminary measurements I have recently re-examined. Figure 4, from Vogel (2005b), shows a record of both the local wind and the temperature in the middle of a flat cellulose acetate model of the sun leaf of a white oak at tree-top height in a mature, largely hardwood forest. Transducers for both leaf temperature and wind speed (unheated and heated thermistors) had response times of around 1 s. The thickness of the model was chosen to match the rate of temperature change and its transmissivity to peak temperature reached with real leaf and model in a very low speed wind tunnel. Occasionally minimizing the current through the wind-speed transducer allowed it to sample local air temperature. Conditions were perceptually calm, shortly after midday in midsummer in the piedmont of North Carolina.

Figure 4.

Representative data from a model matched to the absorptivity, mass, and thermal conductivity of a sun leaf of white oak (Quercus alba) mounted at the top of the forest canopy. Air temperature, mid-blade leaf temperature, and wind speed were typical of a windless summer afternoon in the Carolina piedmont. Note the nonlinear scale for wind speed generated by the heated-bead thermistor anemometer (Vogel, 1981).

Air flow proved highly irregular on time scales both shorter and longer than the time constants of broad leaves. It occasionally dropped below 0.1 m s−1 or increased to 1 m s−1, with peaks and troughs only a minute or two apart. Leaf temperature varied inversely with air speed, although it was unresponsive to the shortest fluctuations and showed a slight time lag. If a cloud obscured the sun (data not shown here), model temperature dropped to ambient within a few seconds.

1. An unfamiliar physical situation

Clearly, the peak temperatures of leaves depend on what might be called ‘nanometeorology’. The record also directs attention to that analytically awkward regime of mixed free and forced convection. In addition, the results of Parkhurst & Pearman (1974) imply that no straightforward quasi-steady approximation can adequately describe the interaction of air flows with leaves. Furthermore, the model underlying Fig. 4 represents a nontranspiring leaf, ignoring possible active control via stomatal aperture and transpirative change.

The flows recorded under these ‘still’ conditions probably result from at least two phenomena. First, as shown in Fig. 5a, the shear-generated near-surface velocity gradients associated with even gentle winds higher up create vorticity. Unsurprisingly, this vorticity can develop into physical vortices, irregular rollers of air traveling normal to their long axes. These will not be the irrotational vortices most familiar to fluid mechanists, in which speed increases to a maximum near their cores, but largely rotational ones, with local speeds decreasing toward the cores. They may underlie the V-shaped wind troughs on traces such as that of Fig. 4 that occur when the roll of a vortex locally balances its lateral motion. Secondly, as shown in Fig. 5(b), there are newly forming thermal vortices, bubbles of ascending air generated by the combination of irregularities in absorptivity and the irregular top of the forest canopy. Eventually such bubbles of slightly warmer air will form ascending tori; near ground level they will merely produce centripetal and upward air movement.

Figure 5.

Two sources of irregularity in air flow close to the ground. (a) The velocity gradient just above the surface often rolls up into travelling vortices (motion shown by dashed line), so local flow varies periodically. (b) Irregular heating generates intermittent flows as bubbles of warmer air move upward.

A longer thermal time constant will reduce the peak temperatures of a leaf in full sunlight, as noted by Ball et al. (1988), and this is especially relevant during periods of very low and variable winds. Having a greater mass per unit area will give a longer time constant. The obvious material to use to increase the mass per unit area is water, which imposes the lowest metabolic cost and has the highest heat capacity of anything available to leaves. Unfortunately, most data for leaf mass per unit area in the literature refer to dry rather than fresh mass, a variable with an uncertain relationship to thermally effective mass.

2. Reducing peak temperatures: fluctuating air flow

The distribution of leaf types in nature supports a thermal role for thickness and water content. Thicker leaves have long been recognized as xeromorphic, reflecting their overrepresentation in dry places, locations where water for transpirative cooling cannot be relied upon and where overheating could therefore be a problem. While particularly good access to sunlight might underlie the thicker palisade layers in mesomorphic sun leaves (see, for instance, Hanson, 1917; Talbert & Holch, 1957), the extra thickness may come as additional water without extra chloroplasts, as in Norway maple (Acer platanoides) (McCain et al., 1988). Furthermore, xeromorphic leaves are commonly much thicker than some particular role in light interception might justify, as noted by, among others, Martin & Clements (1939) and Shields (1950). Both sources also note that xeromorphic leaves can typically transpire rapidly, which is odd if they are challenged primarily by lack of water.

A morphological study by Philpott (1956) may be revealing. She compared the leaf structures of 19 plants from the coastal plain of North Carolina, which lived in small bogs surrounded by forest, with those of 14 related plants from the nearest uplands. With smaller and thicker leaves, the bog plants appear to have greater fresh mass per unit area. Access to water should present no problem in as much as these bogs remain wet and the air above them is notoriously humid. She regarded explanations of their xeromorphy based on physiological dryness or deficiencies of one or another nutrient as unpersuasive. It is more likely that these plants are thermally adapted to the locally low wind, shelterless sunlight, and high humidity that humans find unpleasant.

Kincaid (1976) looked more directly at the effects of the size and thickness of leaves on their thermal time constants. He subjected Ilex (holly) plants to moving and still air in a wind tunnel while illuminating them at near-natural levels. In the tunnel, 20-s wind pulses of either 0.1 or 0.5 m s−1 alternated with equal periods of still air (< 0.01 m s−1), as in Fig. 6. The larger, thinner leaves of upland species both heated more rapidly and reached higher steady-state temperatures than did leaves of species from the normally warmer and calmer rolling piedmont, and these, in turn, heated more rapidly and became hotter than leaves of a species occurring among well-drained coastal dunes.

Figure 6.

Heating of a leaf of American holly (Ilex opaca) held horizontally and illuminated at the level of full sunlight. 20-s periods of still air (< 0.01 m s−1) alternate with equal periods of lateral wind at 0.5 m s−1 (Kincaid, 1976). These nondeciduous leaves are relatively thick, c. 0.35 mm; thinner leaves will be still more responsive.

3. Consequences of thermal constraints

The terms with which we describe natural phenomena affect our thinking about them. Because plants find sunlight the most crucial of inputs, we speak of shade-tolerant and shade-intolerant plants and refer to how well they manage with less than full sunlight. Full sunlight, though, poses an alternative hazard for broad leaves, manageable only with some combination of air movement, near-infrared reflectivity, access to water, and leaf forms that are effective convection generators. The evolution of broad leaves supports the view that this hazard requires management. In particular, leaves with wide uninterrupted areas of blade appear in only the last of the six lineages that produced leaf-like structures, and in that one well after small leaves appeared (Niklas, 1997). Perhaps we could as well speak of sun-tolerant and sun-intolerant plants, regarding such things as the sun leaf–shade leaf heterophylly in terms of ability to tolerate full sunlight as well as reduced sunlight. One would then ask about the effects on leaf structure of sun as well as of shade, as in, for instance, Jackson (1967).

Similarly, one might substitute the term ‘thermophytes’ for most of what now go as xerophytes, recognizing that lack of water simply increases the risk of overheating. The bog plants described by Philpott (1956) are then no longer anomalous. Thermal adaptation is consistent with Hanson's (1917) comment that sun leaves have a far greater density of stomata and can transpire up to 12 times faster than shade leaves. It is also consistent with Shields's (1950) note that xeromorphic leaves may transpire more rapidly than similar mesomorphic leaves.

Such revisionism generates further speculations. Devices besides those considered here might also reduce peak temperatures for leaves in direct sunlight. For instance, as the warm season advanced, an undissected leaf might co-opt a phytophagous insect, directing it with appropriate phytochemicals to produce strategically located holes in its blade. Tiny beetles are likely insects for the role, and casual observations suggest morning glory (Ipomoea spp.) as a beneficiary. Certainly many leaves have nonlethal, insect-generated perforations well proximal to their margins by the end of the growing season.

The sun leaf–shade leaf heterophylly among plants from a variety of habitats has drawn the attention of physiological ecologists such as (besides sources already noted) Smith & Nobel (1977), McCain et al. (1988) and Sack et al. (2006), who have investigated contrasts in net photosynthesis, water use efficiency, water potential, absorptivity, and other important variables. It might be exploited as well for studies of phenotypic metabolic adaptations or other developmental phenomena. It provides systems in which different forms, visually identifiable, inhabit effectively different climates. Yet, as parts of the same organism, they must share identical genotypes, ruling out differences (as shown by Gurevitch, 1988, 1992) with genetic bases. It provides a system for investigating environmental effects on development (as exploited by Jones, 1995). Finally, dealing with rapid temperature changes presents a metabolic challenge that, judging from Schrader et al. (2007), differs substantially from those traditionally considered. How, for instance, might a system such as a sun leaf on a hot, still afternoon keep its enzymatic systems properly coordinated while undergoing drastic and rapid changes in temperature? Elevated temperatures combined with rapid change clearly provoke responses; widespread synthesis of isoprene and its thermoprotective action have been well documented (Sharkey et al., 2008).

Figure 3(c), showing Alibizzia (julibrissin) leaves at night, draws attention to the complementary problem of excessive heat loss at night, especially when clouds do not obscure the open sky. The problem, though, differs in a variety of respects from that of excessive radiative input. Water, through phase change, provides thermal buffering that need not result in substantial loss of the substance, through the formation first of dew, then of frost, then of internal (almost always extracellular) ice. Moreover, convective contact with the surrounding air will tend to form stable near-surface inversions rather than the induced movement noted for heating. Enright (1982) found that leaves permitted to assume a vertical orientation at night had somewhat higher and less fluctuating temperatures and accumulated less dew than leaves constrained to maintain their daytime horizontal orientation. In addition, plants with constrained leaves grew less rapidly. Other aspects of the problem of acute night cooling are treated by Monteith (1981), Leuning & Cremer (1988), Ball et al. (2004), Hendrickson et al. (2004), Nobel (2005), and Vogel (2006).

IV. Very high winds

In most places, episodes of extremely high winds should be sufficiently rare and short that the basic photosynthetic function of leaves could be compromised with minimal long-term cost. While storms may last for hours or days, because of the irregularity of near-ground wind, severe gusts have durations comparable to the lulls previously considered. The mechanically destructive effects of high winds are said to increase with an exponent of velocity well above 1. But figures cited for that relationship should be viewed sceptically as they assume that the rigid structures predominant in human technology. For leaves, which are highly flexible, the particular relationships among wind speed, drag and likely damage should depend on their particular mechanical responses to wind.

1. Quantifying and measuring the drag of leaves

The force and torque about the base of a tree or other seed plant depends on the drag of its leaves, the drag of trunk and branches, and the virtual masses of the latter. For a fully leafed tree the drag of its leaves should be the largest force. Because the leaves center further from the ground than trunk and branches, they will impose a still greater fraction of the torque about the base. By contrast, trunks and branches displace enough volume to have significant virtual mass (the mass of the air they displace, which must be accelerated in the opposite direction; Daniel, 1984), generating forces additional to drag. Furthermore, they might develop oscillations in synchrony with gusts. Damping, though, should ordinarily be great enough to avoid any large component of relative wind from windward sway (de Langre, 2008). Leaves, by contrast, neither displace much volume nor respond with sufficiently long time constants to be especially sensitive to the unsteadiness of gusts. Thus the force exerted by wind on leaves should be unaffected by unsteady effects other than those attributable to the flag-like flexibility of the leaves themselves.

High wind might caused several distinct forms of damage. Leaves may be torn or shredded, they may be pulled off their branches, branches may be broken, or entire trees may suffer breakage or be uprooted. We have as yet too little information to compare the relative risks of these modes of failure with any confidence. Wilson (1980) found in sycamores (Acer pseudoplatanus), both in the field and in a wind tunnel, that leaves suffered greatest damage in the first few weeks after bud break even though wind speeds differed little from those later in the season. My own observations point to tearing and shredding as especially common in newly expanded leaves. Detachment of leaves proves surprisingly rare considering the dramatic reduction in drag it could afford; moreover, defoliation appears less likely than windthrow to be fatal.

A graph of drag versus speed misleadingly emphasizes the nearly inevitable rise of the drag with increase in the speed. Because, for rigid, nonstreamlined objects at moderate and high speeds, drag increases with the square of speed, a more revealing plot looks at drag divided by the square of speed, D/v2, versus speed, v. In this alternative graph, such an ordinary object gives a horizontal line; deviations in slope indicate special behavior. Thus an object that gradually assumes a low-drag configuration will yield a descending line. For instance, if drag varies linearly with speed instead of the square of speed, the slope on a logarithmic graph will be –1.0; if drag is independent of speed, the slope will be –2.0. That slope, of course, is the exponent, b, in the relationship

image(Eqn 5)

(de Langre, 2008, refers to b as the Vogel exponent.)

Wind tunnels large enough to accommodate trees of at least modest size have been available since the 1930s, although the earliest data for the drag of entire trees commonly cited are those of Fraser (1962) as reanalyzed by Mayhead (1973). These data, for Scots pine (Pinus sylvestris), produce an exponent of –0.72, incidentally a greater decrease with speed than that of streamlined shapes, which typically have values between –0.2 and –0.5. For a meter-high seedling of loblolly pine (Pinus taeda), the exponent is –1.13 (Vogel, 1984b); photographs suggest that this lower value results from the longer, more flexible needles of this latter species, needles that will cluster more tightly in high winds than those of P. sylvestris. (For lower speeds, exponents are higher, sometimes even positive, but such speeds present no great mechanical challenge; see Vogel, 1984b; Speck, 2003.)

Many investigations (Cullen (2005) cites copious references; see also Vollsinger et al., 2005) point to an exponent of c. –1.0, that is, to a near-linear relationship, and none to either 0.0 or –2.0. While no empirical work supports an exponent of 0.0, Cullen (2005) still recommends it for arboricultural predictions; that figure has also been used, at least tacitly, by de Langre (2008). The matter can be confusing in as much as referring drag to wind-speed-specific frontal area (‘dynamic drag coefficient’) gives an exponent nearer 0.0 (see Eqn 6), a result of the severe decrease in frontal area as speed increases. For common hardwoods that decrease reaches 70% by a speed of 20 m s−1 (Vollsinger et al., 2005).

Individual leaves, both simple and compound, as well as small clusters, ordinarily give exponents only slightly above those from work on whole trees and multi-leafed branches. Thus Vogel (1989) reported an average exponent of −0.72 ± 0.28 (SD) for 12 kinds of broad leaves and clusters (omitting single white oak leaves, as noted beneath Fig. 7) at speeds between 10 and 20 m s−1. That is consistent with the presumptions that the leaves of a fully foliated tree incur most of its drag and that in substantial winds large-scale sheltering of one leaf by another has only a second-order effect. But universality should not be presumed. The drag of a group of leaves on a branch of holly (Ilex opaca) changed with an exponent of −0.10, while a 1-m-high holly tree did much better, producing an exponent of −1.30 (Vogel, 1984b).

Figure 7.

Drag coefficients for a flag, a rigid flat plate, and a variety of leaves in highly turbulent flows. One leaf has been omitted, that of a white oak (Quercus alba) that tore rather than reconfigured in strong wind. (Modified from Vogel, 1989.)

The literature in fluid mechanics commonly replaces D/v2 with the drag coefficient, Cd, defined as

image(Eqn 6)

where S is surface area and ρ is air density. It provides a fully dimensionless variable that corrects drag for surface area as well as speed, in effect giving a speed- and area-specific drag. Drag coefficients must specify reference areas to be meaningful. The common choices of reference areas reflect the usual focus on rigid objects quite unlike leaves. For present purposes, either of two possible areas might be chosen, (1) the area of one side of a leaf pressed flat or (2) the projected area as a leaf is exposed to sun or sky while subjected to wind. (1) is simplest and least ambiguous to determine as well as representing effective photosynthetic area under ordinary, near-calm conditions. (2) approximates instantaneous effective photosynthetic and aerodynamic areas, the latter being useful for comparisons with better known rigid objects. For present purposes, (1) offers the best combination of ease of measurement and functional relevance. In particular, it generates exponents directly comparable to exponents describing how drag changes with speed (D/v2) that make no reference to specific areas.

As referents for the drag of leaves, two kinds of object are especially relevant: rigid flat plates oriented parallel to the mainstream flow (weathervanes) and flexible flags. Flat plates parallel to flow produce less drag relative to exposed surface than even streamlined forms. Counterintuitively, the fluttering of flags gives them drag coefficients far higher than those of rigid plates, although the factor of increase depends on the geometry and material of the flag and the turbulence of the flow (Hoerner, 1965). A square, leaf-sized flag of flexible polyethylene in a wind tunnel gives drag coefficients about 10 times greater than those of a rigid flat plate parallel to flow (Fig. 7; Vogel, 1989). Were leaves to experience the drag of analogous flags, it is likely that both the leaves themselves and the structures that bear them would be damaged. While the mechanisms responsible for the high drag of flags have been controversial, recent work (see, for instance, Alben & Shelley, 2004; Argentina & Mahadevan, 2005) points to destructive amplification of the vortices they themselves initiate. These analyses should help to elucidate the basis of the sharply contrasting behavior of leaves.

Drag coefficients at 20 m s−1 (again, on original projected area and thus only loosely comparable to data in the engineering literature) range widely but with hints of general patterns. Individual leaves or leaflets suffer more drag (relative to area) than do clusters of leaves or compound leaves, with coefficients typically c. 0.10 compared with 0.07, respectively. The lowest values come from extensively compound leaves. Black walnut (Juglans nigra) and black locust (Robinia pseudoacacia) average 0.032 (Vogel, 1989); a graph in Niklas (1999) gives a similarly low value for Chamaedorea. That average is only about four times that of a rigid flat plate (0.06 m across) parallel to a flow of 20 m s−1 (Fig. 7; Vogel, 1994). Outliers, omitted from the figure, are white oak (Quercus alba) leaves, for which b = +0.97 and Cd = 0.35. In addition, such oak leaves suffer physical damage, tearing at an average speed below 17 m s−1. Other leaves remain intact up to at least 20 m s−1.

We have few other drag coefficients. Those of Cescatti & Marcolla (2004) have been computed rather than measured; those of Fischenich & Dudley (1999) derive from measurements in moving water rather than in air. While rigid objects can be tested in different media as long as the Reynolds number is maintained, the reconfiguration of flexible forms such as leaves will change with fluid density (Vogel, 1994).

2. Devices for reducing drag

Leaves or clusters of broad leaves in high winds are not streamlined in the accepted use of that term. Instead, they reduce drag in ways available only to highly aeroelastic structures. As noted earlier for flags, flexibility per se, which is more likely to increase than to decrease drag, confers no automatic benefit. So drag reduction through flexibility must involve specific adaptive designs. While all relevant schemes have probably not yet been identified, flow-induced reconfiguration comes in at least four fairly distinct guises, as shown in Fig. 8 (Vogel, 1984b, 1989).

Figure 8.

Leaves exposed to turbulent wind at 20 m s−1. (a) Leaf of tulip poplar (Liriodendron tulipifera); (b) cluster of white poplar (Populus alba); (c) pinnate leaf of black locust (Robinia pseudoacacia); (d) branch with leaves of American holly (Ilex opaca). (Many additional photographs appear in Vogel, 1993.)

(1) Simple leaves may curl up into cones with their apices formed by the basal portions of their blades; these cones become ever tighter (more acute) as the wind increases (Fig. 8a).

(2) Similar cones may be formed by clusters of leaves in which each leaf presses against more distal ones, curling less than it would as an individual but enough to fit against the cone's surface (Fig. 8b). Leaves that can do (1) as individuals can apparently also do (2) in groups, but not all leaves that can do (2) also do (1).

(3) Pinnately compound leaves with large numbers of leaflets may form into elongate cylinders, with each leaflet again pressed against more distal ones (Fig. 8c). Leaflet curling, though, is at least partly lengthwise, and the leaflets lie against each other as do scales on a fish.

(4) Leaves pinnately arranged on a branch may bend back along the branch so that they lie with their surfaces pressed together, abaxial to adaxial, to form a stack that gets tighter as the wind increases (Fig. 8d).

All the simple leaves that as individuals curl into cones share two structural features: petioles longer than c. 2 cm and blades extending further proximally than the petiolar attachment point; that is, some degree of basal lobing. These lobes often have a slight upward curl; as upwind extremes they initiate curling upward so an upper leaf surface forms the core of a cone. Occasionally, mainly in softer, early-season leaves, one or both lateral halves of a leaf curl downward. The role of long petioles is less clear; they are usually longer than required to keep basal lobes beyond the parent branch. Also of unclear significance is the relative rarity of serrate edges among leaves that reconfigure as individuals as well as clusters.

Variation in leaf shape within individual trees suggests a better ability to reconfigure among leaves that might experience greater wind. Thus de Soyza & Kincaid (1991) noted wider leaves with more lobing among the leaves of Sassafras albidum growing in open (presumably more wind-exposed) areas, and Kincaid et al. (1998) found more pronounced basal lobes among leaves higher up in a large tree of Pourouma tormentosa in French Guiana.

Features that enable individual coning occur in some but not all members of at least 15 families, an apparent convergence (Vogel, 1998). Convergent features are likely to represent fairly direct results of selection and consequently functional significance (Endler, 1986).

Curling into cluster cones does not require more than the most minimal petiole. Thus clusters of white oak leaves (by contrast with individual ones), with very short petioles, reconfigure well, if beginning at somewhat higher speeds than, for instance, those of red maples. Cluster coning but not individual coning requires that petioles, which are flexurally stiff in order to hold their blades outward, be torsionally flexible. The shorter the petioles, of course, the greater will be the requisite twist per unit length. Niklas (1996) found that sugar maple (Acer saccharum) leaves in wind-exposed areas were not only smaller, but had more flexible petioles than those in protected areas.

Small leaves such as those of birches (Betula) and poplars (Populus) cone only as clusters. White poplars (Populus alba) do so especially readily, probably due to the same bilaterally flattened petioles involved in fluttering in light winds. Comparison of red maples, groups of which form cluster cones in low winds, with white oaks, which require higher speeds, suggests that features promoting cluster coning may incidentally cause fluttering in modest winds. A functional advantage for the conspicuous low-speed shimmering of cottonwoods, aspens, and other Populus species has been enigmatic (see, for instance, Roden & Pearcy, 1993). Quite possibly, shimmering merely accompanies effective clustering in higher winds. Populus leaves resist acute wind damage; even isolated individual leaves of P. alba were not torn in a highly turbulent wind of 31 m s−1 (Vogel, 1989).

Pinnately compound leaves, reconfiguring into elongate cylinders, achieve especially low drag coefficients. Givnish (1978), following other observers, noted their relative prevalence in the canopy flora of lowland tropical rain forest and savannah. While he pointed to factors such as seasonal drought, perhaps in addition their prevalence results from selection for low drag in intermittently high winds. Reconfiguration into stacks has so far been seen only in a holly, Ilex opaca (Vogel, 1984b). While remarkably stable (in part as a result of interlocking of marginal spines) and effective, it involves extreme strains in the short petioles and seems incongruent with a role in what is most often a low, understory tree. Perhaps the behavior becomes significant during the winter, when this evergreen loses the shelter otherwise provided by nearby deciduous trees.

Some additional points about leaves in high winds should be considered. (1) Whatever its proximate cause, the ‘flagging’ of trees exposed to strong, directionally consistent winds might facilitate drag-resisting reconfiguration, at least to the extent that branches participate in the process. (2) Hardwoods of similar habitats have lower drag coefficients than do needled conifers (Vollsinger et al., 2005), suggesting that reduced drag in high winds is not an adaptive advantage for needled forms. (3) A wind speed of 20 m s−1 seems to have become a paradigmatic choice for maximum speed. Despite higher speeds recorded by standard meteorological equipment, it represents a reasonable extreme for what leaves on most trees might experience, based on the measurements of Oliver & Mayhead (1973) during a 1-in-10-yr gale. Still, Johnson et al. (1982) cite higher speeds, albeit only for a few seconds, in a cyclone. (4) Above 20 m s−1 and approaching the point of physical destruction, drag coefficients may (Johnson et al., 1982) or may not (Mayhead, 1973) drop less rapidly with increasing speed; in short, we have too little data to judge the point at which reconfiguration has reached its maximum. (5) Leaf reconfiguration may be easily observed without a wind tunnel by attaching a leaf or group of leaves with string or wire to an appropriate support and extending the assembly out of the window of a moving automobile. Once recognized, reconfiguration becomes evident during storms by following the thrashing of a branch with hand-held binoculars.

V. Leaf form as adaptation

The forms of leaves must represent extremes of multifactorial adaptation even when considering support and maintenance of mechanical integrity alone, a point especially well documented by Niinemets & Kull (1999) and Read & Stokes (2006). As has often been noted, the more factors involved, the more local adaptive optima will exist. Thus the great variation in leaf form, even within particular habitats, needs no special explanation. Attention has traditionally centered on water use efficiency, gas exchange, light interception, and herbivore deterrence. But we should not ignore avoidance of excessive temperatures during lulls in local air movement and minimization of drag and mechanical damage in the gusts of storms.

Understanding the adaptive bases of leaf form, then, challenges the physiologist or physiological ecologist. Aspects of form are too easily ascribed to the particular function under scrutiny, and work linking form with particular functional considerations quite likely reflects the biases of tradition and experimental techniques. Such techniques readily address neither of the present concerns.

Nonetheless, neither concern requires unusually expensive or hard-to-obtain equipment. Both tiny thermocouples and the wires for constructing them have long been available. For that purpose Platt & Wolfe (1950) measured leaf temperatures with microbead thermistors, which may be slightly superior. Thermal imaging equipment that covers the right range of temperatures is now widely available. Very low speed wind tunnels can be simply constructed (Vogel, 1969), and low-speed anemometers present only a slightly greater challenge (Vogel, 1981). The wind necessary for high-speed work can be readily generated. While ordinary household fans do not reach adequate speeds, their propellers can be attached to faster motors with little risk of self-destruction. Tapered ductwork with decreasing cross-sections both upstream and downstream from propellers can double output speed. Turbulence, which is carefully minimized in normal wind tunnels, may more closely represent what leaves experience in nature. Appropriate force transducers can be improvised from the now ubiquitous digital balances.

Several areas stand to benefit from better understanding of the link between form and the spectrum of functional demands. The matter of plant distribution has been mentioned repeatedly here; its relevance to evolution and paleontology (see, for instance, Schlichting, 1986; Royer et al., 2005, 2008) needs no belaboring. Significant agricultural value might come from anticipation of the consequences of leaf form alteration through breeding or selection in stocks intended for use in places of particular air flow characteristics.


Discussions as part of the Leaf Temperature Working Group at Macquarie University renewed my contact with the area considered here. I am grateful for the intellectual rejuvenation provided by its members, Andrea Leigh (the organizer), Marilyn Ball, John Close, David Ellsworth, Adrienne Nicotra, and Sanna Sevanto. The ARC NZ Research Network for Vegetative Function provided support for the workshop.