water loss barrel acanthodes1 - plant physiology · succulent, the barrel cactus ferocactus...

Plant Physiol. (1977) 60, 609-616

Thermal Energy Exchange Model and Water Loss of a BarrelCactus, Ferocactus acanthodes1

Received for publication February 24, 1977 and in revised form June 9, 1977

DONALD A. LEWIS AND PARK S. NOBELDepartment of Biology, University of California, Los Angeles, California 90024

ABSTRACT

The influences of various diurnal stomatal opening patterns, spines,and ribs on the stem surface temperature and water economy of a CAMsucculent, the barrel cactus Ferocactus acanthodes, were examinedusing an energy budget model. To incorporate energy exchanges byshortwave and longwave irradiation, latent heat, conduction, and con-vection as weD as the beat storge in the massive stem, the plant wassubdivided into over 100 internal and externsal regions in the model.This enabled the average surface temperature to be predicted within1 C of the measured temperature for both winter and summer days.

Reducing the stem water vapor conductance from the values observedin the field to zero caused the average daily stem surface temperatureto increase only 0.7 C for a winter day and 0.3 C for a summer day.Thus, latent heat loss does not substantially reduce stem temperature.Although the surface temperatures averaged 18 C warmer for thesummer day than for the winter day for a plant 41 cm tail, thetemperature dependence of stomatal opening caused the simulatednighttime water loss rates to be about the same for the 2 days.

Spines moderated the amplitude of the diurnal temperature changesof the stem surface, since the daily variation was 17 C for the winterday and 25 C for the summer day with spines compared with 23 C and41 C, respectively, in their simulated absence. Ribs reduced the daytimetemperature rise by providing 54% more area for convective heat lossthan for a smooth circumscribing surface. In a simulation where bothspines and ribs were eliminated, the daytime average surface tempera-ture rose by 5 C.

to 15 C above air temperature (3, 15). However, such studieshave not quantified the relative effect of the different energy-dissipating reactions. In the present study the heat transfer andheat storage properties of Ferocactus acanthodes (Lemaire)Britton and Rose were examined so that morphological param-eters and stomatal opening could be related to the thermalstatus and water economy of the plant.Most previous energy balance models for plants have dealt

with energy exchanges between the surfaces of leaves and theirenvironment (3, 11, 13). Leaves are treated as isothermalsurfaces without heat storage, because of their small thicknessand large surface to mass ratio. This is obviously not the casefor F. acanthodes, where the massiveness of the stem leads toappreciable temperature differences around its surface as wellas between the surface and the interior, and the low surface tovolume ratio leads to substantial mass for the storage of heatrelative to the surface area available for dissipation of energy.To facilitate the analysis, the barrel cactus was divided intoapproximately 100 isothermal subvolumes of various geometrieschosen to best represent the plant's thermal structure. A com-puter model was then constructed to handle the interactionsbetween these subvolumes (7) on an hourly simulation basis for24-hr periods so that the temperature distribution and individualenergy exchange processes around the surface could be preciselydescribed. The model permits a quantitative evaluation of theeffects of ribbing, spine frequency, and particular diurnal pat-terns of water vapor conductance on surface temperature andwater loss. Simulations were performed for both winter andsummer days.

THEORYAlthough information on transpiration and photosynthesis by

cacti has become available (1, 14, 16), relatively little progresshas been made in understanding their thermal relations. Gibbsand Patten (4) indicate that the north-south orientation of thevertical cladophylls of Opuntia engelmannii reduces their surfacetemperature compared with an orientation of pad surface moreperpendicular to the solar irradiation. Hadley (5) speculatedthat the surface projections of cacti reflect solar irradiation andthereby reduce the stem temperature. Indeed, Gibbs and Patten(4) had indicated that this was the reason for the differentheating and cooling rates between Opuntia bigelovii with densespines and Opuntia acanthocarpa with a sparse covering ofspines. The relatively large heat capacity and small area forheat dissipation can cause the regions of the massive fleshystems of cacti exposed to direct solar irradiation to become 10

I This investigation was supported by the UCLA Campus ComputingNetwork, Energy Research and Development Administration ContractEY-76-C-03-0012 awarded to the Division of Environmental Biology,Laboratory of Nuclear Medicine and Radiation Biology, and the Uni-versity of California Philip L. Boyd Deep Canyon Desert, ResearchCenter.

Energy Balance Terms. Six heat transfer and storage proc-esses (11, 13) are needed to account for the energy balance of abarrel cactus: (1): shortwave irradiation from the sun; (2): netlongwave radiation exchange; (3): convection; (4): conduction;(5): latent heat loss; and (6): heat storage. The total shortwaveirradiation absorbed by the surface can be represented by:

Shortwave irradiation absorbed = a (Sdiff + Sdi,) (1)where a is the shortwave absorptance, which is assumed to bethe same for both the intercepted diffuse (Sdiff) and direct (Sdir)solar beams. By the Stefan-Boltzmann law the longwave radia-tion emitted by a surface equals earT.4, where e is the emittance;a-, the Stefan-Boltzmann constant; and T, the surface tempera-ture (in degrees Kelvin). The longwave irradiation absorbed isaT,4n, where Tenv is the effective temperature of the environ-ment facing the particular part of the plant being considered.Hence, the net longwave exchange is:

Net longwave exchange = ecr(Te4. - T4) (2)

Heat convection takes place across the air boundary layer atthe plant surface and heat conduction occurs from one part of

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Plant Physiol. Vol. 60, 1977

the plant to another or to the ground:

Convection = hc(Ta - Tj)

Conduction = KAT

where h. is the conventional heat convection coefficient, Ta isthe ambient air temperature, K is the thermal conductivity ofthe medium, and AT is the temperature change over a distanceAx. The transpirational flux of water vapor out of a plant equalsgwvAcwv, where Acwv is the drop in water vapor concentrationfrom the intercellular air spaces in chlorenchymatous tissueunderlying the stem surface (assumed to be saturated withwater vapor) to the surrounding air, and gw, is the associatedconductance. The latent heat loss equals the transpirational fluxtimes the latent heat of vaporization of water (L):

Latent heat = Lgw,.LwX, (5)

Any difference in the algebraic sum of the heat exchangeprocesses represented by equations 1 through 5 leads to a

temperature change of the tissue:

Heat storage = C0V , (6)

where Cp is the heat capacity of volume V which undergoes a

change in temperature AT in time At (At was 1 hr in the model).Nodal System. To describe the energy balance for a barrel

cactus with heat storage and conduction, the stem was dividedinto a series of isothermal subvolumes, or nodes (7). Since thetemperatures occurring near the plant surface were crucial forwater loss considerations, these regions were emphasized in themodel. To evaluate the thermal status of the whole nodalsystem at any instant, the energy balance of all individual nodeswas computed simultaneously, since each nodal temperaturewas affected by the temperatures of all neighboring nodes. Dueto the nonlinear nature of the latent heat and longwave radiationterms for external nodes, usual means for solving simultaneousequations proved to be inappropriate. Consequently, an initialestimate was made based on the previous hour's temperaturedistribution and this was followed by a series of consecutivecorrections on each of the nodal temperatures until the net flowof energy for each node was zero (the algebraic sum of termsrepresented by equations 1-6). This is essentially a modifiedrelaxation technique used in numerical analysis of complexsystems by convergent iteration. The Liebmann method (7)increased computational efficiency by employing newly cor-

rected nodal temperatures in the temperature computations forremaining nodes.A cylindrical barrel cactus with a hemispherical top was

vertically divided into eight nodal levels (Fig. 1A). Each ofthese levels had 17 horizontal nodal positions (Fig. 1B), exceptthe top two levels, which had a single node each. Each level(except the top two) had eight external nodes, which had no

volume and hence no heat storage. The volumes of the othernodes are illustrated in Figure 1C, where a corrected radius R,equal to the external plant radius minus one-half of the ribdepth, was used to calculate the appropriate mass for the heatconduction and storage terms (the other energy exchange termswere based on the actual external stem radius). Central cylindri-cal nodes (nodal position 1 for levels 2 through 6) had approxi-mately 2.7 times the volume of the outer internal nodes (nodalpositions 2 through 9), since the temperature was more uniformin the core tissue. Larger temperature gradients near the top ofthe plant led to the choice of a smaller central node for level 7.The conduction path lengths between nodal centers of mass

were about the same in both the horizontal and vertical direc-tions, heat conduction occurring across the surface area common

to two adjacent nodes. A central node could be in thermal

B

5-1 314

FIG. 1. Nodal system for F. acanthodes. A: Vertical section indicat-ing levels; B: horizontal section indicating positions; C: nodal volumeelements indicating centers of mass (+). L: level separation; R: cor-rected plant radius; RD: rib depth.

contact with as many as 10 neighboring internal nodes, but an

external node conducted heat to or from only the underlyinginternal node. The energy balance of an external node alsoincluded radiation, convection, and latent heat terms. Theactual total surface area, including that of the ribs, was used forthe latent heat and convection terms, while the effective radia-tion area was a circumscribing polygonal surface through whichthe longwave or shortwave irradiation passed (for a plant with26 ribs a circumscribing cylinder would have an area less than1% greater than for the polygonal surface).

MATERIALS AND METHODS

Plant Material. F. acanthodes (Lemaire) Britton and Rose(Cactaceae) was investigated at the University of CaliforniaPhilip L. Boyd Deep Canyon Desert Research Center in thewestern Colorado desert (near Palm Desert, Calif.). A largenatural population of F. acanthodes occurs near the Center,which is located at the base of the Santa Rosa and San Jacintomountains at an elevation of 300 m, 1160 22' W, 330 39' N.Measurements were made on a plant 41 cm tall (ground level tostem apex) in an exposed location relatively free of large rocksand other vegetation. The plant stem had a relatively flat basewith approximately 4 cm of tissue below ground level, a cylin-drical region averaging 26 cm in diameter for the first 28 cm

above the ground, and a hemispherical region for the remaining

13 cm.

Data are presented as average + standard deviation (numberof measurements). All polynomial regression equations used inthis study had regression coefficients of 0.99 or better.Stem Properties. The conductance to water vapor loss (gw,.)

was determined using a Lambda LI-60 diffusion resistanceporometer with a LI-20 sensor (14). Surface temperatures (Ts)were measured with 36-gauge copper-constantan thermocouplesand internal temperatures with 24-gauge thermocouples. Short-wave absorptances (a) of the stem, spines, and apical pubesc-ence were determined using solar irradiation in an integratingsphere radiometer (2); the spines were mounted onto cardboardbefore being placed in the integrating sphere. The thermalconductivity coefficient (K) was determined by measuring theheat flux (using Thermonetics HC21-18-1OEC heat flux plates)and temperature drop (using 36-gauge copper-constantan ther-mocouples) across slabs of stem tissue 1 cm thick subjected todifferential heating. Outputs from all thermocouples and ther-mopiles were recorded with a Doric Digitrend 220 datalogger.The convection coefficient (h,) was determined using a plant

40 cm tall and 26 cm in diameter in which an 800-w immersion

(3)

(4)

610 LEWIS AND NOBEL

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Plant Physiol. Vol. 60, 1977 ENERGY EXCHANGE MODEL OF A BARREL CACTUS

heater was inserted. Thermocouples were placed in the tissue todetermine the radial temperature gradient from which the heatflux can be calculated (7); also, thermocouples at variouslocations in the ribs were used to estimate the local h.. A 45-cm-diameter fan was used to create various wind speeds (mea-sured with Thornthwaite 106 lightweight cup anemometers)under turbulence intensities approximating those found in thefield. A Fritschen net radiometer was placed adjacent to thesurface to obtain the net longwave irradiation (equation 2),while the shortwave and latent heat terms were found to benegligible under the conditions of the h, measurements.

Microclimate. Air temperature (Ta) and relative humiditywere recorded with a WeatherMeasure H311 hygrothermographlocated 1.2 m above the ground in a standard U.S. WeatherBureau shelter to determine the water vapor concentration inthe air, while shielded thermocouples were used to measure Tanear the plant. Effective environmental temperatures weredetermined with a Barnes Engineering PRT-10 IR field ther-mometer directed overhead (sky) or horizontally (mean of thefour compass directions). Wind speeds at various heights weremeasured using the Thornthwaite 106 cup anemometers. Totalsolar irradiation on a horizontal surface was measured with aKipp & Zonen CM 5 Moll-Gorczynski pyranometer; the diffusecomponent (Sdiff) was determined after occluding the directsunlight.Model Computations. Hourly temperatures for individual

nodes were calculated to the nearest degree C based on micro-climatic data using a FORTRAN program executed on an IBM360/91 computer. The temperature of an internal node de-pended on heat storage and conduction terms that are linear intemperature (equations 4 and 6), and hence its temperaturecould be directly solved for using the temperatures of neighbor-ing nodes and the change of its own temperature with time. Theshortwave irradiation absorbed by an external node is independ-ent of temperature (equation 1), heat convection to the air andheat conduction to the underlying internal node depend linearlyon temperature (equations 3 and 4), while the net longwaveexchange (equation 2) and the latent heat term (equation 5) arenonlinear with temperature. Due to these nonlinear aspects,the temperature computation for an external node was startedwith a low trial temperature followed by a number of iterativesteps (where the nodal temperature was successively increasedby 1 C) until the required energy balance of zero was achieved.Based on the density and fractional wet wt for stem tissue of F.acanthodes (14), the heat capacity used was that of water (4.18J g-' C-1). External nodes on levels 1 and 2 (Fig. 1A) were incontact with the soil and their mean temperatures (average ofmeasurements at eight locations around the surface for level 2and four locations for level 1) were entered into the model aspart of the hourly data set. To provide initial nodal temperatureswhile minimizing asymmetries created by the directionality ofshortwave irradiation, the model was started using nighttimeplant temperatures and microclimatic data from the last 4 hr ofthe day previous to the 24-hr periods considered in this study.The amount of shortwave irradiation incident on an external

node depends on the nodal dimensions, orientation to the sun,and Sdiff + Sdir (equation 1). The effective area for radiationinterception by each node is a section of a circumscribingpolygonal surface (with as many sides as there are ribs) justoutside the stem and having a "radius" of R + RD/2 (Fig. 1).For each nodal position and hour of the day for the two timesof year considered, a factor was determined relating Sd1, on ahorizontal plane to the direct solar irradiation incident on eachexternal node. For the cylindrical part of the stem, such factorswere obtained analytically using solar altitude and azimuth for alatitude of 350 N (8) together with the orientations of externalnodes, while the factor was unity for the apex (position 1, level8 in Fig. 1). For the hemispherical region (level 6, Fig. 1), and

opal glass analog of the same dimensions as an external nodewas used to determine the factor empirically for each nodalposition and hourly value of solar altitude and azimuth. Someof the incident shortwave irradiation is intercepted by the spinesand does not reach the stem surface; the degree of shading byspines was determined at various surface locations by measuringthe fractional attenuation of shortwave irradiation.The net longwave irradiation incident on the stem (equation

2) originates from the spines (ecr x the shading factor x T. ,ie4)and from the environment. Three environmental temperatureswere used: (a) the overhead sky temperature for level 8 (Fig.1); (b) a horizontally determined temperature for the cylindricalpart (levels 2-5); and (c) the one-fourth root of the average ofthe fourth power of the previous two environmental tempera-tures for the hemispherical region (level 6). The longwaveemittance was assumed to be 0.969 + 0.007, as found for eightother species of cacti (6).The effective area for the convection (equation 3) and the

latent heat (equation 5) terms was the actual surface area,which is 1.54 times the circumscribing smooth surface used forthe effective radiation area of F. acanthodes (14). The localconvection coefficient (h,) was determined for each nodal levelusing a regression equation involving the measured change inwind speed with height. The apical region of the plant (level 8,position 1) had a relatively high cuticular water vapor conduct-ance of 0.016 cm sec-' that did not undergo diurnal changes(14), while external nodes in levels 1 (below the soil surface)and 2 (Fig. 1) exhibited no stomatal opening and were assigneda zero gw, (the measured gw, was less than 0.001 cm sec-').The gw. for other nodes was either the actual field valueobtained at midheight on the east side of the plant or hypothet-ical values used for special simulations.

Since the external nodes were treated as being infinitesimallythin, they had no thermal contact with adjacent external nodesand therefore conducted heat only to or form their underlyinginternal node. The dense apical pubescence in series with thestem tissue was taken into account in calculating heat conductionbetween position 1 of levels 7 and 8 (Fig. 1). Heat conductionto or from the spines was considered negligible, since the totalarea of the base of the spines in contact with an external nodewas less than 1% of the nodal surface area. The temperaturesof the spines were calculated using the absorbed shortwaveirradiation, net longwave exchange, and convection in an itera-tive procedure analogous to that for external nodes. The latentheat term could be ignored since gwv for the spine surface of F.acanthodes is less than 2.5 x 10-5 cm sec-' (14). It wasassumed that one-half of the spine surface received longwaveirradiation from the environment and the other half from theunderlying external node. The diffuse shortwave irradiationincluding that reflected from the stem was considered incidenton the entire surface area of the spines, while the directshortwave irradiation was incident only on their projected area.to calculate convection, the spines were considered to be iso-thermal cylinders (12) with the wind perpendicular to theirmajor axes.

RESULTS

Plant Characteristics. Morphological data were determinedfor a particular field plant (Table I), while optical and conductiv-ity parameters were measured using other barrel cacti of similardimensions and physiological condition. The color of the spineschanged from dark red at the base of a plant to straw yellow atthe apex, which accounts for the differences in shortwaveabsorptance with level (Table I). The spine frequency andhence the stem shading increased toward the top of the plant.The thermal conductivity of the stem tissue at 25 C was 93% ofthe value for water at that temperature, and K of the apical

611



LEWIS AND NOBEL

pubescent layer (covering a region nearly 5 cm in diameterrepresented by position 1, level 8 in Fig. 1) was about doublethat of air.

Convection coefficients averaged over the four compass direc-tions and various positions on the ribs for wind speeds from 0.1to 7 m sec-' are given in Figure 2 for a normal F. acanthodesand after the spines had been cut off. Compared with theanalogous values at the two sides, the local h, averaged 19%higher upwind and 17% lower downwind for both the normaland spineless conditions; the average h, was highest at the ribridge, 24% lower at midrib, and 70% lower at the base of theribs. The presence of spines reduced h, (Fig. 2), which isequivalent to increasing the effective thickness of the air bound-ary layer.The conductance to water vapor loss (Fig. 3) was measured

on January 16, 1976, which was used for the winter day in themodel, and on July 21, 1976, the summer day. The stomateswere substantially open (gw, > 0.05 cm sec-1) from 2000 to0800 on the winter day, but only from about 0400 to 0600 onthe summer day, a time of the year when the soil was quite dry(14).

Microclimate. The air temperature, effective environmentaltemperature (for the horizontal direction), subsurface soil tem-

Table I. Sunry of Morphological Characteristics of F. acanthodesused in Model

Height above groundDepth below groundDiameter at midheightNumber of ribsRib depthTotal aboveground surface areaSpine lengthSpine diameterSpine shading of stem

levels 2 to 5level 6level 8

Apical pubescence thicknessThermal conductivity

stem tissueapical pubescence

Shortwave absorptancestemapical pubescence (level 8)spine

levels 2 to 5level 6level 8

41 cm4 cm

26 cm261.9 ± 0.4 (26) cm0.47 m25.4 d 2.1 (30) cm0.12 ± 0.031 (30) cm

36 ± 5 (16) %76 ± 3 (16) %84 ± 3 (16) %1.2 cm

0.57 ± 0.03 (10) W m-1 C-10.042 ± 0.015 (10) W m-1 C-1

0.65 ± 0.02 (10)0.61 ± 0.03 (10)

0.69 ± 0.03 (12)o.64 ± 0.03 (12)0.58 ± 0.03 (12)

45 1

40_

35 No spines

30 Normal

25

20

15-

10

5-

I -I0 1 2 3 4 5 6 7

Wind speed (m sec-')FIG. 2. Dependence of convection coefficient on wind speed.

Regression line shown for normal surface with spines is h, = 6.96 +5.27 W + 0.154 w2 - 0.0441 W3; that for plants with spines removedis he = 8.71 + 6.09 W - 0.0850 W2 - 0.0137 W3, where W is the windspeed.


0.15 -

5) ~~~~~WinterE

0

,0.10-

Summer

0.05-

0.0i0000 0400 0800 1200 1600 2000 2400

Solar timeFIG. 3. Diurnal changes in water vapor conductance measured in

the field on the winter day (January 16, 1976) and the summer day(July 21, 1976). The water vapor sensor was placed at midheight on theeast side of the plant.

perature under the stem, and total shortwave irradiation weremeasured hourly on the winter and the summer days (Fig. 4).The total solar insolation was 29.2 MJ m-2 for the summer dayand 9.1 MJ m-2 for the winter day (which became partiallycloudy in the afternoon, reducing the solar irradiation by 1.5MJ m-2 from that expected for a completely clear day). Sincethe diffuse irradiation at any one time did not vary more than ±8% over the plant surface, Sdiff in equation 1 was assumed to beisotropic. The mean hourly wind speed at 2 m above the groundwas 2.48 ± 1.01 (25) m sec-' for the winter day and 1.57 ±0.59 (25) m sec-1 for the summer day. The wind speed profile0.2 m away from the plant at a height H (in m) above theground equaled 0.27 ± 0.71 H - 0.17 ff2 times the wind speedat 2 m. The mean hourly water vapor concentration of the airwas 4.01 ± 0.28(25) g m-3 for the winter day and 6.38 ±0.25(25) g m-3 for the summer day. The mean hourly effectivesky temperature was -14.1 ± 4.1(25) C for the winter day and-4.9 ± 4.3(25) C for the summer day.

Simulations for Field Conditions. To compare predicted andmeasured surface temperatures, computer simulations wereperformed using observed microclimate (Fig. 4) and stem prop-erties (Table I, Figs. 2 and 3) for both winter and summer days.The surface temperatures described refer to the above groundpart of the plant (Fig. 1), which was the same region as thatused to calculate water loss. These nodal temperatures rangedfrom 10 C to 27 C on the winter day and from 23 C to 48 C onthe summer day, while the range in average hourly surfacetemperatures was about two-thirds as great (Fig. 5). The averagesurface temperatures for the external nodes predicted by themodel were within 1 C of the actual mean field temperatures atall times (Fig. 5). When the simulation was performed for 3consecutive days using the above microclimatic data, the averagesurface temperature at the end of each day was the same within0.1 C. Central core temperatures, which in the model rangedfrom 16 to 18 C at midheight on the winter day and 28 C to 37C on the summer day, were also within 1 C of the measuredvalues at each hr.The simulated temperature distribution clearly showed the

differential heating by the direct shortwave irradiation and thethermal time lags. At 1000 on the summer day, the temperatureat midheight was 43 C on the east side, 36 C on the west side,and 29 C at the center; at 1600, the temperatures had become40 C on the east side, 48 C on the west side, and 35 C at thecenter. Differences between internal and external temperatures

612

E3

IZ



Plant Physiol. Vol. 60, 1977 ENERGY EXCHANGE MO[

4- 0020 400

ZOL , f,g4

o40?l

0000 0400 0800 1200 1600 2000 2400Solar time

FIG. 4. Microclimatic data used for the winter (----: January 16,1976) and summer (- July 21, 1976) days. Air temperatures aredesignated by A, environmental temperatures determined with a verticalIR sensor by 0, soil temperatures immediately under the cactus stemby 0, and total shortwave irradiation determined with a horizontalpyranometer by 0.

u

@40

CLE

w

-4

11)

40[

30

20

10

0000 0400 0800 1200 1600 2000 2400

Solar time

FIG. 5. Surface temperatures of F. acanthodes for the winter andsummer days. Range of predicted values for external nodes is indicatedby dashed lines about the average represented by solid line. Actualfield data are shown by 0 (average for 25 thermocouples placedapproximately equidistant from each other over the above ground stemsurface).

were less for the winter day, e.g. at 1000 the southeast side was

23 C at midheight (the east side was then 20 C), the west sidewas 18 C, and the center was 16 C. The different azimuth ofthe sun during the winter caused the southeast to heat morethan the east side in the morning and lessened the bimodalnature of maximum surface temperatures observed for thesummer (Fig. 5), while afternoon cloudiness on the winter day(Fig. 4) reduced the surface temperature somewhat at 1500.During most of the daytime, shortwave irradiation was themain mode of heat transfer into the external nodes, but at night(2000-0400) essentially the only source of heat transfer to theexternal nodes was by conduction from the underlying internalnodes. During the winter night the latent heat loss dissipated74% of the heat into the external nodes at 2000 and 72% at0400; for the summer night the equivalent values were 2 and37%, respectively (cf. Fig. 3). During the daytime the latentheat loss by cuticular transpiration dissipated only 0 to 4% ofthe heat input into an external node.

Because of the stomatal opening pattern (Fig. 3), more water

DEL OF A BARREL CACTUS 613

was lost on the winter date than the summer one (Table II).The hourly water loss from the entire plant surface reached amaximum of 20 g hr-' near 0500 during the summer night withits limited stomatal opening and from about 2100 to 0400 forthe winter night. During the daytime the stomatal closurereduced water loss to about 0.6 g hr-' on the winter day and1.5 g hr-' on the summer day, which had a considerably higherplant surface temperature (Fig. 5) and hence higher Acw,.(equation 5).

Simulations Using Modified Diurnal g,v Patterns. To evalu-ate the effect of various stomatal opening patterns on the waterloss and thermal status of F. acanthodes, five modified gw,.patterns were used in the model. Microclimatic conditions werethe same as used previously for winter or summer days.

First, a zero value for gwv was chosen to abolish transpirationand latent heat loss completely. Compared to field conditions(Fig. 5), the average surface temperature increased only 0.7 Cfor the winter day and 0.3 C for the summer day (Table II).Second, a constant low value of 0.002 cm sec-' for gw. waschosen to represent continuously closed stomates and a realisticcuticular conductance (14). This caused only a 0.1 C decreasein daily surface temperatures compared with a zero gw, (TableIl). The constant low gw, and the resulting decreased transpira-tion led to a 1 to 2 C rise in hourly surface temperatures overthose for field conditions only during the nighttime when latentheat losses were normally most significant to the thermal balanceof the surface (Fig. 6A). As a third variation, the maximum gw,observed for F. acanthodes (14) of 0.23 cm sec-' was used forthe full 24-hr period to simulate the maximum possible temper-ature depression and water loss (no cactus is known for whichthe stomates remain open for 24 hr, and hence this limit isphysiologically unrealistic). Compared with the zero gw, simu-lation, this depressed the average daily surface temperature by2.2 C for the winter day and 6.5 C for the summer day (Table II).Next a square-wave pattern of stomatal opening was simulated

where gw, was 0.002 cm sec-1 during the daytime (0800-1800;this period was chosen based on the winter daylight, Fig. 4) andit had the maximum observed value of 0.23 cm sec-' at night.Under these conditions, 61% more water was lost on the winterday compared with the field gwv pattern, and the summer's dayloss increased 13-fold (Table II). The simulated increase inwater loss caused the surface temperature for the summer dateto decrease 4 C below the field values at night (Fig. 6B), andover a 24-hr period led to a 1.7 C lower average surfacetemperature; the effects for the winter date were less significant(Table II).

Finally, the square-wave gwv pattern was used except that thenighttime gwv was made temperature-dependent (14). Althoughthe winter temperatures were little affected, the plant surfacetemperatures throughout the summer night were then 1 to 2 Ccooler than for field conditions (Fig. 6C). The water loss rate

Table II. Sumary of Daily Water Losses and Average Surface Temperaturesfor Various Diurnal g,r Patterns and Morphological Conditions

Winter Day Su_er Day

Condition Daily Average Daily Averagewater surface water surfaceloss temperature loss temperature

g C g C

Field conditions 221 15.6 73 33.5Zero gvv 0 16.3 0 33.8gv, of 0.002 cm sec-1 9 16.2 29 33.7gw& of 0.23 cm sec-1 708 14.0 1901 27.3Daytime (0800-1800) gw of 355 15.2 968 31.3

0.002 cm sec-1, nighttimegvv of 0.23 cm sec '

Daytime gv. of 0.002 cm 333 15.3 388 32.7sec-1, nighttime g,rtemperature dependent

No spines (field gw ) 206 15.3 72 34.5No ribs (field g,) 148 15.8 47 34.2No spines or ribs (field g. ) 135 15.4 48 35.3

Summer ,,g

40r~~~~

Winter~~~~~~~~~~~~~~~~~~1o*~ r




was always between 25 and 30 g hr-1 throughout both thesummer and winter nights, even though surface temperaturesand hence gw. were markedly different; also, the total waterloss was about the same for the two dates (Table II).

Simulations Removing Spines and/or Ribs. To investigate theeffect that spines have on the thermal status and the associatedwater loss of F. acanthodes, spines were eliminated from theplant by setting the spine-shading factor equal to zero and usingthe convection coefficient for a spineless plant surface (Fig. 2).The average daily surface temperatures of the stem were notmarkedly affected (Table II), being 0.3 C lower in the winterand 0.9 C higher in the summer. However, the average hourlysurface temperatures were substantially lower at night andhigher during the daytime than for normal field conditions (Fig.7A). The over-all amplitude for temperatures of external nodesbecame 23 C for the winter day and 41 C for the summer dayin the absence of spines (cf. 17 C and 25 C, respectively, withspines).The effect of ribbing on the thermal status of the barrel

cactus was investigated by simulating the "elimination'" of theribs, accomplished by setting the total surface area (that usedfor the convection and latent heat terms) equal to the circum-scribed polygonal surface used for the effective radiation area.

No change was made in the corrected plant radius (Fig. 1C) so

that the mass of the stem was unchanged for the heat conductionand storage terms. The convection coefficient used was that forthe plant surface with spines (Fig. 2). Rib elimination caused a

slight increase in average plant surface temperature for bothwinter and summer days (Fig. 7B), while the daily water losswas about 34% less than for the field conditions (Table II).A final set of simulations was performed with both ribs and

spines eliminated using h, determined for the spineless surface.This led to the largest increase in average hourly surfacetemperature above field conditions, 5 C, which occurred from1200 to 1600 on the summer day (Fig. 7C). The average dailysurface temperature increased 1.8 C for the summer day anddecreased 0.2 C for the winter day compared with the field

u

'a<v

E0

C:0

a.3E'a

w

a

4-

,

0000 0400 0800 1200 1600

Solor time

2000 2400

FIG. 6. Deviations in average surface temperature from predictedfield values (Fig. 5) for simulated g,, patterns on winter (stippled) andsummer (cross-hatched) days. A: Constant low gw, of 0.002 cm sec-1;B: daytime (0800-1800) gwv of 0.002 cm sec-t and nighttime gw, of0.23 cm sec-'; C: nighttime g,,, temperature-dependent.

2 -

E0

oB

2__o

0

E 2-1

-2

0000 0400 0800 1200 1600 2000 2400Solar time

FIG. 7. Deviations in average surface temperature from predictedfield values for simulated modifications in surface morphology. A:Spines removed; B: ribs removed; C: no spines or ribs. Data are forwinter (stippled) and summer (cross-hatched) days for field gw. patterns

(Fig. 3).

conditions, while the decrease in total water loss for both days(Table II) was a consequence of the reduction in surface area inthe absence of ribs.

DISCUSSION

An energy budget model with 58 external nodes and 46internal ones (Fig. 1) predicted the average surface temperatureof F. acanthodes to within 1 C of the average measuredtemperature (Fig. 5). Not only was such temperature resolutioncompatible with computing efficiency and measurement practi-cality, but also it permitted a quantitative study of the effects ofvarious stomatal opening patterns and morphological modifica-tions on the thermal status and water loss of the barrel cactus.The importance of transpiration in cooling desert succulents

has been unclear, in part due to lack of knowledge concerningheat storage in the tissue. Here it was found that the latent heatloss significantly affected the surface temperature of F. acan-

thodes only when the tranpsiration rate was substantial. Ingoing from no nocturnal stomatal opening (water vapor con-ductance of 0.002 cm sec-', Fig. 6A) to essentially maximalstomatal opening (g,,. = 0.23 cm sec-' from 1900-0700, Fig.6B), the average hourly plant surface temperature decreased 3to 4 C for the summer night and 1 to 2 C for the winter night(the smaller temperature decrease for the winter night resultedfrom lower surface temperatures, which led to a lower AC,.and lower transpiration rate, cf. equation 5). However, duringthe daytime (0800-1800), the average hourly surface tempera-tures were identical for the two gw. patterns for both winter andsummer conditions. Thus, the water loss at night did notsignificantly affect the plant surface temperatures the following

C/-leZ/ I'

-2

614 LEWIS AND NOBEL



Plant Physiol. Vol. 60, 1977 ENERGY EXCHANGE MODEL OF A BARREL CACTUS

daytime. The latent heat term was insignificant in the energybalance of surface (external) nodes during the daytime (whenguX was 0.0015-0.0032 cm sec-' under field conditions), indi-cating that evaporative cooling is then not important in reducingthe plant heat load. This is in contrast to the conclusions ofGibbs and Patten (4), who indicated that Opuntia engelmaniidoes not reach its critical thermal maximum because coolingthrough limited daytime transpiration maintains a depressedstem temperature. They also concluded that the decreasedcuticular conductance in older pads of 0. engelmanii was mainlyresponsible for the 4 C rise in their temperature from 1100 to1600 over that for younger pads, while the present resultsindicate that changing gw, from 0.002 cm sec-' to zero hadalmost no effect on daytime surface temperatures.The total daily water loss under field conditions was 221 g for

the winter day and only 73 g for the summer day (Table II).When a square-wave pattern of stomatal opening was imposed(nighttime gw, of 0.23 cm sec-' and daytime of 0.002 cmsec-1), the winter transpiration increased moderately, but thesimulated water loss for the summer day increased markedly.The increase for the summer was greater because the stomateswere open longer in this simulation (13 hr) than in the field (3hr) and because the maximum degree of opening was greater inthis simulation than in the field (gw, of 0.23 and 0.06 cm sec-1,respectively, Fig. 3). For the square-wave gw, pattern, the totalwater loss was 2.7-fold higher for the summer day with itswarm surface temperatures than for the winter day with itslower potential evaporation. When the temperature dependenceof stomal opening for F. acanthodes (14) was combined withthe square-wave simulation of gw,, the water loss was lowerthan in the previous square-wave simulation. More important,the water losses for both winter and summer days then becamecomparable (333 and 388 g, respectively, Table II). Also, themaximum hourly water loss was 27 g hr-' for the winter nightand 30 g hr-1 for the summer night, although the water vaporconductances differed by about 3-fold for these two conditions.Watson (17) indicated that cactus tissue has a low thermal

conductivity, but stated no actual values. Gibbs and Patten (4)noted that the apex of the erect stems of Echinocereus engel-manii became appreciably warmer than the rest of the cylindricaltissue and suggested that the time lag for heat conduction downthe stem was a consequence of the low thermal conductivity.The thermal conductivity of the stem tissue of F. acanthodeswas here found to be nearly as high as that of water. This is notentirely unexpected, since the stem density of F. acanthodes is0.99 g cm-3 and its dry wt is only about 10% of the total wet wt(14), indicating the certain tissue properties such as heat capac-ity and thermal conductivity will resemble those of water.

Besides the traditional view that spines protect cacti againstgrazers, they also influence the stem temperature in a numberof ways. Spines moderate the diurnal temperature changes ofthe stem surface by intercepting part of the incoming directshortwave irradiation during the day (the effect on longwaveirradiation during the day was here not as important) and byreducing the outgoing net longwave radiation at night. For F.acanthodes the highest spine frequencies occurred near themeristematic region at the apex (Table I), which did not exhibitpronounced heating unless the spines were removed. Spinesaffect heat convection from barrel cacti by reducing the windspeed near the plant surface. Thus, elimination of spines in-creased the heat convection coefficient (h,) by about 13% (Fig.2). Gibbs and Patten (4) similarly concluded that the densenetwork of spines on 0. bigelovii minimized the convection lossfrom its surface by trapping air. In addition to the increase inh., the generally greater temperature difference between thestem and the air at midday (Fig. 7A) leads to more convectivecooling (equation 3) for spineless plants, while their lowernighttime surface temperature leads to slightly less transpira-

tional water loss. Although minimizing diurnal temperatureextremes, the 36 to 84% shading (Table I) of the stem surfaceby the spines would reduce photosynthesis, since the totalamount of CO., taken up by F. acanthodes at night is directlycorrelated with the photosynthetically active radiation reachingthe stem during the daytime (14).

Ribs can also trap air in some regions, as do spines. Forinstance, h, was over 3-fold higher at the ridge of a rib than atthe inter-rib trough, where air movement would be less. Thedifferences in convection transfer and surface temperature fromthe ridge of a rib to the trough at its base, induced by thedirectionality of the direct shortwave irradiation and compli-cated by morphological irregularities, made an accurate model-ing of the temperature distribution over a rib surface exceedinglydifficult. Therefore, the heat transfer coefficient and surfacetemperature were each averaged over an entire node. Presum-ably as a result of the turbulence and air flow patterns createdby the ribbing, h, expressed on a unit surface area basis was67% greater than for a smooth cylinder of the same outsidediameter under the turbulence intensity appropriate to fieldconditions (12). Since the ribbed surface area for this barrelcactus was 54% greater than that of the circumscribing polygo-nal surface, the total convective loss per level would be justover 2.5-fold higher than for a smooth cylinder. Instead of thediameter, it is often more appropriate to use the cube root ofvolume as the characteristic dimension for such shapes (10).The observed convection coefficient is then 44% greater thanexpected for a smooth sphere, in general agreement with studieson animals of various shapes (10).The simulated rib elimination reduced both the convection

and the latent heat terms by reducing the actual plant surfacearea to that of the circumscribing polygonal surface. Most ofthe rather small increase in surface temperature at night in theabsence of ribs (Fig. 7B) was due to the accompanying decreasein latent heat loss, while the 1 to 2 C rise during the day wasdue to the decrease in heat convection from the stem. Theimportance of ribbing for daytime convective cooling is alsoseen by comparing the spineless plants (Fig. 7, A and C),where rib removal increased the average daily surface tempera-ture by 0.8 C for the summer day (Table II). Although theincreased surface area provided by ribbing proportionally in-creases latent heat loss by transpiration for a given g9,., evapo-rative cooling had little effect on cactus surface temperatures(especially during the daytime) and water is generally a limitedresource in the desert. Besides enabling the bellows-like actionof swelling following rainfall (9) and some daytime convectivecooling, ribbing may be of benefit by increasing the area forabsorbing photosynthetically active radiation during the daytimeand taking up CO. at night. Although this is probably ofsecondary importance since light saturation of photosynthesis isnot usually achieved for most of the stem surface of F. acan-thodes (14), it would still be of some advantage for this slowlygrowing plant.The temperature optimum for nighttime CO., assimilation by

cacti is low, around 10 to 15 C (1, 14, 16). Relatively little isknown about the temperature dependence of the light reactionsor the critical thermal maxima that can be tolerated bothtemperature and exposure periods). Low nighttime tempera-tures apparently favor incorporation of CO., into organic acidsas well as decrease transpirational water loss, while high daytimetemperatures are compatible with decarboxylation of the organicacids and subsequent carbohydrate formation by photosynthesis(1, 16). Nighttime surface temperatures could be decreased byreducing spine coverage or by increasing latent heat loss. Sincethese adaptations are disadvantageous for other reasons, habi-tats with cool nighttime temperatures are probably more favor-able for F. acanthodes and barrel cacti. The soil-plant interfacetemperature of F. acanthodes occasionally exceeds 60 C in the

615



616 LEWIS AND NOBEL

early afternoon, the temperature of the nearby photosynthetictissue being only slightly lower, suggesting a high temperaturetolerance. Stem surface irregularities created by ribbing increaseconvective heat transfer and the spines reduce the shortwaveirradiation reaching the stem surface, thus moderating thepossible daytime rise in stem surface temperature. This may beparticularly critical for the apical meristem of F. acanthodes,where the highest spine frequency and the dense pubescentlayer occurred.

Acknowedgment-We thank W. K. Smith for useful discussions.

LITERATURE CITED

1. DINGER BE, DT PATTEN 1974 Carbon dioxide exchange and transpiration in species ofEchinocereus (Cactaceae), as related to their distribution within the Pinaleno Mountains,Arizona. Oecologia 14: 389-411

2. DUNKLE RV, DK EDWARDS, IT GIER, JT BEVNAS 1960 Solar reflectance integratingsphere. Solar Energy 4: 27-39

3. GATES DM, R ALDERFER, E. TAYLOR 1968 Leaf temperatures of desert plants. Science159: 994-995

4. GIBBS JG, DT PATTEN 1970 Plant temperatures and heat flux in a Sonoran Desertecosystem. Oecologia 5: 165-184


5. HADLEY NF 1972 Desert species and adaptation. Am Sci 60): 338-3476. IDSO SB, RD JACKSON, WL EHRLER, ST MrTCHELL 1969 A method for determination of

infrared emittance of leaves. Ecology 5: 899-9027. KREITH F 1973 Principles of Heat Transfer, Ed 3. Intext Educational Publishers, New

York pp 81-1268. LIST RJ 1968 Smithsonian Meteorological Tables, Ed 6. Smithsonian Institution Press,

Washington DC p 5019. MAcDoUGAL DT, ES SPALDING 1910 The Water-Balance of Succulent Plants. Carnegie

Institution of Washington, Washington DC 77 pp10. MITCHELL JW 1976 Heat transfer from spheres and other animal forms. Biophys J 16:

561-56911. MONTEITH JL 1973 Principles of Environmental Physics. American Elsevier, New York

241 pp12. NOBEL PS 1974 Boundary layers of air adjacent to cylinders. Plant Physiol 54: 177-18113. NOBEL PS 1974 Introduction to Biophysical Plant Physiology. WH Freeman & Co, San

Francisco pp 343-35914. NOBEL PS 1977 Water relations and photosynthesis of a barrel cactus, Ferocactus acan-

thodes, in the Colorado Desert. Oecologia 27: 117-13315. PATTEN DT, EM SMITH 1975 Heat flux and the thermal regime of desert plants. In NF

Hadley, ed, Environmental Physiology of Desert Organisms. Dowden, Hutchinson, andRoss, Stroudsburg Pa pp 1-19

16. TING IP 1975 Physiological adaptation to water stress in desert plants. In FJ Vernberg, ed,Physical Adaptation to the Environment. Intext Educational Publishers, New York pp99-109

17. WATSON AN 1933 Preliminary study of the relation between thermal emissivity and planttemperatures. Ohio J Sci 33: 435-450



water loss barrel acanthodes1 - plant physiology · succulent, the barrel cactus ferocactus...

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