Limits and implications of thermal tolerance in the
limpet, Lottia digitalis
Linnea Aiello
2480 East Brutus Road
P.O. Box 46
Alanson, MI 49706
June 4, 2004
Advisor Dr. Mark Denny
Permission is granted to Stanford University to use the citation and abstract of this paper.
Abstract
Öf all organisms on Earth, invertebrates of the rocky intertidal zones
experience some of the most extreme and varied environments, from near
freezing seawater to hot, dry sunlight. Thus, these organisms experience an
unusually large range of potentially lethal body temperatures. Lottia digitalis, a
high intertidal limpet of the Pacific North American coast, is one such creature.
What is the thermal tolerance of Lottia digitalis, and how often do they see these
body temperatures?
The lethal temperature limits of L. digitalis were found, in air, to vary
depending on length of exposure. At ten minutes of heat exposure, limpet
survivorship (tested 24 hours after exposure) declined from 100% to 0% as
temperature increased from 41 to 45° Celsius. At three hours and forty minutes
of exposure, a similarly steep decline was noted, but at a lower range of
temperatures: from 37 to 40°C.
A heat-budget model was constructed to find how near L. digitalis live to
their thermal maxima, and how often these maxima are exceeded. A heat
budget is a mathematical model that predicts the body temperature of an
organism, based on records of past environmental conditions plus physical
characteristics of the organism. A comparison between the heat extremes
predicted by the heat-budget model and the thermal limits showed that L. digitalis
approaches within 5°C of its thermal limit once every 12 years (on average). L.
digitalis do not live as close to their thermal limit as other intertidal organisms, but
their preference for living on exposed rock surfaces may make them susceptible
to an increase in climatic air temperature.
Introduction
Organisms of the rocky intertidal zone of Monterey Bay experience a wide
variety of environments from frigid water when the tide is in to full sun exposure
on hot days when the tide recedes. Lottia digitalis is a limpet that lives in the
high intertidal zone, from one to three meters above mean lower low water
(Shotwell 1950). L. digitalis prefer vertical rock faces, particularly those facing
west, and tend to live in clusters. Due to its elevation on the rock, this species
sees some of the most extreme terrestrial conditions of any local limpet, as only
L. scabra lives higher in some locations. Absorption of solar energy causes
rocks (and their attached limpets) to warm more than air or water, and L. digitalis
are sessile when the tide is out, so they do not escape to water if the rock
temperature rises (McMahon 1990). While on these emersed rock surfaces,
limpets experience desiccation, osmotic stress, heat stress, and sometimes
death (Williams and Morritt 1995).
Many intertidal species, including Tegula turban snails and Petrolisthes
porcelain crabs, deal with temperature extremes by remaining low on the rocks
near water and hiding in sheltered crevices and underneath algae. It has long
been conjectured that thermal tolerance correlates with vertical position, meaning
organisms that live higher in the intertidal zone (and are therefore exposed to
longer and warmer periods of heat) have higher thermal tolerance. It has been
found that Petrolisthes' maximum habitat temperature is in fact within a few
degrees of its lethal temperature (Stillman 2002). It is not known how the thermal
maximum of a high intertidal organism such as L. digitalis, which prefers high
open rock faces to crevices or algae, relates to the maximum body temperature it
reaches, and that is the impetus for this study.
Previous experiments have been undertaken to determine the tolerance of
L. digitalis to thermal stress. Wolcott (1973) found that L. digitalis were unable to
locomote normally 24 hours after immersion in seawater for fifteen minutes at 38
to 40°C. Hardin (1968) studied L. digitalis mortality after exposure in air for 5, 10,
and 15 hours. He found that almost all survived the tests at 29°C, all died at
34°C, and there was intermediate mortality at 31.5°C. These experimenters
recorded a sampling of air and limpet body temperatures over short periods, but
none attempted to systematically relate their measurements of thermal
tolerances to the periods of time the limpets reached extreme body
temperatures.
Underständing the thermal tolerances of marine organisms potentially
enables us to predict their responses to impending climate change. The
porcelain crabs that live continuously near their limits may be greatly affected by
a climatic increase in air temperature. However, if the ocean does not warm in
concert with the air, porcelain crabs may simply retreat lower on the shore rather
than die. Global warming may have more impact on L. digitalis and other
organisms that spend most of their time in air. Will an increase of a few degrees
push their body temperature over their tolerance threshold??
Materials and Methods.
Determination of thermal tolerance limits. The temperature tolerance of L.
digitalis was measured in air, where they would normally see their maximum
temperatures. Two periods of exposure were used. Previous modeling efforts
predict that the most common period for limpet body temperatures to exceed
30°C is ten minutes (Denny, personal communication). Thus ten minutes was
selected as the shorter exposure time. In general, the probability of encountering
a 30°C thermal event decreases as the period of the event increases. However
there is a peak in probability of encounter for high-body-temperature events
lasting three hours and forty minutes. Though we do not know the physiological
significance of this length of time, it was used as the longer exposure time.
Lottia digitalis were collected from the rocks at Hopkins Marine Station ir
Pacific Grove, CA. I collected limpets from the uppermost parts of their range,
early in the morning while the rocks were still wet and the limpets had not yet
clamped themselves to the rock. If they were firmly attached, I sprayed them
several times with cold seawater to induce them to loosen their grip. Then 1 pried
them off with a sharpened screwdriver, using care not to cut their feet. collected
only limpets between 16 and 22 mm in length, which is a typical size for an adult
L. digitalis. Prior to testing, the limpets were held for less than 6 hours in a finger
bowl with circulating water of 15 to 16°0.
For each test, 15 limpets were placed in a glass beaker of air and allowed
to attach themselves to the walls of the container. The beaker was then covered
with plastic wrap and submerged in a constant-temperature water bath. The
beaker contained several drops of seawater to prevent desiccation. The water
bath was fully warmed up to the experimental temperature prior to immersion of
the beaker. Äfter waiting for the time allotted (either 10 minutes or 3 hours 40
minutes), I removed the beaker and immediately transferred the limpets back to a
15 to 16°C bath of circulating seawater, immersing them fully.
tested for responsiveness of the limpets immediately after testing, and
then 5 minutes, 30 minutes, 1 hour, 2 hours, 6 hours, 12 hours, and 24 hours
later. Responsiveness was defined as some movement of the foot, head, or
mantle when poked with a fingernail. I determined that the best way to elicit
movement was by poking the mantle, which they then retracted. I assumed that
if the limpets were not responding by 24 hours after testing, they were dead.
Each group of 15 limpets was used only once and then returned to the rocks.
Experimental temperature was increased until all limpets died. Both the
temperature at which limpets begin to die and the temperature at which they all
die are important measurements of the lethal temperature.
Introduction to heat-budget model theory. The second part of the experiment
was the construction of a heat-budget model that used four years of
environmental records (wind speed, solar irradiation, tidal height, wave height, air
temperature, sea-surface temperature) to predict the internal temperature of a
limpet over a span of many years. The model calculated an ensemble of
random, hypothetical conditions to which limpets would be exposed. With these
data, one can locate when, and for how long, an organism is likely to see a
particular threshold temperature. By comparing the lethal temperatures of L.
digitalis after a certain length of exposure to the results of the heat-budget model,
determined how near the limpets live to their thermal limits, and how often that
limit is exceeded.
A heat-budget model takes into consideration physical aspects of both
the environment and the organism to determine predicted body temperature.
The basis of the model is an energy-conservation equation that relates the
various ways in which an organism transfers heat to and from the environment
(Gates 1980, Campbell and Norman 1998):
Wsun + WIRskyt WIR,sur+ Weonv + Weond - Wevap + Wmet - Wstored (eg. 1)
where Wsun is energy absorbed from the sun, Win.sky and Wig,surare net infrared
energy transferred between the organism and its surroundings, Weany is energy
gained or lost to convection by wind, Weong is energy gained or lost to conduction
with the rock, Wevap is energy lost to evaporation, Wmet is energy from the limpet's
metabolism, and Wstoreg is stored energy. The essence of this formula is that
energy in minus energy out remains as stored energy.
For a limpet, the stored energy is negligible due the small thermal mass of
the animal, so l assumed that Wstoregis zero. The energy of metabolism is also
approximately zero because limpets are ectotherms with low metabolic rates.
Energy lost to evaporation is effectively zero as L. digitalis lose little water from
underneath their shells (Wolcott 1973). We thus have a simplified equation:
Wsun + WIR,Sky+ WIR,sur+ Weonv + Weond -0
(eq. 2)
Determination of absorptivity. The first part of the heat-budget model is the
energy the limpet receives directly from the sun:
Wsun - 1 Ap
(eq. 3)
where lis the irradiance of the sun, a is the absorptivity of the limpet (measured
as a fraction of light absorbed), and Ap is the projected area of the shell, or the
area which receives sunlight.
Tis measured with a pyranometer, and it is part of the historical data on
which the model is based. To find a, 1 used a Licor 1800 spectroradiometer
equipped with an integrating sphere to measure the absorptivity of L. digitalis
shells. The radiometer records the intensity of light reflected by the shell, as
compared to a white standard, at wavelengths from 360 nm to 1100 nm. Dividing
the shell results by the standard gives the proportion of light reflected.
multiplied the fraction of light absorbed (1 - fraction reflected) by the fraction of
overall solar radiation emitted at each wavelength. I then added the individual
absorptivities over the whole spectrum to obtain a weighted-average absorptivity
of the limpet shell. Trepeated the procedure with a second shell and averaged
the results.
Determination of long-wave radiation received: Net long-wave radiative
transfer between the limpet and the sky and surroundings was calculated from
the Stefan-Boltzmann equation, which quantifies the energy radiated by an
object:
Radiated Watts = ApeaT
(eq. 4)
Here T is the absolute temperature of the object, Ap is the radiative area of the
object, ais infrared emissivity, and gis the Stefan-Boltzmann constant. Because
the rock and limpet are at about the same temperature, there is little net IR
transfer between the two, and that factor was ignored. Most of the IR transfer is
between the limpet and the sky. The net long-wave radiation energy is then:
Wnet = Win - Wout - Vsky AL Esky G Tair - Vsky AL Simpet G Timpet
(eq. 5)
where Vgyy is the fraction of a limpet's lateral area exposed to the sky. The goal
of this equation is to calculate Timpet so we use a Taylor series to reduce eq. 5 to
an approximate expression containing Timpet:
Wnet  Vsky AL Slimpet G Tai(Esky - 1) + 4 Vsky a AL impet GTair (Esky Tair-Timpet) (eq. 6)
Determination of heat transfer coefficient. Energy exchange by convection
was calculated using Newton's Law of Cooling:
Weonv - he (Tair- Timpet) Aconv
(eq. 7)
where h, is the heat transfer coefficient and Acony is the surface area of the limpet
exposed to wind. he is a measure of the heat exhanged as a function of limpet
size, shape, and wind speed, and is expressed in units of Wim2/AT. I measured
he empirically using a low-speed wind tunnel (described in Bell 1995) to find the
rate at which limpets lose heat to the air due to forced convection. Four limpet
models were used in this experiment, described in Table 1. The models are
silver alloy casts of actual L. digitalis. Silver was used because it conducts heat
very well. As a result it maintains a constant temperature throughout its mass,
simplifying the measurement of body temperature.
Each model was heated to above 60°C with a hair dryer and/or soldering
iron and allowed to cool to 30°C in wind of a known velocity. The models have
small holes in the bottom, into which were inserted thermocouple leads and
Wakefield Thermal Compound. These leads were connected to a Campbell
Scientific CR23X Micrologger, which recorded the model temperature, air
temperature inside the wind tunnel, wind speed, and time every five seconds.
The models rested on a 22 cm square by 2 cm tall Styrofoam (a nonconductive
substratum) tile, on the windward side of which were arranged 7 rows of 4 plaster
tiles whose surfaces were cast from a real granite rock. Each tile had exactly the
same shape to promote constant air movement, and was 11 cm square by 2 cm
tall. The silver models were placed on the forward edge of the Styrofoam
nearest the tiles.
Each limpet was tested in three orientations: anterior facing the wind,
sidewise, and posterior facing the wind. For each orientation, three trials were
conducted at each of the following approximate wind speeds: 0.25, 0.5, 1, 2, 3.5,
and 5.5 m/s. Using the temperature-decay and wind-speed data, I calculated the
Nusselt and Reynolds numbers for each limpet model at each wind speed and
orientation. These two numbers provide a way to calculate the heat transfer
coefficient of a limpet of any size. Earlier it was noted that
Weonv - he (Tair- Timpet) Acony
(eq. 8)
Weon and he are both unknown, but we can calculate Weony using the physical
properties of the silver alloy models:
Weonv - ATimpet m Os /t
(eq. 9)
where mis the mass of the model and Og is the specific heat of the silver alloy,
With Weon in hand we can calculate hefor a model at one wind speed and
orientation. The Reynolds and Nusselt numbers are defined as:
Re = Le/v
(eq. 10)
Nu = he Le/Kair
(eq. 11)
Here vis the wind speed in mis, Lais the length of the model in m, Kaj is the
thermal conductivity of air in WimK, and vis the kinematic viscosity of air in m2/s.
Nusselt and Reynolds numbers are related by a general model:
Nu = 10° Reb
(eq. 12)
The values a and b can be found by graphing logio(Nu) vs. logjo(Re), yielding a
line with slope b and y-intercept a:
logio(Nu) = a + blogio(Re)
(eq. 13)
Taveraged the Reynolds and Nusselt numbers for the three replicated
trials of the 4 models, each at 6 speeds and 3 orientations. I plotted logjo(Nu) vs.
logio(Re) and the slopes of the resulting regressions allowed me to calculate ha,
and thereby Nu. The values 10“ and b were later incorporated into the heat¬
budget modeling program.
Determination of energy of conduction with the rock: The energy transferred
by conduction was calculated using Fourier's Law:
Weond - -Krock Abase dTIdy
(eq. 14)
where Krock is the thermal conductivity of the rock, Apase is the area of the base of
the limpet, and dT/dy is the gradient of temperature in the rock. In the model
used here, dT/dy is calculated by numerically solving the heat equation
(essentially, Fick's second equation of diffusion applied to the conduction of heat,
Incropera and DeWitt 2002).
Construction of heat-budget model. Combining these various heating and
cooling factors via equation (2), one can solve for the predicted body temperature
at any time, given the instantaneous environmental conditions and the nature of
the limpet. A computer program can then model the body temperature over
many years based on seasonal, daily, and tidal variation. I entered the data from
the Nusselt and Reynolds results (anterior-facing-wind data only), absorptivity,
representative limpet size, and the constants listed in Table 2 into a generic
limpet heat-budget model devised by M. Denny, which assumes that the limpet is
on a planar surface of known inclination and azimuth.
This program outputs one body temperature for every 10 minutes, as well
as a list of when and for how long the model limpet body temperature exceeded
30°C, and what the maximum temperature was in each stressful period.
modeled the body temperature for 36 years of hypothetical weather, for limpets
1.5 and 2 m above mean lower low water (MLLW) on a vertical rock surface
facing west. Comparing my thermal tolerances to the heat-budget model
provides a prediction of how near L. digitalis lives to its temperature limits.
Results
Thermal limits. In the ten-minute survivorship trials, all Lottia digitalis tested at
41°C or lower had resumed responding 24 hours later. All those tested at 45°0
and above did not survive. In between those two temperatures, limpets showed
a decreasing survival rate with increasing temperature (Fig. 1). For the 220¬
minute trials, limpet mortality began at 38°C, and there was no survival at or
above 40°C, a range which is about 4°C lower than the equivalent range for the
shorter exposure time (Fig. 1).
Heat-budget model. The absorptivities of the two limpet shells were 0.644 and
0.630, which averages to 0.637. Thus, 63.7% of the light these limpets receive is
absorbed. Figure 2 compares the graphs of log Nu vs. log Re for the three
orientations of the limpet models, and the data from the graph is summarized in
Table 3. The values of a and b, and thus the rate of convective cooling, differ
only slightly depending on the orientation of the limpet. The slopes of the linear
regression lines for the three orientations were statistically indistinguishable by
an analysis of covariance (p-0.055).
The results of the 36-year heat-budget model show that the limpet living 2
m above MLLW nearly reached 37°C 3 times (Fig. 3). The limpet that lived only
1.5 m above MLLW saw a lower maximum temperature of about 35°0. When the
body temperature reaches these extreme temperatures, temperature is elevated
for a long period of time, as much as 5 hours above 30°0.
For the theoretical limpet 2 m above MLLW, the frequency of encountering
a thermal event greater than 30°C for just ten minutes is greater than once per
year (Fig. 4). The frequency decreases steadily as the period of the thermal
event increases. For the limpet 1.5 m above MLLW, the probability of a 10-
minute thermal event above 30°C is barely half that of the limpet living only 50
cm higher. At this height, no thermal events lasting longer than 2.5 hours were
encountered in the 36-year period of the test.
Discussion
According to the heat-budget model, Lottia digitalis are predicted not to
reach their lethal temperature in 36 years. For a 10-minute exposure period, the
limpets begin to die at 42°C. The model shows them reaching a maximum of
37°C only three times during the 36-year span, so it appears that L. digitalis
approaches within 5°C of its thermal tolerance about once every 12 years, but it
probably does not get closer than that. Thus, these limpets live much further
away from their lethal limit than the porcelain crabs and turban snails of the low
intertidal, which have maximum habitat temperatures sometimes to within a
degree of their tolerance capacity (Stillman 2002).
The fact that L. digitalis apparently lives far from its thermal limit may
mean that they could tolerate a small increase in air temperature due to global
warming better than other intertidal invertebrates. However, while Tegula and
Petrolisthes may move to shelter themselves from the heat, L. digitalis are
essentially sessile at low tide, making them more vulnerable to climate change.
Though the frequency of mortality events predicted by this model is
immeasurably low, a rise in air temperature, possibly accompanied by changes in
wind and wave patterns, still has the potential to push exposed high intertidal
animals such as L. digitalis over the edge, or at least force them to abandon their
status as a limpet of the high intertidal zone.
These conclusions must be tempered by several caveats. First, the
temperature tolerance tests probably overestimated the true thermal limit,
because certain aspects of the experiments may not fully represent nature. It is
likely that desiccation, for instance, would lower the thermal limit somewhat,
though Wolcott (1973) showed that limpets in the field lose little water. In my
experiment l focused on the effects of heat and eliminated the desiccation factor
by keeping the limpets moist.
Although my conclusions differ from those of earlier experiments on crabs
and turban snails, the inclusion of factors such as desiccation and osmotic stress
may put L. digitalis thermal limits more in line with previously-studied intertidal
organisms. Future experiments might address this question by including
desiccation as a factor in heat tolerance. One useful experiment would be to
measure L. digitalis thermal limits while adjusting both temperature and humidity
level.
Additionally, there are a few inaccuracies in the heat-budget model that
could be improved to get a more realistic picture of the hardiness of L. digitalis.
The model is a simplification of the intertidal zone. It assumes, for example, that
the limpet is shaped like a cone, but a L. digitalis shell has prominent ridges that
may curb or intensify the effects of certain environmental factors. Limpets will
lose some energy via evaporative cooling, but that factor was left out of the
model.
It is difficult to compare the results of the thermal tolerance test for three
hours and forty minutes of exposure to the output from the heat-budget model.
This model recorded thermal events above 30°C and found the maximum
temperature in each event, but it did not give the amount of time spent at that
maximum. In contrast, to understand the importance of the three-hour-forty¬
minute trials, I must determine the highest temperature above which the limpet
spends three hours and forty minutes. This will entail running the modeling
program to search for thermal events above a higher threshold temperature.
Öther extensions of this study should examine the differences in both heat
tolerance and predicted body temperature for L. digitalis of different sizes and
living at different heights on the shore. Size was controlled for in this experiment
by selecting only limpets of intermediate size, and the heat-budget model was
run only for a limpet of length 19 mm. It is clear from Figs. 3 and 4 that a small
difference in intertidal height has a dramatic influence on the probability of
encountering a high-temperature event. The heat-budget modelling program
could be run with other input parameters, including larger size and greater
elevation.
Modelling temperatures for L. digitalis on rocks facing south would also
probably result in higher predicted body temperatures. That L. digitalis seem to
avoid south-facing rocks may indeed be a behavioral adaptation to avoid
unnecessary thermal exposure. It would be revealing to determine how much of
an effect rock orientation has on limpet body temperature. It will also be crucial
to test the heat-budget models by taking field measurements of limpet
temperatures to determine the accuracy of its predictions. Additionally,
throughout this project l attempted to compare my assessment of the significance
of L. digitalis thermal limits to those found in other intertidal species, which may
be an unfair comparison. What would be more illuminating would be to compare
limits and heat-budget models of other limpet species from around the intertidal
zone. It would undoubtedly be exciting to find trends relating species habitat and
how near they live to their thermal limits.
Conclusions
The thermal tolerance limit of Lottia digitalis after 10 minutes of exposure
in air lies between 42 and 45°C; after 3 hours and 40 minutes, between 38 and
40°0. A heat-budget model predicting hypothetical body temperatures over a 36-
year span showed that limpets may only reach 37°C about once per decade.
Thus, L. digitalis apparently live more comfortably distant from their thermal limits
than invertebrates of the low intertidal zone. However, because L. digitalis live in
the high intertidal on exposed rock faces, they may be susceptible to the
increases in air temperature forecasted to accompany global climate change.
Acknowledgements
would especially like to thank my advisor Professor Mark Denny, my
graduate student advisor Luke Miller, and Dr. Jim Watanabe. Thank you also to
the rest of the Denny and Somero labs for the use of their time, equipment, and
space. A final thank you goes to the rest of the faculty, staff, and students of the
Hopkins Marine Station of Stanford University, without whom this project would
have not been possible.
Literature Cited
Bell, E.C. 1995. Environmental and morphological influences on thallus
temperature and desiccation of the intertidal alga Mastocarpus papillatus
Kützing. Journal of Experimental Marine Biology and Ecology 191: 29-55.
Campbell, G.S. and J.M. Norman. 1998. An Introduction to Environmental
Biophysics (2“° Ed.), Springer-Verlag, NY.
Gates, D.M. 1980. Biophysical Ecology, Dover Publ. Inc.
Hardin, Dane D. 1968. A comparative study of lethal temperatures in the limpets
Acmaea scabra and Acmaea digitalis. The Veliger 11(supp): 83-87.
Incropera, F.P. and D.P. DeWitt. 2002. Fundamentals of Heat and Mass
Transfer (5" ed.), John Wiley and Sons, NY.
McMahon, Robert F. 1990. Thermal tolerance, evaporative water loss, air-water
oxygen consumption and zonation of intertidal prosobranchs: a new
synthesis. Hydrobiologia 193: 241-260.
Shotwell, J.A. 1950. The vertical zonation of Acmaea, the limpet. Ecology 31:
647-649.
Stillman, J.H. 2002. Causes and consequences of thermal tolerance limits in
rocky intertidal porcelain crabs, genus Petrolisthes. Integrative and
Comparative Biology 42: 790-796.
Williams, Gray A. and David Morritt. 1995. Habitat partitioning and thermal
tolerance in a tropical limpet, Cellana grata. Marine Ecology Progress
Series 124: 89-103.
Wolcott, Thomas G. 1973. Physiological ecology and intertidal zonation in
limpets (Acmaea): A critical look at "limiting factors". Biological Bulletin
145: 389-422.
Table 1. Properties of silver limpet casts.
Length,
Model
Mass,g
mm
7.85
18
11.07
19.5
D
7.09
14.51
23
Width,
mm
16.5
Height,
mm
Surface
Area,
cm
4.4
5.65
4.4
7.34
Table 2. Values used for construction of heat-budget model.
Value
Parameter
Comment
Representative
Length
19 mm
Limpet Size
Width
15 mm
6 mm
Height
2.303
Krock
Wimk
10
Campbell and
9.2
Cair
Norman 1998
Tair
0.95
long-wave
Slimpet
+10-8
5.67
Wim2/K
Vsky
0261
Kair
Wimk
15111
m'/s
0.251
O.
Jglec
0.637
short-wave absorption
Table 3. Values of a, b, and R“ for each model orientation.
Orientation
anterior facing
0.0416
0.3836
wind
-O.1904
0.4344
sideways
posterior facing
-0.1258
0.4272
wind
0.9553
0.968
0.9819
Fig. 1. Comparison of the survivorship of L. digitalis after 10 minutes and 3
hours, 40 minutes exposure.
Fig. 2. Comparison of the graphs of log Nu vs. log Re for the 3 model
orientations. Slopes of linear regressions for each orientation are not
statistically distinguishable (p=0.055).
Fig. 3. Comparison of the spans of time L. digitalis at 1.5 above MLLW and 2 m
above MLLW spend above 30°0.
Fig. 4. Comparison of the frequency of L. digitalis 1.5 m above MLLW and 2 m
above MLLW experiencing a thermal event above 30°C for given lengths
of time. Error bars represent one standard deviation.
Fig. 1
L. digitalis survivorship
1
AA
24
0.8
0.6
504
0.2

O +
39 41 43 45
35 37
Temperature (degrees C)
—4— Survivorship
after 10 min
exposure
——— Survivorship
after 3:40
exposure
Fig. 2
log Nu vs. log Re: Comparison of 3 Model
Orientations
1.8
1.6

1.4
2

8.
Ar 2.
0.8
0.6
4
4.5
3.5
2
2.5
log Re
x Anterior
facing
wind
- Sideways
A Posterior
facing
wind
Fig. 3
Lengths of Exposure to High Temperatures
350
300
250

200
0
150
40.
100


50

30.00 32.00 34.00 36.00 38.00 40.00
Maximum temperature (degrees C)
4 1.5 m
above
MLLW
2m
above
MLLW
6
Fig. 4
Probability of Thermal Event Exceeding
30 degrees
2.5
S15
A- 1.5 m above MLLW
-2 m above MLLW
1
114
i iedite

100 150
50
200
Length of Event (minutes)