advances.sciencemag.org/cgi/content/full/2/8/e1600825/DC1
Supplementary Materials for
Rising sea levels will reduce extreme temperature variations in tidedominated reef habitats
Ryan Joseph Lowe, Xavier Pivan, James Falter, Graham Symonds, Renee Gruber
Published 17 August 2016, Sci. Adv. 2, e1600825 (2016)
DOI: 10.1126/sciadv.1600825
This PDF file includes:







Supplementary Methods
Supplementary Results
table S1. Tidal amplitudes and reef morphology parameters for sample tidally
forced reefs globally.
table S2. Sensitivity of the projected temperature changes to spring and neap
amplitude variations.
fig. S1. Response of reef temperature to an interacting solar heating cycle and a
diurnal (K1) tidal cycle.
fig. S2. Response of reef temperature to an interacting solar heating cycle and a
diurnal (O1) tidal cycle.
Reference (56)
SUPPLEMENTARY MATERIALS
Supplementary Methods
Model application to assess sensitivity to spring-neap tidal variability
The modelled temperature variability in Results focused on the response to the average tidal amplitude
of each site interacting with the solar cycle. We also investigated the sensitivity of the temperature
variations to spring and neap amplitude variations. For simplicity, we assume a spring-neap amplitude
spring
neap
ratio ( tide
) of approximately 2, which is frequently the case globally (56) (here tide, spring and
/ tide
tide,neap are the spring and neap tidal amplitudes, respectively). Thus, by definition the spring and neap
spring
neap
amplitudes are related to the average amplitude ( tide ) by tide
 4 / 3 tide and tide
 2 / 3 tide ,
respectively, which are included for each site in table S1. With these modified tidal amplitudes, the
*
*
modified values of hmin
and hMSL
were then used in the heat budget model (see Methods) to evaluate the
temperature response for each reef and for each sea level condition (present 0 MSL, +0.7 MSL and +1.5
MSL).
Model application to diurnal tidal regimes
Following the approach detailed in Methods, we applied the reef heat budget model governed by Eqs.
(11)-(14) with diurnal tidal forcing in Eq. (13). For these simulations, we focus on the two major diurnal
tidal constituents: K1 with period 23.93 hr and O1 with period 25.82 hr. To illustrate the thermal
response to these diurnal tides, we consider a hypothetical scenario based on the same Tallon reef
*
*
 0.17 ) and with an elevated mean sea level
example, both at present mean sea level ( hMSL
 0 and hmin
*
*
 0.17 ). In other words, the tidal amplitude, reef morphology, and surface heat
( hMSL
 1.17 and hmin
fluxes remain the same, with only the tidal frequency changing. This allows the results in Fig. 4 with
semidiurnal tidal forcing to be compared with diurnal tidal forcing scenarios.
Supplementary Results
Temperature response to spring-neap tidal variability
In many cases, the predicted changes in diurnal temperature variations ( Tr ) are largely insensitive to
spring-neap variations in tidal amplitude (Table 1 and table S2). This is especially the case for sites
*
where spring-neap changes in hMSL
(table S1) remain either sufficiently small or sufficiently large such
that hydrodynamic regime does not transition from conditions of tidal-truncation to non-tidal-truncation,
*
*
 hmin
 1 . For the +0.7 MSL rise scenarios, examples include: Tallon Island
which occurs when hMSL
*
(with relatively small hMSL
), where Tr changes only from -6% to -8% between spring and neap
*
conditions; and both Ofu and Rarotonga (with relatively large hMSL
), where Tr changes only from -
32% to -39% and from -35% to – 40%, respectively. Other reefs such as Warraber, Cocos and Lady
Elliot are more sensitive to spring-neap tidal amplitude variability, as a result of transitions across these
hydrodynamic regimes. For example, for the same +0.7 MSL rise scenario, changes in Tr for Lady
Elliot differ from -27% under spring conditions to -57% under neap conditions (table S2), versus -39%
*
for the average tidal amplitude (Table 1). This is because for the +0.7 MSL rise scenario, hMSL
varies
*
*
from 1.0 during spring tides (i.e. tidal truncation with hMSL
 hmin
 1 ) to 2.1 under neap tides (i.e. no tidal
truncation). We note further, that the Tr for the average tidal amplitude at Lady Elliot is still very close
to the value of Tr obtained by simply averaging the spring and neap tide values (-39% vs. -42%).
Thus, the values of Tr we report for each reef site based on the average tidal amplitude in Table 1 are
nonetheless highly representative of the long-term averages of Tr , even with spring-neap variations in
tidal amplitude.
Temperature response to diurnal tidal regimes
Figures S1 and S2 illustrate the temperature response (in dimensionless form) to the two major diurnal
tidal constituents (K1 and O1), for the same example reef in Fig. 4. Similar to the response to a
semidiurnal (M2) tide in Fig. 4, there is a modulation of the diurnal temperature fluctuations (black line)
that is governed by the interaction between the K1 and O1 tides with the diurnal tidal cycle. For a K1
tide (fig. S1), the close match to 24 hr results in a very long period (  low  365 day) modulation of the
diurnal temperature fluctuations. For O1, there is a  low  14.2 day modulation that is comparable (but
not the same) as the 14.8 day cycle generated by the M2 tide in Fig. 4. A comparison of figs. S1 and S2
with Fig. 4 shows that the diurnal tide can drive comparable diurnal temperature extremes when low tide
phases of the tide occur near solar noon (i.e. when i  180 ). Similarly, an increase in the mean sea
level reduces the magnitude of the diurnal temperature fluctuations; however, this reduction is notably
smaller than case forced by a semidiurnal (M2) tide in Fig. 4. This arises because the role of advective
heat exchange between the reef and ocean is reduced under diurnal tides, which reduces the dependency
of temperature fluctuations on the mean sea level elevation.
One key difference in these diurnal tidal scenarios is the more substantial variability in the dailyaveraged temperatures (red lines, figs. S1a and S2a) in comparison to the semidiurnal tidal condition
(Fig. 4). Therefore, for reef habitats dominated by diurnal tides, there can be more substantial daily net
heating of a reef when the dominant low tide occurs in the middle of the day.
table S1. Tidal amplitudes and reef morphology parameters for sample tidally forced reefs globally.
Average tide
Spring tide
*
hMSL
 hMSL / tide
Label
Site
MSL
MSL
+0.7 m
+1.5 m
0.00
0.23
0.33
0.33
0.6 m
0.42
0.8 m
tide
*
hmin
present
3.0 m
0.17
1.2 m
Neap tide
*
hMSL
 hMSL / tide
MSL
MSL
+0.7 m
+1.5 m
0.00
0.18
0.25
0.25
0.8 m
0.31
2.38
1.1 m
*
hMSL
 hMSL / tide
MSL
MSL
+0.7 m
+1.5 m
0.00
0.35
0.75
0.5
0.50
1.38
2.38
0.4 m
0.6
0.63
2.38
4.38
1.78
0.5 m
0.8
0.75
2.06
3.56
neap
tide
*
hmin
present
0.38
2.0 m
0.3
0.69
1.19
0.8 m
0.31
1.19
2.19
0.38
0.38
1.03
spring
tide
*
hmin
present
0.50
4.0 m
0.13
0.92
1.58
1.6 m
0.42
1.58
2.92
0.50
0.50
1.38
Ⓐ
Tallon
Ⓑ
Warraber
Ⓒ
Cocos
Ⓓ
Lady
-
Ofu
0.5 m
2.00
2.00
3.40
5.00
0.7 m
1.50
1.50
2.55
3.75
0.3 m
3.0
3.00
5.10
7.50
-
Rarotonga
0.4 m
2.50
2.50
4.25
6.25
0.5 m
1.88
1.88
3.19
4.69
0.3 m
3.8
3.75
6.38
9.38
Island
Island
Islands
Elliot
Labels refer to sites plotted in Fig. 5. Tidal amplitudes are reported for average ( tide ), spring ( tide
spring
*
) and neap ( tide ) conditions. Values of dimensionless reef depth
neap
relative to mean sea level ( hMSL ) are included for present conditions (0 m MSL) and two sea level rise scenarios (+0.7 m MSL, +1.5 m MSL).
table S2. Sensitivity of the projected temperature changes to spring and neap amplitude variations.
Spring tide
Neap tide
Tr
Tr
(% change)
(range)
MSL
+0.7 m
+1.5 m
+0.7 m
+1.5 m
2.5-6.5 oC
2.3-6.0 oC
2.1-5.5 oC
-8%
-25%
-54%
2.0-5.0 oC
1.6-4.1 oC
0.9-2.2 oC
-39%
-45%
-84%
NA
NA
NA
Lady Elliot
-27%
-74%
2.5-5.5 oC
1.8-4.0 oC
-
Ofu
-32%
-61%
1.5-6.0 oC
-
Rarotonga
-35%
-62%
NA
Tallon
Ⓑ
Warraber
Ⓒ
Cocos
Ⓓ
Island
Island
Islands
+1.5 m
-6%
-15%
-17%
(range)
MSL
Ⓐ
+0.7 m
(% change)
MSL
Site
MSL
Tr
MSL
Label
MSL
Tr
present
MSL
MSL
+0.7 m
+1.5 m
2.5-6.5 oC
2.2-5.9 oC
1.8-4.8 oC
-78%
2.0-5.0 oC
1.2-3.0 oC
0.4-1.1 oC
-72%
-88%
NA
NA
NA
0.6-1.4 oC
-57%
-81%
2.5-5.5 oC
1.0-2.3 oC
0.5-1.0 oC
1.0-4.0 oC
0.6-2.4 oC
-39%
-64%
1.5-6.0 oC
0.9-3.7 oC
0.5-2.2 oC
NA
NA
-40%
-64%
NA
NA
NA
present
Labels refer to sites plotted in Fig. 5. Tidal amplitudes ( tide ) represent average values (i.e., intermediate between spring and neap). Diurnal temperature
range changes (%
Tr
change) are relative to present conditions with 0 m MSL. Present temperature ranges ( Tr ) are drawn from literature values and
are projected for different mean sea level rise scenarios (+0.7 m and +1.5 m) using the model.
fig. S1. Response of reef temperature to an interacting solar heating cycle and a diurnal (K1) tidal
cycle. (a) Reef temperature variability (black line, in dimensionless form Tr* per Eq. (3)) over the ~365
*
day cycle, for the same reef morphology and tidal amplitude considered in Fig. 4 (i.e., where hMSL
0
*
 0.17 ). Note that due to the long simulation period individual diurnal temperature fluctuations
and hmin
are difficult to distinguish, so the envelope of the temperature extremes is plotted as the blue envelope.
The red line denotes a 1 day moving average. (b) The maximum diurnal temperature variation Tr*
(defined as the difference between the daily maximum and minimum value of Tr* ), as a function of the
instantaneous phase difference between the tidal and solar cycle ( i ). Results are shown for both a
*
 0 ) shown in (a), as well as a hypothetical scenario where mean
present-day sea level scenario ( hMSL
*
 1.17 ) and tidal
sea level is increased so that the depth at low tide is equal to hmin (equivalent to hMSL
truncation no longer occurs.
fig. S2. Response of reef temperature to an interacting solar heating cycle and a diurnal (O1) tidal
cycle. (a) Reef temperature variability (black line, in dimensionless form Tr* per Eq. (3)) over two ~14
*
0
day cycles, for the same reef morphology and tidal amplitude considered in Fig. 4 (i.e., where hMSL
*
 0.17 ). The red line denotes a 1 day moving average. (b) The maximum diurnal temperature
and hmin
variation Tr* (defined as the difference between the daily maximum and minimum value of Tr* ), as a
function of the instantaneous phase difference between the tidal and solar cycle ( i ). Results are
*
shown for both a present-day sea level scenario ( hMSL
 0 ) shown in (a), as well as a hypothetical
scenario where mean sea level is increased so that the depth at low tide is equal to hmin (equivalent to
*
hMSL
 1.17 ) and tidal truncation no longer occurs.