GSA Data Repository Item 2016084
Eppes, M.C., Magi, B., Hallet, B., Delmelle, E., Mackenzie, P., Warren, K., and Swami, S., 2016,
Deciphering the role of solar-induced thermal stresses in rock weathering: GSA Bulletin,
doi:10.1130/B31422.1.
Establishing that the majority of recorded AE Events reflect
crack growth and not precipitation impacts
SUMMARY
It is likely that some number of AE events is attributable to precipitation impacts. Several
lines of evidence suggest, however, that the majority of recorded AE events reflect crack growth
and were not caused by impacts of rain drops or other precipitation. Lacking direct data on
precipitation impacts at the study site, we explore this indirect evidence in detail below or in the
text. It includes: (1) the operational frequency of the AE sensors employed in this study (150–
450 kHz) likely precludes measurement of most rain drop impacts, which have a low peakfrequency signature (30–50 kHz); although drops of higher frequencies can occur. An analysis of
event frequency data for the entire period of record suggests most measured events were
characterized by higher frequencies (see below); (2) we observe minimal correlations between
rainfall intensity or wind speed and AE rate for times when events occur or between wind
direction and event location; such correlations should exist if impacts are causing events (see
below; Figures DR1, DR4, DR6, DR17–DR20, DR26–34); there are numerous times when
intense rain is falling, but zero events are recorded (see text) (3) new visible cracks on the rock
surface were observed (Figures DR21–DR24) in areas of concentrations of recorded AE activity
(Figures DR19 and DR20; see text); (4) observed regions of maximum permanent surface
extension as recorded by strain gages (Fig. 12) corresponds to areas for which AE data indicate
clusters of events occurred (Figures DR19 and DR20; see text); (5) detailed analysis of existing
weather data from a number of sources indicates a very low or nonexistent likelihood of frozen
precipitation falling on most of the days for which we record the highest numbers of events (see
below; Table DR1); (6) there is a commonality in all AE event clusters in terms of the time of
day in which events occur (Fig. 3) that does not exist for measured precipitation or other
environmental factors (e.g., Figures 5 and 13; see text); and (7) the pilot rock experienced only
53 events, yet it was exposed to rainfall for 3 months (see text). Thus, although we cannot rule
out that some proportion of events are due to impacts, our compiled evidence suggests that a
majority of AE events measured in the boulder are instead related to cracking.
ANALYSIS FOR RAIN IMPACTS
Both experimental and observational AE data for raindrop impacts reveals that such
impacts exhibit characteristic peak frequencies generally below 30–50 kHz (Shigeishi et al.,
2000; Shiotani, 2006). Shiotani (2006) subjected AE-monitored pieces of Portland cement to
both natural precipitation and to in-lab drops from 2 m height. Shigeishi subjected AE-monitored
granite to drops from 2.5 m height. The granite experiment resulted in higher peak frequencies
(50 kHz) than did that of the cement (30 kHz), but the natural precipitation and in-lab
precipitation resulted in similar frequencies for the same material (Shiotani, 2006). These data
provide evidence for a generally low-frequency signature for natural precipitation on granite, but
do not indicate that all impacts are characterized by this low frequency. Freezing rain, defined as
precipitation that falls as supercooled liquid water (liquid phase at T < 0 C) and subsequently
freezes on the ground surface, likely shares the same acoustic emission signature.
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GSA Data Repository Item 2016084
Eppes, M.C., Magi, B., Hallet, B., Delmelle, E., Mackenzie, P., Warren, K., and Swami, S., 2016,
Deciphering the role of solar-induced thermal stresses in rock weathering: GSA Bulletin,
doi:10.1130/B31422.1.
The operational frequency (150 – 450 kHz) of our PK15I sensor should therefore
preclude measurement of rain and freezing rain impacts in most cases. The operational frequency
range of an AE sensor is defined by the peak in the curve of the range of frequencies for which
the sensor is most sensitive. Thus, it is possible, but less likely, for signals of both lower and
higher frequency than those that fall within the operational frequency range to be recorded
(Grosse and Ohtsu, 2008).
Our AE system derived both initiation frequency and average frequency for all hits
associated with events from different AE signal parameters; these frequencies represent proxies
commonly employed in signal frequency studies (Grosse and Ohtsu, 2008). The maximum for
the 4–5 sensors comprising each event averaged 281 kHz initiation frequency and 166 kHz
average frequency. Thus, these frequency data suggest that the majority of AE recorded by our
intermediate-frequency-range sensors are not produced by rain impacts, which are typically
characterized by much lower frequencies. Because existing data for the AE signature of
raindrops is reported in peak frequencies, however, raindrops can result in both lower and higher
frequency AE. The “conservative” value of filtering suggested by Shigeishi et al. (2000) was
80kHz. Therefore it is not possible to rule out the possibility that our AE sensors are recording
less frequently occurring higher-frequency precipitation impacts. We therefore explored several
additional lines of evidence to determine to what extent raindrop impacts might have been
recorded by our system.
Rainfall intensity is an established proxy for both raindrop size as well as overall impactrelated kinetic energy (Best, 1950; Licznar et al., 2008; Van Dijk et al., 2002). If the majority of
AE that we measure are related to rain impacts, a positive correlation between rainfall intensity
and AE rate would be expected, but we do not find such a correlation; to the contrary AE rates
tend to decrease with increasing rainfall intensity (Figure DR1) when all data are considered.
The ponding of water might decrease impact energy associated with raindrops (Guzel and
Barros, 2001) and thus possibly pore saturation could as well. Thus the lack of correlation
between rainfall intensity and AE might be explained by this factor. The exact relationship
between these factors and AE emissions apparently has not been measured (Barros, Ann,
personal commun.). We found that dropping 2 mm to 3 mm diameter raindrops from ~2.5 m
height produced hits but not events, and these results did not apparently change when the rock
was wet, but we did not monitor closely for this potential affect. We find no correlations between
rainfall intensity and AE hit rate when all data considered (Fig. DR29).
Because measured precipitation intensity during our rock’s deployment was heavily
skewed toward lower precipitation rates, we further analyzed the average number of events
occurring in each 0.1 mm/min rainfall intensity bin in order to minimize sampling bias effects on
the trend (Figure DR30). In doing so, a positive trend (R2 = 0.53; p-value = 0.065) is revealed
within the range of precipitation rates for which we had five or more data points; if all data are
considered, there is no visible trend or statistical correlation. The difference in average events per
minute between a rain fall rate of 0.1 mm/m and 0.9 mm/m is around 10 events (Figure DR30C).
These data provide a rough quantification of the possible background noise that may be
associated with the occasional high energy impact of a raindrop. More data at high rainfall
intensities would be necessary to draw more detailed conclusions.
In order to account for times when rain may have been falling but not recorded, given the
0.1 mm/min minimum recording rate of our system, we also compare records of AE events and
rainfall summed over increasingly long periods ranging from 1 to 60 min. For low rainfall totals
(Figures DR31b and DR32b), rainfall and AE events are significantly (p < 0.05) and negatively
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GSA Data Repository Item 2016084
Eppes, M.C., Magi, B., Hallet, B., Delmelle, E., Mackenzie, P., Warren, K., and Swami, S., 2016,
Deciphering the role of solar-induced thermal stresses in rock weathering: GSA Bulletin,
doi:10.1130/B31422.1.
correlated (r < 0), indicating that AE events decrease as rainfall increases. This correlation
becomes less negative for longer lag intervals (up to 60 min), but there is no evidence of low
rainfall events (i.e., low intensity rainfall, like a steady drizzle, that may not register more than
0.1 mm/min) causing anomalous AE events.
Finally, wind can increase the kinetic energy of precipitation impacts (Choi, 2000),
therefore if AE sensors recorded rain impacts, AE rate would be expected to increase with wind
speed, particularly on the windward side of the boulder (see below). We observe no correlation
between wind speed and rates of AE events or AE rate throughout the duration of the record
(Fig. DR4) or for instances when we are assured that rain is falling in that minute (Fig. DR33)
when all data are considered.
Because there are established relationships between rainfall intensity and kinetic energy
(Best, 1950; Licznar et al., 2008; Van Dijk et al., 2002), we further reanalyzed these correlations
with respect to AE energy measured by our sensors for each event, and found no strong trends
with respect to precipitation or wind speed (Figures DR17). Because of the potential for
sampling bias to impact these correlations, we also analyzed the frequency of occurrence of
various environmental conditions (Figures DR17), and then calculated the residual between the
two (Figure DR18) in order to determine if higher-than-expected event rates occurred under any
given environmental condition. Values of zero indicate that AE events are occurring
proportionally to the frequency that the rock experienced that condition, as would be expected if
events are occurring randomly through time. If a majority of events are being driven by raindrop
impacts or high wind speeds, then higher residuals would be expected with increasing values,
and we do not see this result.
INVESTIGATION OF HAIL, ICE PELLETS, OR SLEET IMPACTS
Frozen precipitation includes a wide variety of forms (graupel, snow pellets, ice pellets,
sleet and hail) reflecting distinct formation mechanisms, but it is likely that all forms result in
overall higher AE signal amplitude and frequencies upon impact than those of rain. All forms of
frozen precipitation are reported by National Weather Service (NWS) weather observers.
We could find no published data regarding the Acoustic Emission signature of frozen
precipitation. Thus, some measured AE events may have recorded impacts of hail or other frozen
forms of precipitation, which are associated with generally higher kinetic energy and thus are
more likely to trigger our AE sensors. In order to assess the probability of frozen precipitation
during AE events, we therefore examined our on-site weather data, in combination with
publically available automated weather station data, archived severe weather reports, radarderived weather products, and lightning strike reports (Table DR1). In a majority of cases, we
find zero to low probability of frozen precipitation falling on the rock during event times.
Hail and Graupel
Hail and graupel are frozen precipitation that mainly form in convective clouds – clouds
exhibiting strong, upward air motion such as cumulonimbus clouds. Frozen precipitation with
diameter greater than 5 mm is hail, while all varieties of frozen precipitation forming in
convective clouds are graupel. Other hydrometeor classifications for frozen precipitation include
ice pellets and snow pellets. Graupel or hail can occur any time of the year but is more common
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GSA Data Repository Item 2016084
Eppes, M.C., Magi, B., Hallet, B., Delmelle, E., Mackenzie, P., Warren, K., and Swami, S., 2016,
Deciphering the role of solar-induced thermal stresses in rock weathering: GSA Bulletin,
doi:10.1130/B31422.1.
in spring, summer, and fall when convective storms are more numerous. In general hail is a very
localized phenomenon and relatively rare in any given location.
No hail or graupel was reported in the hourly reports from the KAKH or KCLT NWS
weather stations located within 10–15 km of the study site for the entire period of record. There
is no report of hail with diameter greater than 25 mm within 10 km of the field site for any day
on which events occur from the NOAA Storm Prediction Center (SPC) observer reports
(http://www.spc.noaa.gov/). Haywood Rankin, the property manager for the Redlair Reserve
(www.redlair.org) where the rock was deployed, keeps a weather journal and also reported no
graupel or hail during any days with AE events.
In addition to direct observations of graupel or hail falling in the vicinity of the study site,
lightning strikes and radar data can be used to assess the likelihood of graupel/hail by
determining whether conditions were favorable at specific times and locations for these types of
precipitation. The charging mechanism for lightning requires the presence of significant mass
(quantity) of upward and downward moving ice within the cloud itself (e.g., Blyth et al., 2001),
so the absence of lightning near the deployed rock would indicate a minimal possibility of
graupel or hail precipitating from the cloud.
The presence of ice in the atmosphere, and thus the possibility that it might fall to the
ground prior to melting, can also be evaluated using radar data. NWS and other weather
forecasters regularly use radar data to derive a “Hail Index” based on 3D radar profiles. The Hail
Index is defined as “a product designed to locate storms that have the potential to produce hail”
at https://www.ncdc.noaa.gov/data-access/radar-data/nexrad-products and archived Hail Indices
are used to further assess the likelihood of hail; they can help assess whether conditions were
favorable for hail or not. A favorable condition, however, does not mean that ice in the cloud
reached the ground because, and without direct observation or measurement, whether
graupel/hail struck the ground cannot be confirmed.
We examined lightning (data available at https://www.ncdc.noaa.gov/data-access/severeweather/lightning-products-and-services) and radar (Hail Index https://www.ncdc.noaa.gov/dataaccess/radar-data) data from the 12 highest non-winter AE event days (discussed below), paying
particular attention to two radars located within range of the rock (TCLT in Charlotte, east of the
rock; KGSP in Greenville-Spartanburg southwest of the rock; TCLT is much closer to the rock).
Based on all these data, we conclude there was nearly zero chance of graupel/hail on 5 of the 12
days, a low chance on 4 of the 12 days, and a reasonably high chance on 3 of the 12 days (Table
DR1). Furthermore, hail virtually always falls with rain in nearby vicinity - the dynamics of
severe weather practically guarantees this, therefore the lack of correlation between rainfall
intensity and events further substantiates the unlikelihood that hail fell on a majority of these
high event days.
SLEET
Sleet usually occurs in winter conditions when falling snowflakes melt and refreeze
during their descent due to a relatively warm layer of air overlying a sub-freezing layer of air
near the surface. Radar data can be used to determine the possibility of sleet, but this feature
requires technology that was not installed at KGSP in 2010–2011. Sleet can also occur when
surface air temperatures are slightly above freezing (sleet formation depends more on the
location and depths of the warm and the freezing layers of air above the surface). As previously
mentioned in the text, ~17% of all events occurred when the air was below 0ºC and ~35%
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GSA Data Repository Item 2016084
Eppes, M.C., Magi, B., Hallet, B., Delmelle, E., Mackenzie, P., Warren, K., and Swami, S., 2016,
Deciphering the role of solar-induced thermal stresses in rock weathering: GSA Bulletin,
doi:10.1130/B31422.1.
occurred when the air was between 0º and 5ºC. There are 111 instances on 6 different days when
we record precipitation and temperatures below freezing during our monitoring period; however
we record only 15 AE events on those days. Thus, in general the large majority of events did not
occur when atmospheric temperatures were conducive to sleet.
On January 10th and 11th, freezing temperatures shut down the functioning of our tipping
bucket, and observer reports indicated that primarily freezing rain or snow occurred throughout
event times on the 10th (Fig. 9) and all freezing rain occurred on the 11th. The rise in surface
temperatures associated with each cluster of events that we observed on these dates suggests that
freezing rain, rather than sleet or snow, was falling during event times (See text).
AE events occurred during only 10 out of the 923 min when any rainfall was recorded
while ambient air temperatures were below 5ºC. For the only two high event days that
experienced these conditions (December 4th and December 18th), there are minimal to no
observational reports that suggest that sleet was falling at the rock location (Table DR1).
SUMMARY OF THE EFFECT OF ICE PRECIPITATION ON AE EVENTS
Based on the above analysis for graupel, hail, and sleet, for the top 16 days with the
highest events (comprising 91% of all events), we can unambiguously rule out hail or sleet
impact as the main cause of emissions for 5 of the these days because there is no chance of such
precipitation falling on these days during event times. For the remaining 11 dates, there is a very
low probability of sleet or hail on 8 of them. We explore AE location data (see below) as a final
test of the probability that impacts were causing events on these 11 dates.
AE LOCATION DATA ANALYSIS
As mentioned in the text, a majority of event locations recorded were located in the upper
hemisphere of the rock (Fig. 12). This result is consistent with raindrop impacts falling on an
upper rock surface whose orientation is most normal to raindrop trajectory. We note however
that a significant portion of those upper-hemisphere events actually are located in the nearinterior of the rock (Fig. 12B). Furthermore, the top of the rock also experienced the most
permanent strain (Fig. 11) consistent with a correlation between AE and cracking.
Nevertheless, we further analyze event locations in the context of wind direction because
wind-driven rain may change the direction from which rain is impacting the rock surface. We
first assume that if AE sensors are recording rain, sleet or hail impacts, that the AE events would
be preferentially located on the windward side of the rock. We plot wind direction during all
events (Fig. 19B.) as well as a sub-portion of same data for only times when winds are blowing
at speeds > 3.1 m/s which corresponds to a gentle breeze on the Beaufort wind scale (Fig. 19C).
We also calculated the orientation (projected on a horizontal plane) of a line drawn from the
center of the boulder to each AE location (n = ~30,000) and plot those orientations (Fig.
DR19A). As such, even events falling on the top of the rock will plot directionally unless they
fall right at the very center. The position of the AE event relative to the boulder center are
dominated by two modes (north and east) whereas wind directions during events are dominated
by NE and SW modes, with SW modes being dominant for stronger winds. We observe similar
results for the 11 individual days that had some chance of frozen precipitation (Figure DR20;
Table DR1). We further explore the high event days (one of which is Jan 10, a day that we know
was characterized by a winter storm; the other is Aug. 5 a day when hail is reported within 100
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GSA Data Repository Item 2016084
Eppes, M.C., Magi, B., Hallet, B., Delmelle, E., Mackenzie, P., Warren, K., and Swami, S., 2016,
Deciphering the role of solar-induced thermal stresses in rock weathering: GSA Bulletin,
doi:10.1130/B31422.1.
km of the field site) that experience sustained strong winds during event clusters and also find
that the majority events are not located on the windward side of the boulder (Figure DR34).
These results show that the location of events in a majority of cases, does not correspond with
wind direction, providing further evidence that they are not due to impacts.
REFERENCES CITED
Best, A., 1950, The size distribution of raindrops: Quarterly Journal of the Royal Meteorological
Society, v. 76, no. 327, p. 16–36, doi:10.1002/qj.49707632704.
Blyth, A., Christian, H., Driscoll, K., Gadian, A., and Latham, J., 2001, Determination of ice
precipitation rates and thunderstorm anvil ice contents from satellite observations of
lightning: Atmospheric Research, v. 59-60, p. 217–229, doi:10.1016/S0169-8095(01)00117X.
Choi, E.C., 2000, Variation of wind-driven rain intensity with building orientation: Journal of
Architectural Engineering, v. 6, no. 4, p. 122–128, doi:10.1061/(ASCE)10760431(2000)6:4(122).
Grosse, C.U., and Ohtsu, M., 2008, Acoustic emission testing: Berlin, Springer, 396 p.
doi:10.1007/978-3-540-69972-9.
Guzel, H., and Barros, A.P., Using acoustic emission testing to monitor kinetic energy of
raindrop and rainsplash erosion, in Proceedings Soil Erosion 2001: Honolulu, American
Society of Agricultural and Biological Engineers, p. 525.
Licznar, P., Lomotowski, J., Błonski, S., and Ciach, G.J., 2008, Microprocessor field
impactometer calibration: do we measure drops’ momentum or their kinetic energy?: Journal
of Atmospheric and Oceanic Technology, v. 25, no. 5, p. 742–753,
doi:10.1175/2007JTECHA938.1.
Shigeishi, M., Shiotani, T., and Ohtsu, M., 2000, A consideration about the rainy influence in
field AE measurement: Prog. in acoustic emission X: JSNDI, p. 177–182.
Shiotani, T., 2006, Evaluation of long-term stability for rock slope by means of acoustic
emission technique: NDT & E International, v. 39, no. 3, p. 217–228,
doi:10.1016/j.ndteint.2005.07.005.
van Dijk, A., Bruijnzeel, L., and Rosewell, C., 2002, Rainfall intensity–kinetic energy
relationships: a critical literature appraisal: Journal of Hydrology (Amsterdam), v. 261,
no. 1-4, p. 1–23, doi:10.1016/S0022-1694(02)00020-3.
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GSA Data Repository Item 2016084
Eppes, M.C., Magi, B., Hallet, B., Delmelle, E., Mackenzie, P., Warren, K., and Swami, S., 2016,
Deciphering the role of solar-induced thermal stresses in rock weathering: GSA Bulletin,
doi:10.1130/B31422.1.
TABLE DR1. ASSESSMENT OF THE LIKELIHOOD OF FROZEN PRECIPITATION (SLEET,
GRAUPEL, HAIL) FALLING WHILE MORE THAN 90% OF THE AE EVENTS WERE RECORDED
Date
Total Events
Likelihood of Frozen
Explanation
Precipitation
04-Dec-10
9297
sleet–low
KCLT—zero precip to light rain and ice pellets
hail - zero
KAKH—zero precip. to light rain w/fog and mist
Rankin journal—none noted for entire day
NOAA—no frozen precipitation reported
10-Jan-11
4692
Sleet–low
KCLT—light freezing rain and ice pellets
hail - zero
changing to light freezing rain only
KAKH—light freezing rain fog/mist
Rankin journal—winter weather noted
NOAA—snow
05-Aug-10
3583
sleet–zero
KCLT—no hail reported
hail–medium
KAKH—no hail reported
Rankin journal—none noted for entire day
TCLT Hail Index—high
NLDN lightning—high
18-Dec-10
2657
sleet–low
KCLT—zero to light snow and ice pellets
hail - zero
KAKH—light snow fog/mist
Rankin Journal—none noted for entire day
NOAA—no frozen precipitation reported
14-Aug-10
2135
sleet–zero
KCLT—no hail reported
hail–zero
KAKH—no hail reported
Rankin journal—none noted for entire day
TCLT Hail Index—zero
NLDN lightning—zero
21-Jul-10
1283
sleet–zero
KCLT—no hail reported
hail–zero
KAKH—no hail reported
Rankin journal—none noted for entire day
TCLT Hail Index—zero
NLDN lightning—zero
11-Aug-10
1005
sleet–zero
KCLT—no hail reported
hail–zero
KAKH—no hail reported
Rankin journal—none noted for entire day
TCLT Hail Index—low
NLDN lightning—zero
25-Jul-10
780
sleet–zero
KCLT—no hail reported
hail–zero
KAKH—no hail reported
Rankin journal—none noted for entire day
TCLT Hail Index—low
NLDN lightning—zero
17-Jul-10
691
sleet–zero
KCLT—no hail reported
hail–medium
KAKH—no hail reported
Rankin journal—none noted for entire day
TCLT Hail Index—high
NLDN lightning—low
28-Feb-11
659
sleet–zero
KCLT—no hail reported
hail–low
KAKH—no hail reported
Rankin journal—none noted for entire day
TCLT Hail Index—medium
NLDN lightning—medium
05-Apr-11
654
sleet–zero
hail–low
18-Jul-10
588
sleet–zero
hail–low
27-Apr-11
553
sleet–zero
hail–medium
11-Jan-11
518
sleet–low
hail–zero
KCLT—no hail reported
KAKH—no hail reported
Rankin journal—none noted for entire day
TCLT Hail Index—low
NLDN lightning—zero
KCLT—no hail reported
KAKH—no hail reported
Rankin journal—none noted for entire day
TCLT Hail Index—medium
NLDN lightning—medium
KCLT—no hail reported
KAKH—no hail reported
Rankin journal—none noted for entire day
TCLT Hail Index—high
NLDN lightning—medium
KCLT—light freezing drizzle (small rain)
KAKH— light freezing rain
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GSA Data Repository Item 2016084
Eppes, M.C., Magi, B., Hallet, B., Delmelle, E., Mackenzie, P., Warren, K., and Swami, S., 2016,
Deciphering the role of solar-induced thermal stresses in rock weathering: GSA Bulletin,
doi:10.1130/B31422.1.
Rankin journal—winter weather noted
NOAA—no freezing precip. reported
03-May-11
359
sleet–zero
KCLT—no hail reported
hail–low
KAKH—no hail reported
Rankin journal –none noted for entire day
TCLT Hail Index—medium
NLDN lightning—high
12-Aug-10
358
sleet–zero
KCLT—no hail reported
hail–zero
KAKH—no hail reported
Rankin journal—none noted for entire day
TCLT Hail Index—low
NLDN lightning—zero
For each the 16 days with the highest numbers of events overall for the period of record, we
examined hourly weather reports from regional weather stations KCLT (16 km from site) and KAKH (12
km from site), all available data from NOAA Winter Weather Reports, and referred to property owner,
Haywood Rankin’s weather journal. We report any/all frozen precipitation noted in any of these sources for
the times and dates of events for the study region. For warmer weather days, we also examined radar and
lightning data for the chance that frozen precipitation fell in the vicinity of the rock.
A likelihood of zero indicates an infinitesimal probability that frozen precipitation fell to the ground
because there were no lightning strikes, and hail in the vicinity of the rock was highly improbable. A low
likelihood indicates that weather conditions were minimally favorable to the stated type of precipitation
type, and most reports indicated no such precipitation. Medium likelihood indicates that weather conditions
were generally favorable for such precipitation, but no reports indicated that such precipitation fell.
BBoulder
SSoil
TABLE DR2. MATERIAL PROPERTIES USED TO MODEL TEMPERATURE AND STRESS
Modulus of elasticity
Poisson ratio
Density
Thermal Conductivity
Specific Heat,
(Mpa)
(kg/m3)
(W/m °K)
(J/Kg °K)
53000
0.28
2760
2.6
1000
75
0.35
1600
1.5
750
Page 8 of 8
Emissivity
0.45
0.65
Data Repository Materials
Deciphering the role of solar‐induced thermal stresses in rock weathering
Martha Cary Eppes1*, Brian Magi1, Bernard Hallet2, Eric Delmelle1, Peter Mackenzie3 , Kimberly Warren4, Suraj Swami1, 1Department of Geography and Earth Sciences, University of North Carolina at Charlotte, Charlotte NC 28223
2 Department of Earth and Space Sciences, University of Washington, Seattle Washington, 98195 3 Department of Civil and Environmental Engineering, University of Washington, Seattle Washington, 98195 4Department of Civil and Environmental Engineering, University of North Carolina at Charlotte, Charlotte NC 28223
Figure DR1. Precipitation Intensity vs. event rate for all minutes in which rainfall was recorded at our site and for which AE data are available (n = 3925). R2 = 0.002 ; Pearson r = 0.05; Pearson P‐value = 0.002. The kinetic energy of liquid precipitation is proportional to drop size, which in turn is strongly correlative with rainfall intensity (e.g. Best, 1950; Van Dijk et al., 2002); therefore if our AE sensors are measuring rainfall impacts (including freezing rain which is precipitation falling as liquid water that freezes on cold surfaces) it is expected that a correlation would exist between AE rate and rainfall intensity, which we do not observe. Events occurred during only 147 of these 3925 total minutes when rainfall was recorded. Note that given the tipping bucket capacity of 0.1 mm, all rainfall occurring at greater than 0.1 mm/min rates indicates that rainfall was occurring at a minimum of 0.1 mm/min. during that minute.
6/27/2008 5 events (9 min)
6/30/2008 2 events (5 min)
1st AE Event
9:08 P M
T8
T2
Ambient
Temperature
1st AE Event 8 :32 PM
T2
T8
Ambient T emperature
Temperature
Differential
Temperature
Differential
7/3/2008 1 event (1 min)
7/4/2008 35 events (18 min)
st
1st AE Event 6:34 PM
T2
1 AE Event 1:53 AM
T2
T8
Ambient
Temperature
T8
Ambient
Temperature
Temperature
Differential
Temperature
Differential
7/22/2008 11 event (20 min)
8/10/2008 1 event (1 min)
1 st AE Event 12 :07 A M
1st AE Event 9 :08 PM
T2
T2
T8
T8
Ambient
Temperature
Ambient
Temperature
Temperature
Differential
Temperature
Differential
Figure DR2. Pilot Deployment Data (see text). 55 total AE events were recorded during seven total days for the three month monitoring period (June ‐ August, 2008). Graphs depict time series data (midnight – 11:59) for six of these days. The date, total number of events, and duration of the event cluster are indicated at the top of each graph. Ambient air temperature is depicted as well as rock surface temperature for the two thermocouples that recorded the hottest and coolest temperatures at the time of the event cluster. The red line depicts the running calculation of the difference in temperature between the hottest and coolest temperatures recorded at each minute; similar to the green lines in Figure 4 in the text. The remaining event occurred at 2:11 am on August 7.
Figure DR3. Bivariate correlation between ambient air temperature and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. Figure DR4. Bivariate correlation between wind speed vs. event rate for all minutes in which events occur (n = 1201). Statistics are available in Table 1 of the main text. If rain or other precipitation was falling at rates lower than the capacity of our tipping bucket (Supplementary Information_DR1), and such precipitation was causing impact‐related events, we might expect an overall correlation between wind speed and event rate, which we do not observe. Figure DR5. Bivariate correlation between relative humidity and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. Figure DR6. Bivariate correlation between precipitation rate and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. Figure DR7. Bivariate correlation between barometric pressure and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. Figure DR8. Bivariate correlation between insolation and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. Figure DR9. Bivariate correlation between the average rock surface temperature recorded by all 8 thermocouples and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. Figure DR10. Bivariate correlation between the maximum rock surface temperature recorded by any of the 8 thermocouples and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. Figure DR11. Bivariate correlation between the minimum rock surface temperature recorded by any of the 8 thermocouples and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. Figure DR12. Bivariate correlation between the average daily maximum – minimum rock surface temperature difference recorded for each of the 8 thermocouples (Average (T1 daily max – T1 daily min, T2 daily max – T2 daily min, . . . T8 daily max – T8 daily min) and event rate for each day in which events occur (n = 99). Statistics are available in Table 1 of the main text. Figure DR13. Bivariate correlation between the average per minute rock surface temperature difference recorded between all 8 thermocouples (T1‐T8 Max – T1‐T8 Min) and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. Figure DR14. Bivariate correlation between the average absolute change in temperature from the previous minute calculated for all 8 thermocouples (Average (l T1 during event – T1 in the prior minute l, l T2 during event – T2 during prior minute l, . . . l 8 during event – T8 during prior minute l) and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. Figure DR15. Bivariate correlation between the maximum change in temperature from the previous minute determined between all 8 thermocouples (Maximum (T1 during event – T1 in the prior minute, T2 during event – T2 during prior minute, . . . T8 during event – T8 during prior minute) and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. Figure DR16. Bivariate correlation between the minimum change in temperature from the previous minute determined between all 8 thermocouples (Minimum (T1 during event – T1 in the prior minute, T2 during event – T2 during prior minute, . . . T8 during event – T8 during prior minute) and event rate for each minute in which events occur (n = 1201). Statistics are available in Table 1 of the main text. A
B
Figure DR17. Analysis of AE Energy and Environmental Variables. A. The fraction of the measurement period during which various environmental conditions occurred. B. The fraction of AE event Energy (n = 32,585) measured during the entire monitoring period under those different environmental conditions. Figure DR18. The residual between Figures in 17A vs 17B. By subtracting the differences within individual bins of data, it can be determined to what extent AE energy was expended under different environmental conditions more (positive values) or less (negative values) than if they occurred randomly, and thus proportionately to the condition themselves. A. Event Direction
All Events
B. Wind Direction
During All Events
C. Wind Direction
during All Events for times when wind speed is > “gentle breeze”
Figure DR19. Rose diagrams of event locations and wind direction . A. Azimuthal directions of the line connecting the center of the rock and each event location (projected on a horizontal plane from center outward) derived from all of our AE data for which we had localizations (n = 29,385). B. wind direction measurements made on site for all minutes when events occurred. N=1201. C. wind direction for times when events occurred and wind speeds were greater than 3.1 m/s, a “gentle breeze” on the Beaufort Scale (n = 273). Wind
Dec 4
12/4/2010
1/10/2011
Events
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Events
7/18/2010
2/28/2011
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7/17/2010
12/21/2010
4/27/2011
Figure DR20. Rose diagrams of wind direction and event location direction for different high event days (see text and Supplementary Information_DR1). Wind column represents wind direction (blowing from the direction indicated) measurements made on site for all minutes when events occurred on the dates indicated. Event column represents event directions for the same times, calculated by determining the azimuthal direction of the line connecting the center of the rock and the event location derived from our AE data (projected on a horizontal plane from center outward). Note that events are rarely located on the windward portion of the rock. Figure DR21. Photograph of the pre‐existing “dimple” on the western side of the test specimen boulder before instrumentation and deployment. The circle with the “5” is approximately 2 cm in diameter. At the time of deployment there was no loose material or wide cracks in the zone of the circle or surrounding area. The following image shows the same area after 11 months of exposure. Figure DR22. Photograph of the “dimple” on the western side of the test specimen boulder after instrumentation and 11 month deployment. The circle with the “5” is approximately 2 cm in diameter.
At the time of deployment there was no loose material or wide cracks in the zone of the circle or surrounding area. After deployment, this zone is friable and loose with 0.5 cm size pieces detaching from the rock surface. All cracks appear more distinct, deeper and in some cases longer after deployment. A.
B.
Figure DR23. Photographs of the same region of a portion of the eastern side of the test specimen boulder A. before instrumentation and deployment and B. after an 11 month deployment in the field. Circle with the “3” is in the same location and is ~2 cm diameter in both photographs. The arrow points to the region where a ~1 cm lineation was apparent both prior to and following deployment, however after deployment there is obvious evidence of an open crack. In the circle, a mafic mineral appears to be missing in the after photo in the lower left region of the “H” defined by the 5 mafic minerals in the circle. Figure DR24. Photographs of the same region of a portion of the northern side of the test specimen boulder A. before instrumentation and deployment and B. after an 11 month deployment in the field. Circle is in the same location in both photographs; a clearly delineated crack is present after deployment that was only evident as a lineation of mineral grains prior to deployment. Figure DR25. 24 hour time series data for September 26, 2010 showing event rate and precipitation intensity. This day is typical of many days in which events occur in conjunction with extreme weather in that the event cluster occurred at the onset of precipitation, but then precipitation continued at very high intensities without coinciding events. Sensor 1, top
Temperature, Celsius
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Figure DR26. Validation of thermal component of model. The comparison between the measured (red) and modelled (yellow) surface temperatures for two sensor locations during a representative winter day (January 14, 2011; Figure 4 of text) shows that the model represents the overall diurnal temperature variation well. Higher frequency variations due to clouds and others effects are not addressed.
27
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Figure DR27. Figure DR27. Modelled distribution of the maximum principal stress magnitude in a 20 cm‐boulder at different times of day. Plots highlight regions under tension. Grey colours
indicate regions where the maximum principal stress is compressive, and the other colours
where it is tensile, reaching 0.75 Mpa in yellow regions. The plots do not show regions with high compression because the stresses there are, by convention, negative; these include the outer
portion of the boulder at noon, shown in upper diagram, and the center of the boulder at ~sunset in the lower.
Figure DR28. Histogram of data occurring during indicated temperature rate of change ranges. ex: the 1st column is > 2°C/min and ≤ 3/min°. No bars indicates a value of zero. RED: instances during the entire period of record when the rate of per‐minute temperature change on one or more of the 8 rock surface thermocouples was >2°C/min (n = 3933). BLUE: total numbers of events that occurred under the indicated temperature range. Green: numbers of minutes in which events occurred under the indicated temperature range. Figure DR29. Precipitation Intensity vs. Hit Rate for all minutes in which rainfall was recorded at our site and for which AE hit data are available (n = 3925). R2 = 0.06 ; Pearson r = 0.05; Pearson P‐value = <.001. Hits occurred during 2521 of these 3925 total minutes when rainfall was recorded. The kinetic energy of liquid precipitation is proportional to drop size, which in turn is strongly correlative with rainfall intensity (e.g. Best, 1950; Van Dijk et al., 2002); therefore if our AE sensors are measuring rainfall impacts (including freezing rain which is precipitation falling as liquid water that freezes on cold surfaces) it is expected that a correlation would exist between AE rate and rainfall intensity, which we do not observe. Even at very high precipitation intensities, zero hits are recorded; providing evidence that the majority of hits that our AE sensors are recording are not likely rainfall. We recorded 1404 instances of rainfall with zero hits by any sensor, supporting the idea that our sensors are not overly sensitive to raindrop impacts. A
C
B
Figure DR30. Accounting for sampling bias associated with low intensity rainfall. All precipitation data is per minute. A. Precipitation Intensity vs. Event Rate for all minutes in which rainfall was recorded at our site and for which AE event data are available (n = 3925). B. The frequency of rainfall of different intensity. C. The mean number of events occurring in the same precipitation intensity bins as A & B. Red dots indicate > 5 data per bin. A.
B.
Figure DR31. Bivariate Plots of Rainfall Intensity (mm/min) during each minute when rain and/or events are recorded vs. Events, whereby total events are summed over the past 60, 40, 20, 10, 5, 2, 1, and 0 minutes (indicated as “prior1, etc”). Because events range over several orders of magnitude, the events are plotted as log‐transformed values, such that logevents = log10(events+1). This transform compresses the range of observed values of events, and preserves zero events such that when zero events occur, then logevents = log10(1) = 0 as well. All Figures show the linear correlation coefficient (r), and the statistical significance of the r value (p). A. Graphs depict all data. (n = 5198) B Graphs depict only low rainfall intensities (< 1 mm/min). (n = 5184) The 0 minutes total means that no prior events were considered in the comparison – the raw data. All events are log‐transformed after the raw values are totaled.
A.
B.
Figure DR32. Bivariate Plots of Rainfall vs. Events for all minutes in which rainfall and/or events were recorded, whereby both rainfall and events are summed over the past 60, 40, 20, 10, 5, 2, 1, and 0 minutes (indicated as “prior1, etc”). Because events range over several orders of magnitude, the events are plotted as log‐transformed values, such that logevents = log10(events+1). This transform compresses the range of observed values of events, and preserves zero events such that when zero events occur, then logevents = log10(1) = 0 as well. All Figures show the linear correlation coefficient (r), and the statistical significance of the r value (p). A. Graphs depict all data. N=5198 B Graphs depict only low rainfall intensities (< 1 mmm/min). n = 5184. The 0 minutes total means that no prior events were considered in the comparison – the raw data. All events are log‐transformed after the raw values are totaled.
Figure DR33. Wind Speed vs. Event and Hit Rate for all minutes in which events (or hits) occur and wind speeds are >2 m/sec and precipitation intensity is > 0.1 mm/min (n = 222). Wind v. Events R2 = 0.04; Pearson r = 0.19, Pearson P‐value = 0.004. Wind v. Hits R2 = 0.08 ; Pearson r = 0.28; Pearson P‐value = <0.001. Our tipping bucket recorded rainfall in 0.1mm increments. Therefore this graph depicts all events that occurred when rainfall was actively falling at a minimum rate of 0.1mm/min and winds were at or above a ‘light breeze’ on the Beaufort wind scale (i.e. wind felt on face). If AE sensors were recording raindrop impacts, it would be predicted that the kinetic energy of impacts would increase with windspeed and thus the likelyhood of producing a threshold‐crossing AE event should also increase. The fact that we see no trend provides evidence that the majority of AE events and hits are not recording raindrop impacts. A. Strong Wind (Aug. 5)
B. Events during strong wind (Aug. 5)
C. Strong Wind (Jan. 10)
D. Events during strong wind (Jan. 10)
Figure DR34. Rose diagrams of wind direction and event location direction for the two high event days that experienced multiple minutes of windspeeds >3.1 m/sec. A. wind direction measurements made on site for all minutes when events occurred on Aug. 5 and wind speed was >3.1 m/sec (n = 11). B. Event directions for the same times as (A). (n = 1615). Calculated by determining the azimuthal direction of the line connecting the center of the rock and the event location derived from our AE data (projected on a horizontal plane from center outward) C. wind direction measurements made on site for all minutes when events occurred on Jan 10 and wind speed was >3.1 m/sec (n = 20). D. Event directions for the same times as (C) calculated as above. (n = 668).