PDF full text - engr.uconn.edu

GEOPHYSICAL RESEARCH LETTERS, VOL. 38, L19703, doi:10.1029/2011GL049017, 2011
Vegetation dynamics contributes to the multi‐decadal variability
of precipitation in the Amazon region
Guiling Wang,1 Shanshan Sun,1 and Rui Mei1
Received 22 July 2011; revised 5 September 2011; accepted 7 September 2011; published 7 October 2011.
[ 1 ] Precipitation in most of the Amazon shows multi‐
decadal fluctuations that were linked to oceanic forcing in
the Atlantic. This modeling study shows that vegetation
dynamics may play a major role in such low‐frequency variability in the Amazon. Despite the large amount of annual
precipitation, the presence of a dry season (albeit short) facilitates a strong impact of dynamic vegetation on precipitation
persistence in the model. The year‐to‐year variation of net
primary productivity (NPP) is dominated by that of the dry
season NPP. As a result, above‐normal (below‐normal) precipitation in a particular year can enhance (suppress) vegetation growth, leading to widespread increase (decrease) of
vegetation density in the subsequent year. Precipitation in
the subsequent year is therefore more likely to be above
(below) normal. This damping effect of vegetation enhances
low‐frequency variability of precipitation and leads to recurrent droughts or floods, a result previously considered characteristic of arid and semi‐arid regions. Citation: Wang, G.,
S. Sun, and R. Mei (2011), Vegetation dynamics contributes to the
multi‐decadal variability of precipitation in the Amazon region,
Geophys. Res. Lett., 38, L19703, doi:10.1029/2011GL049017.
1. Introduction
[2] Precipitation in the Amazon region is characterized by
multi‐decadal fluctuations, with recent regime shifts around
1940s and 1970s [Marengo, 2004]. Although El Nino
Southern Oscillation is an important factor influencing the
inter‐annual variability of precipitation in the Amazon [e.g.,
Grimm and Tedeschi, 2009], this low‐frequency variability
seems more related to sea surface temperature in tropical and
subtropical Atlantic (Marengo [2009] and the reviews
therein). While oceanic forcing is an important driver for
precipitation variability, soil moisture and vegetation feedback may also play a major role in regions like the Amazon
where climate is sensitive to land surface conditions [e.g.,
Costa et al., 2007]. This study explores the role of vegetation
dynamics in the low‐frequency variability of precipitation in
the Amazon region.
[3] Numerical modeling studies using climate models of
various complexities coupled with dynamic global vegetation
models (DGVMs) repeatedly demonstrated that vegetation
dynamics is an important mechanism for decadal and multi‐
decadal variability of precipitation in several regions. For
example, Zeng et al. [1999] and Wang and Eltahir [2000a]
using reduced form climate models found that feedback
1
Department of Civil and Environmental Engineering and Center
for Environmental Sciences and Engineering, University of Connecticut,
Storrs, Connecticut, USA.
Copyright 2011 by the American Geophysical Union.
0094‐8276/11/2011GL049017
from dynamic vegetation contributes to perpetuating precipitation anomalies and enhances low‐frequency variability of
rainfall in the Sahel region. This finding is confirmed by
studies using general circulation models (GCMs) coupled
with DGVMs [e.g., Wang et al., 2004; Delire et al., 2004,
2011]. Delire et al. [2004] further demonstrated that this
enhancement of low‐frequency variability by vegetation
dynamics is most likely to occur in the transition zone
between dry and wet climates, i.e., semi‐arid regions, which
is consistent with the locality of strong soil moisture‐
precipitation coupling [Koster et al., 2006].
[4] Here, this study presents evidence from a numerical
model that vegetation dynamics may have contributed to the
observed low‐frequency variability of precipitation in the
Amazon, a region much wetter than the “hotspots” of land‐
atmosphere coupling identified in previous studies. Despite
the large amount of annual precipitation in this region, the
presence of a dry season facilitates a strong feedback between
vegetation and precipitation.
2. Model and Experimental Design
[5] The model used here is the NCAR Community
Atmosphere Model version 3 coupled with the Community
Land Model version 3 including dynamic global vegetation
model (CAM3‐CLM3‐DGVM). Descriptions of the different
model components are given by Collins et al. [2004], Oleson
et al. [2004], and Levis et al. [2004]. At each time step of
the coupled model, CAM3 simulates the atmospheric processes and provides atmospheric forcing to CLM3‐DGVM,
while CLM3‐DGVM simulates the land surface biophysical,
physiological, biogeochemical processes and ecosystem
dynamics and provides surface fluxes to CAM3. Consistent
with the very strong soil moisture‐precipitation coupling in
CAM3‐CLM3 [Koster et al., 2006; Guo et al., 2006; Wang
et al., 2007], precipitation in the model is highly sensitive to
prescribed evapotranspiration (ET) changes [Mei and Wang,
2010; Sun and Wang, 2011]. However, the sensitivity of ET
to prescribed vegetation changes in CLM3 is very low, which
limits the response of precipitation to vegetation changes
[Sun and Wang, 2011]. As a result, in most of the Amazon
region in the model, precipitation increases only slightly with
prescribed increase of vegetation density [Mei and Wang,
2010; Sun and Wang, 2011].
[6] In this study, two main experiments (“Dynamic” and
“Static”) are designed to examine the impact of vegetation
dynamics on precipitation variability using the CAM3‐
CLM3‐DGVM model. Both experiments are 108 years long,
driven with the Hadley Center sea ice and sea surface temperature data (HadISST) [Rayner et al., 2003] during the
period 1901–2008. In “Dynamic”, the model functions
in its normal mode, predicting the year‐to‐year changes of
L19703
1 of 5
L19703
WANG ET AL.: VEGETATION DYNAMICS AND AMAZON RAINFALL
L19703
(e.g., N years). First, the power spectrum of annual precipitation time series is estimated. The power spectrum is then
integrated over the whole frequency domain [0, 1] to derive
a representation for the total variance (Vtot), and the power
spectrum integration over the frequency range [0, N1 ] reflects
the variance with time scales longer than N years (VN). We
use the ratio VN /Vtot as a measure for the fraction of low‐
frequency variability. In this study we examine the low‐
frequency fractions for N = 5 and N = 10, respectively.
The CRU TS 3.0 precipitation at spatial resolution of 0.5 ×
0.5 degrees during the period 1901–2006 is used as the
observational reference.
3. Results
Figure 1. Fraction of precipitation variance with time scale
longer than (top) 5 years and (bottom) 10 years, based on
CRU data over land during the period 1901–2006.
vegetation distribution and structure; in “Static”, DGVM is
turned off and vegetation is prescribed with no inter‐annual
variation. To ensure consistency with the CAM3‐CLM3‐
DGVM climatology, this prescribed vegetation is derived
from the last year of a 200‐year CAM3‐CLM3‐DGVM
simulation driven with climatological SST forcing. This
vegetation state is also used to initialize the model for the
“Dynamic” experiment. With SST varying as observed
during 1901–2008, the difference between “Static” and
“Dynamic” in precipitation variability results from vegetation dynamics modulating the effects of global oceanic
forcing. To quantify the magnitude of low‐frequency variability in precipitation, we use the fraction of precipitation
variance with time scales longer than a certain threshold
[7] Based on the low‐frequency fraction estimated for the
CRU precipitation, three “hotspots” of low‐frequency variability stand out in the Tropics and Subtropics, including
portions of the Amazon, the African Sahel region, and central
Australia. Of these three, Amazon is the only wet climate
regime, for which the details are shown in Figure 1. Fractions
of variance at times scales longer than 5 years and 10 years
both identify an area of strong low frequency variability in the
equatorial Amazon and an area further south.
[8] The model‐simulated precipitation variability in
“Static” (i.e., with SST varying as observed but with static
vegetation) shows a much weaker low‐frequency signal than
the CRU data (Figure 2, left). For example, CRU data indicates vast areas where over 70% of the total precipitation
variance comes from components with time scales longer
than 5 years, and this value is less than 50% in the model with
static vegetation. With dynamic vegetation added to the
model, the signal of low‐frequency variability becomes much
stronger (Figure 2, middle, compared to Figure 2, left), and
the strength of this signal is comparable with observations.
While the enhancement of low‐frequency variability by
dynamic vegetation takes place across all South America
(Figure 2, right), the most significant impact is found in the
area between the equator and 10°S, which overlaps with the
observed equatorial “hotspot” in Figure 1.
[9] The substantial underestimation of low‐frequency
variability by the model without dynamic vegetation indicates that oceanic forcing alone is not enough to cause the
observed low‐frequency variability of precipitation. Despite
differences in the detailed spatial distribution of the low frequency fraction, the reasonable agreement between the model
with dynamic vegetation and the CRU data suggests that
terrestrial biosphere‐atmosphere interactions may have significantly contributed to the low‐frequency variability of
precipitation in the Amazon region.
[10] Despite the large amount of annual precipitation in the
areas of Amazon where the model indicates a strong impact of
dynamic vegetation, the region experiences a dry season of
several months in boreal summer. During the late dry season
and even in the early rainy season, water availability becomes
the limiting factor for vegetation productivity. During the rest
of the year, water is abundant and productivity is limited
primarily by light availability. The modeled year‐to‐year
variation of net primary productivity (NPP) in the region is
dominated by that of the dry season NPP. For example,
averaged over the area (60–70°W, 0–10°S), 86% of annual
NPP variance can be explained by NPP during the July‐
August‐September (JAS) season (which is the late dry season
2 of 5
L19703
WANG ET AL.: VEGETATION DYNAMICS AND AMAZON RAINFALL
L19703
Figure 2. Fraction of precipitation variance with time scale longer than (top) 5 years and (bottom) 10 years simulated by
CAM3‐CLM3‐DGVM (left) with static vegetation and (middle) with dynamic vegetation during 1901–2008, and (right)
the difference between the two.
and transition to rainy season for this specific area in the
model), while 81% of year‐to‐year variance of the JAS NPP
can be explained by soil moisture during the same season
(Figure 3). Note that results in Figure 3 are from the 108‐year
“Static” experiment. Here the “Static” experiment is chosen
over “Dynamic” to minimize the influence of low‐frequency
signal, since low‐frequency variability (which is strong in
“Dynamic”) in both NPP and soil moisture can lead to spurious linear correlation. It is clear from Figure 3 that dry
season water availability, which depends on precipitation in
both the preceding rainy season and the current dry season, is
the main controlling factor for the inter‐annual variation of
NPP therefore for vegetation growth. This establishes the
pathway for precipitation to influence vegetation structure
and density in the model.
[11] As vegetation density increases, ET increases during
seasons when light is not limiting (typical of dry season and
dry‐to‐wet transition season), which favors precipitation.
This is the main pathway for vegetation to influence precipitation in the model. Despite the existence of other offsetting
mechanisms, the overall response is a precipitation increase
with the increase of vegetation density, although the sensitivity is rather low [Mei and Wang, 2010; Sun and Wang,
2011]. Combined with the water‐limited vegetation growth,
this enhances the persistence of precipitation anomalies,
Figure 3. (a) Dependence of annual NPP on the dry season
(July‐August‐September) NPP. (b) Dependence of dry season NPP on soil water in the top five soil layers (summed
up to ∼30 cm). NPP and soil moisture are both averaged over
the region (60–70°W, 0–10°S).
3 of 5
L19703
WANG ET AL.: VEGETATION DYNAMICS AND AMAZON RAINFALL
lengthening both wet and dry episodes. Transitions between
wet and dry are likely triggered by large scale oceanic forcing
and/or internal atmospheric variability.
4. Discussion
[12] In this study, using the NCAR CAM3‐CLM3‐DGVM
model we demonstrate that vegetation dynamics can enhance
the low‐frequency variability of precipitation in the Amazon,
contributing to the observed multi‐decadal fluctuation of
precipitation in this region. This result indicates that the
impact of biosphere‐atmosphere interactions on precipitation
variability bears relevance not only in semi‐arid regions (as
previously found) but also in wet tropical climate with a
distinct dry season.
[13] The found impact of vegetation feedback in CAM3‐
CLM3‐DGVM results from the water‐limited vegetation
growth during the dry season on one hand and the increase of
precipitation with vegetation density on the other. Based on
both modeling and observational studies, macro‐scale
deforestation (often basin‐wide and hypothetical) in the
Amazon would reduce precipitation [e.g., Dickinson and
Kennedy, 1992; Zhang et al., 1996; Werth and Avissar, 2002;
Fu and Li, 2004; Sampaio et al., 2007], while meso‐scale
deforestation (which is more realistic in spatial extent) tends
to enhance convection, cloudiness, and even precipitation
over deforested areas due to mesoscale circulation triggered
by land surface heterogeneity [e.g., Cutrim et al., 1995; Wang
et al., 2000, 2009; Baidya Roy and Avissar, 2002]. The year‐
to‐year variation of vegetation in CAM3‐CLM3‐DGVM is
naturally induced by climate variations, in the form of slow
changes in vegetation density or coverage (as opposed to
complete transition from forest to grassland or to agricultural
land in macroscale deforestation studies). It spans the whole
domain, which is similar to the spatial extent of changes
imposed in macroscale deforestation studies. The direction of
precipitation response to the year‐to‐year vegetation variation in the model is thus consistent with the response found in
macroscale deforestation studies.
[14] A much discussed topic in ecosystem and climate
sciences is the potential for abrupt shift (a.k.a. the “runaway”
behavior) and the underlying mechanism of a positive feedback between the biotic and abiotic components of the system
[e.g., Scheffer et al., 2001; Foley et al., 2003]. It is worth
pointing out that the combination of water‐limited vegetation
growth and precipitation decrease induced by vegetation
degradation found in this study is not sufficient to cause a
positive feedback between vegetation and precipitation. For
example, in the drying phase of a positive feedback, the
magnitude of precipitation reduction induced by vegetation
degradation has to be large enough to cause further degradation of vegetation, leading to a runaway behavior [e.g.,
Wang, 2004]. In CAM3‐CLM3‐DGVM however, the system
is locked to a single equilibrium state due to the low sensitivity of precipitation to vegetation changes in the model [Sun
and Wang, 2011]. The enhancement of low‐frequency variability found in this study is therefore not a result of positive
feedback leading to transitions between two different equilibrium states, as was the case in some models [Wang and
Eltahir, 2000b; Oyama and Nobre, 2003; Wang, 2004].
Instead, in CAM3‐CLM3‐DGVM, following an event leading to vegetation degradation (which can be a drought or
logging), the precipitation amount, although reduced, is still
L19703
enough to support the maintenance and further growth of
the post‐perturbation vegetation, which leads to a negative
feedback and vegetation recovery. During such negative
feedback, vegetation acts as a damper for the inter‐annual
variation in the system, contributing to climate persistence.
For example, in the year following an El Nino drought that
leads to vegetation reduction, due to the long time scale
(ranging from years to decades) of vegetation, vegetation is
likely to be still less than normal, which favors less‐than‐
normal precipitation even though the large scale oceanic
forcing may have gone back to its normal state. Such damping
effects by vegetation on fast (inter‐annual) processes in the
climate system are responsible for the vegetation‐induced
increase of low‐frequency variability found in this study.
[15] Due to the damping effects of vegetation, the several
years following a severe drought in a region may be more
prone to recurrent droughts, making it more likely for drought
years to occur as a cluster. A similar statement holds for flood
years. In the Amazon region, the past decade witnessed two
extreme droughts, one in 2005 and a much more severe one in
2010 that coincided with the local dry season [e.g., Marengo
et al., 2008, 2011; Lewis et al., 2011; Xu et al., 2011]. The
drought in 2010, a “once‐in‐a‐century” event, caused substantial reduction of vegetation greenness across the Amazon
basin south of the equator that did not recover when the rainy
season precipitation returned to normal [Xu et al., 2011].
Results from our study suggests that, in absence of extremely
strong oceanic forcing favoring precipitation in this region,
many areas of Amazon will be prone to recurrent droughts in
the several years following the 2010 drought.
[16] Acknowledgments. This work was supported by funding from
the National Science Foundation (NSF) Climate and Large Scale Dynamics
Program (ATM 0531485). We thank the two anonymous reviewers for their
constructive comments.
[17] The Editor thanks two anonymous reviewers for their assistance
evaluating this paper.
References
Roy, S., and R. Avissar (2002), Impact of land use/land cover change on
regional hydrometeorology in Amazonia, J. Geophys. Res., 107(D20),
8037, doi:10.1029/2000JD000266.
Collins, W. D., et al. (2004), Description of the NCAR Community Atmosphere Model (CAM3.0), Tech. Rep. NCAR/TN‐464+STR, Natl. Cent.
for Atmos. Res., Boulder, Colo.
Costa, M. H., S. N. M. Yanagi, P. J. O. P. Souza, A. Ribeiro, and E. J. P.
Rocha (2007), Climate change in Amazonia caused by soybean cropland
expansion as compared to caused by pastureland expansion, Geophys.
Res. Lett., 34, L07706, doi:10.1029/2007GL029271.
Cutrim, E. D., D. W. Martin, and R. Rabin (1995), Enhancement of cumulus clouds over deforested lands in Amazonia, Bull. Am. Meteorol. Soc.,
76, 1801–1805, doi:10.1175/1520-0477(1995)076<1801:EOCCOD>2.0.
CO;2.
Delire, C., J. A. Foley, and S. Thompson (2004), Long‐term variability in a
coupled atmosphere–biosphere model, J. Clim., 17, 3947–3959,
doi:10.1175/1520-0442(2004)017<3947:LVIACA>2.0.CO;2.
Delire, C., N. De Noblet‐Ducoudre, A. Sima, and I. Gouriand (2011), Vegetation dynamics enhancing long‐term climate variability confirmed by
two models, J. Clim., 24, 2238–2257, doi:10.1175/2010JCLI3664.1.
Dickinson, R. E., and P. Kennedy (1992), Impacts on regional climate of
Amazon deforestation, Geophys. Res. Lett., 19(19), 1947–1950,
doi:10.1029/92GL01905.
Foley, J. A., M. T. Coe, M. Scheffer, and G. L. Wang (2003), Regime shifts
in the Sahara and Sahel: Interactions between ecological and climatic
systems in northern Africa, Ecosystems, 6, 524–532, doi:10.1007/
s10021-002-0227-0.
Fu, R., and W. H. Li (2004), Influence of land surface on transition from
dry to wet season over the Amazon, Theor. Appl. Climatol., 78(123),
97–110.
4 of 5
L19703
WANG ET AL.: VEGETATION DYNAMICS AND AMAZON RAINFALL
Grimm, A. M., and R. G. Tedeschi (2009), ENSO and extreme rainfall
events in South America, J. Clim., 22, 1589–1609, doi:10.1175/
2008JCLI2429.1.
Guo, Z., et al. (2006), GLACE: The Global Land‐Atmosphere Coupling
Experiment. 2. Analysis, J. Hydrometeorol., 7, 611–625, doi:10.1175/
JHM511.1.
Koster, R. D., et al. (2006), GLACE: The Global Land‐Atmosphere
Coupling Experiment. 1. Overview and results, J. Hydrometeorol., 7,
590–610, doi:10.1175/JHM510.1.
Levis, S., G. B. Bonan, M. Vertenstein, and K. W. Oleson (2004),
The Community Land Model’s Dynamic Global Vegetation Model
(CLM‐DGVM): Technical description and user’s guide, Tech. Rep.
NCAR/TN‐459+IA, Natl. Cent. for Atmos. Res., Boulder, Colo.
Lewis, S. L., P. M. Brando, O. L. Phillips, G. M. F. van der Heijden, and
D. Nepstad (2011), The 2010 Amazon drought, Science, 331, 554,
doi:10.1126/science.1200807.
Marengo, J. A. (2004), Interdecadal variability and trends of rainfall across
the Amazon basin, Theor. Appl. Climatol., 78, 79–96, doi:10.1007/
s00704-004-0045-8.
Marengo, J. A. (2009), Long‐term trends and cycles in the hydrometeorology of the Amazon basin since the late 1920s, Hydrol. Processes, 23,
3236–3244, doi:10.1002/hyp.7396.
Marengo, J. A., et al. (2008), The drought of Amazonia in 2005, J. Clim.,
21, 495–516, doi:10.1175/2007JCLI1600.1.
Marengo, J. A., J. Tomasella, L. M. Alves, W. R. Soares, and D. A.
Rodriguez (2011), The drought of 2010 in the context of historical
droughts in the Amazon region, Geophys. Res. Lett., 38, L12703,
doi:10.1029/2011GL047436.
Mei, R., and G. L. Wang (2010), Rain follows the logging in Amazon?
Interpretation of results from the CAM3‐CLM3 model, Clim. Dyn.,
34, 983–996, doi:10.1007/s00382-009-0592-x.
Oleson, K. W., et al. (2004), Technical description of the Community Land
Model (CLM), Tech. Rep. NCAR/TN‐461+STR, Natl. Cent. for Atmos.
Res., Boulder, Colo.
Oyama, M. D., and C. A. Nobre (2003), A new climate‐vegetation equilibrium state for tropical South America, Geophys. Res. Lett., 30(23), 2199,
doi:10.1029/2003GL018600.
Rayner, N. A., D. E. Parker, E. B. Horton, C. K. Folland, L. V. Alexander,
D. P. Rowell, E. C. Kent, and A. Kaplan (2003), Global analyses of sea
surface temperature, sea ice, and night marine air temperature since the
late nineteenth century, J. Geophys. Res., 108(D14), 4407,
doi:10.1029/2002JD002670.
Sampaio, G., C. Nobre, M. H. Costa, P. Satyamurty, B. S. Soares‐Filho,
and M. Cardoso (2007), Regional climate change over eastern Amazonia
caused by pasture and soybean cropland expansion, Geophys. Res. Lett.,
34, L17709, doi:10.1029/2007GL030612.
Scheffer, M., S. R. Carpenter, J. A. Foley, C. Folke, and B. Walker (2001),
Catastrophic shifts in ecosystems, Nature, 413, 591–596, doi:10.1038/
35098000.
L19703
Sun, S., and G. Wang (2011), Diagnosing the equilibrium state of a coupled
global biosphere‐atmosphere model, J. Geophys. Res., 116, D09108,
doi:10.1029/2010JD015224.
Wang, G. L. (2004), A conceptual modeling study on biosphere‐
atmosphere interactions and its implications for physically based climate
modeling, J. Clim., 17(13), 2572–2583, doi:10.1175/1520-0442(2004)
017<2572:ACMSOB>2.0.CO;2.
Wang, G. L., and E. A. B. Eltahir (2000a), The role of ecosystem dynamics
in enhancing the low‐frequency variability of the Sahel rainfall, Water
Resour. Res., 36(4), 1013–1021, doi:10.1029/1999WR900361.
Wang, G. L., and E. A. B. Eltahir (2000b), Ecosystem dynamics and the
Sahel drought, Geophys. Res. Lett., 27(6), 795–798, doi:10.1029/
1999GL011089.
Wang, J. F., R. L. Bras, and E. A. B. Eltahir (2000), The impact of
observed deforestation on the mesoscale distribution of precipitation
and clouds in Amazonia, J. Hydrometeorol., 1, 267–286, doi:10.1175/
1525-7541(2000)001<0267:TIOODO>2.0.CO;2.
Wang, G. L., E. A. B. Eltahir, J. A. Foley, D. Pollard, and S. Levis (2004),
Decadal variability of rainfall in the Sahel: results from the coupled
GENESIS‐IBIS atmosphere‐biosphere model, Clim. Dyn., 22(6–7),
625–637, doi:10.1007/s00382-004-0411-3.
Wang, G. L., Y. J. Kim, and D. G. Wang (2007), Quantifying the strength
of soil moisture-precipitation coupling and its sensitivity to changes in
surface water budget, J. Hydrometeorol., 8(3), 551–570.
Wang, J. F., et al. (2009), Impact of deforestation in the Amazon basin on
cloud climatology, Proc. Natl. Acad. Sci. U. S. A., 106, 3670–3674,
doi:10.1073/pnas.0810156106.
Werth, D., and R. Avissar (2002), The local and global effects of
Amazon deforestation, J. Geophys. Res., 107(20), 8087, doi:10.1029/
2001JD000717.
Xu, L., A. Samanta, M. H. Costa, S. Ganguly, R. R. Nemani, and R. B.
Myneni (2011), Widespread decline in greenness of Amazonian vegetation due to the 2010 drought, Geophys. Res. Lett., 38, L07402,
doi:10.1029/2011GL046824.
Zeng, N., J. D. Neelin, K.‐M. Lau, and C. J. Tucker (1999), Enhancement
of interdecadal climate variability in the Sahel by vegetation interaction,
Science, 286, 1537–1540, doi:10.1126/science.286.5444.1537.
Zhang, H., A. Henderson‐Sellers, and K. McGuffie (1996), Impacts of
tropical deforestation. Part 1: Process analysis of local climate change,
J. Clim., 9, 1497–1517, doi:10.1175/1520-0442(1996)009<1497:
IOTDPI>2.0.CO;2.
R. Mei, S. Sun, and G. Wang, Department of Civil and Environmental
Engineering, University of Connecticut, 261 Glenbrook Rd., U‐2037,
Storrs, CT 06269, USA. ([email protected])
5 of 5