Reconstructing modern stalagmite growth from cave monitoring, local meteorology, and experimental measurements of dripwater films

Abstract

Interpretations of high-resolution proxy datasets from stalagmites require support from long-term cave monitoring data and quantified changes in sample growth rate. One cave site for which the modern climate signal transfer systematics are relatively well characterised by cave monitoring is New St Michael's Cave, Gibraltar. This site provides a rare opportunity to reconstruct modern calcite growth, to link growth with the cave environment and local climate, and to test the sufficiency of existing growth rate theory on monthly to inter-annual timescales. Here, we use a numerical time-series growth rate model, driven by cave monitoring and local meteorological data, and the results of an experimental investigation into variation in dripwater film thickness as a function of stalagmite apex morphology to reconstruct the modern growth (AD 1951–2004) of ‘Gib04a’, a stalagmite retrieved from New St Michael's Cave. Our experimental measurements demonstrate that dripwater film thickness decreases linearly with increasing stalagmite curvature and that the presence of millimetre-scale surface microtopography reduces film thickness by an order of magnitude. We identified changes in growth laminae curvature from a Gib04a cut section to determine film thickness variability through time and combined this with estimated dripwater [Ca2+] and cave air pCO2 seasonality to drive the model. Our reconstruction exhibits strong seasonality and tracks variability in calcite [Sr2+], a trace metal whose incorporation into calcite is partially growth rate-controlled. Reconstructed growth also shows co-variation with seasonal changes in calcite fabric, with high growth corresponding to a greater density of calcite grain boundaries. We also link secular trends in karst recharge, film thickness and Gib04a growth, and assess the overall sensitivity of vertical growth rate to film thickness variability. This approach could be used to characterise the growth of other samples retrieved from well-monitored cave systems and may prove particularly useful in quantifying seasonal bias in geochemical proxy datasets, facilitating greater robustness of palaeoclimate reconstructions.

Full text

Page 1 of 33
Reconstructing modern stalagmite growth
from cave monitoring, local meteorology,
and experimental measurements of
dripwater films
Alexander J. Baker1, *, David P. Mattey2, and James U. L. Baldini1
1Department of Earth Sciences, University of Durham, Science Laboratories, South Road,
Durham, DH1 3LE, U.K.
2Department of Earth Sciences, Royal Holloway, University of London, Egham, TW20 0EX,
U.K.
*a.j.baker@durham.ac.uk
Abstract
Interpretations of high-resolution proxy datasets from stalagmites require support from long-
term cave monitoring data and quantified changes in sample growth rate. One cave site for
which the modern climate signal transfer systematics are relatively well characterised by cave
monitoring is New St Michael’s Cave, Gibraltar. This site provides a rare opportunity to
reconstruct modern calcite growth, to link growth with the cave environment and local
climate, and to test the sufficiency of existing growth rate theory on monthly to inter-annual
timescales. Here, we use a numerical time-series growth rate model, driven by cave
monitoring and local meteorological data, and the results of an experimental investigation
into variation in dripwater film thickness as a function of stalagmite apex morphology to
reconstruct the modern growth (AD 1951-2004) of ‘Gib04a’, a stalagmite retrieved from
New St Michael’s Cave. Our experimental measurements demonstrate that dripwater film
thickness decreases linearly with increasing stalagmite curvature and that the presence of
millimetre-scale surface microtopography reduces film thickness by an order of magnitude.
We identified changes in growth laminae curvature from a Gib04a cut section to determine
film thickness variability through time and combined this with estimated dripwater [Ca2+] and
cave air pCO2 seasonality to drive the model. Our reconstruction exhibits strong seasonality
and tracks variability in calcite [Sr2+], a trace metal whose incorporation into calcite is
partially growth rate-controlled. Reconstructed growth also shows co-variation with seasonal
changes in calcite fabric, with high growth corresponding to a greater density of calcite grain
boundaries. We also link secular trends in karst recharge, film thickness and Gib04a growth,
and assess the overall sensitivity of vertical growth rate to film thickness variability. This
approach could be used to characterise the growth of other samples retrieved from well-
monitored cave systems and may prove particularly useful in quantifying seasonal bias in
geochemical proxy datasets, facilitating greater robustness of palaeoclimate reconstructions.
Keywords: stalagmite, growth rate, analogue experiment, palaeoclimate

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 2 of 33
1. Introduction
High-resolution, precisely-dated, multiproxy geochemical records of late Quaternary climate
change are frequently obtained from stalagmites, particularly in low- and mid-latitude regions
where few alternative proxy archives exist (Fairchild et al., 2006). Cylindrical stalagmites
that have undergone uniform growth are most often sampled for such research, and many
stalagmite records benefit from robust chronologies based on petrographic or geochemical
annual laminae (Baker et al., 2008). The acquisition of multi-annual cave monitoring datasets
is a critical prerequisite for palaeoclimate reconstruction using speleothems (e.g., Mattey et
al., 2008; Spötl et al., 2005).
Existing empirical relationships between cave environmental parameters, such as cave
atmosphere temperature and pCO2 (CO2 partial pressure), and stalagmite growth rate appear
robust (Baker et al., 1998; Baldini et al., 2008; Genty et al., 2001) and recent studies have
attempted to quantify the effects of cave processes, such as ventilation, on stalagmite growth
and net geochemical proxy records (Sherwin and Baldini, 2011; Wong et al., 2011). Previous
speleothem growth studies include modelled spatial variability based on ‘snapshot’ cave
atmosphere CO2 concentration maps (Baldini et al., 2006b; Whitaker et al., 2009) and
comparisons of modelled and actual growth rates. Such studies have compared average
values (Baker and Smart, 1995), investigated the sensitivity of growth rate to cave dripwater
hydrochemistry (Genty et al., 2001), and compared modelled growth with calcite grown in
situ (Sherwin and Baldini, 2011). Collectively, this research provides first-order tests of our
theoretical understanding of both instantaneous calcite growth rate and vertical stalagmite
extension rate. Attempting to link stalagmite growth and morphology to climate variability,
Kaufmann (2003) combined temperature estimates from ice core (GRIP and VOSTOK) and
deep marine sediment core (SPECMAP) proxy data with approximations of glacial-
interglacial precipitation and soil cover changes to drive a model of vertical stalagmite
growth and equilibrium diameter, and Kaufmann and Dreybrodt (2004) adopted the inverse
approach in attempting to derive climatic information from such stalagmite stratigraphies.
Understanding stalagmite growth variability is important for palaeoclimate research for
various reasons. (i) Several studies (e.g., Polyak and Asmerom, 2001; Proctor et al., 2000)
employed stalagmite growth rate itself as a palaeoclimate proxy and others have described
seasonally variable stable isotope ratios (e.g., Johnson et al., 2006; Mattey et al., 2008) and
trace element concentrations (e.g., Huang et al., 2001) in stalagmites that potentially result
from cave ventilation dynamics and/or karst hydrological processes, both of which also affect
stalagmite growth. (ii) High vertical extension rates are conducive to generating high-
resolution geochemical proxy datasets from stalagmites, yet to-date few studies have
characterised stalagmite growth on intra-annual to decadal timescales and its implications for
geochemical climate signal capture. (iii) Seasonal growth rate fluctuations potentially bias net
proxy signals towards the season favourable to deposition (Baldini et al., 2008; Banner et al.,
2007; Fairchild et al., 2006; Frisia et al., 2000; Mattey et al., 2008; Spötl et al., 2005). (iv)
Growth rate variability may be related to climate signal modification by other processes, such
as biomass change above the cave (e.g., Baldini et al., 2005) and surface and epikarst
hydrology (Baker and Bradley, 2010; Bradley et al., 2010; Darling, 2004). Moreover,

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 3 of 33
stalagmite growth rate may provide a proxy for surface or soil temperature (Genty et al.,
2001), rainfall amount (Genty and Quinif, 1996), or vegetation changes (Baldini et al., 2005).
The work of Kaufmann (2003) and Kaufmann and Dreybrodt (2004) represents an important
advance in linking stalagmite growth with climate variability, but the model resolutions used
(1000 and 200 years, respectively) are too low to be directly applicable to many high-
resolution palaeoclimate studies using stalagmites.
The principal non-biological controls on calcareous speleothem deposition (temperature, drip
rate, dripwater [Ca2+], and soil and cave air pCO2) are relatively well understood (Dreybrodt,
1999; Genty et al., 2001). Recent research has characterised their spatio-temporal variability
at certain sites (Banner et al., 2007; Whitaker et al., 2009) and, in particular, highlighted the
importance of cave atmosphere pCO2 dynamics for speleothem palaeoclimatology (Baldini et
al., 2008; Fairchild et al., 2006). Although interpreting climatic variability from stalagmite
morphology alone is challenging (Dreybrodt, 1988), understanding the physical controls on
stalagmite growth, such as drop volume and dripwater film thickness, is necessary for proper
linkage of local climate variability, cave environment systematics, and stalagmite growth
behaviour.
The following equation describes vertical stalagmite extension rate (R0) fed by a punctiform
drip source theoretically (Baker et al., 1998; Baldini et al., 2008; Buhmann and Dreybrodt,
1985; Dreybrodt, 1980; 1999):
R0 = 1174 [Ca2+] - [Ca2+]appδ t-11 - e-α t δ-1 (Equation 1)
where the constant 1174 converts molecular accumulation rate of calcite (mmol mm-1 s-1) to
vertical extension rate (mm a-1); [Ca2+] is the initial calcium cation concentration of the
dripwater (mmol L-1); [Ca2+]app is the apparent dripwater [Ca2+] (mmol L-1) after equilibration
with a given cave atmospheric pCO2; δ is the dripwater film thickness (mm) from which
calcite precipitates according to Ca2+(aq) + 2HCO3−(aq) ↔ CaCO3(s) + CO2(g) + H2O(l); t is the
drip interval (s); and α is a ‘kinetic constant’ (mm s-1) that is sensitive to change in δ and
ambient cave temperature. Note that R0 may also be denoted ‘W0’ (e.g., by Kaufmann, 2003).
This equation was tested by Sherwin and Baldini (2011), who found close agreement between
measured in situ calcite deposition and a model estimate. However, the main source of
uncertainty encountered in this study was in estimating δ, highlighting the need to constrain
this parameter before any time-series reconstruction of stalagmite growth may be attempted.
Of particular interest is whether δ tends to remain constant or varies significantly with time,
according to relationships with other variables.
In this paper, the 51-year growth of a modern stalagmite (‘Gib04a’) retrieved from New St
Michael’s (NSM) Cave, Gibraltar (Mattey et al., 2008), is reconstructed in an a priori
forward model driven by cave monitoring (cave atmosphere pCO2 and temperature and drip
discharge) and local meteorological (surface temperature, rainfall, and water excess) time
series datasets. Additionally, this model is refined with experimental measurements of
dripwater films, which provide basic constraints on the role of film thickness on growth rate.
Our rationale for selecting Gib04a as a target specimen is as follows. (i) Cave monitoring

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 4 of 33
data (continuous logging and spot measurements) are available since 2004 (Mattey et al.,
2008) and modern climate signal transfer systematics have been relatively well constrained at
NSM Cave by Mattey et al. (2010). (ii) Continuous monthly meteorological time series
datasets (surface air temperature and precipitation) are available from the nearby Royal Air
Force Meteorological Office (RAFMO) station, which is also the site of Global Network for
Isotopes in Precipitation (GNIP) sampling since 1962 (Fig. 1), with a temporal coverage
appropriate to drive the time series growth model. (iii) Gib04a underwent relatively fast
vertical extension (~0.9 mm a-1) and exhibits annual petrographic laminae, providing a robust
age model, which is substantiated by annual carbon isotope cyclicity and correct
identification of the atmospheric 14C activity ‘bomb spike’ (Mattey et al., 2008). Altogether,
these factors provide a rare opportunity to (i) develop, to our knowledge, the first time-series
growth reconstruction for a modern speleothem and (ii) test the sufficiency of existing growth
rate theory (as a natural system description) in capturing seasonal and interannual variation.
To conclude, the implications for linking stalagmite growth and local climate are considered.
2. Site description
NSM Cave developed within the dolomitised Gibraltar Limestone Formation of the Rock of
Gibraltar (Gibraltar peninsula, southern Iberia; 36° 9` N, 5° 21` W), whose maximum
elevation is 426 m above mean sea level (Fig. 1). Pervasive fracturing provides extensive
macroporosity, and drips sites within NSM Cave are fed by down-dip and sub-vertical
fracture systems. NSM Cave is at least Pleistocene in age (Rodrı́guez-Vidal et al., 2004),
phreatic in origin, has experienced uplift of ~275 m, and preserves evidence for multiple
phases of drainage and secondary speleothem decoration (Tratman, 1971). NSM Cave has no
known natural entrances; however, a 1 m2 trap door, constructed in 1942 and the only link
with Old St Michael’s Cave, does not significantly disturb the natural chimney-effect
ventilation (Mattey et al., 2010; 2008 and references therein).
Mattey et al. (2010) identified links between ventilation dynamics, calcite fabrics, stable
isotope ratio and trace element seasonality, and dripwater trace element variability. Seasonal
ventilation of NSM Cave is characterised by rapid summer-to-winter increases and winter-to-
summer decreases in cave atmosphere pCO2, between near-atmospheric values and ~3000-
8000 ppm, occurring over several days. Ventilation of this cave system is the focus of on-
going research and therefore a full explication of ventilation processes and controls on cave
air pCO2 variability is beyond the scope of this paper. Here, we make reasonable
simplifications in light of this on-going work, which are explained in the following section.
Mattey et al. (2010) also compared drip discharge and hydrologically-effective precipitation
data and performed groundwater dye tracer experimentation, suggesting that coherence in
dripwater hydrochemistry between separate monitoring sites results from common
hydrochemical control, given the observed distinct recharge responses and inferred epikarst
flow paths for each drip site.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 5 of 33
3. Methods
3.1. Experimental measurements of dripwater film thickness
Collister and Mattey (2008) determined an empirical relationship between stalactite radius
and drop volume experimentally using analogue materials, constraining a previously poorly
understood parameter impacting stalagmite width. Hansen et al. (2013) determined time
constants for CO2 degassing, new pCO2 equilibration, and calcite precipitation using
experimental analogue materials, demonstrating that the geochemical evolution of cave
dripwater is a function of these constants, not simply of CO2 degassing rate. This
experimental literature has implications for cave monitoring and speleothem sampling
strategies. However, the role of stalagmite morphology on vertical extension is yet to be
quantified empirically.
We determined the dependency of dripwater film thickness (δ) on stalagmite curvature and
surface microtopography using 10 plano-convex Al domes (uniform spherical curvature), and
employed image analysis techniques to calculate the thickness of water films formed from a
known volume of water dispensed from a known height. In geometric terms, the domes
utilised for these experimental measurements are chords of spheres of various known radii.
The curved surface area, A, of each dome is given by:
A = 2πρ21-1-x2
ρ2 (Equation 2)
where ρ is the spherical radius and x is the projected radius of the base of the subtended cone
of the chord (i.e., the radius of the circular base of the dome). As x  ρ, A ≈ 2πρ2 (i.e., the
area of a hemisphere). A is expressed here in terms of projected radius because this parameter
is known for all domes. (Alternatively, A may be expressed more simply in terms of arc
length, but use of Eq. 2 favourably avoids the need for additional measurements of arc length
and propagating their associated error to the final δ calculations.)
Each dome was wetted and an 80 μl droplet dispensed onto its apex using a calibrated
mechanical pipette, allowed to spread, and photographed. The position of domes in each
image and the viewshed of the camera were fixed (Fig. S1). Droplets were dyed in order to
create a colour contrast between the droplet and the dome in the image (Fig. S2). For each
image, the Java™-based, public domain software ImageJ (Schneider et al., 2012) was used to
threshold the colour of the dyed water film from that of the surface of the dome (Fig. S2) and
a particle analysis tool was used to determine the projected area (2-D) of the dripwater film,
which was corrected for dome curvature using Eq. 2. Water droplets were dispensed from a
height of 10 mm to prevent splashing and conform to experimental conditions, but this is less
than ‘typical’ drop heights at natural drip sites (see Supplementary Material). Five replicates
were performed for each dome (Fig. 4a).
Simplistically, calculating δ assumes that a droplet spreads radially from the dome’s apex,
forming a uniform disc of curvature equal to ρ. However, because many photographed
droplets exhibited non-circular forms (Fig. S2), it is necessary to avoid this simplification by

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 6 of 33
calculating the (curved) surface area of each dome and the precise proportion covered by the
80 μl droplet. δ is given by:
δ = v
Ad (Equation 3)
where v is droplet volume (mm3) and Ad is the curved surface area of the dripwater film at
rest on the dome (mm2). Using a high-precision balance, we estimated the error associated
with v to be of the order of 0.01 %.
We performed a second set of measurements with non-smooth domes, created by affixing a
layer of laboratory-grade quartzose sand (pre-filtered through a 0.15-0.425 mm particle
mesh) to the surface each dome. The grain size is comparable to previous estimates of δ by
Dreybrodt (1981) and acts as an opposite end-member to the idealised, smooth surfaces. We
favour this analogue for stalagmite surface microtopography because it preserves the original
curvature of each dome, thus isolating the microtopography effect. A second set of δ
calculations was performed. Greater scatter was found for these measurements, so Fig. 4b
shows mean values with 1 standard deviation.
This approach incurs two important uncertainties. (i) The interfacial properties and contact
angles associated with water, air and dry Al are different from those associated with water,
air and dry calcite, potentially giving rise to erroneous results. Dripwater films would be
thickest at a dome’s apex if dispensed onto a dry dome, so wetted dome surfaces were used to
better approximate the interfacial properties of a natural speleothem substrate. Additionally,
we duplicated measurements on Al (with ρ = ∞) using wetted calcite spar, a precaution
undertaken by Collister and Mattey (2008). (ii) In this study, the magnitudes of drop height
and microtopography are constants. Therefore, future experimental work should attempt to
quantify the role of variable drop height and degree of microtopography on film thickness.
3.2. Construction of a time series stalagmite growth model
We derived transfer functions to estimate [Ca2+]app and α, both of which are based on earlier
calculations by Dreybrodt (1999), to provide inputs for Eq. 1. A non-linear relationship
between cave atmosphere pCO2 and [Ca2+]app was determined for a constant temperature of
20 °C (Fig. 2a) and a linear relationship between temperature and [Ca2+]app was determined
for a constant pCO2 of 2000 ppm (Fig. 2b). Combining these relationships gives the
following transfer function:
[Ca2+]app = 1
2 5.872 pCO20.2526 + -0.0167  + 1.5146 (Equation 4)
where pCO2 is that of cave air (atm) and Tc is in-cave temperature (°C).
A non-linear relationship between α and Tc was determined for several values of δ. Selecting
a single value is not necessary because our experimental measurements provide independent
constraints on δ (Fig. 2c) and α depends only on Tc for δ < 0.4 mm (Baker et al., 1998;

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 7 of 33
Hansen et al., 2013). A non-linear relationship between α and δ was determined for a constant
temperature of 20 °C (Fig. 2d). Combining these gives the following transfer function:
α = 1
2 2.22×10-7 Tc2 + 6.36×10-6 Tc + 3.88×10-5+-0.0057 δ2 0.002 δ + 0.0001
(Equation 5)
The constant values for which Eq. 4 and Eq. 5 were derived are those of Dreybrodt (1999)
which best represent conditions at the Gib04a site since cave monitoring began. Mean annual
cave air pCO2 is 2496 ppm and Tc remains constant at 17.9 °C at the Gib04a drip site (Fig. 3),
which is satisfactorily close to the temperature for which the relationships in Fig. 2a and Fig.
2d were derived. Therefore, Eq. 4 and Eq. 5 are used with minimal systematic error and α
varies with δ, rather than assuming a constant value for the entire reconstruction.
Finally, an input time series of dripwater [Ca2+] is required for Eq. 1. Dripwater [Ca2+]
measured at the Gib04a site likely equilibrated with soil pCO2 of ~1 % (Mattey et al., 2010).
Unfortunately, there is no overlap between on-going monitoring at NSM Cave and the period
of modern Gib04a growth (1951-2004). To compensate for this, we linked between dripwater
[Ca2+] and surface environmental parameters. Genty et al. (2001) derived an empirical
relationship between mean annual cave temperature and dripwater [Ca2+] based on data from
temperate European sites. Although this is a useful relationship, it is not appropriate to use
temperature as a single predictor for dripwater [Ca2+] at NSM Cave, despite the similarity
between mean annual surface and cave temperatures (18.3 and 17.9 °C, respectively). In a
Mediterranean climate, with relatively distinct dry and rainy seasons, moisture availability as
well as surface temperature control soil CO2 productivity (Baldini et al., 2008; Murthy et al.,
2003). Measured dripwater [Ca2+] at the Gib04a site is highest in winter, suggesting a
potential connection to moisture availability, and other Mediterranean sites (e.g., Clamouse
Cave, southern France) do not plot along the Genty et al. (2001) relationship. Given these
observations, we performed multivariate regression between NSM Cave dripwater [Ca2+]
(Mattey et al., 2010) and surface environmental (predictor) variables (temperature, rainfall
and potential evapotranspiration) for Gibraltar, obtaining the following expression:
[Ca2+] =---
40.078 (Equation 6)
where P is total monthly precipitation and E is potential evapotranspiration (Fig. 3),
calculated according to the method of Thornthwaite (1948). Dividing by the molecular mass
of Ca (40.078) converts [Ca2+] from ppm to mmol L-1. Combined, Ts and epikarst recharge
explain 67 % of [Ca2+] dripwater variability observed at the Gib04a site, with 0.23 mmol L-1
uncertainty.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 8 of 33
4. Results and discussion
4.1. Relationships between local meteorological variables, cave microclimate, and
stalagmite growth
Gibraltar’s Mediterranean maritime climate is characterised by mean summer (June-August)
and winter (December-February) temperatures of 22.8 and 13.2 °C, respectively, with ~0.7
°C warming over the last ~30 years (Wheeler, 2011), and mean summer (April-September)
and winter (October-March) total precipitation of 135 and 668 mm, respectively, with a ~20
mm decrease mean annual rainfall since 1960 (IAEA/WMO, 2013; Wheeler, 2006; 2007).
Clear seasonality in NSM Cave microclimate exists. Winter months produce seasonally low
temperature, high water excess, high cave atmosphere pCO2, and low dripwater [Ca2+]. The
opposite is therefore true of each during summer months. Dripwater [Ca2+] is not exactly in-
phase with surface temperature because it depends also on water excess, which is sensible
given that existing monitoring data from NSM Cave and from the overlying soil cover show
that cave air pCO2 seasonality is not in exact phase with soil moisture availability (i.e.,
rainfall seasonality). Predictable pCO2 seasonality at the Gib04a site co-varies with modelled
dripwater [Ca2+] because both are primarily temperature-dependent (Fig. 3). Ventilation of
NSM Cave is probably venturi- and/or chimney-type (Mattey et al., 2010) and the subject of
on-going research. These monitoring data are discussed in much greater detail by Mattey et
al. (2010) and indicate fast growth of Gib04a, whose actual mean linear extension rate was
~0.9 mm a-1 during 1951-2004 (Mattey et al., 2008).
4.2. Control of stalagmite apex morphology on film thickness
Dreybrodt (1988) estimated δ to be in the range 0.05 – 0.4 mm, yet microtopography is not
parameterised explicitly in growth models. Baldini et al. (2008) found that δ may tend
towards the upper end of that range (0.32 mm) for a stalagmite exhibiting mm-scale surface
microtopography, consistent with the measurements of Baker et al. (1998), but Kaufmann
(2003) fixed δ at 10-4 mm. Therefore, few constraints on δ exist. We derived two empirical δ-
ρ relationships for smooth and microtopographical surfaces (Fig. 4, Table S1), providing
experimental constraints. Both relationships are linear and negatively correlated. For smooth
surfaces, δ decreases with increasing curvature (r2 = 0.74) because droplets spread under
gravity and are retarded only by surface tension effects. Over microtopography (r2 = 0.47),
spreading is greatly encouraged by capillary action and reduced surface tension. Importantly,
microtopography (0.15-0.425 mm) reduces film thickness by an order of magnitude
compared to idealised, smooth substrates, and our values are consistent with those of Baker et
al. (1998). These results indicate that stalagmites with irregular morphologies or high surface
roughness are less likely to undergo fast vertical extension conducive to generating high-
resolution palaeoclimate records.
For flat surfaces (ρ = ∞), mean δ values for smooth and non-smooth surfaces are similar: 0.93
and 0.77 mm, respectively, indicating flat surfaces behave differently from curved surfaces.
Spreading over a smooth surface under gravity or by capillary action over a

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 9 of 33
microtopographical surface is reduced if that surface is flat, and the effect of
microtopography to encourage spreading is significantly reduced. For comparison, additional
measurements were performed on wetted calcite spar with ρ = ∞, providing natural interfacial
properties between calcite, water and air. Mean δ for flat calcite is 0.83 mm, which is similar
to values for wetted Al (Fig. 4). These observations are important because many actively-
growing stalagmites selected for research, including Gib04a, exhibit uniform cylindrical
morphology and possess low-curvature apexes, particularly if initial surfaces are near-flat
(Dreybrodt, 1999). We speculate that water spreading over curved microtopographical
surfaces is reduced by the development of minute menisci over the substrate (i.e., between
sand grains in our analogue), but this is less significant for stalagmites exhibiting undulatory
rather than granular microtopography.
For low-curvature smooth surfaces (ρ > 75 mm), our empirically-derived δ values
overestimate those of Dreybrodt (1999) and Hansen et al. (2013), highlighting the role of
other mechanical processes affecting the amount of dripwater at rest on a stalagmite surface
and therefore δ. Under experimental conditions, water dispensation onto Al and calcite spar
involves no water loss through mechanical processes, such as splashing. In natural cave
settings, with greater drop heights, the net effect of splashing is a reduction of δ, and
potentially results in unconventional growth features, such as splash coronae, where
maximum calcite accumulation occurs away from the vertical extension axis. Potentially, a
relationship between drip height and amount of water lost by mechanical processes for a
given droplet volume, which depends on stalactite radius and ambient barometric pressure
(Collister and Mattey, 2008), may be demonstrable. Quantifying this and the role of different
types and magnitudes of microtopography will provide future modelling challenges.
In summary, our data show a linear decrease in film thickness with increasing surface
curvature and that the presence of sub-millimetre scale microtopography reduces δ by an
order of magnitude, providing constraints on temporal δ variation in Gib04a, which is
discussed in the following section.
4.3. Constraints on film thickness and reconstructing modern Gib04a growth (1951-
2004)
We estimated the average curvature of 11 visible growth laminae in Gib04a (Fig. 5) and
calculated the associated δ values for each using our empirical relationships (Fig. 4, Table 1).
Excepting laminae 2 and 3, a decreasing trend in δ is found with decreasing equilibrium
diameter of Gib04a during the period 1951-2004, showing broadly uniform stalagmite growth
(Fig. 5). Broadly, these δ estimates for Gib04a are within the range described by previous
research (Dreybrodt, 1999; Kaufmann, 2003), though they tend towards higher values of that
range during the early phase of Gib04a growth. We have not estimated δ for every
macroscopic growth lamina in Gib04a, aiming instead to identify locations at an
approximately regular interval where curvature changes notably. In the Gib04a R0
reconstruction, each value of δ is ‘active’ until the subsequent identified surface (Table 1).

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 10 of 33
The full Gib04a R0 reconstruction shows clear seasonality (Fig. 6, Table S2) that is related to
dependence on surface temperature, water excess, and cave atmosphere pCO2. Total
modelled vertical extension is 55.99 mm, which overestimates Gib04a’s actual growth by
8.16 mm. Overall, model performance demonstrates that existing growth rate theory
sufficiently describes Gib04a growth on seasonal to interannual timescales. However, an
overestimation of calcite growth was also observed by Day and Henderson (2013). These
intriguing deviations from existing theory warrant the application of our modelling approach
to other well-monitored cave sites, given that local meteorological data (surface temperature
and water excess) provide constraints on dripwater [Ca2+] using Eq. 6 or previous work by
Genty et al. (2001) for semi-arid or temperate environmental settings, respectively.
4.3.1. Non-uniform Gib04a growth
Growth laminae 2 and 3 in Gib04a (Fig. 5) represent the development of a splash corona;
during this interval, calcite precipitation has occurred away from the central growth axis. Pre-
Holocene Gib04a growth provided a low-curvature lower edifice above which modern
growth initiated (Fig. 5). Therefore, the development of this feature is unexpected, given the
results of Dreybrodt (1999). Nevertheless, if non-uniform growth and the development of the
splash corona began close to lamina 1, the estimated δ value for this initial surface may be an
overestimate. Additionally, this suggests that shifts in the position of the vertical extension
axis occurred, potentially explaining the ~8 mm model overestimation. At their intersection
with the vertical growth axis, lamina 2 is inclined and lamina 3 is near-flat, and several
laminae immediately below and above lamina 3 exhibit convex (i.e., negative) curvature.
Additionally, several laminae exhibit relatively sharp inflections in ρ (Fig. 5), though these do
not affect the curvature uniformity of calcite deposited immediately above them, and only
one such inflection is proximal to the vertical growth axis. Such observations may be difficult
to make in 2-D sections of slower-growing stalagmites. Our empirical relationships give
realistic δ estimates for negative ρ values, but their physical plausibility is uncertain. The δ
values for laminae 2 and 3 plot away from the linearly decreasing δ trend and several
indistinct or discontinuous laminae are apparent (Fig. 5), both of which produce a period of
low vertical extension and reduced seasonal variability (Fig. 6). This non-uniform growth,
totalling ~6 mm, persisted for ~10 years.
Alternatively, a decrease in calcite saturation index, related to surface temperature changes,
or to changes in drip rate or dry season deposition, may have caused this temporary change in
calcite distribution. However, our growth reconstruction and temperature data do not support
this explanations (see section 4.5) and there is no evidence for decreased dripwater [Ca2+]
saturation in the past (e.g., reduce soil/vegetation cover). Additionally, calcite precipitation
may still occur at the point where water droplets impact a stalagmite (Hansen et al., 2013),
but the distribution of calcite precipitation over pre-existing laminae is affected by splashing.
Vertical calcite accumulation at the central growth axis is reduced by the development of
splash coronae, partly as a result of a reduction in δ.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 11 of 33
4.4. Model validation: comparing growth seasonality with Gib04a petrography and Sr
Stalagmite R0, calcite microfabric and Sr concentrations may be linked because Sr
incorporation into calcite is partially dependent on R0 (Fairchild and Baker, 2012). At low
instantaneous growth rates, Sr may substitute for Ca in the calcite lattice, but is susceptible to
competition with other species such as Mg and Na (Boch, 2008; Fairchild et al., 2001) and
incorporation of organic macromolecules (McGarry and Baker, 2000). At higher rates, Sr
occupies interstitial and defect lattice sites, the abundance of which increases with R0 (Boch,
2008), because the lattice is less able to distinguish between Ca2+ (ionic radius = 1.08 Å) and
larger divalent trace metals, such as Sr2+ (1.44 Å) (Gabitov and Watson, 2006; Huang and
Fairchild, 2001; Lorens, 1981). Therefore, R0 and the effective partition coefficient for Sr in
calcite (Kd
Sr) may co-vary (Fairchild and Treble, 2009; Gabitov et al., 2014; Gabitov and
Watson, 2006). Boch (2008) reported higher Sr and vertical extension rate associated with
porous laminae (summer deposition) in stalagmites sampled from Katerloch Cave, southeast
Austria. However, Borsato et al. (2007) found no ostensible seasonal co-variation between
trace element concentrations and calcite fabric in a stalagmite from Grotta di Ernesto,
northeast Italy, but Sr maxima increased linearly with growth. Experimental evidence
indicates R0 and Sr incorporation are strongly related above R0 ≈ 0.5 mm a-1 (Gabitov and
Watson, 2006), but there is also evidence that R0 increases well above the natural range are
required to produce such co-variation (Day and Henderson, 2013). These results suggest that
links between growth mechanics and Sr variability may vary temporally or from site to site.
For NSM cave, several observations indicate that Kd
Sr should respond to Gib04a R0: (i)
modelled Gib04a R0 falls only occasionally below 0.5 mm a-1, most notably between 1956
and 1965 (Fig. 6), (ii) Gib04a site temperature remained constant over the monitored period
(Fig. 3), and (iii) soil cover above NSM Cave is minimal, so competition between Sr
incorporation and molecular organic matter deposition in speleothem calcite is less a factor
compared with other sites. Therefore, comparing our R0 reconstruction with high-resolution
synchrotron μXRF Sr data, available for the upper ~13 mm (corresponding to 1987-2004) of
Gib04a (Mattey et al., 2010) provides a critical test of the reconstruction’s fidelity.
The R0 reconstruction tracks Gib04a Sr concentrations closely, capturing the seasonal and,
occasionally, the sub-seasonal variability (Fig. 6). Therefore, R0, Sr and calcite fabrics can be
compared with confidence, and across the most recent ~4 mm the discrepancy between actual
and modelled vertical extension is 0.18 mm (Fig. 7). Gib04a exhibits annual couplets of pale
columnar calcite and darker compact calcite (Fig. 7a), which represent winter and summer
deposition, respectively (Mattey et al., 2010). Dark compact calcite is characterised by a
greater density of calcite grain boundaries (Fig. 7b), and this associated with high summer Sr
and R0, although this is less clear for 2000-1 (Fig. 7c, d). This suggests that Gib04a calcite
lattice changes with increased linear extension rate appear to favour Sr incorporation,
consistent with experimental data (e.g., Gabitov et al., 2014). The amplitudes of seasonal R0
and Sr variations match well, though higher frequency variability indicates non-R0 effects
inhibit Sr incorporation. A potential microhiatus in Gib04a growth was identified by Mattey
et al. (2010) at 2001-2, which is characterised by an abrupt change in the density of calcite
grain boundaries (Fig. 7b), indicating that the year-to-year deposition of calcite couplets is

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 12 of 33
not regular. These abrupt changes in calcite fabric are likely due to ventilation dynamics at
NSM Cave. Rapid summer-to-winter increases in cave atmosphere pCO2 from near
atmospheric values occur (Fig. 3), potentially leading to weekly-to-monthly scale cessation of
calcite deposition. However, this is not apparent in reconstructed R0, Sr or other previously-
published trace element data from Gib04a. Dripwater [Ca2+] is sufficient to maintain vertical
extension at lower than average rates ~0.5 mm a-1, through winters when cave air pCO2 is
high.
Ionic competition affects Sr incorporation, implying that the Kd
Sr-Ro relationship may vary
temporally, responding to changes in ionic supply. Despite R0-Sr co-variation apparent in
Gib04a, it is necessary to estimate Sr incorporation. Unfortunately, the available dripwater
hydrochemistry and Gib04a trace element time series datasets do not overlap, but we
compensate for this by calculating Kd
Sr based on an extrapolation of the R0 reconstruction (see
Supplementary Material). Mean R0-derived Kd
Sr is 0.39 (Fig. S3), which is above but close to
the published range of experimentally-determined and natural speleothem values (Day and
Henderson, 2013; Fairchild and Baker, 2012; Gabitov and Watson, 2006), supporting the
fidelity of the R0-Sr comparison.
4.5. Inter-annual growth rate variability
A first order sensitivity analysis suggests that R0 is sensitive to δ variability (see
Supplementary Material and Fig. S4). Inter-annual morphological change in modern Gib04a
growth is characterised by decreasing equilibrium diameter and increasing ρ, resulting in a
decreasing δ trend (Fig. 5). Consequently, α also decreases during the period 1951-2004
according to Eq. 5. The secular decrease in Ro (Fig. 8), most obviously after the non-uniform
growth period, potentially reflects drying in Gibraltar. Stalagmite equilibrium diameter can
reflect long term trends in karst aquifer recharge (and therefore rainfall). An overall ~30 mm
decline in mean annual rainfall and increasing Ts since 1973 result in a linear decrease in total
annual water excess feeding Gib04a (Fig. 8). (Note that 1996/1997 winter rainfall is
anomalous.) Qualitatively, the tapered shape of Gib04a may be explained in this way.
Decreasing Gib04a equilibrium diameter and increasing ρ (Fig. 5) cause decreases in other
growth-determining parameters (δ and α) and result in a secular decline in R0 since 1965,
providing a first-order link between Gibraltar climate and Gib04a’s growth history.
Interestingly, step-like decreases in R0 during the non-uniform growth period and during
1990-1994 coincide with large temperature fluctuations, but secular temperature changes do
not correlate with R0 (Fig. 8). Cave air pCO2 seasonality, which is effectively invariant, also
cannot explain this, indicating that the dominant control on long-term changes in vertical
extension and morphology of Gib04a is karst recharge.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 13 of 33
5. Conclusions
This paper presents (i) experimental measurements of dripwater film thickness performed on
analogue materials, which are used to model δ variation during modern Gib04a growth
(1951-2004), and (ii) the first attempt to reconstruct temporal vertical growth rate variability
in a modern stalagmite. Our experimental measurements demonstrate that δ decreases
linearly with increasing surface curvature and that the presence of sub-millimetre scale
microtopography reduces δ by an order of magnitude compared to idealised, smooth surfaces
(Fig. 4). We attribute these observations to spreading under gravity and by capillary action
versus surface tension effects. By examining changes in growth laminae curvature, we
identified a linearly decreasing δ trend in the Gib04a stalagmite (Fig. 5), consistent with its
uniform tapered morphology (decreasing equilibrium diameter and increasing curvature). A
period of non-uniform growth, with two δ outliers resulting from the development of a splash
corona, occurs during 1956-1965 (comprising ~6 mm vertical extension). Furthermore, a
first-order δ-sensitivity analysis of R0 (using only weighted mean δ and α values)
demonstrates that Gib04a’s total vertical growth is underestimated by an order of magnitude
and non-sensible negative R0 values arise if δ variability is not taken into account.
The Gib04a growth reconstruction, based on cave monitoring, meteorological data, captures
growth seasonality but overestimates total vertical accumulation by ~8 mm. Seasonality in
surface temperature, hydrologically effective precipitation (both of which control dripwater
[Ca2+]), cave atmosphere pCO2, and moderate seasonality in drip interval, at NSM Cave (Fig.
3) forces strongly seasonal growth of Gib04a (Fig. 5 and Fig. 6). Seasonality in R0 co-varies
with high-resolution Sr concentration data (Fig. 6) and Sr partitioning between dripwater and
calcite is captured reasonably by the reconstruction (Fig. S3). A high-resolution comparison
of R0 with Sr and changes in grain-scale calcite fabric across the upper ~4 mm shows that the
amplitude of seasonal R0 and Sr variation is comparable, and both are associated with sub-
annual layers of dense calcite grain boundaries (Fig. 7). An inter-annual decrease in
reconstructed Gib04a R0 is likely linked to a similar decrease in rainfall in Gibraltar since
1960 and this is explained by secular decreases in δ and equilibrium diameter of Gib04a.
Therefore, our results demonstrate that growth rate theory is sufficient on inter- and intra-
annual timescales, but represent not the first example of overestimating vertical extension
rate. Future work should therefore apply our approach to other well-monitored cave systems
to determine whether modifications of growth rate theory are necessary in particular
environmental settings.
Recent research has indicated that (i) seasonal dripwater trace element hydrochemistry, if
recorded by stalagmites, may provide geochemical markers of seasonal growth laminae
(Fairchild and Treble, 2009; Wong et al., 2011), and (ii) δ controls the time constant for CO2
degassing (Hansen et al., 2013). In light of these results, our empirical constraints on the
relationship between δ and stalagmite morphology and R0 modelling results provide a timely
test of stalagmite growth rate theory. Immediate experimental and modelling studies should
quantify the roles of drop height and microtopography magnitude (involving various
stalagmite morphologies) on vertical growth. Future possibilities include constraining past
variability in multiple environmental parameters from stalagmite data; such an approach is

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 14 of 33
tenable because only a limited proportion of parameter space will produce good model fits to
data (e.g., Sr concentrations), and there are now studies confirming the sufficiency of existing
growth rate theory on various time scales. Finally, for well-monitored cave systems,
modelling growth provides a way to quantify biases in geochemical proxy data, aiding the
interpretation of records irrespective of resolution.
Acknowledgements
This research was funded by a Sir Kingsley Dunham Studentship awarded to AJB. We
gratefully acknowledge C. Wintrip, Chief Mechanical Technician in Durham’s School of
Engineering and Computing Sciences, for machining the experimental apparatus and D.
Wheeler, University of Sunderland, for kindly providing meteorological data. E. Llewellin, T.
Watton and I. Walczak are thanked for helpful discussion. We are grateful to C. Day and two
anonymous reviewers, whose comments much improved the first draft of this paper, and G.
Henderson for his editorial assistance.
Author contributions
AJB and JULB designed the experimental set-up for dripwater film measurements. AJB
undertook the measurements and devised the time series model. DPM conducted cave
monitoring, sampled Gib04a, and conducted trace element analyses. AJB analysed the
modelling results and wrote the paper. All authors approved the final manuscript draft.
References
Baker, A. and Bradley, C., 2010. Modern stalagmite δ18O: Instrumental calibration and
forward modelling. Glob. Planet. Change 71, 201-206.
Baker, A., Genty, D., Dreybrodt, W., Barnes, W. L., Mockler, N. J., and Grapes, J., 1998.
Testing theoretically predicted stalagmite growth rate with Recent annually laminated
samples: Implications for past stalagmite deposition. Geochim. Cosmochim. Acta 62,
393-404.
Baker, A. and Smart, P. L., 1995. Recent flowstone growth rates: Field measurements in
comparison to theoretical predictions. Chem. Geol. 122, 121-128.
Baker, A., Smith, C. L., Jex, C., Fairchild, I. J., Genty, D., and Fuller, L., 2008. Annually
Laminated Speleothems: a Review. Int. J. Speleol. 37, 193-206.
Baldini, J. U. L., McDermott, F., Baker, A., Baldini, L. M., Mattey, D. P., and Railsback, L.
B., 2005. Biomass effects on stalagmite growth and isotope ratios: A 20th century
analogue from Wiltshire, England. Earth Planet. Sci. Lett. 240, 486-494.
Baldini, J. U. L., McDermott, F., and Fairchild, I. J., 2006. Spatial variability in cave drip
water hydrochemistry: Implications for stalagmite paleoclimate records. Chem. Geol.
235, 390-404.
Baldini, J. U. L., McDermott, F., Hoffmann, D. L., Richards, D. A., and Clipson, N., 2008.
Very high-frequency and seasonal cave atmosphere PCO2 variability: Implications for

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 15 of 33
stalagmite growth and oxygen isotope-based paleoclimate records. Earth Planet. Sci.
Lett. 272, 118-129.
Banner, J. L., Guilfoyle, A., James, E. W., Stern, L. A., and Musgrove, M., 2007. Seasonal
variations in modern speleothem calcite growth in Central Texas, USA. J. Sed. Res.
77, 615-622.
Boch, R., 2008. Stalagmites from Katerloch Cave, Austria: Growth dynamics and high-
resolution records of climate change. PhD thesis, Leopold-Franzens-Universität
Innsbruck.
Borsato, A., Frisia, S., Fairchild, I. J., Somogyi, A., and Susini, J., 2007. Trace element
distribution in annual stalagmite laminae mapped by micrometer-resolution X-ray
fluorescence: Implications for incorporation of environmentally significant species.
Geochim. Cosmochim. Acta 71, 1494-1512.
Bradley, C., Baker, A., Jex, C. N., and Leng, M. J., 2010. Hydrological uncertainties in the
modelling of cave drip-water δ18O and the implications for stalagmite palaeoclimate
reconstructions. Quat. Sci. Rev. 29, 2201-2214.
Buhmann, D. and Dreybrodt, W., 1985. The Kinetics of Calcite Dissolution and Precipitation
in Geologically Relevant Situations of Karst Areas 1. Open System. Chem. Geol. 48,
189-211.
Collister, C. and Mattey, D., 2008. Controls on water drop volume at speleothem drip sites:
An experimental study. J. Hydrol. 358, 259-267.
Darling, W. G., 2004. Hydrological factors in the interpretation of stable isotopic proxy data
present and past: a European perspective. Quat. Sci. Rev. 23, 743-770.
Day, C. C. and Henderson, G. M., 2013. Controls on trace-element partitioning in cave-
analogue calcite. Geochim. Cosmochim. Acta 120, 612-627.
Dreybrodt, W., 1980. Deposition of calcite from thin films of natural calcareous solutions and
the growth of speleothems. Chem. Geol. 29, 89-105.
Dreybrodt, W., 1981. The kinetics of calcite precipitation from thin films of calcareous
solutions and the growth of speleothems: revisited. Chem. Geol. 32, 237-245.
Dreybrodt, W., 1988. Processes in Karst Systems: Physics, Chemistry, and Geology. Springer
Series in Physical Environment. 4. Springer-Verlag, Berlin. 288 pp.
Dreybrodt, W., 1999. Chemical kinetics, speleothem growth and climate. Boreas 28, 347-
356.
Fairchild, I. J. and Baker, A., 2012. Speleothem Science: From Process to Past Environments.
Blackwell Quaternary Geoscience Series. Wiley-Blackwell, Chichester. 432 pp.
Fairchild, I. J., Baker, A., Borsato, A., Frisia, S., Hinton, R. W., McDermott, F., and Tooth,
A. F., 2001. Annual to sub-annual resolution of multiple trace-element trends in
speleothems. J. Geol. Soc. 158, 831-841.
Fairchild, I. J., Smith, C. L., Baker, A., Fuller, L., Spötl, C., Mattey, D., McDermott, F., and
E.I.M.F., 2006. Modification and preservation of environmental signals in
speleothems. Earth-Sci. Rev. 75, 105-153.
Fairchild, I. J. and Treble, P. C., 2009. Trace elements in speleothems as recorders of
environmental change. Quat. Sci. Rev. 28, 449-468.
Frisia, S., Borsato, A., Fairchild, I. J., and McDermott, F., 2000. Calcite fabrics, growth
mechanisms, and environments of formation in speleothems from the Italian Alps and
southwestern Ireland. J. Sed. Res. 70, 1183-1196.
Gabitov, R. I., Sadekov, A., and Leinweber, A., 2014. Crystal growth rate effect on Mg/Ca
and Sr/Ca partitioning between calcite and fluid: An in situ approach. Chem. Geol.
367, 70-82.
Gabitov, R. I. and Watson, E. B., 2006. Partitioning of strontium between calcite and fluid.
Geochem. Geophys. Geosys. 7, Q11004.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 16 of 33
Genty, D., Baker, A., and Vokal, B., 2001. Intra- and inter-annual growth rate of modern
stalagmites. Chem. Geol. 176, 191-212.
Genty, D. and Quinif, Y., 1996. Annually laminated sequences in the internal structure of
some Belgian stalagmites - Importance for paleoclimatology. J. Sed. Res. 66, 275-
288.
Hansen, M., Dreybrodt, W., and Scholz, D., 2013. Chemical evolution of dissolved inorganic
carbon species flowing in thin water films and its implications for (rapid) degassing of
CO2 during speleothem growth. Geochim. Cosmochim. Acta 107, 242-251.
Huang, H. M., Fairchild, I. J., Borsato, A., Frisia, S., Cassidy, N. J., McDermott, F., and
Hawkesworth, C. J., 2001. Seasonal variations in Sr, Mg and P in modern
speleothems (Grotta di Ernesto, Italy). Chem. Geol. 175, 429-448.
Huang, Y. M. and Fairchild, I. J., 2001. Partitioning of Sr2+ and Mg2+ into calcite under karst-
analogue experimental conditions. Geochim. Cosmochim. Acta 65, 47-62.
IAEA/WMO, 2014. Global Network of Isotopes in Precipitation. The GNIP Database.
Johnson, K. R., Hu, C. Y., Belshaw, N. S., and Henderson, G. M., 2006. Seasonal trace-
element and stable-isotope variations in a Chinese speleothem: The potential for high-
resolution paleomonsoon reconstruction. Earth Planet. Sci. Lett. 244, 394-407.
Kaufmann, G., 2003. Stalagmite growth and palaeo-climate: the numerical perspective. Earth
Planet. Sci. Lett. 214, 251-266.
Kaufmann, G. and Dreybrodt, W., 2004. Stalagmite growth and palaeo-climate: an inverse
approach. Earth Planet. Sci. Lett. 224, 529-545.
Lorens, R. B., 1981. Sr, Cd, Mn and Co distribution coefficients in calcite as a function of
calcite precipitation rate. Geochim Cosmochim Ac 45, 553-561.
Mattey, D. P., Fairchild, I. J., Atkinson, T. C., Latin, J.-P., Ainsworth, M., and Durell, R.,
2010. Seasonal microclimate control of calcite fabrics, stable isotopes and trace
elements in modern speleothem from St Michaels Cave, Gibraltar, in: Pedley, H. M.
and Rogerson, M. (Ed.) Tufas and Speleothems: Unravelling the Microbial and
Physical Controls. Geological Society of London Special Publication 336. pp. 323-
344.
Mattey, D. P., Lowry, D., Duffet, J., Fisher, R., Hodge, E., and Frisia, S., 2008. A 53 year
seasonally resolved oxygen and carbon isotope record from a modern Gibraltar
speleothem: Reconstructed drip water and relationship to local precipitation. Earth
Planet. Sci. Lett. 269, 80-95.
McGarry, S. F. and Baker, A., 2000. Organic acid fluorescence: applications to speleothem
palaeoenvironmental reconstruction. Quat. Sci. Rev. 19, 1087-1101.
Murthy, R., Griffin, K. L., Zarnoch, S. J., Dougherty, P. M., Watson, B., Van Haren, J.,
Patterson, R. L., and Mahato, T., 2003. Carbon dioxide efflux from a 550 m3 soil
across a range of soil temperatures. Forest Ecol. Man. 178, 311-327.
Patra, K. C., 2001. Hydrology and Water Resources Engineering. CRC Press, Boca Raton,
Florida. 561 pp.
Polyak, V. J. and Asmerom, Y., 2001. Late Holocene climate and cultural changes in the
southwestern United States. Science 294, 148-151.
Proctor, C. J., Baker, A., Barnes, W. L., and Gilmour, R. A., 2000. A thousand year
speleothem proxy record of North Atlantic climate from Scotland. Clim. Dyn. 16,
815-820.
Rodrı́guez-Vidal, J., Cáceres, L. M., Finlayson, J. C., Gracia, F. J., and Martı́nez-Aguirre, A.,
2004. Neotectonics and shoreline history of the Rock of Gibraltar, southern Iberia.
Quat. Sci. Rev. 23, 2017-2029.
Schneider, C. A., Rasband, W. S., and Eliceiri, K. W., 2012. NIH Image to ImageJ: 25 years
of image analysis. Nat. Methods 9, 671-675.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 17 of 33
Sherwin, C. M. and Baldini, J. U. L., 2011. Cave air and hydrological controls on prior
calcite precipitation and stalagmite growth rates: Implications for palaeoclimate
reconstructions using speleothems. Geochim. Cosmochim. Acta 75, 3915-3929.
Spötl, C., Fairchild, I. J., and Tooth, A. F., 2005. Cave air control on dripwater geochemistry,
Obir Caves (Austria): Implications for speleothem deposition in dynamically
ventilated caves. Geochim. Cosmochim. Acta 69, 2451-2468.
Thornthwaite, C. W., 1948. An approach toward a rational classification of climate. Geogr.
Rev. 38, 55-94.
Tratman, E. K., 1971. The formation of the Gibraltar Caves. Trans. Cave Res. Group G.B. 13,
135-143.
Wheeler, D. A., 2006. The Gibraltar climate record: Part 1 – the history of weather
observations. Weather 61, 36-39.
Wheeler, D. A., 2007. The Gibraltar climate record: Part 2 – precipitation. Weather 62, 99-
104.
Wheeler, D. A., 2011. The Gibraltar climatic record – Part 3. Temperature. Weather 66, 259-
265.
Whitaker, T., Jones, D., Baldini, J. U. L., and Baker, A. J., 2009. A high-resolution spatial
survey of cave air carbon dioxide concentrations in Scoska Cave (North Yorkshire,
UK): implications for calcite deposition and re-dissolution. Cave Karst Sci. 36, 85-92.
Wong, C. I., Banner, J. L., and Musgrove, M., 2011. Seasonal dripwater Mg/Ca and Sr/Ca
variations driven by cave ventilation: Implications for and modeling of speleothem
paleoclimate records. Geochim. Cosmochim. Acta 75, 3514-3529.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 18 of 33
Surface
ρ (mm)
ρ¹ (mm¹)
Height (mm)
Mean δ (mm)
11
36.5
0.027
45.59
0.232
10
29.0
0.034
42.35
0.129
9
40.0
0.025
36.03
0.267
8
58.0
0.017
29.56
0.379
7
77.0
0.013
25.15
0.440
6
72.0
0.014
19.85
0.427
5
88.0
0.011
17.21
0.464
4
155.0
0.006
12.21
0.535
3
25.5
0.039
8.09
0.061b
2
39.0
0.026
7.06
0.257b
1
157.0
0.006
0.00
0.536a
0.365c
Table 1. Film thickness for Gib04a growth laminae based on experimental
measurements. Estimated curvature and associated mean film thickness (given as the mean
of values calculated using both transfer functions in Fig. 4) for 11 growth surfaces identified
in Gib04a (Fig. 5). For each surface, height denotes the start point of the interval of vertical
calcite accumulation for the estimated δ is used in the growth model.
a Initial surface from which modern growth initiated.
b Non-uniform stalagmite growth (see text for discussion).
c Growth-weighted mean value.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 19 of 33
Figure 1. Location and most recent survey map (undertaken in 2007) of NSM Cave and
location and map of Gibraltar with locations of Gibraltar’s RAFMO/GNIP station at North
Front (World Meteorological Organisation station code: 8495; 36.2 °N, 5.4 °W, 5 m asl).
Topographic contour lines on the Gibraltar map are in 100 metre intervals. Figure adapted
from Mattey et al. (2010).

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 20 of 33
Figure 2. A synthesis of data originally presented by Dreybrodt (1999) and transfer functions
derived from these data by bivariate regression, which are used in the time series growth
reconstruction for Gib04a. (a) A power law fit (correlation coefficient, r2 = 0.95) between
[Ca2+]app and cave atmosphere pCO2 for a constant cave temperature of 20 °C. (b) A linear fit
(r2 = 0.99) between [Ca2+]app and temperature for a constant pCO2 of 0.002 atm. (c) A 2nd-
order polynomial fit (r2 = 0.91) between the ‘kinetic constant’ (α) and cave temperature for
all data. (d) A 2nd-order polynomial fit (r2 = 1) between α and film thickness (δ) for a
constant temperature of 20 °C. A linear fit (r2 = 0.89) is also shown for comparison, but not
used in the growth reconstruction (grey line). Terms are defined in the text.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 21 of 33
Figure 3. Monitoring data (2004-2009) from the Gib04a drip site in NSM Cave (Fig. 1) and
calculated model parameters: cave atmosphere pCO2 spot measurements (squares) and
monthly mean trend (red line); dripwater electrical conductivity (triangles); modelled
dripwater [Ca2+] using Eq. 6 (circles); drip discharge (filled triangles); surface temperature
measured at Gibraltar’s RAFMO station (crosses) and continuously logged cave air
temperature (grey line); surface water excess (blue – positive, red – negative) calculated by
subtracting potential evapotranspiration (E) from total monthly rainfall (GNIP data). We
calculated E according to the method of Thornthwaite (1948), following Mattey et al. (2008),
with heat index values and reduction factors taken from Patra (2001). Cave monitoring data
were originally published by Mattey et al. (2010; 2008). RAFMO meteorological data ©
Crown Copyright, the Met Office.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 22 of 33
Figure 4. Change in film thickness (δ) as a function of surface curvature (ρ) for wetted
surfaces; δ increases with decreasing curvature. (a) Smooth surfaces (r2 = 0.74; p = 8.48×10-
16; n = 50) and (b) surfaces with 0.15 – 0.425 mm microtopography (r2 = 0.47; p = 0.09; n =
9). Mean values for wetted calcite spar (red; n = 7; σ = 0.012) are shown in (a). The δ values
determined for smooth surfaces are an order of magnitude greater than those for
microtopographical surfaces. In the case of flat (infinite curvature) surfaces, δ values are
similar, indicating that wet Al provides a useful, though not perfect, analogue for calcite,
supporting recent research (e.g., Collister and Mattey, 2008).

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 23 of 33
Figure 5. Cut section of the modern growth of Gib04a (AD 1951-2004). The dotted line
indicates the hiatus separating ancient (pre-Holocene) and modern growth, termed growth
surface 1. The dashed lines indicate laminae 2 to 11. For each lamina, estimated curvature
(mm) is given on the left, with corresponding mean δ values plotted against height (see also
Table 1). Laminae 2 and 3 (highlighted green) represent non-uniform stalagmite growth. The
dashed red line indicates the vertical growth axis and the black arrows indicate clear
inflections in laminae curvature that are visible in this 2-D cut section. See text for
discussion.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 24 of 33
Figure 6. The full R0 reconstruction (black), with a magnification of the period January 1987
to April 2004 that is compared with Gib04a Sr concentration (blue). Sr data originally
published by Mattey et al. (2008).

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 25 of 33
Figure 7. Comparison of modelled growth during the period 2000 to April 2004
(corresponding to the upper ~4 mm of Gib04a) with (a) Gib04a petrography, (b) an electron
backscatter grain boundary map of the area outlined in (a), and (c) high-resolution Sr
concentration transect across the upper ~4 mm of Gib04a (blue), each of which were
originally published by Mattey et al. (2010). (d) Reconstructed growth seasonality over this
period, totalling 4.18 mm (black). Both Sr and R0 are plotted as normalised z-Scores,
calculated by subtracting the mean and dividing by 1 standard deviation, so that the
amplitude of seasonal changes in each dataset may be compared fairly. Vertical grey shading
illustrates the association of R0, Sr, and grain-scale calcite fabric. See text for discussion.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 26 of 33
Figure 8. Comparison of R0 (grey; black curve is a 12-month running mean) with Ts
anomalies (red), P anomalies (pale blue; dark blue curve is a 24-month running mean), and
total annual water excess during the period 1951-2004 (grey). The non-uniform period of
Gib04a growth (Fig. 6), an inflection in secular Ts variability, and the anomalously wet
1996/1997 winter are indicated.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 27 of 33
Supplementary Material
Reconstructing modern stalagmite growth from cave monitoring,
local meteorology, and experimental measurements of dripwater films
Alexander J. Baker1, *, David P. Mattey2, and James U. L. Baldini1
1 Department of Earth Sciences, University of Durham, Science Laboratories, South Road, Durham,
DH1 3LE, U.K.
2 Department of Earth Sciences, Royal Holloway, University of London, Egham, TW20 0EX, U.K.
* a.j.baker@durham.ac.uk
S1. Experimental setup for δ measurements
The experimental setup (Fig. S1) uses a fixed camera viewshed in order to obtain consistent
images of water droplets. An example photograph (Fig. S2) shows a drip at rest on the
surface of a curved wetted Al surface. An 80 μl droplet spreads over a dome apex for
between ~0.5 and ~3 seconds under wetted conditions. Therefore, the time allowed for each
droplet to spread is different depending on dome curvature because the more curved the
dome, the longer the spreading time. However, each droplet was able to come to rest on the
domes we used, which are 50 – 90 mm in diameter, without loss of water.
The addition of dye slightly alters the flow properties of the water used in our experimental
measurements. However, it is difficult to provide a quantitative assessment of this because
image analysis is less precise when using non-dyed water. Determining the boundary of a
water film using image analysis (Fig. S2) is very precise when a detectable colour contrast
exists. However, our measurements are in close agreement with those of Baker et al. (1998),
obtained with a Vernier spherometer and without dye, suggesting that the effect of dying on
water flow is minimal.
Photographs were processed (colour thresholding, binary conversion, scaling and particle
analysis) using ImageJ (Schneider et al., 2012). Image analysis provide a precise
measurement of the projected area covered by the dispensed water droplet and ultimately of
mean film thickness because droplet volume and surface curvature are known (Eq. 3). Our δ
calculations are provided in Table S1.
S2. Sr partitioning and additional validation of Gib04a growth
reconstruction
To further test the validity of the R0 reconstruction, how well its output captures the
partitioning of Sr between calcite and dripwater solution is examined. Unfortunately, the
available dripwater hydrochemistry and Gib04a trace element time series datasets do not
overlap, which is compensated for by calculating Kd
Sr based on modelled R0. We extended the

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 28 of 33
R0 reconstruction beyond the sampling date of Gib04a, through the cave monitoring period,
and derived Kd
Sr variability from these hypothetical vertical growth rate values using the
relationship of Gabitov and Watson (2006). (Our aim is not to provide modelling constraints
on Kd
Sr in speleothem calcite that may be used directly in future studies; we aim only to
undertake an assessment of the R0-Sr comparison for Gib04a.) Mean calculated Kd
Sr between
2005 and 2007 is 0.39 (Fig. S3), which is higher than but close to experimentally-determined
values (Day and Henderson, 2013; Gabitov et al., 2014; Gabitov and Watson, 2006; Huang
and Fairchild, 2001; Lorens, 1981; Tang et al., 2008; Tesoriero and Pankow, 1996) and
natural speleothem calcite values deposited at cave temperatures comparable to those of NSM
Cave (Bourdin et al., 2011; Gascoyne, 1983). This overestimation is expected, given the
higher vertical extension rate of Gib04a relative to the rates considered in those studies. This
comparison is made cautiously because higher Kd
Sr values in some experimental studies were
derived at instantaneous growth rates which are higher than those applicable to speleothem
deposition (Day and Henderson, 2013). Nevertheless, this result is broadly consistent with
association between vertical calcite growth, calcite fabrics, and Sr concentration variability
identified in Gib04a (Fig. 7), but other factors (e.g., karst hydrology, crystallographic growth
kinetics) influence Sr incorporation into speleothem calcite (Fairchild and Baker, 2012).
S3. Sensitivity of vertical extension rate to δ
The full R0 reconstruction, including surface environmental variables and dripwater [Ca2+],
calculated using Eq. 6, are provided in Table S2. Quantifications of the sensitivity of R0 to
various parameters are largely absent from the literature. We conducted a first-order
assessment of the δ-sensitivity of R0 by re-calculating Gib04a R0 during the period 1951-2004
using constant values of δ and α and comparing this to the original Gib04a growth
reconstruction. Theoretically, assessing R0’s sensitivity to δ alone is not possible because α
partially depends on δ (Eq. 5 and Fig. 2c, d). Therefore, this sensitivity test takes α into
account, but because Tc is approximately constant (Fig. 3), primarily reflects δ. Gib04a R0
was recalculated using a weighted mean values of δ (0.365 mm; Table 1) and α (5.12×10-4
mm s-1). All other growth conditions remained as per the original R0 reconstruction (Fig. 6).
Recalculated in this way, the total vertical Gib04a growth during 1951-2004 is 6.3 mm,
which underestimates actual vertical growth by an order of magnitude. The recalculated data
are poorly, negatively correlated with the original reconstruction (r2 = 0.23) and exhibit much
scatter. Many recalculated R0 values are negative (Fig. S4), which suggest potential re-
dissolution of previously-deposited calcite (Baldini et al., 2006a; Whitaker et al., 2009),
causing microhiatuses in growth, but the original R0 reconstruction and Sr data indicate that
this is not the case. Moreover, the largest R0 values in the original monthly reconstruction,
though potential overestimates, in fact correspond to negative values in the recalculation with
constant δ. The seasonal timing of these negative values therefore indicates they are
implausible. Overall, this strongly suggests that using a single value for δ is not appropriate
for modelling R0 on interannual timescales and classical stalagmite growth can be

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 29 of 33
significantly sensitive to δ, with important implications for quantifying the cave and
meteorological controls on Gib04a morphology and vertical growth.
Supplementary references
Baker, A., Genty, D., Dreybrodt, W., Barnes, W. L., Mockler, N. J., and Grapes, J., 1998.
Testing theoretically predicted stalagmite growth rate with Recent annually laminated
samples: Implications for past stalagmite deposition. Geochim. Cosmochim. Acta 62,
393-404.
Baldini, J. U. L., Baldini, L. M., McDermott, F., and Clipson, N., 2006. Carbon dioxide
sources, sinks, and spatial variability in shallow temperate zone caves: Evidence from
Ballynamintra Cave, Ireland. J. Cave Karst Stud. 68, 4-11.
Bourdin, C., Douville, E., and Genty, D., 2011. Alkaline-earth metal and rare-earth element
incorporation control by ionic radius and growth rate on a stalagmite from the
Chauvet Cave, Southeastern France. Chem. Geol. 290, 1-11.
Day, C. C. and Henderson, G. M., 2013. Controls on trace-element partitioning in cave-
analogue calcite. Geochim. Cosmochim. Acta 120, 612-627.
Fairchild, I. J. and Baker, A., 2012. Speleothem Science: From Process to Past Environments.
Blackwell Quaternary Geoscience Series. Wiley-Blackwell, Chichester. 432 pp.
Gabitov, R. I., Sadekov, A., and Leinweber, A., 2014. Crystal growth rate effect on Mg/Ca
and Sr/Ca partitioning between calcite and fluid: An in situ approach. Chem. Geol. In
press.
Gabitov, R. I. and Watson, E. B., 2006. Partitioning of strontium between calcite and fluid.
Geochem. Geophys. Geosys. 7, Q11004.
Gascoyne, M., 1983. Trace-element partition coefficients in the calcite-water system and
their paleoclimatic significance in cave studies. J. Hydrol. 61, 213-222.
Huang, Y. M. and Fairchild, I. J., 2001. Partitioning of Sr2+ and Mg2+ into calcite under karst-
analogue experimental conditions. Geochim. Cosmochim. Acta 65, 47-62.
Lorens, R. B., 1981. Sr, Cd, Mn and Co distribution coefficients in calcite as a function of
calcite precipitation rate. Geochim Cosmochim Ac 45, 553-561.
Schneider, C. A., Rasband, W. S., and Eliceiri, K. W., 2012. NIH Image to ImageJ: 25 years
of image analysis. Nat. Methods 9, 671-675.
Tang, J., Köhler, S. J., and Dietzel, M., 2008. Sr2+/Ca2+ and 44Ca/40Ca fractionation during
inorganic calcite formation: I. Sr incorporation. Geochim. Cosmochim. Acta 72,
3718-3732.
Tesoriero, A. J. and Pankow, J. F., 1996. Solid solution partitioning of Sr2+, Ba2+, and Cd2+ to
calcite. Geochim. Cosmochim. Acta 60, 1053-1063.
Whitaker, T., Jones, D., Baldini, J. U. L., and Baker, A. J., 2009. A high-resolution spatial
survey of cave air carbon dioxide concentrations in Scoska Cave (North Yorkshire,
UK): implications for calcite deposition and re-dissolution. Cave Karst Sci. 36, 85-92.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 30 of 33
Figure S1. Illustration of the experimental procedure for obtaining δ measurements from a
fixed quantity of dyed water dispensed onto a wetted, curved Al surface. Terms are defined
by Eq. 2 and Eq. 3. Note that figure is not to scale and that the morphology of the dripwater
film in section view is also schematic.

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 31 of 33
Figure S2. Top-view example photograph of a curved wetted aluminium surface with 80 μl
dyed water droplet dispensed onto its apex. The droplet spreads, indicated by the dashed
arrows, over the uniformly curved surface (ρ = 37.5 mm in this image). The outline of the
water film (solid white line), as determined by ImageJ, is accurate. Spreading does not
necessarily displace existing water from pre-wetting the surface. Note that the image shows
only the central area of the dome’s surface; the width of this dome, 2x, is equal to 90 mm
(Fig. 2).

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 32 of 33
Figure S3. Kd
Sr time series derived from an extrapolation of the Gib04a R0 reconstruction
beyond the sampling date and into the cave monitoring period (diamonds). The mean Kd
Sr
value of 0.39 is higher than but close to the range described by published data (coloured bars;
not plotted against x-axis) (Bourdin et al., 2011; Day and Henderson, 2013; Gabitov et al.,
2014; Gabitov and Watson, 2006; Gascoyne, 1983; Huang and Fairchild, 2001; Lorens, 1981;
Tang et al., 2008; Tesoriero and Pankow, 1996).

Baker, A. J., Mattey, D. P., and Baldini, J. U. L., 2014. Earth and Planetary Science Letters 392, 239-249
Page 33 of 33
Figure S4. Quantification of δ-sensitivity of Gib04a R0. Values recalculated with constant δ
and α (y-axis) versus original R0 reconstruction as per Fig. 6 (x-axis). Linear regression
between these two datasets gives r2 = 0.23 (p = 1.04×10-43; n = 684).