Available online at www.sciencedirect.com Geochimica et Cosmochimica Acta 72 (2008) 438–448 www.elsevier.com/locate/gca d13C profiles along growth layers of stalagmites: Comparing theoretical and experimental results Douchko Romanov a,*, Georg Kaufmann a, Wolfgang Dreybrodt b a Institute of Geological Sciences, FU Berlin, Malteserstr. 74-100, Building D, 12249 Berlin, Germany b Karst Processes Research Group, Institute of Experimental Physics, University of Bremen, 28359 Bremen, Germany Received 29 May 2007; accepted in revised form 6 September 2007; available online 1 November 2007 Abstract The isotopic carbon ratio of a calcite-precipitating solution flowing as a water film on the surface of a stalagmite is deter- À mined by Rayleigh distillation. It can be calculated, when the HCO3 -concentration of the solution at each surface point of the stalagmite and the fractionation factors are known. A stalagmite growth model based entirely on the physics of laminar flow and the well-known precipitation rates of a supersaturated solution of calcite, without any further assumptions, is À employed to obtain the spatial distribution of the HCO3 -concentration, which contributes more than 95% to the dissolved inorganic carbon (DIC). The d13C profiles are calculated along the growth surface of a stalagmite for three cases: (A) isotopic equilibrium of both CO2 outgassing and calcite precipitation; (B) outgassing of CO2 is irreversible but calcite precipitation is 13 in isotopic equilibrium. (C) Both CO2 outgassing and calcite precipitation are irreversible. In all cases the isotopic shift d C increases from the apex along the distance on a growth surface. In cases A and B, calcite deposited at the apex is in isotopic equilibrium with the solution of the drip water. The difference between d13C at the apex and the end of the growth layer is independent of the stalagmite’s radius, but depends on temperature. For case A, it is about half the value obtained for cases B and C. In case C, the isotopic composition of calcite at the apex equals that of the drip water, but further out it becomes practically identical with that of case B. The growth model has been applied to field data of stalagmite growth, where the thickness and the d13C of calcite precipitated to a glass plate located on the top of a stalagmite have been measured as function of the distance from the drip point. The calculated data are in good agreement to the observed ones and indicate that depo- sition occurred most likely under conditions B, eventually also C. A sensitivity analysis has been performed, which shows that within the limits of observed external parameters, such as drip rates and partial pressure of carbon dioxide P CO2 in the cave, the results remain valid. Ó 2007 Elsevier Ltd. All rights reserved. 1. INTRODUCTION d18O and d 13C, have been the focus of research for decades. Recent studies show that in particular d18O time series are Stalagmites are now recognized as proxies of environ- useful to recover paleoclimate temperatures during the past. mental signals (McDermott, 2004; McDermott et al., As an example, Mangini et al. (2005) have shown that the 2006; Fairchild et al., 2006, 2007). They can grow for time temperatures during the last 2000 years can be recon- spans from 103–105 years, and carry paleoclimatic informa- structed. The medieval climate optimum and the little ice tion, which by use of accurate dating techniques such as age have been identified by time series from stalagmites in Uranium series (Ford and Williams, 2007), can be con- the Central Alps (Mangini et al., 2005; Vollweiler et al., verted into time series. Oxygen and carbon isotopic signals 2006). Niggemann et al. (2003) have found the existence of sub-Milankovitch cycles during the last 6000 years from a stalagmite of the Atta Cave, Sauerland, Germany. Wang * Corresponding author. Fax: +49 30 838 70729. et al. (2001) have reported on oxygen isotope records E-mail address: [email protected] (D. Romanov). from five stalagmites of Hulu Cave in China bearing a 0016-7037/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.gca.2007.09.039 d13C profiles along growth layers of stalagmites 439 remarkable resemblance to oxygen records from Greenland the solution within a few percent is represented by the À 13 ice cores. These recent advances show the high potential of HCO3 ions. Therefore the enrichment in C can be ob- d 18O time series. tained by (Usdowski et al., 1979; Mickler et al., 2004) ! However, caveats must be given and an exact interpreta- ÂÃaÀ1 HCO À t tion of such data depends on many variables. Especially for 13 13 ÂÃ3 ð Þ R À ¼ R À ð0Þ ð1Þ HCO3 HCO3 À isotopic records one has to assume that isotopic fraction- HCO3 ð0Þ ation occurs under isotopic equilibrium conditions (Hendy, 13 1971). When kinetic fractionation operates, speleothems ex- where RHCO À is the isotopic ratio R = [rare_isotope]/[abun- 3 13 12 hibit a positive correlation of d18O and d13C for samples ta- dant_isotope] = C/ C at time t or at time zero, respec- ken along a growth surface and records from such tively. a is the fractionation factor taking into account stalagmites should be regarded with care. that carbon is lost by CO2-degassing and precipitation of In view of these problems detailed knowledge on the for- calcite. It takes different values for the two extremes dis- mation in isotopic signals on stalagmites is needed, first to cussed above. This will be discussed later in the text. À avoid errors and second to identify other signals, such as The concentration [HCO3 ] is related to the concentra- tion of [Ca2+]by drip rates to the apex of a stalagmite, which yield additional ÂÃ ÂÃ information of paleoprecipitation. 2þ À Ca ¼ 2 Á HCO3 ð2Þ A first step into this direction has been taken by Mu¨h- linghaus et al. (2007). They have modeled variations in This is the relaxed equation of charge balance valid for the d13C isotope profiles along the growth layer of a stalagmite pH values mentioned above (Dreybrodt, 1988). by use of a multi-box model. From their results they con- The precipitation rate F of calcite to the solid in an open clude that the interval between two drips to the apex of system is given by (Buhmann and Dreybrodt, 1985; Dreyb- the stalagmite most significantly determines the variations rodt et al., 1997): in the d13C profiles. F ¼ a ðc À ceqÞ; ð3Þ In this paper we present a new method to model the variations of d13C along growth layers of stalagmites. This with a the kinetic rate coefficient (Table 1). From this one model is based entirely on the physics and chemistry of cal- obtains the time evolution of the calcium concentration [Ca2+]=c in a thin sheet of water as: cite precipitation and isotopic chemistry. It does not need any ad hoc assumptions as used in earlier models on stalag- ÀÁ t Á d cðtÞ¼c þ c À c Á exp À ; ð4Þ mite growth (Dreybrodt, 1999; Kaufmann, 2003), which eq 0 eq a served as basis for the work of Mu¨hlinghaus et al. (2007). 2+ c is the actual concentration of Ca in the solution, c0 the 2+ 2. THEORETICAL BACKGROUND initial concentration of Ca , and ceq is the equilibrium concentration with respect to calcite. The time constant is given by d/a, where d is the depth of the water film. Eqs. When calcite precipitates from a H2O–CO2–CaCO3 solution in a thin water film to a calcite surface, carbon is (1)–(4) are the basic ingredients to calculate the isotopic transferred from the solution to the solid and as a result compositions for calcite deposited to stalagmites. À 2+ If one knows the time of contact of a parcel of water of the global chemical reaction 2HCO3 +Ca fi with the calcite surface and the position on the stalagmite’s H2O+CO2 + CaCO3, carbon dioxide must degas. This could happen in two different ways. In the first forward surface at this time it is possible to calculate its isotopic À and backward reactions for both carbon isotopes are al- composition of HCO3 . The calcite precipitated from this most equal. The products formed escape from the solution parcel of solution then contains the imprint of the solu- and do not interact with it again. Under such conditions the tion’s isotopic composition. To know the position of a se- products are in isotopic equilibrium with the solution, when lected element of a parcel of water one needs a model of they are generated. This, however, requires slow deposition the precipitation rates on the surface of the stalagmite. rates, whereby the Ca2+-concentration at the surface of the The first model of stalagmite growth and the evolution solid must be close to saturation with respect to calcite. of its morphology has been reported by Dreybrodt (1988, 1999) and later by Kaufmann (2003). This model assumes Furthermore the CO2 in the surrounding atmosphere must that the stalagmite is covered by a stagnant water film of be almost in equilibrium with the CO2 in the solution. The other extreme is irreversible fast precipitation with no back- depth between 0.005 and 0.03 cm, from which calcite is pre- cipitated during the time s between two drops. When a new ward reaction and consequently fast degassing of CO2, which is diluted into the surrounding atmosphere and lost drop impinges to the apex the entire water film is replaced irreversibly from the solution. Such irreversible processes by the new solution. To account for the fact that the depo- result in kinetic fractionation, whereas the first produces sition rates must decrease with distance from the axis one equilibrium fractionation.