Stalagmite δ18Ο series currently provide the most robustly dated characterization of glacial terminations. However, uncertainties associated with the stalagmite δ18Ο proxy record arise due to the complexity of flow within karst aquifers. Here we use an integrated climate-soil-groundwater lumped parameter hydrological model to demonstrate the range of potential stalagmite δ18Ο hydrological responses to significant global climate changes. Pseudoproxy stalagmite δ18Ο series were generated for millennial length model simulations, using general circulation model time-slice data for 12, 11, and 10 ka for eastern China. Our model demonstrates that the variability within published δ18Ο records from Chinese stalagmites falls within that of modeled pseudoproxy series. We utilize model output to (i) quantify hydrological uncertainty (specifically the relative importance of changing precipitation amount, isotopic composition, and water balance); (ii) identify any nonstationarity in δ18O variability and its relationship to climate change; and (iii) demonstrate the processes that produce low-frequency power in stalagmite δ18Ο.
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 Over millennial and longer time scales, stalagmite δ18Ο provides a precisely datable proxy of global change [Wang et al., 2001, 2008; Cheng et al., 2009, 2012]. The primary source of speleothem δ18Ο is precipitation, which has been investigated for modern-day East Asia [Dayem et al., 2010]. Precipitation is subject to evaporative fractionation in the soil and shallow epikarst. Drip-water δ18Ο is further modified by water storage and mixing within the soil, epikarst, and karst. Finally, fractionation occurs during speleothem deposition. These processes have been quantified to varying degrees using hydrological models of mixing and storage in the karst [Bradley et al., 2010; Baker et al., 2012] and geochemical models of isotope fractionation during stalagmite deposition [Scholz et al., 2009].
 Our objective in this paper is to quantify the range of possible stalagmite δ18Ο signatures introduced by hydrological variability over glacial to interglacial transitions. We use a lumped parameter model to generate multiple millennial length pseudoproxy simulations of stalagmite δ18Ο across the onset of the Holocene. Using output from the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Mk3L general circulation model, we model paleoclimate scenarios to derive pseudoproxy series to compare with speleothem δ18Ο. As an example, we use speleothem δ18Ο from Hulu Cave, Nanjing, China [Wang et al., 2001] using data from the U.S. National Climate Data Center (http://www.ncdc.noaa.gov/paleo/). Stalagmites from this cave, situated at 35 m depth in Ordovician limestone, provide replicated records of speleothem δ18O for the last glacial termination.
 We use a modified version of the karst hydrology model used by Bradley et al.  to model stalagmite δ18Ο (see Figure S1 in the supporting information). The model envisages five water stores: (i) Soil, (ii) Epikarst, (iii) Karst Store 1, (iv) Karst Store 2, and (v) an Overflow Store. Each store drains monthly at a rate proportional to the volume of water stored (see supporting information for code). The sole hydrological input to the model is precipitation (P) (to Soil Store), and outputs are evapotranspiration (ET) (from Soil Store) and drip-water flow within the cave and drainage. Model constraints include the following: (i) no flow occurs from the Soil Store when surface temperatures (T) are <0.0°C; (ii) flow from the Epikarst to Karst Store 2 (F4) occurs when Epikarst water storage exceeds threshold Epicap; and (iii) flow from Karst Store 2 to the Overflow Store (F7) occurs when the former exceeds threshold Ovcap. The model assumes that fracture flow between stores is the dominant flow process, an acceptable assumption for mature limestones with low primary porosity. The model has previously been shown to produce pseudoproxy stalagmite δ18O series that agree with modern stalagmite δ18O for three sites (Gibraltar, NW Scotland, and Ethiopia) in Bradley et al. .
 The δ18Ο composition of each store is modeled as a function of precipitation (δ18Οp) and store δ18Ο in the preceding time step, allowing for evaporative fractionation in the Soil Store. Individual drip-water δ18Ο series are generated by assuming that drip-waters are (i) solely derived from a particular water store; (ii) the product of mixing of waters draining from a selection of water stores; and (iii) a combination of store drainage and recent precipitation δ18Ο (arising through preferential flow through the soil and limestone). Stalagmite δ18Ο series (Stal_1 to Stal_6) are derived from each drip-water δ18Ο series by allowing for calcite fractionation (we use the commonly applied method of Kim and O'Neil , where T is the mean temperature of the preceding 12 months).
 As input data, we utilized 1000 year series of monthly T, P, and ET representative of the climate of Nanjing, China, for time slices 12, 11, and 10 ka, a period that encompasses the Younger Dryas event. P and T series were obtained using the CSIRO Mk3L climate system model version 1.2, a reduced-resolution atmosphere-land-sea ice-ocean general circulation model [Phipps et al., 2011, 2012]. The model was integrated to equilibrium under 12, 11, and 10 ka boundary conditions but without any North Atlantic freshwater flux during the Younger Dryas. The Earth's orbital parameters were set equal to the appropriate values for each epoch, and the land ice sheets were specified according to the ICE-5G reconstruction v1.2 [Peltier, 2004]. The atmospheric greenhouse gas concentrations specified are shown in Table S1 in the supporting information. After reaching equilibrium, the model was integrated for a further 1000 years to generate the climatological output used in this study. Monthly potential ET was estimated following Thornthwaite : despite the known limitations of this method [Chen et al., 2005], it is a practical approach for monthly time steps and with limited ET input parameters. For δ18Op, we take the monthly mean precipitation δ18Ο from the last glacial maximum (21 ka) general circulation modeling of Pausata et al. , applying a 1σ variance for all months of 1.6‰ (the mean variability in the modern IAEA Nanjing GNIP data). Isotope and climate data were obtained from the International Atomic Energy Association: (http://www-naweb.iaea.org/napc/ih/index.html). Given our relatively poor knowledge of δ18Op variations from glacial to interglacial periods, δ18Op was not varied between the 12, 11, and 10 ka time-slice model simulations. A 1500 year input series was generated from the 1000 year monthly series of P, T, ET, and δ18Op by repeating 500 years of the data at the start of the series. This helped us discount model initiation effects and ensured that the karst water stores had reached their equilibrium size before the time periods presented here.
 In our model, the principal hydrological control on drip-water δ18Ο is the relative size of each store in relation to water inflows and outflows. Where storage volume is large in relation to the drainage rate, δ18Ο variability will be low and drip-water supply will be continuous, whereas a high drainage rate relative to storage volume results in high δ18Ο variability and discontinuous outflow. Because we are comparing records for stalagmites exhibiting continuous deposition for 103–104 years, we are able to constrain the drainage function of a particular water store accordingly. A series of model runs were completed to determine the preferred parameter set (i.e., drainage functions and initial storage volumes in each store), focusing initially on parameters describing F3 and F5 followed by Epicap and Ovcap. We first varied the F5 drainage term systematically from 0.2 to 0.001 and identified (i) the time when the model output stabilized (i.e., F3 ≈ F5) and (ii) the water volume in each store at this time. Final selected parameters (F3: 0.008; Epicap: 400 mm) yielded a range of steady state water stores (i.e., Epikarst Store 2 to 10 times greater than Soil Store). Ovcap was then defined as 100 mm, ensuring that flow to the Overflow Store (F7) occurred regularly. The steady state parameters for F3 = 0.008 were used to determine the optimum term for F5 (flow from the epikarst). For a drainage parameter of 0.005, the relative sizes of the Karst, Epikarst, and Soil Stores were preserved. If this term is too large (i.e., 0.05), then Karst Store 1 emptied quickly and was smaller in size than the Soil Store; however, if the term was too small (0.0005), very little water flowed from Karst Store 1, which became too large in size.
 To demonstrate the stability of the model, we first present modeled water movement for three 50 year periods chosen arbitrarily from the 12, 11, and 10 ka 1000 year time slices (Figure 1). Further examples are provided in Figure S2 in the supporting information. Input series (P and ET); fluxes to and from the epikarst (F1 and F3); fluxes to and from Karst Store 1 (F3 and F5), Karst Store 2 (F1 and F4), and the Overflow Store (F7); and the water volume in each store are shown, together with six different modeled pseudoproxy stalagmite series: Stal_1 to Stal_6. These are presented as 5 year smoothed data to better reflect typical stalagmite sampling resolution.
 The pseudoproxy series vary markedly as a result of differences in the inferred water flow path and in the extent to which drip-water isotopic composition is attenuated by mixing within water stores of varying size within the karst. Figure 1 demonstrates that there is a clear seasonal cycle in the main input series of P and ET, which accounts for the variation in F1 (flows to Epikarst) over time. Flow from the Epikarst (F3) is strongly attenuated but varies according to any changes in water storage, while there are no seasonal variations in flow from Karst Store 1. However, the volume of water stored in Karst Store 1 is ~1.5 times greater than in the Epikarst Store, and hence the model predicts a considerable range in the isotopic composition of the different stalagmite series. Little variation is found in those series fed by drip-waters from the main water stores (the Epikarst and Karst Stores 1 and 2), but where preferential flow occurs, recent δ18Op influences the stalagmite series, imparting a clear seasonal trend. Thus, the same model input series can yield a range of possible stalagmite δ18O series that reflect water routing though the karst and the degree of mixing that has occurred.
 Figure 2 shows pseudoproxy δ18O output for two representative series, Stal_5 and Stal_3, shown as boxplots of results from all karst model configurations, for the 12, 11, and 10 ka time slices, compared to actual stalagmite data. Pseudoproxy data for all model output are presented in Figure S3 in the supporting information. Pseudoproxy mean δ18Ο are 1.5‰ heavier than the stalagmite series: a mismatch in absolute isotope values between series was expected given our use of best available δ18Op data, which was from the Last Glacial Maximum, and here we only consider the relative changes in δ18Op. Figure 2 shows that there is a first-order correspondence between the two stalagmite δ18Ο records but second-order differences between stalagmites in the same cave in the timing and amplitude of the δ18Ο series. Comparison with pseudoproxy δ18Ο demonstrates that this variability of individual observed stalagmite records is of the same order of magnitude as that modeled. Pseudoproxy Stal_3, which has a preferential flow component, has the greatest variability in δ18Ο with a consistent 2σ variability of 1.65‰ at 12, 11, and 10 ka. In comparison, Stal_5, where waters are derived from the Karst Store 1, has a smaller but nonstationary 2σ variability of 0.36, 0.34, and 0.33‰ at 12, 11, and 10 ka, respectively. We consider this nonstationarity in speleothem δ18O over time in more detail later in the paper.
 First, we consider the magnitude of δ18O change between the 12, 11, and 10 ka simulations: mean pseudoproxy δ18O decreases by 0.36‰, whereas the stalagmites decrease by ~1–2‰. This could be attributed to changes in δ18Op over time, as this parameter was held constant in the three time-slice input series. We can use the model to investigate the relative importance to stalagmite δ18O of changes in precipitation intensity and δ18Op, temperature, and water balance. Our model output demonstrates that with no change in precipitation δ18Op, a pseudoproxy δ18O response of −0.36‰ is generated (Figures 1 and 2). This can be attributed to the temperature-dependent fractionation of δ18O during calcite precipitation (−0.24‰ K−1 following Kim and O'Neil ) between the mean temperature of the 12 and 10 ka time slices (10.5 vs. 12.2°C; using −0.24‰ K−1 would produce a speleothem response of −0.41‰). The influence of changes in precipitation amount and water balance on stalagmite δ18O over this time period is therefore negligible (~0.05‰ and less than the analytical precision of typical carbonate isotope measurements). This is confirmed in Figure 3, which demonstrates no change in the mean δ18O of water between soil, epikarst, and karst stores between 12, 11, and 10 ka. For our Chinese example, the highest rainfall occurs in the warmest summer months due to the influence of monsoonal climate conditions (Figure S4 in the supporting information). In theory, cooler glacial conditions and lower ET could limit groundwater recharge to summer months (when the soil is not frozen) and, in warmer, postglacial conditions (with higher summer ET), recharge could become more evenly distributed through the year. However, input conditions (Figure S4) and model output (Figure 3) demonstrate that summer precipitation is so dominant at 12, 11, and 10 ka that the effects of changes in water balance are negligible in the case of our Chinese example. The change in water balance could become more significant when considering the implications of the larger temperature changes expected over the complete glacial to interglacial transition (3–7°C for warming for T-I (Termination 1) [Liu et al., 2012; Shakun et al., 2012]) particularly at sites with lower annual P and where P ≈ PET (for example, semiarid regions, karst regions such as those found in Australia and Arabian Peninsula). Our modeling also demonstrates that changes in P amount, such as that arising from an intensification of monsoon intensity, will have little effect on stalagmite δ18O, at least over the 12, 11, and 10 ka time slices (Figure S5). With groundwater recharge dominated by monsoon rain, changes in precipitation intensity have relatively little effect on total recharge and therefore speleothem δ18O.
 The combination of general circulation and karst modeling permits the quantification of pseudoproxy δ18O sensitivity to both T and δ18Op. T drives the T sensitive fractionation of δ18O during calcite precipitation (here we use −0.24‰ K−1 following Kim and O'Neill ), which would lead to a decrease in speleothem δ18O of between ~0.7 and ~1.6‰ for the range 3–7°C for warming for T-I. Over the 12 to 10 ka period investigated here, and using a fixed δ18Op input series, a decrease in pseudoproxy δ18O of −0.41‰ can be attributed to the change in T, allowing the residual difference between pseudoproxy and actual stalagmite series to be attributed to other factors such as changes in precipitation amount, water balance, and δ18Op. With the effects of precipitation amount and water balance both negligible for this case study, decreases in mean stalagmite δ18O of 1.26‰ and 1.53‰ for stalagmites H82 and PD, respectively, between 12.5–12.0 ka and 11.0–10.5 ka can be attributed to changes in δ18Op (0.85 to 1.12‰). Our results can be compared to the findings of Pausata et al. , who used a fully coupled general circulation model that included abrupt addition of freshwater in to the North Atlantic and off-line isotope-enabled general circulation model to simulate a 1.3‰ change in stalagmite δ18O at Hulu and attributed 0.9‰ to changes in δ18Op and 0.2‰ to changes in precipitation amount for changes in temperature and precipitation of 1.9°C and 4%, respectively.
 Our pseudoproxy series also demonstrate variability in δ18O (the standard deviation of pseudoproxy δ18O at each time step calculated from all model configurations) that is nonstationary over time and sensitive to model configuration (see Figure S6 in the supporting information). The variability of Stal_1 and Stal_6 is higher and more variable than other pseudoproxies. Flow routes associated with both these pseudoproxy series stalagmites, supplied by overflow from Karst Store 2 and the Overflow Store, respectively, are affected by overflow routing and volume of water stored in comparison to specified thresholds (Ovcap; Epicap). Actual stalagmite δ18O variability can be expected to increase for model configurations where recharge to these stores becomes discontinuous, albeit at rates that are still sufficient to maintain continuous speleothem deposition. An increase in variability in modeled stalagmite δ18O is observed from the 12 to 10 ka time slices by the Stal_2, Stal_3, and Stal_4 series, although to a lesser extent. All three series receive inflow from the Epikarst Store, with varying proportions of preferential flow. The volume of water stored in the epikarst will decrease due to increased ET, as shown in Figure S4, which in turn leads to increased pseudoproxy δ18O variability.
 It is also interesting to note that the pseudoproxy series in Figures 1 and 3 only preserve low-frequency, decadal-scale variability. This is demonstrated in the spectral analyses presented in Figure 4. Inspection of model output demonstrates that this loss of high-frequency, annual-scale variability originates in the model, predominantly in the epikarst and karst stores (see Figure 3). It is only in the soil store where the δ18O of high recharge events can significantly affect the overall store isotope composition. Isotope variability can therefore be introduced in this store as a result of recharge events where P> > ET, store volume is low in the preceding time step, and the isotopic composition of event water is significantly different from the mean. However, when subsequently mixed with other karst stores, this high-frequency variability is smoothed, and only low-frequency periodicity remains in the speleothem δ18O record. This finding has two important implications: (1) where high-frequency variation of δ18O is observed in speleothems, a karst modeling approach can be used to determine whether this can be attributed to internal cave processes (e.g., kinetic fractionation) or is a climate signal (e.g., in the case of tropical cyclones, where high recharge events of distinct isotope composition may occur [Frappier et al., 2007]); (2) that any low-frequency signal contained in speleothem δ18O is likely to be modulated by the interplay between P, ET, and the properties of the soil store.
 Our hydrological modeling approach has permitted a quantitative assessment of the relative importance of changes in the temperature, precipitation, and water balance and specifically the timing and amount of groundwater recharge on stalagmite δ18O over glacial transitions. The pseudoproxy series demonstrate the extent to which variability between published stalagmite δ18O records can be specifically attributed to hydrological variability. Importantly, it demonstrates that “wiggle matching” of stalagmite δ18O series should not be attempted, at least over decadal-centennial time scales, particularly where stalagmite δ18O variability is similar to that which can be ascribed to hydrological variability. This finding is likely to be generally applicable to all stalagmite δ18O records, although the absolute hydrological uncertainty will vary on a site-by-site basis.
 We identify nonstationarity in pseudoproxy δ18O variability that is a response to changing water balance and its effects on karst aquifer storage. This demonstrates that changes in stalagmite δ18O variability over time cannot be simply attributed to changes in any single climate parameter, given the extent to which groundwater storage and flux are sensitive to the water balance. We demonstrate the importance of considering the water balance, which although not affecting pseudoproxy δ18O over the 12 to 10 ka period would be expected to be a factor in determining stalagmite δ18O during periods of significant ΔT (e.g., over glacial terminations). The water balance would also be expected to affect stalagmite δ18O for lower values of ΔT in regions where recharge is more sensitive to ET. Further research is needed to quantify the importance of this process.
 Finally, our pseudoproxy series lose high-frequency power and contain only low-frequency information. Our results demonstrate that this signal transformation arises from the soil store through changes in the water balance, with the δ18O of high recharge (P> > ET) events modulating the mean soil store δ18O composition and volume. For speleothem samples whose recharge is dominated by the properties of this store (such as our pseudoproxies Stal_2 and Stal_3) this may yield high-frequency δ18O records of high-recharge events. However, for speleothem δ18O series with significant karst storage (such as those represented by pseudoproxies Stal_1 and Stal_5), the extent to which low-frequency information at decadal to centennial time scales demonstrates periodicity, which is climatically driven as opposed to an amplification of soil storage properties, requires further research.
 We would like to thank our presubmission reviewers, Joshua Larsen, Adam Hartland, Charlotte Cook, and Bryce Kelly and the comments of two anonymous reviewers.
 The Editor thanks 2 anonymous reviewers for their assistance in evaluating this paper.