1. Introduction

Speleothems are valuable archives of paleoenvironmental information. Their isotopic compositions of O and C and trace element contents, e.g., Mg, Sr, and Ba, are valuable sources of data on local conditions, such as the amount of precipitation or mean air temperature (Baker et al., 1993; Frisia et al., 2003; Roberts et al., 1998; Hu et al., 2008; Yuan et al., 2004; Wang et al., 2001, 2005; Fairchild and Baker, 2012). The additional advantage of speleothems is the fact that their age can be precisely estimated by the U-series method (Ivanovich and Harmon, 1992; Fairchild and Baker, 2012). Speleothem archives cover long periods of time and are usually one of the most continuous terrestrial archives. However, due to changing deposition conditions (e.g., temperature/humidity) or percolating water chemistry, breaks (hiatuses) in speleothem crystallization and erosional events are possible and relatively common (Fairchild and Baker, 2012).

According to Sadler (1981), sedimentation is essentially a discontinuous process. This is also true in the case of speleothems. Speleothems growth depend on specific conditions, such as the availability of water and its chemical composition, temperature, and CO₂ pressure in the cave atmosphere, which must be lower than that in the dripping water so the degassing process can occur (Fairchild and Baker, 2012). In many cases, those requirements for speleothems crystallization are fulfilled only during the wet and/ or warm season of the year. Therefore, speleothems deposition occurs seasonally (Banner et al., 2007). However, seasonal sedimentation breaks are usually not detectable, and their duration is shorter than the resolution of the potential

paleoenvironmental records. Sedimentation breaks with durations longer than the resolution of the studied record (hiatuses) are an important problem in age-depth model construction, but they are themselves a source of additional and valuable climatic information. Their occurrence can relate to environmental changes such as turning into colder/ dryer climates or very local conditions such as changes in seepage water systems. The potential missing time hidden inside the hiatus is not only the duration of the potential break in sedimentation but also the time connected with potentially eroded strata.

The estimated age scale (chronology) for speleothems should consider the occurrence of the hiatuses. The most classic way to do that, commonly used in published works, is the dating of speleothem layers just below and above the hiatus visible in macro- or microscopic images and the calculation of the duration of the missing part of the profile based on the time difference between those two ages (Fankhauser et al., 2016; Steponaitis et al., 2015). However, this approach does not consider the fact that the sampled points are usually not placed directly on the hiatus borders. Therefore, the estimated hiatus duration includes, in addition to the deposition break duration and the part of the potentially eroded record, time recorded in the part of the profile between the dated points and hiatus. The more reliable solution is independent construction of age-depth models for parts of speleothems separated by hiatuses and the hiatus duration estimation based on the modeled ages of the hiatus borders (Lauritzen, 1995; Holzkamper et al., 2005; Vaks et al., 2006; Spötl and Mangini, 2007; Couchoud et al., 2009; Vansteenberge et al., 2016). This solution requires several reliable dating results or other time benchmarks for every continuous deposition phase. In some cases, such as a small thickness of the deposition phase or low quality of the speleothem material (e.g., high contamination by thorium (Th) and uranium (U) from the noncarbonate fraction or high porosity), it is not possible to obtain enough dating results for reliable age-depth model estimation (Jo et al., 2011). In such situations, the classic age-depth model approach cannot be used, and part of the stalagmite is left without precise chronology (see Jo et al., 2011). However, the problem can be solved by using other potential sources of chronological information.

Here, we present several examples of speleothem records with clearly visible hiatuses and possible methods of estimating the durations of the hiatuses. The first and the simplest example is the PD-4 stalagmite (Demänovská Cave System, Slovakia), where the hiatus duration can be estimated based on the classic age-depth modeling approach. The second example, the SC-3 stalagmite (Szczelina Chochołowska Cave, Tatra Mts., Poland), represents the situation where the alternative approach - oxygen isotopic stratigraphy (OIS) - is used to obtain additional chronological information for the part of the stalagmite located between hiatuses and where only one U-series age is available. Finally, the OIS and age-depth modeling approaches were tested on previously published data from Spain, Macedonia and South Korea. The last example is the flowstone profile in Ledena Dvorana (LDH; Snežna Cave, Slovenia). The LDH profile is divided by ten principal hiatuses. Its chronology is based on a set of paleomagnetic benchmarks. However, their number is too low for the estimation of age-depth models for every deposition phase by classic age-depth modeling. This profile is an example of how the chronology of the whole profile can be estimated based on OIS and independent age benchmarks.

2. Material and Local Settings

PD-4 stalagmite

The PD-4 stalagmite was collected in the Demänovský jaskynný systém (Demänová Cave System, DCS). The DCS is situated in the Nízke Tatry (Low Tatra) Mountains (Western Carpathians, Slovakia; 19.58° E 49° N; the entrance elevation is 812 and 837 m.a.s.l; Fig. 1A). The total length of the DCS corridors is approximately 41.4 km (Herich, 2017). The PD-4 sample was taken in the Pekelný Dóm Chamber, located at the lower level of the DSC with the active underground stream of the Demänovka Stream. PD-4 is an approximately 385-mm-long calcite stalagmite of light cream color. The stalagmite is divided into two parts by a layer of sand cemented by calcite. This layer documents the break in calcite crystallization and filling of the cave passage by sand. The part of the stalagmite below the sand layer is 96 mm long. The calcite here is laminated and has several macroscopically visible pores. These pores do not contain any detrital particles or younger crystallization traces. The part of the stalagmite above the sand layer is 290 mm long, and it has lamination, color and porosity similar to that of the lower part (Fig. 1C).

Fig 1

Sample localization: A – map of Central Europe; B – map of Korea; C – PD-4 stalagmite (photo by J. Pawlak); D – SC-3 stalagmite (photo by J. Pawlak); E – sketch of the LDH profile with sampled sections (rectangles) and principal hiatuses (lines); F – LDH flowstone.

3. Methods

4. Results

Classic approach U-series dating and age-depth modeling (PD-4 stalagmite)

The results of U-series dating of the PD-4 stalagmite are presented in Table 1. The reported errors represent 2 standard deviations. Based on U-series ages, two age-depth models for continuously deposited parts of the stalagmite have been constructed. The model for the older part was calculated based on 11 U-series ages (Fig. 2). According to the model, stalagmite growth started at 48−1+1.2ka, and the cessation of its growth was at 32−8.5+3.2the part of the stalagmite younger than the sand layer was estimated based on 8 U-series ages (Fig. 2). It shows that ka. The model for calcite crystallization started again at 16.4−0.6+0.7continued until the present time. Based on the two ages, the age of the cessation in growth of the older stalagmite part and the age of the start of crystallization for the younger part, it is possible to estimate the duration of the sedimentation break. Taking into account the stratigraphic order, ka and has the duration of the deposition break could be estimated as 15.8−9.2+5.6ka. The additional U-series age is taken from the thin calcite layer (Fig. 1C) inside the sand, and this age is 19±0.2 ka (Fig. 2). The layer records short calcite crystallization phases in the period of cave flooding and sand deposition, indicating a bimodal character of sand deposition.

Fig 2

Age-depth models for the PD-4 stalagmite with estimated hiatus duration.

Table 1

U-series dating results for the SC-3 and PD-4 stalagmites.

sample	H [mm]	U [ppm]	234U/238U AR	230Th/234U AR	230Th/232Th AR	Age [ka]
SC-5	182±1	1.038 ± 0.002	1.158 ± 0.002	0.970 ± 0.005	7842 ± 46	290 ± 7
SC-6	192±1	0.610 ± 0.002	1.105 ± 0.002	0.944 ± 0.004	45 ± 0.2	273 ± 5
SC-8	198.5±1	1.000 ± 0.006	1.158 ± 0.002	0.936 ± 0.005	3345 ± 21	254 ± 5
SC-9	200±1	0.941 ± 0.002	1.100 ± 0.002	0.915 ± 0.008	9078 ± 90	242 ± 7
PD4-1	4±1	1.659 ± 0.003	1.143 ± 0.001	0.351 ± 0.001	374 ± 2	46.6 ± 0.2
PD4-2	12.5±1	2.000 ± 0.01	1.197 ± 0.003	0.334 ± 0.002	654 ± 4	43.8 ± 0.3
PD4-3	23±1	3.335 ± 0.006	1.182 ± 0.003	0.322 ± 0.002	2401 ± 18	41.9 ± 0.3
PD4-4	38±1	2.578 ± 0.004	1.161 ± 0.001	0.320 ± 0.001	2254 ± 8	41.7 ± 0.2
PD4-5	40±1	2.330 ± 0.01	1.185 ± 0.003	0.314 ± 0.002	2960 ± 17	40.7 ± 0.3
PD4-6	50±1	1.840 ± 0.01	1.179 ± 0.003	0.311 ± 0.005	832 ± 13	40.1 ± 0.7
PD4-7	58±1	3.540 ± 0.007	1.152 ± 0.001	0.305 ± 0.001	781 ± 3	39.3 ± 0.1
PD4-8	73±1	2.111 ± 0.004	1.149 ± 0.002	0.295 ± 0.002	2352 ± 19	37.9 ± 0.3
PD4-9	86±1	3.700 ± 0.020	1.142 ± 0.001	0.297 ± 0.001	210 ± 1	37.8 ± 0.3
PD4-10	88±1	2.320 ± 0.004	1.160 ± 0.002	0.282 ± 0.002	220 ± 2	35.8 ± 0.2
PD4-11	90±1	2.318 ± 0.010	1.203 ± 0.004	0.277 ± 0.005	1043 ± 17	35 ± 0.7
PD4-12	107±1	0.751 ± 0.005	1.269 ± 0.007	0.133 ± 0.003	81 ± 2	15.5 ± 0.4
PD4-13	129±1	1.479 ± 0.009	1.219 ± 0.004	0.103 ± 0.002	671 ± 15	11.9 ± 0.3
PD4-14	154±1	1.183 ± 0.007	1.215 ± 0.004	0.082 ± 0.001	338 ± 4	9.4 ± 0.2
PD4-15	183±1	1.386 ± 0.008	1.235 ± 0.003	0.084 ± 0.001	332 ± 6	9.3 ± 0.2
PD4-16	224±1	1.243 ± 0.007	1.242 ± 0.002	0.056 ± 0.001	585 ± 14	6.3 ± 0.2
PD4-17	291±1	1.467 ± 0.009	1.249 ± 0.002	0.055 ± 0.001	667 ± 13	6.2 ± 0.2
PD4-18	364±1	1.469 ± 0.008	1.277 ± 0.003	0.049 ± 0.001	293 ± 6	5.4 ± 0.1
PD4-19	377±1	2.088 ± 0.013	1.302 ± 0.007	0.023 ± 0.001	115 ± 6	2.5 ± 0.1

U-series and age-depth modeling combined with oxygen isotope stratigraphy (SC-3 stalagmite)

A series of fifteen U-series ages were obtained from the whole stalagmite (Błaszczyk et al 2020). In our study, we have used only dates located close to H1 and H2 hiatuses (Table 1). The reported errors represent 2 standard deviations. Only one U-series data point, 273 ± 5 ka, was obtained for the layer between the hiatuses (H2 and H1 on Fig. 3). Based on one U-series age, it is not possible to estimate the age-depth model for this part of the stalagmite. The older and younger parts of the studied stalagmite have well-defined age-depth models estimated by MOD-AGE software. The age range of this deposition phases is 327±7 ka and 289±4 ka for the older phase and 250−7+10to 200−17+20ka for the younger phase.

Fig 3

Age-depth models for the SC-3 stalagmite with the estimated durations of the hiatuses H1 and H2: A – the age-depth model chart of the whole profile; B– enlarged H1 and H2 zones; age-depth model for the oldest deposition phase (green lines); age-depth model for the deposition phase between H1 and H2 (blue lines); and age-depth model for the youngest deposition phase (red lines).

For the part of the stalagmite between hiatuses, an age-depth relation was constructed using the OIS approach using the LR04 combined record (Lisiecki and Raymo, 2005) as a reference curve. The set of fifteen samples for δ¹⁸O analyses was collected from this part of the stalagmite located between the H1 and H2 hiatuses (188–196.5 mm; Fig. 4A) at a resolution of one sample per 0.5 mm. The value of δ¹⁸O varies in the range of 1.8‰ (from -7.8‰ to -6‰). Three age benchmarks have been used. The first is the U-series dating result obtained for this part of the stalagmite (Table 1) as an independent age benchmark with a normal distribution. The other two benchmarks are border ages from age-depth models of the parts below the H1 hiatus and above the H2 hiatus. The OIS (Fig. 4B) places the deposition of the stalagmite parts located between the hiatuses in the age range between 282−3+1and263−1+2.5ka (Fig. 3). The δ¹⁸O record has been correlated with the LR04 record using GenCorr software (Pawlak and Hercman, 2016).

Fig 4

The δ¹⁸O data for the SC-3 profile: A – the δ¹⁸O record in the depth scale; B – the result of the correlation with the LR04 record.

Based on the three independent age-depth models, it is possible to estimate the time duration of the H1 and H2 hiatuses. The H1 hiatus covers the time between 289±4 and 282−3+1ka, and its duration could be estimated as 7±6 ka. The H2 hiatus covers a longer time period between 263−1+2.5 and250−7+10Fig. 5A. The δ¹⁸O values vary from -9.5‰ to almost ka, and its duration was estimated as 13.5−12+11ka (Fig. 3).

Fig 5

The results of OIS for the LDH profile: A – the δ¹⁸O record of the LDH profile in a depth scale; B – age-depth models estimated based on the OIS and the PM approaches (black lines); C – the δ¹⁸O record of LDH placed in both age scales and compared with the LR04 record (gray line).

Paleomagnetism (PM) combined with oxygen isotope stratigraphy (OIS) – (Ledena Dvorana – LDH profile)

The LDH δ¹⁸O record in its depth scale is presented in -6.5‰. The record has a clearly visible depleting trend from the 200-cm mark (bottom of the profile) to the top 20 cm. The youngest 20 cm of the record is characterized by a rapid increase from -9.5‰ to -7.5‰ δ¹⁸O. Apart from these trends, the record contains thirteen cyclic changes with amplitudes of approximately 1‰. The LDH section contains several visible breaks in deposition, seen as thick lines in Fig. 6. Three of the magnetozone borders are located at the hiatuses. It must be assumed that part of those magnetozones must be not deposited or eroded. These age benchmarks (magnetozone boundaries) cannot be used for chronology construction and duration estimation of deposition breaks. Therefore, for the purpose of chronology construction, we use only those PM benchmarks that are located inside the episodes of continuous deposition phases.

Fig 6

LDH profile: A – sketch of the LDH profile with sampled sections (rectangles) and principal hiatuses (lines); B – the result of OIS and the PM age-depth modeling, with detected hiatuses and their duration (gray rectangles). Arrows show the relation between the hiatuses visible in the profile and the hiatuses detected by the model.

The combination of the PM information and the OIS approach (OIS+PM) allows GenCorr (Pawlak and Hercman, 2016) to search for optimal positions within the time intervals defined by the PM benchmarks (Fig. 5C; black line). The OIS+PM correlation places the LDH profile between 2.95 and 5.1 Ma (Fig. 5C; black line). With this solution, the LDH δ¹⁸O record is in good agreement with the principal trend in the LR04 δ¹⁸O record, and the major peaks in the two records are also well correlated (Fig. 5C; black line).

The OIS+PM age-depth model suggests nine hiatuses (Fig. 6B). These hiatuses are in good agreement with the principal hiatuses observed in the LDH profile (Fig. 6A; thick lines). The gray rectangles in Fig. 6B show the suggested duration of those hiatuses.

5. Discussion

The estimation of hiatus duration is a common geological problem. In fact, based on the chronological information only, it is not possible to estimate the hiatus duration, which is understood as a non-deposition time. The calculated time is rather a sum of “non-deposition time” plus the time recorded in potentially eroded strata. The time missed in the hiatus can be estimated by the calculation

of two independent age-depth models for the parts of the profile below and above the hiatus. This method is commonly used in speleothem science (Lauritzen, 1995; Holzkamper et al., 2005; Vaks et al., 2006; Spötl and Mangini, 2007; Couchoud et al., 2009; Vansteenberge et al., 2016). The classic age-depth modeling approach on data from the PD-4 stalagmite allows us to estimate the hiatus duration (Fig. 2) as 15.8 ka. It is the time of a break in calcite deposition and possible erosion of the older part of the stalagmite. At this time, caves were flooded a minimum of two times and sand deposition occurred. U-series data of 19±0.2 ka were obtained for samples taken from the thin calcite layer (Fig. 1C) inside the sand, observed only in the axial part of the stalagmite, documenting a short episode of calcite crystallization just after the LGM.

However, in some cases, it is not possible to estimate a reliable age-depth model for continuously deposited parts of the speleothem. First, the quality of the calcite material, for example, strong detrital contamination or extremely low uranium content, may prevent reliable isotope dating results. Second, the studied speleothem age may be beyond the range of the dating method. In such cases, we have limited age information available. Sometimes, obtaining any chronological information is extremely important due to the importance of the paleoenvironmental record preserved in the studied speleothem. The only solutions for obtaining some chronological information are using relative or non-isotopic methods, for example, paleomagnetism, bioindicators, or isotopic stratigraphy. Commonly used paleoclimatic proxies in speleothem science are changes in oxygen isotopic composition. This creates opportunities for using the correlation of the oxygen isotopic record from the studied speleothem with the global/regional reference oxygen curve (OIS approach).

However, the OIS approach presents a few important problems that must be solved. First is the selection of the proper reference curve. The use of marine stack records such as LR04 is common and reliable when we can assume that the correlated δ¹⁸O record reflects over regional changes. Isotopic changes in the studied record and reference curve must be coincident (in the confidence bands of the records) and controlled by the same factors. The main factors shaping the δ¹⁸O speleothem records during the last 200 ka in Europe is temperature (Różański et al., 1993; Moseley et al., 2015; Kern et al., 2019; Comas-Bru et al., 2020) and δ¹⁸O composition of precipitation, source effect. The Atlantic Ocean is the main source of moisture for precipitation on the European continent (McDermott et al., 2011). The LR04 is a foraminifera benthic stack record, basing on 57 globally distributed sites. The benthic stack record reflects the variability in δ¹⁸O of global nature, and it is driven mostly by changes in the global ice volume. The δ¹⁸O speleothem records, driven mostly by source effect and temperature effect, can also reflect long time changes of global nature. Therefore, they can be correlated with LR04 stack record if the global signal is not biased by the influence of regional or local effects. There are differences in the local stacks from Atlantic and Pacific Oceans (Lisiecki and Stern, 2016). The Atlantic regional stacks, which resemble LR04 during MIS 5, display a more gradual transition than the Pacific stacks during glacial–interglacial transitions like MIS 5e/5d. Additionally, there is ca. 0.7 ka bias observed between stack records from Indian and Pacific Oceans. However, majority of the records from LR04 stack (40 sites) is located on Atlantic Ocean (Lisiecki and Raymo, 2005). Therefore, LR04 stack is biased toward Atlantic stack records and is suitable for correlation with European speleothems. When there is more than one potentially available reference curve, running test correlations with all available reference records is recommended, and those that give the better correlation quality indicator are chosen. In the study of RP-66 flowstone from the Reciska Pecina Cave (Hercman et al., submitted) in Slovenia, three potential reference curves were considered: LR04 (Lisiecki and Raymo, 2005), the stack of oxygen isotope records for Mediterranean Sea sediments (Wang et al., 2010), and the PISO record (Channell et al., 2009). Sixty test correlations were performed for each of those reference curves. The results unambiguously show that the correlations with the MEDI record have the best correlation quality results (Fig. 7) and used for detailed study.

Fig 7

The results of testing reference curves: A – quality indicators for the series of test correlations with different reference curves; B – Reciska Pecina curve correlated with the MEDI curve (Wang et al. 2010); C – Reciska Pecina curve correlated with the LR04 curve (Lisiecki & Raymo 2005); D – Reciska Pecina curve correlated with the PISO curve (Channell et al. 2009).

Next, the reference curve and the studied record should be characterized by similar resolution.

Lower resolution causes the loss of recorded information, which makes correlation more difficult. The results of the published tests (Pawlak and Hercman, 2016) show that when the distance between data points becomes larger than the signal period in the record, it causes a large decrease in the correlation quality (Pawlak and Hercman, 2016). The use of OIS for profiles with hiatuses requires a preliminary test of the method used to correlate sensitivity to the lack of part of the record in the correlated profile (breaks in deposition) and how it can influence the normalization procedure, especially if the local extremum is missing in the hiatus part. During initial work with the correlation procedure, we performed a set of tests to determine how the potential hiatus influences the whole correlation procedure, including normalization (Pawlak and Hercman, 2016). The results show that the whole procedure can be robust until the hiatus is no longer than approximately 15% of the whole correlated record length.

The Macedonian stalagmite OH2 (Regattieri et al., 2018) chronology is based on U-series ages (Fig. 8). The U-series ages for this stalagmite have approximately 20 ka large uncertainties, and they are not in proper order (Fig. 8). Therefore, the age-depth models estimated by StalAge (in original paper) and calculated here by MOD-AGE have large error bands. We correlated the δ¹⁸O records from this stalagmite with the stack of oxygen isotope records for Mediterranean Sea sediments (MEDI; Wang et al., 2010). From the previous works in a Mediterranean basin, we know that the δ¹⁸O records from stalagmites reflect the changes in Mediterranean Sea isotopic composition (Ayalon et al., 2002). The age-depth model obtained by OIS correlation agrees with the age-depth models based on U-series ages. The obtained confidence band varies from ca. 4 to 10 ka. Those differences reflect the quality of correlation for different parts of the correlated records. Intervals with wider confidence bands have larger alignment error, and it reflects the fact that single pick on correlated record can be aligned to reference curve in a different way with similar correlation quality.

Fig 8

The comparison of age-depth models for stalagmites from an unsurveyed Macedonian cave located near Lake Ohrid (Regattieri et al. 2018): A – the results of age-depth model estimation – (1) age-depth model made by the authors; (2) age-depth model made by MOD-AGE; (3) age-depth model made by the OIS approach; B – the result of the correlation with the MEDI record (Wang et al. 2010).

The correlation of the older part is reliable, and the shape of the OH2 δ¹⁸O records agrees with the MEDI record and has a better position than its original chronology (Fig. 8). Therefore, the OIS information potentially improves the existing chronology if the assumption about the synchronicity of the records is met. The correlation for the δ¹⁸O record from the younger part of the stalagmite is more problematic. The GenCorr software correlates only the main trend of the OH2 record here, and the short time pick does not meet its analog on the MEDI curve in this position.

The thin layers located between the two hiatuses may not have enough U-series ages or other independent age benchmarks for age-depth model construction (e.g., Jo et al., 2011, Błaszczyk et al., 2020). In the case of the SC-3 stalagmite, there are three continuous episodes of calcite deposition separated by the two hiatuses. The oldest and the youngest growth phases have sets of reliable U-series ages. Therefore, the classic age-depth modeling approach has been used for the estimation of age borders for the oldest and the youngest crystallization phases (Błaszczyk et al., 2020). The problem is the thin (approximately 10 mm thick) crystallization phase between the hiatuses H1 and H2, where only one reliable U-series age was obtained. The OIS application allows us to estimate the age-depth model between the H1 and H2 hiatuses and estimate their duration as 7±6 and 13.5−12+11ka (Figs. 3 and 4). A similar problem, as described for the SC-3 stalagmite, was identified for the chronology of the stalagmite from Korean Daeya Cave (DY-1; Jo et al., 2011). Stalagmite DY-1 contains three growth phases (A, B, and C), separated by the two hiatuses (Fig. 9). The 5-mm-thick phase B is located between the two hiatuses, and its age is documented by only one U-series age. Therefore, the authors were not able to estimate a robust age-depth model for this phase based on the classic age-depth modeling approach. The authors estimate the mean growth rate for phase B based on the U-series ages below and above the hiatus (0.5 mm.1 ka^-1). In fact, the estimate assumes the duration of the hiatus is approximately 0 ka. The published record of δ¹⁸O from DY-1 has been presented only on a depth scale (Jo et al., 2011). Here, for DY-1 data, we used the same OIS approach as that in the case of the SC-3 stalagmite (Fig. 9). The δ¹⁸O record from phase B of the DY-1 stalagmite can be correlated well with the MIS 5e/5d transition time (Fig. 8A). Additionally, it is in agreement with the published U-series age (Fig. 8B). Based on the added chronological information, the duration of the younger hiatus can be estimated as 97.5−0.5+0.8ka. The duration of the older hiatus was rather short, probably less than 1 ka. Based on our approach, the mean growth rate for phase B was between 0.3 and 0.5 mm.ka^-1. Using the proposed approach allows us to estimate the chronology for the full profile of the studied stalagmite. There are many stalagmites, where the chronology error is not well defined (Comas-Bru et al., 2020). For example, the authors do not provide the continuous confidence bands for their chronology of the speleothem from Spanish Cobre Cave. Its chronology is based on the sets of U-series samples and fluorescence lamina counting (Fl). They only stated that the 2 σ error of the estimated age-depth model is 1.5 ka, and it includes the U-series age error; the potential error of Fl is not included. This speleothem has three growing phases divided by two principal hiatuses (Rossi et al., 2014). The age difference between the dated points counted by the Fl is in good agreement with the U-series ages (Fig. 10; black line). The main problem with this dataset is the low number of U-series ages for the youngest growing phase (Ph3) and their large uncertainties of more than 3.5 ka (Fig. 10). Even, if estimated by Fl, age-depth model fits the U-series age well. The age-depth model here should be considered as less reliable. The MOD-AGE software requires at least three dated points for age-depth model calculation. Therefore, we used MOD-AGE here only to estimate the age-depth model for the Ph1 and Ph2 phases (Fig. 10). The age-depth models estimated by MOD-AGE are generally smoother than the Fl models. However, the Fl models are in good agreement with the MOD-AGE models (Fig. 10; black lines and red lines). The OIS approach was used here as a third method for estimating the durations of hiatuses. The δ¹⁸O recorded in stalagmites from Cobra Cave is under the strong influence of moisture from Atlantic sources (Rossi et al., 2014). Therefore, we chose the GRIP record as the reference record. The GRIP chronology bases on ice flow and snow accumulation model “ss09sea” (Johnsen et al., 2001). To check potential diachronicity with speleothem records, the Greenland ice core record can be compared with Hulu Cave stalagmite (Lisiecki and Stern 2016). The comparison by matching the onset of interstadials on both records shows differences up to 0.8 ka (Lisiecki & Stern 2016). Observed chronological bias is lower than the large uncertainty of U-series ages measured in the stalagmite from Cobra Cave (Rossi et al., 2014). Therefore, in this specific case, correlation with the GRIP record can bring additional chronological information. The results of the performed correlation are in agreement with the age-depth model estimated by MOD-AGE (Fig. 10A; red and blue lines). During the hiatus (H1), the GRIP record has strong events of low values, which increases the reliability of this correlation (Fig. 10B). The age-depth model estimated by the OIS approach is sharper than the Fl model. However, for the Ph1 and Ph2 phases, it is in good agreement with the Fl model. In the case of the Ph3 phase, both models are in agreement with two U-series ages. However, the age-depth model estimated by the OIS approach suggests additional growth cessation between 102 and 98 ka. The model estimated by Fl is more regular (Fig. 10A). However, due to large errors of U-series ages for Ph3, its reliability is low. Additionally, the correlation of the δ¹⁸O record from Ph3 with the GRIP record is not reliable. The GenCorr software is not able to find positions with a sufficiently low mean distance between the correlated records. At that time, local factors had a stronger influence on δ¹⁸O. Therefore, its shape does not reflect regional and global changes well and cannot be used as alternative age-depth model.

Fig 9

The result of correlation of the DY-1 δ¹⁸O record with the LR04 record: A – the δ¹⁸O record correlated with LR04; B – age-depth model estimated for phase B (blue lines) and age-depth models estimated for phases A and C based on the U-series ages (data from Jo et al. 2011) – (1) LR04 record; (2) DY-1 δ¹⁸O record; (3) age-depth model made by the authors (Jo et al. 2011); (4) age-depth model made by the OIS approach.

Fig 10

The comparison of age-depth models for stalagmites from Spanish Cobra Cave (Rossi et al. 2014): A – the results of age-depth model estimation – (1) age-depth model made by the authors, fluorescence lamina counting (Fl); (2) age-depth model made by MOD-AGE; (3) age-depth model made by the OIS approach; B – the result of the correlation with the GRIP record.

In the previous examples, we used U-series ages as the pointed age benchmarks, and every depositional episode had at least one defined age benchmark. The last example (LDH profile) is beyond the U-series age limits. Additionally, the uranium concentrations measured in a set of samples from this profile are lower than 0.07 ppm (Häuselmann et al., 2015). It is far too low for eventual application of U–Pb dating. The LDH profile chronology is based on eight paleomagnetic benchmarks (Table 2). The whole profile has ten principal hiatuses and eleven sedimentation phases. Therefore, the number of points with defined ages is far too low to estimate age-depth models for the individual sedimentation phases. In this case, due to the LDH profile age and its duration, the LR04 stack record is the only robust δ¹⁸O record available that covers the required interval.

One of the advantages of GenCorr software is the sensitivity for deposition breaks (see Pawlak & Hercman 2016). The OIS+PM chronology may be verified by comparisons of the locations of hiatuses derived from the correlation results with their actual positions in the LDH section (Fig. 6A). The whole LDH profile is correlated to the LR04 record with no assumption about continued/discontinued deposition (Fig. 5; black line). The OIS+PM age-depth model suggests nine hiatuses, all of which can be identified with breaks in the LDH lithological log (arrows between panels A and B in Fig. 6). However, within the LDH speleothem profile, the accuracy of the OIS chronology will depend primarily on the precision of the field measurements of PM sample position. These were mostly within 1–2 cm, with a maximum of 4 cm (Table 2). In general, we may state that unconformities/hiatuses detected by the combined OIS+PM chronology are in relatively good agreement with the lithological log.

A comparison of the ages estimated for the LDH with the GPTS records (Ogg 2012) shows that hiatuses can significantly distort magnetozone stratigraphic relationships, especially their thicknesses. This effect is particularly strong for zones N2 and N3 in the younger part of the LDH profile and for zones N6 and R6 in the older segments. The duration of breaks in deposition is much longer than that suggested by Bosák et al., (2002). The longest periods of non-deposition are detected inside the N3, R2, and R3 zones and cover time spans of approximately 185, 100 and 95 ka, respectively (Fig. 11).

Fig 11

The comparison of the GPTS record (Ogg 2012) with the time scale of the LDH section obtained by integrated OIS and PM chronology: 1 – normal polarity, 2 – reverse polarity, 3 – non-deposition time (hiatus).

6. Conclusions

Deposition breaks in speleothems are often caused by climatic factors, so they are carriers of climatic information. Hence, the correct and possibly accurate estimation of the durations of breaks is important for accurate paleoclimatic reconstructions.

The approach based on two dated points located close to hiatus boundaries may not be precise enough to estimate the time hidden in the hiatus because dated points are never located directly on the hiatus boundaries. The age-depth modeling approach gives robust results. However, it is not always possible to have a sufficient number of age data to calculate independent age-depth models for individual depositional phases.

Our study shows different situations in several examples of speleothems with hiatuses: (1) stalagmite PD-4 (Slovakia), where the hiatus duration was estimated by the classic age-depth modeling approach based only on U-series data; (2) stalagmite SC-3 (Poland), where oxygen isotopic stratigraphy is used to establish the chronology in a part of the stalagmite with only one U-series age; and (3) the flowstone profile from Ledena Dvorana in Slovenia, where the chronology bases on paleomagnetic benchmarks and oxygen isotopic stratigraphy. Additionally, the three examples selected from the literature: (1) a stalagmite from Daeya Cave (Korea); (2) a stalagmite from Cobre Cave (Spain); and (3) one stalagmite from a Macedonian cave located near Lake Ohrid, were used. In the case of two examples, first from Cobra Cave and second from the Macedonian cave, the long δ¹⁸O record can have episodes when local conditions have a strong impact on its values, and this part of that record cannot be correlated to the reference curve. Therefore, the results of the OIS correlation should be verified by independent chronology, such as U-series ages. Nevertheless, the OIS approach combined with the independent chronological information, such as U-series ages, can be helpful for the detection of hiatuses and estimation of their duration. Finally, the flowstone profile of the Ledena Dvorana (LDH; Slovenia)-layered complex, divided by ten principal hiatuses, is an example of a profile where the OIS approach is the only reliable option for determining the chronology of all deposition phases. The obtained OIS age-depth model is in accordance with PM benchmarks and with hiatuses detected in the profile. Generally, the OIS correlation can be a useful tool for the estimation of duration of hiatuses and chronology of the speleothem profiles beyond the U-series age limits. Additionally, the OIS approach can be used for the improvement of the existing chronologies with a large error. The main threats for this approach are potential diachronicity of the reference curve and correlated record.