The cave site has been explained in detail by Treble et al. (2013). Briefly, the field site Golgotha Cave is 200 m in length and up to 25 m in width (Fig. 1), and developed in Quaternary aeolianite, which consists of wind-blown calcareous sands that were deposited along the southwest coast of Australia (Brooke et al., 2014). Vadose zone water flow, and subsequent widening by ceiling collapse, formed the cave chambers. Treble et al. (2013) described the cave site as being developed in the Spearwood system of the Tamala Limestone and is mantled by a variable thick layer of sand formation having depths of between 0.3 and 3 m. Diffuse (or matrix) flow is likely to be dominant in the Tamala Limestone formation due to its high matrix porosity as 0.3–0.5 (Smith et al., 2012). Karst in this region is also called “syngenetic” (Treble et al., 2013), implying processes like preferential vertical dissolution and varying morphology of the subsurface caprock. These processes may establish vadose zone preferential flow extending to the cave ceiling, with occasional rapid delivery of percolating waters deep into the calcarenite which end up seeping through to the cave ceiling. Therefore, this young limestone formation offers various opportunities for preferential flow into the host rock and storage within it (Brooke et al., 2014). Golgotha Cave was chosen because (a) it is located in an intensively studied karst area (Treble et al., 2013, 2015, 2016), which has over 10 years of manual and 3 years of automated drip water monitoring, (b) it contains actively growing speleothems, and (c) it is accessible year-round.

Based on previous studies at this site, we determined previously that Chamber 1 (Fig. 1b–d) is mostly dominated by matrix flow representing water flowing down and seeping through the rock matrix, characterized by both icicle-shaped and soda-straw stalactites with slow drip rates of low variability. In contrast, Chamber 2 (Fig. 1b and e) is typically controlled by fracture and combined flow, with high drip rates that are shown to vary over time depending upon the mode of water delivery to the preferential flow system. In fracture flow, water moves along the fracture orientation, forming curtain-shape stalactites in the direction of highest fracturing. Finally, combined flow is defined as the combination of conduit, matrix, and fracture flow, resulting in a circular pattern of stalactite formation.

A comprehensive description of the climate at our study site has been presented in Treble et al. (2013). To summarize, the site is a Mediterranean climate, associated with wet winters and dry summers. Annual rainfall recorded at Forest Grove weather station (Fig. 1a, 5 km away from the study site) is 1136.8 ± 184 mm, among which ∼ 75 % occurs between May and September, with an average daily maximum temperature variation from 16 ∘C (in July) to 27 ∘C (in February; BoM, 2017). Typically, the peak rainfall begins in late autumn (May) and the wet season continues until end of September with a median monthly rainfall of ∼ 100 mm. Each hydrological year is defined as April to March, as April has the lowest water budget (precipitation less evapotranspiration).

As reported in previous studies, all hydrological years have water deficit during the dry season (October to April) and significant infiltration during the wet period. Low evaporative conditions during winter should permit increased infiltration to the caves, enhancing the drip discharge response to winter rainfall. The hydrological year 2012 had roughly similar annual rainfall of 1008.6 mm to the long-term annual mean, whereas 2013 was rather wet (total rainfall of 1239.8 mm) and 2014 was a relatively dry year with a total rainfall of 943.8 mm. Recorded rainfall was significantly above average in the 2013 hydrological year for various weather stations in Western Australia (BoM, 2017). Therefore, our site had a wetter winter in 2013 with an estimated annual recharge of 858.67 mm which is very much above average (10-year mean annual recharge is 564 mm).

Data acquisition and pre-processing has been previously described in Mahmud et al. (2016) and is concisely summarized here. Stalagmite drip loggers (http://www.driptych.com) were set up in approximate transects throughout the two large chambers from higher to lower ceiling elevations in 34 locations and have been monitored since August 2012. Both chambers of Golgotha Cave have contrasting discharge, dune facies, and karst features (Fig. 1). Data loggers were set to record continuously at 15 min intervals. The notation used for site identification follows the same style as described in previous studies, consisting of a numerical number (representing the chamber) and a letter/roman number (representing a drip site within the given chamber, with a letter indicating the sites having both manual and automatic drip counts and a roman number specifying the sites only having drip logger data). Based on previous studies of the site, 29 sites are considered in the time series analysis although short periods of poor quality data were omitted if they were associated with changes in the mean and variability at the time of fieldwork. This impacted sites 1A, 1B, 2A, 2B, 2E as the logger was temporarily placed aside every 6 weeks in order to sample water from a collection bottle underneath the logger. Time series gaps are filled with synthetic data based on the drip statistics and correlation between drip rates.

As previously reported, drip rates in Chamber 1 are generally very low (the fastest drip rate was 25 drips per 15 min) consistent with the predominance of matrix flow in this chamber. However, it is obvious that most drip loggers exhibit a clear response to the 2013 wet winter and also indicate the substantial interannual variation in discharge between three hydrological years. All Chamber 1 drip sites (except Site 1x) show a gradual drip rate decrease during summer 2012 to winter 2013 due to below average rainfall in 2012. Then after displaying the sudden increase in all drip discharges that express the 2013 wet winter, the drip rates further reduce due to the dry 2014 hydrological year. This intra-annual variation is identified to be much greater than the interannual discharge variation of the drip sites, as previously observed in Baker et al. (1997). This suggests that high-resolution intra-annual drip rate data is helpful to obtain a complete picture of changing flow variability with recharge. The high resolution of the data sets includes precise characterization of the temporal behavior of an individual drip, illustrating the differences inherent to the drip sites.

In contrast, Chamber 2 drip rates present more variability between sites both in intra- and interannual discharges, except few very slow dripping sites. Of the Chamber 2 drips, the slow drip sites have the lowest coefficients of variation (COVs) and lowest discharges, indicative of matrix flow types. The timing of maximum drip rates is generally delayed in Chamber 2 versus Chamber 1: Chamber 1 drip rates typically peak in late spring/early summer (October–December) while Chamber 2 drips tend to peak a few months later (December–May), reflecting a longer water residence time. This may be a function of the thicker ceiling above Chamber 2 (40.24 versus 32.33 m) but also heterogeneity in flow paths to each chamber. Overall the drip response to the 2013 wet winter is amplified in Chamber 2 versus Chamber 1, consistent with the presence of greater fracture flow in Chamber 2.

By applying morphological analysis of ceiling features acquired by lidar data, Mahmud et al. (2015) distinguished three flow patterns (i.e., matrix flow, fracture flow, and a combination of conduit, fracture, and matrix flow) for the observed ceiling morphological features. All the drip sites were then characterized according to this flow classification in Mahmud et al. (2016), which is used here as a reference for clustering similar drip time series.

Research involving automated drip monitoring systems is increasing, for example at Cathedral Cave in Wellington (Cuthbert et al., 2014) and Harrie Wood Cave in the Snowy Mountains, Yarrangobilly (Markowska et al., 2015). The variability of the drip discharge might not only be a function of discharge itself; it could also depend on the sampling frequency. We investigate this possibility by plotting the COV versus sampling interval (the original 15 min and calculated by resampling the data at 1 h, 1 day, 1 week, and 1 month). COV is supposed to be artificially high at the high frequency of 15 min because of sampling bias that artificially increases the noise. The resampling at low frequencies is simply a way of smoothing out this noise. Using the optimum sampling frequency to minimize its effect on drip variability, we plot drip rate histograms to identify the response of drips between the flow classifications and the response to intra- and interannual variability in infiltration. We also plot the autocorrelation functions (ACFs) to investigate the relationship between the strength of correlation and the lidar-based flow type. Finally, we summarize the mean discharge of drip sites in relation to the variability in discharge using the optimum sampling frequency. These are the same drip discharge parameters as used in the classification method proposed by Friederich and Smart (1982), Fairchild et al. (2006), and Baker et al. (1997) that were based on manual drip collection at low frequency.

We employed multidimensional scaling (MDS), which allows data dimensionality reduction, i.e., mapping complex multidimensional data on a low-dimensional manifold. MDS is a technique that embeds a set of points in a low-dimensional space, so that the distances between the points resemble as closely as possible a given set of dissimilarities between the objects they represent (Birchfield and Subramanya, 2005). MDS requires a distance matrix to be computed in which a single scalar number characterizes the similarity between any two time series. In our case, each drip logger is an object and a specific distance between drip loggers is considered to characterize the similarity between any two loggers. It takes an input matrix giving dissimilarities between pairs of items and outputs a coordinate matrix whose configuration minimizes a loss function. MDS is also known as principal coordinates analysis (PCoA). MDS operates on a distance or dissimilarity matrix (Pisani et al., 2016), which is different than principal component analysis (PCA) that is based on a covariance matrix. Even if PCA and MDS methods can return the same results in specific contexts, MDS can be considered more general because it remains valid for non-Euclidean distances, such as the distance matrix (D) chosen in this study. MDS is used to translate these distances into a configuration of points defined in an n-dimensional Euclidean space (Cox and Cox, 1994). MDS results in a set of points arranged so that their corresponding Euclidean distances indicate the dissimilarities of the time series. According to Birchfield and Subramanya (2005) the basic steps of performing the MDS algorithm are as follows: i.

Construct the distance matrix D: one key component in clustering is the function used to measure the temporal similarity (or distance) between any two time series being compared. To define an appropriate measure of similarity between time series, we determine two factors: firstly, the offset (O) to match two time series based on their maximum correlation, and secondly the complement of the correlation coefficient (1 - R) between the time series (Jex et al., 2012). Initially, we compute the cross-correlation function, a measure of similarity of two time series as a function of the displacement of one relative to the other. The cross-correlation function is an estimate of the covariance between two time series, y1t and y2t, at lags k = 0, ±1, ±2, …. The offset (O) is defined as the lag time based on the maximum correlation between two time series. Next, we define R as the correlation coefficient with the time series being moved by the offset amount O to have maximum correlation coefficient. Both O and R are calculated to all n(n - 1)/2 pairs of drip data, where n is the number of drip data. Here, we use the original recorded drip counts in 15 min interval. The sampling bias discussed in Sect. 3.1 only affects the drip variability, not the cluster analysis. Moreover, high-resolution (15 min interval) data are more suited for the cluster analysis because it allows better defining the cross-correlation between drips, as sometimes the offset of maximum correlation O might be less than a day. Finally, the distance matrix D is computed for each pair of loggers using the following equation (Jex et al., 2012):D=O(1-R).The distance matrix (D) is square, symmetric, and has dimension equal to the number of drip loggers.

We test the variability of drip discharge COV with the sampling frequency in Fig. 2, to find the optimum sampling frequency that minimizes sampling artifacts while maximizing the capture of natural variability. For high discharge, COV increases with sampling frequency, which we explain by the smaller sampling interval better capturing the actual drip variability. For low discharges, COV also increases with sampling frequency, which we explain by the variability introduced due to drip rates being less than the sampling frequency. From the data presented in Fig. 2, we can conclude that for both chambers and to compare all different types of flow, a sampling frequency of 1 day gives the minimum COV, which does not change significantly with a finer sampling frequency. Therefore, we use a sampling frequency of 1 day that minimizes sampling artifacts while maximizing the capture of natural variability. For Golgotha Cave, this would be to sum the 15 min drip rates over a 1-day period. This optimized sampling frequency is used to plot the histograms (Sect. 4.2) and ACFs (Sect. S1 in the Supplement), and to examine the drip discharge behavior with drip variability for various flow types (Sect. 4.3).

Figure 3 shows the drip rate histograms for representative drip sites and different flow categories with optimum sampling frequency of 1 day. Drip sites are organized from lowest to highest discharge in each flow classification. Slow dripping soda-straw flows (e.g., sites 2xi, 2iii, and 1v) show variation of drips with seasonality and the response to wetter recharge period with an approximate 6-month lag, which suggests the drip water is supplied from storage in the limestone formation. Among these, Site 1v displays the response to recharge in much shorter duration, the 6 months following 2013 recharge and then a shift to lower flow rates which may represent flow poaching. The histograms for icicle and combined flow systems represent unimodal skewed to bimodal distributions, indicating the shift to higher drip rates in response to the wetter 2013 hydrological year (except Site 2xiii, which shows a shift to lower drip rates). The rest of the fracture sites show bimodal or multimodal distributions. With the limited temporal scale of the analysis, it seems that the histograms with skewed distributions represent the consequences of wetter 2013 hydrological year. These skewed distributions seem to have higher drip rate response to the drier 2014–2015 period rather than the earlier normal/wetter years. This clearly denotes potential refilling of storage within the system during the 2013 wet winter, and later supplying drip water in 2014–2015 seasons. In contrast, the bimodal distribution of Site 2viii indicates the drip response to the annual cycle of wet and dry seasons of each hydrological year with an approximate 6-month lag. Several bimodal (e.g., Site 1x) and multimodal (e.g., sites 2xvi, 2vi) distributions, characterized as fracture flow, also distinguishes the dry period of 2012–2013 (having low drip rates) from the later period of 2013 wet winter (with high drip rates).

We investigate the use of ACFs to analyze drip behavior using the optimum sampling frequency of 1 day and until lags of 365 days. We do not find significant yearly autocorrelation with this limited 3 years of data. In some drips, a negative correlation occurred, but it is very insignificant and no physical process can explain a negative yearly correlation. Therefore, we plot ACFs in Fig. 4 for different flow categories with the optimum sampling frequency of 1 day and lag time of 200 days. All sites have an autocorrelation that persists for at least a month, and often much longer. However, there is no relationship between the strength or the temporal decay of the correlation and the lidar-based flow classification. This indicates the presence of ample storage in the system, supplying all stalactite types.

We examine the hydrological behavior of the drips at daily resolution with respect to mean discharge and flow variation in Fig. 5. It is clear from Fig. 5 that there is no relationship between COV and flow type. One soda-straw discharge (Site 2xi) has seasonal dryness, a very low discharge, and a very high coefficient of variation due to its irregular dripping. Otherwise, nearly all soda-straw flow, icicle flow, combined flow and fracture flow drips have COV < 60 %, with the exception of one fracture flow site showing the highest COV (Fig. 5). But in general, there is little difference in the COV between classification types, probably reflecting the ample storage (Sect. S1) due to the dominance of primary porosity at this cave. We do not clearly observe increasing variability with decreasing discharge within similar flow type, in contrast to other studies from older, fractured rock limestones (Smart and Friederich, 1987; Baldini et al., 2006; Baker et al., 1997). This shows that Golgotha Cave drip sites do not fit within the drip classification method proposed by Smart and Friederich (1987) and Baker et al. (1997), which were based on manual drip counts with limited number of intermittent drip sites. Moreover, we utilize drip data from a cave with primary porosity, capturing the full range of flow types from matrix through to fracture, whereas the previous classifications only captured slow vs. fast drips that were likely dominated by fracture flow paths given the host rock setting.

The clustering results are overlaid upon the chamber ceiling images in Fig. 6 and also summarized in Tables 1 and 2 with the average drip discharges and flow type classification based on lidar. Average drip discharges are calculated from the 15 min drip rates. As mentioned above, drip logger time series are deemed similar if they are well correlated and only have a small offset with each other, and so these time series should cluster together. Most of the drip sites that are identified as matrix flow (soda-straw and icicle flow) cluster together in C1. However, three of the icicle flow sites with drip rates greater than 4 per 15 min fall in C2. The combined flow category and the fracture type usually cluster in C3 and C4, respectively. Therefore we observe that our clustering generally agrees with the morphology-based flow classification of Mahmud et al. (2016). Few of the flow classes show exceptions, for example Site 2vi is a fracture type flow and cluster in C1. This site has really high discharge with high variability, showing irregular drip rate.

One consistent feature that appears from the cluster analysis of Fig. 6 is the spatial homogeneity of the clusters in Chamber 1, suggesting that they are spatially connected, or that their flow paths are connected to the same hydrological domain (the karst matrix), and supporting the overall dominant matrix flow patterns (both soda-straw and icicle). Chamber 2 presents a completely different situation, where it is obvious that drip sites can have similar behavior (well correlated with a small lag), and be spatially distinct features, separated by spans of approximately 6 m (Fig. 6). In particular, clusters 3 and 4 are spatially scattered, representing the presence of fractures and combined flow systems throughout the chamber ceiling. This indicates an overall strong heterogeneity of the flow paths between the surface and the cave for Chamber 2. Hence, in Chamber 2 we expect flow paths to be more complex with routing between multiple stores and interconnected fracture networks potentially resulting in non-linear response to infiltration. This is supported by drip water δ18O data for this chamber (Treble et al., 2013).