Groundwater follows a myriad of flow paths between the recharge areas to where it discharges into streams or rivers. Consequently, groundwater discharge does not have a discrete age but rather has a distribution of transit times. MTTs are commonly estimated using lumped parameter models (LPMs) that describe the distribution of water with different ages or tracer concentrations in simplified aquifer geometries (Maloszewski and Zuber, 1982, 1996; Maloszewski et al., 1983; Cook and Bohlke, 2000; Maloszewski, 2000; Zuber et al., 2005). LPMs represent a viable and commonly used alternative to estimating MTTs using numerical groundwater models that rely upon hydraulic parameters that are seldom known with certainty and which vary spatially. However, the LPMs are only approximations of actual flow systems and the MTTs may be broad estimates rather than specific values.

The LPMs may be utilised with stable (O, H) isotopes or major ions if the concentrations vary seasonally in rainfall (e.g. Soulsby et al., 2000; McGuire and McDonnell, 2006; Tetzlaff et al., 2007, 2009; Hrachowitz et al., 2009, 2010; Kirchner et al., 2010). Determining MTTs from stable isotope ratios or major ion concentrations relies on tracking the delay and dampening of the seasonal variations between precipitation and discharge. However, use of these tracers typically requires sub-weekly sampling over time periods equal to or exceeding that of the transit times (Timbe et al., 2015). In addition, these tracers become ineffective when transit times exceed 4 to 5 years as the initial variations in rainfall are progressively dampened to below the point at which they can be detected (Stewart et al., 2010).

Gaseous tracers (e.g. 3He, chlorofluorocarbons, or SF6) are effective in determining residence times of groundwater (Cook and Bohlke, 2000) but are difficult to apply to surface water due to gas exchange. With a half-life of 12.32 years, tritium (3H) has been used to estimate MTTs of up to 150 years (e.g. Morgenstern et al., 2010; Stewart et al., 2010). Unlike other radioactive tracers (e.g. 14C), 3H is part of the water molecule and its activities are affected only by radioactive decay and dispersion and not by geochemical or biogeochemical reactions in the soils or aquifers. Because 3H activities are not affected by processes in the unsaturated zone, the MTTs reflect both recharge through the unsaturated zone and flow in the groundwater system.

Utilisation of 3H as a tracer is facilitated by the fact that the 3H activities of rainfall have been measured globally for several decades (International Atomic Energy Agency, 2016). Due to atmospheric nuclear testing, 3H activities of rainfall peaked during the 1950s and 1960s (the “bomb pulse”). The bomb-pulse 3H activities in the Southern Hemisphere were much lower than in the Northern Hemisphere (Tadros et al., 2014) and have now largely declined to below those of modern rainfall (Morgenstern et al., 2010). As a consequence, MTTs can generally be determined from single 3H measurements (Morgenstern et al., 2010; Morgenstern and Daughney, 2012) in an analogous manner to how other radioactive isotopes (e.g. 14C or 36Cl) are used in regional groundwater systems. This also allows MTTs at different streamflows to be estimated (Morgenstern et al., 2010; Duvert et al., 2016; Cartwright and Morgenstern, 2015, 2016a, b).

Using LPMs to estimate MTTs has a number of uncertainties. Due to the attenuation of the 3H bomb pulse in the Southern Hemisphere, the suitability of the LPM can no longer be evaluated by time-series 3H measurements (Cartwright and Morgenstern, 2016a) as is still possible in the Northern Hemisphere (e.g. Blavoux et al., 2013). Hence, LPMs must be assigned based upon knowledge of the geometry of the flow system and/or information from previous time-series studies in similar catchments. While not being able to assess the form of the LPM results in uncertainties in the calculated MTTs, the MTTs are less sensitive to the choice of LPM than is the case in the Northern Hemisphere (e.g. Blavoux et al., 2013).

Rivers can receive water from numerous stores, including groundwater, tributaries, soil water, and perched aquifers, each of which may have different MTTs. The mixing of water from different flow systems potentially produces water samples with a residence time distribution that does not correspond to those in the LPMs, and calculated MTTs are lower than actual MTTs. This is known as the aggregation error (Kirchner, 2016; Stewart et al., 2017) and it increases as the difference between the transit times of the individual endmembers increases. For transit times estimated from single 3H activities, the aggregation error decreases with an increasing number of endmembers as the mixing of numerous aliquots water with different transit times is similar to what is represented by the LPMs (Cartwright and Morgenstern, 2016a).

Despite the uncertainties in calculating MTTs, because the 3H activities of the remnant bomb-pulse waters have largely decayed, Southern Hemisphere waters with low 3H activities have longer MTTs than waters with high 3H activities. This permits relative mean transit times to be readily assessed. Because 3H is radioactive, there is no requirement for flow in the catchment to be time-invariant as long as the flow path geometry remains relatively constant.

Fundamentally, MTTs are a function of the recharge rate, length of groundwater flow paths, and rates of groundwater flow, and parameters that control those factors will control the MTTs. Large catchments may have some long groundwater flow paths and consequently have long MTTs (e.g. McGlynn et al., 2003; Hrachowitz et al., 2010). Catchments with higher drainage densities (i.e. higher total stream length per unit area) may contain numerous short groundwater flow paths and consequently have short MTTs (e.g. Hrachowitz et al., 2009). Large groundwater storage volumes will likely also result in long MTTs (e.g. Ma and Yamanaka, 2016). Groundwater flow is likely to be more rapid through steeper catchments due to the higher hydraulic gradients, resulting in shorter MTTs (e.g. McGuire et al., 2005). Forested catchments may have higher evapotranspiration and lower recharge rates than cleared catchments (Allison et al., 1990), and the degree of forest cover exerts a control on MTTs (e.g. Tetzlaff et al., 2007). The hydraulic conductivities of the bedrock and soils are also important in controlling the timescales of water movement through catchments (e.g. Tetzlaff et al., 2009; Hale and McDonnell, 2016).

Identifying the controls on MTTs is important for understanding catchment functioning. It also potentially allows first-order estimates of MTTs to be made in similar catchments for which detailed geochemical tracer data do not exist. In some catchments, correlations between 3H activities and major ion geochemistry or the runoff coefficient (the proportion of rainfall exported from the catchment by the stream) also allow first-order estimates of MTTs to be made (Morgenstern et al., 2010; Cartwright and Morgenstern, 2015, 2016a).

This study evaluates the range of and controls on MTTs in headwater streams from the upper Gellibrand catchment of the Otway Ranges in southeastern Australia. Specifically, we test the following hypotheses. Firstly that, in common with headwater catchments elsewhere in southeastern Australia, the MTTs are several years to decades. Secondly, that the MTTs are most likely controlled by catchment attributes such as land cover, slope, or drainage density. Lastly, that shallower water stores within the catchment become progressively mobilised during higher rainfall periods contribute to streamflow at those times. We also use this study to evaluate whether there are geochemical proxies that could be used to make first-order predictions of MTTs at times when no 3H data are available. Documenting MTTs is critical to understanding and protecting headwater catchments and, while this study is based on a specific area, the results have relevance to catchments globally. There is not a complete understanding of the range of MTTs in headwater catchments, nor what controls these. Thus, these are important gaps in our understanding of headwater catchments.

River water samples were collected from eight locations in the catchments (Fig. 1). Lardners Creek was sampled at an active gauging station (Lardners Gauge) that is maintained by the Department of Environment, Land, Water and Planning (DELWP) (site 235210) and from the Lardners Creek East Branch (Upper Lardners), approximately 3.5 km upstream from Lardners Gauge. Love Creek was sampled at Kawarren (Love Creek Kawarren), approximately 1 km upstream of DELWP gauging station 235234 and at the Wonga Road crossing (Love Creek Wonga), approximately 4.5 km downstream of Kawarren. River water samples were collected from the Gellibrand River, Porcupine Creek, Ten Mile Creek, and Yahoo Creek at the sites of former DELWP gauging stations (sites 235235, 235241, 235239, and 235240, respectively).

Streamflow at the time of sampling was determined for each of the eight locations with the exception of Upper Lardners, which is ungauged. Sub-daily streamflow is currently measured at Lardners Gauge (site 235210) and at Love Creek (site 235234) (Department of Environment, Land, Water and Planning, 2017) (Fig. 1). Streamflow at James Access on the Gellibrand River was estimated using a correlation (R2=0.97, p value = 10-8) between streamflow at the former gauging station at this location and that at the existing Upper Gellibrand River gauging station (site 235202), approximately 7 km upstream (Fig. 1). Likewise, streamflow at the Porcupine Creek, Ten Mile Creek, and Yahoo Creek sampling sites was estimated using correlations (R2=0.95, 0.77, and 0.84, respectively, with p values < 10-6) between streamflow at the former gauging stations at these locations and the Love Creek gauging station.

River water samples were collected from each site in July 2014, September 2014, March 2015, and September 2015 (Supplement). An additional round of river water samples was collected from Lardners Gauge, Porcupine Creek, Ten Mile Creek, and Love Creek Kawarren in November 2015. The water samples were collected from close to the centre of the streams using a polyethylene container fixed to an extendable pole. Additional data for James Access are from Atkinson (2014). A single precipitation sample was collected from Birnam in the Otway Ranges near Ten Mile Creek (Fig. 1) in September 2014 using a rainfall collector. The collector consisted of a polyethylene storage container equipped with a funnel positioned approximately 0.5 m above ground level. Prior to collection of the precipitation sample, the collector had been in the field for 78 days, during which time approximately 198 mm of rainfall was recorded at Forrest while 431 mm of rainfall was recorded at Mount Sabine (Department of Environment, Land, Water and Planning, 2017).

The electrical conductivity (EC) and pH of the river water and precipitation samples was measured in the field using a calibrated TPS^® hand-held water quality meter and probes. The EC measurements have a precision of 1 µS cm-1. Cation concentrations were measured at Monash University using a Thermo Fischer ICP-OES on samples that had been filtered through 0.45 µm cellulose nitrate filters and acidified to a pH < 2 using double-distilled 16 M HNO3. Anion concentrations were measured at Monash University on filtered, unacidified samples using a Metrohm ion chromatograph. The precision of the cation and anion analyses, based upon replicate sample analysis, is ±2 % while accuracy based on analysis of certified water standards is ±5 %. HCO3 concentrations were measured by colorimetric titration with H2SO4 using a Hach digital titrator and reagents and are precise to ±5 %. Concentrations of total dissolved solids (TDSs) were determined by summing the concentrations of cations and anions. Geochemical data are presented in the Supplement.

3H analysis was conducted at the GNS Water Dating Laboratory in Lower Hutt, New Zealand. The samples were vacuum distilled and electrolytically enriched prior to analysis by liquid scintillation counting, as described by Morgenstern and Taylor (2009). Following further improvements the sensitivity is now further increased to a lower detection limit of 0.02 TU (tritium units) via tritium enrichment by a factor of 95, and reproducibility of tritium enrichment of 1 % is achieved via deuterium calibration for every sample. 3H activities are expressed as absolute values in tritium units where 1 TU represents a 3H / 1H ratio of 1 × 10-18. The precision (1σ) is ∼ 1.8 % at 2 TU.

Catchment attributes (Table 1) were determined using ArcGIS 10.2 (ESRI, 2013) and datasets from DataSearch Victoria (2015). The hydrology modelling tools in ArcGIS were used to generate the stream network from a 20 m digital elevation model. A threshold catchment area of 50 Ha reproduces the observed perennial stream network of the area. Catchment areas upstream of each sampling site and drainage densities were determined using the watershed tool. Mean slopes were calculated using the spatial analysis tools. Vector-based land use datasets were converted to raster formats and reclassified. Land use was assigned as forest (native vegetation and plantations) and cleared land, which includes urban and agricultural regions. Runoff coefficients were calculated using streamflow data for each of the catchments (except Upper Lardners) for March 1986 to July 1990 (Department of Environment, Land, Water, and Planning, 2017), the only interval for which continuous streamflow data are available for each catchment. The runoff coefficient calculations assumed a uniform average annual rainfall of 1.3 m for each catchment (Bureau of Meteorology, 2016). Correlations between catchment attributes and other parameters are considered to be strong where R2≥0.7.

The lumped parameter models implemented in the TracerLPM Excel workbook (Jurgens et al., 2012) were used to estimate MTTs. The 3H activity of water sampled from a stream at time t(C0(t)) is related to the input (Ci) of 3H via the convolution integral: C0(t)=∫0∞Cit-Tg(T)e-λTdT, where T is the transit time, t-T is the time that the groundwater entered the flow system, λ is the decay constant (0.0563 yr-1 for 3H), and g(T) is the exit age distribution function, for which closed-form analytical solutions have been derived (e.g. Maloszewski and Zuber, 1982, 1992, 1996; Kinzelbach et al., 2002). MTTs were estimated by matching the predicted 3H activities from the LPMs to the observed 3H activities of the samples.

As discussed earlier, the use of single 3H activities to estimate MTTs requires that an LPM be assigned. Here two LPMs were utilised: the exponential piston-flow model (EPM) and the dispersion model (DM), which are among the most commonly used LPMs (McGuire and McDonnell, 2006; Stewart et al., 2010). The EPM describes flow in aquifers with both exponential and piston-flow portions. This model may be applied to unconfined aquifers where recharge through the unsaturated zone resembles piston flow and flow within the aquifer resembles exponential flow (Morgenstern et al., 2010). TracerLPM defines an EPM ratio, which represents the relative contribution of exponential and piston flow (Jurgens et al., 2012). The EPM ratio is 1/f-1, where f is the proportion of aquifer volume exhibiting exponential flow.

The dispersion model is based on the one-dimensional advection–dispersion equation for a semi-infinite medium (Jurgens et al., 2012). While this model can be applied to a wide variety of aquifer configurations, conceptually it is probably less realistic than other LPMs. Nonetheless, it has been successfully used to predict tracer concentrations over time in a number of flow systems (e.g. Maloszewski, 2000). Utilisation of this model requires defining a dispersion parameter, Dp, which represents the ratio of dispersion to advection.

The average annual 3H activities of modern rainfall in central and southeastern Australia are predicted to vary between 2.4 and 3.2 TU (Tadros et al., 2014). 3H activities of 9- to 17-month rainfall samples from elsewhere in Victoria are between 2.72 and 2.99 TU (Atkinson, 2014; Cartwright and Morgenstern, 2015; Cartwright et al., 2018) and fall within the range of predicted 3H activities for their locations. Interpolating the data from that study suggests that modern rainfall in the Otway Ranges has an annual average 3H activity of ∼ 2.8 TU (which is slightly lower than the ∼ 3.0 TU recorded at Melbourne ∼ 150 km to the east of the study area). A value of 2.8 TU was used as the average annual 3H activity of modern (2010 to 2016) rainfall as well as for the years prior to the atmospheric nuclear tests (pre-1951). The 3H input in the intervening years is based on the 3H activities of rainfall in Melbourne (International Atomic Energy Agency, 2016; Tadros et al., 2014). These were decreased by 6.7 % to account for the expected difference in 3H activities in the rainfall between the Otway Ranges and Melbourne.

There are several uncertainties in the MTT calculations. The analytical uncertainty ranges between 0.02 and 0.04 TU (Supplement). To assess the effect of uncertainties in rainfall 3H activities, MTTs were recalculated assuming that modern and pre-1950 rainfall had an average 3H activity of either 2.4 or 3.2 TU, with the 3H activities of the intervening years adjusted proportionally. As this range encompasses the estimated annual 3H activities of rainfall over most of central and southeastern Australia, it allows a conservative estimate of uncertainties to be made.

The aggregation or macroscopic mixing of waters also introduces uncertainties (Kirchner, 2016; Stewart et al., 2017). Consider a stream fed by several tributaries. The expected MTT (MTTe) can be calculated using the streamflow data, 3H activities, and MTTs of each tributary via MTTe=aMTT1+bMTT2+cMTT3+… (Stewart et al., 2017). In Eq. (2), a, b, and c, represent the fraction of total flow contributed by tributaries 1, 2, and 3. If the aggregation is minimal, MTTe will be similar to that estimated from the measured 3H activity via the LPM. The successful application of Eq. (2) relies on the MTTs of the different tributaries being defined by their 3H activities (which in itself may not be straightforward due to aggregation within those sub-catchments). Nevertheless, it provides a broad estimate of the error due to macroscopic mixing that is otherwise difficult to assess.

The volume (V in m3) of groundwater stored within an aquifer that interacts with the stream (sometimes referred to as the turnover volume) is related to the MTT by V=Q⋅MTT, where Q is streamflow (m3 yr-1) (Maloszewski and Zuber, 1982, 1992; Morgenstern et al., 2010).

Streamflow was highest during July 2014 (Supplement), ranging from 8.6 × 103 m3 day-1 at Ten Mile Creek to 255 × 103 m3 day-1 at James Access. Discharge was lowest during March and November 2015, ranging from 0.1 × 103 m3 day-1 at Ten Mile Creek to 8.8 × 103 m3 day-1 at James Access. Figure 2 illustrates the streamflows for the sampling rounds relative to the flow duration curves for the catchments. Samples were generally collected between the 10th and 100th percentiles of streamflow, which encompasses a wide range of flow conditions. Samples were collected during the recession periods after high-flow events that follow rainfall or during baseflow conditions (Fig. 3). Overland flow was not observed during any of the sampling events and small ephemeral tributaries in the catchments were dry.

Runoff coefficients range from 33 and 39 % at Lardners Gauge and James Access, respectively, to between 9 and 12 % at Porcupine Creek, Ten Mile Creek, Yahoo Creek Wonga, and Love Creek Kawarren (Table 1). The higher runoff coefficients at Lardners Gauge and James Access relative to the other catchments may be due to the fact that these rivers drain steeper catchments and are underlain almost entirely by low hydraulic conductivity Otway Group basement rocks (Fig. 1).

As discussed above, the annual average 3H activities of modern rainfall in much of central and southeastern Australia are between 2.4 and 3.2 TU (Tadros et al., 2014). The 78-day precipitation sample collected from near Ten Mile Creek in September 2014 had a tritium activity of 2.45 TU. This is lower than both the expected 3H activities for the Otway Ranges (∼ 2.8 TU: Tadros et al., 2014) and those of 9- to 12-month rainfall samples elsewhere in Victoria (2.72 to 2.99 TU: Atkinson, 2014; Cartwright and Morgenstern, 2015, 2016a; Cartwright et al., 2018). However, the Ten Mile Creek sample reflects rainfall over only part of the year and may not be representative.

Tritium activities of the rivers are < 2.14 TU, which are lower than the average annual 3H activities of modern rainfall and indeed the Ten Mile Creek rainfall sample. The 3H activities vary from 0.20 TU at Porcupine Creek in March 2015 to 2.14 TU at Yahoo Creek in July 2014 (Fig. 4). The higher 3H activities in the rivers are within the range of 3H activities of 1.80 to 2.25 TU for soil pipe water in higher elevations in the Gellibrand Catchment (Atkinson, 2014) (Fig. 4). In general, 3H activities were highest at high streamflow (July 2014) and lowest at low streamflow (March and November 2015).

The 3H activities of Love Creek at the upstream (Love Creek Kawarren) and downstream (Love Creek Wonga) locations in individual events varied by < 0.1 TU. The 3H activities in Lardners Creek between Upper Lardners and Lardners Gauge were slightly more variable (up to 0.17 TU). The range of 3H activities between the events was most variable at Porcupine Creek (0.20 to 1.97 TU), followed by Yahoo Creek (0.43 to 2.14 TU), Love Creek Kawarren (0.48 to 1.91 TU), Love Creek Wonga (0.55 to 1.88 TU), Ten Mile Creek (0.44 to 1.74 TU), Upper Lardners (1.54 to 1.99 TU), James Access (1.73 to 2.08 TU), and Lardners Gauge (1.64 to 1.97 TU) (Fig. 4). Overall, the highest 3H activities were similar across all catchments but the lower 3H activities varied considerably. The 3H activities increase with increasing streamflow up to approximately 104 m3 day-1, above which 3H activities do not increase appreciably (Fig. 4). Despite differences in catchment size, slope, geology, and land use, there is a strong correlation between 3H activities and streamflow across the catchments (3H = 0.2613ln⁡(Q)+0.8973; R2=0.75, p value = 0.15).

River water geochemistry is similar across all catchments and is dominated by Na, Cl, and HCO3 (Supplement). TDS concentrations are generally less than 100 mg L-1 at Lardners Gauge, Upper Lardners, and James Access but typically exceed 200 mg L-1 in Love Creek Wonga, Love Creek Kawarren, Porcupine Creek, Ten Mile Creek, and Yahoo Creek. TDS concentrations increase downstream in Lardners and Love creeks and are inversely correlated with streamflow in all catchments.

At Love Creek, Ten Mile Creek, Yahoo Creek, and Upper Lardners, there is no correlation between 3H activities and EC, TDS, or major ion concentrations (Fig. 5). However, at Porcupine Creek, there is a strong correlation (R2 > 0.95, p value < 0.01) between 3H activities and EC, TDS, and all major ion concentrations with the exception of chloride, nitrate, and sulfate. In addition, there is a strong correlation (R2=0.86, p value = 0.01) between 3H activities and TDS at Lardners Gauge (Fig. 5).

At Upper Lardners, James Access, and Ten Mile Creek, there is a strong correlation (R2 > 0.8, p values < 0.11) between nitrate concentration and 3H activities (Fig. 6a). The range of nitrate concentrations (0.08 to 2.0 mg L-1) were relatively similar during each sampling event across all catchments except for in July 2014, when nitrate concentrations exceeded 3 mg L-1 at Love Creek Kawarren and Love Creek Wonga. A similar correlation exists between sulfate concentrations and 3H activities at James Access and at Upper Lardners, but not at Ten Mile Creek (Fig. 6b). However, sulfate concentrations at these locations are lower than they are in the other catchments.

It is important to determine how the water stores that contribute to streamflow change between high and low flows. Groundwater inflows are most probably the dominant source of water during the summer months. However, at times of higher streamflow there may be mobilisation of younger shallower water stores (e.g. water from the soils or the regolith) as the catchment wets up (e.g. Hrachowitz et al., 2013; Cartwright and Morgenstern, 2015, 2016a) or mixing between baseflow and recent rainfall (e.g. Morgenstern et al., 2010). The river water samples were collected during baseflow conditions or during recession periods after high streamflows that follow rainfall (Fig. 3) when recent rainfall is less likely to directly contribute to streamflows. That the major ion geochemistry varies little with streamflow also suggests that there is not significant dilution of groundwater inflows with recent rainfall during the sampling periods (e.g. Sklash and Farvolden, 1979; Kennedy et al., 1986; Jensco and McGlynn, 2011; Cartwright and Morgenstern, 2015).

Together, these observations suggest that there is no significant direct input of recent rainfall during the sampling periods. The flow system is concluded to be a continuum that is dominated by older groundwater inflows at low flows while progressively shallower and younger stores of water (such as soil water or perched groundwater) are mobilised during wetter periods. The observations that nitrate and sulfate concentrations in several of the catchments are higher at high streamflows (Fig. 6) may reflect the input of contaminants from recent agricultural activities to the streams. This observation agrees with the conceptualisation that shallower stores of water in the catchment, which are more likely to be impacted by contamination, are mobilised during the wetter periods of the year.

If the conceptualisation of the flow system is correct, MTTs may be calculated using a single LPM. If there were some dilution by recent rainfall, using a single LPM yields the minimum MTT of the baseflow component (Morgenstern et al., 2010). MTTs in the headwaters catchments were estimated using the EPM and the DM. For the EPM, EPM ratios of 0.33 (75 % exponential flow), 1.0 (50 % exponential flow) and 3.0 (25 % exponential flow) were adopted. The EPM model accords with the expected geometry of flow in the catchment (vertical recharge through the unsaturated zone followed by flow along flow paths of varying length), and EPM models with these EPM ratios have reproduced the 3H time series in headwater catchments with similar geometries elsewhere (Maloszewski and Zuber, 1982; Morgenstern and Daughney, 2012; Blavoux et al., 2013; Morgenstern et al., 2010). For the DM, Dp values of 0.05 and 0.5 were adopted, which are appropriate for kilometre-scale flow systems (Zuber and Maloszewski, 2001; Gelhar et al., 1992). Utilisation of a variety of LPMs allows the impact of the assumed model on the MTTs to be assessed.

Calculated MTTs ranged from approximately 7 years at Yahoo Creek in July 2014 to 230 years at Porcupine Creek in March 2015 (Table 3). In general, the lowest MTTs were estimated from the EPM with EPM ratio = 3.0 while the highest MTTs were estimated using the DM with Dp=0.5. Because of the remnant bomb-pulse 3H, a few samples with 3H activities between 1.2 and 1.7 TU yield MTTs that are non-unique for models with high piston flow components (i.e. the EPM with EPM ratio = 3.0 and the DM with Dp=0.05; Table 3, Fig. 7). The choice of the LPM has little impact on MTTs for 3H activities greater than 1 TU (Fig. 7). However, as 3H activities decrease, the relative difference between the MTTs from the different LPMs increases. At the lowest 3H activity of 0.20 TU, the difference between the MTT estimates is approximately 164 years.

MTTs for Lardners Gauge, Upper Lardners, and James Access were similar, and are between 7 and 26 years. In contrast, MTTs for Porcupine Creek ranged from approximately 7 to 230 years, while those for Ten Mile Creek, Yahoo Creek, Love Creek Wonga, and Love Creek Kawarren ranged from approximately 13 to 150, 7 to 15, and 10 to 140 years, respectively. In all catchments, the longest MTTs are recorded at the lowest streamflows (March 2015) while the shortest MTTs occur at the highest streamflows (July 2014 and September 2015) (Fig. 8). At Lardners Gauge, James Access, Porcupine Creek, and Love Creek, the samples collected at the highest flow rates have MTTs that are slightly longer than those of the samples collected at the second highest streamflow (Fig. 8). Whether this reflects changes to the flow system or is due to uncertainties in the MTT estimates is not certain.

The volume of water in the aquifers that contributes to the streamflow may be estimated from Eq. (3). Both the Lardners Gauge and the Love Creek Wonga catchments have active streamflow monitoring, and the calculations are carried out for these catchments. Using the relationships between MTT and streamflow (Fig. 8) and streamflow data for 2014 and 2015 (Department of Environment, Land, Water, and Planning, 2017), the average MTT for the two catchments is estimated to be 29.7 years (Love Creek Wonga) and 10.8 years (Lardners Gauge). For the average annual streamflow over those 2 years, the turnover volumes are 2.6 × 105 m3 (Love Creek Wonga) and 4.5 × 105 m3 (Lardners Gauge). These volumes are small relative to the likely volumes of water stored in the catchments. For the catchment areas (Table 1) and a porosity of 0.1 to 0.3, which is appropriate for most soils and aquifers, this volume of water could be stored in a layer that is 0.01 to 0.1 m thick.

The uncertainties in the MTTs arising from the analytical uncertainties (Supplement) range from ±0.9 years for the sample with the highest 3H activity to ±10 years for the sample with the lowest 3H activity. These equate to relative uncertainties of ∼ ±10 %. Having to assume an LPM reflects a major uncertainty for calculating the MTTs, especially for waters with 3H activities < 1 TU (Fig. 7). For a water with a 3H activity of 2 TU, the uncertainty in MTTs is ±1.2 years (±13 %), while for waters with 3H activities of 1 and 0.5 TU they are ±5 years (±8 %) and ±31 years (±30 %), respectively. The EPM with an EPM ratio of 3.0 and the DM with a Dp value of 0.05 have a large component of piston flow and are possibly less realistic representations of the flow systems; however, the differences between the MTTs estimated using the other LPMs are still considerable.

The influence of uncertainties in the 3H input was assessed by varying the modern and pre-bomb-pulse 3H activities between 2.4 and 3.2 TU and adjusting the 3H activities in the intervening years accordingly. As discussed above, this encompasses the predicted range of average annual 3H activities in most of central and southeastern Australia. These calculations used the EPM with an EPM ratio of 1.0 but the effect is similar in the other models. The relative difference between MTTs is generally highest when 3H activities exceed 1 TU (Fig. 9). For 3H activities of 2 TU, the uncertainty in MTTs is ±5 years (±54 %), while for waters with 3H activities of 1 and 0.5 TU they are ±10 years (±15 %) and ±5 years (±5 %), respectively.

3H activities in rainfall can vary seasonally. Catchments with MTTs in excess of a few years do not preserve seasonal variations in stable isotope ratios or major ion concentrations (Stewart et al., 2010). In a similar way, the seasonal variation in rainfall 3H activities are unlikely to be preserved in the catchment waters (Morgenstern et al., 2010). Thus, using annual 3H activities as the input is appropriate. However, if recharge has a strong seasonality, its 3H activities may be different from those of annual rainfall. Rainfall in the Otway Ranges is distributed throughout the year and it is likely that some recharge occurs throughout the year. Less recharge probably occurs during summer due to some rainfall being lost to evapotranspiration. However, as is the case elsewhere in the Southern Hemisphere (Morgenstern et al., 2010), the 3H activities in summer rainfall are closely similar to the average annual 3H activities (Tadros et al., 2014; International Atomic Energy Agency, 2017). The observation that the 3H activities of summer (December to February) rainfall at Mount Buffalo in northeastern Victoria were similar (2.86 TU) to those of two annual rainfall samples (2.99 and 2.85 TU) support this assertion (Cartwright and Morgenstern, 2015). With such a seasonal distribution of 3H activities, the uncertainties in MTTs resulting from using the average annual 3H activities are less than those that arise from the general uncertainty in the 3H input function.

The impact of macroscopic mixing was estimated using Eq. (2) and the streamflow data and MTTs for Porcupine, Ten Mile, and Yahoo creeks that flow into Love Creek upstream of Love Creek Kawarren (Fig. 1). The analysis used the EPM with an EPM ratio of 1.0 (Table 3), but again similar results were obtained with the other LPMs. Based on the streamflow data, these three streams contribute 77 to 82 % of total stream flow at Love Creek Kawarren (Table 3). The remaining portion of flow in Love Creek is assumed to be contributed by undefined inputs such as groundwater inflow and inputs from smaller tributaries. It was assumed that there was one unidentified input, the 3H activity of which was estimated by the difference between the weighted 3H activities of Porcupine, Ten Mile, and Yahoo creeks and the 3H activity at Love Creek Kawarren. The MTT of this input was determined from the 3H activity using the EPM.

In March 2015, the estimated MTT calculated using the LPM at Love Creek Kawarren was higher than MTTe calculated using Eq. (2) by 3.7 years or 4 % (Table 4). At other times, the differences were 3.9 to 7.4 years (18 to 37 %). These calculations may not truly address aggregation as there may be more than one unidentified additional store of water and there may be aggregation within the individual sub-catchments (which impacts their estimated MTTs). Nevertheless, they do indicate that the potential uncertainties in MTTs due to aggregation are potentially several years (as discussed by Stewart et al., 2017). For waters with similar 3H activities, Cartwright and Morgenstern (2016a) estimated that the aggregation error may be up to 20 % where two waters with MTTs of 10 and 50 years or 1 and 5 years mixed but noted that this error became progressively lower if more stores of water with a similar range of MTTs mixed.

If the uncertainties are uncorrelated, the overall uncertainty is given by the square root of the sum of the squares of the individual uncertainties. The analysis assumes that uncertainties due to analytical uncertainties and aggregation are uniformly 10 and 20 %, respectively, and the uncertainties from the range of LPMs and the 3H input of rainfall are as discussed above. For a water with a 3H activity of 2 TU, the overall uncertainty in MTTs are approximately ±60 % (±5.4 years), whereas for waters with 3H activities of 1 and 0.5 TU they are ±28 % (±17 years) and ±38 % (±35 years), respectively.

While these uncertainties are considerable, the observation that the 3H activities of the streams are locally 10 % of those of modern rainfall (and far less than the rainfall 3H activities at the peak of the bomb pulse) necessitates that the MTTs must be several decades. Because the aggregation error, which is probably the most difficult to assess, results in MTTs being underestimated (Kirchner et al., 2016; Stewart et al., 2017) some MTTs may be longer than calculated. Relative differences in MTTs between and within catchments may be estimated with more certainty. Because the catchments are located in a relatively small area, the 3H inputs are likely to be closely similar. Thus, uncertainties in the 3H input are thus less likely to impact the comparison of MTTs between catchments. Additionally, as the geometry of the flow system in each catchment is unlikely to vary substantially at different streamflows, not being able to assess the suitability of the LPM has less impact on the relative differences in MTTs at different streamflows in the same catchment.

There are weak (R2≤0.7) or no correlations between 3H activities and catchment area, drainage density, or forest cover (Table 2). There is a strong correlation between 3H activities and average slope (R2=0.87, p value 0.01) during March 2015, when streamflow was lowest but not at other times. The variability of MTTs from James Access, Lardners Gauge, and Upper Lardners (which occur on the Otway Group: Fig. 1) and from Porcupine Creek, Yahoo Creek, Love Creek, and Ten Mile Creek (which have similar lithologies in their catchments: Fig. 1) indicates the MTTs are not simply related to the geology. A combination of the catchment properties together with the hydraulic properties of the soils and aquifers or evapotranspiration rates likely control the MTTs. The hydraulic properties and evapotranspiration rates are probably spatially variable and are difficult to estimate, which makes it difficult to assess their influence. The observation that relationships between 3H activities and streamflow in all the catchments are similar (Fig. 4) suggests that the MTTs at high flows reflect the inflow of water from the shallower water stores which will be largely independent of the catchment attributes.

There are strong positive correlations between 3H activities and the runoff coefficient (R2=0.94, p value = 0.27) (Fig. 10). This may be due to both the runoff coefficient and MTTs being controlled by the rates of recharge and groundwater flow. The Lardners Gauge and James Access sites have much higher runoff coefficients than the other catchments, and the correlation with 3H activities may reflect the difference between the two groups of catchments. If this is the case, the runoff coefficient may be useful in determining gross rather than subtle differences in MTTs.

EC and streamflow were measured on a monthly basis at the gauging station on Porcupine Creek (site 235241) between January 1990 and January 1994 (Department of Environment, Land, Water and Planning, 2017). A strong correlation between MTTs and EC at this location (MTT = 1.362 e0.0061⋅EC: R2=0.96, p value = 10-8) allows MTTs at this site to be estimated over this 4-year period (Fig. 11). The estimated MTTs range from 3 to 50 years, with the longest MTTs corresponding to low summer flows and the shortest MTTs during high winter flows. Although based upon a limited number of samples, these results demonstrate the high variability of transit times within the catchment and the value of finding proxies for 3H.