Delineating extent and magnitude of river flooding to lakes across a northern delta using water isotope tracers

Hydrological monitoring in complex, dynamic northern floodplain landscapes is challenging, but increasingly important as a consequence of multiple stressors. The Peace‐Athabasca Delta in northern Alberta, Canada, is a Ramsar Wetland of International Importance reliant on episodic river ice‐jam flood events to recharge abundant perched lakes and wetlands. Improved and systematic monitoring of landscape‐scale hydrological connectivity among freshwater ecosystems (rivers, channels, wetlands, and lakes) is needed to guide stewardship decisions in the face of climate change and upstream industrial development. Here, we use water isotope compositions, supplemented by measurements of specific conductivity and field observations, from 68 lakes and 9 river sites in May 2018 to delineate the extent and magnitude of spring ice‐jam induced flooding along the Peace and Athabasca rivers. Lake‐specific estimates of input water isotope composition (δI) were modelled after accounting for influence of evaporative isotopic enrichment. Then, using the distinct isotopic signature of input water sources, we develop a set of binary mixing models and estimate the proportion of input to flooded lakes attributable to river floodwater and precipitation (snow or rain). This approach allowed identification of areas and magnitude of flooding that were not captured by other methods, including direct observations from flyovers, and to demarcate flow pathways in the delta. We demonstrate water isotope tracers as an efficient and effective monitoring tool for delineating spatial extent and magnitude of an important hydrological process and elucidating connectivity in the Peace‐Athabasca Delta, an approach that can be readily adopted at other floodplain landscapes.

America, climate-driven reductions in mid-to high-elevation snowpack and headwater glacier volumes are reducing river flow and altering hydrological processes at downstream connected freshwater ecosystems (Barnett et al., 2008;Sauchyn, St-Jacques, & Luckman, 2015;Schindler & Donahue, 2006). Small shifts in hydrological conditions can result in cascading ecological changes in small, shallow, freshwater lakes and wetlands (Prowse et al., 2006;Schindler & Donahue, 2006;Schindler & Smol, 2006;Smol et al., 2005). These changes are generally poorly understood at the landscape scale, because data provided by research projects and monitoring programs are typically of insufficient spatial and temporal scales to adequately capture episodes of hydrological connectivity (Fausch, Torgersen, Baxter, & Li, 2002). To address this, comprehensive and systematic hydrological monitoring of complex, northern freshwater landscapes requires innovative approaches to ensure they are effective and sustainable.
Challenges to landscape-scale monitoring of key hydrological events have long prevailed in the Peace-Athabasca Delta (PAD), a complex floodplain landscape in northern Alberta, Canada. Spanning 6,000 km 2 , the PAD is one of the world's largest inland boreal freshwater deltas and receives input from two major rivers, the Peace River and the Athabasca River, as well as the smaller Birch River (Timoney, 2013).
The hundreds of shallow lakes and wetlands that characterize the PAD provide important habitat for a variety of biota and natural resources for indigenous communities. In recognition of its ecological, historical, and cultural significance, the PAD is a Ramsar Wetland of International Importance and contributed to the listing of Wood Buffalo National Park (WBNP) as a United Nations Educational, Scientific and Cultural Organization (UNESCO) World Heritage Site. Lakes and wetlands of the PAD are influenced to varying degrees by river floodwater, snowmelt, rainfall, and evaporation, resulting in a broad spectrum of spatially varying hydrological regimes (PADPG, 1973;Pietroniro, Prowse, & Peters, 1999;Prowse & Conly, 2002;Wolfe et al., 2007). The PAD is a lowrelief system where small changes in water levels can alter hydrological connectivity and set forth temporal patterns of change in limnology, habitat availability, biodiversity and ecosystem productivity (Monk, Peters, & Baird, 2012;Wiklund, Hall, & Wolfe, 2012).
Freshwater availability has declined over large portions of the PAD, stimulating research that has long focused on deciphering effects of upstream industrial development, including the WAC Bennett Dam on the Peace River, and climate change on the frequency of ice-jam flood events because of the importance of this hydrological process as a recharge mechanism for lakes and wetlands in the delta (Beltaos, 2014;Hall, Wolfe, & Wiklund, 2019;Wolfe, Hall, Edwards, & Johnston, 2012). Recently, Remmer, Klemt, Wolfe, and Hall (2018) used an array of datasets, including measurements of water isotope composition and water chemistry collected one year after a major ice-jam flood event in 2014, as well as paleohydrological records, to assess the effects of flooding on lake conditions in the PAD. They found that the 2014 flood event had short-lived, mostly within-year effects on water balance of the flooded lakes, which they attributed to a diminishing influence of river floodwaters as a consequence of cumulative and unrelenting effects of climate change. Given the importance of spring ice-jam floods and their declining influence during recent decades, tracking the occurrence and characterizing the effects of flood events that do occur is crucial to monitoring efforts and design of potential mitigation strategies.
The extent of prior flood events in the PAD has typically been estimated from aerial surveys (Straka & Gray, 2014) and, on occasion, satellite imagery (e.g., Pavelsky & Smith, 2008;Töyrä & Pietroniro, 2005). But, because of the dynamic and somewhat unpredictable nature of ice-jam flood events, delineation of flood extent from aerial observations is highly dependent on the timing and location of flight paths and absence of obstructions that impair detection of river floodwaters into lakes and vegetated terrain (e.g., cloud cover). Neither of these approaches can readily be used to distinguish magnitude of flooding across a landscape nor distinguish different sources of water that may have entered lakes such as river floodwaters versus snowmelt or rainfall. There remains a clear need for a systematic, measurable, and in situ approach to track spatial extent, as well as magnitude, of river flood events on lakes of the PAD and their effect on lake water balances.
Landscape-scale monitoring and assessment of lake hydrological conditions using water isotope tracers has proven to be an effective approach in many remote, northern, water-rich locations (e.g., Brock, Wolfe, & Edwards, 2007;Gibson & Edwards, 2002b;MacDonald et al., 2017). In northern floodplains, this approach is particularly wellsuited to partition the relative roles of important hydrological processes on lake water balances because of the strong sensitivity of lake water isotope compositions to influence of isotopically depleted river water versus isotopic enrichment caused by evaporation. For example, water isotope data have been used to estimate the spatial extent of flood events in the PAD  as well as the Slave River Delta located farther downstream within the Mackenzie River Basin . In these studies, spring river floodwater dilution to lakes deemed to have flooded was estimated from the difference between the spring and previous fall measurements of water isotope composition. The modelling approach assumed that the spring isotopic depletion was entirely due to the influence of river floodwaters even though there were also likely contributions from snowmelt and/or rainfall. Nonetheless, the flood extent maps utilizing water isotope tracers aligned well with other evidence and demonstrated the usefulness of collection of lake water samples across these landscapes to obtain this information.
Here, our objective is to delineate the extent and magnitude of a spring ice-jam flood event in the PAD that occurred in late April and early May 2018 using water isotope tracers, supplemented by measurements of specific conductivity and field observations. Improving upon previous approaches utilized in the PAD  and Slave River Delta , which did not account for influence of precipitation, we set the water isotope data against an isotope framework established from 16 years of meteorological conditions and online resources, and then develop a set of landscape-specific binary mixing models that allow estimation of the proportion of input to flooded lakes attributable to river floodwater and precipitation (snow or rain). These results demonstrate the value of systematic water sampling and isotope analysis for monitoring and assessment of lake hydrological conditions in dynamic floodplain landscapes such as the PAD.

| Study area
The PAD is episodically fed in the north by the Peace River and more frequently in the south by the Athabasca River ( Figure 1). This results in distinct sectors with lakes possessing wide-ranging water balances largely depending on the relative influence of river water. The northern Peace sector (to the north of PAD 37 [Jemis Lake]) is a relic delta that receives floodwater only during infrequent high-elevation spring ice-jam flood events. Consequently, lakes are typically isolated or perched (i.e., closed-drainage) and strongly influenced by evaporation (PADPG, 1973;Pietroniro et al., 1999;Wolfe et al., 2007). Lakes in the southern Athabasca sector (PAD 37 and areas to the south) span a broad gradient of hydrological conditions from those that frequently receive river water in the active delta regions (i.e., restricted-drainage) during both the spring ice-jam and open-water seasons to those that are more substantially influenced by evaporation (i.e., closed-drainage). Broad shallow lakes in the central, low-lying portion of the delta receive continuous river inflow (i.e., open-drainage). Groundwater is considered to be a negligible component of lake water balances in the PAD due to discontinuous permafrost, low hydraulic conductivity of flood-deposited fine-grained sediment (clay and fine silt) that line basins, and low horizontal gradients between lakes (Nielsen, 1972;Prowse, Peters, & Marsh, 1996;Wolfe et al., 2007).  (Jasek, 2019). Prior to and during this period, ice cover on the Peace River thermally degraded along the reach adjacent to the PAD and was too weak to generate dynamic breakup and substantial overland flooding in the northern Peace sector. However, backwaters from the downstream ice-jam on the Slave River, combined with arrival of a "jave" (ice-jam-release waves; Beltaos, 2008)

| Data collection
During May 15-17, 2018, a set of 68 lakes and 9 river sites spanning the range of hydrological conditions across the PAD were sampled with the aid of a helicopter ( Figure 1). Water samples and in-situ measurements were collected from a depth of~10 cm in a mid-lake location (or mid-channel for the river sites). Samples for oxygen and hydrogen isotope analysis were stored in sealed 30 ml high-density polyethylene bottles, and in-situ measurements of specific conductivity were obtained using a YSI ProDSS sonde. Due to the shallow depth of lakes in the PAD, the lake volumes are generally well-mixed at the time of sampling. Thus, the sampling approach provides measurements representative of the total lake storage. Water isotope compositions of the lake and river samples were measured by Off-Axis Integrated Cavity Precipitation (Coplen, 1996). Analytical uncertainties are ±0.09‰ for δ 18 O and ±0.4‰ for δ 2 H. Field observations (described below) were recorded at the time of sampling for each lake.

| Data analysis
To determine the flood status for each sampled lake, water isotope compositions were compared with river water isotope compositions, considering simultaneously values of specific conductivity and field observations. Lakes were designated as flooded if (a) water isotope values were close to or overlapping with the isotopically depleted river water isotope compositions, (b) specific conductivity values were close to the range of the river water values (Peace sector: 164.5 to 176.5 μS/cm; Athabasca sector: 179.5 to 188.5 μS/cm), and (c) there was visible evidence of flooding, such as water colour and turbidity (assessed in situ) similar to the closest river or channel, and flooded lake margins and debris (i.e., logs) that appeared to have been carried in by the recent floodwaters. In the few instances where flood status was less obvious, hydrological conditions of nearby lakes were considered in combination with field observations. These cases are detailed in Section 3.
A previously developed isotope framework representing average conditions during 2000-2015 (Remmer et al., 2018) and a coupledisotope tracer approach (Yi, Brock, Falcone, Wolfe, & Edwards, 2008) were used to calculate the isotope composition of input water (δ I ) for each flooded lake (Figure 2; Appendix). As prescribed by the coupledisotope tracer approach (Yi et al., 2008), all lake water isotope compositions experiencing the same atmospheric conditions will fall on lakespecific evaporation lines terminating at δ* (i.e., the limiting nonsteady-state isotope composition of a lake approaching desiccation), and their intersection with the Local Meteoric Water Line (LMWL) provides an estimate of δ I for each lake. In this way, we were able to estimate the isotope composition of the input water entering lakes from our measurement of the isotope composition of lake water. For flooded lakes, we assume that δ I consists primarily of floodwater supplied during the flood event and, to a lesser degree, precipitation received during the same period. We recognize that the δ I values may also reflect some signal of input water during prior years, although this is likely to be minimal because of the tendency for large volumes of river water to enter the very shallow lakes of the PAD (typically <1-m maximum depth) when they flood.
A set of four Meteoric Water Line Segments (MWLS) were developed capturing the range of lake input water isotope compositions that result from mixing of either rain or snow with floodwater from the Peace or Athabasca river. Rainfall and snowmelt input includes both precipitation falling directly on the lake surface and runoff from the lake catchment that entered the lake during the period captured by our water isotope samples. Estimates of average ice-free season for Peace sector lakes containing a mixture of floodwater and snowmelt, for Athabasca sector lakes containing a mixture of floodwater and rainfall, and, for Athabasca sector lakes containing a mixture of floodwater and snowmelt, Values generated by Equations 1-4 represent estimates of the proportion of input water attributable to river floodwaters and do not necessarily represent the total amount of river floodwater in the lake at the time of sampling because nearly all lakes contained pre-existing water. The one exception is PAD 20, which had desiccated prior to the flood event.
Because the rain and snow end-member isotope compositions are not based on local measurements, but rather derived from a global model, and the values can certainly vary, we consider these endmember values to be the largest uncertainty in our modelling approach. Thus, a sensitivity analysis that incorporated uncertainty in the precipitation end-member isotope compositions was performed to evaluate their influence on flood magnitude estimates. We adjusted rain and snow end-member δ 18 O values by ±1.08‰ and ±1.88‰, respectively, based on 1 standard deviation (SD) of the monthly values. The "OIPC minus" scenario represents application of SD values subtracted from the rain and snow end-member isotope compositions, whereas the "OPIC plus" scenario represents application of SD values added to the rain and snow end-member isotope compositions. The sensitivity analysis was performed using δ 18 O values, because a binary mixing model would produce the same result using δ 2 H values. To visualize flood magnitude and explore spatial patterns, the proportion of input water attributed to river floodwater was interpolated between lakes across the surface of the delta. Spatial autocorrelation F I G U R E 2 Schematic δ 18 O-δ 2 H diagram illustrating water isotope compositions of two hypothetical lakes, one that has received input water consisting mainly of river floodwater and rain (δ L−1 ) and one that has received input water consisting mainly of river floodwater and snowmelt (δ L−2 ). Each lake plots along a lake-specific evaporation line. The intersection of lake-specific evaporation lines with Meteoric Water Line Segments (snow-to-river [blue] or river-to-rain [red]) provides an estimate of input water isotope composition (δ I ). Important features of the LEL include the steady-state isotope composition for a terminal basin (δ SSL ), which represents the special case of a lake at hydrological and isotopic steady state in which evaporation exactly equals inflow, and the limiting non-steady-state isotope composition (δ*), which indicates the maximum potential isotopic enrichment of a lake as it approaches complete desiccation. The LEL is anchored at the mean annual isotope composition of precipitation (δ P ). Parameters used in the isotope mass-balance model to derive δ I include the lake water isotope composition (δ L ) and the isotope composition of evaporated vapor from the lake (δ E ). See Appendix for further details was assessed using Moran's I (Anselin, 1995). Interpolation was generated using a multiquadratic radial basis function, a deterministic interpolation technique suitable for environmental monitoring (Rusu & Rusu, 2006), with the function and optimal parameters determined through cross-validation. Analyses were performed using ArcMap 10.6 software.

| Flood status of lakes
Several lake-water isotope compositions cluster around the river isotope compositions when plotted in δ 18 O-δ 2 H space, which we interpret to reflect substantial influence of river floodwaters (Figure 3a). In contrast, many lake water isotope compositions also plot along the LEL between δ P (isotope composition of weighted mean annual precipitation) and δ SSL (isotope composition of a terminal lake at hydrological and isotopic steady state) indicating evaporative enrichment, which may have occurred during the spring and previous ice-free seasons in the absence of flooding (Figure 3b). The isotope compositions of non-flooded Peace and Athabasca sector lakes overlap, suggesting the influence of evaporative isotopic enrichment in the absence of flooding was comparable across the delta (Figure 3b).
There are a few exceptions (8 of 68 lakes) to our strictly isotopebased interpretation of flood status (described further below). These include some lakes that are positioned along the LEL (PAD 27, 14, 58, and 50; Figure 3a), but other data and observations indicate that they received some river floodwaters in 2018. Other exceptions include lakes that are positioned close to the MWLS (PAD 9, M2, M10, and M5; Figure 3b), but measurements of conductivity and field observations led to interpretation that they did not receive river floodwaters in 2018.
Four of the lakes that were offset from the MWLS were considered flooded based on measurements of specific conductivity and visual observations ( Figure 3a, Table 1). Three lakes are in the Peace sector (PAD 14, 50, 58) and one lake is in the Athabasca sector (PAD 27). PAD 50 was highly turbid and field observations noted the water colour matched the nearby Claire River, which was observed to be receiving water from the Peace River. We suspect this lake, which had    Table 1). Lakes M2 and M5 had very low turbidity and specific conductivity was lower than expected if river water had entered the basins. We suspect these lakes may be influenced by isotopically depleted snowmelt draining through elevated sand dunes located in their catchments. Lake water at PAD 9 was very shallow and clear, which we attribute to a strong influence of isotopically depleted snowmelt. At M10, turbidity of the water was observed to be low, water levels appeared normal, and lake water colour was comparable to nearby lakes (M8 and M9) that we confidently ascertained did not receive river floodwater.
In total, 44% (30/68) of sampled lakes received river floodwaters based on consideration of the water isotope compositions, specific conductivity, and field observations ( Table 1). Nine of 32 (28%) sampled lakes in the Peace sector were classified as flooded, and 21 of 36 (58%) lakes in the Athabasca sector were classified as flooded.

| Calculation of proportion of input to lakes attributable to river floodwater
Based on calculation of δ I values, the input water to each flooded lake was determined to consist mainly of a mixture of either Peace (north   (Table 2). Based on Equations 3 and 4, respectively, the proportion of input water attributable to river floodwater in Athabasca sector lakes dominated by precipitation in the form of rain ranged from 93% to 98% with an average of 95.5%, and the proportion of input water attributable to river floodwater in lakes dominated by precipitation in the form of snow ranged from 82% to 94% with an average of 86.3% ( Table 2). The average proportion of input water attributable to river floodwater in the flooded lakes was 87.2% (n = 30), with comparable ranges and averages in the Peace (69-98%, avg = 86.9%, n = 9) and Athabasca sector (82-98%, avg = 87.2%, n = 21; Table 2).

| Delineation of flood extent and magnitude
Calculations of the proportion of input to lakes attributable to river floodwater were interpolated across the surface of the PAD using a radial basis function to visualize flood extent and magnitude T A B L E 2 Isotope composition of input water, percent river input, percent precipitation input, precipitation type and source of floodwaters for 30 lakes in the Peace-Athabasca Delta that flooded in spring of 2018 average absolute difference for the OIPC plus scenario = 2.4% (minimum = −4.6, maximum = 2.9%), Figure 5c).

| DISCUSSION
The lateral interaction of rivers and their floodplains is often an important determinant of patterns of biodiversity and species richness (Gregory, Swanson, McKee, & Cummins, 1991;Johnson & Host, 2010;Junk, Bayley, & Sparks, 1989;Ward, 1998;Welcomme, 1979), and monitoring of hydrological connectivity should be considered a vital component of efforts to conserve the ecological integrity of floodplain landscapes. However, measurement of hydrological connectivity can be difficult to obtain in water-rich landscapes, especially during short-lived, episodic flood events (Lindenmayer et al., 2008).
Ice-jam floods provide a period of increased hydrological connectivity among rivers, channels, lakes and wetlands of the PAD, and decline in their frequency has remained a prominent concern for decades in recognition that these flood events are critical to maintaining ecological integrity. Thus, it is imperative to track flood events and their influence on hydrological connectivity when they occur, even if some of their effects are short-lived (see Remmer et al., 2018). Historically, this has been done mainly by observation from aircraft, and methods have recently been developed to map flood extent from satellite imagery (Pavelsky & Smith, 2008;Töyrä & Pietroniro, 2005). However, neither of these approaches readily allow quantification of flood magnitude, and the mapped flood extents can be strongly influenced by the timing of observations.
Recently, an international organization has identified the need to illon Coupé and Rivière des Rochers (Jasek, 2019). Results from our study identify that these high river levels led to flooding of several lakes adjacent to these channels (e.g., 96% river floodwater input at PAD 54; Figure 4, 5, 6, Table 2), which has long been observed to occur during high water events on the Peace River (e.g., PADPG, 1973;Wolfe et al., 2006). Interpolation indicates that input to lakes in these areas was dominated by river water, and that the proportion of input water attributed to river floodwater decreased with increasing distance from the channels, consistent with independent observations made during aerial surveys indicating there was minimal overland Our sensitivity analysis has demonstrated that incorporating reasonable uncertainty of both the snow and rain end-member isotope compositions does little to change the outcome at the scale presented in Figure 5, which is most appropriate for ecosystem management purposes. Indeed, the most important delineation in our approach is simply whether the lake flooded or not, which water isotope tracers, supplemented by measurements of specific conductivity and field observations, effectively identify. Nonetheless, surveys of rain and snow isotope compositions could better constrain these end-members and be used to assess for spatial heterogeneity, thereby enhancing the accuracy of the model and estimates of flood magnitude.
We acknowledge other uncertainties in this modelling approach. none of the lakes identified as flooded by our approach were estimated to have less than 60% of their input attributed to river floodwaters, even those at the outer margin of the flooded area. There are at least two possible explanations for this outcome. One is that our methods are not sufficiently sensitive to detect flooding when this value is less than 60% due to insufficient change in water isotope values, specific conductivity, and other sources of information. The second is that flooding to these shallow, small volume lakes rarely ever results in less than 60% of the input attributable to river floodwater because once rivers overbank, they supply so much water to the flat terrain that more than half of the lake input is due to this hydrological process. Clearly, this suggests a need for further refinement and testing of our methods and more data acquisition to distinguish these possibilities. Also, interpolation of the calculated proportion of input water attributable to river floodwater is limited in some areas of the delta (e.g., Claire River and the northeastern area of the Athabasca sector) by a low density of sampled lakes. Although more lake sampling sites could be added, the set of 68 sampled lakes provides considerable coverage for tracking the main patterns of flooding and hydrological connectivity across the landscape. Despite these uncertainties, the flood map generated by our approach represents a marked improvement over other approaches because it is less prone to logistical limitations (i.e., sampling can occur after a flood occurs, not at the exact moment of flooding) and can quantify spatial variation in the magnitude of flood influence on lakes.

| CONCLUSIONS AND RECOMMENDATIONS
River water entered lakes in the PAD during an ice-jam flood event in late April to early May 2018. Here we used water isotope tracers, supplemented by measurements of specific conductivity, and field observations, to delineate the extent and magnitude of flooding. We present an isotope-based approach, incorporating a landscape-specific set of binary mixing models that allow estimation of the proportion of input water to lakes attributable to river floodwater and rainfall or snowmelt. Nearly half of the 68 lakes we have sampled since 2015 as part of developing the foundation of a monitoring program received river floodwaters in spring 2018, and the estimated proportion of lake input provided by river floodwater to the flooded lakes averaged 87.2%. We found that flooding in the northern Peace sector was primarily limited to lakes along the Chenal des Quatre Fourches and the northern reaches of the Revillon Coupé. Flooding in the Athabasca sector was much more extensive, but did not reach the eastern terminus of the Athabasca Delta as floodwater was conveyed northwards through the Embarras River and into Mamawi Creek, a continuing legacy of the Embarras Break through that occurred in 1982 (Kay et al., 2019;Timoney, 2013;Wolfe et al., 2008).
Monitoring data are an essential component of science-based policy, and long-term records are the most likely to contribute to policy (Hughes, Beas, Barner, & Brewitt, 2017). However, obtaining resources to support continuous long-term monitoring remains a challenge (Lovett et al., 2007). Cost-effective measurements of important variables can increase the likelihood of the long-term sustainability of a monitoring program, allowing them to survive during times of lean budgets and, thus, increase the probability that the data will contribute to policy and decision making. This is particularly true in remote northern landscapes, which present additional logistical and financial challenges (Mallory et al., 2018). For example, conventional water gauges are expensive to install and maintain at a landscape scale and are frequently damaged or lost during the flood event they aim to capture (e.g., Jasek, 2019

CONFLICTS OF INTEREST
We declare no conflicts of interest.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.

A P P E N D I X A : Meteorological calculations
Relative humidity (h) and temperature (T) were calculated as the average (monthly) evaporation-flux-weighted values during the period of 2000-2015 using climate data from Environment Canada and the National Research Council of Canada. The average ice-free season h and T were flux-weighted based on potential evapotranspiration determined by Thornthwaite (1948): where T a is the monthly average temperature and E t is the monthly total evaporation. E t was calculated using the equation: where L is the average day length in hours in a month, N is the number of days in the month, I is the annual heat index, and a is a calculated coefficient. I was calculated as the total of each ice-free month using the equation: and I i was calculated using the equation: and a was calculated using the equation: a = 0:49 + 0:0179 Á I −7:71 Á 10 −5 Á I 2 + 6:75 Á 10 − 7 Á I 3 ðA6Þ

A P P E ND I X B: Isotope framework
Isotope framework parameters were calculated (in decimal notation) using approaches described in Gonfiantini (1986), Gibson and Edwards (2002b), Edwards, Wolfe, Gibson, and Hammarlund (2004), and Yi et al. (2008), which are based on the linear resistance model of Craig and Gordon (1965).
The LEL for the PAD region was determined using a 16-year average of environmental conditions described above, as well as preexisting isotopic data and calculated evaporation-flux-weighted terms.
The LEL was determined as a regression of the isotope composition of precipitation (δ P ), the isotope composition of a terminal basin at steady state (δ SSL ) and the theoretical limiting non-steady-state composition of a water body approaching complete desiccation (δ*). δ P was obtained from the Online Isotopes in Precipitation Calculator (Bowen, 2016;Bowen & Revenaugh, 2003;IAEA/WMO, 2015). δ SSL was determined from the average isotope composition of PAD 18, a terminal basin at isotopic and hydrologic steady state located in an elevated portion of the PAD (Yi et al., 2008). δ* was calculated from Gonfiantini (1986): where h is the relative humidity (see E.1), δ AS is the isotope composition of atmospheric moisture for the ice-free season (Gibson, Edwards, & Prowse, 1999), ε k is the kinetic separation factor between liquid and vapour phases, ε* is the equilibrium separation factor between liquid and vapour phases, and α* is the equilibrium liquidvapour isotope fractionation factors (Horita & Wesolowski, 1994). α* for δ 18 O where T represents the interface temperature in degrees Kelvin. The equilibrium separation factor between liquid and vapour phases is expressed as: and the kinetic separation factor between liquid and vapour phases is expressed as for δ 2 H and ε k = 0:0142 1− h ð Þ ðA12Þ for δ 18 O, where h is the relative humidity (Gonfiantini, 1986). Isotope composition of atmospheric moisture for the ice-free season (δ AS ) was calculated using the equation from Gibson et al. (1999): Results of the isotope framework calculations are reported in Table A1.
A P P E ND I X C: Calculation of isotope composition of lake input water δ I was estimated as the intersection of a regression through δ E and δ* and the Meteoric Water Line Segment, utilizing the coupled isotope tracer approach (Yi et al., 2008). δ E was calculated using the Craig and Gordon (1965) equation: Temperature and relative humidity values for the calculation of δ E were the same as those used in the framework calculation (fluxweighted average; see Table A1).