Received: 1 December 2017 Accepted: 29 November 2018

DOI: 10.1002/hyp.13363

S P E C I A L I S S U E : WA T E R I N TH E C R I T I C A L ZON E

Hydrologic functioning of the deep critical zone andcontributions to streamflow in a high‐elevation catchment:Testing of multiple conceptual models

Ravindra Dwivedi1 | Thomas Meixner1 | Jennifer C. McIntosh1 | P.A. Ty Ferré1 |

Christopher J. Eastoe2 | Guo‐Yue Niu1 | Rebecca L. Minor3 | Greg A. Barron‐Gafford3 |

Jon Chorover4

1Department of Hydrology and Atmospheric

Sciences, University of Arizona, Tucson,

Arizona

2Department of Geosciences, University of

Arizona, Tucson, Arizona

3School of Geography and Development and

with Biosphere 2, University of Arizona,

Tucson, Arizona

4Department of Soil, Water and

Environmental Science, University of Arizona,

Tucson, Arizona

Correspondence

Ravindra Dwivedi, Department of Hydrology

and Atmospheric Sciences, University of

Arizona, Tucson, AZ 85721.

Email: ravindradwivedi@email.arizona.edu

Funding information

Geological Society of America; Graduate and

Professional Student Council; Water

Resources Research Center; Division of Earth

Sciences, Grant/Award Number: EAR‐1331408

476 © 2018 John Wiley & Sons, Ltd.

Abstract

High‐elevation mountain catchments are often subject to large climatic and topo-

graphic gradients. Therefore, high‐density hydrogeochemical observations are needed

to understand water sources to streamflow and the temporal and spatial behaviour of

flow paths. These sources and flow paths vary seasonally, which dictates short‐term

storage and the flux of water in the critical zone (CZ) and affect long‐term CZ evolu-

tion. This study utilizes multiyear observations of chemical compositions and water

residence times from the Santa Catalina Mountains Critical Zone Observatory,

Tucson, Arizona to develop and evaluate competing conceptual models of seasonal

streamflow generation. These models were tested using endmember mixing analysis,

baseflow recession analysis, and tritium model “ages” of various catchment water

sources. A conceptual model involving four endmembers (precipitation, soil water,

shallow, and deep groundwater) provided the best match to observations. On aver-

age, precipitation contributes 39–69% (55 ± 16%), soil water contributes 25–56%

(41 ± 16%), shallow groundwater contributes 1–5% (3 ± 2%), and deep groundwater

contributes ~0–3% (1 ± 1%) towards annual streamflow. The mixing space comprised

two principal planes formed by (a) precipitation‐soil water‐deep groundwater (dry and

summer monsoon season samples) and (b) precipitation‐soil water‐shallow groundwa-

ter (winter season samples). Groundwater contribution was most important during the

wet winter season. During periods of high dynamic groundwater storage and

increased hydrologic connectivity (i.e., spring snowmelt), stream water was more geo-

chemically heterogeneous, that is, geochemical heterogeneity of stream water is

storage‐dependent. Endmember mixing analysis and 3H model age results indicate

that only 1.4 ± 0.3% of the long‐term annual precipitation becomes deep CZ ground-

water flux that influences long‐term deep CZ development through both

intercatchment and intracatchment deep groundwater flows.

KEYWORDS

conceptual models, critical zone, dynamic storage, endmember mixing analysis, tritium model ages

Hydrological Processes. 2019;33:476–494.wileyonlinelibrary.com/journal/hyp

DWIVEDI ET AL. 477

1 | INTRODUCTION

In high‐elevation montane environments, the structure of the critical

zone (CZ), that is, the zone spanning from the top of the tree canopy

to the bottom of active groundwater circulation (National Research

Council, 2001), exerts strong control over surface water hydrologic

response (Ameli et al., 2017; Chorover, Derry, & McDowell, 2017; H.

Kim, Dietrich, Thurnhoffer, Bishop, & Fung, 2017; McIntosh et al.,

2017; Trostle et al., 2016). The geochemical composition of stream

water is the result of contributions from water stores that are spatially

distributed across the CZ. These stores include near surface and deep

groundwater stores, such as soils and fractured bedrock aquifers,

respectively (Ajami, Troch, Maddock, Meixner, & Eastoe, 2011). Addi-

tionally, changes in the chemistry of groundwater as it traverses the

CZ provide insights into geochemical processes regulating long‐term

CZ evolution (McIntosh et al., 2017). Understanding stream water

composition, including variation in concentration‐discharge relations

across multiple elements (Ameli et al., 2017; Chorover et al., 2017;

Godsey, Kirchner, & Clow, 2009; H. Kim et al., 2017; Liu, Conklin, &

Shaw, 2017; McIntosh et al., 2017; Trostle et al., 2016), requires the

proper identification of not only geochemically distinct water stores

for a given CZ structure but also time‐dependent variation in their rel-

ative contributions to streamflow. Most important, this approach

enables moving from a “black box” level of understanding, that is, con-

sidering the whole CZ structure as a simple well‐mixed bucket, to a

“grey box”‐level understanding that acknowledges distinct CZ stores,

their time‐variant inputs to surface water, and the residence times of

groundwater in different stores.

While identifying distinct CZ stores and their streamflow contri-

butions is important, such an understanding is incomplete without

identifying how the stores are connected and how such connections

evolve over time (Covino, 2016; Kirchner, 2006; McDonnell, 2017).

We propose that testing competing alternative hypotheses (Chamber-

lin, 1965; Ferre, 2017) of conceptual model elements and how their

spatial connections evolve temporally will provide an improved under-

standing of montane CZ functioning. An improved understanding of

CZ scale hydrological processes will help to advance CZ science to a

point where predictions can be made about long‐term CZ functioning,

including the effects of climate or land use change.

Previous studies have shown a relationship between deep subsur-

face flow paths and dynamic CZ storage, that is, the storage that

changes seasonally (Kirchner, 2009; Sayama,McDonnell, Dhakal, & Sul-

livan, 2011). Larger dynamic storage led to widespread hydrological

connectivity and movement of deep groundwater (Ajami et al., 2011;

Heidbüchel, Troch, & Lyon, 2013; McIntosh et al., 2017). We hypothe-

size that high‐storage conditions can likewise lead to heterogeneity of

stream water composition, such that stream chemistry deviates from

patterns predicted from conservative mixing of known subsurface

water stores. For example, Barthold et al. (2011) noted that the number

of endmembers required to explain streamwater composition increased

with the tracer set size, which the authors suggested was related to

either the larger spatial extent or larger temporal extent of their sam-

pling period. However, it remains unclear precisely how variation in

dynamic storage affects stream chemistry or the size of the tracer set

required to explain its temporal evolution with endmember mixing

analysis (EMMA). Therefore, an exploration of the relationships

between CZ dynamic storage and stream water composition is needed.

The importance of deep CZ fluxes on storage and hydrologic pro-

cesses in high‐elevation montane systems is unresolved. Deep CZ

water can strongly affect surface water composition, particularly

where residence times are long. The percolation of meteoric water—

groundwater fluxes below the root zone (Guan, 2005)—into fractured

bedrock is central to the “aggressive” role of water in CZ evolution; it

drives the long‐term creation of subsurface porosity for reservoir stor-

age by carrying oxidants (e.g., dissolved O2) and acids (e.g., dissolved

CO2) that promote primary mineral dissolution. For a montane CZ, this

deep CZ groundwater flux can be referred to as the mountain ground-

water discharge (MGD) to headwater streams. As interpreted in this

work, MGD for a headwater catchment is the fractured bedrock

groundwater that is discharging and sustaining streamflow under dry

conditions. In a modelling study of 3D nested mountainous catch-

ments, Gleeson and Manning (2008) suggested MGD flux depends

not only on the topographic ruggedness and relief but also on water

table configuration, bedrock properties, mountain drainage network,

percentage perennial length of the headwater streams, groundwater

circulation depth, and the topographic character (e.g., topographic

relief) of the catchment adjacent to the catchment under study (due

to intercatchment deep groundwater flow). Welch, Allen, and van

Meerveld (2012) report similar model findings in terms of the effects

of topography, groundwater circulation depths, and intercatchment

deep groundwater flow on MGD fluxes, but they also note the influ-

ence of change in recharge magnitude, which were significant up to

the first 3 years of upgradient recharge perturbations. Therefore,

research approaches that improve our current understanding of deep

bedrock flow processes and their contribution to seasonal streamflow

generation are required.

This study combines hydrochemical modelling (i.e., principal com-

ponents analysis [PCA] and EMMA), new water transit time results (3H

model ages), and baseflow recession analysis to address the following

questions:

1. What are the different water stores in the CZ that contribute to

streamflow, how do these contributions vary seasonally, and

what are the controlling hydrological processes?

2. How does dynamic CZ water storage influence geochemical het-

erogeneity of stream water?

3. What are the annual water fluxes through the deep CZ that con-

tribute to the long‐term evolution of deep CZ porosity and sus-

tain streamflow under dry conditions?

These questions were addressed by testing multiple conceptual model

frameworks through analysis of long‐term hydrogeochemical and tran-

sit time observations.

2 | STUDY SITE AND METHODS

2.1 | Study site and data used

The study focuses on the Marshall Gulch catchment (MGC), a high‐

elevation catchment in the Santa Catalina Mountains Critical Zone

478 DWIVEDI ET AL.

Observatory (SCM‐CZO), near Tucson, Arizona in the southwestern

United States (Figure 1; Figure S1 in Supporting information or SI).

MGC, which is part of the Sabino Creek watershed, has a total drain-

age area of 1.55 km2 and ranges in elevation from 2,635 to 2268 m

above mean sea level (amsl). The mean topographic slope is 23.64o.

Soil depth within MGC ranges from 0 to 1.5 m (Pelletier & Rasmussen,

2009), and the soils are mostly sandy loam (Holleran, 2013). The two

dominant bedrock types (Figure 1b) are peraluminous granite of the

Eocene Wilderness Granite Suite, mostly in the upper MGC, and

metasedimentary rocks (schist) of the Proterozoic Apache Group and

Troy Quartzite, mostly in the lower MGC (Dickinson et al., 2002).

The vegetation at the site is mostly Madrean upper montane

conifer‐oak forest and Rocky Mountain aspen forest at high elevations

to Madrean pine‐oak woodland at lower elevations (Data source:

NatureServe, 2004). The study site is located in a wilderness area

where deep drilling is prohibited (the existing instrumentation is

shown in Figure 1a and Figure S1). Therefore, no wells other than pie-

zometers less than 1.5 m deep are available for sampling groundwater,

and most of the existing instrumentation is installed in Granite and

Schist subcatchments (Figure 1a).

FIGURE 1 (a) Marshall Gulch catchment (MGC; catchment boundary isZone Observatory (SCM‐CZO), is a headwater catchment for the larger Sainstrumentation are highlighted. (b) geology map of MGC and nearby areaPitts, Stephen, & Bolm, 2002); and (c) the general relationship between MGBasin. Note: (1) the red triangle in (c) shows the discharge measurement siteCreek watershed, (2) MLWD well is the Mount Lemmon Water district weGeological Survey (2018), whereas that shown in (c) is obtained from PRIS

Our analysis is based on observations of solute chemistry in

stream water, precipitation, and soil water between 2011 and early

2017, and periodic observations (in 2016 and 2017) of solute chemis-

try and tritium concentrations in Huntsman and Pigeon springs, Mt.

Lemmon water district (MLWD) well, soil, and stream waters. Further-

more, hydrological observations (precipitation, streamflow and mean

air temperature, the latter as a surrogate for snowmelt behaviour)

from year 2008 to 2016 (i.e., water years 2009–2016) are used. All

stream, spring, well, soil water and precipitation chemistry, precipita-

tion, streamflow, and groundwater depth data are available on the

SCM‐CZO website (http://criticalzone.org/catalina‐jemez/data/

datasets/).

A review of the hydrologic observations from water year 2009 to

2016 show a bimodal pattern for both precipitation and streamflow

(Figure S2 in SI). Climate is subhumid with mean annual precipitation

(MAP) of 920 mm (estimate obtained from 30‐year precipitation nor-

mals [1981–2010] from PRISM climate model [PRISM Climate Group,

2018]); however, MAP was 525 mm, estimated using mean daily pre-

cipitation from water year 2009 to 2016, consistent with prolonged

drought conditions (Arizona State Climate Office, 2018). Of the total

shown in green), located within the Santa Catalina Mountains Criticalbino Creek watershed (boundary shown in red). Existings (geographic information system data source: Dickinson, Hirschberg,C, Sabino Creek watershed, Santa Catalina Mountains, and Tucson(USGS gage # 09484000; situated at ~829 m elevation) for the Sabinoll, and (3) the digital elevation model in (a) is obtained from U.S.M Climate Group (2016)

DWIVEDI ET AL. 479

MAP, 44% falls during October 1 to May 20 (i.e., “winter” season),

~53% falls during July through September months (i.e., “summer mon-

soon” season), and a small percentage ~3% falls during May 21

through June 30 (i.e., “dry” season) of a water year. Average annual

specific stream discharge was 203 mm from water year 2009 to

2016, representing ~38% of the total annual precipitation. There are

two peaks in the streamflow time series: one during late winter and

the other during the summer monsoon. Discharge was ephemeral

(Figure S3A) with ~12% probability of flows less than ~10−6 mm/day

(including no streamflow) as per the period‐of‐record flow duration

curve. Because of ephemeral streamflow, there are no data when con-

ditions at the field site were extremely dry. The hypsometric curve is a

standard S‐shape (Figure S3B in SI). Average annual temperature was

10.40°C, and it ranged from 1.5 to 19.9°C for a water year (Figure S2

in SI).

2.2 | Estimating tritium (3H) model ages

Water samples were collected for 3H in 1 L HDPE bottles and

analysed at the University of Arizona Environmental Isotope Labora-

tory. The estimation of 3H model ages (t3H) depends on the 3H half‐life

(t1/2 = 12.32 years [Lucas & Unterweger, 2000]), initial 3H concentra-

tion (Co), and concentration at the sampling time [C(t)] (Equation 1).

The sample set included three samples each for soil, Huntsman spring

and stream waters and one sample each for the Pigeon spring and

MLWD well for a winter season; one sample each for Huntsman

spring and stream waters for a dry season; and one sample for soil

water and two samples for stream water and three samples for Hunts-

man spring water for a summer monsoon season (Table S1 in SI). For

Co, an initial concentration of (a) 4.1 ± 0.5 TU was used for soil water

samples that were expected to sample shorter flow paths, and (b) 6.3

TU ± 0.8 TU was used for spring and stream waters that were affected

by contributions from deep flow paths (more details are provided in

Section S1 in SI).

t3H ¼ t1=2ln 2ð Þ ln

Co

C tð Þ� �

(1)

2.3 | Endmember mixing analysis

EMMA was used to estimate seasonal streamflow contributions from

distinct CZ water stores and annual water fluxes through the deep

CZ. On the basis of EMMA method of Hooper (2003), as modified

by Barthold et al. (2011), we included 37 of 42 measured tracers in

our PCA. The full list of tracers includes dissolved inorganic carbon,

dissolved organic carbon, F, Cl, SO4, Na, Mg, Al, Si, K, Ca, Cr, Fe, Co,

Ni, Cu, Zn, Y, Cd, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb,

Lu, Pb, δ2H, Sr, Mo, Ba, As, Se, Sn, and Sb. Stable O and H isotope data

for precipitation and streamflow are available from 2006 to 2010,

whereas weekly to biweekly stream chemistry observations started

in 2009. To avoid issues related to data gaps, we accepted tracers with

at least 90% data availability (shown by the red line in Figure S6 in SI)

and consequently excluded Cd, Pb, δ2H, Sn, and Sb.

In EMMA, with the compiled stream chemistry data set for the

MG‐Weir (Figure 1a), several stream chemistry diagnostic plots were

created following Hooper (2003) to identify conservative solutes and

the dimension of the mixing space required to explain stream water

compositions. The full compiled data set for the MG‐Weir was used

to identify conservative solutes, dimensionality of the required mixing

space, and appropriate endmembers. The main simplifying assump-

tions involved in EMMA are (Christophersen & Hooper, 1992; Hooper,

Christophersen, & Peters, 1990): (a) different water stores within the

CZ structure are geochemically distinct and their chemical composi-

tion does not vary significantly over time or space within any given

CZ water store, and (b) a mixture of various types is conservative.

EMMA starts with creating bivariate solute–solute plots and then it

moves on to create residuals versus observed concentration plots

(more details are provided in Sections S2 in SI). Finally, the following

three guidelines were used to evaluate the required dimensionality

of the mixing space (more details are provided in S3 in SI):

(G1) retain all eigenvalues higher than one (Hooper, 2003; Jöreskog,

Klovan, & Reyment, 1976);

(G2) retain as many eigenvectors as needed to explain approxi-

mately 80–90% of the variability of the observed data set

(Christophersen & Hooper, 1992); and

(G3) retain a minimum number of eigenvectors such that the pattern

between residuals and observed concentrations for a conserva-

tive tracer is random (Hooper, 2003).

2.4 | Estimation of total number of outliers to amixing space and maximum dynamic CZ water storage

We followed a two‐step procedure to evaluate potential relationships

between dynamic CZ water storage and geochemical heterogeneity of

stream water. In the first step, we determined the total number of out-

liers to the proposed mixing spaced formed from the vertices of the

identified distinct CZ water stores. In the second step, we estimated

maximum CZ dynamic storage. Seasonal stream water compositions

are defined as geochemically heterogeneous when a significant frac-

tion of compositions plot outside of the proposed mixing space.

2.4.1 | Estimating outliers for any N‐dimensionalmixing space and contributions from each endmembertowards streamflow

The method of Christophersen and Hooper (1992) was used to

estimate the fractional contribution of each endmember for each

stream water composition. Any negative fractional contribution

defined that composition as an outlier to the N‐dimensional mixing

space. An outlier for the mixing space was reprojected back on the

N‐dimensional (where N is the number of vertices) mixing space by

substituting the negative fractional contribution from any endmember

as zero and then redistributing the negative fractions to the remaining

positive fractions from the other endmembers with the condition

that all endmember fractions must sum to unity. Further details and

480 DWIVEDI ET AL.

all mathematical equations and expressions are provided in the

Section S4 in SI.

2.4.2 | Baseflow recession analysis for estimatingseasonal maximum dynamic CZ storage

For estimating maximum seasonal dynamic CZ storage, a two‐pronged

strategy was adopted. In the first step, the standard procedure from

Ladson, Brown, Neal, and Nathan (2013) was employed for using the

Lyne and Hollick (Lyne & Hollick, 1979) recursive low‐pass digital filter

(Equation 2) for separating a daily streamflow value Q(t) into

stormflow (or quick flow; S[t]) and baseflow (B[t]). The rationale

behind using this filter for separating baseflow from quickflow compo-

nent lies in the understanding that quickflows generally represent low

period (i.e., high frequency) fluctuations in the observed streamflow,

whereas baseflows represent sluggish groundwater flow, character-

ized by high‐period (i.e., low frequency) fluctuations. Several studies

report the recursive digital filter better models the baseflow

hydrograph than other methods (Arnold & Allen, 1999; Nathan &

McMahon, 1990); it provides realistic baseflow responses (Ladson

et al., 2013; Mau & Winter, 1997), and the modelled baseflows com-

pare well with field‐based observations (Arnold & Allen, 1999). In

the recursive filter equation (Equation 2), α is known as the filter

parameter. A value of 0.925 was used for α, as suggested by Nathan

and McMahon (1990) and used for numerous other studies

(Arciniega‐Esparza, Breña‐Naranjo, & Troch, 2016; Troch et al.,

2017; Voepel et al., 2011).

B tð Þ ¼ αB t − 1ð Þ þ 1 − α2

� �Q tð Þ þQ t − 1ð Þð Þ (2)

In the standard procedure of applying the Lyne and Hollick's digital fil-

ter (Ladson et al., 2013), the daily streamflow time series for a given

period of record was reflected 30 time steps before and after the

period of record using the existing observations, and the filter was

passed three times in the following order: forward, backward, and for-

ward. Furthermore, for the first forward direction filter application, the

observed daily streamflow time series was used. For subsequent filter

applications, the resultant time series from the last filter application

was used as input time series with the condition that at any time step

or any order of filter application, the modelled baseflow is always less

than or equal to the observed streamflow on the corresponding time

step. The final modelled baseflow hydrograph is shown in Figure S10

in Supplements. In the second step, assuming a linear reservoir behav-

iour for MGC, the reservoir constant (Kres; with units days) was esti-

mated using a least‐square optimization approach. The assumption

of linear reservoir behaviour for MGC is consistent with other studies

that considered catchments of varying scales located in diverse cli-

matic settings (e.g., van Dijk, 2010, Arciniega‐Esparza et al., 2016;

Peña‐Arancibia, van Dijk, Mulligan, & Bruijnzeel, 2010; Troch et al.,

2017). van Dijk (2010) suggests a linear reservoir assumption provides

a better compromise between the filter's simplicity and its perfor-

mance than does a nonlinear reservoir. The baseflow at any time (t)

can be related to the baseflow (B0) at some previous time, t0, using

Equation (3) (Arciniega‐Esparza et al., 2016; van Dijk, 2010) when

there is negligible groundwater recharge.

B tð Þ ¼ B0e−t=Kres (3)

Differentiating Equation (3) leads to Equation (4).

−dB tð Þdt

¼ B tð ÞKres

(4)

Taking natural log of both sides of Equation (4) leads to Equation (5).

log −dB tð Þdt

� �¼ log B tð Þð Þ − log Kresð Þ (5)

Following Arciniega‐Esparza et al. (2016) approach, a least‐square

optimization of Equation (5) is performed for the estimation of the

optimal value of the parameter log(Kres). For the sake of brevity, we

present the final result from this analysis in the form of Expression

(6) for Kres. In Equation (6), M is the total number of B(t) and −d(B(t)/

dt combinations, which are obtained from the baseflow recession anal-

ysis.

Kres ¼ exp −∑M

i¼1 log − dB tð Þdt

� �i− ∑M

i¼1 log B tð Þð ÞiM

0@

1A (6)

From the simulated B(t) time series using the recursive low‐pass digital

filter, −B(t)/dt and B(t) are estimated for baseflow recession analysis

using the “scaled‐Δt” approach of Rupp and Selker (2006) and using

a MATLAB® code provided by Dr. H. Ajami (H. Ajami, Personal com-

munication, 2017; see also Ajami et al., 2011). Furthermore, in the

code, the time step size dt in the recession analysis is considered adap-

tive with the maximum step size allowed up to 8 days, following Ajami

et al. (2011).

Dynamic storage S(t) for any baseflow B(t) was estimated using

Equation (7). The maximum seasonal dynamic storage was also esti-

mated using Equation (7) with B(t) being replaced by maximum sea-

sonal baseflow (Arciniega‐Esparza et al., 2016).

S tð Þ ¼ Kres × B tð Þ (7)

In Section S5 of SI, we report a sensitivity analysis for (a) the filter

parameter value, (b) other measures of baseflow such as mean and

median for estimating mean and median seasonal dynamic storages,

(c) filter type, (d) linear versus nonlinear baseflow recession behaviour

for MGC and, to understand the sensitivity of our findings to our

selected method for baseflow recession analysis.

3 | RESULTS

3.1 | Seasonal 3H model ages

Tritium concentrations in all water samples exhibited the following

ranges: (a) soil water: 3.1–5.0 TU (Tritium units); (b) Huntsman spring

water: 2.1–7.2 TU; (c) Pigeon spring water: 2.9–3.5 TU; (d) MLWD

well water: 2.9–3.3 TU; and (e) stream water: 2.3–4.4 TU (Table S1

in SI). These values correspond to modelled 3H “ages” of (a) soil water:

3 ± 1.9 years (mean ± one standard deviation); (b) Huntsman spring

water: 11 ± 5.7 years; (c) Pigeon spring water: 12 ± 2.6 years; (d)

DWIVEDI ET AL. 481

MLWD well water: 13 ± 2.3 years; and (e) stream water:

12 ± 3.6 years.

During the winter season, soil water had the shortest residence

time, whereas the Huntsman spring had the oldest mean 3H model age

(Figure 2). During summer monsoon, 3H model ages are significantly

younger (by 5 years) for Huntsman spring than for stream water. In

fact, the range of mean 3H model age for Huntsman spring water is

much larger (~10 years; minimum age ~6 years and a maximum age

~16 years) in comparison with either soil water (range ~2 years) or

stream water (range ~4 years). For both winter and summer monsoon

seasons, the standard deviations of 3H model ages increases

downgradient from soil water to stream water (Table S1 in SI). During

the dry season, the Marshall Gulch stream generally ceases to flow

(with ~12% probability of streamflow less than 10−6 mm/day;

Figure S3A in SI). During the periods when there was some water in

the stream, the sampled 3H model ages were 4 years older for stream

water than for Huntsman spring.

In total, 3H model age results indicate three principal model age

groups:

1. high mean age (10–20 years) group: This group includes winter

season Huntsman spring, Pigeon spring, MLWD well, and stream

water samples, older ages during dry season and older ages dur-

ing summer monsoons for stream water samples;

2. an intermediate (5–10 years) mean age group: This group includes

dry season and older ages during summer monsoons for Hunts-

man spring, younger ages during summer monsoons, and dry sea-

sons for stream water samples;

3. a low (0–5 years) mean age group: This group includes soil water

samples and younger ages for the Huntsman spring water during

summer monsoons and dry seasons.

It is important to note that the 3H model ages in various water

samples may be underestimated, as a result of nonlinear mixing of

FIGURE 2 Mean tritium (3H) model ages forsoil water (integrated soil water or ISWsample location), spring waters (Huntsmanand Pigeon Springs), Mt. Lemon WaterDistrict well, and stream water (representingthe Marshall Gulch stream) during winterseason (shown by values within blue circles),dry seasons (shown by values within orangecircles), and summer monsoon seasons (shownby values within red circles)

3H from multiple flow paths from various source waters (Torgersen

et al., 2013).

3.2 | Identification of conservative tracers, minimummixing space dimension, and mixing spaceendmembers

Six chemical tracers (Cl, Na, Mg, K, Ca, and Sr), which were identified

as behaving relatively conservatively (see Section S2 in SI for more

details) and not impacted by colloidal transport in MGC (Trostle

et al., 2016), were used in the subsequent mixing analysis. A three‐

dimensional (3D) mixing space was found optimal (Section S3 in SI

provide more details). A higher dimensional mixing space was not jus-

tified by the data. The first three eigenvectors were retained, and all

mixing space diagrams are presented in 3D space with four

endmembers—defined as the CZ stores with distinct geochemical sig-

natures—representing the vertices of the mixing space.

The following criteria (Barthold et al., 2011; Christophersen &

Hooper, 1992; Liu, Hunsaker, & Bales, 2013; Liu, Parmenter, Brooks,

Conklin, & Bales, 2008b) were used to identify four endmembers for

the 3D mixing space: (a) a suitable endmember should form a vertex

of the mixing space, which circumscribes all/most of the stream water

chemistry observations in the principal component or the U‐space, (b)

the number of mixing space outliers should be minimum with a proper

choice of the four selected endmembers, (c) the distance between the

solute space and the U‐space for an endmember should be as small as

possible, (d) a proper choice of the four selected endmembers should

be able to represent the observed stream water compositions for con-

servative tracers. With the four selected criteria, a number of potential

endmembers were tested (Table 1). Furthermore, in our test, we

included water samples from the Pigeon and Cold springs, which are

near the field site. The Pigeon and Cold springs are not located within

TABLE 1 A list of potential endmembers considered for the proposed three‐dimensional mixing space and outcome of the endmember selectiontest

Potential endmembername

Endmembercode Description

Endmembertesting results

Rain None Median of the rain water composition time series This endmember plotted very similarly toprecipitation endmember

Snow None Median of the snow water composition time series This endmember plotted very similarly toprecipitation endmember

Soil water (granite) None Median of the soil water compositions observed withinthe Granite subcatchment

These endmembers lie in between the linejoining the precipitation and soil water(Schist) endmembersSoil water (Granite

and Schist)None Median of the soil water (Granite) and soil water (Schist)

compositions to form a single set

Baseflow None Streamflow during a dry season Found not suitable

Huntsman spring None Independent water samples Found not suitable

Cold spring None Independent water samples Found not suitable

Precipitation EM1 Median of the rain and snow water compositions put togetherto form a single set

Found suitable

Soil water EM2 Median of soil water compositions within the Schist subcatchment Found suitable

Deep groundwater EM3 Independent water samples for Pigeon spring Found suitable

Shallow groundwater EM4 From one of the extreme stream water composition observations Found suitable

Note. The final selected endmembers are provided with a code (second column).

482 DWIVEDI ET AL.

the MGC boundary (Figure 1a), but these springs are located within

the larger Sabino creek watershed, and they are upgradient from the

MGC boundary.

A plot of the various potential endmembers in the projected (U‐)

space indicates that precipitation, soil water (Schist), and Pigeon spring

are suitable endmembers to the proposed 3D mixing space (Figure 3a).

The precipitation endmember (called EM1 in Figure 3a) forms a vertex

of the mixing space, and therefore, it fulfils the criterion ‘a.” The pre-

cipitation endmember represents not just direct precipitation at the

stream site but also short flow paths (e.g., direct run‐off). Out of the

three soil water choices, that is, soil water (Granite), soil water (Granite

and Schist), soil water (Schist), as an endmember, soil water (Schist)

forms a vertex of the proposed mixing space, and thus, it fulfils crite-

rion “a.” Therefore, soil water (Schist), which is called the soil water

endmember in Figure 3a, is selected as the second endmember. Sev-

eral options were tested for the third endmember, such as Cold spring,

Huntsman Spring, baseflow, and Pigeon spring (no data are currently

available for MLWD well). Although it is generally assumed that

baseflow (streamflow during dry season) is representative of deep

groundwater (Ajami et al., 2011), results indicate that MGC baseflow

FIGURE 3 (a) Principal component space (orU space) plot of the streamflow observationsalong with various endmembers including

precipitation (EM1), soil water (EM2), deepgroundwater (EM3), shallow groundwater(EM4), and other water samples such as ColdSpring, Huntsman Spring, and baseflow. Thefour endmembers and the streamflowobservations resemble a butterfly type mixingpattern. (b) A simplified presentation of theproposed butterfly mixing space, which iscomposed of the precipitation, soil water,deep groundwater, and shallow groundwaterendmembers. (c) Pattern of the medianconcentrations (on a log‐scale) of varioustracers in endmembers EM1 through EM4.Note: (1) small circles are in (a) and (b)represent stream water chemistryobservations with the following colourscheme: Winter season samples are shown inblue, dry season in orange and summermonsoon season in red, and (2) bigger circlesin (a) and (b) are used for endmembers withthe following colour scheme: EM1 in blue,EM2 in green, EM3 in orange, and EM4 in red

DWIVEDI ET AL. 483

is a mixture of various water sources and is not deep groundwater

alone (filled purple circle in Figure 3a). Therefore, baseflow cannot

be considered as an endmember for MGC. Similarly, Cold Spring is

not a good candidate for the third endmember, as it does not form a

vertex of the proposed 3D mixing space. Pigeon spring, however,

appears to be a good candidate for the third endmember for the fol-

lowing reasons: (a) it fulfils the criterion “a” and forms a vertex of

the mixing space; (b) it closely resembles the deep fractured bedrock

water, that is, Ca‐HCO3 (Mohrbacher, 1984) or Na/Ca‐HCO3 (Olson,

1982) type; and (c) its mean 3H model age is within the range for

the high‐3H model age group.

Pigeon spring is located outside the MGC boundary in a different

geologic unit (Figure 1b). Pigeon spring water forming one of the ver-

tices of the mixing space suggests either a deep groundwater reservoir

that has not yet been sampled within the MGC or deep groundwater

flow recharged outside of the MGC boundary that is discharging at

MGC streamflow site through larger scale deep flow paths. The

Pigeon spring water is referred to as the deep groundwater

endmember or EM3.

An exhaustive search for the third endmember led to a situation

where there were no more observed potential endmembers to test

for the fourth endmember. MGC does not have any deep boreholes

or monitoring wells. Therefore, all previously mentioned endmember

search criteria were used for identifying the last endmember, that is,

one with extreme geochemical signature, from all of the stream water

chemistry observations (see Figure 1a for the observation location, i.e.,

MG‐Weir). The fourth endmember, identified from the stream chemis-

try observations, forms a vertex of the proposed 3D mixing space

(Figure 3a). All stream chemistry observations were tested for the low-

est number of the mixing space outliers, and the observation itself rep-

resented an extreme endmember. Liu et al. (2013) used a similar

method for identifying a groundwater endmember from stream chem-

istry observations for several catchments. For the selected fourth

endmember, the total number of outliers to the proposed mixing space

are ~61%, thereby fulfilling criteria “a” and “b” together. Furthermore,

there are no endmembers from stream chemistry observations, as a

possible fourth endmember option, for which the number of outliers

to the mixing space is less than ~61%. Finally, a test of criteria “c”

and “d” against all the four proposed endmembers showed these

endmembers acceptably fulfil those criteria (Section S6 in SI), and

therefore, these endmembers were used in the subsequent analysis.

In terms of spatial mapping of the fourth endmember, we hypoth-

esize that this endmember is representative of the shallow groundwa-

ter store, which lies above the deep bedrock aquifer for the following

reasons: (a) Si concentration in this endmember (=12.6 mg/l) is

between soil water (9.1 mg/l; Schist subcatchment) and deep ground-

water (14.4 mg/l; Pigeon spring); (b) this endmember does not plot in

the precipitation‐soil water‐deep groundwater endmember space, and,

in fact, it forms one of the vertices of the proposed four‐endmember

mixing space (Figure 3a,b for a simplified representation); (c) although

this endmember is based on one of the stream chemistry observations,

the concentration patterns for various chemical constituents (Figure 3

c) do not indicate a proportional shifting of the deep groundwater

endmember water composition due to its mixing with either precipita-

tion or soil water endmembers; (d) fractional streamflow contributions

for this endmember do not show any correlation with the total

streamflow (see Section S7 and Figure S16 and S17D in SI) as

observed for the other endmembers; and (e) whereas the water type

for the deep groundwater is Ca‐HCO3 type, which match positively

with the regional deep bedrock aquifer water, the water type for the

shallow groundwater endmember is Mg‐SO4 type (see Section S8 and

Figure S18 in SI).

The mixing space represented by the four endmembers resembles

two planes joined at one edge and looks like a butterfly (Figure 3a for

a 3D presentation of the mixing space with all stream water samples

and Figure 3b for a simplified presentation of the mixing space). This

pattern is referred to as the butterfly mixing pattern. The body of

the butterfly is composed of precipitation and soil water endmembers,

whereas the wings of the butterfly are formed by a combination of

three endmembers, such as precipitation‐soil water‐deep groundwater

for the right wing and precipitation‐soil water‐shallow groundwater

for the left wing. Most interestingly, given the spatial and temporal

nature of the flow paths in the MGC, most of the stream water sam-

ples fall either on the right wing (mostly dry and summer monsoon

season samples, precipitation‐soil water‐deep groundwater) or the left

wing (mostly winter season samples, precipitation‐soil water‐shallow

groundwater). There are a few samples that represent a combination

of all four endmembers (Figure 3a).

3.3 | Seasonal contribution of various CZ waterstores towards streamflow

The principal contributors to Marshall Gulch streamflow, during all

seasons and throughout all years sampled, are precipitation and soil

water (80–98.3% total); contributions from deep or shallow ground-

water are significantly lower (1.7–20% total; Figure 4a). Furthermore,

fractional streamflow contributions from both precipitation and soil

water endmembers show a strong correlation with total streamflow

(see Section S7 in SI). During the winter season (average seasonal spe-

cific discharge = ~150 mm), percentage contributions from precipita-

tion and soil water are ~36.3 and 62%, respectively, whereas shallow

and deep groundwater contribute only ~1.7% in total. In comparison

with the winter season, during the dry season (average seasonal spe-

cific discharge = ~3 mm), streamflow contributions from both precipi-

tation (~33%) and soil water (47%) were lower, but soil water

contributions decreased by ~15%, whereas precipitation contribution

decreased by ~3%. A lower soil water contribution to streamflow

can be attributed to a higher evapotranspiration water demand during

the dry season. Most interestingly, the contribution from the deep

groundwater endmember increased significantly (compared with the

relative contribution from this endmember in winter season) up to

~18%, and the contribution from the shallow groundwater, that is,

the perched water table at the top of the fractured bedrock,

endmember increased only slightly (2% increase, as compared with

contribution from this endmember in winter season). In total, shallow

and deep groundwaters contribute ~20% of dry season streamflow.

Finally, during the summer monsoon (average seasonal specific dis-

charge = ~50 mm), the results indicate a slight increase in the precip-

itation contribution (by ~12%, as compared with its relative

FIGURE 4 Percentage seasonal contributions from various endmembers towards streamflow generation before uncertainty analysis (a) and afteruncertainty analysis (b) that involves considering temporal variabilities observed in precipitation and soil water endmembers

484 DWIVEDI ET AL.

contribution during dry season) and a slight decrease in soil water con-

tribution to streamflow. Contributions from both shallow and deep

groundwaters also decreased by ~8% and 1%, respectively. In total,

shallow and deep groundwater contribute only ~11% to total stream

flow during the summer monsoon season.

While in the above analysis, we used the complete stream water

composition dataset, we performed sensitivity analysis to address

the following question: What would be the percentage streamflow

contributions from various endmembers for various seasons if only

25%, 50%, or 75% of the total stream water composition observations

were used in EMMA? Our sensitivity analysis results (discussed in

detail in SI S9) suggest that, except when the data used cut‐off is

25% (significant undersampling), the fractional seasonal streamflow

contributions are quite similar in summer monsoon and in dry season.

For winter season, increasing the % data used cut‐off from 25% to

100% increases streamflow contributions from both precipitation

and soil water endmembers, but % contributions from shallow and

deep groundwater endmembers decrease. This result is expected,

because streamflow in MGC is dominated by precipitation and soil

water endmembers.

The seasonal streamflow contributions from various water stores

are estimated assuming no significant temporal or spatial variation in

tracer concentration. The mixing space formed by the four water

stores, that is, precipitation, soil water, and deep and shallow ground-

waters, only includes 39% of all stream water samples. Indeed, analysis

(see Section 3.2) suggests significant temporal variation in tracer con-

centrations in both precipitation and soil water endmembers (e.g., K

and Ca both have a coefficient of variation higher than 1 in the two

endmembers; see Section S10 in SI). When such temporal variations

are included in our analysis for the precipitation and soil water

endmembers by also including the stream water compositions that

lie within median + one standard deviation of the centre of the pro-

posed mixing space, the percentage number of outliers decreases to

~15%. The proposed mixing space then contains 85% of the observa-

tions, which is adequate due to the unknown behaviour of the

responses of the fractured bedrock aquifer. Subsequently, we per-

formed uncertainty analysis in hydrograph separation due to the tem-

poral variabilities involved in EM1 and EM2 endmembers. In this

analysis, we increased the concentrations of the conservative tracers

by median concentration + one standard deviation in both

precipitation and soil water endmembers, first sequentially and then

simultaneously. We excluded cases when median concentrations of

conservative tracers are decreased by one standard deviation, as the

tracer concentrations are found negative for this case. Our sensitivity

analysis suggests the following ranges in the seasonal contributions

from various endmembers (Figure 4b and Table S7 in SI):

• For winter season: % contributions of precipitation (EM1), soil

water (EM2), deep groundwater (EM3), and shallow groundwater

(EM4) are 52.4 ± 17%, 44.3 ± 18.1%, 0.1 ± 0.1, and 3.2 ± 1.8,

respectively;

• For summer monsoon season: % contributions of EM1, EM2,

EM3, and EM4 are 60 ± 14.1%, 33.1 ± 11.9%, 4.1 ± 4.2, and

2.8 ± 1.8, respectively;

• For dry season: % contributions of EM1, EM2, EM3, and EM4 are

51.1 ± 17.4%, 36.05 ± 12.6%, 9.05 ± 7, and 3.8 ± 1.7, respectively.

Furthermore, on an annual time scale, when the complete stream

water data set is considered (see Table S8 in SI), the percent contribu-

tions to streamflow from precipitation endmember varies from 39% to

69%, soil water endmember varies from 25% to 56%, shallow ground-

water endmember varies from ~1% to 5%, and deep groundwater

endmember varies from ~0% to 3%. A wide range in streamflow con-

tributions from various endmembers suggests that the assumption of

insignificant temporal variation in endmember tracer concentrations

should be verified (similar to the suggestions by [Genereux, 1998;

McDonnell, Bonell, Stewart, & Pearce, 1990]), and it should be a part

of the EMMA (if long‐term data are available for any proposed

endmembers).

3.4 | Maximum seasonal dynamic CZ storage

Maximum dynamic water storage in the CZ (~55 mm) was observed

during the winter season (Figure 5a). Lower values were observed

for the summer monsoons (~17 mm) and dry period (~7 mm), despite

less incoming precipitation during the winter (~43% of the total annual

precipitation). This result is consistent with previous results in the

study area, and the greater southwestern region, that indicate winter

precipitation plays a larger role in groundwater recharge compared

FIGURE 5 (a) Total maximum dynamiccritical zone storage (vertical bars and left‐hand side y‐axis) and percentage of datapoints falling outside (circles and right‐handside y‐axis) of the proposed butterfly mixingspace (Figure 3b), for each season. (b)Conceptual model CM1 is a two‐endmembermodel involving only precipitation and soilwater. Various conceptual models in (c) are acombination of three out of four endmembersincluding precipitation (EM1), soil water(EM2), deep groundwater (EM3), and shallowgroundwater (EM4). Note: (1) the totalprecipitation (P) values in a particular seasonfor a hydrologic year are also shown on theplot (a), (2) the numbers at the bottom in (a)indicate the % of observations used incalculating the mixing space outliers, (3) smallcircles are in (b) and (c) represent stream waterchemistry observations with the followingcolour scheme: winter season samples areshown in blue, dry season in orange, andsummer monsoon season in red, and (4) biggercircles in (c) are used for endmembers with

the following colour scheme: EM1 in blue,EM2 in green, EM3 in orange, and EM4 in red

DWIVEDI ET AL. 485

with summer precipitation (Ajami et al., 2011; Cunningham et al.,

1998; Kalin, 1994; Mohrbacher, 1984; Olson, 1982). Note that the

estimated maximum seasonal dynamic storages are based on the Lyne

and Hollick (1979) recursive digital filter and a linear reservoir assump-

tion for MGC. A detailed sensitivity analysis (Section S5 of SI) for the

filter parameter, filter type, linear versus nonlinear reservoir assump-

tion, and the selection of a baseflow statistics, that is, using mean or

median versus maximum seasonal baseflows, suggest that although

the estimated values of the seasonal dynamic storages are

dependent on a variety of assumptions, the pattern of these estimated

storages is consistent with winter > summer monsoon> dry season.

The linear correlation between estimated annual maximum dynamic

storage and annual precipitation is weak, with an R2 value of ~0.07

(Figure S21 in SI). This suggests (a) annual precipitation is not the sole

factor dictating dynamic CZ storage, and (b) other factors such as

evapotranspiration and seasonality of precipitation may exert impor-

tant controls.

4 | DISCUSSION

4.1 | Testing of alternative conceptual models fordistinct CZ water stores

Here, we compare competing conceptual models (CMs) of CZ water

stores that contribute to streamflow with the objective that testing

competing alternative hypotheses of conceptual model elements and

how their spatial connections evolve temporally will provide an

improved understanding of montane CZ functioning. We start with a

simple model involving only two endmembers (precipitation and soil

water) and reflect a hydrologic system dominated by surface pro-

cesses and shallow soil processes. We then move to three endmember

models that include some component of a deeper groundwater sys-

tem. Finally, we discuss what we consider the best representation of

the system, a four‐endmember model that requires both a shallow

and a deep groundwater system to explain the observed hydrologic

and geochemical data.

4.1.1 | Streamflow sourced from precipitation andsoil waters alone (CM1)

A simple, two‐component model (CM1) could explain MGC stream

discharge, as it includes the main contributors to stream flow, precip-

itation and soil water stores (Figure 5b), and numerous streamflow

observations fall within the precipitation and soil water endmembers

in the U1‐space (Figure 5b). In a recent ecohydrological modelling

study by Chang et al. (2018), authors have used this conceptual model

for simulating ecohydrological fluxes at MGC. However, CM1 does

not include deep bedrock flow processes, which are necessary to

explain stream water chemistry and residence times. For example,

our EMMA analysis (Figure 3c) indicates that shallow and deep

groundwater, not included in CM1, are the principal contributors of

major lithogenic cations (Ca and Mg). In addition, 3H model ages (inter-

mediate age group [5–10 years] and high‐age group [10–20 years])

require contributions of deeper, longer flow path waters to

streamflow. Most importantly, earlier work for MGC (Ajami et al.,

486 DWIVEDI ET AL.

2011) suggests that groundwater sources are required to sustain

streamflow under dry conditions.

4.1.2 | Streamflow sourced from three constantendmembers (CM2)

Precipitation, soil water, and deep groundwater (CM2A)

Whereas several stream chemistry observations (especially summer

monsoon and dry season samples) can be explained by the CM2Amodel

(Figure 5c), this model is insufficient for MGC, as it does not honour rel-

evant processes that affect stream water composition. If this model is

accepted and the hypothesized shallow groundwater endmember is

ignored, then we implicitly overlooked the non‐conservative behaviour

of Si, and we have also ignored the stream water compositions that do

not fall on the EM1–EM2–EM3 projected space (Figure 5c). As Si is a

major weathering product for most sites (White, 2003; White & Blum,

1995), and it is a useful tool for understanding subsurface chemical

denudation processes (Frisbee, Tolley, &Wilson, 2017; Frisbee, Phillips,

White, Campbell, & Liu, 2013; Frisbee et al., 2016), ignoring the non‐

conservative behaviour of Si or stream water chemistry observations

(especially winter season samples) is problematic. Therefore, the model

CM2A is abandoned, and other models with the same mixing space

dimension are considered next.

Precipitation, soil water, and shallow groundwater (CM2B)

Although several stream water composition observations (especially

winter season samples) can be explained by the CM2B model

(Figure 5C), there are several deficiencies with this model. For exam-

ple, with omission of a deep groundwater endmember, we have

underestimated major cation (Ca and Na) concentrations and

overlooked the longest flowpaths contributing to MGC. Most impor-

tantly, with the CM2B model we cannot replicate the high 3H model

mean age group (10–20 y). Therefore, the CM2B model is not a good

choice for MGC and we abandon this model in favour of testing the

CM2C model next.

Precipitation, shallow, and deep groundwaters (CM2C)

With CM2C, the percentage of outliers (~1.7%) is significantly lower

than for either model CM2A (~58%) or CM2B (~46%; see Table S9

in SI). However, there are several perceptual–conceptual issues with

this model. Model CM2C ignores contributions from soil water. Fur-

thermore, it cannot explain the lowest mean 3H model age group (0–

5 years). Most importantly, this model is inconsistent with the

expected hydraulic conductivity contrast between the soil layer and

weathered bedrock. A number of researchers have shown that such

a contrast results in lateral flow through the soil layer being a signifi-

cant contributor to streamflow generation (Liu et al., 2013;

McDonnell, 1990; Tromp‐van Meerveld, Peters, & McDonnell, 2007).

Due to these shortcomings, we abandon this model and search for

an improved conceptual model that requires increasing the mixing

space dimension by one.

In terms of three‐endmember conceptual models, there is one

more model that involves soil water, shallow, and deep groundwater

stores. However, if this conceptual model is accepted, then the per-

centage number of outliers is exceedingly high ~97% (Table S9 in SI),

and the lack of contributions from precipitation, given for MGC's

steep topography (mean slope = 23.64o), presents a perceptual–

conceptual difficulty. Therefore, this conceptual model is abandoned.

4.1.3 | Streamflow sourced from four endmembers(CM3)

The model CM3 that involves four endmembers and their associated

source waters (Figures 2 and 3a,b) is consistent with our observations

and findings. This model presents a number of benefits in comparison

with other lower dimensional models (Figure 5b,c). In this model, all

four endmembers—including precipitation, soil water, as well as waters

from both shallow and deep groundwater stores—contribute to

streamflow and regulate its chemistry in various seasons (Figure 3a).

This model performs better than those that ignore interflow (e.g.,

CM2C; Figure 5c), because soil water is the source of interflow. Fur-

thermore, this model includes contributions from the hypothesized

shallow weathered bedrock aquifer that is distinct in terms of both

geochemical signature (Figure 3c) and dominant water type (Section

S7 in SI) from the other endmembers. Most importantly, in comparison

with other models (e.g., CM2B), this model includes streamflow contri-

butions from the deep regional groundwater endmember, that is,

regional groundwater that is recharged outside the MGC boundary.

The deep regional groundwater endmember represents

intercatchment flow through the longest and/or deepest flow paths

that defy surface water boundaries and affect stream water quantity

and quality at MGC. Finally, as CM3 includes hydrogeochemical pro-

cesses both occurring and hypothesized for shallow and deep ground-

water stores, this model is able to represent shallow and deep flow

processes in contrast to conceptual models that ignore them (e.g.,

CM1 or CM2A or CM2B; Figure 5b,c).

Most importantly, the CM3 model is consistent with all three 3H

model age ranges (low range: 0–5 years, intermediate range: 5–

10 years, and high range: 10–20 years; Section 3.1) to explain distribu-

tion of residence times in stream. Nonetheless, there are some limita-

tions and uncertainties with this model, and further subsurface

explorations are required, especially for testing our hypothesis related

to the shallow groundwater endmember and its spatial extent. For

example, we hypothesized that EM4 represents water from the shal-

low bedrock aquifer that lies between the soil layer above and the

deep bedrock below. Furthermore, as this endmember shows low cor-

relation with streamflow (Section S7 in SI), the zone is expected to

have lower permeability than the soil layer above and the deep frac-

tured bedrock below. As an alternative to the laterally extensive layer

for representing EM4, this endmember can also be represented by a

localized zone near the stream water observation site that has very

low permeability. Therefore, future subsurface explorations are

needed to better characterize and test the hypothesis of a laterally

extensive shallow groundwater flow zone.

Despite limitations, CM3 enables an improved conceptualization

relative to prior hydrologic models of MGC. For example, on the basis

of convolution integral approach and using stable water isotopes for

three summer monsoon seasons, Heidbüchel et al. (2013) suggested

that during high‐catchment storage conditions both deep (upper

unconfined aquifer) and shallow (soil water) flow paths are active

DWIVEDI ET AL. 487

and that under dry conditions, only shallow flow paths are active. Our

results indicate that there are deeper regional flow paths that deliver

older water (~17 years old; the highest [mean + one standard devia-

tion] 3H model age observed for stream water in this work) and these

flow paths seasonally contribute to streamflow generation. We report

these deeper flow paths at MGC are related to the regional groundwa-

ter or intercatchment flow that is recharged outside the MGC bound-

aries but discharges at the MGC outlet, (MG‐Weir; Figure 1a). Frisbee

et al. (2016) suggested that such intercatchment deep groundwater

flow can occur in various bedrock types and can affect stream water

quality even in small mountainous catchments, consistent with our

findings here. Moreover, our findings are consistent with the field

observations of Frisbee et al. (2017), where deep groundwater contri-

butions to a small mountainous catchment were noted. Similarly,

numerical modelling results from Gleeson and Manning (2008) and

Welch et al. (2012) for 3D nested catchments show that regional

groundwater, which is recharged in an upslope catchment, can

contribute/discharge in the downslope catchment.

FIGURE 6 Endmember mixing analysis, 3H model “age,” and baseflowgeneration processes and their seasonal characters during (a) winter seasofigure shows the butterfly‐type mixing space with precipitation, soil water, dvertices. Note, (1) the early (blue) and late (purple) season water table locaseason (see Section 3.4 and Figure 5a), (2) the horizontal columns in eachendmembers (see Figure 4b), and (3) the open boundary in a, b, and c conrepresented by deep groundwater endmember

As an improvement to the existing conceptual model for MGC, the

proposed conceptual model (i.e., CM3) not only includes the summer

monsoon season as done in the study of Heidbüchel et al. (2013) but

alsowinter precipitation events,which have different hydrologic behav-

iour because of diminished evapotranspiration. The conceptual model

proposed by Ajami et al. (2011) also indicates seasonal change in the

nature of the flow paths based on two dry season 3H samples (we incor-

porated these 3H observations and such observations from Cunning-

ham et al., 1998 in our analysis) and stable water isotope results.

4.2 | Streamflow generation processes and theirseasonal characteristics

4.2.1 | Winter season

Early winter precipitation events in the MGC give rise to a rapid satu-

ration of relatively thin and coarser soils above the granite bedrock

type than soils above the schist bedrock type, and therefore, there is

recession analysis results‐based interpretation of the streamflown; (b) dry season; and (c) summer monsoon. The centre part of theeep groundwater, and shallow groundwater stores as the mixing spacetions are shown here to highlight variation in dynamic storage withplot show % seasonal streamflow contributions from variousceptual models suggests intercatchment groundwater flow, which is

488 DWIVEDI ET AL.

more contribution of soil water or shallow groundwater from the

Granite subcatchment towards streamflow than contributions from

the Schist subcatchment (Figure 6a). As the average soil thickness

above the granite bedrock (86 cm; Heidbüchel et al., 2013) is lower

(indicating less storage is needed to fill a soil column), and the soil type

is coarser (suggesting a higher saturated hydraulic conductivity once

soil pores are filled) than soils overlying the schist bedrock (100 cm

and fine soil type; Heidbüchel et al., 2013), subsequent rains form a

transient saturated zone above the granite bedrock (Figure S22A).

The transient saturated zone above the granite bedrock causes lateral

flow across the soil‐shallow bedrock interface in the form of interflow,

which is consistent with the crack and pipe flow mechanism proposed

by McDonnell (1990).

We hypothesize due to a finer soil type, smaller pore size distribu-

tion, and larger soil thickness, more sustained water inputs are

required for a transient saturated zone to form above the Schist bed-

rock. Our hypothesis is supported by the transient fractional soil water

endmember contribution towards streamflow (Figure S16 in SI), which

peaks during the midwinter season, that is, around the end of a calen-

dar year. As the total water input to MGC increases during the early

winter season, when evapotranspiration demand is low, a transient

saturated zone develops, and interflow occurs within the soil layer

above the Schist bedrock, connecting the hillslope to the stream

(Figure 6a). Such a “wetness‐dependent interconnectivity” (Phillips,

2010) for a hillslope is also reported in literature (Newman, Campbell,

& Wilcox, 1998), and such interconnectivities are thought to be

responsible for incomplete mixing of various subsurface flow paths.

A second lateral flow path zone is hypothesized to form within

the shallow bedrock aquifer across the interface between shallow

and deep bedrock aquifers (Figure 6a). The mobilization of shallow

bedrock water (represented by the shallow groundwater endmember,

whose seasonal streamflow contribution is 3.2%) is caused by perco-

lated water through the bedrock hollows (Tromp‐van Meerveld &

McDonnell, 2006; Tromp‐van Meerveld et al., 2007), that is, depres-

sions in the bedrock microtopography, which pushes the old water

in front of the newly recharged water in the aquifer, consistent with

the translatory or piston flow mechanism (Buttle, 1994). The fourth

water source, deep groundwater (with seasonal streamflow contribu-

tion =0.1%) is mobilized to the stream due to recharge from bedrock

hollows formed between the shallow bedrock at the top and deep

bedrock below (both with fracture porosity; see Figure S23 in SI for

outcropping bedrocks at MGC). This newly recharged water pushes

old water from deep bedrock fractures, consistent with the highest3H model ages (16 ± 3 years, Figure 3 and Table S1 in SI), representing

water stored from past several winter season recharge pulses to

streamflow, which again is consistent with the translatory or piston

flow mechanism (Buttle, 1994). The seasonal streamflow contributions

from precipitation and soil water endmembers are 52.4% and 44.3%,

respectively.

By late winter season, streamflow contributions from precipita-

tion, soil water, and shallow groundwater are at their peak (indicated

by a higher late season water table elevation, Figure 6a). However,

streamflow contributions from deep groundwater are mostly unaf-

fected by recent winter recharge events, as indicated by a lower con-

tribution from deep bedrock aquifer during the winter season relative

to summer monsoon. This indicates a time lag in the deep bedrock

aquifer response, consistent with findings reported by Manga (1999,

2001) for high‐elevation catchments in the Oregon and California Cas-

cade range. Therefore, it is possible that the streamflow contributions

observed during late winter are, in fact, indicative of recharge pulses

from the preceding summer monsoons and previous winters (e.g.,

Heuer, Brooks, & Tonnessen, 1999; Martinec, 1975; McIntosh et al.,

2017; Williams & Melack, 1991).

4.2.2 | Dry season

During dry seasons between summer monsoons and the winter

snow/rains, precipitation is low, evapotranspiration demand is high,

and soil moisture content is low (Figure 6b). Therefore, there is no sig-

nificant water flow across the soil–bedrock interface to recharge the

deep groundwater aquifer. Additionally, all water stores in the CZ

are disconnected from the stream, and it runs dry. The numerical

modelling study by Gleeson and Manning (2008) that includes 3D

mountainous catchments suggests that under lower water table eleva-

tion conditions (with respect to the elevations of the headwater

streams), discharge from the regional groundwater flow paths can shift

to lower elevations, which can contribute to intermittent character of

the headwater streams under dry conditions, as we reported here for

MGC. Of the average seasonal specific discharge of ~3 mm, % contri-

bution from precipitation, soil water, and shallow and deep groundwa-

ter endmembers are 51.1%, 36.05%, 3.8%, and 9.05%, respectively.

4.2.3 | Summer monsoon

Groundwater stores and flow paths active at the end of the winter

season are also active during the summer monsoon, albeit with a lower

intensity. During the summer monsoons, MGC receives intense short‐

duration storm events (Desilets, Ferré, & Ekwurzel, 2008). When these

events are closely spaced, precipitation can lead to significant

increases in catchment groundwater storage on an event basis and

transient build‐up of a saturated zone above the soil‐shallow bedrock

interface. This interpretation is supported by a transient build‐up of

the water table elevations above the soil‐shallow bedrock interface

at various piezometer locations within the granite (Figure S22A in SI)

and schist subcatchments (Figure S22B in SI). There are a few excep-

tions, however. The first exception is higher contributions from near

surface run‐off (represented by the precipitation endmember whose

percentage contribution is 60% of the seasonal streamflow;

Figure 6c) to streamflow, which is also indicated by significantly lower3H model ages during this season (see Section 3.1 and also Figure 2) in

comparison with winter season. The other exception is that

streamflow contribution from the deep bedrock aquifers (4.1% of

the seasonal streamflow) is higher than the shallow bedrock aquifer

(2.8% of the seasonal streamflow) during this season, compared with

the winter season (Figure 6a).

We hypothesize that a part of the larger deep groundwater con-

tribution to streamflow during summer monsoons is related to the

time‐lagged response of the deep groundwater, and this time lag

appears “seasonal” for MGC. Previous studies (Heidbüchel et al.,

2013; Holleran, 2013; and Heidbüchel [personal communication])

DWIVEDI ET AL. 489

indicate an increase in clay content with depth within soil above the

Schist bedrock. The modelling studies by Wilson and Guan (2004) indi-

cate that soil layering has a large impact on vertical water movement,

and it may cause downslope soil water flow if the surface topography

is steep. Thus, it is plausible that although the lateral connectivity is

high for the shallow bedrock aquifer within the Granite subcatchment,

dry pockets (McNamara, Chandler, Seyfried, & Achet, 2005), that is,

localized unsaturated zones, persist in the shallow bedrock aquifer

within the Schist subcatchment. Such localized unsaturated zones

(see also Bockgard & Niemi, 2004; Tromp‐van Meerveld et al., 2007)

restrict whole hillslope connectivity for this aquifer and consequently

its contribution towards streamflow. Thus, a number of mechanisms

can lead to the behaviour observed for the shallow bedrock aquifer

groundwater contribution, which in literature is referred to as the

“Equifinality” in the stream generation processes (Buttle, 1994;

Genereux & Hooper, 1998). Geophysical studies or deep drilling are

needed to better characterize the spatial extent of the shallow frac-

tured bedrock aquifer and also to assess the degree of hydraulic con-

ductivity contrast between this aquifer and soil zone above and deep

fractured bedrock aquifer below.

4.3 | Dynamic CZ storage and geochemicalheterogeneity of stream water

A strong positive relationship exists between seasonal dynamic CZ

storage and geochemical heterogeneity of stream water (Figures 5a).

Note that the geochemical heterogeneity of stream water was defined

FIGURE 7 Comparison of percentagecontribution of Mountain GroundwaterDischarge (MGD) to long‐term streamflow forthe Marshall Gulch catchment or MGC (thisstudy, highlighted by red hollow rectangle)with literature values for other headwater

montane catchments (assumed equivalent tothe highest sampling location for which eitherendmember mixing analysis or tracer injection‐based or reach‐based water balance estimatesfor MGD % are reported in the literature).Note: Data source: (1) Valles Caldera sites—Liu,Bales, Conklin, and Conrad (2008); (2)Colorado Rocky Mountain Loch Vale site—Clow et al. (2003), (3) Black Forest Mountainssite—Uhlenbrook, Frey, Leibundgut, andMaloszewski (2002), (4) Sierra Nevada site—Liu et al. (2017), (5) San JuanMountains sites—Frisbee, Phillips, Campbell, Liu, and Sanchez[2011], (6) Colorado Rocky Mountain GordonGulch, Como creek, and Green Lake Valley foursites—Cowie (2014), (7) Panola Mountain site—Tromp‐van Meerveld et al. (2007), (8) Sangrede Cristo site—Frisbee et al. (2017), (9) ChuskaMountains site—Tsinnajinnie, Frisbee, andWilson (2017), (10) Cascade range sites—Gannett, Lite, Morgan, and Collins (2001), (11)Catskill Mountain site—Harpold, Lyon, Troch,and Steenhuis (2010), and (12) Laurel Hill site—Dewalle, Swistock, and Sharpe (1988)

by measuring the number of outliers to the mixing space formed by

geochemically distinct CZ water stores in the study site (Section

2.4.1). For each season, the following relationships between total max-

imum dynamic storage and the percentage (%) total number of outliers

to the mixing space were found: (a) 55 mm/~55%, respectively for

winter; (b) ~17 mm/~5%, respectively for summer monsoons; and (c)

~7 mm/~0.8%, respectively for dry seasons. A linear regression analy-

sis between the two variables indicates a statistically significant (at

90% confidence level) relationship (% number of outliers = 1.17 × maxi-

mum CZ dynamic storage−10.52) with R2 value of 98.5%, and there-

fore, 98.5% of stream water geochemical heterogeneity can be

attributed to the variability in the seasonal CZ dynamic storage. It is

important to note that the estimates of seasonal total number of out-

liers to the proposed mixing space were affected by sampling biases.

For example, ~64% of the stream chemistry observations were from

winter season, ~33% were from the summer monsoon, and the

remaining ~3% were from the dry season (bottom numbers in

Figure 5a). Nonetheless, given the intermittent nature of the

streamflow at the Marshall Gulch site (inset plot in Figure 6b), such

sampling biases were unavoidable.

We have also evaluated if our findings in terms of a larger per-

centage of outliers with respect to the proposed mixing space are

affected by temporal variabilities in precipitation and soil water

endmembers (see Section S10 and Tables S5 and S6 in SI). Our uncer-

tainty analysis results suggest although the details in the % of outliers

vary due to temporal variabilities in precipitation and soil water

endmembers, the order of % of outliers in various seasons (our main

focus) remains the same, that is, % of outliers in winter season >

490 DWIVEDI ET AL.

summer monsoon > dry season. Our finding in terms of storage‐

dependent geochemical heterogeneity of stream water is an essential

outcome of the seasonally evolving hydrologic connectivity of various

CZ stores to streamflow (Section 4.2 and Figure 6), and it clearly illus-

trates the effects of CZ storage on not only surface and subsurface

flow paths but also the geochemically distinct behaviours that these

different flow paths lead to.

4.4 | Long‐term annual deep CZ groundwater fluxesthat help evolve deep CZ porosity

A robust and conservative estimate of the mean annual deep CZ

fluxes or MGD fluxes for MGC is 4.5 ± 0.9% of the long‐term annual

streamflow (Figure 7) or 1.4 ± 0.3% of the long‐term annual precipita-

tion (920 mm; Section 2.1). These MGD flux estimates represent com-

bined contributions from the shallow and deep aggressive

groundwaters, as they carry oxidants (e.g., dissolved O2) and acids

(e.g., dissolved CO2) that promote primary mineral dissolution and help

evolve matrix porosity.

A lower MGD rate is reported here relative to other studies

(Figure 7; Table S10 in SI provides all data used in creating this plot).

The MGD value for MGC (~4.5% of the annual streamflow) is lower

than that for the Jemez River Basin Critical Zone Observatory in the

Valles Caldera, New Mexico (~10% of the annual streamflow), consis-

tent with a higher bedrock porosity for the volcanic site. It is important

to note, however, that the MGD rates for the Jemez River Basin Crit-

ical Zone Observatory headwater catchments vary from 0% (for the La

Jara catchment) to ~20% (for Redondo creek) of the annual

streamflow there. To illustrate the widest difference, the MGD rate

estimates for the Fish run catchment located in Laurel Hill, Pennsylva-

nia, are significantly larger (81.6%). Some possible reasons for these

differences in MGD flux estimates are the following:

• The fractured bedrock aquifers differ in terms of fracture density

and fracture network connection;

• during the present study period, MGC received significantly lower

MAP (~525 mm) than the long‐term estimates of 920 mm

(obtained from the PRISM climate model; see Section 2.1). Thus,

significantly lower MGD estimates for MGC from this study are

consistent with ongoing drought conditions (Arizona State Cli-

mate Office, 2018).

• In so far, as spatiotemporal distributions in precipitation affect

mountain groundwater recharge (Guan, 2005) and how water is

stored and discharged from hillslopes (Harman & Sivapalan,

2009), the intensity and duration of precipitation events at MGC

may be different from the events observed in other regional

studies;

• vegetation characteristics (e.g., density, rooting depth, and type of

vegetation) and the strategies used by local vegetation can signif-

icantly affect groundwater recharge (Crosbie, Jolly, Leaney, &

Petheram, 2010; Donohue, Roderick, & McVicar, 2007; Guan,

2005; Kim & Jackson, 2012; Maxwell & Condon, 2016; Phillips,

Walvoord, & Small, 2004; Scanlon et al., 2006) even under the

same climatic conditions (Phillips et al., 2004), and therefore, it is

quite possible that the vegetation at MGC (with rooting depth

extending well into the bedrock layer; Pelletier et al., 2013) is

more effective in water extraction from the deep CZ and thus

reducing MGD fluxes than the vegetation at other sites;

• contributions from flow paths that bypass streamflow, which were

not included in MGD flux estimates, may be significant. For exam-

ple, 3D numerical modelling of nested mountainous catchments

suggests that when water table elevation is lower than the eleva-

tion of the headwater streams, more regional flow can bypass

headwater streams (Gleeson and Manning, 2008). Similarly, the

authors also showed that topographic ruggedness, mountain

drainage network, and groundwater circulation depths may also

control the discharge of regional groundwater to headwater

streams and the deep groundwater fluxes through a catchment,

as intercatchment flow.

For item (d), representing deeper flow paths that do not emerge at

streamflow sites or assessing their impact on deep CZ functioning is

a major challenge (see also Berghuijs & Kirchner, 2017; Kirchner,

2009). We do not have observations (deep boreholes) to constrain

these deeper flow paths at the Marshall Gulch site. For these reasons,

numerical modelling that conforms to our current understanding of

hydrological processes and the improved conceptual model (see Fig-

ures 2 and 6) is needed to evaluate contributions from deep flow

paths that bypass streamflow but still contribute towards deep CZ

water fluxes.

5 | CONCLUSIONS

We used EMMA, 3H model ages and baseflow recession analysis

methods for identifying geochemically distinct water stores across a

CZ structure, relevant hydrogeochemical processes, impacts of CZ

storage on stream water chemistry and long‐term estimates of aggres-

sive deep CZ fluxes for a high‐elevation montane CZ. On the basis of

testing several competing conceptual models for source water identi-

fication and hydrological processes, we found a conceptual model

involving precipitation, soil water, shallow groundwater, and deep

groundwater stores to be acceptable. In these four water source

types, soil water had the lowest mean 3H model ages (0–5 years), shal-

low groundwater had intermediate mean 3H model ages (5–10 years),

and deep groundwater had the longest mean 3H model age range (10–

20 years). Our results further indicate that water fluxes from precipita-

tion (seasonal streamflow contribution: 33–73%) and soil water (sea-

sonal streamflow contribution: 21–62%) stores constitute a large

part of the seasonal streamflows, and thus, the Marshall Gulch site

is, to a large extent, characterized by hydrological processes (e.g., con-

tributions from precipitation and lateral flow across the soil–bedrock

interface) that are spatiotemporally well connected to streamflow. A

graphical representation of the four endmembers in three‐principal‐

component space is referred to as a “butterfly mixing pattern.” The

main body of the pattern is formed by precipitation and soil water

endmembers, whereas its two wings are formed by a combination of

three endmembers (precipitation‐soil water‐shallow groundwater and

precipitation‐soil water‐deep groundwater). With respect to the role

DWIVEDI ET AL. 491

of CZ dynamic storage on stream water chemistry, we found the num-

ber of outliers to the proposed mixing space increases with the

dynamic storage. In other words, geochemical heterogeneity of stream

water composition increases with CZ storage, or geochemical hetero-

geneity is storage‐dependent. Finally, using EMMA, a long‐term mean

annual estimate of active deep groundwater flux through the deep CZ,

that is, MGD, was found to be ~4.5% (±0.9) of the long‐term annual

streamflow or ~1.4% (±0.3) of the long‐term annual precipitation. As

the MGD flux estimates in this study are derived using comprehensive

long‐term hydrogeochemical observations, they provide a representa-

tive estimate of active deep groundwater fluxes through the bedrock

aquifers that are available for promoting primary mineral weathering

reactions and alterations of the primary, that is, depositional porosity

of the deep CZ structure. Finally, an improved understanding of sea-

sonal streamflow generation processes (one of the main contributions

of this work) provides a much needed foundation for future studies

that evaluate various transit time distributions and hydrochemical

response models.

ACKNOWLEDGMENTS

This research was supported by the National Science Foundation

Grant EAR‐1331408 in support of the Catalina‐Jemez Critical Zone

Observatory; student research grant from the Geological Society of

America to RD; research grant from Water Resources Research Cen-

ter, The University of Arizona, to T. M., T. F., and J. M. Furthermore,

this research work is supported by the research and travel grants to

the corresponding author from the Graduate and Professional Student

Council at the University of Arizona. In terms of individual support, we

would like to thank Mr. Michael Stanley, Manager, Mt. LemmonWater

District, Nathan S. Abramson, Matej Durcik, Mary Kay Amistadi, Alissa

White, Tyler Rockhill, Andres Sanchez, Marisa Earll, and Nicole Weber.

We would also like to thank Dr. F. Liu, Department of Agriculture and

Environmental Science, Lincoln University, Missouri, for his EMMA

method‐related help. The corresponding author would like to thank

Jessie Dwivedi for her editorial help and their children, Darcy and

Noah Dwivedi, for their patience while she reviewed various versions

of this work. Finally, we would like to thank the anonymous reviewers

for their comments and suggestions that helped us improve the quality

of this work. All the data sets used in our work are available publicly at

http://criticalzone.org/catalina‐jemez/data/datasets/.

ORCID

Ravindra Dwivedi https://orcid.org/0000-0001-9369-132X

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How to cite this article: Dwivedi R, Meixner T, McIntosh JC,

et al. Hydrologic functioning of the deep critical zone and con-

tributions to streamflow in a high‐elevation catchment: Testing

of multiple conceptual models. Hydrological Processes.

2019;33:476–494. https://doi.org/10.1002/hyp.13363