Streamflow Depletion Modeling: Methods for an Adaptable and Conjunctive Water

Management Decision Support Tool

Xander Huggins, Tom Gleeson , Hailey Eckstrand, and Ben Kerr

Research Impact Statement: Developed a transparent, transferable methodology for quantifying howgroundwater pumping depletes streamflow relative to environmental flows.

ABSTRACT: Groundwater pumping depletes streamflow, which can have significant ecological impacts depend-ing on the magnitude of depletion relative to environmental flow needs. Streamflow depletion estimates fromgroundwater pumping have been quantified using both analytical and numerical methods, but are not routinelycompared to environmental flow needs or used in practical water management tools. Decision support tools thatincorporate groundwater dynamics are becoming increasingly necessary for water managers as groundwaterregulations become more important in environmental policy, particularly concerning the preservation of environ-mental flow needs. We develop and apply methods for a web-based decision support tool for conjunctive ground-water and surface water management, demonstrated using a case study watershed in British Columbia,Canada. Open-source data are analyzed with a combination of spatial algorithms and previously developed ana-lytical models, such that the tool can be applied to other regions. Streamflow depletion estimates are calculatedin four regions in the largely undeveloped Bulkley Valley, British Columbia. Our transparent methodology hasgeographic and data input flexibility which is a significant improvement on currently existing water manage-ment tool methods.

(KEYWORDS: streamflow; streamflow depletion; environmental flow; groundwater hydrology; groundwatermanagement; surface water/groundwater interactions; watershed management; geographic information system(GIS); geospatial analysis.)

INTRODUCTION

Groundwater and surface water resources areintrinsically connected (Winter et al. 1998) andgroundwater abstraction inevitably leads to stream-flow depletion, defined as the loss of streamflow dueto pumping (Barlow and Leake 2012; Konikow andLeake 2014). Groundwater withdrawals causedecreased groundwater discharge (baseflow) and/orincreased stream infiltration to aquifers (Chen andShu 2002). Streamflow depletion can reduce

streamflow below local water requirements such asthe ecological flow needs of the stream (Sophocleouset al. 1995; Baldenkov and Shtengelov 2015). Inextreme cases, groundwater abstractions can trans-form a perennial stream to an ephemeral one, as hasbeen observed in the High Plains aquifer for example(Gleeson et al. 2010). Compromising environmentalflow needs results in detrimental impacts on aquaticecosystems, water quality, and biotic interactions(Watson et al. 2014), meaning environmental flowsare an important consideration when evaluating pro-posed groundwater developments.

Paper No. JAWRA-17-0096-P of the Journal of the American Water Resources Association (JAWRA). Received August 9, 2017; acceptedMay 7, 2018. © 2018 American Water Resources Association. Discussions are open until six months from issue publication.

Department of Civil Engineering (Huggins, Gleeson), University of Victoria, Victoria, British Columbia, CAN; and Foundry Spatial Ltd.(Eckstrand, Kerr), Victoria, British Columbia, CAN (Correspondence to Gleeson: tgleeson@uvic.ca).

Citation: Huggins, X., T. Gleeson, H. Eckstrand, and B. Kerr. 2018. “Streamflow Depletion Modeling: Methods for an Adaptable and Con-junctive Water Management Decision Support Tool.” Journal of the American Water Resources Association 1–15. https://doi.org/10.1111/1752-1688.12659.

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Streamflow depletion has been assessed using bothsimple analytical solutions (e.g., Glover and Balmer1954; Jenkins 1968; Hunt 1999) and more complexnumerical models (e.g., Eggleston et al. 2012; Nielsenand Locke 2012; Starzyk 2012). Numerical modelsprovide the opportunity to represent system featuresthat cannot be included in analytical solutions suchas three-dimensionality, complex and realistic rivergeometries, spatial variability of hydraulic propertieswithin hydrogeologic units, and recharge. However,numerical models are also more computationallyexpensive, require data that are often not available,and are specific for the region of study, thus they arenot readily transferable between regions. For thesereasons, we focus on analytical solutions that havebeen evaluated generally (Christensen 2000; Rath-felder 2015), compared to numerical solutions (Sopho-cleous et al. 1995; Rathfelder 2015), tested andvalidated in a single drainage ditch (Hunt et al.2001) and compared to a numerical model from onespecific hydrologic environment: humid, low topogra-phy Michigan (Reeves et al. 2009; Li et al. 2016).Analytical models solve the unsteady groundwaterflow equation (Theis 1941) and differ by their geomet-ric and hydrogeologic simplifications. Early analyticalmodels are based on significant geometrical andhydrogeological simplifications, such as a stream ofinfinite length, linear geometry, homogeneous aquiferproperties, and a nonimpeding, fully penetratingstreambed (Glover and Balmer 1954). Later, morecomplex analytical models have been developed forpartially penetrating streams with streambed conduc-tance and semiconfined or layered aquifers (Hantush1965; Hunt 1999, 2009; Singh 2003; Ward and Lough2011). A central and critical component of analyticalmodel selection is the evaluation of data availabilityand reliability.

The most prominent online, conjunctive, manage-ment screening tool to date is the State of Michigan’sWater Withdrawal Assessment Tool, developed toprevent adverse resource impacts, improve publicunderstanding of groundwater withdrawal impacts,minimize water use conflicts, and facilitate planningfor sustainable water use (Hamilton and Seelbach2011). The Water Withdrawal Assessment Tool inte-grates three models sequentially: a groundwaterwithdrawal model, a streamflow model, and a fishimpact model (Miller 2008). The groundwater with-drawal model implements a modified version of theHunt (1999) analytical model (Reeves et al. 2009).The online tool allows users to input a proposedwater withdrawal with a specified location, pumpingcapacity, well casing depth, aquifer type, pumpingschedule, and withdrawal source. The final output,an aggregate of the three sequential models, is theevaluation of how the proposed groundwater

withdrawal fit within a four-category “AdverseResource Impact” zonal rating which quantifies theability of the affected streams to support fish popula-tions. Zone A indicates a low risk of causing anadverse resource impact, zones B and C indicateincreasing risk, and zone D indicates that an adverseresource impact would occur, and which wouldrequire a site-specific review before developmentcould occur (Hamilton and Seelbach 2011).

The Water Withdrawal Assessment Tool was a sig-nificant advance in interactive and conjunctivegroundwater and surface water management since itexplicitly considers low flows, the thermal regimesthat support fish populations, and multiple with-drawal sources. However, the tool also possesses limi-tations. The Water Withdrawal Assessment Tool isapplicable solely for the state of Michigan as it usesspatial models that were developed to suit the localgeologic and ecologic characteristics throughout thestate and as its data are partially proprietarilysourced. Additionally, the Tool’s Report Assessmentlacks transparency and specificity through its zonalresults. To our best knowledge, the methods for anonline and interactive tool for conjunctive water man-agement that is geographically flexible, that operatessolely on open-source data, and that quantitativelyevaluates and presents streamflow depletion esti-mates at the resolution of individual stream reachesdo not exist.

Our objective was to develop and apply themethodologies for a novel, interactive decision sup-port tool for conjunctive water resources manage-ment. The motivation for the development of such atool is to provide resource managers, water users,and other stakeholders with an easily accessibleview of the current and future cumulative effects ofwater withdrawals from surface and groundwatersources. In this study, we apply the most feasibleand appropriate analytical models to a case studywatershed in British Columbia, Canada, with noveland replicable methods that can be applied acrossany geography with sufficiently available and appro-priate data.

METHOD DEVELOPMENT

Data Requirements

Streamflow depletion models have three generaldata requirements: surface water data, groundwaterabstraction data, and hydrogeologic data (Figure 1).Surface water data include the stream network withflow rates, stream widths, streambed properties, and

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streambed penetration (Figure 1a). Stream networkswith flow rates have been mapped globally, forexample, by Lehner et al. (2008) as well as at higherresolution (Chapman et al. 2012; Carlisle et al.2016). However, stream width, streambed proper-ties, and stream penetration are generally poorlyknown and mapped. Well withdrawal data consist ofwell location, depth, pumping rates, and operationdates or schedules (Figure 1a). Well locations anddepths are generally available but well pumpingrates and operation dates or schedules are generallyrarely available. Hydrogeologic data can consist ofaquifer and subsurface properties such as porosity,permeability, hydraulic conductivity, aquifer thick-ness, transmissivity, storativity, and thus aquiferdiffusivity (Figure 1b). The availability of hydrogeo-logical data varies greatly. All of the aforementionedhydrogeological data are available for select regions,but this availability is not universal. Porosity andpermeability (which can be subsequently convertedto hydraulic conductivity and transmissivity) havebeen mapped globally (Gleeson et al. 2014; de Graafet al. 2015). Other data such as anisotropy, hetero-geneity, or storativity, however, have not beenmapped or estimated globally or even systematicallyacross any continent to the best knowledge of theauthors (Figure 1b). Aquifer properties can also bequantified with the parameter aquifer diffusivitywhich is the ratio of transmissivity and storage.Globally available porosity and permeability datawere selected as the base hydrogeologic data layerin this method.

To ensure the method consistently uses the best-available data, we overlay and replace low-resolutiondata with higher resolution data where available. Asan example, low-resolution coarse hydrogeologic data,shown in Figure 1b, can be directly overlain andreplaced by local, higher resolution hydrogeologicdata (Figure 1c). Thus, streamflow depletion esti-mates utilizing this method will be more accurate inlocations where more data are available in higher

resolutions, yet calculable for all locations, regardlessof data resolution. Thus, estimates determined withthis method possess varying degrees of physical accu-racy, as determined by local data resolution and qual-ity. The benefit of this method is to allow forstreamflow depletion estimates to be attuned withlocal data availability and quality, yet to consistentlyprovide streamflow depletion estimates in any loca-tion meeting minimum data requirements, often inregions where no streamflow depletion estimates cur-rently exist. While hydrogeologic data were used inthe example above, the same “overlay-and-replace”process can be applied to all other required data. Forexample, regional-scale stream networks may beinclusive of only higher order perennial streams andrivers, while local-scale watercourse data may appendlower order streams to the watercourse network. Sim-ilarly, regional-scale groundwater abstraction datamay only include commercial and industrial waterwithdrawals, while local-scale well data may includedomestic water wells. In regions where variablestreamflow data such as mean monthly streamflowsare unavailable, mean annual streamflow data maybe used. Thus, the method uses all available data,and then preferentially selects, based on scale, thedata to use to ensure the best possible depletion esti-mates given the local data availability.

Analytical Models

Since the layering of hydrogeologic systems andthe distribution of confined aquifers is generallypoorly understood and mapped globally, contempo-rary analytical models such as Hunt (2009) or Wardand Lough (2011) that incorporate these settings arenot appropriate for the geographic flexibility thismethod seeks. Instead, we focus on analytical modelsof unconfined aquifers in connection with adjacentstreams, selecting a low complexity model (Gloverand Balmer 1954; henceforth referred to as the

FIGURE 1. (a) Generic watershed with a homogeneous subsurface and randomly located wells. Blue lines represent surface watercourses,and black dots represent wells. (b) The same watershed, now incorporating low-resolution hydrogeologic data, represented by red, blue, pur-ple, and green layers indicating distinct hydrogeologic units. (c) The same watershed, with high-resolution hydrogeologic data replacing low-resolution hydrogeologic data where available, with the yellow layer representing the high-resolution hydrogeologic unit. It can be seen thatthe low-resolution hydrogeologic data are retained where no better alternative data exist.

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Glover method) and a moderate complexity model(Hunt 1999; henceforth referred to as the Huntmethod). Glover and Balmer (1954) derived an earlyand highly simplified analytical solution for stream-flow depletion similar to Theis’ (1941) solution (Singh2000) but with a fully penetrating stream as oneboundary condition (Figure 2a). Major limitations ofthis solution lie in its simplifying assumptions(Table 1). Therefore, the Glover method providesenvironmentally conservative estimates, and actualstreamflow depletion may be significantly less thancalculated for a given pumping time. However, theGlover method was selected to be the first analyticalmodel due to its ease of implementation, with onlyfour required input parameters: the pumping rate ofthe well, the well to stream distance, and the aqui-fer’s transmissivity and storativity. Where availablehydrogeological data can be sparse across regions, asolution that requires minimal data inputs is impor-tant. The governing equation of the Glover method is:

DQs

Qw¼ erfc

ffiffiffiffiffiffiffiffiffiffiffiSyd2

4st

r !; ð1Þ

where DQs is streamflow depletion [L3/T], Qw is thewell’s pumping rate [L3/T], Sy is the aquifer’s specificyield [–], d is the shortest well to stream distance [L],s is the aquifer’s transmissivity [L2/T], and t is timesince the beginning of pumping [T].

Hunt (1999) derived a slightly more complex ana-lytical solution that incorporates streambed impe-dance and a nonfully penetrating streambed throughthe thickness of the aquifer (Figure 2b). Key differ-ences from the Hunt model, when compared to theGlover model, lie in the simplifying assumptions(Table 1), most notably: the semipervious streambed,and the partial penetration of the streambed throughthe aquifer that are accounted for in the Hunt model.

Both dynamics are included in Hunt’s governingequation, which is presented below.

DQs

Qw¼ erfc

ffiffiffiffiffiffiffiffiffiffiffiSyd2

4st

r !�

expk2t4Sy

sþ kd

2s

!erfc

ffiffiffiffiffiffiffiffiffiffik2t4Sy

s

sþ

ffiffiffiffiffiffiffiffiffiffiffiSyd2

4st

r0@

1A;

ð2Þ

where k is streambed conductance [L/T].The Hunt method builds from the Glover method and

will produce a depletion less severe than would be pre-dicted by the Glover method for given pumping timesshorter than the time required to reach a new steadystate. The Hunt method introduces a term for streambedconductance, k, defined as the product of the width andthe hydraulic gradient of the streambed divided by thethickness (Christensen 2000), and represents the abilityof the streambed to conduct water between the streamand the subsurface (Chen and Shu 2002). Verticalhydraulic conductivity and stream dimensions are veryrarely available thus approximations are required.Reeves et al. (2009) considered the vertical aquifer con-ductivity and depth as an approximation of thestreambed conductance term in the following:

k ¼ wKv

ds; ð3Þ

where w is streambed width [L], Kv is verticalhydraulic conductivity [L/T], and ds is vertical dis-tance between streambed and top of well screen [L].

Reeves et al. (2009) further suggested that verticalhydraulic conductivity is approximated at one-tenthof the horizontal hydraulic conductivity, and welldepth be used as an approximation of the vertical dis-tance between the bottom of the streambed and the

FIGURE 2. Representative cross sections of: (a) the Glover and Balmer (1954) solution and (b) the Hunt (1999) solution.A fully penetrating stream, without streambed, can be seen in the Glover cross section, while a partially penetrating stream,

with streambed, can be seen in the Hunt cross section.

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top of the well screen, resulting in the following, sim-plified version of Equation (3):

k ¼ sw10bdw

; ð4Þ

where s is transmissivity [L2/T], b is aquifer thick-ness [L], and dw is well depth [L].

We adopt the same approximations as made in theState of Michigan’s Water Withdrawal AssessmentTool (Reeves et al. 2009) with further minor modifica-tions. First, due to the topography, particularly inmountainous regions, the bottom of wells can belocated above streams which result in negative dw

values and thus negative values for k, which are notphysically meaningful. Therefore, we replace dw withthe absolute value of ds (vertical distance betweenstreambed and top of well screen) to represent verti-cal elevation difference. Second, some combinations ofparameter values in Equation (4) lead to large valuesof streambed conductance (k ≫ 1) even though k isgenerally considered to be �1 such as 10�3 or 10�4

(Christensen 2000; Hunt et al. 2001). Large k lead toEquation (2) being computationally unsolvable onstandard computing devices due to large exponents(> order 200) within the complementary error term inEquation (2), exceeding maximum precision limits.We therefore set an upper limit of k = 1 by setting allk > 1 to k = 1, and conducted a sensitivity analysis todetermine if this upper limit impacted results. In allcases, streamflow depletion for situations where largek were reset to k = 1, produced insignificant differ-ences in the modeled streamflow depletion.

Two approaches were considered for estimatingstream width. The first method was consistent withthe approach taken by de Graaf et al. (2015) in theirhigh-resolution, global-scale groundwater model, anempirical formula from Lacey (1930):

Wchn � Pbkfl ¼ 4:8�ffiffiffiffiffiffiffiffiffiffiffiQbkfl

p; ð5Þ

where Wchn is stream width [L], Pbkfl is wettedperimeter at bankfull flow [L], 4.8 is an empiricalcoefficient [T0.5/L0.5], and Qbkfl is stream discharge atbankfull flow [L3/T].

The second method took the approach of Reeveset al. (2009) which utilizes drainage area to derivestream width. This formula is presented below.

w ¼ 3:28 � 10ð0:522358�logðda�1:60932Þ�0:18786Þ; ð6Þ

where w is bankfull stream width [L] and da is drainagearea [L2]. The second approach was selected for imple-mentation for a number of reasons: (1) stream widthresults were found to be more accurate within the studyarea, (2) the method does not require bankfull dischargeestimates which are not widely available, and (3) exist-ing streamflow depletion assessment tools employ simi-lar methodologies.

Depletion Apportionment

A well withdrawing water may impact streamflowin multiple streams, thus the depletion caused by any

TABLE 1. Assumptions for the Glover and Hunt methods.

Glover method assumptions Hunt method assumptions

• Stream is straight, infinitely long

• Constant stream stage

• Streambed penetrates entire thickness of aquifer

• No streambed impedance

• Aquifer has constant thickness

• Aquifer has infinite extents; lateral boundaryconditions do not influence the responseto pumping

• Aquifer materials have homogeneous properties

• Aquifer is bound, at bottom, by impervious layer

• Stream is only source of recharge

• Operating well is screened over entire aquiferthickness

• Pumping rate is constant, steady

• Water table drawdown due to pumping isnegligible

• Stream is straight, infinitely long

• Constant stream stage

• Aquifer has constant thickness

• Aquifer has infinite extents; lateral boundaryconditions do not influence the response to pumping

• Aquifer is homogeneous and isotropic in allhorizontal directions

• Water table drawdown due to pumping is negligible

• Streambed cross section has horizontal andvertical dimensions negligible to the saturatedaquifer thickness

• Pumping rate is constant, steady

• Seepage flow rates from the stream into theaquifer are linearly proportional to the changein piezometric head across the semipervious layer

• The Dupuit approximation

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well must be apportioned between impacted streams.Reeves et al. (2009) examined different stream appor-tionment algorithms for a single watershed in Michi-gan, finding that none of the methods produced astatistically significant difference in error characteris-tics compared with a numerical groundwater model.Reeves et al. (2009) thus implemented an inverse dis-tance weighting apportionment method since it: (1)produced a reasonable overall pattern of streamflowdepletion compared with the numerical model, (2) isthe most straightforward to implement in a web appli-cation, and (3) has some theoretical basis (Wilson1993). While Reeves et al. (2009) utilized inverse dis-tance weighting, this methodology employs squaredinverse distance weighting apportionment approach tominimize the summative weighting of numerous dis-tant stream reaches from skewing the depletion esti-mates for the most proximal streams.

fi ¼1d2i

Rj¼1;n1d2j

; ð7Þ

where fi is the fraction of pumping rate attributed tostream reach i, di is the distance from well to streamreach i, and n is the number of stream segmentsaffected by well.

Based on an assumption that each well’s cone ofdepression propagates at equivalent rates and

magnitudes in all radial directions, as is requiredwhen implementing squared inverse distanceweighted apportionment, a spatial algorithm was cre-ated that determines the nearest point on eachstream reach that is linearly exposed to the well. Thespatial algorithm generates 360 straight lines at one-degree increments propagating radially away fromthe well. At each intersection of a line vector and astream reach, the distance is calculated between thatintersection with the stream and the well. Wheremany straight line vectors intersect with a commonstream reach, the distance associated with the near-est intersection per stream reach was retained. Thisdistance was subsequently used to perform thesquared inverse distance weighting process. It is withthese identified stream reaches, and their respectivedistances that the inverse distance squared weightingis applied (Figure 3). It should be noted that onlystream reaches directly exposed to the well (i.e., withno surface water features existing directly in-betweenthe stream reach and the well) are considered in thedepletion apportionment process. While streamreaches that are not exposed to the well do notreceive direct apportionment in the depletion calcula-tions, they may well still be predicted to deplete dueto associative depletion estimates in their upperreaches.

The depletion relationship between each well andstream reach, as dictated by the analytical model

FIGURE 3. Conceptual depiction of the streamflow depletion apportionment method, for an artificial scenario where only one well is in thevicinity of a stream network. It can be seen that only stream reaches C, G, and H will receive apportioned streamflow depletion from theoperating well. Stream reaches A, B, D, E, and F will not be apportioned streamflow depletion as they are not linearly exposed to the operat-ing well. The stream reaches C, G, and H will have their depletion estimates calculated with the distances of c, g, and h, respectively, as dic-tated by their nearest point to the operating well. In this scenario, the depletion experienced by stream reach G would include the depletionapportioned to its upstream reach C.

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applied, is preserved throughout the apportionmentprocess. Thus, it is possible for a stream receiving lessapportionment from one well than another stream toexperience greater depletion if the first stream hashigh transmissivity material between it and the well.Ultimately, the cumulative depletion in a surfacewater network by a well is limited by its abstractionrate; however, the rate of progress of depletion isdetermined by individual well-stream reach dynamicsand the distribution of apportionments between them.In sum, the estimated volumetric depletion perstream reach is calculated at any given time throughthe product of the operating well’s steady pumpingrate, the value of the Hunt or Glover equation (ratioof volumetric depletion to pumping rate) at the giventime, and the apportioned percentage of streamflowdepletion allocated to the specific stream reach. Sub-sequently, this estimated volumetric depletion can benormalized to predepletion streamflow rates utilizingthe formula presented below:

SFDN ¼ DQQNaturalized

� 100; ð8Þ

where SFDN is normalized streamflow depletion [%],DQ is the estimated change in streamflow due topumping [L3/T], and QNaturalized is the naturalized,nondepleted estimated streamflow [L3/T].

The streamflow depletion apportionment method isinfluenced by the structure of the spatial data repre-senting the stream network. The algorithm identifiesunique reach entities in the data, but does not distin-guish these reaches by length or modify the appor-tionment to incorporate reach length or geometricrelationship or angle of exposure into the calculation.This will result in increased depletion being allocatedto segmented stream reaches exposed to operatingwells, and decreased depletion being allocated to long,nonsegmented stream reaches also exposed to thesame operating wells. Thus, directional inequalitiesof depletion exist in this method, yet to our bestknowledge, a better alternative does not exist. Theeffect of river geometry between wells and associatedstreams has also been determined to be a factor dueto the length of river that is exposed to pumping (Liet al. 2016). Additionally, in this methodology, lakesand ponds are treated as stream reaches. Thethroughflow rate of the water body is used asthe stream reach’s flow rate, and the spatial extent ofthe water body is considered in the apportionment pro-cess. Perched lakes were not considered in the develop-ment of our method, which stands as a limitation ofthe methodology, yet are also a class of lakes which donot apply to the analytical models utilized herein.

All wells are modeled to estimate streamflowdepletion from their recorded start date of pumping

operations. Thus, streamflow depletion estimates forpresent time will include the progressed depletionimpacts of the preexisting well network, as willstreamflow depletion estimates for a specified time inthe future with the further developed impacts of saidpreexisting wells. Where pumping schedules are notspecified in the best-available data, constant pumpingrates are assumed. In the governing analytical equa-tions of our method (Equations 1 and 2), the parame-ter of time simply needs to be consistent with theother parameters whose dimensions include thedimension of time. In our method, we calculate allstreamflow depletion estimates with the time unit ofdays but report all estimates at a monthly frequency.

CASE STUDY

A case study was conducted to demonstrate thefeasibility and function of the methods presentedabove and the necessity of such a water managementdecision support tool. The case study watershed ofthe Bulkley Valley (British Columbia, Canada) wasselected due to its topographical variation (boundedby the Hudson Bay and Babine Mountains), its vari-ety of watercourse sizes (from ephemeral headwatersto the 260-km long Bulkley River), and its spectrumof development (from undeveloped regions to townssuch as Smithers, population approximately 5,000).The stream network and well locations were derivedfrom the British Columbia Freshwater Atlas (Pro-vince of British Columbia 2010), and wells data (Pro-vince of British Columbia 2017) which are both freelyavailable to the public. A hydrologic model was previ-ously developed for the region after Chapman et al.(2012) and used to determine naturalized monthlyaverage flow for stream reaches. Global-scale hydro-geological data were retrieved from the freely avail-able GLobal HYdrogeology MaPS (GLHYMPS) ofpermeability and porosity (Gleeson et al. 2014). Moredetailed aquifer data were accessed through the Bri-tish Columbia Ministry of Environment’s aquifersdatabase (Province of British Columbia 2011).

As depicted in Figure 4, four regions within thestream network in the Bulkley Valley were selectedfor modeling streamflow depletion. The four regionswere visually selected, based on the intentionsto select regions that captured a representativespectrum of the topography and stream networkcomplexity present in the Bulkley Valley. Thedetailed, step-by-step methods developed are pre-sented throughout this section for the West Topleyregion, while final depletion estimates are ultimatelyprovided for all four case study regions. Figure 5

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demonstrates the depletion apportionment process forboth a single well and the complete, more complex wellnetwork in the West Topley region. In the well net-work, each well has its spatially assigned hydrogeo-logic data, which is implemented in tandem with theinverse distance squared weighting apportionment toeach individual stream reach to create a unique rela-tionship between each well and every stream reachexposed to it. The number of relationships simultane-ously modeled is illustrated by the number of greenlinkages, which become numerous even in a small casestudy such as this.

To illustrate the process of the tool, results areprovided in Figure 6 by increasing levels of complex-ity, and demonstrated in the West Topley case studyregion. To begin, we look at the simplest level ofanalysis: the depletion a single well imparts on a sin-gle stream (Figure 6a). This calculation is performedas if no other streams or stream reaches exist. Pre-dictably, this depletion estimation is significant as itis not apportioned among streams. Subsequently(Figure 6b), we look at the depletion that a singlewell imparts on the entire stream network. Depletionapportionment is performed in this step, thus thedepletion from the single well is allocated betweenall exposed stream reaches. Figure 6c introduces theentire well network and presents the depletion dueto the entire well network on the entire streamnetwork, applying the same methodology used in theFigure 6c but simultaneously for every well in thenetwork. Lastly, in Figure 6d, a proposed well inthe well network is implemented to simulate a well

proposal query, imitating the ultimate purpose of themethodology. The proposed well was modeled at thedepth of the average groundwater well in BritishColumbia, approximately 49.8 m (as determined fromthe British Columbia Ministry of Environment welldataset), and with a continuous pumping rate of 100gallons per minute. For simplicity, the results pre-sented in each component of Figure 6 are the resultsof the Glover method, calculated to the month ofAugust in 2050.

To demonstrate the fine temporal specificity of thedeveloped methods, Figure 7 presents streamflowdepletion estimates using both the Glover methodand the Hunt method for four representative monthsof the years 2016 and 2050, and represents a scenarioinclusive of the complete well network. The methodsallow for depletions to be calculated at any time inthe future. The four months presented in Figure 7(February, May, August, and November) weredeemed by the authors to be representative monthsof every season, and sufficient to present as to avoidpresenting all 12 months for both methods and forboth years (2016 and 2050).

Figure 8 quantifies the variation between methodsmore explicitly than in Figure 7 by showing the nor-malized depletion results for the stream reach in theWest Topley case study region with the smallest flowrates. The results are presented for each month ofthe year, showing the depletion estimate progression.The bottom of each bar represents the 2016 depletionestimate (denoted with a hollow circle), and the top ofeach bar represents the 2050 depletion estimate

FIGURE 4. The location of the Bulkley Valley watershed within British Columbia and the four case study locations within the watershed.

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(denoted with a filled circle), per method. The Glovermethod always begins with initial depletion estimatesthat are greater, and that progress at a faster rate,than the Hunt method, as discussed in AnalyticalModels. The Glover method results predict thestream would be entirely depleted for seven monthsof the year by 2050 (months January, February,March, July, August, September, and December). Theinitial depletion estimate in the month of August,thus for the year 2016, using the Glover method pro-duces an estimate already at 100% of naturalizedstreamflow and is the reason why no progress bar isvisible for the month. However, when observing Huntmethod results, it can be seen that only the month ofAugust has flows that are vulnerable to becomingcompletely depleted by the well network operatingstatus quo. Significantly, the Hunt method showsmonths January, February, March, July, August,September, and December having depletion estimatesexceeding 20% by or before the year 2050. Thus, theHunt method still provides valuable insight regardingstreamflow depletions while being less inflated andmore physically relevant than the Glover method.

To illustrate the geographic flexibility of the meth-ods presented above, the analysis conducted on theWest Topley case study region thus far is replicatedover three other geographies within the Bulkley Val-ley watershed, as identified in Figure 4. The resultspresented below, in Figure 9, are for the four charac-teristic months in the year 2050 (as presented in Fig-ure 7), using only the Hunt method. The depletion

estimates that envelop a lake represent normalizeddepletions as if the lake were simplified to itsthroughflow rate; however, inverse distance weight-ings for apportionment are calculated to the nearestshoreline of the lake. Across geographies, the devel-oped methods estimate streamflow depletions dynam-ically through time, identify depletions that wouldindicate threatened environmental flows of streams,and support the need for environmental foresight ofgroundwater withdrawals through governance.

DISCUSSION

The primary utility of the methodology will be inproviding initial assessments of conjunctive surfacewater and groundwater sustainability. The Glovermethod consistently provides depletion estimates fargreater than the Hunt method for the time spans inwhich they were evaluated but both methods havesignificant geometric and hydrogeologic simplifica-tions. In areas where a more complete knowledge ofthe subsurface is available, more complex numericalinvestigations are advised.

The use of the methods in the study region proved tobe a successful application of integrated streamflowdepletion analytical models using open-sourced data.The study region revealed individual stream reachesthat are at risk of depleting below ecological flow

FIGURE 5. Stream apportionment algorithm results for (a) a singular well and (b) a small well network.

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needs, and even more pronounced instances of streamreaches estimated to turn ephemeral due to stream-flow depletion from groundwater abstraction. Themajor limitation of the methodology remains dataavailability and, subsequently, the necessary simplify-ing assumptions required to enable the use of availabledata. While data availability is significantly increasedthrough the strategy of utilizing open-sourced data,uniform data coverage over broad geographies islacking. We hope that tools similar to those thatthis methodology would support will motivate theincreased collection and release of data. Both the

Glover and the Hunt analytical models were devel-oped under assumptions that are often inconsistentwith physical realities (Table 1). The assumptions ofstraight streams of infinite length, constant stage,and homogeneous and isotropic aquifers of constantthicknesses and infinite horizontal extents that existin both models, severely reduce the quantitative per-tinence of both models. The Glover model, whichassumes a streambed penetration of the entire thick-ness of the aquifer, and neglects streambed impe-dance, even less resembles typical physicalconditions.

FIGURE 6. Streamflow depletion model results presented with incremental complexity. (a) Where a single operating well is depleting themost proximal stream with unapportioned impacts. (b) Where a single operating well is depleting the adjacent stream network with appor-tioned impacts. (c) Where the network of existing wells is depleting the adjacent stream network with apportioned impacts. (d) Where thenetwork of existing wells with the addition of a proposed well is depleting the adjacent stream network with apportioned impacts. All resultsare presented for August 2050, utilizing the Glover method and demonstrate the additive effects of multiple wells within a network.

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FIGURE 7. Normalized streamflow depletion results for the West Topley case study region, as depicted in Figure 4,for (a) the Glover method in 2016, (b) the Hunt method in 2016, (c) the Glover method in 2050, and (d) the Hunt method in 2050.

All results are presented for the months of February, May, August, and November.

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A limitation in testing this methodology is thatstreamflow depletion is not a directly measurablephenomenon, so existing streamflow observations ormodels in the case study region of the Bulkley Valley(British Columbia, Canada) cannot be used directlyfor validation of the methodology. However, and asaforementioned, the utility of this method is to sup-port an initial water management screening tool forlocations that have no currently existing water man-agement modeling results. Furthermore, the authorsdo not claim this method to be equivalent of any site-or region-specific study, but rather an initial tool forwater managers to consult. The novelty of the pre-sented methodology is most evident in (1) its flexibil-ity that enables screening-level, streamflow depletionestimates to be made over any geography where theminimum data requirements exist; (2) how environ-mental impacts are not aggregated and presented incategorical or zonal scores, but in explicit streamflowdepletion quantities at a stream reach resolution andat any month within the simulation period; and (3)the spatial algorithm created for the apportionmentof streamflow depletions is an advancement on

technological ability to model complex hydrogeologicaldynamics proportionately.

This methodology extends the State of Michigan’sWater Withdrawal Assessment Tool, making neces-sary modifications to enable a comparable equivalentwherever sufficient data exist, while makingimprovements to its function and its presentation ofresults, as identified by the authors. Particular modi-fications in the technical approach to that of theWater Withdrawal Assessment Tool include modifica-tions in determining streambed conductance values,particularly in taking the absolute value of the wellbottom to stream elevation difference and in puttinga limit on the streambed conductance value, in esti-mating streamflow depletion on the time scale ofdecades into the future, in employing square inversedistance weighting apportionment as opposed toinverse distance weighting, and in developing thespatial algorithm to execute the apportionmentprocess, as described above. While the Water With-drawal Assessment Tool will remain more pertinentfor the state of Michigan, this methodology willallow any region meeting the minimum data

FIGURE 8. A comparison between (a) the Glover method and (b) the Hunt method for approximating streamflow depletion. The selectedstream utilized for this comparison is buffered in red, and is subject to one operating well, unapportioned among other streams. The bottomof each bar in the graph above (hollow circle) indicates the estimated normalized depletion in 2016, while the top of each bar (filled circle)represents the estimated depletion in 2050. It should be noted that the Glover model result for the month of August begins in 2016 at valueof 100% of mean monthly discharge, and thus its progress bar is not visible.

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FIGURE 9. Normalized streamflow depletion results for the four case study locations: (a) North Smithers, (b) South Smithers, (c) Telkwa,and (d) West Topley, as depicted in Figure 4. Results are reported for the months of February, May, August, and November for the year

2050 using the Hunt method. The variability and severity of normalized depletion is perhaps best observed in (b) South Smithers.

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requirements to execute and consult preliminary,screening-level groundwater-driven streamflow deple-tion estimates.

CONCLUSIONS

Here, we present a methodology to analyticallymodel streamflow depletion at unprecedented detail,per stream reach and per month until the year2050. Our use of open-source data enables geo-graphic adaptability in implementation. The resultsimprove our ability to proactively and conjunctivelymanage water resources including environmentalflow needs:

1. The methodology is an advancement on theapplication of open-sourced groundwater andsurface water analytical methods to supportinformed, proactive decision-making and sustain-able development of groundwater resources,especially to better safeguard ecological flowneeds.

2. The method’s main successes are in the imple-mentation and optimization of a wide variety ofopen-source data, its utilization of multiple well-known analytical models, and the development ofa novel spatial algorithm to apportion and simul-taneously model streamflow depletions acrossnumerous unique stream-well interactions.

3. The method marks an advancement in explicitdepletion estimate result presentation, allowingfor numeric depletion estimates to be viewed perstream reach, at monthly time intervals, fromtime present through 2050.

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