Document [original]

RESEARCH ARTICLE

Enhancing urban runoff modelling using water stable isotopes

and ages in complex catchments

Aaron Smith

| Doerthe Tetzlaff

1,2,3

| Christian Marx

| Chris Soulsby

2,3

IGB Leibniz Institute of Freshwater Ecology

and Inland Fisheries Berlin, Berlin, Germany

Geographisches Institut, Humboldt University

Berlin, Berlin, Germany

Northern Rivers Institute, School of

Geosciences, University of Aberdeen,

Aberdeen, UK

Institute of Applied Geosciences, Technische

Universität Berlin, Berlin, Germany

Correspondence

Aaron Smith, IGB Leibniz Institute of

Freshwater Ecology and Inland Fisheries

Berlin, Berlin, Germany.

Email: aaron.smith@igb-berlin.de

Funding information

Bundesministerium für Bildung und Forschung;

Deutsche Forschungsgemeinschaft; Einstein

Stiftung Berlin; Leverhulme Trust

Abstract

Increased urbanization, coupled with the projected impacts of climatic change, man-

dates further evaluation of the impact of urban development on water flow paths to

guide sustainable land-use planning. Though the general urbanization impacts of

increased storm runoff peaks and reduced baseflows are well known; how the com-

plex, non-stationary interaction of the dominant water fluxes within dynamic urban

water stores sustain streamflow regimes over longer periods of time is less well quan-

tified. In particular, there is a challenge in how hydrological modelling should inte-

grate the juxtaposition of rapid and slower flow pathways of the urban ‘karst’

landscape and different approaches need evaluation. In this context, we utilized

hydrological and water stable isotope datasets within a modelling framework that

combined the commonly used Hydrologic Engineering Center Hydrological Modelling

System (HEC-HMS) urban runoff model along with a simple hydrological tracer mod-

ule and transit time modelling to evaluate the spatial and temporal variation of water

flow paths and ages within a heavily urbanized 217 km

catchment in Berlin,

Germany. Deeper groundwater was the primary flow component in the upper

reaches of the catchment within fewer urbanized regions, while the addition of

wastewater effluent in the mid-reaches of the catchment was the dominant water

supply to sustain baseflow in the lower main stem stream, with additional direct

storm runoff and shallow subsurface contributions in the more urbanized lower

reaches. Water ages from each modelling approach mirrored flow contributions and

water age mixing potential in subsurface storage; with older average water and lower

young water contributions in less urbanized sub-catchments and younger average

water and higher young water contributions in more urbanized regions. The results

from the first step towards more integrated tracer-aided hydrologic modelling tools

for similar peri-urban catchments, given the potential limitations of simpler model

frameworks. The results have broader implications for assessing the uncertainty in

evaluating urban impacts on hydrological function under environmental change.

KEYWORDS

hydrological modelling, urban hydrology, water ages, water stable isotopes

Received: 7 November 2022 Revised: 13 January 2023 Accepted: 13 January 2023

DOI: 10.1002/hyp.14814

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium,

provided the original work is properly cited.

Hydrological Processes. 2023;37:e14814. wileyonlinelibrary.com/journal/hyp 1of17

https://doi.org/10.1002/hyp.14814

1|INTRODUCTION

With an increasing proportion of the global population living within

high-density urban environments (currently >50%, United

Nations, 2018) and the projected impact of climate change on built

areas (Güneralp et al., 2015; Pang et al., 2022), there is a need for con-

tinual improvement of hydrological understanding to provide an evi-

dence base for various stakeholders to make informed decisions

about urban water resources. In particular, the need to maintain the

provision of ecosystem services, such as drinking water supplies or in-

stream flows, which can be dependent on urban groundwaters and

surface waters (European Environment Agency, 2014; Turner

et al., 2021), has increased the importance of evaluating the complex

interactions between evolving urban landscapes and their sensitivity

to hydrological change. While urban environments have been the

focus of many hydrological modelling studies, these have traditionally

focused on engineered drainage and stormwater management, with

limited evaluation of ecohydrological fluxes in urban green spaces,

which can comprise a significant proportion of urban landscapes

(McGrane, 2016). Much of this limited evaluation is due to the inher-

ent complexities of integrating the ‘natural’and ‘engineered’compo-

nents of urban hydrological systems which have very different spatial

patterns and temporal dynamics and thus limit the use of traditional

modelling and analytical approaches (Fletcher et al., 2013). This has

subsequently led to increasing focus in the recent years on character-

izing the spatio-temporal heterogeneity of urban/rural landscape

water interfaces in different geographical settings (e.g. Fidal &

Kjeldsen, 2020). However, there remains a need to understand the

interaction of artificial drainage (and wastewater effluents) and the

more ‘natural’hydrology –sustaining in-stream habitats and dry sea-

son groundwater recharge –of rural and urban green spaces. This

research need is urgent given the rapid urban growth at a time of pro-

jected reductions in water availability in many areas due to climate

change (Nguyen et al., 2010; Olsson et al., 2009).

In the wider field of hydrological modelling, recent trends have

been towards more process-based conceptualizations of catchment

function that have been driven by model and data fusion. In particular,

the increased use of water stable isotopes in undisturbed catchments

has facilitated more detailed studies on understanding upscaling, flow

path evaluation, mixing processes and storage dynamics across a wide

range of environments (Kuppel et al., 2018; Smith et al., 2021; Tetzlaff

et al., 2018). Tracer-aided models in undisturbed catchments generally

conceptualize and quantify the dominant hydrological processes mod-

ulating interactions between fluxes and storage; the related flow path

dynamics and associated water ages. However, urban areas are

‘messy’hydrological systems with complicated juxtaposed (engi-

neered/natural) flow path systems, additional water sources

(e.g. wastewater effluent), operational water diversions (e.g. urban

flood management), abstraction (e.g. crop irrigation, garden use), and

continuous development of rural and urban spaces. Due to the highly

complex nature of urban landscapes and the relatively limited use of

water stable isotopes in urban catchments, there is a high potential

for the use of water stable isotopes and tracer-aided models in urban

areas to provide richer insights into important process interactions

and hydrological impacts (Ehleringer et al., 2016).

To improve understanding of process interactions and water par-

titioning in urban landscapes, there has been an increased use of more

complex ecohydrological modelling approaches to characterize flux

dynamics in urban green spaces (Gillefalk et al., 2022; Ichiba

et al., 2018; Meili et al., 2020). Relatively few of these modelling

approaches utilize tracers such as water stable isotopes to better con-

strain water flux estimations (e.g. Gillefalk et al., 2021). Rather, many

of the recent modelling approaches have sought to transform the

existing modelling frameworks developed for undisturbed watersheds

into urban areas. With the large data requirements needed to con-

strain more physically based ecohydrological models in undisturbed

landscapes (e.g. Kuppel et al., 2018), increased complexities within

urban environments dictate that a similar approach would require an

even more extensive data network (Ichiba et al., 2018). Despite the

data measured from engineered structures (e.g. major abstractions,

wastewater effluent, diversions), data collection is often still con-

strained with limited hydrometric measurements, other than climatic

variables and discharge data. Using this limited data can then result in

over-parameterization of more complex models (Petrucci &

Bonhomme, 2014), and higher uncertainty of the role of more perme-

able urban green space in influencing groundwater recharge and

stream flow generation (McGrane, 2016). Consequently, using isoto-

pic data in more simple modelling frameworks, such as transit time

models and mixing analysis, can provide significant insights into urban

catchment functionality with fewer spatial data requirements and

model parameters. These model frameworks have been successful at

identifying the separation of rapid impervious-influenced flow dynam-

ics from the more permeable areas of urban green space dominated

by subsurface processes (Marx et al., 2021; Soulsby et al., 2014). Fur-

thermore, the inclusion of evaluating water ages and transit times in

such frameworks can provide the added benefit of further under-

standing water movement and mixing in more complex environments.

However, the information content and robustness of urban catchment

hydrological processes gained from models of varying complexities

are not always clear. As such, there is a need for continued explora-

tion of appropriate model complexity to integrate insights from urban

water stable isotopes and take steps towards a more holistic under-

standing of the hydrology of urban areas.

The City of Berlin, Germany, is an extensive urban area

(900 km

) with a population of >4 million people and an annual pop-

ulation growth of 1% per year; it is also situated in a region with

already high water stress and significant water exploitation (European

Environment Agency, 2014). These coupled factors have significant

implications for urban water resources given the projections of

warmer and drier climatic conditions in the coming decades (Huang

et al., 2013; Huang et al., 2015). Extensive surveys of surface water,

groundwater, precipitation (Kuhlemann et al., 2020) and soil water

(Kuhlemann et al., 2021) have characterized the stable isotopic

dynamics in Berlin's hydrological systems over the past 3 years. This

has resulted in considerable insights into the role of different water

sources in driving stream water dynamics. In particular, intensive

2of17 SMITH ET AL.

water stable isotope-based investigations of hydrological processes

have been undertaken within the Panke catchment within northern

Berlin, which has helped quantify the relative influence of the heavily

engineered systems and more natural green spaces on water move-

ment (Marx et al., 2021).

Here, we leverage that water stable isotope data with an explora-

tion of model complexity by incorporating mixing processes with the

Hydrologic Engineering Center Hydrologic Modelling Systems (HEC-

HMS) model, a widely used urban runoff model. We also utilize transit

time modelling to help understand the timescales of water movement

within this intensively urbanized catchment. The overall aim of the

article is to use isotope-aided modelling as the first step in a learning

framework to guide the evolution of more realistic, integrated

approaches to urban hydrological modelling, starting with reduced

parameterization compared with fully distributed, urban ecohydrologi-

cal models. Specifically, we aim to (1) Quantify the spatial and tempo-

ral variability of dominant streamflow components within a heavily

urbanized catchment; assessing in particular, the increasing down-

stream influence of managed effluents and abstractions on the flow

regime. (2) Evaluate hydrological model performance and process con-

sistency through the integration of water stable isotopes and water

age estimation. (3) Assess the change in isotopic dynamics and esti-

mated stream water ages over the length of the stream due to

changes in impervious areas and other anthropogenic influences

(e.g. wastewater treatment plants, WWTP) on mixing. (4) Evaluate the

limitations of this preliminary approach and recommend directions for

quantitative evaluation of hydrological processes with tracers within

urbanizing landscapes.

2|METHODOLOGY

2.1 |Study site background

The Panke is a mesoscale (217 km

) urban catchment; the headwaters

are located in the more rural State of Brandenberg, Germany, the river

then flows through the heavily urbanized landscape of Berlin before

discharging into the River Spree (Figure 1). The catchment is one of

the major tributaries transferring urban runoff from northern Berlin.

Similar to the surrounding region, the catchment has low-lying topog-

raphy, with only 97 m of relief over the length of the catchment

(30 km) and an average catchment slope of 2.4% (Marx et al., 2021).

The soils are heavily disturbed within Berlin, but primarily can be clas-

sified as freely draining sandy loams with smaller regions of loamy

sand. The underlying geology was formed from deposition in the last

glaciation (Frick et al., 2019), consisting of >100 m of Quaternary

deposits (Limberg & Thierbach, 2002). Two aquifer systems are

formed in the near-surface geological units, with a smaller, partially

confined aquifer dominating groundwater-surface water exchange in

the more elevated plateau in the eastern part of the catchment and

the larger, unconfined Panke aquifer controlling flow through the

main Panke valley (Marx et al., 2021).

FIGURE 1 (a) Elevation and

stream channel network

(b) percent impervious surface

cover, location of isotope

measurements and sub-

catchment (SC) locations (Table 1)

measurement locations in (b).

Groundwater aquifer and well

locations are presented in Marx

et al., 2021.

SMITH ET AL.3of17

Vegetation within the Panke encompasses a wide range of land

uses, inclusive of conifer forests (mainly Scots Pine (Pinus sylvestris)

(north-west, Sub-Catchment (SC) 2 in Figure 1), arable land (east, SC4

in Figure 1), and broadleaf trees and grassed areas (Table 1). Urban-

ized areas contribute to approximately 24% of the catchment (Marx

et al., 2021). Broadleaf trees (e.g. oak (Quercus robur) and Birch (Betula

pendula) and grasses dominate urban vegetation types and are found

in more abundance in the southern reaches of the catchment).

The climate within the catchment is warm and temperate, with

maritime influence (Köppen Index Cfb). The average annual precipita-

tion (2011–2020) is 590 mm, with mild annual temperatures

(10.3C) ranging from monthly averages of 1.2C in winter to 20Cin

summer (Figure 2; DWD, 2022). Large summer rainfall events are

driven by high-intensity convective cells which can result in >80 mm

of precipitation within a few hours (Figure 2a), while winter precipita-

tion is more frequent, but is generally lower intensity frontal rainfall.

The region is drought-sensitive, with the most recent drought

(420 mm annual precipitation in 2018) causing limited groundwater

recharge and vegetation stress over extensive parts of the State of

Brandenberg which surrounds Berlin (Kleine et al., 2020; Smith, Tet-

zlaff, Kleine, et al., 2020). Total precipitation is evenly split between

summer and winter rainfall contributions. Short periods of sub-

freezing temperatures can occur in mid-winter (Figure 2b). Humidity

undergoes seasonal cycles, with drier air during the summer (monthly

average 68%) and wetter air during the winter (monthly average 88%)

(Figure 2c).

2.2 |Urban catchment hydrology

Runoff generation in the Panke catchment is naturally dominated by

groundwater flow in shallow sub-aquifers in the east and the primary

unconfined aquifer through the main river valley flowing from north

to south east (Marx et al., 2021). Flow paths through the deeper

groundwater system are decadal to millennial in age, sourcing waters

from outside the catchment as part of a regional aquifer which

encompassed an area from the German-Polish border to Berlin

(Bednorz & Brose, 2017; Massmann et al., 2007).

Anthropogenic influences on catchment characteristics, water

sources and flow paths are extensive throughout the catchment due

to urbanization, land-use management and engineering structures.

Throughout the catchment, urban stormwater overflows (SWOs) are

estimated to contribute an annual average of 0.1 m

/s (10% of

streamflow at the catchment outlet). In the upper reaches of the

catchment, SWOs are comprised of urban runoff (e.g. separate sewer

storm drain), while in the lower reaches combined sewer networks

incorporate higher volumes of water due to urban storm drainage and

urban wastewater. The SWOs in the gauged upstream sub-

catchments (SC1 and SC3, Figure 1b) are nonlinearly underlain with

urban storm drains that discharge directly into the upper Panke during

lower flows and overflow into the urban wastewater system during

higher flows. The other northern headwater catchment (SC2, Figure 1

b) has small contributions from effluent discharging from a Wastewa-

ter Treatment Plant (WWTP); with effluent feeding a wetland and for-

ested area to artificially maintain water levels (0.05 m

/s).

Evapotranspiration from the wetland limits the influence of WWTP

effluent on downstream discharge. Effluent inflow from the large

Schönerlinde WWTP (serving 700 000 people) occurs in the mid-

reaches of the catchment (Figure 1a,1m

/s baseflow), and the previ-

ous water stable isotope analysis has shown it to be the dominant

water source within the main stem of the Panke (Marx et al., 2021).

Increased density of urbanization occurs downstream of the effluent

inflow, and is accompanied by a manually operated diversion weir

(at Pase, Figure 1a) for flood control with flow directed to the neigh-

bouring Nordgraben channel in large rainfall events. The weir

operation is designed to reduce flow peaks but retain water within

the canalized network downstream. In conjunction with the incised

upper stream network, the canalized lower stream network is

characterized among the most heavily modified riverine morphology

in Berlin (Senate Department for Urban Development and the

Environment, 2012).

2.3 |Measured data

Climate data were available from multiple weather stations within

Berlin, established and maintained by the Deutscher Wetter Dienst

for precipitation, air temperature, humidity, air pressure and wind

speed (DWD, 2022). Radiation data (short and longwave radiation)

were available from ERA5 reanalysis datasets as hourly datasets

TABLE 1 Sub-Catchment properties of vegetation cover and total catchment area.

Sub-catchment Impervious (%) Broadleaf (%) Conifer (%) Crop (%) Grass (%) Area (km

)

SC1 19.6 15.1 4.6 34.6 25.0 41.7

SC2 5.2 25.7 35.8 6.7 25.8 54.6

SC3 22.0 25.2 1.7 22.5 27.6 18.0

SC4 9.9 10.4 5.2 50.4 23.2 40.4

SC5 25.8 27.2 2.6 17.9 25.5 6.4

SC6 31.3 17.8 0.8 10.2 38.8 5.0

SC7 27.5 27.5 1.3 15.6 27.1 28.1

SC8 29.3 29.0 1.6 3.9 35.2 17.0

SC9 53.3 27.5 2.8 0.0 15.4 6.7

4of17 SMITH ET AL.

(Hersbach et al., 2019; Figure 2d)Senate Department for the Environ-

ment, Transport and Climate Protection (SenUVK, 2021). Four of the

measurement locations are along the main stem of the Panke, with an

additional measurement of tributary water level at Flaischlenstraβe

which is runoff from an area dominated by arable agriculture

(Figure 1a,b). Wastewater from Schönerlinde WWTP has partially dis-

charged into the Panke since 2015 (SenUVK, 2021), and additional

measurements of diverted water outflow (Pase) into the Nordgraben

were available from 2011. Water level was translated to discharge

using established rating curve (developed by the Senate Department).

Rating curves were updated as necessary through periodic evaluation

against measured discharge. Infrequent high flow gauging to establish

the upper range of the rating curve and potential sedimentation and

seasonal channel vegetation growth can create some uncertainty in

the rating curves.

Precipitation water samples for isotope analysis were taken using

an autosampler at the Urban Ecohydrological Observatory at Steglitz

(10 km south of Panke) (Kuhlemann et al., 2021). Samples have been

collected since the beginning of 2019, with additional grab samples at

Berlin Buch climate station within the Panke taken during 2020,

which showed good comparability with Steglitz (Marx et al., 2021). A

layer of paraffin (3 mm) was added to all sample containers to prevent

evaporation. Stream water samples were taken through grab sampling

throughout the Panke from October 2019 to December 2020 (loca-

tions on Figure 1b). Samples were taken monthly until April 2020, and

from April 2020 to December 2020 biweekly sampling increased tem-

poral sample resolution. Stream sampling included three upstream

locations (PankeU, Krontaler U/S and Krontaler, Figure 1b) with

further sampling of the WWTP effluent. Stream water downstream of

Bürgerpark was sampled daily (Figure 1b). Sampling of the local aqui-

fer system was conducted monthly (Marx et al., 2021).

Water samples were decanted and filtered (2 μm cellulose ace-

tate) and refrigerated until water stable isotope measurement. Cavity

Ring-Down Spectroscopy was conducted using a L2130-I Isotopic

FIGURE 2 Climate data at

Berlin Buch (52.59N 13.45E)

climate station within the Panke

for (a) precipitation (b) air

temperature and (c) humidity

(DWD, 2022). (d) Radiation data

from ERA5 Reanalysis products

within the catchment (Hersbach

et al., 2019).

SMITH ET AL.5of17

Water Analyser (Picarro, Inc. Santa Clara, USA, 2020) for deuterium

(δ

H) and oxygen-18 (δ

O). Analytical precision was ±0.1‰and

± 0.025‰for δ

H and δ

O, respectively. Analysis of water samples

was conducted with periodic measurement of known isotopic stan-

dards to verify measurement accuracy. Further details on isotopic

standardization are presented in Marx et al. (2021).

2.4 |Hydrological modelling system (HEC-HMS)

The Hydrologic Engineering Center Hydrologic Modelling System

model was developed by the US Army Corps of Engineering for dend-

ric watersheds and incorporates numerous model structural compo-

nents to address both short-term (event-based) and long-term (multi-

year) hydrological analysis (Feldman, 2000). Model structure options

are available for evapotranspiration, canopy and surface storages,

infiltration, surface runoff transform method, baseflow, and flood

routing, with parameterizations of processes defined for each sub-

catchment. Details of the utilized model structure components are

presented below, with mode detailed descriptions of other model

structure options provided in Feldman (2000) and Scharffenberg and

Fleming (2008).

Spatial distribution of water storage and fluxes (Figure 3) is con-

ducted at a sub-catchment scale. Outflow from each sub-catchment is

collected by the stream network and routed downstream. The effects

of vegetation on sub-catchment water availability are considered

using a simple canopy bucket storage approach, which considers max-

imum canopy storage, canopy crop coefficient and root-water usage

method. Incoming precipitation is intercepted by canopy storage until

canopy storage is filled (Figure 3). Excess precipitation is transmitted

to the land surface, while canopy storage is emptied by evaporation

prescribed by the potential evapotranspiration rate. Precipitation

reaches the land surface which is categorized as either directly con-

nected impervious surfaces or pervious surfaces. Precipitation on

impervious surfaces is translated to direct flow to the channel (Q

while precipitation on pervious surfaces (surface storage, Figure 3) are

subject to the model structure for hydrological partitioning and loss

estimations (Figure 3). Infiltration from pervious surfaces is assumed

to an average representation of infiltration in all previous areas in the

sub-catchment.

To provide simulations of both storage dynamics and associated

fluxes for tracer mixing, the hydrological loss is estimated using the

soil moisture accounting loss method (Bennett & Peters, 2000)

(Figure 3). Surface water on pervious surfaces is available for infiltra-

tion to the soil storage at the beginning of each time-step, with poten-

tial infiltration rates (i

pot

(t)) and capacity determined by the maximum

infiltration rate (i

max

), and the current and maximum soil storage (S(t)

and S

max

ipot tðÞ¼imax 1StðÞ

Smax



:ð1Þ

Water that does not infiltrate remains in the surface storage until the

water is either evaporated or infiltrates in the subsequent time-steps.

Surface water exceeding the maximum depression storage is trans-

lated to the channel as direct flow. Soil storage is partitioned into

upper zone storage and tension zone storage, where all soil storage

only loses water to evapotranspiration, and only the upper zone stor-

age can percolate to deeper water storages. Flow into and out of dee-

per storages (two storages) is defined through the percolation rates:

Ppot i,tðÞ¼Pmax iðÞ Si,tðÞ

Smax iðÞ



1Siþ1,tðÞ

Smax iþ1ðÞ



,ð2Þ

where P

pot

(i,t) is the potential percolation from storage in layer i, and

is dependent on the maximum possible percolation rate (P

max

(i)) and

the ratio of current soil storage volumes (S(i,t)) to maximum storage

volumes (S

max

) of layer iand layer i+1. The actual percolation

act

(i,t)) is the minimum of the potential percolation and the available

water for percolation. The lateral flow (Q

) out of the deeper storages

(not soil storage) is defined using the vertical water balance and a

routing storage parameter (GW

Qgi,tþ1

ðÞ

¼Pact i1,tðÞþSi,tðÞPpot i,tðÞ0:5Qgi,tðÞt

GWRþ0:5tð3Þ

with the total volume (V) of water released from storage:

Vi,tðÞ¼0:5GWQi,tþ1ðÞþGWQi,tðÞðÞt:ð4Þ

FIGURE 3 Schematic of the sub-catchment model structure.

Schematic of the isotope mixing module. Storage mixing for isotopes

adds passive storage to the water balance output from HEC-HMS.

Surface storage is representative of pervious soil regions. Pis

precipitation, Imp is impervious, Ei is interception evaporation, Qd is

direct flow, Esurf is evaporation from surface storage, Es is soil

evaporation, Tr is transpiration, Qg1 is lateral flow from groundwater

storage 1, and Qs2 is lateral flow from groundwater storage 2.

6of17 SMITH ET AL.

The sub-catchment hydrograph transformation is estimated using the

Snyder unit hydrograph method. This uses unit hydrographs to trans-

late catchment runoff to sub-catchment hydrograph peak flows

(Feldman, 2000). River flood routing in channelized reaches is esti-

mated using the Muskingum–Cunge approach (Cunge, 1969), using

channel length, slope, Manning's nvalues, and channel shape to route

water. Channel shape was assumed to be rectangular to simplify cal-

culations, and automatic estimation of space and time-step for routing

was used to ensure numerical stability.

The Penman–Monteith method (Monteith, 1965) is used to esti-

mate potential evapotranspiration using a combination of energy bal-

ance and mass transfer approaches (Allen et al., 1998). Potential

evapotranspiration is estimated using short- and long-wave radiation,

wind speed, air temperature, air and vapour pressure in conjunction

with a reference albedo and crop coefficient to account for differ-

ences in vegetation and aerodynamic resistance.

2.5 |Water stable isotope mixing and flow

components module

Mixing of water stable isotopes (δ

H and δ

O) and water ages was

conducted using the estimated fluxes and storages from calibrated

results of the HEC-HMS model. Thus, the isotopes were not used as a

calibration constraint for flux quantification, but rather as an indepen-

dent check on the simulations. To incorporate the additional effects

of passive storage on damping the isotopic dynamics (e.g. Birkel

et al., 2011), an additional storage parameter for the soil, upper and

lower groundwater storages was included in addition to the dynamic

storage simulated by water balance variations. Mixing within each

storage (dynamic +passive) is conducted using amount-weighted,

complete and uniform mixing assumptions for each time-step as with

other isotopic modelling approaches (Ala-Aho et al., 2017; Kuppel

et al., 2018). At the end of each time-step, one time-step is added to

each average water age in storage to account for the ageing of water.

As fractionation in the stream was previously identified as negligible

except for the WWTP effluent component (Marx et al., 2021), frac-

tionation effects from evaporation were also assumed to be negligible

and were not considered within the isotope mixing module. WWTP

effluent isotopic compositions were added as measured external

source water to the catchment.

2.6 |Parameterization, calibration and uncertainty

analysis

The HEC-HMS model was set up to best utilize the available discharge

and stream isotope datasets by setting sub-catchment drainage areas

to each measurement location. Further consideration was made for

differences in regional landcover characteristics (Table 1). The model

was set to run on 12-h time-steps to balance representation of rapid

event-based urban runoff effects as well as groundwater-generated

baseflow component. Model testing was used to identify sensitive

parameters to be used in calibration (Table S1), which primarily

revealed the soil water loss parameters as the most sensitive parame-

ters for calibration. Insensitive parameters were held constant at

default values. WWTP effluent was added as an additional source of

water using measured inflow time-series above Krontaler (Figure 1a),

and a diversion element was included with measured diverted dis-

charge to incorporate the manual operation of the weir at Pase

(Figure 1a). The model was set up to run from January 2013 to

December 2020, using the first 2 years as model spin-up as WWTP

effluent was not measured until 2015.

Input forcing data (Section 3.1) included data from the surround-

ing weather stations (DWD, 2022) and re-analysis datasets for short-

and long-wave radiation (Hersbach et al., 2019). Measured DWD cli-

mate data (DWD, 2022), in particular the timing and quantity of pre-

cipitation events, were compared to evaluate the spatial

heterogeneity of precipitation and incorporate this in the modelling

approaches. Precipitation amount and timing notably differed from

the northern to the central sub-catchments (i.e. precipitation north of

SC2 to Berlin Buch station in SC3), with the northern stations receiv-

ing less rainfall than the southern stations. Therefore, the two north-

ern catchments (SC1 and SC2) utilized a distance weighted

precipitation input.

To enable the model spin-up of the isotope mixing module, a sto-

chastic model was created for isotopic precipitation inputs from 2013

to the beginning of measurement in 2019. The stochastic model uti-

lized precipitation amount, temperature, humidity, wind speed, and a

randomization factor fit against measured data (2019–2020,

=0.89). Used for spin-up purposes only, this generated long-term

dataset is presented in Figure S1. The isotopic WWTP effluent was

gap-filled to produce a continuous input time series for downstream

locations. On comparative sample days (weekly sampling) over a two-

year period, variability in in WWTP effluent isotopic signatures was

much lower than stream water (standard deviation 1.5‰v. 4.7‰

for δ

H for WWTP and streamwater, respectively). Gap filling was

conducted using a simple approach with the mean and a randomiza-

tion term defined using the percentiles of measured data, in a method

similar to bootstrapping. As much of the observed variability was due

to larger convective events, and WWTP discharge variability was low,

average variability (daily) is likely lower than observed variability.

Calibration of HEC-HMS was conducted using the optimization

toolbox with the Simplex Search Algorithm (Lagarias et al., 1998).

Maximum iterations were set to 1000 with an objective tolerance

(rate of change of Nash–Sutcliffe efficiency, NSE; Nash & Sut-

cliffe 1970) set to 1 E-4. Calibration search criteria (iterations and tol-

erance) were evaluated throughout the calibration to ensure that the

criteria did not influence search objectives. The convergence of the

model parameters to the global maximum through the optimization

algorithm was tested by changing initial parameters.

For consistency in calibration approaches, the isotope module

used the Simplex Search Algorithm set-up in Matlab

. We utilized the

fminsearchbnd package (D'Errico, 2022) to define the upper and lower

SMITH ET AL.7of17

parameter bounds, and calibrated using the NSE (Nash &

Sutcliffe, 1970), Kling-Gupta (KGE) (Gupta et al., 2009), and mean

absolute error (MAE). The NSE and KGE were multiplied by 1to

provide a minimum search value. Similar to the HEC-HMS calibration,

changes in initial values were tested to ensure a global maximum was

reached.

Model uncertainty was evaluated for all model outputs using the

Generalized Likelihood Uncertainty Estimation (GLUE) methodology

(Beven & Binley, 1992). The CURE toolbox (Page et al., 2022) was

used to model uncertainty bounds, defined as the output 95th

percentiles.

2.7 |Transit time estimations

Mean transit times (MTTs) of streamflow at various locations through-

out the catchment were estimated independently using the measured

H in precipitation and in streamflow. We used a two-parallel linear

reservoir (TPLR) transit time model which has previously been shown

to be effective in peri-urban environments in accounting for differ-

ences in urban and nonurban areas and contrasted results to the more

commonly used gamma distribution transit time model which has

been shown to be applicable to a wide range of catchments (Godsey

et al., 2010). Input precipitation δ

H was weighted by amounts in the

convolution equation:

CtðÞ¼

Cin tτðÞPin tτðÞgτðÞdτ

gτðÞPin tτðÞdτ

,ð5Þ

where τis the transit time, C(t) is the isotopic composition in stream-

flow, C

(tτ) is the input isotopic composition at time tτ,P

(tτ)is

the precipitation at time tτand g(τ) is the transit time distribution

given for TPLR as follows:

gτðÞ¼

τf

exp τ

τf



1ϕðÞ

τs

exp τ

τs



:ð6Þ

The transit time distribution has three parameters, ϕis the fraction of

fast water flow (0–1, e.g., urban storm flow), τ

and τ

are the mean

residence times of the fast and slow flow reservoirs. Transit times

estimated downstream of WWTP effluent utilized HEC-HMS simula-

tions to define the contribution of WWTP water in stream:

Cout tðÞ¼CtðÞ 1QWWTP tðÞ

ðÞ



þCWWTP tðÞ QWWTP tðÞ

ðÞ



,ð7Þ

where Q

WWTP

(t) is the total flow from WWTP in the stream at time

tand Q(t) is the total flow in the stream at time t. The transit time

model was calibrated using the Simplex Search Algorithm in Matlab

(D'Errico, 2022) using NSE, KGE and MAE.

3|RESULTS

3.1 |Discharge and source water contribution

The HEC-HMS model reproduced seasonal discharge dynamics and

general responses throughout the catchment reasonably well

(Figure 4and Table 2); however, the heavier emphasis of the NSE on

peak flows revealed a limitation of the model and especially the input

data to capture all precipitation events; especially summer convective

cells. These high peaks primarily occurred in the headwater catch-

ments (discharge at PankeU, Figure 4a), where the magnitude of most

peak events was under-estimated (e.g. summer convection events in

2017–2019). In particular, the measured peak flow event in mid-2017

experienced a multi-day lag which was not evident in the precipita-

tion, and the extent of the lag was not observed for other events or in

the other sub-catchments. Additionally, measured discharge events

occurred without measured precipitation (e.g. 2019 peak, Figure 4a),

revealing the influence of precipitation heterogeneity. Discharge in

the mid-eastern sub-catchments (discharge at Flaischlenstraβe,

Figure 4c) had only minor deviations with the exception of the 2017–

2018 winter; however, the underestimation did not propagate down-

stream (discharge at Heinersdorfer, Figure 4d). Discharge at Krontaler

(Figure 4b) had a slight over-estimation in 2018 and 2019, but

showed a good representation of discharge dynamics downstream of

the WWTP inflows (Table 1, discharge KGE). Discharge estimations

improved further downstream of the diversion (Table 1), with more

minor event-based deviations from measurements. The largest down-

stream deviation occurred at Bürgerpark at the beginning of 2020

where simulated discharge notably exceeded measured discharge

(Figure 4e). This deviation was not evident in the simulations immedi-

ately upstream at Heinersdorfer (Figure 4d).

Simulations from tributary and headwater catchments (Figure 4f,

h) were dominated by deeper groundwater contributions, with shal-

lower sub-surface sources of interflow providing an increased contri-

bution to streamflow during winter months. Direct flow peaks from

surface runoff occur in both the summer and winter months, driven

by larger precipitation events. Discharge locations downstream were

heavily influenced by the WWTP effluent contributions (Figure 4g, i,

j), which dampened discharge dynamics and produced a much higher

baseflow component (Figure 4b, d, e). The WWTP contribution to

streamflow was greatest during the summer months when upstream

discharge contributions were lower (e.g. Figure 4a). The simulated

total contribution of WWTP effluent was similar to measured

discharge-based estimations (dashed line Figure 4g), with a modelled

under-estimate when discharge was over-estimated (Figure 4b).

Through most of the mainstream channels, WWTP effluent contribu-

tion increased during the 2018 summer drought, exaggerating the

influence of WWTP effluent on baseflow conditions. WWTP contri-

butions were damped further downstream (Figure 4i, j) through fur-

ther tributary contributions. These contributions were exaggerated by

the diversion of water at Pase which removed 0.85 m

/s (45% of

discharge) and greatly impacted the total contribution of WWTP

water.

8of17 SMITH ET AL.

3.2 |Stream water stable isotopes and mean

water ages

The isotope mixing module with an additional passive storage compo-

nent (Table 3) produced satisfactory simulations of water stable

isotopes in stream water throughout the catchment (Figure 5and

Table 1). Although the presented results focus on δ

H, simulations for

O were of a similar quality (see insets in Figure 5). Larger events in

the upstream sites were well captured, though there was a slight

over-estimation of baseflow isotopic signals towards the end of

the simulation (Figure 5a,b). The WWTP effluent immediately

downstream damped the isotopic dynamics and further reduced the

uncertainty (Figure 5c) due to the large contribution of inflows

(Figure 4g). Daily sampling at the outlet revealed higher isotopic vari-

ability than was evident in the less frequently sampled upstream sites.

The mixing module was able to capture the general dynamics (Table 1)

in addition to some of the larger precipitation events; however, some

summer convective events (e.g. June and July 2020) were not cap-

tured by the model due to the high groundwater contribution that

was simulated (Figure 4i,j).

Estimated water ages (from isotope mixing) in the stream

decreased from the tributaries to the outlet (Figure 5e). In the

FIGURE 4 Simulated discharge at major sampling sites, shown in relation to the simple schematic on the left of the figure at (a) PankeU,

(b) Krontaler, (c) Flaischlenstrasse, (d) Heinersdorfer and (e) Burgerpark. The contribution of flow for each discharge site from direct flow,

interflow, groundwater, and added wastewater are in subplots fjrespectively. The dashed line in subplot g represents the estimated total

contribution of WWTP effluent using measured discharge only. For visual aid, the contributions are displayed as moving monthly averages.

TABLE 2 Efficiency criteria from HEC-HMS (discharge), isotope mixing module (IM) and transit time calibration. Values presented are the

best-obtained efficiency criteria. Discharge efficiency is shown with NSE and KGE in parentheses.

Location Discharge Isotope mixing δ

H (KGE) TPLR TTD δ

H (KGE) Gamma TTD δ

H (KGE)

PankeU 0.14(0.26) 0.59 0.65 0.71

Krontaler U/S N/A 0.55 0.46 0.41

Krontaler 0.45(0.73) 0.86 0.72 0.68

Flaischlenstraβe 0.40(0.48) N/A N/A N/A

Heinersdorfer 0.51(0.69) N/A N/A N/A

Burgerpark 0.50(0.74) 0.40 0.48 0.47

SMITH ET AL.9of17

upstream catchment, the mean age of water was 11.6 years with

younger water influences during rainfall events driving the simulated

age of storm events to 2.2 years; however, the water age estimates

had large uncertainty. Water ages reduced further downstream

(before the WWTP inflow), with a mean water age of 3.6 years and

event-based depressions to 0.6 years (Figure 5f). The much youn-

ger water ages additionally reduced the water age uncertainty

(Figure 5f). The contribution of WWTP effluent (inflow age of 0 days)

further reduced estimated average water ages (2.2 years), but

increased event variability due to WWTP effluent controls

(Figure 5g). While there was increased impervious area percentages

towards the south of the catchment, higher simulated groundwater

contribution (Figure 4j) slightly increased the simulated water ages

towards the outlet of the catchment (Figure 5h) with a mean age of

4.5 years (event-based variability 2.9 years). Increased uncertainty

at the outlet was the result of divergence of water age estimates

from different efficiency criteria (Table 4). The divergence of water

age estimates was only present at the outlet due to the increased

data availability (daily data) which further revealed more variability

than the biweekly data. Larger, nonlinear variability of water age in

the southern reaches of the catchment reflected the diversion of high

flows out of the catchment at Pase with smaller upstream volume to

dampen the incoming younger water from the southern sub-

catchments.

3.3 |Transit time distributions and water ages

Similar to the isotope mixing module, the transit time modelling

approach yielded satisfactory results for the water stable isotope

time-series at the stream sites throughout the catchment (Figure 6

and Table 1). Like the mixing module, simulations late in the period

(end of 2020) for δ

H stream values were overestimated, with a larger

deviation in the transit time model (Figure 6a,b). Additionally, the

influence of large precipitation events (e.g. June 2020) were not

apparent within the transit time models (Figure 6b). Similar to the iso-

tope mixing module, isotopic dynamics and uncertainties were

reduced downstream of the WWTP inflow (Figure 6c). Water stable

TABLE 3 Mean and standard deviation of passive storage (mm) additions to shallow soil, groundwater, and deep groundwater storage used

for water stable isotope mixing at different locations within the catchment.

Shallow soil storage Shallow groundwater storage Deeper groundwater storage

Upstream (SC1) 7.77 ± 3.9 96.4 ± 23.73 1929.52 ± 236.5

Mid-Reach (SC2-SC5) 0.21 ± 0.73 0.12 ± 0.47 22.09 ± 17.74

Downstream (All remaining sub-catchments) 60.79 ± 12.98 97.52 ± 54.07 7.46 ± 7.86

FIGURE 5 Simulated (mean and 95 percentiles) and measured (red circles) stream deuterium from the mixing module in (a) PankeU,

(b) Krontaler U/S, (c) Krontaler and (d) Burgerpark. Measured and simulated isotopes in δ

H-δ

O space are shown for each time series. Estimated

mean water ages for each site are shown in subplots e–h, respectively. Note that there is a compression of the spatial scale on the schematic for

the downstream reaches (Krontaler to Burgerpark).

10 of 17 SMITH ET AL.

isotope dynamics were increased towards the outlet; however, similar

to the mixing module, the transit time models were unable to capture

the larger day-to-day variability from convective precipitation at the

outlet (e.g. June and July 2020).

Water ages generally decreased from upstream to downstream

with the exception of the TPLR transit time model at Krontaler U/S

(Table 4). Estimated transit times in the upstream sites (Figure 6e,f)

showed wide uncertainty bounds for both transit time models despite

relatively narrow isotopic bounds (Figure 6). The TPLR TTD model

showed an increasing proportion of water from the fast-flowing reser-

voir (higher slope for shorter transit times) with increased distance

downstream, mirroring the increase in impervious surfaces

TABLE 4 Mean water ages (± temporal variability, in years) of streamwater at different locations in the catchment for each model and

efficiency criteria. Note that the mean water ages include all ‘best’model parameter sites.

Average water age from each efficiency criteria

KGE NSE MAE

Isotope Mixing Module PankeU 18.9 ± 3.7 8.9 ± 1.6 7.0 ± 1.4

Krontaler U/S 5.2 ± 1.0 2.8 ± 0.5 2.7 ± 0.4

Krontaler 3.3 ± 1.7 1.8 ± 0.9 1.7 ± 0.9

Burgerpark 10.9 ± 7.9 1.3 ± 0.4 1.3 ± 0.4

Two parallel linear reservoir TTD PankeU 1.1 ± 0.3 2.1 ± 0.5 1.8 ± 0.3

Krontaler U/S 1.1 ± 0.4 1.6 ± 0.3 1.5 ± 0.3

Krontaler 0.2 ± 0.2 0.5 ± 0.3 0.4 ± 0.2

Burgerpark 0.3 ± 0.2 0.5 ± 0.2 0.6 ± 0.2

Gamma TTD PankeU 0.4 ± 0.1 2.0 ± 0.3 2.2 +0.3

Krontaler U/S 0.4 ± 0.1 1.3 ± 0.1 1.1 ± 0.1

Krontaler 0.1 ± 0.1 0.4 ± 0.2 0.3 ± 0.2

Burgerpark 0.2 ± 0.1 0.6 ± 0.2 0.6 ± 0.2

FIGURE 6 Simulated TPLR stream deuterium and cumulative transit time distributions of two parallel linear reservoir (TPLR) and Gamma

functions for (a and e) PankeU, (b and f) Krontaler U/S, (c) Krontaler, and (d and g) Burgerpark. The range in median water age is shown for each

site. Krontaler isotopes are a mixture of Krontaler U/S and WWTP inflow (no calibrated transit time distribution) and that there is a compression

of the spatial scale on the schematic for the downstream reaches (Krontaler to Burgerpark).

SMITH ET AL.11 of 17

downstream. Uncertainty in the transit time and water age estimates

decreased towards the outlet of the catchment (Figure 6g).

Average water ages at different locations in the catchment varied

depending on the model used (isotope mixing module or TTD) and on

the efficiency criteria used for optimization (Table 4). The TTD models

consistently revealed younger water ages than were estimated from

the isotope mixing module (Table 4) and were most noticeable in the

headwater catchment (PankeU, Table 4). The difference between the

isotope mixing module and TTD models were reduced further down-

stream where younger water and WWTP effluent dominated stream-

flow. The use of different efficiency criteria revealed their importance

for the evaluation of water ages for both the mixing module and TTD

models. Using the NSE and MAE as optimization efficiency produced

relatively consistent water ages and isotopic simulations (Table 4),

while KGE produced notably different water age estimates without

significant changes to the isotopic simulations (Figures 5and 6and

Table 4). In the isotopic mixing module, the KGE optimization greatly

increased water age estimations, while decreasing water age estima-

tions in TTD estimations.

4|DISCUSSION

4.1 |Evaluating urban hydrological processes

Through the application of relatively simple model frameworks as

learning tools, we could use isotope data and the concept of water

age to gain insights into spatiotemporal patterns of hydrological

function within a heavily modified urbanizing landscape. This helped

to constrain the identification of dominant catchment-scale flow paths

and water sources, as well as to identify how key processes changed

through wet, and in particular, dry years (e.g. 2018 and 2019) which

will likely occur through much of Europe more frequently under

climatic change (Cammaleri et al., 2020; Gudmundsson &

Seneviratne, 2016).

By utilizing a simple semi-distributed model framework, we

gained further insights into the likely importance of groundwater and

shallow subsurface contributions to streamflow at multiple locations

within the catchment. In the northern, more rural regions of the catch-

ment in Brandenburg, the simulated high proportion of streamwater

contribution from groundwater (Figure 4f) was broadly consistent

with previous tracer-based mixing models of source apportionment in

the catchment (Marx et al., 2021). This is more generally similar to the

dominant runoff processes identified for other rural catchments sur-

rounding Berlin (Smith et al., 2021; Smith, Tetzlaff, Gelbrecht,

et al., 2020; Wu et al., 2022). However, unlike such rural

groundwater-dominated catchments where flow variations are mostly

seasonal and large storm-event driven flow peaks are rare, both small

and large events are evident in the Panke. Unsurprisingly, this reflects

direct runoff contributions from impervious surfaces translating rap-

idly to the stream, as has been shown in other peri-urban catchments

(Soulsby et al., 2015), though their overall contributions to annual

stream flow are relatively small. However, the simple model structure

and calibration was unable to capture some of the larger events

(Figure 4). Missed peak events in modelling the upper catchment

could be due to multiple factors including the complex distribution of

SWO thresholds that were spatially variable within the catchment or

high heterogeneity of urban precipitation inputs (Liu & Niyogi, 2019;

Lorenz et al., 2019). Given the limited number of these events, and

their occurrence during summer, peak flows also may be uncertain

due to limited measurements to characterize peak flow rating curves

(Sikorska et al., 2013; Westerberg & McMillan, 2015) and/or the

impact of vegetation in the channel overbank increasing rating curve

uncertainty during peak flow events when over bank flow occurs

(Perret et al., 2020). Furthermore, while heterogeneity in precipitation

sources was incorporated within the modelling framework, known

uncertainties particularly of convective precipitation heterogeneities

within urban landscapes likely affect event-based discharge simula-

tions during summer (Meierdiercks et al., 2010; Singh et al., 2020).

The effects of urbanization on rainfall spatial patterns and quantities

may also be affected by the degree of urbanization, where spatial dif-

ferences have been shown between urban core areas and suburbs

(Yang et al., 2021). In catchments like the Panke, covering spatial het-

erogeneity from the urban core to suburbs and more naturalized

areas, high-spatial resolution precipitation distribution networks may

be needed to reduce discharge modelling uncertainties of summer

peak flows (via missed events).

Spatially, the model highlighted the importance of soil storage

within peri-urban catchments, where maximum soil storage changed

from upstream to downstream at rates inversely proportional to the

increase in impervious surfaces (Table S1). These soil storage dynam-

ics govern percolation (Equation 2), whereby the smaller maximum

storages of groundwater in the model domain facilitate more rapid

water movement consistent with a shallow groundwater system. The

importance of such shallow groundwater systems for the rapid devel-

opment of storm runoff is consistent with other urban studies

(e.g. Berthier et al., 2004).

The actual evapotranspiration estimated within the model

(Table S2) was within the range of estimates for previous study sites

in Berlin (Gillefalk et al., 2021,2022; Kuhlemann et al., 2021); how-

ever, the water loss estimates were at the low-end of feasible ranges.

The estimates may be lower than expected due to multiple factors,

including the lower influence of green space sensitivity due to the cal-

ibration bias to blue water fluxes at the sub-catchment scale, and the

differences in model structure on estimation (e.g. single v. multi-layer

root-water uptake and Penman v. energy balance approach)

(e.g. Duarte Rocha et al., 2022). The inclusion of total ET (and dynam-

ics) within the calibration process has been shown to improve the

overall performance of modelled ET volume in other studies

(e.g. Kuppel et al., 2020); however, this will likely result in a degrada-

tion of discharge performance (e.g. summer peak flows) and due to

the complexity of the hydrology (and limited spatial ET data availabil-

ity), consideration should be given to evaluating the feasibility of

parameter ranges controlling ET.

Lastly, the model revealed the sensitivity of the estimated flow

contributions to process uncertainties and temporal variability. This

12 of 17 SMITH ET AL.

was most apparent immediately downstream of the WWTP effluent

inflow, where the model under-estimated the significance of the

WWTP effluent as a percent of contribution within the stream due to

the over-estimation of streamflow upstream of the effluent (2018–

2020, Figure 4a). With the over-estimation of flows late in the simula-

tion period likely driven by an underestimation of evapotranspiration

during drier periods, the significance of more constrained evapotrans-

piration estimations is highlighted. Downstream, the proportion of

summer streamflow derived from WWTP effluent (max 73%) was

similar to previous end-member mixing estimates (80%) (Marx

et al., 2021), and underlines the higher importance of WWTP effluent

for maintaining summer baseflows. However, model results revealed

more temporal variability than end-member mixing (Figure 4), suggest-

ing increased groundwater and subsurface flow contributions during

winter recharge events. Modelled estimates and dynamics were rela-

tively consistent with the long-term separation of downstream dis-

charge into upstream and WWTP effluent (Figure 4g), and may

suggest more adequate capture of event-based variability that was

not possible previously with 3-month isotope mixing windows

(Inamdar et al., 2013; Marx et al., 2021).

4.2 |Effect of urbanization on catchment water

stable isotopes and water ages

Using the fluxes and storage dynamics from the semi-distributed

model with uniform and complete isotopic mixing assumptions in indi-

vidual model stores, stream water isotopes were reasonably repro-

duced and were relatively well-constrained around the

measurements. As with other lumped storage models incorporated

with water stable isotopes (Birkel et al., 2011), the addition of passive

storages (i.e. for relatively slow moving water) was necessary to

account for isotopic damping (Table 3). The passive storage revealed

the dominant influence of groundwater mixing within the upper

catchment, further to additional storage and mixing than in the more

urbanized downstream catchments. Despite the under-estimated

WWTP effluent contribution immediately downstream (Figure 4g),

resulting from an over-estimated groundwater contribution (with simi-

lar isotopic signature, Marx et al., 2021), both δ

H and δ

O were well

simulated.

As with the isotope mixing module, both functional forms of tran-

sit time models (TPLR and gamma) were able to reproduce stream

water isotopes, though the mixing module generally produced better

isotopic simulations and the TPLR performed better than the gamma

distribution. The better performance of the TPLR is consistent with

the previous evaluations of transit time distributions in urban catch-

ments where the engineered and more natural hydrological systems

provide binary flow systems that are well estimated by two fast and

slow flow reservoirs (Soulsby et al., 2014). The transit time models

were unable to fully constrain the larger isotopic variability in the daily

samples at the catchment outlet than the less frequently sampled sites

upstream (Table 2). The limited variability in simulations relative to the

measurements may be due to multiple factors. Heterogeneity in

precipitation may be highly pronounced in urban catchments, where

cityscapes can alter the magnitude of summer storms, and variability

in spatial patterns (Liu & Niyogi, 2019; Lorenz et al., 2019). This

impacts volumetric inputs (potentially higher amounts between pre-

cipitation stations) and thereby isotopic compositions in recharge and

runoff due to these through volumetric differences. This is supported

by modelled data as peak flow and stream isotopes are under-

estimated for the same events (e.g. 2019, Figures 4and 5). Additional

analysis of the sensitivity of spatio-temporal precipitation patterns

and magnitudes may further help to improve model results. Further,

stream isotope signature variability is affected by the sample resolu-

tion, where the outlet is near-daily and upstream sites are biweekly,

which has been shown to influence model mixing and interpretation

(Birkel et al., 2010). Finally, with increased downstream urbanization,

the higher variability could be due to an exceedance of the sewer sys-

tem threshold causing SWOs mixing within the stream (Quaranta

et al., 2022). However, the influence of the SWO is dependent on the

total SWO volume, stream discharge volume, infiltration within the

SWO system (e.g. groundwater seepage; Rodriguez et al., 2020), tap

water leakage, and the difference in isotopic composition of the SWO

and stream discharge. In particular, the lower isotopic composition of

groundwater as seepage contributions to SWO could lower the mod-

elled isotopic composition of stream water towards those observed

during the winter months when groundwater levels are the highest.

Water age evaluation within urban environments is complex due

to significant changes to flow paths, engineered structures

(e.g. drainage and diversions), water abstractions, and point load addi-

tions (WWTP). These numerous hydrologic changes directly influence

the proportion of ‘new’water (i.e. <2 months, Kirchner, 2016), which

can further be divided into young ‘new’water (e.g. precipitation) and

young but ‘older’recycled water (e.g. WWTP). The mixing approach

provided an estimate of the separation of these water sources. In

streams with no WWTP effluent, 16% of the natural flow was rainfall

<2 months old. In streams with WWTP effluent, only 9% of flow was

comprised of rainfall <2 months old. The estimates for stream flow

inclusive of WWTP effluent were similar to young water fractions

previously and independently estimated for all flow (6%, Marx et al.

(2021)). These young ‘new’water proportions, while relatively con-

strained within the mixing module, are slightly larger but more uncer-

tain with the transit time models (12%–35%). Such young water

fractions also carry unknown uncertainties of potential mixing of the

direct flow component, which may be directly influenced by ground-

water seepage and drinking water leakage into the SWO systems

(e.g. Karpf & Krebs, 2013). Splitting young water (i.e. water entering

the stream within the past 2 months) into ‘new’(i.e. rainfall) and ‘old’

(i.e. WWTP) can have significant implications on interpretation.

Within the Panke, ‘older’young water (WWTP effluent) accounted

for 41% of the total flow despite the new addition to the catchment

which has a much more damped isotopic variability.

Interestingly, despite the relatively constrained discharge and

water stable isotope simulations, the uncertainty in water ages was

not well constrained for any of the isotopic modelling approaches

(Figures 5and 6); with differences between the semi-distributed

SMITH ET AL.13 of 17

isotopic mixing and transit time approaches. While all isotopic model-

ling approaches showed decreasing water ages and transit times as

percent urban cover increased - consistent with transit time studies in

other urban environments (Soulsby et al., 2014,2015)–and had mod-

erate overlapping uncertainty bounds, the transit time models resulted

in much younger average water age estimates (Table 4). However, the

transit time distributions for young water (<200 days) are highly

uncertain as the contributions of rapidly mobilized young water are

not constrained by discharge estimations (as in the isotope mixing),

which amplifies the larger uncertainty of the distribution tails already

present within these approaches (Kirchner, 2016). Furthermore, there

was more convergence of water age estimations with the choice of

efficiency criteria used in calibration. Water ages for the different

modelling approaches converged when either NSE or MAE were uti-

lized, as both efficiency metrics penalized excessive simulated isotopic

variability of younger water influence within the TTD models. For the

isotope mixing module, the use of KGE resulted in much older water

ages throughout the catchment (Table 4), which damped isotopic vari-

ability beyond the direct flow contributions of larger events. These

results reveal the different sensitivity of the various efficiency criteria

for model evaluation. This seems particularly apparent across model

structures in urban environments where nonlinearities of flow contri-

bution (e.g. SWOs), which if not adequately captured by the model

structure, may result in overemphasis of incorrect flow paths.

4.3 |Limitations, wider implications and

future work

The use of complementary modelling approaches within a learning

framework to gain insights into the effect of urbanization on water

fluxes and ages provided a more general opportunity to assess the

wider implications of hydrological model conceptualizations –in par-

ticular, flow path and ecohydrology –within heavily urbanized sys-

tems. The continued development of urbanized areas, coupled with

climatic change, places greater urgency on understanding these pro-

cesses to evaluate long-term implications for urban water availability

(Nguyen et al., 2010; Olsson et al., 2009).

While modelling studies within urban environments have a long

history, much of the focus has been on the evaluation of urban storm

drainage and flooding with relatively little focus on the differentiation

of flow path contribution and water ages (Gillefalk et al., 2021). Con-

current discharge and isotopic datasets provided an opportunity to

quantitatively understand the changes in flow path contribution from

more rural to more urbanized regions of a catchment which provides

further insight into the likely impact of future urbanization on fluxes

(e.g. discharge, groundwater flow and evapotranspiration) (Soulsby

et al., 2015). These coupled datasets proved to be invaluable within

this study to spatially constrain model parameterization as required by

the model structure (Feldman, 2000). While calibration provided spa-

tial patterns of model parameters associated with differing degrees of

urbanization regardless of sub-catchment size (Table S1), these pat-

terns were calibration-dependent and the transferability to other

catchments may be limited. Further, the significant influence of the

WWTP effluent and weir diversion (Pase) likely influenced the param-

eterization, and further work is needed to evaluate how flow manage-

ment affects hydrological parameterization. While the

evapotranspiration estimated from the model was within previous

estimates, the overall estimate was still low causing some over-

estimation of discharge. The implementation of evapotranspiration

estimates as forcing data has been shown to have the potential to

improve model discharge performance (Zare et al., 2021) and could

help further constrain source water estimations, particularly in natural

groundwater dominated environments like the study area (Smith

et al., 2021). Gridded input of evapotranspiration could further help to

limit spatial biasing at the sub-catchment scale in lumped modelled

caused by reduced heterogeneity influences (Salvadore et al., 2015).

While the simpler hydrological structure approach reduced

parameterization compared to a more physically based or fully distrib-

uted modelling approach, this ultimately compromized the isotopic

modelling. The use of physically based modelling can result in no addi-

tional parameterization needs for tracer mixing (e.g. EcH

O-iso,

Kuppel et al., 2018), which reduces uncertainty over flow path repre-

sentation and mixing simultaneously without increasing degrees of

freedom. While the isotopic mixing module used provided insight to

total mixing volumes, the additional parameterization and use of cali-

brated hydrological results reduced the emphasis on flow path identi-

fication and was likely the main reason for the higher water age

uncertainty. The uncertainty of the more simple transit time models

was more predictable given the already well-known problem of cap-

turing large uncertainties of complex flow processes in urban environ-

ments using black-box models (Bonneau et al., 2017). In particular,

convective precipitation cells which produce high-intensity rainfall,

and are important in summer, can cause non-linearities in the quantity

of stormwater reaching the streams (e.g. Launay et al., 2016) which

directly influences how well more simple models running on a 12 h

time step can capture complex flow, dynamic responses.

5|CONCLUSION

We utilized a distributed rainfall-runoff model with an isotope mixing

model as a learning framework to better understand the hydrology of

a complex 217 km

heavily urbanized catchment in Berlin, Germany.

The approaches focused on evaluating flow paths and water ages

while optimizing the information content from available datasets and

reducing parameterization, with both coupled semi-distributed hydro-

logical tracer mixing, and evaluation of stream water transit times

throughout the catchment. Upstream headwater catchments with less

urbanization showed very high groundwater contribution to stream-

flow, important for sustaining baseflows during the drier summer

months. Lower summer baseflow resulted in the more pronounce

influence of direct runoff from impervious surfaces during convective

precipitation events. Wastewater effluent contributions dominated

streamwater downstream of a major wastewater treatment plant,

though with a decreased influence of effluent and direct urban runoff

14 of 17 SMITH ET AL.

after a stream weir diversion. Water ages in stream water showed a

notable decrease downstream in the catchment as the proportion of

urban area increased. Younger, more rapid water contributions were

the driving forces behind downstream isotopic variability despite lim-

ited discharge variability due to the wastewater treatment effluent

and flow diversion. Utilizing simple tracer-aided models within a learn-

ing framework can help to provide a further understanding of urban

catchment hydrology through the lens of water ages while aiding in

the identification of the spatio-temporal variation in dominant pro-

cesses that are unique to urban environments. The approach taken

within this study provides a stepping stone to further hydrological and

ecohydrological exploration within urban landscapes.

ACKNOWLEDGEMENTS

We acknowledge the BMBF (funding code 033W034A) which sup-

ported the stable isotope laboratory at IGB. Funding for DT was also

received through the Einstein Research Unit ‘Climate and Water

under Change’from the Einstein Foundation Berlin and Berlin Univer-

sity Alliance. We acknowledge funding from the graduate School

Urban Water financed by Interfaces Deutsche Forschungsge-

meinschaft, Grant/Award Number: (GRK2032/2). CS is also funded by

the ISOLAND Project of the Leverhulme Trust, Grant Number: (RPG-

2018-425). CM and CS are funded for the project MOSAIC by the

Einstein Stiftung Berlin, Grant/Award Number: EVF-2018-425. The

authors would like to thank the two anonymous reviewers and editor

(Jim McNamara) for the comments and feedback which has improved

the manuscript. Open Access funding enabled and organized by Pro-

jekt DEAL.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available on

request from the corresponding author. The data are not publicly

available due to privacy or ethical restrictions.

ORCID

Christian Marx https://orcid.org/0000-0001-7648-1603

Chris Soulsby https://orcid.org/0000-0001-6910-2118

REFERENCES

Ala-Aho, P., Tetzlaff, D., McNamara, J. P., Laudon, H., & Soulsby, C. (2017).

Using isotopes to constrain water flux and age estimates in snow-

influenced catchments using the STARR (spatially distributed tracer-

aided rainfall-runoff) model. Hydrology and Earth System Sciences,

21(10), 5089–5110. https://doi.org/10.5194/hess-21-5089-2017

Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. (1998). Crop

evapotranspiration—guidelines for computing crop water require-

ments. FAO Irrigation and Drainage Paper (FAO) (56): 300p.

Bednorz, F., & Brose, D. (2017). Altersdatierung mittels Isotopenanalytik

zur Verweilzeitbestimmung und Identifizierung von Speisungsanteilen

des Grundwassers in Brandenburg. Brandenburgische Geowissenschaf-

tliche Beiträge,19,83–101.

Bennett, T., & Peters, J. (2000). Continuous soil moisture accounting in the

hydrologic engineering center hydrologic modeling system (HEC-HMS).

Building Partnerships,1–10. https://doi.org/10.1061/40517(2000)149

Berthier, E., Andrieu, H., & Creutin, J. D. (2004). The role of soil in the gen-

eration of urban runoff: Development and evaluation of a 2D model.

Journal of Hydrology,299(3–4), 252–266. https://doi.org/10.1016/j.

jhydrol.2004.08.008

Beven, K., & Binley, A. (1992). The future of distributed models: Model cal-

ibration and uncertainty prediction. Hydrological Processes,6(3), 279–

298. https://doi.org/10.1002/hyp.3360060305

Birkel, C., Dunn, S. M., Tetzlaff, D., & Soulsby, C. (2010). Assessing the

value of high-resolution isotope tracer data in the stepwise develop-

ment of a lumped conceptual rainfall-runoff model. Hydrological Pro-

cesses,24(16), 2335–2348. https://doi.org/10.1002/hyp.7763

Birkel, C., Tetzlaff, D., Dunn, S. M., & Soulsby, C. (2011). Using time

domain and geographic source tracers to conceptualize streamflow

generation processes in lumped rainfall-runoff models. Water

Resources Research,47(2), 1–15. https://doi.org/10.1029/

2010WR009547

Bonneau, J., Fletcher, T. D., Costelloe, J. F., & Burns, M. J. (2017). Storm-

water infiltration and the ‘urban karst’–A review. Journal of Hydrol-

ogy,552, 141–150. https://doi.org/10.1016/j.jhydrol.2017.06.043

Cammaleri, C., Naumann, G., Mentaschi, L., Bisselink, B., Gelati, E.,

Roo, A., & Feyen, L. (2020). Diverging hydrological drought traits over

Europe with global warming. Hydrology and Earth System Sciences,24,

5919–5935. https://doi.org/10.5194/hess-24-5919-2020

Cunge, J. A. (1969). On the subject of a flood propagation computation

method (Muskingum method). Journal of Hydraulic Research,7(2),

205–230.

D'Errico, J. (2022). Fminsearchbnd. MATLAB Central File Exchange.

https://www.mathworks.com/matlabcentral/fileexchange/8277-

fminsearchbnd-fminsearchcon

Duarte Rocha, A., Vulova, S., van der Tol, C., Förster, M., & Kleinschmit, B.

(2022). Modelling hourly evapotranspiration in urban environments

with SCOPE using open remote sensing and meteorological data.

Hydrology and Earth System Sciences,26, 1111–1129. https://doi.org/

10.5194/hess-26-1111-2022

DWD. (2022). CDC (Climate Data Center). https://www.dwd.de/DE/

klimaumwelt/cdc/cdc_node.html;jsessionid=

A28B6A63B4B7E4DCB78444CD24A3CDD8.live31094

Ehleringer, J. R., Barnette, J. E., Jameel, Y., Tipple, B. J., & Bowen, G. J.

(2016). Urban water –A new frontier in isotope hydrology†.Isotopes

in Environmental and Health Studies,52(4–5), 477–486. https://doi.

org/10.1080/10256016.2016.1171217

European Environment Agency. (2014). Water use in Europe —quantity

and quality face big challenges. https://www.eea.europa.eu/signals/

signals-2018-content-list/articles/water-use-in-europe-2014

Feldman, A. (2000). Hydrologic modeling system technical reference man-

ual. In Hydrologic modeling system HEC-HMS technical reference manual

(March) (p. 148). U.S. Army Corps of Engineers.

Fidal, J., & Kjeldsen, T. R. (2020). Accounting for soil moisture in rainfall-

runoff modelling of urban areas. Journal of Hydrology,589, 125122.

https://doi.org/10.1016/j.jhydrol.2020.125122

Fletcher, T. D., Andrieu, H., & Hamel, P. (2013). Understanding, manage-

ment and modelling of urban hydrology and its consequences for

receiving waters: A state of the art. Advances in Water Resources,51,

261–279. https://doi.org/10.1016/j.advwatres.2012.09.001

Frick, M., Scheck-Wenderoth, M., Schneider, M., & Cacace, M. (2019). Sur-

face to groundwater interactions beneath the City of Berlin: Results

from 3D models. Geofluids,2019,1–22. https://doi.org/10.1155/

2019/4129016

Gillefalk, M., Tetzlaff, D., Hinkelmann, R., Kuhlemann, L. M., Smith, A.,

Meier, F., Maneta, M. P., & Soulsby, C. (2021). Quantifying the effects

of urban green space on water partitioning and ages using an isotope-

based ecohydrological model. Hydrology and Earth System Sciences,

25(6), 3635–3652. https://doi.org/10.5194/hess-25-3635-2021

Gillefalk, M., Tetzlaff, D., Marx, C., Smith, A., Meier, F., Hinkelmann, R., &

Soulsby, C. (2022). Estimates of water partitioning in complex urban

landscapes with isotope-aided ecohydrological modelling. Hydrological

Processes,36, e14532. https://doi.org/10.1002/hyp.14532

SMITH ET AL.15 of 17

Godsey, S. E., Aas, W., Clair, T. A., de Wit, H. A., Fernandez, I. J., Kahl, J. S.,

Malcolm, I. A., Neal, C., Neal, M., Nelson, S. J., Norton, S. A., Palucis, M.

C., Skjelkvåle, B. L., Soulsby, C., Tetzlaff, D., & Kirchner, J.W. (2010),

Generality of fractal 1/f scaling in catchment tracer time series, and its

implications for catchment travel time distributions. Hydrological Pro-

cesses,24, 1660-1671. https://doi.org/10.1002/hyp.7677

Gudmundsson, L., & Seneviratne, S. I. (2016). Anthropogenic climate

change affects meteorological drought risk in Europe. Environmental

Research Letters,11(4), 44005.

Gupta, H. V., Kling, H., Yilmaz drought, K. K., & Martinez, G. F. (2009).

Decomposition of the mean squared error and NSE performance cri-

teria: Implications for improving hydrological modelling. Journal of

Hydrology,377(1), 80–91. https://doi.org/10.1016/j.jhydrol.2009.

08.003

Güneralp, B., Güneralp, I., & Liu, Y. (2015). Changing global patterns of

urban exposure to flood and hazards. Global Environmental Change,31,

217–225. https://doi.org/10.1016/j.gloenvcha.2015.01.002

Hersbach, H., Bell, B., Berrisford, P., Biavati, G., Horányi, A., Muñoz

Sabater, J., Nicolas, J., Peubey, C., Radu, R., Rozum, & I., et al. (2019).

ERA5 monthly averaged data on single levels from 1979 to present.

Copernicus Climate Change Service (C3S) Climate Data Store (CDS).

https://doi.org/10.24381/cds.f17050d7

Huang, S., Krysanova, V., & Hattermann, F. F. (2013). Projection of low

flow conditions in Germany under climate change by combining three

RCMs and a regional hydrological model. Acta Geophysica,61(1), 151–

193. https://doi.org/10.2478/s11600-012-0065-1

Huang, S., Krysanova, V., & Hattermann, F. F. (2015). Projections of cli-

mate change impacts on floods and droughts in Germany using an

ensemble of climate change scenarios. Regional Environmental Change,

15, 461–473. https://doi.org/10.1007/s10113-014-0606-z

Ichiba, A., Gires, A., Tchiguirinskaia, I., Schertzer, D., Bompard, P., &

Ten, V. M. C. (2018). Scale effect challenges in urban hydrology

highlighted with a distributed hydrological model. Hydrology and Earth

System Sciences,22(1), 331–350. https://doi.org/10.5194/hess-22-

331-2018

Inamdar, S., Dhillon, G., Singh, S., Dutta, S., Levia, D., Scott, D.,

Mitchell, M., Van Stan, J., & McHale, P. (2013). Temporal variation in

end-member chemistry and its influence on runoff mixing patterns in a

forested piedmont catchment. Water Resources Research,49(4), 1828–

1844. https://doi.org/10.1002/wrcr.20158

Karpf, C., & Krebs, P. (2013). Modelling of groundwater infiltration into

sewer systems. Urban Water Journal,10(4), 221–229. https://doi.org/

10.1080/1573062X.2012.724077

Kirchner, J. W. (2016). Aggregation in environmental systems-part 1: Sea-

sonal tracer cycles quantify young water fractions, but not mean tran-

sit times, in spatially heterogeneous catchments. Hydrology and Earth

System Sciences,20(1), 279–297. https://doi.org/10.5194/hess-20-

279-2016

Kleine, L., Tetzlaff, D., Smith, A., Wang, H., & Soulsby, C. (2020). Using

water stable isotopes to understand evaporation, moisture stress, and

re-wetting in catchment forest and grassland soils of the summer

drought of 2018. Hydrology and Earth System Sciences,24(7), 3737–

3752. https://doi.org/10.5194/hess-24-3737-2020

Kuhlemann, L. M., Tetzlaff, D., & Soulsby, C. (2020). Urban water systems

under climate stress: An isotopic perspective from Berlin. Germany.

Hydrological Processes,34(18), 3758–3776. https://doi.org/10.1002/

hyp.13850

Kuhlemann, L. M., Tetzlaff, D., Smith, A., Kleinschmit, B., & Soulsby, C.

(2021). Using soil water isotopes to infer the influence of contrasting

urban green space on ecohydrological partitioning. Hydrology and

Earth System Sciences,25(2), 927–943. https://doi.org/10.5194/hess-

25-927-2021

Kuppel, S., Tetzlaff, D., Maneta, M. P., & Soulsby, C. (2018). EcH2O-iso

1.0: Water isotopes and age tracking in a process-based, distributed

ecohydrological model. Geoscientific Model Development,11(7), 3045–

3069. https://doi.org/10.5194/gmd-11-3045-2018

Kuppel, S., Tetzlaff, D., Maneta, M., & Soulsby, C. (2020). Critical zone

storage controls on the water ages of ecohydrological outputs. Geo-

physical Research Letters,47, e2020GL088897. https://doi.org/10.

1029/2020GL088897

Lagarias, J. C., Reeds, J. A., Wright, M. H., & Wright, P. E. (1998). Conver-

gence properties of the Nelder–Mead simplex method in low dimen-

sions. SIAM Journal on Optimization,9(1), 112–147. https://doi.org/10.

1137/S1052623496303470

Launay, M. A., Dittmer, U., & Steinmetz, H. (2016). Organic micropollutants

discharged by combined sewer overflows –characterisation of pollut-

ant sources and stormwater-related processes. Water Research,104,

82–92. https://doi.org/10.1016/j.watres.2016.07.068

Limberg, A., & Thierbach, J. (2002). Hydrostratigrafie von Berlin—

Korrelation mit dem Norddeutschen Gliederungsschema. Brandenbur-

gische Geowissenschaftliche Beiträge,9(1/2), 65–68.

Liu, J., & Niyogi, D. (2019). Meta-analysis of urbanization impact on rainfall

modification. Scientific Reports,9, 7301. https://doi.org/10.1038/

s41598-019-42494-2

Lorenz, J. M., Kronenberg, R., Bernhofer, C., & Niyogi, D. (2019). Urban

rainfall modification: Observational climatology over Berlin, Germany.

Journal of Geophysical Research: Atmospheres,124, 731–746. https://

doi.org/10.1029/2018JD028858

Marx, C., Tetzlaff, D., Hinkelmann, R., & Soulsby, C. (2021). Isotope hydrol-

ogy and water sources in a heavily urbanized stream. Hydrological Pro-

cesses,35(10), 1–20. https://doi.org/10.1002/hyp.14377

Massmann, G., Pekdeger, A., Heberer, T., Grützmacher, G., Dünnbier, U.,

Knappe, A., Meyer, H., & Mechlinski, A. (2007). Drinking-water pro-

duction in urban environments—Bank filtration in Berlin. Grundwasser,

12(3), 232–245. https://doi.org/10.1007/s00767-007-0036-7

McGrane, S. J. (2016). Impacts of urbanisation on hydrological and water

quality dynamics, and urban water management: A review. Hydrologi-

cal Sciences Journal,61(13), 2295–2311. https://doi.org/10.1080/

02626667.2015.1128084

Meierdiercks, K. L., Smith, J. A., Baeck, M. L., & Miller, A. J. (2010). Hetero-

geneity of hydrologic response in urban watersheds. JAWRA Journal of

the American Water Resources Association,46, 1221–1237. https://doi.

org/10.1111/j.1752-1688.2010.00487.x

Meili, N., Manoli, G., Burlando, P., Bou-Zeid, E., Chow, W. T. L.,

Coutts, A. M., Daly, E., Nice, K. A., Roth, M., Tapper, N. J., Velasco, E.,

Vivoni, E. R., & Fatichi, S. (2020). An urban ecohydrological model to

quantify the effect of vegetation on urban climate and hydrology

(UT&C v1.0). Geoscientific Model Development,13(1), 335–362.

https://doi.org/10.5194/gmd-13-335-2020

Monteith, J. (1965). Evaporation and environment. Symposia of the Society

for Experimental Biology,19, 205–234.

Nash, J. E., & Sutcliffe, J. V. (1970). River flow forecasting through concep-

tual models part I - a discussion of principles. Journal of Hydrology,

10(3), 282–290. https://doi.org/10.1016/0022-1694(70)90255-6

Nguyen, V. T., Desramaut, N., & Nguyen, T. D. (2010). Optimal rainfall

temporal patterns for urban drainage design in the context of climate

change. Water Science and Technology: A Journal of the International

Association on Water Pollution Research.,62(5), 1170–1176.

Olsson, J., Berggren, K., Olofsson, M., & Viklander, M. (2009). Applying cli-

mate model precipitation scenarios for urban hydrological assessment:

A case study in Kalmar City, Sweden. Atmospheric Research,92, 364–

375. https://doi.org/10.1016/j.atmosres.2009.01.015

Page, T., Smith, P., Beven, K., Pianosi, F., Sarrazin, F., Almeida, S.,

Holcome, L., Freer, J., & Wagener, T. (2022). The CURE Uncertainty

Estimation Toolbox. http://www.uncertain-future.org.uk/?page_

id=26

Pang, X., Gu, Y., Launiainen, S., & Guan, M. (2022). Urban hydrological

responses to climate change and urbanization in cold climates. Science

16 of 17 SMITH ET AL.

of the Total Environment,817, 153066. https://doi.org/10.1016/j.

scitotenv.2022.153066

Perret, E., Renard, B., & Le Coz, J. (2020). A rating curve model accounting

for cyclic stage-discharge shifts due to seasonal aquatic vegetation.

Water Resources Research,57, e2020WR027745. https://doi.org/10.

1029/2020WR027745

Petrucci, G., & Bonhomme, C. (2014). The dilemma of spatial representa-

tion for urban hydrology semi-distributed modelling: Trade-offs among

complexity, calibration and geographical data. Journal of Hydrology,

517, 997–1007. https://doi.org/10.1016/j.jhydrol.2014.06.019

Quaranta, E., Fuchs, S., Liefting, H., Schellart, A., & Pistocchi, A. (2022). A

hydrological model to estimate pollution from combined sewer over-

flows at the regional scale: Application to Europe. Journal of Hydrology:

Regional Studies,41, 101080. https://doi.org/10.1016/j.ejrh.2022.

101080

Rodriguez, F., Le Delliou, A.-L., Andrieu, H., & Gironas, J. (2020). Ground-

water contribution to sewer network baseflow in an urban catchment-

case study of pin sec catchment, Nantes, France. Water,12,3.https://

doi.org/10.3390/w12030689

Salvadore, E., Bronders, J., & Batelaan, O. (2015). Hydrological modelling of

urbanized catchments: A review and future directions. Journal of Hydrol-

ogy,529(P1), 62–81. https://doi.org/10.1016/j.jhydrol.2015.06.028

Scharffenberg, W., & Fleming, M. (2008). Hydrologic modeling system

user's manual. Transform (September): 290.

Senate Department for the Environment T and CP (SenUVK). (2021). Was-

serportal Gewässerkundliche Messdaten. wasserportal.berlin.de

Senate Department for Urban Development and the Environment. (2012).

Morphology of water bodies—Overall assessment (WRRL), p. 7.

Sikorska, A. E., Scheidegger, A., Banasik, K., & Rieckermann, J. (2013). Con-

sidering rating curve uncertainty in water level predictions. Hydrology

and Earth System Sciences,17, 4415–4427. https://doi.org/10.5194/

hess-17-4415-2013

Singh, J., Karmakar, S., PaiMazumder, D., Ghosh, S., & Niyogi, D. (2020).

Urbanization alters rainfall extremes over the contiguous

United States. Environmental Research Letters.,15(7), 74033.

Smith, A., Tetzlaff, D., Gelbrecht, J., Kleine, L., & Soulsby, C. (2020). Ripar-

ian wetland rehabilitation and beaver re-colonization impacts on

hydrological processes and water quality in a lowland agricultural

catchment. Science of the Total Environment,699(9), 134302. https://

doi.org/10.1016/j.scitotenv.2019.134302

Smith, A., Tetzlaff, D., Kleine, L., Maneta, M. P., & Soulsby, C. (2020). Iso-

tope-aided modelling of ecohydrologic fluxes and water ages under

mixed land use in Central Europe: The 2018 drought and its recovery.

Hydrological Processes,34(16), 3406–3425. https://doi.org/10.1002/

hyp.13838

Smith, A., Tetzlaff, D., Kleine, L., Maneta, M., & Soulsby, C. (2021). Quanti-

fying the effects of land use and model scale on water partitioning and

water ages using tracer-aided ecohydrological models. Hydrology and

Earth System Sciences,25(4), 2239–2259. https://doi.org/10.5194/

hess-25-2239-2021

Soulsby, C., Birkel, C., & Tetzlaff, D. (2014). Assessing urbanization impacts

on catchment transit times. Geophysical Research Letters,41, 442–448.

https://doi.org/10.1002/2013GL058716

Soulsby, C., Birkel, C., Geris, J., & Tetzlaff, D. (2015). Spatial aggregation of

time-variant stream water ages in urbanizing catchments. Hydrological

Processes,29(13), 3038–3050. https://doi.org/10.1002/hyp.10500

Tetzlaff, D., Piovano, T., Ala-Aho, P., Smith, A., Carey, S. K., Marsh, P.,

Wookey, P., Street, L., & Soulsby, C. (2018). Using stable isotopes to

estimate travel times in a data-sparse Arctic catchment: Challenges

and possible solutions. Hydrological Processes,32(12), 1936–1952.

https://doi.org/10.1002/hyp.13146

Turner, S. W. D., Rice, J. S., Nelson, K. D., Vernon, C. R., McManamay, R.,

Dickson, K., & Marston, L. (2021). Comparison of potential drinking

water source contamination across one hundred U.S. cities. Nature

Communications,12(1), 1–12. https://doi.org/10.1038/s41467-021-

27509-9

United Nations. (2018). World urbanization prospects: The 2018

revision. United Nations.

Westerberg, I. K., & McMillan, H. K. (2015). Uncertainty in hydrological sig-

natures. Hydrology and Earth System Sciences,19, 3951–3968. https://

doi.org/10.5194/hess-19-3951-2015

Wu, S., Tetzlaff, D., Yang, X., & Soulsby, C. (2022). Disentangling the influ-

ence of landscape characteristics, hydroclimatic variability and land

management on surface water NO

–N dynamics: Spatially distributed

modeling over 30 yr in a lowland mixed land use catchment. Water

Resources Research,58(2), e2021WR030566. https://doi.org/10.

1029/2021wr030566

Yang, L., Ni, G., Tian, F., & Niyogi, D. (2021). Urbanization exacerbated

rainfall over European suburbs under a warming climate. Geophysical

Research Letters,48(21), e2021GL095987. https://doi.org/10.1029/

2021GL095987

Zare, M., Pakparvar, M., Jamshidi, S., Bazrafshan, O., & Ghahari, G. (2021).

Optimizing the runoff estimation with HEC-HMS model using spatial

evapotranspiration by the SEBS model. Water Resources Management,

35(8), 2633–2648. https://doi.org/10.1007/s11269-021-02855-x

SUPPORTING INFORMATION

Additional supporting information can be found online in the Support-

ing Information section at the end of this article.

How to cite this article: Smith, A., Tetzlaff, D., Marx, C., &

Soulsby, C. (2023). Enhancing urban runoff modelling using

water stable isotopes and ages in complex catchments.

Hydrological Processes,37(2), e14814. https://doi.org/10.

1002/hyp.14814

SMITH ET AL.17 of 17