Permafrost strongly controls hydrological processes in cold regions. Our
understanding of how changes in seasonal and perennial frozen ground
disposition and linked storage dynamics affect runoff generation processes
remains limited. Storage dynamics and water redistribution are influenced by
the seasonal variability and spatial heterogeneity of frozen ground, snow
accumulation and melt. Stable isotopes are potentially useful for quantifying the
dynamics of water sources, flow paths and ages, yet few studies have employed
isotope data in permafrost-influenced catchments. Here, we applied the
conceptual model STARR (the Spatially distributed Tracer-Aided Rainfall–Runoff model), which facilitates fully distributed simulations of hydrological
storage dynamics and runoff processes, isotopic composition and water ages.
We adapted this model for a subarctic catchment in Yukon Territory, Canada,
with a time-variable implementation of field capacity to include the
influence of thaw dynamics. A multi-criteria calibration based on stream
flow, snow water equivalent and isotopes was applied to 3 years of data.
The integration of isotope data in the spatially distributed model provided
the basis for quantifying spatio-temporal dynamics of water storage and ages,
emphasizing the importance of thaw layer dynamics in mixing and damping the
melt signal. By using the model conceptualization of spatially and temporally
variable storage, this study demonstrates the ability of tracer-aided
modelling to capture thaw layer dynamics that cause mixing and damping of the
isotopic melt signal.
Introduction
High-latitude regions are experiencing some of the most rapid rates of
environmental change as a consequence of global warming
, with limited process-based
benchmarks against which the implications are assessed. Permafrost, seasonal
frost and snowmelt strongly control the hydrology and mechanisms of runoff
generation in subarctic and arctic regions . There is an
enhanced interest in understanding runoff processes in permafrost areas, as
they are highly susceptible to climate warming . Knowledge
of streamflow generation mechanisms and associated hydrological pathways is
fundamental for understanding the functioning of these catchments and the
likely impacts of changes in energy and water availability
. However, despite the enhanced interest, logistical
difficulties in gauging and monitoring remote northern environments limit
empirical studies and process understanding . Thus, understanding how changes in permafrost distribution and
associated storage dynamics affect the hydrology of catchments with
permafrost is essential for reducing uncertainties in predicting the effects of
climate change .
Permafrost depth and distribution are highly variable across circumpolar
regions and exert a primary influence on runoff pathways, acting as an
aquitard that restricts deep drainage and hydrological exchanges
. Environments where permafrost is spatially discontinuous are
particularly complex, as soil storage and water redistribution are also
affected by the seasonal variability of the active layer . Seasonally frozen ground (the active layer) acts as
a transient subsurface zone that reduces permeability, limiting snowmelt
infiltration and redistribution of water within the soils . The influence of frozen ground on soil hydrology varies widely
based on the depth of the frozen layer, the pore-size distribution and pore space volume containing ice, and the temperature of the soils, which can
result in considerable exchanges of latent energy . While
the physics of heat and mass transfer are well defined, our ability to
accurately observe and simulate these processes is complicated by the
inherent variability in soil properties and the lack of instrumentation to
track all phases of water in the soil . Furthermore, in the
subarctic and low arctic regions, the widespread presence of highly permeable organic
soils influences runoff generation mechanisms . The occurrence of overland flow is typically limited, with
subsurface drainage across hillslopes in the near-surface organic layer
acting as the primary flow pathway, particularly during freshet and large
rain events .
Unlike rainfall-dominated catchments, the heterogeneous pattern of snow
accumulation and melt introduces complexities when inferring the hydrological
response of cold catchments. Vegetation and topography act as first-order
controls on snow accumulation and redistribution, as trapping wind from shrub
vegetation causes increased accumulation and redistributed snow settles in
areas of reduced wind velocity . The widespread expansion of shrub vegetation is a notable
feature throughout northern circumpolar regions due to a
warming climate, which influences surface–atmosphere exchanges and melt
. Topography has a similarly
important role through slope and aspect effects, with the energy balance of
northern catchments resulting in runoff contributing areas that are highly
variable in space and time .
Logistical difficulties associated with access and data collection in many
high-latitude catchments limit the possibilities for empirical studies and
process understanding. This makes stable isotopes a potentially valuable tool
for hydrological monitoring and advancing process understanding. Stable
isotopes are useful in estimating water transit or travel times (TTs), defined
as the elapsed time between water entry to, and exit from, a catchment as
stream discharge. Few studies have employed isotope methods in permafrost-influenced catchments to determine source waters . Often, isotopic data
were employed to explore runoff processes based on hydrograph separation or
conceptual models for individual events , but to our knowledge, no spatially distributed tracer-aided
models have been applied to snowmelt-dominated permafrost catchments.
Estimating TTs and water ages within a catchment requires models that
incorporate time-variant inputs from snowmelt and soil thaw, processes that
can be difficult to measure in cold heterogeneous environments. In addition,
various time-variant restrictions on infiltration during melt and on
percolation as thaw progresses result in variable flow pathways that
influence TTs in a complex manner . Capturing these
processes in hydrological models remains a challenge. STARR (the Spatially
distributed Tracer-Aided Rainfall–Runoff model) facilitates fully distributed
simulations of hydrological storage dynamics and runoff processes as well as
the associated isotopic compositions and age distributions
. The most recent advancements in STARR improve
modelling of the spatially distributed mass balances of snow accumulation and
melt along with simulation of the isotopic composition of meltwater
. STARR is now capable of simulating
interactions between water storage, flux and isotope dynamics, with
multi-criteria calibration in snow-influenced environments
.
The Wolf Creek Research Basin (WCRB), together with an alpine sub-catchment
(Granger Basin; GB), is a long-term experimental site in subarctic Canada,
with various gauging and weather stations and a rich data record
. WCRB has been widely used as an international
inter-comparison site for hydrological and biogeochemical research and model
development
and is considered a representative montane discontinuous permafrost catchment
.
Here, we further develop STARR to simulate the spatio-temporal dynamics of
storage in the permafrost-influenced GB alpine catchment of WCRB. The
specific objectives are the following:
adapt STARR for discontinuous permafrost catchments to capture thaw layer dynamics that vary in time and
space,
conduct a multi-criteria calibration to simulate isotope fluxes in snowpack dynamics and
streamflow,
use the model to assess the temporally and spatially variant storage dynamics in soils influenced by freeze–thaw processes and the associated ages of resulting water fluxes.
This study demonstrates the value of tracer-aided modelling to quantify
catchment water storage and age dynamics in a permafrost-influenced environment
for the first time.
Study site and dataStudy site
The 7.8 km2 Granger Basin (60∘32′ N, 135∘11′ W)
is a subarctic alpine catchment within WCRB
(Fig. 1a), 15 km south of Whitehorse, Yukon Territory, Canada. WCRB has a
dry seasonal subarctic climate (Köppen classification Dfc) with a 30-year
climate normal (1981–2000) reported for Whitehorse International Airport (706 m a.s.l)
of -0.1∘C and an annual precipitation of 262.3 mm, with
approximately 40 % falling as snow. However, precipitation at WCRB ranges
in magnitude and phase with elevation , and GB has on
average considerably higher precipitation than Whitehorse.
The elevation of GB ranges between 1310 and 2080 m a.s.l. (Fig. 1b). At
lower elevations, the main river valley trends west to east with
predominantly south- and north-facing slopes (Fig. 1c, d). The geology is
primarily sedimentary, consisting of limestone, siltstone, sandstone and
conglomerate, overlain by a mantle of glacial till . Atop
bedrock, stony till and other glacial drift cover most of the basin. Soils in
the top metre below 1650 m a.s.l. are sandy to silty. At lower elevations,
the upper layer of soil is an organic layer with variable thickness up to
0.4 m, consisting of moss, lichens and peat (Fig. 1f). The organic layer has
an average porosity ϕ = 0.88 and an average density ρ=124 kg m-3, while the deeper mineral layer has an average porosity
ϕ=0.49 and an average density ρ=1104 kg m-3.
Approximately 70 %–80 % of the GB is assumed to be underlain by
permafrost , the disposition of which being controlled
primarily by elevation and aspect. North-facing slopes and higher elevation
areas are considered to have permafrost, whereas south-facing slopes are
dominated by seasonal frost . The basin is situated in the
shrub taiga and alpine tundra ecozones, above treeline
(∼1200 m a.s.l.). Vegetation includes low-lying grasses, willow shrubs
(Salix Sp.) and Birch (Betula Sp.) at lower elevations.
Only few white spruces (Picea glauca) are present. Tall shrubs
(>2 m) occur along the riparian corridor in the lower basin (Fig. 1e). The
upper basin is dominated by bare rock and alpine tundra with limited
vegetation .
Granger Basin (GB) characteristics showing (a) location
within the Wolf Creek Research Basin (WCRB), stream network and gauging
station, (b) topography, (c) slope, (d) aspect,
(e) vegetation types and (f) soil types. Lower (LB) and
upper basin (UB) areas are marked.
Data
Meteorological data (air temperature – T, wind speed, solar radiation and
relative humidity) were recorded every 15 min at the Buckbrush weather station
(BB; 1312 m a.s.l.), located ∼2.8 km from the GB outlet in an area
of WCRB with similar characteristics to GB (Fig. 1a). To fill gaps in the
meteorological data, a linear regression between the Alpine weather station
(1615 m a.s.l.) 6.2 km from BB within WCRB was used over the period
2008–2017 (with a R2 on average >0.67; T had the best fit with
R2∼0.96). T records were adjusted for altitude, assuming the moist
adiabatic lapse rate of -0.006∘C m-1 a.s.l.
. The daily precipitation time series integrated data from
two precipitation gauge instruments at the BB weather station: a Geonor
T-200B gauge deployed in a standard configuration with a single Alter shield
and a tipping-bucket rain gauge. The challenge of measuring precipitation in
these regions has been discussed by . According to the
experimental relationship suggested for WCRB, a wind factor correction has
been applied to precipitation. Finally, altitude effects were considered,
assuming a 0.05 % increase in the isotopic composition of precipitation for
each 100 m increase in elevation. describe the
elevation-dependent climatology of WCRB and the relationship between
meteorological variables among the long-term weather stations used in this
study.
Automated snow pillow measurements from the BB weather station were averaged
to obtain a daily time series of snow water equivalent (SWE). The instrument
converts weight of the snow overtop the snow pillow into SWE. Stream
discharge was calculated at the outlet of GB using a rating curve updated
each year. A stilling well was instrumented with a pressure transducer
(Solinst Levelogger) and compensated with a co-located Solinst Barologger
measuring the pressure and stage every 15 min. Manual flows were made using a SonTek
Flowtracker for a range of flow conditions and with salt dilution gauging
during periods when the channels were ice-covered. The loggers were in place
from mid-April to October, when they were removed to prevent freezing.
Stable water isotope samples were collected from stream water, precipitation
and snowmelt. Stream water isotopic composition was taken both from grab
samples and an ISCO autosampler located at the gauging station of GB. The
samples had an average sampling frequency of <2 d both in 2015 and 2016
during the sampling period (mid-April to October, same as the discharge
measuring period). Only a few samples were collected with snowmelt lysimeters
in 2015 and 2016 at different locations in the bottom valley of GB. Rainfall
samples were collected using samplers adapted after from
different locations both in the Granger Basin and WCRB. Stable isotope ratios of
δ2H (and δ18O, which was not used here) were
determined using a Los Gatos Research DTL-100 water isotope analyzer at the
University of Toronto. Five standards of known isotope composition, with
δ2H ranging from -154 ‰ to -4 ‰, were
used for calibration, in addition to periodic checks using the international
standard VSMOW2. During analytical runs, samples were interweaved with
standards at a ratio of 3:1. For periods when precipitation isotopes were
not sampled, they were estimated via a linear regression between
precipitation δ2H and T. In addition to T and
precipitation time series, the precipitation isotopic composition was
spatially distributed to account for altitude effects at a rate of
-0.04 ‰ m-1 a.s.l. for δ2H.
Soil hydrological properties were mapped by splitting the model domain of the
entire GB into two main hydropedological units, each with different
properties and hydrological responses: the upper basin (UB) and lower basin
(LB; Fig. 1f). The UB includes areas at upper elevations
(>1650 m a.s.l.) where bare soil is classified as regolith,
bedrock outcrops occur and the organic layer is absent. The LB aggregates the
other soil classes comprised of organic soil of varying thickness, including
riparian soil. The model domain was also divided into four classes based on
vegetation properties (Fig. 1e): a tall shrub class that occurs
mainly in the riparian areas of the LB, shrub at lower elevations but not in
riparian areas, short shrub in areas in the central basin and no vegetation in the UB.
Parameters and their range of variation during calibration.
CategoryNameUnit of meas.DescriptionMinMaxSnowsfcorr(–)Correction factor for snowfall on top of wind correction00.3TTlow(∘C)Temperature below which all precipitation is snow-20TThigh(∘C)Threshold temperature above which all precipitation is liquid02SoilfcapUB(–)Volumetric field capacity (upper basin)0.30.8fcr(–)Field capacity rate12.5ASP(–)Aspect field capacity rate (for south-facing cells)11.2ksUB(d-1)Recession coefficient to determine outflow from soil storage (upper basin)540ksLB(d-1)Recession coefficient to determine outflow from soil storage (lower basin)540KsPow(–)Power coefficient12βSeepage(–)Recession coefficient to determine soil recharge into groundwater0.11LP(–)Fraction of limiting actual evaporation0.11Cflux(–)Parameter for maximum capillary flux0.011IsotopesdeplOffset(‰)Offset parameter, equilibrium between ice and liquid0-19Efrac(‰)Snow sublimation fraction080GWpas(mm)Mixing volume groundwater1200SMpas(mm)Mixing volume soil1200Model development for frozen soil and thaw layer dynamics
STARR is a
spatially explicit hydrological model aimed at simulating water fluxes,
storage dynamics, isotope ratios and water ages. It is based on a
HBV-type (Hydrologiska Byråns Vattenbalansavdelning-type)
conceptual structure for representing soil and
groundwater storages and fluxes in terms of water flow and isotopic
composition. Briefly, the model equations of the different routines
(interception, snow, soil and groundwater) are applied to each grid cell. For
each compartment, isotope ratios are estimated according to mixing equations
with the assumption of complete mixing. The snow module is built on the
assumption that the interception efficiency decreases with canopy snow load
and increases with canopy density and, further, that snow unloading increases
with time . The snow module is also energy-based; hence
it accounts for the sublimation fractionation of snow isotopes both of canopy-intercepted snow and the ground-level snowpack as well as the isotopic
depletion of snowmelt. Water ages are estimated by tracking the storage cell
by cell at each time step, so the water ages dynamically and spatially
evolves. Full details about the model structure, parameters and equations are
given in and in . Here,
according to the parameter sensitivity analysis conducted in previous
applications of the model, some of the parameters were randomized from
initial ranges and then calibrated to optimize the model in a Monte Carlo
approach (Table 1). Other parameters were kept fixed to specific values
selected through preliminary testing runs.
The overarching goal of STARR is to keep the model structure simple while
representing the spatial distribution of dominant hydrological processes for
a given environment – in this case, subarctic alpine with discontinuous
permafrost. Applying the model to GB required conceptualization of the impact
of frozen soil by modelling the field capacity of the soil as time-variant to
represent active-layer storage . The approach used was to
(i) limit available soil storage when the soil is frozen, (ii) make available
soil storage gradually increase when temperatures are above 0 ∘C to
a maximum value and then (iii) reduce available soil storage during the
refreezing period (Fig. 2). The freezing dynamics were implemented by setting
the field capacity (FC) to a minimum value (FCmin) when t<t1
(where t1 is the beginning of the thaw period) or t>t4 (where t4 is
the end of freeze back), linearly increasing for t between t1 and t2
(where t2 is the time of maximum thaw) up to the maximum value
FCmax and linearly decreasing between t3 (where t3 is the
onset of freeze back) and t4 (Eq. ; Fig. 2):
Field capacity (FC) parameter set to be time-variable. FC is set to
a minimum value (FCmin) when t<t1 or t>t4, with t increasing
linearly between t1 and t2 up to the maximum value FCmax
and linearly decreasing between t3 and t4. The top image is a schematic
representation of a soil cell to help visualize the variable FC. FC is
dependent on the soil parameters: fcap (volumetric field capacity), sd
(soil depth), ASP (aspect) and fcr (field capacity rate; calibrated
parameter).
In addition, to make this frozen soil approximation spatially consistent with
field observations, a parameter (ASP) accounting for aspect was included.
Specifically, south-facing slopes were considered to have consistently higher
available soil storage than the cells facing different cardinal directions.
The parameter ASP was set to 1 if the cell was non-south-facing and randomly
sampled from the range 1.0–1.2 for south-facing cells. This indicates that
the time-variant available storage for a south-facing cell was permitted to
be, at maximum, 20 % higher than a non-south-facing cell. The FC is the
product of soil depth (sd) and the volumetric field capacity (fcap), and the
time-variant FC is defined from FCmin (Eq. ) and
FCmax (Eq. ):
2FCmin=sd⋅fcap,3FCmax=FCmin⋅fcr⋅ASP,
where fcr is the field capacity rate parameter used to calibrate the ratio
between FCmin and FCmax. To avoid unreasonable FC
values, the fcap parameter was randomly sampled and optimized during the
calibration process. For simplicity, the intervals of the piecewise function
(Eq. ) were set a priori, according to site knowledge based
on previous observations of frozen ground development . The
endpoints were set as following: t1 to 1 May, t2 to 15 July, t3 to 1 October
and t4 to 1 November. Thus, FC was set to its minimum for November–April,
linearly increasing from May to mid-July, being at its maximum until October and
finally sharply decreasing to represent soil freeze back. Despite most
parameters values being set for the whole catchment, some were set to reflect
the properties related to soil, vegetation and aspect classifications
(Fig. 3).
Aggregation used to set the spatially variable parameters:
(a) soil classification for two calibrated parameters (fcap is volumetric field capacity and ks is recession coefficient) and one fixed
parameter (sd is soil depth), (b) vegetation classification for five
fixed parameters (ccov is canopy coverage, LAI is leaf area index,
cH is canopy height, cMax is maximum canopy storage and cgf is canopy gap fraction), and (c) aspect classification for ASP
parameter that was calibrated if south-facing or set to 1 for any
non-south-facing aspect.
A multi-variate calibration approach was
applied to optimize the model according to three variables: discharge, SWE
and stream water isotope values. To obtain model efficiencies of discharge
and stream water isotopes, we compared observations of both at the gauging
station with simulated values at the outlet cell. For SWE, we compared the
observed SWE at BB and the catchment average of simulated snowpack for each
time step. However, the simulated values were dependent on elevation, and it
was not possible to compare simulations and observations directly as
measurements were taken at BB, outside of GB. We ran 7000 simulations in a
Monte Carlo approach, each one being characterized by a parameter set randomly
sampled from an initial range (Table 1). In each simulation, years 2014 and
2015 were looped in order to initialize the system in terms of stabilizing
both water storage and isotope values. A multi-variate calibration was then
conducted for the study period 1 January 2014 to 31 December 2016, and for
each simulation, three efficiencies were determined: Kling–Gupta efficiency
KGE; for evaluating discharge and SWE and mean absolute error
(MAE) for evaluating δ2H simulations. The empirical cumulative
distribution functions of these efficiencies were used to select the 100
simulations showing simultaneously the highest values of KGE for discharge
and SWE and the lowest value of MAE for stream water δ2H. KGE
was chosen for hydrometric variables, as it is based on equal weighting of
linear correlation, bias ratio, and variability. KGE tends to be a more
balanced approach than the Nash–Sutcliffe efficiency NSE;, with less
biasing to peak runoff . For evaluating simulation results
for stable isotopes, MAE was chosen, as the error range estimates are of the
same scale as observation variability and MAE provides advantages over the
root-mean-square error (RMSE; i.e. MAE is a more stable measure of the
magnitude of average error, while the RMSE can be confounded by the variable
functional relationship between the RMSE and average error; ).
Time series results were based on the 100 best simulations, while the spatial
model outputs were based on the best simulation according to the same method
used for the 100 best simulations and were therefore dependent on the
intrinsic characteristics of the selected simulation.
The approach used in STARR allows estimation of the spatial distribution and
dynamic variation of water ages. In addition to the isotopic composition,
water ages were computed according to a full-mixing assumption within each
cell and time step, according to passive storage parameters for soil and
groundwater reservoirs in the model (Table 1). Water ages of total runoff
(i.e. overland flow and lateral soil and groundwater fluxes) were estimated
using a mass balance for each cell that tracked all inflows and outflows and
quantified total runoff. During each time step, water stored in each model
compartment becomes a day older, with the age of incoming precipitation taken
as 1 d. The age of water in each compartment evolves dynamically through
mixing and water exchange between compartments and cells. Stream water ages
evaluated at the outlet cell are the time-variant integration of all water
fluxes from different catchment compartments, each having their own age
distributions similar to. All simulations were
performed at 100 m × 100 m resolution and at a daily time step.
ResultsTemporal dynamics of water fluxes, storage and age
During the study, measured discharge ranged from 0.001 to 1.1 m3 s-1 (Fig. 4). There were limited discharge measurements between
October and April, except for occasional under-ice measurements. Seasonal
variability in flow was more marked than the inter-annual variation (standard
deviation across all years for the sampling period April–October is
σ=0.139, while for each year, σ2014=0.147,
σ2015=0.145 and σ2016=0.116). In each year, the first
recorded flow peak was related to snowmelt, while later in the summer,
discharge was most responsive to large rainfall events (Fig. 4a, b). In 2014,
the peak discharge (1.1 m3 s-1) occurred at the beginning of
July,
following a 36 mm rain event. In 2015 the peak was 0.67 m3 s-1,
recorded at the end of May during the spring melt. In 2016, peak flow
(0.85 m3 s-1) was measured in mid-June following a 31 mm rain
event, at the end of the snowmelt period.
Time series of (a) observed precipitation isotopic
signature of δ2H (‰) and observed rainfall (mm). Time
series of simulated (grey) and observed (b) discharge Q
(m3 s-1), (c) stream water isotopic signature
δ2H (‰), (d) catchment average snow water
equivalent (SWE; mm) and snowmelt isotopic signature δ2H
(‰), and (e) stream water ages (days) at outlet. Dark grey bands
show ranges of selected best 100 runs (Best sim), and black lines are the
median simulation (Median sim) among the 100 best simulations (Best
sim).
Measured precipitation δ2H ranged from -76.9 ‰ to
-180.2 ‰, showing seasonality with more depleted values in winter
and more enriched values in summer. In contrast to the variable precipitation
signal, the stream water δ2H measurements exhibited a highly
damped signal that lacked the clear depression usually associated with alpine
catchments during the snowmelt. If anything, δ2H shows some
enrichment from the snowmelt period until the summer, albeit with some limited
short-term variability (Fig. 4c). The sparse snowmelt δ2H
samples were on average -155.3 ‰, which is more enriched than the
minimum stream water values. The snowpack generally begins to accumulate in
late August or early September, reaching a peak the following spring before the
main melt period in late April to May. The highest value of the observed SWE (230 mm) was measured in April 2014 (Fig. 4d). In 2016,
peak SWE was lower than in the other years (112 mm).
Given the complexity of the catchment hydrology, the model simulated the
discharge dynamics quite well over the 3 years, with KGE values ranging
from 0.48 to 0.70 across the 100 best simulations (Fig. 4b; Table 2). The
snowmelt freshet was well reproduced, both in terms of timing and peak, yet
the simulated recession limbs were slightly steeper than observed. The early
summer period was characterized by the highest discharge peaks both in 2014
and 2016, which was well represented by the model. The largest
underestimation of the simulated discharge was during July and August 2016
during rain-driven events. The main challenge in reproducing the stream water
δ2H composition (Fig. 4c) was the limited seasonal
variability of the signal, coupled with some shorter day-to-day variation.
Despite the difficulties in reproducing this damped signal, the span of the
efficiency across the 100 best runs (MAE between 4.41 and 5.84 ‰) was
similar to the model performance obtained in previous model applications in
snowmelt-driven catchments . The simulated
signal did reproduce a slight depletion after melt, followed by enrichment,
although the measured melt signal showed greater seasonal mixing and damping,
though greater day-to-day variation,
than the simulated signal.
Efficiency ranges of 100 best calibrations, selected to
simultaneously have the highest KGE for discharge and SWE and lowest MAE for
stream δ2H.
Observed and simulated temporal SWE dynamics (averaged across the catchment)
are shown in Fig. 4d. The snowpack model output was highly dependent on
elevation, yet the spatially averaged time series reasonably reproduced the
SWE measurements, with KGEs ranging from 0.71 to 0.72 across the 100 best
simulations. Overall, catchment average SWE was underestimated in 2014 and
overestimated in 2016, despite capturing the peak. In 2015, the first part of
the accumulation period was overestimated by the model, whereas the second
part underestimated accumulation prior to melt. The melt period in 2015 was
shorter than in 2016, and the decline from high values of SWE to 0 was more rapid
(26 d in 2015 from early May to end of May, against 61 d in 2016 from
mid-April to mid-June). Moreover, in early April 2016 the simulated melt
period was interrupted by a period of refreezing, which delayed the simulated
melt compared to the measured. Due to the scarcity of snowmelt isotope
samples, it was not possible to include these observations in the calibration
(Fig. 4d). However, simulated snowmelt δ2H was reasonable, as
the majority of the observations in 2015 and 2016 fell within the uncertainty
bands of the simulated composition.
Figure 4e shows the simulated stream water ages at the outlet cell of the
catchment. The median water age over the calibration period was 290 d.
Stream water ages showed clear seasonal dynamics: a steady increase to
>1 year (with large uncertainty) when deeper sources sustained low flow
periods in winter. Ages were reduced to <9 months in the early phases of
the melt, gradually decreasing to around 6 months in the late summer, as
younger water from melt and summer precipitation was an increasingly dominant
source of runoff. The uncertainty was considerably reduced during high flow
periods.
Spatial variability of water fluxes, storage and ages
Figures 5, 6 and 7 provide spatially distributed estimates of select model
outputs (i.e. simulated SWE, soil storage volumes and ages of water fluxes
from each cell) at hydrologically relevant dates or averaged over specific
periods. The patterns in the SWE maps (Fig. 5) reflect the influence of the
vegetation parametrization (e.g. presence of shrubs in the lower basin with
interception and unloading processes) in addition to the influence of
elevation. In 2015, the simulated snow accumulation was less variable across
the catchment compared to the more heterogeneous snowpack in 2016. In 2015,
melt occurred with a short time lag between lower and upper elevations (16 d
difference when SWE = 0 in the lowest and highest catchment cells). In
contrast, in early 2016 simulated SWE values were more heterogeneous across
the catchment. Highest simulated averaged values occurred when the lower
catchment had values ≤50 mm, whereas the upper basin reached 300 mm.
In contrast to the rapid melt in 2015, the time lag between the day when
SWE = 0 occurred at the lowest and the highest cell in the catchment was
59 d. This reflected the slower observed melt, though the modelled melt was
delayed.
Spatial distribution of snow water equivalent SWE (mm) for the day
of peak SWE in both study years: (a) 23 February 2015 and
(b) 19 March 2016.
Spatially simulated liquid soil water storages are shown in Fig. 6 for
different periods. The highest simulated values of soil water storage
occurred immediately after the melt period in 2015 (Fig. 6a) and in 2016
(Fig. 6b). As the melt period was shorter and occurred more uniformly across
the catchment in 2015 compared to 2016, the variability in soil storage
across the cells was lower in 2015 than in 2016 (standard deviations
σ=13.8 mm compared with σ=22.2 mm in 2015 and 2016,
respectively). In 2016, the upper basin cells received considerable water
inputs (up to 183 mm) from melt, while in the lower basin the storage was
lower than 36 mm. In addition, estimated soil water storage averaged on
biweekly windows provided information on the spatial variability in soil
water storage, as the thaw layer increased while soils approached the highest
overall field capacity (Fig. 6c and d). The highest field capacity occurred
when the available storage was maximized (Fig. 6e and f) and then when
available liquid storage was declining during freeze back (Fig. 6g and h).
Overall, spatial patterns in the soil storage maps reflect a combination of
the empirically based parametrization of aspect (south-facing and non-south-facing) as well as the distinct vegetation and soil characteristics of the
upper and lower basin.
Spatial distribution of simulated water soil storages (mm). Daily
snapshots on first snow-free day in the year: (a) 28 May 2015 and
(b) 18 June 2016. Values averaged over 15 d: (c)
1–15 July 2015, (d) 1–15 July 2016,
(e) 1–15 September 2015, (f) 1–15 September 2016,
(g) 1–15 October 2015 and (h) 1–15 October 2016. Note
that scales in (a) and (b) are different to the scales in
(c).
Simulated ages of runoff (as combined overland flow and lateral flow from
model cells) varied across the catchment during the period simulated
(Fig. 7), according to the spatial variation of storage reservoirs and water
fluxes. Deep groundwater contributions were generally negligible, consistent
with the conceptual model of hydrology in GB that accounts for runoff generation
occurring primarily from shallow lateral flow in the upper organic soil
layers (Carey and Woo, 2001). Estimated water ages were predominantly
influenced by soil runoff ages, as overland flow only occasionally occurred
during melt. Overall, patterns of simulated water ages reflected flow path
lengths and soil storage patterns, with ages increasing along drainage
directions from hillslopes towards the valley bottom. Cells located at the
convergence of the longest flow paths had modelled water ages consistently
older than in the other catchment cells (usually older than 300 d). From the
oldest ages immediately following melt (catchment average of 295 d for 2015
– Fig. 7a – and 233 d for 2016 – Fig. 7b), as stored water was displaced, water
ages decreased with increasing soil storage, summer precipitation and
discharge in July (catchment average of 242 d for July 2015 – Fig. 7c – and
catchment average of 234 d for July 2016 – Fig. 7d), reaching the youngest
overall ages at the end of the summer (catchment average of 177 d
September 2015 – Fig. 7e – and 185 d for September 2016 – Fig. 7f). Ages
increased again in October (2015 in Fig. 7g and 2016 in Fig. 7h), when the
availability of soil storage became restricted as refreezing occurred. Water
ages after melt were greater in 2015 than in 2016. This is consistent with
the different characteristics of the snowmelt periods in the 2 years in
terms of timing, magnitude and heterogeneity across the catchment. As in
2015,
melting was more homogenous compared to 2016, and the day after complete
snowmelt (i.e. the first day with SWE = 0 in all cells) occurred less
than 1 month after highest values of SWE, the hydrological system was still
affected by the mobilization of old water in storage, and the influence of
newer meltwater became stronger several days later. However, the melt period
in 2016 was longer with a gradual decrease in the snowpack (2 months from
high values of SWE to 0), and so the model compartments had already time to be
filled with newer water inputs, which made the overall age pattern younger.
Spatial distribution of simulated water ages (days) of runoff
contributions (overland and lateral flow) from model cells. Daily snapshots
on first snow-free day in the year: (a) 28 May 2015 and (b)
18 June 2016. Values averaged over 15 d: (c) 1–15 July 2015,
(d) 1–15 July 2016, (e) 1–15 September 2015, (f)
1–15 September 2016, (g) 1–15 October 2015 and (h)
1–15 October 2016.
DiscussionHow well can spatially distributed tracer-aided modelling capture thaw layer dynamics and runoff generation in permafrost catchments?
In discontinuous permafrost environments, storage dynamics and water
distribution are strongly affected by the seasonal variability of frozen
ground, the heterogeneity in snow accumulation and melt, and (particularly in
alpine areas) the strong variability in energy receipt due to low sun angles
. There has been limited application of isotopes
to investigate water sources and pathways in permafrost regions
. There have been fewer studies that have used hydrological
models that explicitly incorporate tracers in permafrost and snow-dominated
regions e.g.. Here, a spatially distributed model
that integrates isotopic composition and discharge was applied to simulate
runoff generation, stable isotopes, snowmelt and track water ages. By taking
thaw dynamics into account, a time-variant available soil storage was
implemented for the first time in STARR. Previous
applications of STARR demonstrated that multiple data sets and calibration
criteria helped to constrain models and provided information on the relative
value of observations , guiding experimental
design and providing information on gaps in process understanding
. In this work, by incorporating a simple but distributed
conceptualization of thaw dynamics, STARR was able to effectively simulate
the temporal dynamics of discharge with an adequate damping of the stream
isotope signal. Despite the large variability in storages and fluxes – which
are well-documented for GB – the model was able to efficiently simulate the
three calibration variables, providing confidence that the dominant governing
processes were generally well simulated and parameters well represented. That
said, although the overall damping of the isotopes was captured, the detailed
short-term day-to-day variation was not. Also, the model exaggerated the
effect of the depleted snowmelt pulse reaching the stream.
At WCRB and GB, previous research has documented how frozen ground status,
organic soils, aspect and permafrost dominate the hydrological response to
rain and snowmelt events . In
complex alpine landscapes, aspect and altitude control the timing of melt and
the subsequent delivery of water to soils. Organic soils are hydrologically
complex, with a high porosity that can rapidly convey water to the stream
when thawed or near 0 ∘C during melt. Lateral flow in organic soils
is a key process in subarctic permafrost regions, as hydraulic conductivity
is typically orders of magnitude greater than underlying mineral substrates
. The descent of the frost table
along permafrost slopes allows deeper flow pathways to become active even as
water tables typically fall, muting streamflow response .
Areas without permafrost are thought to contribute less to runoff, yet the
overall disposition of permafrost in alpine landscapes is difficult to fully
ascertain and the relative influence of deeper
groundwater flow is uncertain at present. Given this complexity, the
day-to-day isotope dynamics are likely underpinned by more localized
spatially heterogeneous processes, which are probably not fully captured by
the current model set-up .
This is because in this study, STARR was set up to best represent
the process understanding described above by (i) splitting the model domain
into two hydropedological units based on organic soil presence, (ii)
including a classification based on aspect to reflect permafrost presence and
available soil storage, and (iii) allowing soil storage to be time-variant to
reflect the seasonal development of frozen ground. Previous research in GB
highlighted the importance of spatially representing processes in both
field and modelling studies. For example, for the snowmelt period,
divided GB into nine hydrological response units (HRUs)
based on similarities in hydrological, physiographic, vegetation and soil
properties. showed that a distributed hydrological model
based on five HRUs was necessary to describe the observed magnitudes of both
snowmelt and basin runoff. In this work, we explicitly simulated processes in
GB at a 100 m scale. Model results support the observations that overland
flow is largely absent in this basin and that
spatially represented melt is critical in accurately predicting snowmelt
freshet . The spatial representation of
processes in GB was also important in simulating biogeochemical processes as
shown in . However, it is likely that the 100 m grid is
too coarse to pick up small-scale processes, which might affect the
day-to-day isotope variability.
Spatio-temporal variations in water storage, flux and ages
Spatial heterogeneity in modelled hydrological response was most strongly
influenced by the timing and magnitude of ground freeze–thaw and also by the
heterogeneities of inflows from snowmelt. Simulated melt rates were highly
variable among years due to the disparate nature of snow accumulation and
contrasts in melt rates across elevation, vegetation type and aspect. The
differential melt rates affect various aspects of hydrological response,
including the distribution of soil storage, isotopic composition and water
ages. STARR explicitly tracks the spatial distribution of water isotopes from
melt and rainfall inputs and through the soil system to the stream. This
approach provides an additional temporal dynamic of soil water ages
throughout the catchment. Linking runoff generation processes to water ages
is similar to, yet distinct from, hydrograph separation approaches that
isolate sources of water . Other
techniques for estimating water ages, such as convolution integral transit
time distributions , lumped conceptual models
and storage selection functions , are
useful, yet they are limited in terms of capacity to track the spatial distribution of
water ages in the catchment. To our knowledge, there has been no estimate of
spatially distributed water age in subarctic and arctic regions.
Simulated water ages at the end of the melt season were older than in any
other season, as the main water source at this time is the stored water
within the catchment which is being mixed with, and displaced by, snowmelt
(Figs. 4 and 7). So the main source of water at the end of the snowmelt
period is relatively old water that has been stored in the catchment over
winter. The sources of water that lead to streamflow response have been
previously studied in GB and other permafrost catchments using stable
isotopes and more traditional hydrograph separation techniques
. Conceptual models often suggest that low
storage capacities and high runoff ratios observed during the freshet must be
dominated by inflow from directly connected melt, or “new” water, as
opposed to “old” water that resides in the catchment over winter when soils
are frozen. However, empirical results have been variable, with some
catchments showing a predominance of new water or old water depending on site characteristics and/or the time of
year. While the cause of the differing new and old water contributions is
unclear, there appears to be considerable inter-annual variability based on
hydrological conditions of the ice-rich soil and the nature of melt
. In this study, water ages as determined by
STARR were the oldest after melt and then decreased throughout the summer. While
there was considerable variability within the catchment, this pattern
generally holds until freeze back begins in October and soil storages
decline. The decline in soil storage, however, represents a dynamic liquid
water storage, not total water storage in soils. For GB,
reported event water contribution from two-component hydrograph separation
ranging from 10 % to 26 %, suggesting that most of the water
reporting to the outlet during freshet is old water (up to 90 %). This
observation agrees well with results of STARR, suggesting that
streamflow water during freshet is primarily displaced old water that has
resided in the watershed over winter. This is also consistent with the
findings of recent small catchment observations at Trail Valley in Canada
and larger-scale observations in the catchment of the
Ob River in Russia .
The mechanism of old water displacement from soil storage to the stream
during melt results in the mixing and dampening of the isotope signal
. This appears to be the case in GB, where despite the
presence of frozen ground and permafrost, multiple years of study suggest
that pre-event water predominates, and model results presented here suggest
that water is oldest during freshet. Previous model runs in snow-influenced catchments (in Idaho, US; Sweden; and Ontario,
Canada), not affected by permafrost, showed a dominance of young soil water
ages during melt, followed by a gradual increase in water ages. The
difference to these previous studies suggests that the permafrost and thaw of
frozen ground play a key role in the predominance of old water during freshet
in GB. The question remains as to how soils that are largely frozen or at
0 ∘C during melt can contribute old water to the stream and why the
new water signal from large volumes of meltwater is strongly damped. The
most plausible explanation is the presence of organic soils, which are able
to mix and transmit water during melt, even at 0 ∘C. It is also
worth noting that the freshet also coincides with the “first flush” of
high DOC values, underlining the mobilization of organic-rich soil waters by
the melt . The ability of organic-rich soil horizons to
mix and dampen isotope signals has been documented in other cold environments
. In GB, organic soils cover much of the basin, and
empirical studies have shown that their high porosity allow several hundred
millimetres of total water storage when saturated . Depending upon
their moisture content at freeze back, there may be a considerable infiltration
opportunity during melt .
hypothesized a mechanism where in the early stages of melt, there is limited
transfer of water to the stream until unsaturated storage capacity is
satisfied and infiltrating meltwater supplies sensible heat to bring soils
to 0 ∘C (yet not necessarily thawed). At this time, mixing with
pre-meltwater occurs and runoff generation begins. It is instructive that
the contribution of old water increases throughout the melt period
, which corresponds to the age estimates from
STARR. Furthermore, the differences in ages between years (Fig. 7),
particularly during melt, support the observations that there is considerable
inter-annual variability in the ages and source of water contributions, which
are linked to conditions of the previous fall and the rate and timing of
melt.
The use of STARR as a spatially distributed tracer-aided model provided a
number of new insights into the hydrology of GB, which has a rich history of
observation and model application. While prior work identified the dominance
of old water during freshet , STARR
was able to support this finding in a conceptual model that captured the
dominant runoff generation mechanisms and mixing processes. The role of
organic soils and variable soil storage was highlighted through multiple
lines of evidence, and the importance of over-winter storage and melt
dynamics on water ages was partially clarified. The implications of this
enhanced understanding are important in terms of hydrological and
biogeochemical response to climate change. In this region, temperatures are
warming rapidly, particularly in winter . Changes in flows
and biogeochemical fluxes for northern regions have been reported at larger
scales , yet their link to process understanding at
the headwater scale remains scarce. At the larger continental scale of arctic
river basins, increased temperatures have been shown to decrease in amounts
of catchment water storage due to increased thaw and evapotranspiration
, suggesting a gradually decreasing influence of permafrost
on controlling hydrological function. This possible scenario of an
accelerating hydrological cycle in cold regions requires further multi-scale
investigation. At the headwater scale, the fact that there is considerable
inter-annual variability in the hydrological and isotopic response suggests
large potential variability in ages, which may amplify as the soil freezing
regimes change. Furthermore, the influence of permafrost thaw on water ages
remains unclear. Considering how water ages links to soil contact times and
biogeochemical processes, further application of age estimation and
understanding water storage dynamics may aid in understanding ecosystem
response in a warmer world.
Conclusions
In this work, we applied the spatially distributed, tracer-aided model STARR
to a cold, permafrost-influenced catchment in Yukon Territory, Canada. The
model was subject to multi-criteria calibration with multi-year field data to
simulate runoff, snowpack dynamics and stream isotope composition. The model
captured all three variables reasonably well, and notably, the highly damped
stream isotope signature was reproduced. Critical to this was the
conceptualization of the thaw layer dynamics and thick organic soils, which
provided a sufficient mixing volume that buffered the snowmelt isotope
signature prior to water reporting to the stream network. Simulation results
from the model output correspond with previous field investigation and
hydrograph separation studies that indicate relatively old water (pre-event)
dominating runoff generation during spring freshet. The relatively flashy
nature of spring freshet in this largely frozen alpine catchment may seem
counter-intuitive to this finding, yet water stored within the catchment from
the previous year is the main source of stream water at the end of the melt
season and explains isotopic damping of the signal. This result has important
implications for processes that drive inter-annual variability and
biogeochemical cycling, as there are considerable time lags in the system. How
climate warming affects frozen ground and water ages is uncertain, yet water
ages will likely increase with a reduction in the cold season. Another important
conclusion is that the snowmelt regime, which is variable each year, is an
important factor in controlling water ages.
Data availability
The model code and the data are available upon request.
Author contributions
TP adapted a model developed in earlier work led by DT and CS and carried out the modelling with support from CS and AS. Data used for model calibration and testing were collected by NS. DT was the Principal Investigator (PI) on the ERC project VeWa. All authors were involved in the data and model interpretation. TP prepared the paper, with contributions from all co-authors.
Competing interests
The authors declare that they have no conflict of
interest.
Special issue statement
This article is part of the special issue “Understanding and
predicting Earth system and hydrological change in cold regions”. It is not associated with a conference.
Acknowledgements
This work was funded by the European Research Council (project GA 335910
VeWa). We also thank funding from the Natural Sciences and Engineering
Research Council's Changing Cold Regions Network and the Global Water Futures
programme. We gratefully acknowledge the assistance of Heather Bonn, Renée
Lemmond, David Barrett and Tyler de Jong for their help in the collection of
field data. We acknowledge support by the German Research Foundation (DFG) and the Open Access Publication Fund of Humboldt-Universität zu Berlin.
Financial support
This research has been supported by the Framework 7, European Research Council (project GA 335910, VeWa grant).
Review statement
This paper was edited by Howard Wheater and reviewed by two
anonymous referees.
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