HYDROLOGICAL PROCESSES
Hydrol. Process. (2014)
Published online in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/hyp.10214
Hydrological model uncertainty due to precipitation-phase
partitioning methods
Phillip Harder* and John W. Pomeroy
Centre for Hydrology, University of Saskatchewan, 117 Science Place, Saskatoon, Saskatchewan, S7N 5C8, Canada
Abstract:
Precipitation-phase partitioning methods (PPMs) that are used in simulating cold-region hydrological processes vary significantly.
Typically, PPMs are based on empirical algorithms that are driven by readily available near-surface air temperature but ignore the
physical processes controlling precipitation phase by not incorporating humidity. Because these lack any physical basis, there is
uncertainty in their spatial and temporal transferability. Recently, humidity-based methods that have a stronger physical basis and
smaller uncertainty have been developed. To quantify the uncertainty that empirical PPMs introduce into hydrological simulations, a
cold-region hydrological modelling platform was used with a physically based PPM and a selection of empirical PPMs to calculate a
set of snow regime and streamflow regime indices. The empirical PPMs included a single air temperature threshold and a double air
temperature threshold, whereas the physically based PPM used a psychrometric energy balance model. All calculations were run
with near-surface meteorological observations that typically drive hydrological models. Intercomparison of the hydrological
responses to the PPMs highlighted substantial differences between the wide range of responses to empirical algorithms and the very
small uncertainty due to physically based methods. Uncertainty of hydrological processes, quantified by simulating over a range of
air temperature thresholds, reached 20% for the rainfall fraction, 0.4 mm/day for basin discharge, 160 mm of peak snow water
equivalent, 36 days for hydrological uncertainty snow cover duration, 26 days for snow-free date and 10 days for peak discharge
date. The implication of this research is that the reduced uncertainty derived from implementing physically based PPMs, for
operational or research purposes, are greatest for snowpack prediction in mountain basins. However for streamflow discharge
calculations, the reduced uncertainty was greatest in prairie and alpine basins due to the additional effects of precipitation phase
calculations on frozen soil infiltration and summer snowmelt processes respectively. Copyright © 2014 John Wiley & Sons, Ltd.
KEY WORDS
precipitation phase; snowfall–rainfall transition; prairies; mountains; arctic; cold region hydrology; uncertainty
estimation; western Canada; snow hydrology
Received 11 November 2013; Accepted 8 April 2014
INTRODUCTION
The separation of precipitation into rainfall or snowfall is
one of the most sensitive parameterizations in simulating
cold-region hydrological processes (Loth et al., 1993).
Meteorological conditions near the ground surface are often
used to identify phases in hydrological models that are
uncoupled from atmospheric processes (Feiccabrino and
Lundberg, 2008). Full solutions implemented in atmospheric models to resolve precipitation phase require
information on topography, atmospheric lapse rates and
surface interactions with the atmosphere (Marks et al., 2013),
limiting their application in hydrological models. Despite
examples of physically based approaches utilizing the
psychrometric energy balance to predict precipitation phase
(Steinacker, 1983), hydrological applications often correlate
*Correspondence to: Phillip Harder, Centre for Hydrology, University of
Saskatchewan, 117 Science Place, Saskatoon, Saskatchewan, S7N 5C8,
Canada.
E-mail: [email protected]
Copyright © 2014 John Wiley & Sons, Ltd.
daily average air temperature (Ta) to precipitation-phase
observations (Feiccabrino and Lundberg, 2008; Fassnacht
et al., 2013). Daily average Ta is the most readily available
meteorological variable, and so the spatial density of
temperature observations has much to do with its popularity
for determining precipitation phase. However, empirical
Ta–phase relationships have no physical basis and so
cannot be applied without calibration to times, sites,
regions or elevations beyond their calibration range. Despite
this concern, the uncertainty that precipitation-phase
partitioning methods (PPMs) introduce into hydrological
modelling has not been previously quantified.
Three types of PPMs, which span the range of available
surface-based methods, are tested in this paper. The
simplest and most commonly used PPM applies a single
air temperature (Tt) threshold to define all precipitation as
rainfall when Ta is warmer and as snowfall when Ta is
cooler (Leavesley et al., 1983) (hereafter T0). Tt can
range from 1 to 4 °C as a daily value (Feiccabrino and
Lundberg, 2008). Values of Tt are site specific because of
local meteorological conditions and local topographic or
P. HARDER AND J. W. POMEROY
vegetation effects, which serve to decouple site-specific
meteorological conditions from the governing atmospheric
processes, including atmospheric stability (Olafsson and
Haraldsdottir, 2003). These effects include terrain and
canopy shading, wind exposure or shelter (Marks et al.,
2013), and intensity of precipitation. The values of Tt are
either assigned arbitrarily or set by calibration based on local
measurements of snowfall or rainfall occurrence and Ta.
Double-threshold PPMs use a cooler threshold to define
100% snowfall and a warmer threshold to define 100%
rainfall, with the range between thresholds considered to be of
a mixed phase. At a specific point in space and time, a phase is
usually not mixed, but when modelling over larger spatial or
temporal scales, then a phase can often be mixed, making a
fractional approach more realistic across space and averaging
interval. Quick and Pipes (1976), in the UBC watershed
model, suggested 0.6 and 3.6 °C as thresholds with a linear
interpolation in the mixed-phase range (hereafter UBC). The
range of values in daily-timescale double-threshold methods
can vary significantly from the Quick and Pipes values,
ranging from an all-snowfall threshold down to 1 °C to an
all-rainfall threshold of up to 11 °C (Fassnacht et al., 2013).
In contrast to empirical methods, Harder and Pomeroy
(2013) proposed a physically based approach to estimate a
phase by utilizing a psychrometric energy balance method.
By relating the calculated temperature of a falling
precipitation particle or hydrometeor to observations of
rainfall and snowfall, a physically based PPM was
developed (hereafter PSY). The calculation of the hydrometeor temperature uses the psychrometric equation to take
into account the latent and sensible heat fluxes occurring
between a falling hydrometeor and the atmosphere. It is
similar to the classic wet-bulb calculation in that it uses the
psychrometric relationship but differs as it is applied to
falling hydrometeors using atmospheric exchange relationships for precipitation particles in turbulent air that were
developed for blowing snow particles (Pomeroy et al.,
1993). The application of the PSY method, like other
physically based PPMs such as that proposed by Marks et al.
(2013), is limited to areas with observations of both
humidity and Ta. Harder and Pomeroy (2013) showed that
accuracy is greatly improved where hourly or sub-hourly
observations are available. These observations are becoming more widespread. Where humidity measurements are
sparse, it should be noted that they can be interpolated more
reliably than Ta or precipitation (Susong et al., 1999) and so
the use of humidity information is not a serious limitation
to applying PSY. PSY was tested against in situ
observations of precipitation phase at multiple elevations
in the Canadian Rockies and shown to consistently
outperform empirical methods, even when those methods
were calibrated to local conditions (Harder and Pomeroy,
2013). Further details on the PPMs implemented in this
paper are provided in the appendix.
Copyright © 2014 John Wiley & Sons, Ltd.
Studies that have varied the parameters of empirical
PPMs in hydrological models have focused on the impact
of precipitation phase on snowpack processes. The largest
effects are changes in the depth and density of a
snowpack (Loth et al., 1993; Lynch-Stieglitz, 1994;
Fassnacht and Soulis, 2002). A common suggestion to
reduce error is to use locally derived or calibrated Ta–
phase relationships (Fassnacht and Soulis, 2002), and
these can reduce error where detailed observations for
calibration exist but are problematic where there are no
accurate precipitation-phase observations. In Canada, the
advent of unmanned automated weather stations over the
last 15 years has introduced substantial inaccuracies in
precipitation-phase determination compared with that by
manual observation. This has limited the capacity to
evaluate changes in empirical PPM calibrations over time
or even to evaluate their performance using standard
meteorological station precipitation data. A consequence
of errors in empirical PPMs is that they are accumulated
in snowpack simulations, which can lead to systematic
overestimation or underestimation of peak snow water
equivalent (SWE) and depth (Lynch-Stieglitz, 1994) and
hence snowmelt runoff. Varying the PPM also leads to
differences in the calculated energy balance of a snowpack
(Loth et al., 1993; Fassnacht and Soulis, 2002).
Overestimating rainfall advects more energy to the
snowpack, increases snowpack liquid water content, leads
to earlier warming and ripening, increases latent heat
transfer to snow, lowers the albedo and raises the snow
surface temperatures relative to reality (Loth et al., 1993).
Overwinter rainfall events can introduce ice layers into cold
snowpacks (Marsh and Pomeroy, 1996) and reduce the
infiltrability of frozen soils (Gray et al., 1985); both
processes impact runoff efficiency during snowmelt and so
need to be estimated accurately in hydrological models.
Rainfall on isothermal snowpacks can create rain-on-snow
flooding and, once snow has melted, generate rapid rainfall–
runoff (Marks et al., 1999). PPMs that define warmer values
of the Ta thresholds (reducing rainfall proportion) in error
result in less energy being transferred from the atmosphere
into the snowpack and an increase in SWE from reality
(Fassnacht and Soulis, 2002). The translation of differences
in snow cover due to different PPMs affects streamflow
estimation; the warmer the Ta threshold, the larger and later is
the snowmelt streamflow peak (Fassnacht and Soulis, 2002).
It is clear that there is uncertainty introduced into
hydrological calculations from the introduction of empirical PPMs, but this uncertainty has not been systematically
quantified. Further, the impact of physically based, and
therefore less uncertain, PPMs on hydrological prediction
has not been explored. The objective of this paper is
therefore to quantify the uncertainty that empirical PPMs
introduce into hydrological simulations of snowpack and
discharge regimes.
Hydrol. Process. (2014)
HYDROLOGIC MODEL UNCERTAINTY OF PRECIPITATION-PHASE METHODS
METHODOLOGY
Cold-region hydrological model
The flexible Cold Regions Hydrological Model (CRHM)
platform was used to create models with which the effect of
varying PPMs on snow processes at the hydrological
response unit (HRU) scale and hydrological processes at the
basin scale can be assessed. CRHM is a modular objectoriented hydrological model creation platform based on
decades of cold-region hydrological process research in
western and northern Canada (Pomeroy et al., 2007).
CRHM allows model complexity to vary, from conceptual
to physically based representations, in order to match the
data availability and uncertainty in process parameters for
the basin in question. CRHM modules, which represent
specific hydrological process algorithms or data transformations, are coupled by the software in an integrated and
cascading manner to create purpose-built models suited to
specific applications. To quantify hydrological processes
over a landscape, CRHM uses HRUs, which are spatial units
of mass and energy budget calculation that are defined on
the basis of having similar drainage, aerodynamic and
biophysical parameters – similar to the concept of the
catena. The flexible approach of CRHM and inclusion of a
full range of snow process algorithms make it useful for
hydrological simulation, diagnosing the adequacy of
hydrological understanding and for assessing the uncertainty of hydrological process algorithms in cold regions. An
advantage for this study was that CRHMs had previously
been created for the study sites of interest and were available
for application in an uncertainty analysis.
Hydrological models
The effect of precipitation-phase uncertainty in hydrological modelling was assessed at HRU and basin scales.
Models were driven with meteorological station observations of Ta, relative humidity, wind speed and precipitation and assessed with measurements of snowpack and
streamflow discharge. Some sites also had solar radiation
measurements. HRU-scale simulations of snowpack regime for four HRUs in a CRHM of Marmot Creek research
basin reveal how specific snow redistribution and ablation
processes are affected by PPMs in a mountain basin. Basinscale CRHMs simulated basin discharge from a wide range
of hydrological processes in the Marmot Creek, Wolf
Creek, Granger Basin and Creighton Tributary research
basins, demonstrating how uncertainty in precipitation
phase generates hydrological uncertainty over a wide range
of hydroclimatic conditions (Figure 1).
Marmot Creek research basin. Marmot Creek research
basin, 9.4 km2, is situated in the Kananaskis Valley,
Alberta, in the Canadian Rockies. Its vegetation includes
sparsely vegetated alpine tundra, alpine meadows and
sub-alpine and montane forests with forest clearings
(Swanson et al., 1986). The climate is dominated by long
cold winters and cool wet summers. Mean daily Ta
(1968–2012) at a mid-elevation site (clearing: 1845 m)
Figure 1. Research basins showing land cover and location in western Canada. (a) Wolf Creek, Yukon Territory, showing Granger Basin within it, (b)
Marmot Creek, Alberta, (c) Creighton Tributary, Saskatchewan. Spatial land cover data for Creighton Tributary are unavailable, but the basin is
dominated by cropland (85%) with the remainder grassland (Gray et al., 1985)
Copyright © 2014 John Wiley & Sons, Ltd.
Hydrol. Process. (2014)
P. HARDER AND J. W. POMEROY
ranges from 11.7 °C in July to 10.7 °C in January.
Annual mean precipitations of 638 mm at the valley
bottom and 1100 mm at upper elevations are recorded
(Storr, 1967). Data from seven meteorological stations
including precipitation at three elevations were used to
drive the model. Soil moisture initial states in the model
were reinitialized from observations each model year. The
years modelled spanned 2006–2011 for the entire basin
and 2008–2011 for the HRU scale. The CRHM structure
used in modelling Marmot Creek is visualized in Figure 2.
The complex model structure (36 HRUs) and parameters
used in this study are taken from Fang et al. (2013). The
mountain environment hydrological processes that the
model considers include the following:
• Incoming shortwave radiation to slopes (Garnier and
Ohmura, 1970).
• Longwave radiation (Sicart et al., 2006).
• Snow albedo (Verseghy, 1991).
• Canopy processes including rainfall and snowfall
interception, sublimation and subcanopy radiation
(Pomeroy et al., 1998; Ellis et al., 2010).
• Blowing snow redistribution and sublimation (Pomeroy
and Li, 2000).
• Snowmelt from an energy balance model (SNOBAL)
suitable for deep mountain snowpacks (Marks et al., 1999).
• All-wave radiation for evapotranspiration (Granger and
Gray, 1990).
• Frozen-soil infiltration (Zhao and Gray, 1999) and
rainfall infiltration (Ayers, 1959).
• Actual evapotranspiration from unsaturated surfaces
using an energy balance and extension of Penman’s
equation to unsaturated conditions (Granger and Gray,
1989; Granger and Pomeroy, 1997) and evaporation
from saturated surfaces (Priestley and Taylor, 1972).
• Hillslope processes based on a soil moisture balance by
Leavesley et al. (1983) and modified by Dornes et al.
(2008) and Fang et al. (2010) to more realistically
describe surface–groundwater interactions and subsurface flow. The subsurface comprises a recharge and
lower soil layer, which interact with surface processes
and upstream and downstream HRU runoff; these
upper layers in turn interact with a lower groundwater
layer. Lateral and vertical flows are calculated between
all layers with an implementation of Darcy’s law
accounting for differences in HRU slope and effective
hydraulic conductivities. Brooks and Corey’s (1964)
relationship is used to adjust the saturated hydraulic
conductivity for unsaturated conditions.
• Water routing among the HRUs uses the Muskingum
method (Chow, 1964).
HRU-scale modelling
The PPMs were also evaluated at the HRU scale in
Marmot Creek to calculate the effect that phase
Figure 2. Flow chart of information exchange among physically based hydrological modules for simulating hydrological processes in the Marmot Creek
Cold Regions Hydrological Model. The line colours correspond to radiant energy fluxes or state variables (red), meteorological inputs (blue), liquid water
fluxes or state variables (black), snow fluxes or state variables (green) and water vapour fluxes (orange)
Copyright © 2014 John Wiley & Sons, Ltd.
Hydrol. Process. (2014)
HYDROLOGIC MODEL UNCERTAINTY OF PRECIPITATION-PHASE METHODS
uncertainty had on HRU snow regimes at sites with
differing snow redistribution and ablation process operation (Table I and Figure 3). The HRU-scale models
differed slightly from the basin-scale model in that not all
hydrological processes needed to be represented for each
HRU, specifically as follows:
• Clearing: a clearing where there is no forest interception as there is no canopy and blowing snow
redistribution is suppressed by the surrounding forest
• Forest: a forest where blowing snow processes are
suppressed by the canopy
• Ridge: an exposed alpine ridge where there is no
canopy that may intercept snowfall
Creek model calculates are similar to the Marmot Creek
model with the only differences being as follows:
• Incoming shortwave radiation is estimated with a semiempirical approximation (Shook and Pomeroy, 2011).
• Snowmelt is calculated with the energy budget
snowmelt model suitable for shallow, cold snowpacks
(Gray and Landine, 1988).
• Snow albedo uses a prairie-derived algorithm suitable for
shallow, patchy snowpacks (Gray and Landine, 1987).
• Soil routine was modified by Dornes et al. (2008) for
tundra soils.
• All routing was by Clark’s (1945) lag and route algorithm.
Observations of snow depth and density taken along
long snow survey courses were compared with simulated
snowpacks. The snow courses consist of fixed transects
with observation of snow depths (ruler) and densities
(ESC-30 snow tubes). The spacing and number of points
vary between survey sites and are summarized in Table I.
Granger Basin. Granger Basin is a small (8 km2)
gauged alpine/shrub-tundra sub-basin of Wolf Creek
where intensive field observations were made using five
meteorological stations and substantial snow surveys
(Pomeroy et al., 2003). As there is detailed information
for this small portion of Wolf Creek, a more complex
model with five HRUs is justified, which comprise an
Wolf creek. Wolf Creek Research Basin is located in
the Upper Yukon River Basin near Whitehorse, Yukon.
The basin (~195 km2) contains alpine tundra, sub-alpine,
shrub tundra, taiga and boreal forest ecosystems. The
climate is cold and dry. The coldest (January) and warmest
months (July) have daily average Ta of 17.7 and +14.1 °C,
respectively, at the valley bottom (MacDonald et al., 2009).
Precipitation is low, with annual amounts between 300 and
400 mm, of which approximately 40% is snowfall (Pomeroy
et al., 1999). Observations from three meteorological
stations located in the alpine, shrub tundra and forest
elevation zones were available for this analysis over
1994–2002. A simple model of Wolf Creek was set up and
parameterized with three HRUs (alpine, shrub tundra and
forest), which correspond to the major ecozones and
driving meteorological data (Pomeroy et al., 2010). The
number of HRUs corresponds to the size of the basin, its
major sources of hydrological variability and the density of
information. The hydrological processes that the Wolf
Figure 3. Schematic of hydrological response unit-scale models with
characteristic hydrological processes: (a) clearing and forest and (b)
treeline and ridge
Table I. Hydrological response unit (HRU) scale in Marmot Creek research basin, Alberta
HRU
Forest
Clearing
Ridge
Treeline
Description (area)
Major snow processes
Snow course point
spacing (m)
Number of snow
course depth points
Mid-elevation forest (10 000 m2)
Mid-elevation clearing
(10 000 m2)
Upper-elevation alpine
ridgetop (36.9 m2)
Upper-elevation treeline larch
forest (15 m2)
Interception, subcanopy radiation
Snow accumulation
5
5
16
21
Blowing snow erosion
5
32
Blowing snow deposition,
interception, subcanopy radiation
5
19
Note: Snow course observation frequencies vary from monthly intervals during the accumulation period to weekly intervals during the ablation period.
Copyright © 2014 John Wiley & Sons, Ltd.
Hydrol. Process. (2014)
P. HARDER AND J. W. POMEROY
upper basin, plateau, valley bottom and north-facing
and south facing slopes, following Dornes et al. (2008).
The Granger Basin model differs from the Wolf Creek
model as it does not include the canopy module; there
is no forest cover in the Granger Basin. A complete
discussion of model set-up and parameter selection is
given by Pomeroy et al. (2010). Modelled water years
spanned 1999–2001.
Creighton Tributary, Bad Lake research basin. Creighton
Tributary is a stream draining into Bad Lake that forms
part of the Bad Lake research basin near Totnes in
southwestern Saskatchewan. Meteorological, snowpack
and streamflow observations were made as part of the
International Hydrological Decade by the Division of
Hydrology, University of Saskatchewan (1967–1986). A
model was developed for the Creighton Tributary basin
(11.4 km2), which is dominated by silty-clay and clayloam soils with ~85% of the basin area consisting of
cultivated agricultural land and the remainder being
grassland (Gray et al., 1985). Creighton Tributary is
characterized by poorly drained, level, open farmland and
highland with rolling topography. The basin is semi-arid
with ~300 mm of annual precipitation (Gray et al., 1985).
For a discussion of model set-up and parameterization, see
Pomeroy et al. (2007). Modelling spanned the 1974 and
1975 water years. The Creighton Tributary model quantified
the following processes for a prairie environment:
• Incoming radiation to slopes (Garnier and Ohmura, 1970)
• Snow albedo (Gray and Landine, 1987)
• Blowing snow redistribution and sublimation (Pomeroy
and Li, 2000)
• Snowmelt calculated with the energy budget snowmelt
model (Gray and Landine, 1988)
• Snowmelt frozen-soil infiltration (Zhao and Gray,
1999) and rainfall infiltration (Ayers, 1959)
• Actual evapotranspiration from unsaturated surfaces
using an energy balance and extension of Penman’s
equation to unsaturated conditions (Granger and Gray,
1989; Granger and Pomeroy, 1997)
• Soil moisture balance based on Leavesley et al. (1983),
which calculates the soil moisture balance, groundwater storage, subsurface and groundwater discharge,
depressional storage and runoff for control volumes of
two soil layers and a groundwater layer
• Surface water routed with Clark’s (1945) lag and route
algorithm
Precipitation-phase determination in CRHM
The standard CRHM structure is flexible and until this
study was limited to using a single-threshold or doublethreshold Ta approach to partition precipitation. In the
Copyright © 2014 John Wiley & Sons, Ltd.
double-threshold approach, a cooler temperature
(tmax_allsnow) defines precipitation as snowfall, and a
warmer temperature (tmax_allrain) defines precipitation
as rainfall, with linear interpolation between the two
defining a mixed phase. A single threshold is defined
when tmax_allsnow and tmax_allrain are the same. PPMs
that do not fit this structure can be implemented with the
CRHM macro feature, a feature that allows users to
implement new methods. The T0, UBC and PSY PPMs
were implemented in the CRHMs in this study and are
shown in Figure 4a; as PSY varies with humidity, the
PSY rainfall fraction values are plotted for various RH.
After this study, PSY was implemented as the default
PPM in CRHM.
Hydrological indices
Several hydrological indices were used to describe
changes to the hydrological cycle calculations in CRHM
due to differences in PPMs. The indices used, units,
description and equations are summarized in Table II. The
indices are based on annual simulations, and the hydrological year started on 1 Oct for all basins. Discharge varies
with basin size and climate; thus, values were normalized
by basin area and presented with units of depth (mm).
Uncertainty analysis
To quantify the uncertainty of Ta-based models, a range
of single-threshold and double-threshold Ta PPMs that
correspond to that of many published methods were
defined (Feiccabrino and Lundberg, 2008). The models
were defined by generating all possible permutations of
tmax_allsnow (0–2.5 °C) and tmax_allrain (0–6 °C) for
every 0.5 °C interval (Figure 4b). The resulting 63
different single-threshold and double-threshold Ta PPMs
were then run in CRHM to generate a range of
hydrological simulations. The uncertainty of the hydrological simulations as a result of varying the Ta methods is
calculated as
uncertainty ¼
∑ni¼1 ðMaxi Mini Þ
n
(1)
where Min and Max refer to the lowest and highest values
of a model output variable from the 63 model runs, i is the
index (time step) of the value and n is the number of
values (total time steps). The units of uncertainty are the
same as the hydrological variable being considered. The
uncertainty and differences between PPMs are summarized using mean values over an entire hydrological year
(1 October–30 September).
There is a large body of literature on parameter
uncertainty in hydrological models, and common techniques to assess uncertainty include Monte Carlo methods
and generalized likelihood uncertainty estimation
Hydrol. Process. (2014)
HYDROLOGIC MODEL UNCERTAINTY OF PRECIPITATION-PHASE METHODS
Figure 4. Precipitation phase shown as the rainfall fraction (rainfall/total precipitation) as a function of temperature for (a) specific precipitation-phase
methods and (b) a range of empirical air temperature (Ta) precipitation-phase methods implemented in Cold Regions Hydrological Model. Note that for
(b) there are 63 separate precipitation-phase methods plotted that represent all permutations of tmax_allsnow (0–2.5 °C) and tmax_allrain (0–6 °C)
parameters for every 0.5 °C interval
Table II. Hydrological variables considered
Variable
Units
Monthly rainfall
fraction
Daily discharge
mm/day
Peak discharge
Peak discharge day
Peak snow water equivalent
Snow-free date
mm/day
days
mm
days
Snow cover duration
days
a
Description
Equation
rain fall ðmmÞ
total precipitation ðmmÞ
Monthly rainfall as a fraction of
total monthly precipitation
Daily discharge as depth of flow ratea
Peak annual daily dischargea
Date of peak daily dischargea
Maximum seasonal snow accumulation
First day in spring when snow water
equivalent reaches zero (even if subsequent
snow accumulation takes place)
Number of days each year with snow on
ground, including days of intermittent
snow cover in summer
discharge ðm3 =day1 Þ
basin area ðm2 Þ*1000
max½discharge ðm3 =day1 Þ
basin area ðm2 Þ*1000
Date(discharge = max(discharge))
max[daily SWE (mm)]
min(Date[daily SWE (mm) = 0]) > 1 Jan
count[daily SWE (mm) > 0]
Basin scale only. Discharge quantifies all surface and subsurface basin outflows.
(GLUE) (McIntyre et al., 2002). These methods use
calibration, usually to streamflow, to specify model
parameters from a range of possible values. CRHM does
not provide internal provision for calibration, so all model
parameters, other than precipitation-phase parameters, are
fixed throughout the modelling exercise. Monte Carlo and
GLUE methods are inappropriate to analyse the uncertainty introduced by Ta methods, as the range in temperaturephase parameter values is very limited. All parameters in
this range are of interest as they correspond to the ranges
reported in the literature (Feiccabrino and Lundberg,
2008). A simpler approach that regularly samples the
parameter range is therefore appropriate.
Copyright © 2014 John Wiley & Sons, Ltd.
RESULTS
Uncertainty at HRU scales
Rainfall fraction uncertainty due to empirical PPMs for
individual HRUs within Marmot Creek is large, with the
greatest uncertainty in summer months when there is a
mixture of snowfall and rainfall due to the high elevation
(Figure 5). The least uncertainty during winter months
and the greatest uncertainty during the summer months
are at the high-elevation ridge and treeline HRUs, which
are consistently snowy in winter but with mixed
precipitation in the summer. Uncertainty across the
modelling period (Table III) was slightly greater at forest
Hydrol. Process. (2014)
P. HARDER AND J. W. POMEROY
Figure 5. Monthly rainfall fraction for (a) forest (1848-m elevation), (b) clearing (1845-m elevation), (c) ridge (2323-m elevation) and (d) treeline (2294-m
elevation). Uncertainty from the range of all Ta precipitation-phase methods (PPMs) is plotted as a grey area overlain by UBC (green), PSY (blue) and T0 (red) PPMs
Table III. Uncertainty caused by the range of empirical air temperature-based precipitation-phase models in hydrological process
simulations
Variable
Hydrological response unit
Monthly rainfall fraction
Peak snow water equivalent
Snow-free date
Snow cover duration
Basin
Monthly rainfall fraction
Daily discharge
Peak discharge
Peak discharge date
Peak snow water equivalent
Snow-free date
Snow cover duration
Units
Uncertainty
mm
days
days
Clearing
0.202 (0.17)
43.9 (17.8)
25.5 (15.3)
35.8 (8.1)
Forest
0.185 (0.17)
18.6 (5.3)
20.2 (5.9)
30.5 (6.5)
Ridge
0.172 (0.182)
63.8 (31.2)
15.5 (7.5)
28.2 (5.3)
Treeline
0.179 (0.19)
159.6 (54.7)
20.8 (3.4)
35.2 (6.9)
mm/day
mm/day
days
mm
days
days
Marmot Creek
0.183 (0.155)
0.40 (0.67)
4.6 (2.2)
7 (11.1)
35.4 (19.5)
16.2 (11.1)
24.8 (3.8)
Granger Basin
0.186 (0.211)
0.12 (0.27)
6.6 (8.9)
10.0 (8.7)
7.4 (2.5)
5.7 (3.8)
16.3 (8.5)
Wolf Creek
0.164 (0.178)
0.03 (0.04)
1.0 (1.0)
5.9 (25.1)
4.2 (4.3)
11.4 (16.5)
35.2 (8.8)
Creighton Tributary
0.105 (0.171)
0.15 (0.33)
2.2 (2.1)
0.0 (0)
2.0 (0.1)
2.0 (2.8)
3.0 (1.4)
Note: Values correspond to the mean uncertainty over the water year, and bold values represent the greatest mean uncertainty, with standard
deviation in brackets.
and clearing HRUs (0.185 and 0.202 of rainfall fraction)
than at ridge and treeline HRUs (0.179 and 0.172 of
rainfall fraction). The rainfall fractions for specific PPMs
follow the sequence: T0 > PSY > UBC (Figure 5), with
the differences greater in summer months and lesser
during winter months at ridge and treeline HRUs and
Copyright © 2014 John Wiley & Sons, Ltd.
muted but with opposite behaviour at the forest and
clearing HRUs.
The uncertainty in daily SWE due to empirical PPMs is
generally small over much of the winter season and
increases dramatically during spring as shown in Figure 6.
Occasionally (e.g. 2010 at clearing and treeline HRUs),
Hydrol. Process. (2014)
HYDROLOGIC MODEL UNCERTAINTY OF PRECIPITATION-PHASE METHODS
Figure 6. Daily snow water equivalent (SWE) for (a) forest (1848 m), (b) clearing (1845 m), (c) ridge (2323 m) and (d) treeline (2294 m). Uncertainty
from the range of all Ta PPMs is plotted as a grey area overlain by UBC (green), PSY (blue) and T0 (red) precipitation-phase methods. Observed SWE is
plotted as black dots
uncertainty develops early in winter and persists throughout the duration of the seasonal snowpack. The peak SWE
uncertainty due to empirical PPMs increases with
snowpack and redistribution processes and so ranges
from 19 mm for the forest HRU up to 160 mm for the
treeline HRU (Table III). The annual snow-free date and
snow cover duration uncertainties are smaller at forested
and high-elevation sites and vary from 16 and 28 days,
respectively, at the ridge HRU and up to 26 and 36 days,
respectively, at the clearing HRU. For specific PPMs, the
SWE (including the peak SWE) follows the sequence
PSY > UBC > T0 (Figure 6), despite UBC producing the
lowest rainfall fraction. The PSY PPM consistently
simulates a later and higher peak SWE and a later snowfree day than do the others. The UBC PPM simulates a
slightly higher and later peak SWE than does T0.
Uncertainty at basin scales
At the basin scale, the uncertainty for monthly rainfall
fraction weighted by basin hypsometry varies seasonally.
Figure 7 shows the greatest rainfall fraction uncertainty in
all PPMs over the relatively cool and wet summer months
in the Marmot Creek, Granger Basin and Wolf Creek
models. Alternatively, the Creighton Tributary model has
the greatest uncertainty in rainfall fraction during the
Copyright © 2014 John Wiley & Sons, Ltd.
spring and fall months that are hydrologically important
on the prairies. Rainfall fractions due to the specific PPMs
were ranked T0 > PSY > UBC. Uncertainty in empirical
PPMs was smaller during the relatively cold winters,
where Ta remains much colder than the phase transition
range, in the Granger Basin, Wolf Creek and Creighton
Tributary models. However, in Marmot Creek, winter
PPM uncertainty remained notable because of the
relatively warm winter temperatures at low elevations in
the basin.
Snow water equivalent uncertainty is less evident at the
basin scale than at the HRU scale – this lack of emergence
with scale is due to the range of elevations in most basins
studied. The largest uncertainty in SWE was at Marmot
Creek, where uncertainty persisted through most winter
periods and then increased dramatically in spring just
before and during the snowmelt period (Figure 8 and
Table IV). This time of year, Marmot Creek receives
much of its annual precipitation, and because this is also
much warmer than mid-winter, phase-change uncertainty
translates directly into SWE uncertainty. Granger Basin
also had notable SWE uncertainty, and this persisted yearround owing to its high elevation and sub-arctic climate
(Figure 8). In contrast, Wolf Creek had the most
uncertainty in summer owing to its strong continentality
of very cold winters and moderate summers, and
Hydrol. Process. (2014)
P. HARDER AND J. W. POMEROY
Figure 7. Monthly rainfall fraction for (a) Marmot Creek, (b) Granger Basin, (c) Wolf Creek and (d) Creighton Tributary. Uncertainty from the range of
all Ta precipitation-phase methods (PPMs) is plotted as a grey area overlain by UBC (green), PSY (blue) and T0 (red) PPMs. As the modelling periods
vary in time and duration, the x-axes differ between basins
Creighton Tributary had most SWE uncertainty in spring as
this is a wet period on the Canadian Prairies and also the
time of snowmelt and so near to phase-change threshold
temperatures. On average, UBC estimates a smaller peak
SWE than does PSY in the Marmot Creek model, in contrast
to simulating very similar SWE in the Granger Basin, Wolf
Creek and Creighton Tributary models (Table IV). At
Granger Basin, there is strong seasonality in SWE difference
due to various PPMs, as PSY simulates greater SWE than
does UBC over the winter and less in the shoulder and
summer seasons. The uncertainty in the first snow-free day
varied most in the Marmot Creek and least in the Creighton
Tributary models (Table IV). PSY produced a later estimate
of the snow-free day than did the UBC or T0 methods. The
empirical PPM uncertainty associated with the duration of
annual snow cover varied by up to 36 days in the Wolf
Creek model. The T0 simulated an annual snow cover
duration that was 33 days shorter than that simulated by PSY
in the Wolf Creek model. In contrast, snow duration using
UBC does not vary from PSY for the Marmot Creek and
Creighton Tributary models, whereas UBC duration is
longest in the Granger Basin model and shortest in the Wolf
Creek model (Table IV).
The empirical PPM uncertainty for basin-scale daily
discharge volume is greatest in the Granger Basin and
Copyright © 2014 John Wiley & Sons, Ltd.
Creighton Tributary models and is very small for both
Marmot and Wolf Creeks (Figure 9 and Table IV). At
Granger Basin, ranking of discharge by specific PPM was
T0 > PSY > UBC. The Creighton Tributary model
showed the opposite ranking. The T0 method simulates
an earlier annual peak relative to PSY. The UBC method
varies with respect to PSY as the annual peak occurs after
PSY for the Marmot Creek and Granger Basin models
with minimal difference for the Wolf Creek and
Creighton Tributary models.
DISCUSSION
Varying the PPM in a hydrological model changes the
estimated quantities of rainfall, snowfall and total
precipitation. The total precipitation varies with the
correction of the wind-induced undercatch when precipitation is identified as snowfall instead of rainfall. The
PPMs affect the timing of rainfall and snowfall,
complicating the understanding of a hydrological response to varying phase. For instance, estimating rainfall
instead of snowfall can introduce rapid albedo decay, rain
on snowmelt, release of intercepted snow, suppression of
blowing snow and rainfall–runoff. The hydrological
Hydrol. Process. (2014)
HYDROLOGIC MODEL UNCERTAINTY OF PRECIPITATION-PHASE METHODS
Figure 8. Daily snow water equivalent for (a) Marmot Creek, (b) Granger Basin, (c) Wolf Creek and (d) Creighton Tributary. Uncertainty from the range
of all Ta precipitation-phase methods (PPMs) is plotted as a grey area overlain by UBC (green), PSY (blue) and T0 (red) PPMs. As the modelling periods
vary in time and duration, the x-axes differ between basins
response to these changes varies considerably by basin
and antecedent condition.
The PSY method tends to estimate less rainfall (and
more snowfall) relative to the T0 method, which forces all
phase transition at 0 °C (Harder and Pomeroy, 2013). The
PSY method uses humidity information, and so its
relationship to UBC and T0 method performance varies
with RH as well as temperature. In less humid conditions,
PSY identifies less precipitation as rainfall (and more as
snowfall) than does the UBC model (Figure 4a). The UBC
model was calibrated in relatively humid mountains in
British Columbia and so underestimates snowfall in drier
conditions (Fassnacht et al., 2013).
Varying the identification of phase affects the total
amount of precipitation, as wind-induced undercatch
corrections are only applied when precipitation is
identified as snowfall. These corrections are a consequence of the deformation of the wind field over a gauge
orifice, causing displacement and acceleration of snow
particles and reduced effective fall velocities (Thériault
et al., 2012). The uncertainty of undercatch due to
differing PPMs varies by basin as it is influenced by wind
speed and the fraction of precipitation occurring near the
transition range. At Wolf Creek and Granger Basin, windinduced undercatch was compensated for by direct
Copyright © 2014 John Wiley & Sons, Ltd.
correlation to a corrected precipitation record at
Whitehorse International Airport, and so no correction
was applied within CRHM that could be influenced by phase
estimation. The Marmot Creek and Creighton Tributary
CRHMs calculated undercatch correction for Alter and
Nipher shields, respectively. This correction resulted in annual
precipitation differing by 20 and 12 mm between the UBC and
T0 models for the Marmot Creek and Creighton Tributary
basins, respectively. The Nipher correction was based on a
World Meteorological Organization (WMO) intercomparison
between a Nipher-shielded storage gauge and a Double Fence
Intercomparison Reference gauge (Goodison et al.,
1998). The Alter correction used a method from
MacDonald and Pomeroy (2007) based on an intercomparison between Alter-shielded and WMO-corrected
Nipher-shielded gauges in the Canadian Prairies.
HRU scale
The influence of elevation on phase partitioning is
apparent in Figure 5. As Ta generally decreases with
elevation because of adiabatic expansion, the warmer
winter Ta at lower elevations (winter mean Ta 5.3 °C
over the modelling period) is nearer to the transition range
than are those at high elevations (winter mean Ta 6.8 °C
Hydrol. Process. (2014)
Copyright © 2014 John Wiley & Sons, Ltd.
0.0
2.0
3.3
17.4
4.2
0.2
days
days
0.04
3.0
4.70
0.05
0.6
1.3
mm
mm/day
mm/day
days
Granger Basin
0.051
10.2
2.2
14.8
6.0
days
days
Marmot Creek
0.034
21.4
0.038
0.023
42.3
Forest
Clearing
mm
Units
0.027
Ridge
1.4
11.2
0.4
0.003
0.2
0.2
Wolf Creek
0.02
6.8
0.2
41.7
UBC
Note: UBC and T0 values are presented as absolute difference from PSY.
Hydrological
response unit
Monthly rainfall
fraction
Peak snow water
equivalent
Snow-free date
Snow cover
duration
Basins
Monthly rainfall
fraction
Daily discharge
Peak discharge
Peak discharge
date
Peak snow water
equivalent
Snow-free date
Snow cover
duration
Variable
1.0
0.0
0.2
0.04
0.2
0.0
Creighton Tributary
0.014
9.0
10.2
67.7
0.029
Treeline
14.0
14.0
31.7
0.03
0.4
2.3
Marmot Creek
0.059
28.5
25.8
59.7
0.077
Clearing
3.0
5.3
4.6
0.03
2.7
5.3
Granger Basin
0.055
21.2
17.5
31.3
0.059
Forest
15.5
16.2
71.3
0.068
Ridge
8.1
33.2
2.5
0.003
0.2
4.4
Wolf Creek
0.057
T0
0.5
1.5
1.0
0.01
1.2
0.5
Creighton Tributary
0.027
20.5
27.8
127
0.070
Treeline
Table IV. Comparison of hydrological process simulations using empirical precipitation-phase models (UBC and single temperature threshold) with that using the psychrometric
energy balance model
P. HARDER AND J. W. POMEROY
Hydrol. Process. (2014)
HYDROLOGIC MODEL UNCERTAINTY OF PRECIPITATION-PHASE METHODS
Figure 9. Cumulative annual discharge for (a) Marmot Creek, (b) Granger Basin, (c) Wolf Creek and (d) Creighton Tributary. Uncertainty from the range
of all Ta precipitation-phase methods (PPMs) is plotted as a grey area overlain by UBC (green), PSY (blue) and T0 (red) PPMs. As the modelling periods
vary in time and duration, the x-axes differ between basins
over the modelling period), leading to greater winter
rainfall fraction uncertainty at low elevations than at
upper elevations.
The uncertainties of snow processes vary with the
amount of snow accumulation, which itself is a consequence of various snow redistribution and ablation
processes. The treeline HRU model, simulating a treeline
drift, shows the largest uncertainty in peak SWE because
snow accumulation is dependent on blowing snow
transport to the drift, which is very sensitive to precipitation
phase and the role of rainfall in suppressing, and fresh
snowfall in enhancing, snow erosion over the upwind fetch
(Li and Pomeroy, 1997). The ridge HRU (blowing snow
source), clearing HRU (no interception and no blowing
snow) and forest HRU (interception) show smaller
uncertainties in peak snow accumulation than does the
treeline HRU. This is evidence that snow redistribution
processes that remove snow (interception and blowing
snow erosion) result in smaller uncertainty in snow
accumulation than processes that add snow by blowing
snow transport. The treeline HRU simulation is challenging as treeline snow regimes are sensitive to both blowing
snow deposition and canopy interception processes and
any errors in their simulation. For example, treeline snow
accumulation in 2010 is greatly overestimated by the
model relative to observations. Fang et al. (2013) found
Copyright © 2014 John Wiley & Sons, Ltd.
that the likely reason is that the blowing snow processes
parameterized in CRHM do not consider wind direction,
and in this year, synoptic systems acted to vary wind
direction from the typical direction, changing the upwind
fetch area and hence snow transport volumes.
The snow regime simulations demonstrate the effect of
these different PPM biases on prediction. The T0 method
estimates a higher rainfall fraction and shallower SWE
accumulation than does the UBC method (Figures 5 and
6). The PSY method also estimates a higher rainfall
fraction but, in contrast, greater SWE accumulation than
does the UBC method. This behaviour is due to PSY
being dependent upon Ti in contrast to UBC, which is
dependent on Ta. The difference between Ti and Ta is
primarily dependent upon RH, but the magnitude of the
difference increases with Ta and so is subject to
seasonality. PSY identifies slightly more snowfall than
UBC during the snow accumulation and early melt
seasons (October–May), leading to greater estimates of
spring SWE even though it identifies less annual snowfall
than UBC because of an increase in summer rainfall
fraction relative to that from the UBC method. The
influence of precipitation-phase estimation on spring
snowpacks is very important as an increase in rainfall
will induce rapid melt, whereas an increase in snowfall
retards melt and accumulates more snow on the ground.
Hydrol. Process. (2014)
P. HARDER AND J. W. POMEROY
Basin scale
The basins modelled vary in climate, topography,
vegetation and area, all of which influence the model
structure and hydrological processes considered. The
uncertainty due to PPMs can be seen to be largely a
function of climate, vegetation and topography but is also
influenced by model complexity and basin size. Wolf
Creek, Granger Basin and Creighton Tributary have
relatively cold and dry climates, whereas Marmot Creek
is warmer and wetter. Marmot Creek, Wolf Creek and
Granger Basin have much more relief than Creighton
Tributary. Marmot and Wolf Creeks have substantial
evergreen forest cover and hence snow interception
processes. Wolf Creek is a large basin, whereas Marmot
Creek, Granger Basin and Creighton Tributary are all
smaller. The Marmot Creek model is the most complex,
with 36 HRUs, followed by Granger Basin with five
HRUs and Wolf Creek and Creighton Tributary both
having three HRUs.
The small basins with high relief, Marmot Creek and
Granger Basin, have the greatest uncertainty from
empirical and specific PPMs in terms of precipitation
phase and therefore snow accumulation (Figures 7 and
8 and Table IV). The large uncertainty of Marmot Creek
(1600- to 2825-m elevation) and Granger Basin (1310- to
2100-m elevation) can be related to the range of Ta owing
to lapse rates being applied to the elevation differences
between HRUs. Over a wide range of Ta, any PPM will
have a higher probability of varying precipitation phase at
some elevation over many events. Creighton Tributary,
which has mild relief, has a much lower precipitationphase uncertainty for most of the year as Ta is assumed to
be uniform across the basin and there is strong seasonality
in temperature. Also, whereas other basins show long
periods of phase uncertainty coinciding with large
amounts of precipitation near the phase transition, the
Creighton Tributary only shows a short period of phase
uncertainty in spring and fall months, and these months
have a relatively small portion of the annual precipitation
and so little influence on peak SWE. Snow processes at
Marmot Creek are the most uncertain largely because of
the occurrence of most precipitation occurring near the
transition range, with 60% of precipitation occurring
between 5 and 5 °C at the clearing HRU; thus, a change
in PPM will have large impacts on duration of snow
cover. By contrast, the greater uncertainty of Wolf Creek
snow cover duration is attributed to the increased
occurrence of snowfall simulated in summer months
due to the cool Yukon summer.
Daily discharge at Marmot Creek and peak discharge
and timing of peak at Granger Basin show greater
uncertainty than at other basins (Figure 9 and Table IV).
This is believed to be a consequence of the large amount
Copyright © 2014 John Wiley & Sons, Ltd.
of precipitation that Marmot Creek receives and hence its
large discharge compared with other basins, which often
have ephemeral streamflow, but may also be a consequence of sensitivity to rain-on-snowmelt events, which
have high runoff efficiencies (Marks et al., 1999).
Although daily discharge quantities may vary more with
PPM at Marmot Creek than at the other basins, the
relative differences in discharge is much larger for basins
with ephemeral streamflow such as Creighton Tributary.
For Marmot Creek, Granger Basin and Wolf Creek
basins, T0 produces the most discharge and higher and
earlier peak flows, followed by PSY and UBC, implying
that these models produce more discharge with methods
that estimate a greater rainfall fraction of total precipitation. The interaction of phase and precipitation intensity
can also be important. A large precipitation event
identified as snowfall will not contribute to discharge at
the time of its occurrence but will accumulate as SWE,
whereas large precipitation volumes identified as rainfall
either cause snowmelt or direct runoff and lead to
simulations of high streamflows with short lag times.
All basins studied are characterized by wet spring and
early summer periods. Canadian Prairie basins, such as
Creighton Tributary, are particularly ineffective at
transforming rainfall into discharge because of flat
topography, high unfrozen-soil infiltration rates and
higher evapotranspiration rates in summer than those
during spring snowmelt (Gray et al., 1989). Therefore,
methods that identify more snowfall, such as UBC and
PSY, lead to much greater discharge in prairie basins. As
a result, Creighton Tributary had a relatively large
uncertainty in annual discharge volume despite having a
relatively small uncertainty in precipitation phase, SWE
or snowpack accumulation or duration. This result shows
that soil processes can be strongly affected by precipitation phase and can have an overwhelming control on
basin hydrological response to phase determination.
Attribution of uncertainty
The uncertainty analysis attributed the differences
between basins solely to the PPMs. The basins modelled
all have different model structures, which can modify
how uncertainty in precipitation phase translates into
uncertainty in snowpacks and discharge, but differences
due to model implementation are considered negligible
for two reasons. First, both small mountain headwater
basins (Marmot Creek and Granger Basin) had the highest
uncertainty in many hydrological and snow parameters
even though the model structures are very different in
terms of number of HRUs and process algorithm
employed. This shows that the interaction between PPMs
and basin physiography and climate is consistent
regardless of model structure. Second, a test to compare
Hydrol. Process. (2014)
HYDROLOGIC MODEL UNCERTAINTY OF PRECIPITATION-PHASE METHODS
Creighton Tributary with clearing (an HRU of Marmot
Creek), with both models using the energy balance
snowmelt model (EBSM) module, revealed the inability
of EBSM to model the deep alpine snow cover correctly;
EBSM accumulated 2.5 times the snowpack of SNOBAL
and far more than measured. The EBSM snowmelt and
albedo models were developed for shallow prairie, not
deep alpine, snow covers. This shows that sites with
different manifestations of the same hydrological processes need to be represented with the appropriate
models; otherwise, model structure uncertainty from
process simulation errors will overwhelm any uncertainty
due to different PPMs. The uncertainty due to errors in
model structure, when using the most appropriate process
representations, will be secondary to the uncertainty due
to the PPMs.
parameterization from calibration to streamflow is
difficult or impossible. The relationship between empirical and semi-physical methods is temporally variable,
leading to complex relationships between hydrological
simulations that use these methods. The uncertainty in the
identification of precipitation phase constitutes a significant source of error in hydrological modelling that has
been underappreciated in previous research. The implication of this research is that the benefits for snowpack
prediction of implementing a physically based PPM with
less uncertainty are greatest for mountain basins and least
for prairie basins. However, for streamflow discharge
prediction, the benefits were not emergent with scale and
are greatest for the smaller basins. This effect may have
been enhanced by the influence of frozen-soil processes in
multiplying streamflow uncertainty in small prairie and
alpine basins.
CONCLUSIONS
ACKNOWLEDGEMENTS
Many approaches have been used in hydrological modelling to identify precipitation phase, but the uncertainty due
to these approaches has not been assessed before. This
study compared the uncertainty that a selection of PPMs
introduces into hydrological modelling over a variety of
basins, climates, vegetation covers, topographies and
scales. The magnitude of the uncertainty associated with
modelling using empirical Ta PPM methods is up to 0.2 for
rainfall fraction, 0.4 mm/day for mean daily discharge and
160 mm of peak SWE. The timing of variables showed
considerable uncertainty with variations of up to 36 days
for snow cover duration, 26 days for snow-free date and
10 days for peak discharge date. PPMs caused greater SWE
uncertainty, where processes such as blowing snow
deposition increased snow accumulation, and less uncertainty, where processes such as snow interception and
blowing snow erosion ablated SWE. The magnitude of the
uncertainty among basins was a function of how climate
and topography influenced snow redistribution, melt and
runoff processes. Snowpacks in small high-mountain
basins (Marmot Creek and Granger Basin) were most
sensitive, owing to having more precipitation occurring in
the transition temperature range and their topography
causing a wide range of Ta during the snow season. In
contrast, Creighton Tributary, being flatter and having a
highly continental climate, showed the least uncertainty in
snowpack but very high uncertainty in annual streamflow
discharge because of the impact of precipitation phase on
runoff and infiltration processes.
The uncertainty introduced by setting unidentifiable
parameters for empirical methods was reduced with PSY,
which has no parameters to set, and there was little loss in
predictive power using PSY instead of a calibrated
empirical method, which makes PSY attractive where
Copyright © 2014 John Wiley & Sons, Ltd.
This paper relies on observations in experimental basins
collected over several decades by groups led by Don
Gray, Rick Janowicz, Raoul Granger and others with
significant field data collection by Dell Bayne, Newell
Hedstrom, Mike Solohub, May Guan and many students.
Tom Brown developed the CRHM platform, and Xing
Fang, Pablo Dornes and Matt MacDonald helped to create
the CRHM models used. The comments and suggestions
by Danny Marks and two anonymous reviewers are
gratefully acknowledged. Funding has been primarily
provided by NSERC with substantial contributions from
CRC, CFCAS, CERC, DIAND, NERC, NOAA, Environment Canada, AESRD, Nakiska Mountain Resort,
USDA-ARS, Yukon Environment and others.
REFERENCES
Ayers HD. 1959. Influence of soil profile and vegetation characteristics on
net rainfall supply to runoff. In Proceedings of Hydrology Symposium
No. 1: Spillway Design Floods. National Research Council Canada:
Ottawa; 198–205.
Brooks RH, Corey AT. 1964. Hydraulic properties of porous media.
Hydrology Paper No. 3, Colorado State University, Fort Collins.
Chow VT. 1964. Handbook of Applied Hydrology. McGraw-Hill, Inc.:
New York.
Clark CO. 1945. Storage and the unit hydrograph. In Proceedings of
American Society of Civil Engineering 69: 1419–1447.
Dornes PF, Pomeroy JW, Pietroniro A, Carey SK, Quinton WL. 2008.
Influence of landscape aggregation in modelling snow-cover ablation
and snowmelt runoff in a subarctic mountainous environment.
Hydrological Sciences Journal 53: 725–740.
Ellis CR, Pomeroy JW, Brown T, MacDonald J. 2010. Simulation of snow
accumulation and melt in needleleaf forest environments. Hydrology
and Earth System Sciences 14: 925–940.
Fang X, Pomeroy JW, Westbrook CJ, Guo X, Minke AG, Brown T.
2010. Prediction of snowmelt derived streamflow in a wetland
dominated prairie basin. Hydrology and Earth System Sciences 14:
991–1006.
Hydrol. Process. (2014)
P. HARDER AND J. W. POMEROY
Fang X, Pomeroy JW, Ellis CR, MacDonald MK, DeBeer CM, Brown T.
2013. Multi-variable evaluation of hydrological model predictions for a
headwater basin in the Canadian Rocky Mountains. Hydrology and
Earth System Sciences 17: 1635–1659.
Fassnacht SR, Soulis ED. 2002. Implications during transitional periods of
improvements to the snow processes in the land surface scheme –
hydrological model WATCLASS. Atmosphere–Ocean 40: 389–403.
Fassnacht SR, Venable NBH, Khishigbayar J, Cherry ML. 2013. The
probability of precipitation as snow derived from daily air temperature
for high elevation areas of Colorado, United States. Cold and mountain
region hydrological systems under climate change: towards improved
projections. IAHS Publication 360: 65–70.
Feiccabrino J, Lundberg A. 2008. Precipitation phase discrimination in
Sweden. In 65th Eastern Snow Conference, Fairlee (Lake Morey),
Vermont, USA; 239–254.
Garnier BJ, Ohmura A. 1970. The evaluation of surface variations in solar
radiation income. Solar Energy 13: 21–34.
Goodison BE, Louie PYT, Yang D. 1998. WMO solid precipitation
measurement intercomparison: final report. WMO/TD No. 872.
Granger RJ, Gray DM. 1989. Evaporation from natural non-saturated
surfaces. Journal of Hydrology 111: 21–29.
Granger RJ, Gray DM. 1990. A net radiation model for calculating daily
snowmelt in open environments. Nordic Hydrology 21: 217–234.
Granger RJ, Pomeroy JW. 1997. Sustainability of the western Canadian
boreal forest under changing hydrological conditions-2-summer energy
and water use. In Sustainability of Water Resources under Increasing
Uncertainty, Rosjberg D, Boutayeb N, Gustard A, Kundzewicz Z,
Rasmussen P (eds). IAHS Publ No. 240. IAHS Press: Wallingfordl;
243–250.
Gray DM, Landine PG. 1987. Albedo model for shallow prairie
snowcovers. Canadian Journal of Earth Sciences 24: 1760–1768.
Gray DM, Landine PG. 1988. An energy-budget snowmelt model for the
Canadian prairies. Canadian Journal of Earth Sciences 25: 1292–1303.
Gray DM, Landine PG, Granger RJ. 1985. Simulating infiltration into
frozen prairie soils in stream flow models. Canadian Journal of Earth
Science 22: 464–474.
Gray DM, Pomeroy JW, Granger RJ. 1989. Modelling snow transport,
snowmelt and meltwater infiltration in open, northern regions. In
Northern Lakes and Rivers, Mackay WC (ed). Occasional Publication
No. 22. Boreal Institute for Northern Studies, University of Alberta:
Edmonton; 8–22.
Harder P, Pomeroy JW. 2013. Estimating precipitation phase using a
psychrometric energy balance method. Hydrological Processes. DOI:
10.1002/hyp.9799
Leavesley GH, Lichty RW, Troutman BM, Saindon LG. 1983.
Precipitation–runoff modelling system: user’s manual. Report 834238. US Geological Survey Water Resources Investigations: 207.
Li L, Pomeroy JW. 1997. Estimates of threshold wind speeds for snow
transport using meteorological data. Journal of Applied Meteorology
36: 205–213.
List RJ. 1949. Smithsonian Meteorological Tables, Sixth Revised Edition.
Smithsonian Institution Press: Washington, DC; 527.
Loth B, Graf H, Oberhuber J. 1993. Snow cover model for global climate
simulations. Journal of Geophysical Research 98: 10451–10464.
Lynch-Stieglitz M 1994. The development and validation of a simple
snow model for the GISS GCM. Journal of Climate 7: 1842–1855.
MacDonald JP, Pomeroy JW. 2007. Gauge undercatch of two common
snowfall gauges in a prairie environment. In Proceedings of the 64th
Eastern Snow Conference, St. John’s, Newfoundland, Canada: 119–126.
MacDonald MK, Pomeroy JW, Pietroniro A. 2009. Parameterising
redistribution and sublimation of blowing snow for hydrological
models: tests in a mountainous subarctic catchment. Hydrological
Processes. DOI: 10.1002/hyp.7356
Marks D, Domingo J, Susong D, Link T, Garen D. 1999. A spatially
distributed energy balance snowmelt model for application in mountain
basins. Hydrological Processes 13: 1935–1959.
Marks D, Winstral A, Reba M, Pomeroy JW, Kumar M. 2013. An
evaluation of methods for determining during-storm precipitation phase
and the rain/snow transition elevation at the surface in a mountain basin.
Advances in Water Resources. DOI: 10.1016/j.advwatres.2012.11.012.
Marsh P, Pomeroy JW. 1996. Meltwater fluxes at an arctic forest-tundra
site. Hydrological Processes 10: 1383–1400.
Copyright © 2014 John Wiley & Sons, Ltd.
McIntyre N, Wheater H, Lees M. 2002. Estimation and propagation of
parametric uncertainty in environmental models. Journal of
Hydroinformatics 4(3): 177–198.
Olafsson H, Haraldsdottir SH. 2003. Diurnal, seasonal, and geographical
variability of air temperature limits of snow and rain. In Proceedings of
ICAM/MAP 2003, Brig, Switzerland; 473–476.
Pomeroy JW, Gray DM, Landine PG, 1993. The Prairie Blowing Snow Model:
Characteristics, Validation, Operation. Journal of Hydrology 144: 165–192.
Pomeroy JW, Li L. 2000. Prairie and Arctic areal snow cover mass
balance using a blowing snow model. Journal of Geophysical Research
105(D21): 26619–26634.
Pomeroy JW, Parviainen J, Hedstrom N, Gray DM. 1998. Coupled
modelling of forest snow interception and sublimation. Hydrological
Processes 12: 2317–2337.
Pomeroy JW, Hedstrom N, Parviainen J. 1999. The snow mass balance of
Wolf Creek: effects of snow, sublimation and redistribution. In Wolf
Creek Research Basin: Hydrology, Ecology, Environment, Pomeroy
JW, Granger R (eds). Environment Canada: Saskatoon; 15–30.
Pomeroy JW, Toth B, Granger RJ, Hedstrom NR, Essery RLH. 2003.
Variation in surface energetics during snowmelt in a subarctic mountain
catchment. Journal of Hydrometeorology 4: 702–719.
Pomeroy JW, Gray DM, Brown T, Hedstrom NR, Quinton W, Granger
RJ, Carey S. 2007. The cold regions hydrological model: a platform for
basing process representation and model structure on physical evidence.
Hydrological Processes 21: 2650–2667. DOI: 10.1002/hyp.6787
Pomeroy JW, Semenova OM, Vinogradov YB, Chad E, Vinogradova,
TA, Macdonald M, Fisher EE, Dornes P, Lebedeva L, Brown T. 2010.
Wolf Creek cold regions model set-up, parameterisation and modelling
summary. Centre for Hydrology Report No. 8. University of
Saskatchewan, Saskatoon, Saskatchewan; 107.
Priestley CHB, Taylor RJ. 1972. On the assessment of surface heat flux and
evaporation using large-scale parameters. Monthly Weather Review 100: 81–92.
Quick M, Pipes A. 1976. A combined snowmelt and rainfall runoff model.
Canadian Journal of Civil Engineering 3: 449–460.
Shook KR, Pomeroy JW. 2011. Synthesis of incoming shortwave radiation
for hydrological simulation. Hydrology Research 42: 433–446.
Sicart JE, Pomeroy JW, Essery RLH, Bewley D. 2006. Incoming longwave
radiation to melting snow: observations, sensitivity and estimation in
northern environments. Hydrological Processes 20: 3697–3708.
Steinacker R 1983. Diagnose und Prognose der Schneefallgrenze. Wetter
& Leben 35: 81–90.
Storr D. 1967. Precipitation variations in a small forested watershed. In
Proceedings of the Annual Western Snow Conference, Boise, Idaho: 11–17.
Susong D, Marks D, Garen D. 1999. Methods for developing time-series
climate surfaces to drive topographically distributed energy and water
balance models. Hydrological Processes 13: 2003–2021.
Swanson RH, Golding DL, Rothwell RL, Bernier PY. 1986. Hydrologic
effects of clear-cutting at Marmot Creek and Streeter watersheds,
Alberta. Northern Forestry Centre Information Report NOR-X-278,
Canadian Forestry Service, Edmonton, Alberta; 33.
Thériault JM, Rasmussen R, Ikeda K, Landolt S. 2012. Dependence of
snow gauge collection efficiency on snowflake characteristics. Journal
of Applied Meteorology and Climatology 51: 745–762.
Thorpe AD, Mason BJ. 1966. The evaporation of ice spheres and ice
crystals. British Journal of Applied Physics 17: 541–548.
Verseghy DL. 1991. CLASS-A Canadian land surface scheme for GCMs,
I. soil model. International Journal of Climatology 11: 111–133.
Zhao L, Gray DM. 1999. Estimating snowmelt infiltration into frozen
soils. Hydrological Processes 13: 1827–1842.
APPENDIX: PRECIPITATION-PHASE PARTITIONING
METHODS
T0
A PPM that utilizes a single threshold to define all
precipitation as rainfall when Ta is warmer and snowfall
when Ta is cooler than a specified threshold Ta (Leavesley
et al., 1983).
Hydrol. Process. (2014)
HYDROLOGIC MODEL UNCERTAINTY OF PRECIPITATION-PHASE METHODS
T a ≥ T t jRainfall
(A1)
T a < T t jSnowfall
(A2)
Tt is the threshold Ta with daily values that can range from
1 to 4 °C (Feiccabrino and Lundberg, 2008).
psychrometric energy balance method. The temperature
of a hydrometeor (Ti), a falling precipitation particle, is
governed by the turbulent latent and sensible heat fluxes
between it and the atmosphere and physically related to
the phase of the hydrometeor. The Ti was related to
observations of rainfall fraction to develop a physically
based PPM. For an hourly time interval, fr is estimated as
UBC
A double-threshold PPM that uses a cooler threshold to
define snowfall and a warmer threshold to define rainfall,
with a mixed phase between thresholds. Quick and Pipes
(1976) suggested 0.6 and 3.6 °C as thresholds with linear
interpolation between.
(A3)
T a ≥ 3:6jRainfall
0:6 > T a < 3:6j f r ¼ ðT a =3Þ 0:2
(A4)
T a ≤ 0:6jSnowfall
(A5)
where fr is the rainfall fraction.
fr ¼
rainfall
rain fall þ snowfall
(A6)
PSY
Harder and Pomeroy (2013) proposed a physically
based approach to estimate a phase by utilizing the
Copyright © 2014 John Wiley & Sons, Ltd.
fr ¼
1
1 þ 2:50286*0:125006T i
(A7)
D L ρT a ρsatðT i Þ
λt
(A8)
Ti is calculated as
Ti ¼ Ta þ
where L is the latent heat of sublimation or vaporization (J/kg), ρT a and ρsatðT i Þ are water vapour densities
(kg/m3) in the free atmosphere and at the saturated
hydrometeor surface, respectively, and D is the diffusivity of water vapour in air (m2/s) (estimated by Thorpe
and Mason, 1966),
1:75
Ta
5
(A9)
D ¼ 2:06*10 *
273:15
and λt is the thermal conductivity of air (J/m/s/K)
(estimated by List, 1949),
λt ¼ 0:000063*T a þ 0:00673
(A10)
Hydrol. Process. (2014)