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Journal of Hydrology 517 (2014) 652–667
Contents lists available at ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier .com/locate / jhydrol
Constraining snowmelt in a temperature-index model using
simulatedsnow densities
http://dx.doi.org/10.1016/j.jhydrol.2014.05.0730022-1694/� 2014
Elsevier B.V. All rights reserved.
⇑ Corresponding author at: Jet Propulsion Laboratory, 4800 Oak
Grove Drive, MS233-304, Pasadena, CA 91101, United States. Tel.: +1
626 318 9440.
E-mail addresses: [email protected],
[email protected] (K.J.Bormann).
Kathryn J. Bormann a,b,⇑, Jason P. Evans a, Matthew F. McCabe ca
Climate Change Research Centre and the ARC Centre of Excellence for
Climate System Science, University of New South Wales, Sydney,
Australiab Jet Propulsion Laboratory, California Institute of
Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, United
Statesc Water Desalination and Reuse Center, King Abdullah
University of Science and Technology, Thuwal, Saudi Arabia
a r t i c l e i n f o
Article history:Received 27 October 2013Received in revised form
29 May 2014Accepted 31 May 2014Available online 11 June 2014This
manuscript was handled byKonstantine P. Georgakakos,
Editor-in-Chief
Keywords:Snow densitySnow modellingMelt factorDegree-day
factorWarm maritime snowpack dynamicsSnow depth
s u m m a r y
Current snowmelt parameterisation schemes are largely untested
in warmer maritime snowfields, wherephysical snow properties can
differ substantially from the more common colder snow
environments.Physical properties such as snow density influence the
thermal properties of snow layers and are likelyto be important for
snowmelt rates. Existing methods for incorporating physical snow
properties intotemperature-index models (TIMs) require frequent
snow density observations. These observations areoften unavailable
in less monitored snow environments. In this study, previous
techniques for end-of-season snow density estimation (Bormann et
al., 2013) were enhanced and used as a basis for generatingdaily
snow density data from climate inputs. When evaluated against 2970
observations, the snow den-sity model outperforms a regionalised
density-time curve reducing biases from �0.027 g cm�3 to�0.004 g
cm�3 (7%). The simulated daily densities were used at 13 sites in
the warmer maritime snow-fields of Australia to parameterise
snowmelt estimation. With absolute snow water equivalent
(SWE)errors between 100 and 136 mm, the snow model performance was
generally lower in the study regionthan that reported for colder
snow environments, which may be attributed to high annual
variability.Model performance was strongly dependent on both
calibration and the adjustment for precipitationundercatch errors,
which influenced model calibration parameters by 150–200%.
Comparison of the den-sity-based snowmelt algorithm against a
typical temperature-index model revealed only minor differ-ences
between the two snowmelt schemes for estimation of SWE. However,
when the model wasevaluated against snow depths, the new scheme
reduced errors by up to 50%, largely due to improvedSWE to depth
conversions. While this study demonstrates the use of simulated
snow density in snowmeltparameterisation, the snow density model
may also be of broad interest for snow depth to SWEconversion.
Overall, the study responds to recent calls for broader testing of
TIMs across different snowenvironments, improves existing snow
modelling in Australia and proposes a new method forintroducing
physically-based constraints on snowmelt rates in data-poor
regions.
� 2014 Elsevier B.V. All rights reserved.
1. Introduction
Understanding how snow water resources are distributedthroughout
snow-affected catchments is imperative for waterresource planning
in many regions worldwide. The snow waterresources contained within
small and isolated snowfields havebeen identified as particularly
vulnerable in a warming climate(Bicknell and McManus, 2006).
Regular observations of snow waterequivalent (SWE) are currently
unavailable at catchment scales
(Dozier and Painter, 2004), and the available point-based
observa-tions are of limited use for snowmelt prediction (Rice and
Bales,2010). Snow models that estimate SWE distribution from
morereadily available climate observations are therefore essential
forbridging the gap between available snow observations and
infor-mation demand.
Temperature-index snow models (TIMs) have fewer staticparameters
and less complex data requirements than energy bal-ance models, and
despite their relative simplicity retain a some-what physical basis
(Ohmura, 2001). As such, TIMs are oftenselected over energy balance
approaches in less monitored catch-ments, have demonstrated skill
in snowmelt estimation (Jostet al., 2012) and continue to be used
for catchment-scale studies(Shamir and Georgakakos, 2006). Unlike
energy balance models,
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K.J. Bormann et al. / Journal of Hydrology 517 (2014) 652–667
653
TIMs require rigorous calibration with snow observations
(Kumaret al., 2013). In these models, the melt factor (units of mm
�C�1 day�1
or cm �C�1 day�1) directly relates daily snowmelt rates
tonear-surface air temperature. Sub-daily attribution of melt
factorshas also been used to introduce diurnal cycles in snowmelt
rates(Tobin et al., 2013). During model calibration, the melt
factor (oftenreferred to as the degree-day factor) is the
adjustable parameterthat is tuned for optimum model performance. As
such, the meltfactor is not selected based on the physical
characteristics thatinfluence snowmelt rates, which include
elevation, aspect, poten-tial solar exposure, forest cover,
physical snow properties and cli-mate influences (Marsh et al.,
2012; Musselman et al., 2012).
Many studies have demonstrated the benefits of
incorporatingphysical influences such as solar radiation, cold
content or landscapefeatures into TIM based snowmelt algorithms
(Brubaker et al., 1996;Hock, 1999; Jost et al., 2012). These
methods of modifying snowmeltestimation generally involve the
modulation of melt factor valueswith potential solar radiation
exposure, using landscape informa-tion such as aspect, slope or
elevation. Few studies have exploredthe use of physical snow
properties (such as snow density) for pre-scribing melt factors and
melt behaviour (DeWalle et al., 2002;Rango and Martinec, 1995),
particularly beyond the confines of pointobservation locations. The
integration of physical snow propertiesinto snowmelt
parameterisation schemes in TIMs is appealing insmall, marginal
snowfields where snow properties (in particularsnow densities) can
differ substantially from most (cold) snowfieldsglobally (Bormann
et al., 2013). Methods for distributing existingdensity-based
snowmelt parameterisations, such as that describedin Rango and
Martinec (1995), beyond point locations may beparticularly useful
in these snowfields.
The Australian snowfields are a good example of a
marginalsnowpack with unique snow properties (Bormann et al.,
2013).With relatively long snow observation records in some areas,
thesesnowfields provide an ideal region for the extension of
existingsnow modelling techniques to the less-studied warmer snow
envi-ronments. In this study, an existing method for
end-of-seasonsnow density estimation (Bormann et al., 2013) has
been extendedto support a snow density model that generates daily
snow densi-ties from climate inputs. Many of the existing models
that are usedto statistically simulate snow densities from climate
variables donot operate at daily time scales (McCreight and Small,
2013). The
Fig. 1. Study region in southeast Australia (left). The state
borders mark the state of Newarea above 1400 m (snowline, Ruddell
et al., 1990) is shaded grey, the red boxes are in sthe crosses
indicate precipitation gauge locations. The snow site numbers
correspond witlegend, the reader is referred to the web version of
this article.)
density model development for daily estimations is one of
themajor contributions presented in this study. The simulated
dailysnow densities were used to apply the Rango and Martinec(1995)
method for snowmelt parameterisation in TIMs. The modelswere tested
at multiple point locations throughout the largest con-tiguous
snowfield in Australia. The model performance was thencompared to a
typical air-temperature-based snowmelt estimationmethod that was
developed for the region in previous studies(Schreider et al.,
1997; Whetton et al., 1996). While this study islimited to
point-based modelling, the objective was to provide
aphysically-based foundation to enable spatial distribution of
themodel beyond point locations and across the entire region.
Thisstudy proposes a snow density algorithm that may be
readilyapplied at catchment scales, extends the limited state of
snowmodelling in Australia and responds to recent calls for the
testingof TIMs in different snow environments (Jost et al.,
2012).
2. Data
2.1. The study region
Alpine catchments that are situated in southeast Australia (Fig.
1)contribute snowmelt to streamflows in the largely arid and
agricul-turally important Murray-Darling river system. The
Murray-Darlingbasin is considered Australia’s ‘‘food bowl’’ and is
currently the focusof much political debate due to over allocation
of water resourcesand declining health of waterways (Kingsford,
2009). The snow-affected areas range from approximately 1400–2200 m
in elevation,with around half of the terrain lying below 1550 m.
The climatolog-ical mean freezing level during winter has been
estimated at around1500 m (Budin, 1985), which places large areas
of snow in thisregion at or below the atmospheric freezing level.
The largest contig-uous snow covered area in Australia is situated
in the state of NewSouth Wales (NSW) (Fig. 1) and is the focus
region of this study.These maritime snowfields may be considered a
typical exampleof relatively warm and marginal snowfields
worldwide.
2.2. Snow data and model sites
Snow observations collected by Snowy Hydro Ltd. wereobtained
manually using Federal samplers (Snowy Hydro Ltd.,
South Wales (NSW), Victoria (VIC) and the Australian Capital
Territory (ACT). Theitu snow site locations, the open diamonds mark
temperature observation sites andh descriptions in Table 1. (For
interpretation of the references to colour in this figure
-
Table 1Snow observation site inventory.
Note: Shaded rows highlight the sites that were used to evaluate
the snow density model only.
654 K.J. Bormann et al. / Journal of Hydrology 517 (2014)
652–667
personal communication, March 17, 2014) for 16 snow
coursesthroughout the NSW snowfields. One site was omitted due to
ashort record period of only three years leaving 15 snow
observa-tion sites with record periods exceeding 39 years (Table
1). The sitelocations are shown in Fig. 1. The data at these sites
include snowwater equivalent (SWE), snow density and snow depth,
which havebeen retrieved at irregular sampling frequencies ranging
from 6 to60 day intervals during winter months. Typically
measurementsare retrieved every 7–14 days. For each observation,
multiple mea-surements were obtained manually at 20 m spacings
along snowcourse transects and the sample mean was recorded. Most
of thesite records extend back to the early 1960s and collectively
samplethe full elevation range of the snowfields (Table 1). The
sites werecategorised into three elevation bands: low elevation
sites1800 m (n = 3). Four slope aspect categories werealso
classified, including NE (0–90�), SE (90–180�), SW (180–270�) and
NW (270–360�). For reasons discussed in Section 3.1,
the TIMs model could not be configured at two of the 15 sites
listedin Table 1. However, these sites were used to evaluate the
snowdensity model.
2.3. Meteorological data
Daily precipitation and temperature data for the region
wereobtained from both the Bureau of Meteorology (BoM) and
SnowyHydro Ltd. There were limited climate observations at
altitudesabove the snowline (Fig. 1) and spatially consistent
climate obser-vations at each of the snow sites were not always
available. Dailytemperature and precipitation time series were
prepared at eachof the 15 snow sites from the point-based
meteorological observa-tions to match the snow data period of
record at each site. Gapsand missing data were filled by merging
records from nearby sta-tions when required, favouring sites at
higher altitude for the pre-cipitation data. A lapse rate of 5.5 �C
km�1 (Appendix 4 in Ruddellet al. (1990)) was used to adjust air
temperature observations to
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K.J. Bormann et al. / Journal of Hydrology 517 (2014) 652–667
655
account for elevation differences between climate stations
andsnow observation sites. The daily precipitation observations
wereadjusted for undercatch biases using a mass balance
technique,further details of which are provided in the Method
section.
Small-scale orographic effects were detected at several high
ele-vation precipitation gauges, where very low winter
precipitationtotals were observed at sites near the summit
(>2000 m). The accu-mulated winter precipitation at these sites
did not correlate wellwith neighbouring sites (
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656 K.J. Bormann et al. / Journal of Hydrology 517 (2014)
652–667
minimum air temperature data to generate snowfall
accumula-tions. The Rango and Martinec (1995) snowmelt
parameterisationscheme was selected as it incorporates the physical
state of thesnow in melt estimation. The model was compared to a
snowmeltscheme used previously in the study region, which employs
onlyair temperatures to estimate snowmelt (Schreider et al.,
1997).Each of the two snowmelt schemes use a single melt
parameterto constrain the sensitivity of the snow pack. Snowmelt is
gener-ated as soon as air temperatures rise above 0 �C, without
consider-ation of cold content or snowpack ripening. Mean
observedtemperatures at the soil-snow interface in the study region
rarelyfall below 0.4 �C (Sanecki et al., 2006). The melt factors
for bothsnowmelt schemes were calibrated and evaluated at each
siteusing a split-sample calibration and evaluation process. The
modelconfiguration and calibration process are detailed in the
followingsections.
3.2.1. Snow accumulationFollowing Schreider et al. (1997), daily
snow accumulation A (in
mm), is a function of daily precipitation (mm), POBS and the
tem-perature-dependent probability of precipitation falling as
snowPrs[Tmin], where Tmin is the daily minimum surface
temperature(Eq. (2)).
A ¼ Prs½Tmin� � POBS ð2Þ
The probability of snow (Prs) for each day was approximatedfrom
daily minimum temperature using the curve developed forthe region
by Ruddell et al. (1990), who used over 16,000 observa-tion days.
From the non-linear probability curve, the probability ofsnowfall
reaches a maximum of 1 when daily minimum air tem-peratures are
below �3.0 �C, provides equal parts rain and snow(Prs = 0.5) at 1.5
�C and rapidly declines after minimum air temper-atures exceed 2.0
�C from a probability of 0.2 to near-zero proba-bility of snow at
4.0 �C. The non-linear probability curve was alsoused to separate
the total daily precipitation into rain and snowcomponents for the
undercatch adjustment (Section 3.1). Theprobability-based method of
estimating snowfall from total pre-cipitation data is considered a
more sophisticated method of esti-mating snow accumulation than
adopting a single temperaturethreshold (for example, 0 �C), and may
be an important distinctionin regions that experience a prevalence
of mixed rain/snow precip-itation, although this is not examined in
this study.
3.2.2. Snowmelt parameterisation schemesTIMs snowmelt schemes
use air temperature as a proxy for con-
straining snowmelt and may be expressed generally by Eq.
(3).
Mp ¼MF � ðTmean � TrefÞ ð3Þ
where Mp is the potential snowmelt (mm day�1), Tmean is the
meandaily air temperature, MF is the melt parameter (mm �C�1
day�1)and Tref is a reference temperature above which melt starts
to occur.In this study Tref is set to 0 �C. The melt parameter is a
crucial ele-ment that constrains snowmelt rates and must be
rigorously cali-brated. Therefore, two alternative schemes for
prescribing themelt parameter both spatially and temporally are
provided.
Scheme 1: Melt factor based on simulated snow density.The Rango
and Martinec (1995) method of melt parameter esti-
mation (Eq. (4)) draws on observed relationships between
meltparameter values and snow densities (DeWalle et al., 2002),
andprovides a technique for incorporating the spatial and
temporalinfluence of snow properties on snowmelt dynamics. By
allowingthe melt factor to increase proportionally with snow
density, thesimple model provides some representation of the
increasing ther-mal conductivity and decreasing albedo that also
occurs as snowages. The temporal representation captures the
time-basedcorrelation between snow densification and snow albedo
decay
processes, although the authors acknowledge that these
processesare not physically linked. These factors may be
particularly impor-tant in maritime snowfields with relatively high
snow densities,snow densification rates and interannual variability
(Bormannet al., 2013). The melt factor is described as:
MF ¼ k � qsqw
ð4Þ
where the calibration coefficient k is set to 1.1 (mm �C�1
day�1) inthe source reference, qs is snow density (in g cm�3) and
qw is thedensity of water (assumed to be 1 g cm�3). To account for
regionaldifferences, the parameter k is treated as a calibration
constant inthe present study.
One of the major drawbacks with the Rango and Martinecmethod of
melt factor parameterisation is the reliance on regularsnow density
observations. These observations are only availableat in situ point
measurement sites and are not always recordedvariables.
Density-time curves are commonly used to approximatesnow densities
at catchment scales or in data poor regions(Mizukami and Perica,
2008; Sturm et al., 2010). However, in mar-ginal maritime
snowfields the interannual variability in snow den-sities can be
significant, and mean density-time curves may notcapture important
year-to-year variance (Bormann et al., 2013).As such, a snow
density model was developed to estimate dailysnow densities from
climate-based variables. These density esti-mates may be used to
inform the Rango and Martinec methodfor melt factor estimation in
lieu of observations. The snow densitymodel predictions were
compared to values from a density-timecurve that was obtained by
applying a linear regression to the fullset of snow density
observations, from all sites in the region(n = 2970). The resulting
density-time curve is expressed in Eq. (5).
qsd�t ¼ 0:001369 � doyþ 0:1095 ð5Þ
where qsd-t is the estimated snow density (g cm�3) and doy is
theday of year.
The foundations of the snow density model are the climate-based
multiple linear regressions (MLR) that have been used toestimate
spring snow densities in the study region in previouswork (Bormann
et al., 2013). These MLR’s exploit relationshipsbetween seasonal
climate variables and the highly metamor-phosed end-of-season snow
pack properties, and are capable ofcapturing some of the high
interannual variability observed inspring snow densities within
maritime environments. The end-of-season snow densities obtained
from these existing MLR’s mustthen be extrapolated at daily
timesteps to the start of each seasonto adequately inform the Rango
and Martinec melt parameterisa-tion. The current work presents a
model to leverage daily snowdensity estimates from the
end-of-season values that may beobtained from the MLR’s.
Early season snow density may be considered similar to
‘‘fresh’’or ‘‘newly settled’’ snow density. In the study region,
the snow den-sity observations are typically obtained at 7–14 day
intervals.Therefore the observations correspond to ‘‘newly
settled’’ snow(with settling times �7 days on average) rather than
true ‘‘fresh’’snow. Chen et al. (2010) observed short-term
densification ratesof fresh snow of 0.004 g cm�3 .h�1 from 5th hour
after depositionto the 291st hour (or 12.1 days). During 7 days
(between measure-ment dates), fresh densities are expected to
increase from 0.01–0.26 g cm�3 (Judson and Doesken, 2000) to
0.08–0.32 g cm�3. Asthere was relatively low variability observed
in ‘‘newly settled’’snow densities in the region, a constant
density of 0.26 g cm�3 atJune 1 (the start of the Austral winter)
was adopted. The adopteddensity for ‘‘newly settled’’ snow of 0.26
g cm�3 lies within theexpected range after initial settling.
The late and early snow density estimates provide two
con-straints on the seasonal snow density profile, for which a
linear
-
Fig. 2. Schematic of snow density model. Both the solid and
dashed lines representpossible scenarios for simulated snow density
profiles for varying estimated springsnow densities (x). Note: June
1 is the start of Austral winter.
K.J. Bormann et al. / Journal of Hydrology 517 (2014) 652–667
657
snow densification rate between the two points was adopted.
Fromthis linear profile, daily snow density estimates may be
retrieved(Fig. 2). The assumption of linearity for snow density
with timefocuses the model to the long-term evolution of snowpack
bulkdensity throughout the entire snow season. Short-term
influencesthat add ‘‘noise’’ to the long-term snow density signal,
such assnowfall events and subsequent rapid compaction of fresh
snow(McCreight and Small, 2013), are not captured by the snow
densitymodel presented in this study.
For this study the existing MLR’s that can be used to
estimateAustralian spring snow density (Bormann et al., 2013) were
furtherenhanced to include all available data in NSW (increasing
the num-ber of snow density measurement sites from 4 in the
previousstudy to 17 (see sites in Table 1). The new enhancements
increasedthe spatial representativeness of the MLR’s by sampling a
widerrange of sites and incorporating additional landscape
inputs,including:
(a) a potential relative radiation predictor variable (PRR);(b)
separate regressions for forested and exposed sites;(c) removal of
depth related predictor variables (maximum
depth and the interactive depth-temperature term), as theywill
not be available during daily snowpack simulations; andthe
(d) extension of spring snow density date from September 1
toOctober 1 to facilitate longer snow seasons at higher eleva-tion
sites.
Following Bormann et al. (2013), the annual climate
predictorsused to derive the revised MLR’s were evaluated over
wintermonths only (JJA) with Tmax = maximum temperature (�C), log
Pre-c = log transform of the daily mean precipitation (cm
day�1),MRF = daily mean melt-refreeze events (events day�1), PRR
=monthly mean potential relative radiation, Elev = site
elevation(km) and Lat = absolute latitude. The MLR model predictor
setswere limited to five terms to reduce model complexity, and
themodel coefficients were optimised using 10-fold
cross-validationas described in Hastie et al. (2009) to obtain best
estimatesof model coefficient values and provide an indication of
out-of-sample model error. For more detail on climate
predictorderivation, cross-validation and the MLR model selection
for springsnow density estimation, refer to Bormann et al.
(2013).
The snow density model (which uses the climate-based MLR’sas a
foundation) was then applied to each of the snow model
sitesindividually, to generate daily snow density estimates at each
ofthe 15 sites for the full simulation periods. As both the
climateand landscape inputs differ between sites, the model
producesdifferent density profiles for each year at each site.
These snowdensity time series allow melt factors in the Rango and
Martinecscheme to vary both spatially and temporally.
Scheme 2: Melt factor based on air temperature.In previous
studies, Schreider et al. (1997) introduced an
albedo-related factor (Af) into the temperature-index model
struc-ture to account for the increasing melt rates that occur as
snowalbedo reduces with snow age (Baker et al., 1990). The
albedo-related factor is determined from empirical relationships
betweenmean monthly temperatures and melt factors and were
developedspecifically for the Australian snowfield region (Eq.
(5)).
MpðiÞ ¼ MF � Tmean � Af ðmonth; TmonthÞ ð6Þ
where the albedo-related factor Af ðmonth; TmonthÞ is
determinedfrom the mean monthly temperature.
Af ¼Tmonth
12þ 7
6for March; April and May;
Af ¼Tmonth
24þ 12
13for June; July and August;
Af ¼Tmonth
8þ 5
4for remaining months:
Af defaults to a value of 1 if Tmonth < �2 �C, and MF is used
as acalibration factor.
Snowmelt Scheme 2 has been adopted in previous snow model-ling
studies in Australia (Hennessy et al., 2003; Schreider et al.,1997;
Whetton et al., 1996) and was included in the present studyfor
comparison and benchmarking purposes.
3.3. Model calibration and evaluation
The calibration and evaluation of model parameters was
under-taken using a split-sample technique, which involved dividing
thesimulation periods at each site into two. The model calibration
andevaluation were conducted in two stages with: (a) the first
halfused to calibrate or train the model parameters and the last
halfreserved for model testing; and (b) the model calibration
con-ducted using the last half of the data and evaluation using the
firsthalf of the sample. Observed variability in the Australian
snow-fields is relatively high and therefore a relatively long
minimumtraining period of 20 years was adopted to obtain a
reasonable cal-ibration at each site. There were sufficient data
periods at all 13NSW snow model sites (those with CE estimates) to
use thesplit-sample approach. The split-sample method results in
differ-ent training periods for each site, as the periods of record
differslightly. Generally, the first half sample (hereby known as
F50)covers the period from the 1960s to the mid-1980s and the last
halfsample (known as L50) starts in the mid to late 1980s and
extendsto 2009. Actual periods for each site are included in Table
1.
Four evaluation statistics, including bias, mean absolute
error(MAE), root mean squared error (RMSE) and the coefficient of
effi-ciency (NSE), were used to determine optimum model
parameters(MF and k) through calibration at each site for each
split-sampleperiod. The bias, MAE and RMSE were calculated
followingWillmott and Matsuura (2005) and the NSE was calculated
follow-ing Nash and Sutcliffe (1970). During calibration, the
evaluationstatistics were determined for a range of possible model
parametervalues using all available SWE observations in each period
(F50 orL50). For each snowmelt scheme, the MF or k parameter
that
-
Fig. 3. Sensitivity results showing all four evaluation
statistic profiles for snowmeltScheme 1, at a single site. The red
line reflects model efficiency (NSE) (right Y axis),the blue lines
represent MAE, bias and RMSE (left Y axis). The grey lines
referencezero on both axes and the green vertical lines indicate
the potential melt parametervalues (at local minima/maxima). The
optimum calibrated parameter value (2 inthis example) is marked
with text. (For interpretation of the references to colour inthis
figure legend, the reader is referred to the web version of this
article.)
658 K.J. Bormann et al. / Journal of Hydrology 517 (2014)
652–667
resulted in the lowest model error was extracted for each
evalua-tion statistic, providing four potential melt parameter
values foreach snowmelt scheme. A graphical representation of the
calibra-tion results (Fig. 3) shows the error profiles for each
evaluation sta-tistic over the parameter ranges tested, where the
potentialparameter values for each statistic occur at cost function
globalminima or maxima (vertical green lines in Fig. 3). The
optimisedcalibration parameter that considers all four statistics,
is obtainedby averaging the four potential melt factor values.
Consequently,the calibration factors vary between sites. In Scheme
1, the calibra-tion parameter (k) physically represents the overall
effect oflandscape characteristics such as elevation, aspect, solar
exposureand forest cover on snowmelt rates. In Scheme 2 the
calibrationparameter (MF in mm �C�1 day�1) physically represents
the samelandscape characteristics as well as snow pack properties.
Modelevaluation using multiple cost-functions avoids limitations
ofsingle evaluation statistics (Willmott and Matsuura, 2005)
andtherefore provides more robust model calibration (Ritter
andMuñoz-Carpena, 2013).
Fig. 4. Simulated snow density profile (SIM – blue solid line)
with snow density observatand (b) high elevation Site 12 during a
moderate snow year of 2003. (For interpretationversion of this
article.)
After calibration, both snowmelt schemes were evaluated
usingsnow depths as well as the SWE data that were not used during
theprecipitation adjustment for each split-sample. Scheme 2 has
beenpreviously tested and calibrated using only snow depth
observa-tions (and not SWE) in the smaller Victorian snow fields
whichlie �150 km south of the study region (Hennessy et al., 2008).
Pre-vious Scheme 2 evaluations adopted a constant snow density
of0.4 g cm�3 to convert simulated SWE to snow depth. Here,
theevaluation of Scheme 2 will be expanded to include both
SWEdepths and snow depths in the larger NSW snowfields
(studyregion). The daily snow densities that were simulated for
Scheme 1were expected to improve SWE to snow depth conversions,
andtherefore reduce errors in modelled snow depth.
4. Results
To assess the full benefit of the snow density model in
inform-ing snowmelt estimation, the model must first be
evaluatedagainst the full set of density observations. The TIMs
were thenevaluated for SWE and snow depth estimation, and
finallythe spatial distribution of calibrated melt factor values
wasexamined.
4.1. Snow density estimation
The updated MLR’s for snow density estimation on October 1(mid
spring) provided slightly different relationships for exposedand
forested sites (Eq. (7)) than previous work (Bormann et al.,2013).
The simulated snow densities were still predominatelyinfluenced by
the previously identified predictors including eleva-tion, seasonal
precipitation and MRF events, although the newMLR’s include the
solar radiation exposure term PRR on exposedsites.
qs EXPOSED ¼ 0:01095Tmax þ 0:0401 log �Prec� 0:1759MRFþ
0:0007145PRR þ 0:19263 ð7Þ
qs FOREST ¼ 0:0374 log �Prec� 0:5471Elevþ 0:3767Lat� 0:08750MRF�
12:1566
When the revised MLR models were evaluated against
availablespring snow densities in September (n = 722), mean errors
of0.048 g cm�3 and an R2 of 0.22 were obtained. The MLR’s
presentedin Bormann et al. (2013) produced a mean error between
0.029 and0.043 g cm�3, (depending on snow type), and an R2 of
0.38(n = 192). The updated MLR’s (Eq. (7)) produce similar mean
errors
ions (OBS – black dots) at: (a) low elevation Site 13 during a
low snow year of 1992;of the references to colour in this figure
legend, the reader is referred to the web
-
Fig. 5. Simulated and observed snow densities during June –
September (inclusive) for the full period of record at all 15 snow
observation sites from: (a) the snow densitymodel; and (b)
regionalised density-time curve. Marker styles group the data into
the three elevation bands of low (orange circles), mid (grey
crosses) and high (blue squares)and the red dashed line is the 1:1.
(For interpretation of the references to colour in this figure
legend, the reader is referred to the web version of this
article.)
Table 2Snow density model performance for three elevation
bands.
No. of observations Snow density model Density-time curve
R2 Bias (g/cm3) MAE (g/cm3) R2 Bias (g/cm3) MAE (g/cm3)
All 2970 0.37* �0.004 0.055 0.34* �0.027 0.062(14%) (16%)
Low elevation 867 0.22* �0.010 0.064 0.21* 0.050 0.076(18%)
(21%)
Mid elevation 1301 0.35* 0.001 0.056 0.30* 0.022 0.063(15%)
(16%)
High elevation 802 0.50* �0.005 0.044 0.57* 0.009 0.046(11%)
(12%)
Forest sites 748 0.44* �0.009 0.061 0.30* 0.042 0.076(17%)
(21%)
Exposed sites 2256 0.34* �0.001 0.053 0.36* 0.021 0.057(14%)
(15%)
High solar exposure 1101 0.26* �0.007 0.061 0.23* 0.043
0.071(17%) (20%)
Low solar exposure 1865 0.41* �0.002 0.052 0.40* 0.017
0.057(13%) (14%)
High wind exposure 321 0.46* 0.003 0.060 0.32* 0.000 0.073(14%)
(17%)
Low wind exposure 2649 0.34* �0.005 0.055 0.33* 0.030 0.061(15%)
(16%)
* Indicates statistical significance at the 95% level.
K.J. Bormann et al. / Journal of Hydrology 517 (2014) 652–667
659
to the previously published MLR’s for spring density
estimation,while incorporating over three times as many data points
from amuch broader range of sites to the previous work. The
increasedsite variability represented in the present study may
contributeto the observed correlation reduction. The absolute
errors indicatethat the revised MLR’s are comparable to those
presented previ-ously (Bormann et al., 2013) and are considered to
be withinacceptable error limits.
An assumption of the snow density model (Fig. 2) was that
theseasonal profiles were relatively linear from June 1 to October
1(start of winter to mid spring). While this assumption is
reasonablein most seasons, complex snow density profiles were
observed atlow elevation sites, which violated the assumption of
linearity. Atthese sites, mid-season snow disappearance that was
immediatelyfollowed by low snow densities when the pack was
reformed withnew snow was observed. The mid-season low snow
densities thatare associated with intermittent snow packs were
partially cap-tured with a simple ‘‘reset’’ of the snow density
model back to
the ‘‘newly settled snow’’ density constant (0.26 g cm�3)
whenthe snow depth reached zero. The ‘‘reset’’ feature also
allowedthe snow density model to delay snow densification until the
snowpack actually formed, which may be well after the arbitrary
startdate (June 1) in low snow years and at low elevation sites
ashighlighted in Fig. 4a. The difference in seasonal densification
ratesbetween the two sites is apparent in Fig. 4 and is one of
thestrengths of the snow density model.
With overall biases of �0.004 g.cm�3 and mean absolute errorsof
14%, the snow density algorithm performed relatively well com-pared
to the full set of snow density observations (during June
–September, inclusive) as shown in Fig. 5a. The model
performanceincreased linearly with elevation (R2 = 0.45 at the 95%
significancelevel, not shown). The poorer performance of the model
at low ele-vation sites is clear when the evaluation is confined to
the threeelevation bands (Table 2). Snow densities are best
estimated athigh elevations (>1800 m), in forested areas rather
than exposedslopes and at sites with low solar exposure (Table 2),
which
-
Table 3Simulated SWE (mm) calibration and evaluation
statistics.b
Snowmelt scheme
Statistic (mm)
All sites (n=13)
F50 Calibration*
L50 Evaluation*
L50 Calibration
F50Evaluation
1
BiasAll
Accum.Melt
-26.2 -7.6% -4.9%
-16.3%
-27.5-8.3% 3.7%
-22.8%
-34.1-10.3% 0.2%
-24.7%
-3.5-1.0% 0.3% -7.1%
MAEAll
Accum.Melt
113.2 32.8% 37.1% 42.7%
115.534.7% 42.7% 42.7%
100.430.2% 38.0% 36.1%
135.739.3% 42.4% 51.1%
RMSE 206.5 183.2 158.1 249.6
R2 0.71 0.71 0.77 0.63
2
BiasAll
Accum.Melt
-27.7 -8.0% -7.1%
-14.9%
-24.1-7.2% 4.5%
-20.6%
-36.9-11.1% -0.6%
-25.4%
-14.3-4.1% -2.6%
-10.3%
MAEAll
Accum.Melt
110.7 32.1% 35.7% 42.8%
117.535.3% 42.9% 44.3%
103.831.2% 38.1% 39.1%
129.937.6% 40.8% 50.3%
RMSE 206.5 188.5 164.9 241.7
R2 0.72 0.70 0.76 0.64
a The table shading groups the simulations by melt parameter
values, where calibration parameters determined during the F50
period were used to evaluate the model in theL50 period. The values
in bold represent absolute values of bias or MAE (in mm) for all
data, which includes both the accumulation and the melt phases.
b Evaluation statistics exclude SWE data that was used to
estimate snowfall undercatch.
Fig. 6. SWE evaluation at all sites (L50 evaluation results).
The results for Scheme 2 were omitted as there was little
difference between the two snowmelt schemes for SWEestimation. The
marker styles reflect elevation (a) of which are described in Fig.
5 and aspect (b). In (b) the blue crosses represent north east
facing slopes (NE), the grey circlesrepresent south east facing
slopes (SE), the black asterisks mark south west facing slopes (SW)
and the orange squares identify north west facing slopes (NW).
(Forinterpretation of the references to colour in this figure
legend, the reader is referred to the web version of this
article.)
660 K.J. Bormann et al. / Journal of Hydrology 517 (2014)
652–667
suggests that the precipitation term in the MLR has
considerableinfluence. The snow density model provides improved
snowdensity estimates with overall bias values that are an order of
mag-nitude lower than those obtained from a regionalised
density-timecurve (Fig. 5b and Table 2).
The density-time curve does not account for interannual
vari-ability, which contributes to the broader scatter in Fig. 5b
as wellas the ‘capped’ spring snow density at �0.49 g cm�3
(correlatingto the last observation date of each season in
mid-spring nearOctober 4). The annual variability in seasonal
density error statis-tics is reduced by 36% when interannual
variability is considered,from 0.0038 g cm�3 for the density-time
curve to 0.0028 g cm�3
for the density model. The reduced variance in interannual
errorsuggests that the ability of the snow density model to respond
toannual variability is important. The further reduced skill of
thedensity-time curve at low elevation sites is clear in Fig. 5b.
Overall,the snow density algorithm is considered capable of
providingrealistic snow density estimates, beyond the capability of
regiona-lised density-time curves, to the Scheme 1 within the
TIMs.
4.2. SWE estimation
The snow model generally captures the SWE depth
variabilityacross the region (13 sites) with model biases between
�3.5 and
-
Table 4Simulated snow depth (mm) calibration and evaluation
statistics.
Snowmelt scheme
Statistic (mm)
All sites (n=13)
F50 Calibration*
L50 Evaluation*
L50 Calibration
F50 Evaluation
1
BiasAll
Accum.Melt
39.85.1% 15.3% -9.2%
36.74.7% 16.4% -12.8%
22.93.0% 13.3% -14.5%
90.411.5% 20.5% 0.3%
MAEAll
Accum.Melt
271.534.5% 42.2% 42.6%
291.337.6% 46.9% 43.8%
259.833.6% 42.0% 8.3%
321.540.6% 47.5% 51.4%
RMSE 441.5 440.0 393.1 541.2
R2 0.73 0.67 0.73 0.64
2
BiasAll
Accum.Melt
66.18.4% 6.5% 13.0%
73.29.5% 12.1% 9.0%
43.75.7% 7.6% 3.8%
97.412.3% 10.0% 18.8%
MAEAll
Accum.Melt
294.2 37.4% 40.0% 55.3%
318.841.2% 46.9% 55.7%
287.537.2% 42.0% 51.0%
340.543.2% 44.2% 65.3%
RMSE 545.4 499.7 455.6 632.0
R2 0.74 0.70 0.74 0.66
a The table shading groups the simulations by melt parameter
values, where calibration parameters determined during the F50
period were used to evaluate the model in theL50 period. The values
in bold represent absolute values of bias or MAE (in mm) for all
data, which includes both the accumulation and the melt phases.
Fig. 7. Snow depth evaluation results at all sites for Scheme 1
(left) and Scheme 2 (right) during the L50 period. The marker
styles reflect elevation and are described in Fig. 5.
K.J. Bormann et al. / Journal of Hydrology 517 (2014) 652–667
661
�27.5 mm (or �1% to �8%) and MAE’s between 100.4 and135.7 mm,
with little difference between the two snowmeltschemes (Table 3).
Model performance was generally better duringthe snow accumulation
phase (i.e. June – August) with mean eval-uation biases of 2%
compared to values of 15% during melting(Scheme 1). The model
biases were generally low during the F50period in both calibration
and evaluation simulations (1960s tomid to late 1980s). Across the
entire region, the modelled SWEestimates are generally centred
about the observations for all val-ues of SWE providing an R2 =
0.71 (the L50 evaluation plots areshown for example in Fig. 6a). At
SWE depths less than 800 mm,the model may provide significant
underestimates. Many of theseunderestimates are observed on
equator-facing slopes that receiveafternoon sun (NW), as can be
seen in Fig. 6b. In contrast, slopesfacing southwest (SW) are less
exposed to direct solar radiationand show very low SWE biases
(1%).
4.3. Snow depth estimation
In contrast to the previous section, the evaluation of
simu-lated snow depths at all sites highlight important
differencesbetween the two snowmelt schemes (Table 4). While the
snowmodel tends to overestimate snow depths for both
snowmeltschemes, Scheme 1 biases of 37–90 mm were at least
7–50%lower than values for Scheme 2. The largest errors in Scheme
2were observed at large snow depths and maximum seasonalSWE (at low
elevation sites) (Fig. 7), where snow density errorsfrom the
assumed constant density of 0.4 g cm�3 had the great-est impact
during conversion from SWE. With negative SWEbiases for both
schemes, the general overestimation in snowdepth reflects the
general underestimation of snow density (neg-ative snow density
biases, Table 2). These results confirm theexpected benefits of the
snow density model for SWE to depth
-
Fig. 8. Temporal variability in the annual mean model bias (SWE
– relative to maximum annual observed SWE) for all sites for both
snowmelt schemes (solid lines –Scheme 1 = blue and Scheme 2 =
orange). The horizontal dashed lines show the mean annual biases.
For reference, the maximum annual observed SWE is included
(thindashed line). (For interpretation of the references to colour
in this figure legend, the reader is referred to the web version of
this article.)
Table 5Mean calibrated melt parameters for two different
training periods (PADJUSTED).
Snowmeltscheme
Melt factor % Difference
First half trainingperiod (F50)
Last half trainingperiod (L50)
Scheme 1 (k) 2.73 2.57 6Scheme 2 (MF) 10.45 9.66 8
Mean 7
662 K.J. Bormann et al. / Journal of Hydrology 517 (2014)
652–667
conversion. Scheme 1 tends to overestimate snow depths duringthe
accumulation phase and underestimate snow depths duringsnowmelt,
which suggests that the underestimation of snowdensities from the
density model occurs mostly during snowaccumulation. The
differences between the snowmelt schemesfor snow depth estimation
are most prominent when the packexperiences intermittent snowmelt
throughout the season, ratherthan at the end of the season when
snowmelt is rapid and theschemes converge.
Fig. 9. Relationship between calibrated melt factors at each
site (averaged between F5linear regressions shown calculated using
all data for each site and are significant to the
4.4. Spatial and temporal variability in model performance
Quite different annual SWE profiles were observed betweenmodel
sites, from the patchy and intermittent snow cover at sitesnear the
snowline (1, 2 and 13), to the more consistent seasonalsnow
profiles at high accumulation sites at the top of the range(4, 5
and 15). On a site-by-site basis, a range of performances
wereobserved with R2 values ranging from 0.56 to 0.84 at 10 of the
eval-uation sites. Reduced performance at the remaining sites (1, 2
and13) was observed with R2 values of 0.24–0.52. These three
sitesexperience low SWE accumulation (generally < 400 mm
maxi-mum), high solar exposure and intermittent snow cover and
areresponsible for the reduced snow model performance at low
SWEdepths.
The annual performance of the snow models for SWE estima-tion
for the full data record (F50 and L50) is presented in Fig. 8.The
maximum deviation in model performance from the meanoccurred in
years 1968, 1973, 1975, 1977, 1998 and 2004. The lar-ger deviations
in model performance during these years highlightthe interannual
variability experienced in the Australian snow-fields and the
challenges of snow modelling in the region. A weak
0 and L50 calibration periods) and elevation for both snowmelt
schemes. The bold95% level. The thin linear regression lines
represent each leave-one-out realisation.
-
K.J. Bormann et al. / Journal of Hydrology 517 (2014) 652–667
663
negative correlation was observed between annual model biasesand
SWE depth, as the model tended to overestimate SWE duringlow snow
years and underestimate SWE during high snow years.
4.5. Physical representation of calibrated melt factors
When the snow models were calibrated during the first half ofthe
observations (F50), the mean melt factor values were �7%higher than
those obtained when the model was calibrated onthe second half of
the observations (L50) (Table 5). The relativelysmall shift in
optimum model parameters between calibrationperiods indicates that
optimum model parameters are notcompletely stable through time.
Statistically significant negative correlations were
observedbetween calibrated melt factors and elevation for both
snowmeltschemes and precipitation forcing data (R2��0.80 and �0.39
forPOBSERVED and PADJUSTED respectively at a 95% significance
level, withp values
-
664 K.J. Bormann et al. / Journal of Hydrology 517 (2014)
652–667
better during the accumulation period (Table 3). By excluding
15%of the available SWE observations during accumulation
events>50 mm (see Appendix A), the overall SWE evaluation is
conductedusing an increased proportion of observations taken during
themelt phase. Therefore, the values presented in Table 3 may
beconsidered conservative estimates of actual model
performance.
5.3. Choice of snowmelt scheme in warm maritime environments
For SWE estimation, the differences between the two schemeswere
small. The sites with least discrepancy between the snow-melt
schemes were at low elevations, where snow accumulationwas low and
the snow disappeared very quickly once meltingstarted to occur.
Over such short time scales the choice of snow-melt scheme becomes
far less important than other factors. Previ-ous studies that
compare snowmelt schemes in TIMs have foundlarger differences
between schemes for SWE estimation, whichhave largely been
attributed to melt factor discrepancies (Hock,1999). In this study
the melt factors provided by the air-tempera-ture based method
(Schreider et al., 1997) differ from thoseobtained through the
density-based method (Rango andMartinec, 1995). The difference in
melt factors was largest duringsnow accumulation months (June and
July) where far less variabil-ity in melt factors was obtained from
the air-temperature basedmethod. Much smaller differences in melt
factors between thetwo schemes were observed during spring
(September) when thesnowpack is losing mass rapidly.
The introduction of a more physically-based snowmelt
param-eterisation into the TIMs using Scheme 1 was expected to
improvesnow model performance by appropriately enhancing daily
meltrates during warmer years, where the snowpack is more likely
tobe ‘‘ripe’’ for melting throughout the season despite cold
contentnot explicitly being considered by the model. Instead, SWE
profilesfor the two schemes were very similar and did not reflect
theobserved discrepancies in melt factors between the schemes.While
the details of the snowmelt schemes in the present studydiffer from
previous work, the results suggest that the choice ofsnowmelt
scheme in warm maritime environments is much lessimportant for SWE
estimation than other factors, such as the qual-ity of
meteorological inputs and regional calibration. These resultsdo not
support future efforts to improve snowmelt estimation inTIMs for
maritime environments with melt algorithmmodifications.
5.4. The impact of precipitation and climate forcing on
modelparameters
The problem of snowfall deficiencies in precipitation data is
notuncommon (Rasmussen et al., 2012) and was observed in the
stationprecipitation data from the NSW alpine region. The
precipitationerrors due to undercatch were estimated to be as much
as 56% atthe high elevation sites and �20–30% at mid-elevation
sites. Themagnitude of these precipitation errors is within the
range of previ-ously documented undercatch errors in general
(Rasmussen et al.,2012), and across an elevation gradient
(Fassnacht, 2004). A simplemultiplication factor applied to the
probability-based snowfall com-ponent (PSNOW) of the precipitation
observations (based on Tmin)proved useful in correcting these
precipitation undercatch errors,reducing SWE biases in the snow
model from �12% to 2% (or �50to +9 mm for POBS and PADJ
respectively). Precipitation undercatchcorrections based on mass
balance techniques have previously dem-onstrated agreement with
aerodynamic precipitation correctionmodels and have been used to
improve modelling in glacial catch-ments in Italy (Carturan et al.,
2012).
The present study shows that precipitation undercatch biasesalso
significantly influence calibrated melt factor parameters.
During model calibration, melt factors are generally
optimisedfor model performance and resulting calibration parameters
maypartially compensate for all sources of model error, including
forc-ing data biases and model structural errors (Stisen et al.,
2012).Results from this study suggest that broad-scale climate
factorsmay also influence model calibrations, with a shift in
optimummodel parameters of 7% between the split-sample
periods.Climatologically, the F50 calibration period was more
likely to be‘wetter’ than the L50 period due to a higher prevalence
ofLa-Niña-like conditions, negative phase of the Southern
AnnularMode (which brings the westerly storm track closer to the
moun-tains) and prevailing drought conditions during the 2000s
(Chubbet al., 2011; Van Dijk et al., 2013). These large-scale
climatologicalfeatures may have contributed to the slightly higher
melt factorvalues obtained for the F50 period, where more winter
precipita-tion resulting in deeper snowpacks and increased
cloudinessduring the F50 period would require increased snowmelt
rates todeplete the snow pack rapidly during the spring melt,
particularlyat higher elevation sites. With increased cloudiness,
the solar radi-ation component of the energy balance would be
reduced. Theseresults confirm previous suggestions that wet and dry
years havea role in TIMs calibrations (Kumar et al., 2013) and may
be aresponse to energy balance components and dominant
snowmeltprocesses.
After appropriate snowfall adjustments, the mean calibratedmelt
factor values for the region, generally exceed the typical val-ues
previously obtained in northern hemisphere studies by�6 mm �C�1
day�1 (Scheme 2) and 1.5 (Scheme 1). Previous stud-ies for the
region using snowmelt Scheme 2 employ a spatiallyand temporally
constant melt factor of 2.9 mm �C�1 day�1 thatwas generated at a
single site in NSW (the mid-high elevationwell-monitored Site 12)
(Schreider et al., 1997; Whetton et al.,1996). The results
presented here suggest that the previouslyadopted value at this
site was too low and a melt factor closer to8.4 mm �C�1 day�1 would
be more appropriate. The reason forthe melt factor underestimation
in the previous studies may beattributed to the unaccounted
precipitation undercatch. A lowermelt factor of 2.2 mm �C�1 day�1,
which is much closer to the valueadopted by these previous studies,
was obtained through calibra-tion in the present study when the
unadjusted precipitation inputdata were used (POBSERVED). The
spatial variability in melt factorspresented here also indicate
that the previously adopted spatiallyconstant melt factor of 2.9 mm
�C�1 day�1 may be improved to bet-ter represent spatial variability
in snowmelt, as acknowledged bythe previous authors.
Recent studies have highlighted the importance of spatial
vari-ability in melt factors in TIMs (Kumar et al., 2013). These
studiesstrongly support the development of methods for spatial
distribu-tion of melt parameters beyond calibration points as an
essentialcomponent of catchment-scale snow models. The negative
rela-tionship between elevation and calibrated melt factors (Fig.
9) iscrucial for parameterising spatially-distributed TIMs.
Interestingly,the negative relationship derived from the model
calibrations dis-agrees with the conceptual model provided in Hock
(2003), whichindicates higher melt factor values with elevation.
Hock (2003)provides a large table of documented melt factors across
a rangeof glacial and non-glacial sites. Using this data, we have
plottedmelt factor against elevation and confirmed that the
relationshipis positive (as the conceptual model indicates).
However, for non-glacial sites the relationship is negative and is
consistent withthe results presented in our manuscript. Since Hock
(2003) onlyprovides non-glacial information for two sites, we
extended thistest analysis to include results from several other
non-glacial stud-ies (Lang and Braun, 1990; Hodgkins et al., 2012;
DeWalle et al.,2002 and Rango and Martinec, 1995). When all the
data from thesestudies were collated, we confirm that the
relationship remains
-
Fig. A1. Schematic of the mass balance correction technique for
estimating precipitation undercatch at snow-affected observation
sites. Px represents the total snowfall depthbetween t0 and t1 if
undercatch error was zero.
K.J. Bormann et al. / Journal of Hydrology 517 (2014) 652–667
665
negative between melt factor values and elevations at
non-glacialsites (R2 = 0.30, p = 0.02 not shown). Bare ice has a
much loweralbedo than snow and will therefore absorb more solar
energy.As solar radiation absorption is the primary driver for
snow/icemelt, it is reasonable to expect different melt dynamics at
glacialand non-glacial sites.
Reported melt parameters from previous studies should
beinterpreted with caution as input data biases and model
structuralerrors are not commonly reported, and substantial changes
in meltfactors obtained through calibration may be obtained for
relativelysmall input data errors. The results presented here show
that therelationship between elevation and calibrated melt factors
isrobust and errors in melt factors of �5.9% to 22.6% may
beexpected beyond calibration locations. The impact of this
magni-tude of errors on simulated SWE may, in part, be inferred
fromthe split-sample calibration results, where a difference of
11–14%in calibration factor between F50 and L50 (Table 5) yields
TIMsSWE biases of up to 29.8 mm (Table 3). The results also
providean indication of the magnitude of melt factor changes that
mayoccur with typical precipitation undercatch errors.
It is important to note that while precipitation undercatch
canhave a significant influence on SWE simulations, air
temperaturemeasurements in snow-affected areas can incur mean daily
biasesof +0.6 to +2.2 �C due to radiative heating (estimated from
informa-tion presented in Huwald et al., 2009). Measurement biases
fromtypical air temperature sensors over snow packs vary with
windspeed and solar radiation exposure and as such can vary
consider-ably throughout the day. Adjusting daily air temperature
data toaccount for these biases is desirable, but opportunities are
limitedin data-sparse regions without independent measurements
thatare unaffected by radiative heating. If air temperature biases
wereconsidered, the calibrated melt factor values would likely
reduce toaccount for the increased melt forcing, while optimising
modelperformance. Note that Raleigh and Lundquist (2012) find that
inthe maritime snowfields of the western US, forward-type
models(such as the TIMs presented in the present study) are more
sensi-tive to snowfall forcing, which is a combination of both
precipita-tion and temperature inputs.
6. Conclusions
With point-based models operating for at least 39 years at
13sites that were located throughout the NSW snowfields in
Austra-lia, this study provides one of the most comprehensive
modellingefforts for the region and contributes towards snow model
testingin warm maritime environments. The present study builds
onexisting techniques for end-of-season snow density estimation
to
provide a method for obtaining daily snow density estimates
thatoutperform density-time curves in the Australian region. One
ofthe main advantages of the enhanced snow density model is
thecapability to incorporate important interannual variability
andimprove SWE to depth conversions. The climate based snow
den-sity technique may therefore be of use in maritime snowfields
inother regions where interannual variability in snow propertiescan
also be high or where snow observations are limited.
Modelparameters would likely require recalibration in areas
outsideNSW.
The choice of snowmelt scheme was found to be less importantthan
other factors for SWE estimation in the warm maritime envi-ronment
due to rapid snowmelt. However, improved snow depthestimates were
obtained when the daily snow density model wasused to inform SWE to
depth conversion compared to using regio-nal climatologies. The
extension of the model evaluation metricfrom SWE to snow depth is
an important aspect of rigorous modeltesting in the region that
allows model development to beexpanded to areas with only snow
depth measurements. Consider-able spatial distribution of melt
factors was also observed, reflect-ing the variability of snowmelt
sensitivities when overall solarradiation is high. The calibrated
melt factors show a large sensitiv-ity to precipitation forcing and
a correlation with elevation and to alesser extent potential solar
exposure. These types of relationshipsare essential for spatial
application of such models. While the pres-ent study demonstrates
the use of the snow density model forparameterisation of a
temperature-index snow model, the modelmay be useful to those
interested in other aspects of snow researchsuch as SWE/snow depth
conversions.
Acknowledgements
We thank Andrew Nolan, Jason Venables, Shane Bilish andJohanna
Speirs at Snowy Hydro Limited for their cooperation inproviding the
data along with comments on the manuscript, andTristan Sasse for
valuable suggestions during manuscript prepara-tion and planning.
J.P. Evans was supported by an AustralianResearch Council Future
Fellowship (FT110100576).
Appendix A
The mass balance approach estimates precipitation undercatchby
assuming that observed SWE accumulation depths should rec-oncile
with observed total precipitation, if all falling precipitationis
captured by the gauge and air temperatures are below
freezing.Therefore any precipitation deficit during these
conditions may beattributed to undercatch error as presented in
Fig. A1. The ratio of
-
666 K.J. Bormann et al. / Journal of Hydrology 517 (2014)
652–667
observed total precipitation and SWE accumulation depths over
acommon time period provides an estimate of the
undercatch,expressed as gauge catch efficiency ratio (CE) (Eq.
(A1)).
CE ¼Pt1
t0PSWEt1 � SWEt0
ðA1Þ
wherePt1
t0P is the sum of daily precipitation between snowobservations
at dates t0 and t1 (where t0 is the date at which snowaccumulation
commenced and t1 is when the snow accumulationceased) and
SWEt1–SWEt0 is the observed SWE change betweenthese dates. A CE
value of 0.5 indicates that 50% of the total precip-itation
observed on the ground (as SWE) was uncollected by theprecipitation
gauge, and a CE of 1.0 indicates complete precipitationcollection.
Fig. A1 provides a schematic of the mass balancecorrection
technique.
The mass balance technique estimates the CE achieved at
theprecipitation gauges during snowfall days (i.e. when mean air
tem-peratures were below freezing). The SWE observations
werecollected at irregular intervals during winter
(measurementsobtained at 7–14 day intervals) and as such the mass
balance wasapplied at irregular time steps. The SWE accumulation
observedbetween two observation dates may be the cumulative result
ofseveral precipitation days or events. To account for multi-day
timesteps, the daily precipitation was summed over the entire
intervalbetween SWE observation dates. At low SWE depths or whenSWE
accumulations between measurements were small andSWEt1–SWEt0 ? 0,
the signal to noise ratio for SWE accumulationsis expected to be
high. Similarly, as the time interval between SWEobservations
increases, the cumulative impact of factors such assublimation,
evaporation and mid-period snowmelt occurringbetween SWE
measurements increases. To minimise these twopotential sources of
error, the CE calculations were only performedfor events where SWE
accumulation between the two observationdates were greater than 50
mm and the interval between observa-tions was shorter than 14 days.
These limitations both increasedthe signal to noise ratio and
reduced potential sources of error,and were optimised during an
iterative sensitivity analysis.
After the SWE accumulation and time thresholds were used tomask
the data, any CE values that were calculated for single
snowaccumulation events (t0–t1) that were greater than 1.0 (�20% of
allevents) were omitted, as this suggests that other processes
(otherthan undercatch) were also influencing the mass balance.
Thesub-sample of SWE estimates based on these criteria resulted
inthe mass balance analysis using only a small fraction of the
totalSWE observations
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Constraining snowmelt in a temperature-index model using
simulated snow densities1 Introduction2 Data2.1 The study region2.2
Snow data and model sites2.3 Meteorological data2.4 Landscape
data
3 Method3.1 Adjustments for snowfall undercatch biases3.2
Temperature-index model (TIMs)3.2.1 Snow accumulation3.2.2 Snowmelt
parameterisation schemes
3.3 Model calibration and evaluation
4 Results4.1 Snow density estimation4.2 SWE estimation4.3 Snow
depth estimation4.4 Spatial and temporal variability in model
performance4.5 Physical representation of calibrated melt
factors
5 Discussion5.1 Snow density modelling5.2 Snow modelling
challenges in maritime snow environments5.3 Choice of snowmelt
scheme in warm maritime environments5.4 The impact of precipitation
and climate forcing on model parameters
6 ConclusionsAcknowledgementsAppendix AReferences