Journal of Hydrology - University of New South...

Journal of Hydrology 517 (2014) 652–667

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Journal of Hydrology

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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


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 (


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.


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.)


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.


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.)


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.


�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


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.


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


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.


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


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 (2.0.CO;2http://dx.doi.org/10.1175/1520-0450(1990)029<0179:TADOPS>2.0.CO;2http://dx.doi.org/10.1111/j.1745-5871.2006.00409.xhttp://dx.doi.org/10.1111/j.1745-5871.2006.00409.xhttp://dx.doi.org/10.1016/j.jhydrol.2013.01.032http://dx.doi.org/10.1016/j.jhydrol.2013.01.032http://dx.doi.org/10.1002/(SICI)1099-1085(199610)10:10<1329::AID-HYP464>3.0.CO;2-Whttp://dx.doi.org/10.1002/(SICI)1099-1085(199610)10:10<1329::AID-HYP464>3.0.CO;2-Whttp://refhub.elsevier.com/S0022-1694(14)00458-2/h0030http://refhub.elsevier.com/S0022-1694(14)00458-2/h0030http://dx.doi.org/10.1002/hyp.8099http://dx.doi.org/10.1002/hyp.8099http://dx.doi.org/10.4461/GFDQ.2012.35.4http://dx.doi.org/10.4461/GFDQ.2012.35.4http://dx.doi.org/10.1007/s11769-010-0434-0http://dx.doi.org/10.1007/s11769-010-0434-0http://dx.doi.org/10.1175/JHM-D-10-05021.1http://dx.doi.org/10.1007/s11269-009-9486-2http://dx.doi.org/10.5194/tc-7-433-2013http://dx.doi.org/10.1002/wrcr.20123http://dx.doi.org/10.1146/annurev.earth.32.101802.120404http://dx.doi.org/10.1146/annurev.earth.32.101802.120404http://dx.doi.org/10.1016/j.advwatres.2012.07.013http://dx.doi.org/10.1029/2005RG000183http://dx.doi.org/10.1016/j.advwatres.2012.08.010http://dx.doi.org/10.1016/j.advwatres.2012.08.010http://refhub.elsevier.com/S0022-1694(14)00458-2/h0095http://refhub.elsevier.com/S0022-1694(14)00458-2/h0095http://dx.doi.org/10.3354/cr00706http://refhub.elsevier.com/S0022-1694(14)00458-2/h0105http://refhub.elsevier.com/S0022-1694(14)00458-2/h0105http://refhub.elsevier.com/S0022-1694(14)00458-2/h0105http://refhub.elsevier.com/S0022-1694(14)00458-2/h0110http://refhub.elsevier.com/S0022-1694(14)00458-2/h0110http://refhub.elsevier.com/S0022-1694(14)00458-2/h0115http://refhub.elsevier.com/S0022-1694(14)00458-2/h0115http://dx.doi.org/10.1002/hyp.8458http://dx.doi.org/10.1029/2008WR007600http://dx.doi.org/10.1016/j.jhydrol.2009.09.021http://dx.doi.org/10.1016/j.jhydrol.2011.11.045http://refhub.elsevier.com/S0022-1694(14)00458-2/h0140http://refhub.elsevier.com/S0022-1694(14)00458-2/h0140http://refhub.elsevier.com/S0022-1694(14)00458-2/h0145http://refhub.elsevier.com/S0022-1694(14)00458-2/h0145http://dx.doi.org/10.1016/j.advwatres.2013.03.006http://dx.doi.org/10.1016/j.advwatres.2013.03.006


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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

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