estimating precipitation phase using a psychrometric energy

HYDROLOGICAL PROCESSESHydrol. Process. (2013)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.9799

Estimating precipitation phase using a psychrometric energybalance method

Phillip Harder and John Pomeroy*Centre for Hydrology, University of Saskatchewan, 117 Science Place, Saskatoon, Canada

*CofE-m

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Abstract:

Precipitation phase is fundamental to a catchment’s hydrological response to precipitation events. Phase is particularly variableover time and space in the Canadian Rockies where snowfall or rainfall can occur any month of the year. Phase is controlled bythe microphysics of the falling hydrometeor, but microphysical calculations require detailed atmospheric information that is oftenlacking for hydrological analyses. In hydrology, there have been many methods developed to estimate phase, but most areregionally calibrated, and many depend on air temperature (Ta) and use daily time steps. Phase is not only related to Ta, but toother meteorological variables, and precipitation events are temporally dynamic, adding uncertainty to the use of daily indices toestimate phase. To better predict precipitation phase, the psychrometric energy balance of a falling hydrometeor was calculatedand used to develop a method to estimate precipitation phase. High quality precipitation phase and meteorological data wereobserved at multiple elevations in a small Canadian Rockies catchment, Marmot Creek Research Basin, at 15-min intervals overseveral years to develop and test the method. The results of the psychrometric energy balance method were compared to phaseobservations, to other methods over varying time scales and seasons and at varying elevations and topographic exposures. Theresults indicate that the psychrometric energy balance method performs much better than Ta index methods and that thisimprovement, and the accuracy of the psychrometric energy balance method, increases as the time step of calculation decreases.Copyright © 2013 John Wiley & Sons, Ltd.

KEY WORDS snowfall; rainfall; precipitation; phase change; Canadian Rockies; energy balance; models

Received 24 September 2012; Accepted 25 February 2013

INTRODUCTION

A robust understanding of precipitation intensity, duration,amount and phase is crucial to hydrological predictionapplications in cold regions (Gray, 1970). The uncertainty ofthese predictions is strongly influenced by the quality of theinput data (Zehe et al., 2005) of which accurate precipitationphase is fundamental. Precipitation phase varies widely overspaceandtime,andthisvarianceisespeciallyhighinmountains.Elevation exerts a strong control on temperature,water vapour,andhenceprecipitationphase,asvisualizedin thesnowlineofastorm, which is a consequence of the interaction betweenatmosphericlapseratesoftemperatureandhumidity,mesoscalemechanisms, synoptic controls such as upslope or downslopeeventsandtopography(Minderetal.,2011;Marksetal.,2013).

PHASE CHANGE PHYSICS

The phase of precipitation at the ground surface is influencedby the properties of the atmosphere that precipitation mustpass through. These properties include temperature, verticalthickness, humidity, stability, precipitation characteristics andinteractions between hydrometeors (Gray and Prowse, 1992).The relative importance of these properties varies withsynoptic conditions. The factors influencing phase in the

orrespondence to: John Pomeroy, Centre for Hydrology, UniversitySaskatchewan, 117 Science Place, Saskatoon, Canadaail: [email protected]

pyright © 2013 John Wiley & Sons, Ltd.

condensation region of an air mass, while important, are ofless influence to phase at the surface than the characteristics ofthe atmosphere throughwhich the hydrometeor, an individualwater or ice particle, travels (Thériault and Stewart, 2010).During its fall, a hydrometeor can be visualized physically asa drop of water (frozen or liquid) falling through a dynamicvapour continuum. Latent heat can be added to thehydrometeor through condensation or removed thoughevaporation/sublimation which is a function of the vapourpressure deficit and enhanced ventilation of a fallinghydrometeor which itself is a function of fall velocity andof prevailing wind conditions within the atmosphere(Stewart, 1992). Sensible heat can also be added or removed,which is primarily a function of the relative temperature of thehydrometeor to the atmosphere and a ventilation coefficient(Stewart, 1992). The sensible and latent heat fluxes determinethe internal energy and temperature of the hydrometeorwhichultimately determines the phase of the hydrometeor when amelting term is included. Additionally hydrometeors have arange in size distributions that can lead to multipleprecipitation types existing concurrently, changing phase atdifferent rates, leading to mixed precipitation events(Thériault and Stewart, 2010). In temperate and cold regionenvironments, precipitation is formed in the atmosphere as asolid (snow) and the phase at the surface is determined bywhether it melts into rain (liquid) or not (Stewart, 1992). Thismelting process is controlled by the sensible heat flux, asdetermined by the temporally dynamic temperature lapserate, and the latent heat flux, as determined by the humidity

P. HARDER AND J. POMEROY

structure of the atmosphere. Phase can change over thecourse of travel if the energy available is enough to meetthe latent heat of fusion requirements to melt or refreezethe hydrometeor. Thus, the factors affecting the temper-ature and humidity structure of the atmosphere such asatmospheric stability, layer thickness and heterogeneity,inversions and synoptic weather systems (Fassnacht et al.,2001) exert a strong control on the melting process andultimately phase.

PHASE CHANGE CALCULATIONS INHYDROLOGY

Phase calculations of hydrometeors falling through theatmosphere, are typically implemented by numericalmicrophysical schemes, implemented in atmosphericmodels (Thériault and Stewart, 2010; Minder et al.,2011). Whilst many factors influence the phase ofprecipitation, and conditions at the ground surface provideonly a limited indication of the atmospheric processesoccurring (Feiccabrino and Lundberg, 2008), full solutionsto resolve the phase of hydrometeors require informationon topographic influences, atmospheric lapse rates andsurface interactions with the atmosphere (Marks et al.,2013), which has limited their application in hydrologicalmodels.Commonly, precipitation phase determination techniques

for hydrology have focused on relating phase to dailyaverages of meteorological variables measured at the groundsurface. Early work in this area by the US Army Corps ofEngineers (1956) and Auer (1974) showed a snow to raintransition in air temperatures (Ta) from 0 �C to 6 �C. Manyother approaches have been suggested since then and range incomplexity. The simplest and most commonly used methodis to define a single threshold that defines all precipitation asrain above, and snow below, a specified Ta (Leavesley et al.,1983). These values can range from �1 �C to 4 �C on thedaily time scale (Saelthun, 1996), and are site specific (Markset al., 2013) and dependent on atmospheric stability (Olafssonand Haraldsdottir, 2003). Also used is a double threshold,whereby a lower threshold defines all precipitation below assnow and an upper threshold defines all precipitation above asrain. The range between thresholds is then considered to bemixed and proportional to a linear or curvilinear regressionbetween the defined thresholds (Pipes and Quick, 1977). TheUSGS Hydrological Simulation Program (HSPF) modelcalculates a critical temperature that varies with Ta and dewpoint temperature (Td) (Bicknell et al., 1997). Whilst thismethod considers humidity, it does so in an empiricalmanner,and so its spatial and temporal transferability is uncertain.Curvilinear rain ratio methods have been proposed thatinclude seasonal corrections (Kienzle, 2008). Other temper-ature methods consider the diurnal temperature range(Leavesley et al., 1983) and the temperature structure of thenear surface atmospheric boundary layer (Gjertsen andOdegaard, 2005). The daily time step of most of thesemethods is a legacy of non-automated mountain weatherstations with max–min thermometers and uncertain humiditymeasurements and is less relevant now with automated

Copyright © 2013 John Wiley & Sons, Ltd.

weather stations containing hygrothermometers controlled byelectronic measurement and control dataloggers.Despite examples of physically based approaches that

utilize the psychrometric energy balance to predictprecipitation phase (Steinacker, 1983), hydrologicalapplications often use daily temperature statistics along withempirical Ta correlations that have no physical basis toestimate precipitation phase (Feiccabrino and Lundberg,2008) and so are site or region specific and cannot be appliedwithout calibration to other sites or regions. The lack of highaltitude weather stations with detailed precipitationmeasurements in many parts of the world makes suchcalibrations impossible for the most catchments. Further,these Ta proxies need to be recalibrated regularly to provideeffective estimates as climatic characteristics affecting phasevary over time (Marks et al., 2013) which adds uncertainty totheir application in hydrologically non-stationary conditions(Milly et al., 2008) that are particularly acute in themountainsof western North America (Mote et al., 2005).In addition to Ta proxies, other methods integrate

observation of atmospheric humidity by consideringproperties such as Td and thermodynamic ice bulbtemperature (Marks et al., 2013). Considering phasedifferentiation within a single precipitation event, Markset al. (2013) found that transition timing was better estimatedby the 0 �C Td than by the 0 �C ice bulb threshold when 15min time intervals were used. However, phase discriminationusing a daily interval showed little differences between theTa,Td and ice bulb threshold methods (Marks et al., 2013). Inabsence of other methods, thresholds can be used todifferentiate phase but are limited, especially Ta thresholds,in that they do not consider mixed precipitation nortemporally variable meteorological conditions. Thesefindings emphasize the temporal scaling implications ofprecipitation phase discrimination and dependence of phaseon humidity (Marks et al., 2013).

HYDROMETEOR TEMPERATURE CALCULATIONS

A parameter that has a strong physical basis to determineprecipitation phase is the hydrometeor temperature (Ti)(Steinacker, 1983; Sugaya, 1991; Stewart, 1992). TheTi approximates the temperature at the surface of a fallinghydrometeor by accounting for the surface thermodynamicfluxes which itself are controlled by the energy and massbalance of the falling hydrometeor. The Ti can be consideredsimilar to the ventilated ice/wet bulb temperature. Thedifference in water vapour, a function of the relativehumidity, between a saturated surface, such as a hydrometeor,and an unsaturated air mass will induce evaporation orsublimation. This involves a latent heat flux, evaporation orsublimation, whichmust be balanced by the sensible heatfluxand therefore a difference in temperature between the air anda saturated surface exists. These differences are related to thelatent heat of water and specific heat capacity of air.Conceptually, Ti is the lowest temperature a hydrometeorwill reach due to evaporation of water (Ahrens, 2009). Thepsychrometrically controlled relationship between Ta, Td andTi in unsaturated conditions is:

Hydrol. Process. (2013)DOI: 10.1002/hyp

PRECIPITATION PHASE USING A PSYCHROMETRIC ENERGY BALANCE

Td < Ti < Ta (1)

In saturated conditions, however, the relationship is:

Td ¼ Ti ¼ Ta (2)

To clarify, saturation in this study is with respect to icewhen the Ta is at or below 0 �C and with respect to waterwhen above 0 �C. In regions with frequently saturatedconditions Ti and Td follow patterns of Ta closely and thevarious phase estimation methods will yield similar results(Yamazaki, 2001; Fuchs, 2006). The problem is that Td orTa methods are often applied to unsaturated conditionswhere they are invalid. All Ta methods are not physicallybased as they do not incorporate the effects of humidity onlatent heat transfer (Stewart, 1992). While Td is a functionof both Ta and humidity, it only describes the coolingnecessary for an unsaturated parcel of air to reachsaturation over constant pressure. The dewpoint temper-ature does not consider sensible and latent heat fluxes to thehydrometeor and thus does not have a physical relationshipto phase, though it can be used to improve empiricalmethods to estimate phase and has shown some success inthis regard (Marks et al., 2013).Ti can be calculated using near-surface meteorological

variables that are normally collected at weather stations:temperature and humidity, presuming that the near-surfacemeteorology represents an equilibrium condition for the fallinghydrometeor. Earlymethods of calculating the thermodynamicice/wet bulb temperatures, ofwhich calculations ofTi are basedon, used a classic application of the coupled energy and massbalance with psychrometric charts, based on the initialunderstanding of thewet bulb depression developed byCarrierin the early 1900s (Gatley, 2004). Common calculationapproaches since then considered equations which requireimplicit solutions (Olsen, 2003; Fuchs, 2006) or over-simplified parameterizations (Yamazaki, 2001). Alternatively,solutions are available which were developed for sublimationrate calculations based on the laboratory experiments ofThorpe and Mason (1966), modified by Schmidt (1972) andPomeroy et al. (1993) for application to blowing snowparticlesmoving in the atmosphere. Following Pomeroy and Gray(1995), the sublimation rate for an ice crystal of mass m (kg)and surface temperature Ts(K) is,

dm

dt¼ 2prShD rTa � rsat Tsð Þ

� �¼ 2prNu

ltL

Ts � Tað Þ (3)

where Ta is the air temperature [K], L is the latent heat ofeither sublimation or vaporisation [J kg-1], rTa is the watervapour density [kg m-3] in the free atmosphere , rsat(Ts) isthe saturated water vapour density [kg m-3] at thehydrometeor surface , r is the ice crystal radius (m),Sh and Nu are the Sherwood and Nusselt numbers(dimensionless) which index the degree of turbulenttransfer of water vapour and energy from the particlesurface to the air, lt is the thermal conductivity of air(J m-1 s-1 K-1), and D is the diffusivity of water vapour inair (m2 s-1). One can assumeTs is equal toTi due to the largesurface area/volume relationship and low thermal conduc-


tivity within the hydrometeor (Chang and Davis (1974) andWatts and Farhi (1975) in Tardif and Rasmussen (2010)).Equation (4) provides an iterative solution for Ti, based onEquation (3) and derived in Appendix A, which modifies Tawith a term for the psychrometric exchange ratio multipliedby the latent heat and vapour density gradient term. Thepsychrometric exchange ratio of the air [m3 K kg-1]quantifies the turbulent exchange of the water vapor andenergy transfer between the hydrometeor and atmosphereand is a function of Ta.

Ti ¼ Ta þ D

ltL rTa � rsat Tið Þ� �

(4)

This approach assumes thermodynamic equilibrium, andinsignificant net radiant energy to falling hydrometeors,which may not always be the case (Schmidt, 1972).Nevertheless, Equation (4), as a psychrometric energybalance relationship, should provide amore robust andmorephysically based index of precipitation phase than using Taor Td directly.

OBJECTIVES

In light of the theoretical problems and practical difficulties inapplying empirical estimation techniques to estimateprecipitation phase, the objectives of this paper are to:

1. Propose a psychrometric energy balance method toestimate precipitation phase that is consistent with theknown physics of falling hydrometeors,

2. Assess the temporal scaling of this phase estimationmethod using field measurements.

3. Assess the accuracy of various hydrological approaches,including the new method, to estimating phase change

This is done using high-quality data collected atdifferent elevations from a mountain research basin inthe Canadian Rockies. The dataset is divided so thatobservations used to develop the new relationship are notused to evaluate it.

METHODS

Site

Marmot Creek Research Basin (MCRB) is situated in theKananaskis Valley, Alberta located approximately 70 kmwest of Calgary in the Front Ranges of the Canadian Rockies(Figure 1). The vegetation is typical of a sub alpine valley as itvaries between sparsely vegetated alpine regions, alpinemeadows and sub alpine andmontane forests (Swanson et al.,1986). The climate is dominated by long cold winters andcool wet summers. Average temperatures range from 14.1 �Cin July, to �7.5 �C in January with annual averageprecipitation of 638 mm recorded at the valley bottom andup to 1100 mm at upper elevations (Storr, 1967).MCRB has experienced significant anthropogenic

impacts due to forest manipulation studies conductedby the Canadian Forestry Service that also resulted ina long-term hydrometeorological dataset from 1962



to 1987 (Swanson et al., 1986). The basin was recently re-instrumented by the University of Saskatchewan Centre forHydrology (Pomeroy et al., 2012), and up to 12 stationsacross the basin have been collecting data since 2005. Thethree stations used in this analysis are the Hay Meadow(HM, large pasture in mixed-wood forest, 1436 m), UpperClearing (UC, large clearing in coniferous forest, 1845 m)and Fisera Ridge (FR, alpine treeline site, 2325 m) stations.Complete details can be found in Table I. Data from aMeteorological Service of Canada station in a large forestclearing at the Biogeoscience Institute Barrier Lake FieldStation, located 10 km east of MCRB, is also used toprovide an independent validation dataset.

Data cleanup

The analysis of precipitation phase requires hightemporal resolution and reliable precipitation and othermeteorological data. Data to determine precipitationphase is based on observations every 15 min at UC since2005, FR since 2007 and HM since 2008. All stationsreceive frequent visits and maintenance. All sites wereinstrumented with a Geonor T-200B Series weighinggauge that uses a vibrating-wire weighing transducer tomeasure accumulated precipitation, but not phase.Whilst giving measurements with a high degree ofprecision, but with important systematic errors,weighing gauge data must be carefully quality controlledto remove wind induced jitter effects and drift that canbe seen in Figure 2.A supervised data quality assurance and control

procedure was instituted to remove obvious errors andnoise from the Geonor precipitation datasets. Theprocedure applied the following rules sequentially to theraw accumulated precipitation observations:

Figure 1. Marmot Creek Research Basin showing selected meteorological


1. If changes in raw cumulative precipitation >10 mmand<�10 mm occur over a 15 min interval, then theobservation was removed.

2. If the raw accumulated precipitation observation wasgreater than 620 mm, it was removed.

3. All missing/removed accumulated observations wereassumed to be equal to the last previous observedaccumulated observation.

4. After removal of spurious data (1–2) and gap filling (3)differences of>20 mm or<�20 mm in the accumulatedprecipitation data were assumed to be due to emptying orrecharging ofGeonor liquid and these differences removedto form continuous accumulated precipitation record.

5. Removal of problematic sections, e.g. due to sensor faults,if exist.

6. Jitter removed from accumulated precipitation throughapplication of a rolling maximum, where a cumulativeprecipitation observation is retained if greater than theprevious maximum observed cumulative precipitation.

7. Supervised correction of gauge drift events.

The rolling maximum is a filter intended to remove allremaining jitter from the dataset. It works by retaining acumulative precipitation observation for a time step only if itis greater than the previous maximum observed cumulativeprecipitation. Otherwise, the previous maximum is assumedto be the cumulative precipitation. The rolling maximumworks well in that it preserves cumulative change and thetiming of precipitation events. Unfortunately, in thepresence of gauge drift (Figure 2a), the rolling maximumcan mask precipitation events if the gauge drift is larger thanthe subsequent precipitation event. In addition, it may notcatch the precise start of a precipitation event asprecipitation must first exceed the rolling maximum whichcan take several time steps of precipitation. To address these

stations, basin boundary, topographic contours and location in western


Table I. Marmot creek meteorological stations and instrumentation

Site Fisera Ridge Upper Clearing Hay Meadow

Record 10/2006 – presente 6/2005 - presente 7/2006 – presente

UTM (11U) 626107 5646559 628150 5646577 630742 5645259Elevation (m) 2325 1845 1436VariableAir temperature/relativehumidity

Vaisala HMP45C212 Vaisala HMP35C Vaisala HMP45C212

Outgoing and incomingshortwave radiation

Kipp & Zonen CNR1a LI-COR LI200S Kipp & Zonen CNR1

Snow depth SR50 SR50 SR50-45Rainfall Hydrological Services

TBRGd TB4Hydrological ServicesTBRG TB4

Texas ElectronicsTE525M

Total precip. (rain and snow) Geonor T-200B b Geonor T-200B Geonor T-200B c

a Instrument added October 2007.b Instrument added October 2008.c Instrument added July 2005.d Tipping Bucket Rain Gauge.e Data up to 2012-07-09 utilized in analysis.


issues, a graphical intercomparison of the auto-filtered dataversus raw data was employed to identify erroneousdepartures between the auto-filtered and raw data. Thesedepartures were then corrected by manually replacing theauto-filtered accumulated precipitation data with the actualchange from the raw data. These corrections werepredominantly implemented to capture the beginning ofprecipitation events and to correct the total amount ofprecipitation observed when there was a long intervalbetween events in which evaporation effects became large.

Phase identification

Confidence in phase identification increases if morethan one instrument is used to observe phase. Errors in thetiming of rainfall from tipping bucket raingauges (TBRG)

Figure 2. Examples of Upper Clearing raw and corrected cumulative precipitation from Geonor T-200B weighing gauge. a) Significant evaporatio(manual correction of 1.95mm over 2 h period) and minor jitter between Thursday and Sunday precipitation events. b) Diurnal drift (no correction) an

with minor jitter

Copyright © 2013 John Wiley & Sons, Ltd. Hydrol. Process. (2013DOI: 10.1002/hy

in cold weather mean that rainfall alone cannot be used todetermine precipitation phase. Therefore, phase wasmanually identified for each 15 min measurement ofprecipitation from the Geonor using measurements ofrainfall, Ta, relative humidity, albedo (outgoing/incomingshortwave radiation) and snow depth, as follows.

• Geonor Weighing Gauge: is a cumulative record ofboth rainfall and snowfall events. Geonor precipitationis assumed to be the true amount of precipitationrelative to TBRG and phase was only identified if theGeonor recorded precipitation.

• Tipping Bucket Rain Gauge: is a measure of the totalamount of liquid precipitation accumulated up to thattime. Rainfall was identified if both the TBRG and

nd

)p


Geonor recorded precipitation in approximately thesame magnitude and timing. Snowfall was identified ifa TBRG event occurred after a Geonor precipitationevent, and if this was determine to be due to melt ofsnow accumulation in the gauge orifice from solarheating of the instrument or an increase in Ta.

• Albedo: Rainfall was identified if the albedo was low(0.1–0.2) over bare ground and <0.6 or decreasing forrain on snowpack. Snowfall was identified if the albedowas greater than 0.8. When the measured albedoexceeded 1.0, it was assumed that this was due to snowcovering the upward looking radiometer.

• Snow Depth: an ultrasonic depth gauge (SR50) wasused to measure distance to the surface (ground orsnowpack surface). An increase in snow depth wasused to identify snowfall, whilst no change or adecrease in snow depth was used to identify rainfall.

• AirTemperature (2m): If theTawas greater than 10 �C, thenall precipitation was presumed to be rainfall, and if less than�10 �C, then all precipitation was presumed to be snowfall.

As an example of the uncertainty in precipitation phasedetermination and the usefulness of other meteorologicalvariables to identify phase, a mixed-phase precipitation eventstarting April 12, 2011 is presented with the associatedmeteorological data in Figure 3. Accumulated total precip-itation from the Geonor weighing gauge (black line) shows a20mm event spanning from the early morning of 16/09/10 tonoon 17/09/10. The tipping bucket recorded low intensityliquid precipitation over the course of the 16th, but does notcapture the intensity of the accumulating precipitation, andmeasures a large high intensity event on the afternoon of the17th (after the event as described by the Geonor has ended).From this, one can infer that the precipitation event began asrain but transitioned throughout the 16th to snow and thesubsequent spike in tipping bucket was an observation of thesnow melting in the orifice and dripping into the tippingbucket. In this event, the snowdepth (black dots) confirms theoccurrence of snowfall due to the observed snowaccumulation, but due to scatter, the actual point of phasechange cannot be determined from the snow depth

Figure 3. Precipitation phase identification in the


observations. Integrating albedo observations (red line), onecan clearly identify the timing of the phase change when thealbedo jumped from 0.2 to 1.0. This increase in albedocoincides with an increase in the surface reflectanceindicating fresh snow on the ground or that the incomingradiometer was covered by fresh snow. By using the fourinstruments available for this event, one can confidentlydetermine that the phase of the precipitation changed andmore importantly when the phase change occurred.Precipitation phase was identified at the UC, FR and HM

sites (Figure 1). Personal judgment, integrating additionalconsiderations such as seasonal trends, patterns and timing,was required in some situations when the sensor behaviourswere unclear or contradicted each other. The longest andhighest quality dataset was UC, which was used to developthe Ti phase relationship, whilst the HM and FR had shorterusable records due to missing data and were used forverification. At the HM and FR sites, phase identificationprimarily relied on observations of albedo and snow depth,which are considered the most reliable indicators of phase,as the tipping bucket rain gauge observations wereintermittent and highly unreliable. Following determinationof phase, the precipitation identified as snow was correctedfor wind-induced gauge undercatch. Deformation of thewind field over a gauge orifice causes displacement,acceleration of snow particles and reduced effective fallvelocities, leading to an undercatch in recorded snowfall(MacDonald and Pomeroy, 2007). The snowfall wascorrected for undercatch following an algorithm developedfor Alter-shielded Geonor gauges by MacDonald andPomeroy (2007).

ANALYSIS AND RESULTS

Phase observations

Cumulative snowfall and rainfall at the UC site in 0.1�C increments over seven years are shown in relation to 2m Ta and Ti in Figure 4. Cumulative precipitation phase isuseful to visualize the amount of snowfall and rainfallover time; their annual values are hydrologically importantfor runoff generation. It is apparent that the greatest amount of

context of associated hydrometeorological data



precipitation falls at temperatures near 0 �C – indicating theimportance of accurate phase determination at this site.Temporal scaling of phase is evident when comparing 15minto daily values.When comparing the 15min (Figure 4a and c)to daily time intervals (Figure 4b and d), one can see that thedaily scale shows a broader temperature range associatedwithmixed precipitation than does the 15min scale. At the 15min interval, the transition between rain and snow occursover a narrower temperature range (less snow at temperatures0o C) for the Ti (Fig. 4a) than the Ta (Fig. 4c), suggesting thatthe Ti could be a better predictor for phase than Ta.Some hydrological calculations such as blowing snow

transport (Li and Pomeroy, 1997) unloading of interceptedsnow (Ellis et al., 2010), snowmelt (Marks et al., 1998) andinfiltration into frozen soils (Gray et al., 2001) requiredetailed information on the occurrence of winter rainfalland are strongly influenced by even small amounts of rain.These calculations are sensitive to the frequency of rainfalland snowfall events, and so snowfall and rainfall frequencydistributions were calculated with respect to the Ti and Tafrom the same dataset as above for large and small events(Figure 5). The frequency of rainfall and snowfall showssimilar behaviour to the cumulative amounts shown inFigure 4, in that the temperature range formixed precipitationincreases with time scale such that the daily frequencydistributions are broader than 15 min distributions. Thus,observations available to estimate phase, when averaged

Figure 4. Cumulative snowfall and rainfall in every 1 �C increment for the 15and air (c and d) temperatures at


to the appropriate time scale, require a phase determina-tion methodology that can take into account thesedifferences in information. In addition, by dividing thedistribution by precipitation event sizes, one can observethat the phase transition range narrows for larger events. AKolmogorov–Smirnov test, a non-parametric test todetermine if two samples come from the same distribu-tion, comparing the 15 min and hourly frequencydistributions shows that they are statistically similar toeach other, but different than the daily distribution.

Proposed precipitation phase estimation relationship

To relate Ti (Equation (4)) to phase observations, thefraction of precipitation as rainfall, fr, was calculated fromfield data for each 0.1 �CTi increment. This rainfall fraction isexpressed as;

fr Tið Þ ¼X

Tirainfall mmð ÞX

Tirainfall mmð Þ þ

XTisnowfall mmð Þ (5)

where Ti is the mean temperature of a 0.1 �C Ti increment.Figures 4 and 5 show that there is no sharp measured

phase change at Ti=0 as hypothesized by Marks et al.(2013) and so no strictly physical calculation of phase ispossible using Equation (4). This may be due to variability

min (a and c) and daily (b and d) time interval for hydrometeor (a and b)Upper Clearing for 2005–2011



in local precipitation and meteorology over the observationinterval, lack of thermodynamic equilibrium in fallinghydrometeors, theoretical errors and/or measurement errors.The measured relationship between Ti and the rainfallfraction, fr, is sigmoidal and so was fitted to the functionshown in Equation (6).

fr Tið Þ ¼ 11þ b � cTi (6)

Where b and c are the best fit coefficients and Ti is thehydrometer temperature defined in Equations (4) and (5).The measured fr versus Ti and the fitted curves for threetime scales are presented in Figure 6. Performance wasassessed with the root mean square difference (RMSD)and mean bias (MB). The RMSD is a weighted measureof the difference between observation and simulation andhas the same units as the observed and simulated values.The MB indicates the ability of the relationship todifferentiate precipitation phase; a positive value or anegative value of MB implies over prediction or underprediction, respectively. The b and c parameters andRMSD and MB for each relationship are presented inFigure 6. The mixed phase transition temperature rangeand the scatter of the relationship both increase with thetime interval. The combination of Equations (4) and (6) isa physically based relationship for mixed precipitation

Figure 5. Frequency distributions of hydrometeor temperature versus precipitand b), hourly (c and d) and 15 min (e and f) tim


phase proportion that relies on the psychrometric energybalance calculation of Ti and a parameterization to adjustfor scatter due to time scale, observation error, deviationfrom thermodynamic equilibrium assumptions and otherfactors. Whilst it contains empirical elements, its physicalbasis should provide robustness in application to otherenvironments and the calibration factors are time-scaledependent which is useful in rescaling it to measurementsof varying intervals.

Phase estimation method evaluation

The proposed physically based psychrometric energybalance relationship calibrated to UC (Equation (6)) wascompared to several other approaches of phase estimationusing observations from FR, HM and the BiogeoscienceInstitute Barrier Lake Field Station (BGSI). The methodsare described in the literature review and include:

• threshold_T: single threshold Ta, 0 �C. (example:Marks et al., 2013)

• threshold_Ti: single threshold Ti, 0 �C. (example:Marks et al., 2013)

• HSPF: Hydrological Simulation Program Fortranmethod, relating threshold temperature to Ta and Td.(Bicknell et al., 1997)

• UBC: double Ta threshold, 0.6 �C and 3.6 �C, with mixedphase linearly interpolated (Pipes and Quick, 1977)

ation phase for small (a, c and e) and large (b, d and f) events on the daily (ae intervals at Upper Clearing for 2005–2011


Figure 6. Hydrometeor temperature and rain ratio for the Upper Clearing (2005–2011) and the root mean square difference and mean bias of the fittedrelationship for a) 15 min, b) hourly and c) daily time scales


• Kienzle: seasonallyvariable curvilinearmethod implementedwith default values (temperature threshold (Tt) = 2 �C andtemperature range (Tr) = 13 �C). (Kienzle, 2008)

• Kienzle_adj: Kienzle implemented with values calibratedto UC observations (Tt=1.5 � C and Tr=7.8 � C)

• proposed psychrometric energy balance Ti method(Equation (6)) for:

• daily scale (Ti_daily)• hourly scale (Ti_hourly)• 15 min scale (Ti_15min)

Note that the proposed psychrometric energy balancemethod was calibrated using the UC dataset and thenvalidated with the FR and HM datasets at varying timeintervals and the BGSI dataset was used for the daily intervalonly. The FR (high elevation) and HM (low elevation) siteswere also useful for assessing the performance of phaseestimation relationships at varying elevations, and the BGSIsite was used to assess the relationships on a completelyindependent dataset outside of the research basin. Allcomparison methods were originally developed for the dailytime scale making application to sub-daily timescalespotentially problematic. Regardless, all methods wereemployed on the daily, hourly and 15 min time steps. Theproposed psychrometric energy balancemethod is temporallyscalable, and the b and c parameters were varied with respectto the time step in question.Predictive power was assessed through several statistical

tests that include RMSD, coefficient of determination (R2),MB and rain error. The R2 is a measure of the modelsability to explain the variability. Finally, rain error is thedifference in percentages between the predicted andobserved rain as a percentage of total precipitation; positive


values imply an over prediction of rain and therefore anunder prediction of snow and vice versa. The results oftesting several phase differentiation procedures, includingthe proposed physically based method, are shown forcalibration datasets in Figure 7 and validation datasets inFigure 8. Only the Kienzle_adj method and Ti_daily,Ti_hour, Ti_15min methods were calibrated (to UC data).The calibration comparison results, Figure 7, show that

the psychrometric energy balance Ti_daily method worksthe best at daily time scales. At the hourly scale, the Kienzlemethods worked the best, though the Ti_hour performancewas very comparable, with Kienzle showing slightly betterscores for RMSD, R2 and MB than Kienzle_adj. For the 15min scale, the physically based Ti method worked best withKienzle_adj and Ti_15min showing similar scores forRMSD and R2 and the Kienzle having slightly better MBand error values. RMSD values cannot be compared acrosstime scales directly due to combined impact of an increase inthe sample size and decline in absolute errors observed withan increase in temporal scale. The R2 and MB values arecomparable amongst time scales because the quantities varywith scale. The rain error can also be directly consideredacross scales as only the number of observations, not thefinal precipitation amounts, needed to calculate the finaldifference in percentages between the predicted andobserved rain percentages increases with an increase intemporal resolution. The RMSD drops by an order ofmagnitude from daily to sub-daily time scales whilst the R2

and rain error do not vary with scale.The comparison of methods with the validation dataset,

in Figure 8, shows that without local calibration, theKienzle and Ti_daily methods perform relatively less wellthan where they are calibrated onsite. On the daily timestep, the UBC method was most accurate. On the hourly

)p

Figure 7. Precipitation phase determination methods intercomparison at calibration site (UC) with statistics against observations showing (a) root meansquare difference, (b) coefficient of determination (R2), (c) mean bias, (d) rain error. Best results for each time interval and test denoted by *


time scale, the physically based Ti_hour is by the mostconsistently accurate method, though on the 15 min scaletheKienzle_adj does slightly better than the Ti_15min. TheTi method results show that its physical basis provides arobustness that transcends site characteristics, localcalibration and time steps.

DISCUSSION

Precipitation phase dynamics and temporal scaling

The importance of temporal scaling needs to be understoodto properly estimate precipitation phase. On short time scales(15 min), the mixed-phase transition ranges are quite small,2.9 �C and 4.9 �C for Ti and Ta, respectively, butincrease as the time interval increases to daily, forinstance 7.6 �C and 10.7 �C for Ti and Ta, respectively.This is largely due to precipitation events occurringunder temperature conditions that do not correspond tothe mean daily temperature used by daily time stepphase differentiation methods. The uncertainty intro-duced by the larger range of mixed phase transitionneeds to be addressed in differentiation methods to betterquantify phase. This is a compelling reason to use hourlyor shorter time periods rather than daily for precipitationphase estimation. Since most hydrological models nowuse hourly meteorological data there is little reason to usedaily methods given the much greater scatter inrelationship between phase and Ti or Ta at longer time

Copyright © 2013 John Wiley & Sons, Ltd. Hydrol. Process. (2013DOI: 10.1002/hyp

scales. The importance of this is further exemplified bythe peak in precipitation frequency near 0 �C found forMarmot Creek. The implication is that if improperdifferentiation methods are utilized, a large portion ofthe precipitation may be misclassified.

Method comparison

Quantifying the predictive power of the various ap-proaches in consideration of model complexity and datarequirements permits the relativemerits of eachmethod to beassessed. The commonly used threshold Ta is simple to useand requires onlyTa, but provides a very poor approximationof phase. As suggested by Marks et al. (2013), replacing theTa threshold with a Ti threshold appreciably increases theaccuracy, but also requires humidity measurements. Dailytemperature algorithms calibrated from large datasets andbased only on Ta (UBC) performed well and couldoutperform the proposed physically based Ti method ondaily time steps, where no local calibration was available. Iflocal calibration was available, then the Kienzle methodbecause of its non-linear functions performed well, but atsites without local calibration, its performance was substan-tially degraded despite its regional derivation in the CanadianRockies in Alberta. The proposed physically based psychro-metric energy balance method to estimate phase usingtemperature and humidity was consistently the most robustand accurate at various time steps and sites and had only asmall decline in performance when tested away from the

)

Figure 8. Precipitation phase determination methods intercomparison at validation sites (FR, HM and KFS) with statistics against observationshowing (a) root mean square difference, (b) coefficient of determination (R2), (c) mean bias and (d) rain error. Best results for each time interval and

test denoted by *


calibration site. At sub-daily time intervals it performedconsistently better than other methods. Whilst there wasan improvement in model performance as time stepsdecreased to sub-daily, there was little difference betweenhourly and 15 min time steps, suggesting that use ofstandard hourly data is adequate for phase estimation.

Climate change implications

Recent climate change is causing higher air temper-atures, but estimates of humidity from measurementsand models show much greater uncertainty (IPCC,2007). One of the major impacts of climate change isthat rising temperatures will lead to shifts fromsnowfall to rainfall (Nayak et al., 2010; Shook andPomeroy, 2012). This work shows that research intoclimate change impacts on precipitation needs toconsider changes to both Ta and humidity to properlyestimate future precipitation phase.

CONCLUSIONS

A large proportion of precipitation in the Canadian Rockiesoccurs at air temperatures within 10 �C of the freezing point,and so accurate determination of precipitation phase iscrucial for determining snow hydrology and rainfall–runoffrelationships. Falling hydrometeors are subject to turbulenttransfer of heat andwater vapourwith the atmosphere, and so


s

the Ti, as estimated from the psychrometric equation energybalance, is a more physically based method of calculatingprecipitation phase than is Ta alone. A psychrometric energybalance calculation of Ti was proposed from existingblowing snow sublimation turbulent transfer equations as abasis to estimate precipitation phase.The relationship between phase and Ta or Ti was

examined for several years using a high quality datasetfrom a Canadian Rockies catchment and found to scalewith time, such that there was a smaller mixed-phasetransitional temperature range at shorter time intervals. Titransition ranges decreased from 7.6 �C to 2.9 �C as timesteps decreased from daily to 15 min. This suggests thatpredictive methods for phase which adjust for the timestep of observational inputs can show improved predic-tive power as time step decreases. To take advantage ofthis, the Ti was estimated by the psychrometric energybalance equation and used to estimate rainfall fraction atvarious time steps using a sigmoidal function whoseparameters are time-step dependent – this is a newpsychrometric energy balance method to estimate precip-itation phase in hydrological models.A detailed examination of precipitation phase dynamics

at several elevations in a Canadian Rockies catchmentshowed that this new psychrometric energy balancemethod can be a stronger and more consistent predictorof phase than the commonly employed Ta based methods.The improvement over results of daily Ta index methods

)p


increased as the time step decreased to sub-daily periods.The overall implication of this study is that psychro-metric energy balance methods should be used toestimate precipitation phase instead of Ta alone andshould be applied at the hourly time step. Given thathumidity and Ta measured together by readily-availablehygrothermometers and the hourly time step correspondsto the recording interval of most modern meteorologicalstations, there are few impediments foreseen to adoptionof the new method in hydrological models. There areimplications of this analysis for climate change research;the inclusion of humidity in the new phase calculationmethod implies that analysis of rain/snow ratios forfuture climates needs to consider changes in humidity aswell as Ta. Further work will quantify the impact of theimplementation of this method into a physically basedhydrological model on snow hydrology in a wider varietyof environments.

ACKNOWLEDGEMENTS

The support of the Canada Research Chairs Program,Alberta Environment and Sustainable Development,National Science and Engineering Research Councilthrough its Discovery Grants, Research Equipment Grantsand Graduate Scholarships, University of CalgaryBiogeoscience Institute, and Canadian Foundation forClimate and Atmospheric Sciences (CFCAS) through theIP3 Network is gratefully acknowledged.

APPENDIX A. HYDROMETEOR TEMPERATURE(Ti) DERIVATION

Mass balance of a sublimating ice sphere from Pomeroyand Gray (1995):

dm

dt¼ 2prDSh rTa � rsat Tsð Þ

� �(A:1)

Where:

r

Copyrigh
t
= ice crystal radius [m]
D = diffusivity of water vapour in air [m2 s-1] Sh = the Sherwood number which indexes the
degree of turbulent transfer of water vapourfrom a particle surface to air

rTa
= water vapour density in the free atmosphere[kg m-3]
rsat(Ts)
= saturated water vapour density at thehydrometeor surface [kg m-3]
Energy balance of a sublimating ice sphere fromPomeroy and Gray (1995):

Ldm

dt

� �¼ 2prltNu Ts � Tað Þ (A:2)

Where:

L
= latent heat of sublimation or vaporisation [J kg-1] lt = thermal conductivity of air [J m-1 s-1 K-1]
© 2013 John Wiley & Sons, Ltd.

Nu
=Nusselt numberwhich indexes the degree of turbulenttransfer of energy from a particle surface to air
Ta
=air temperature [K] Ts = surface temperature of ice sphere [K]
Combining A.1 and A.2 gives:

L2prDSh rTa � rsat Tsð Þ� �

¼ 2prltNu Ts � Tað Þ (A:3)

Assuming:

• Nu = Sh for a blowing snow particle in turbulentatmosphere (Lee, 1975) or falling raindrop (Tardifand Rasmussen, 2010)

• Ts =Ti due to the large surface area/volume relationshipand weak heat conduction within the raindrop (Changand Davis (1974) and Watts and Farhi (1975) in Tardifand Rasmussen (2010))

Simplifying A.3 gives:

LD rTa � rsat Tið Þ� �

¼ lt Ti � Tað Þ (A:4)

Rearranging A.4 to solve for Ti gives:

Ti ¼ Ta þ D

ltL rTa � rsat Tið Þ� �

(A:5)

Solution for A.5 is achieved iteratively. Iterativesolution methods such as the Newton–Raphston approachcan be utilized to increase the efficiency of solution.Remaining parameters are quantified as:

D following Thorpe and Mason (1966):

D ¼ 2:06 � 10�5 � Ta273:15

� �1:75

(A:6)

r following Dingman (2002):vapour pressure, e [kPa] is:

e ¼ RH

100� 0:611e 17:3T

237:3þT (A:7)

Where:

RH
= relative humidity [%] T = temperature [�C] Then applying the ideal gas law:
r ¼ mwe

R T(A:8)

Where:

mw
= the molecular weight of water 0.01801528 [kg mol-1] R =Universal Gas Constant 8.31441 [J mol-1 K-1]

Figure A1. Hydrometeor temperaure (a) and psychrometric exhange ratio (D/lt) (b) is plotted versus air temperaure. Hydrometeor temperature (b) iplotted with relative humidity ranging from 100% (linear line) to 0% for every 10% visualising the hyrodometeor temperature relative humidity

relationship.


lt following List (1949):

lt ¼ 0:000063 � Ta þ 0:00673 (A:9)

L has small temperature dependency, thus for heat ofsublimation (Ls, T< 0 � C ) (Rogers and Yau, 1989):

Ls ¼ 1000 2834:1� 0:29T � 0:004T2� �

(A:10)

and for heat of vaporisation (Lv,T≥ 0�C)

Lv ¼ 1000 2501� 2:361Tð Þð Þ (A:11)

The depression of Ti relative to Ta is a function of both Taand RH (Figure 9 a)). Ta and RH act to modify the vapourdensity gradient between the atmosphere and the hydrome-teor; Ta by varying the maximum vapour density (as afunction of saturation vapour pressure) and RH by definingthe vapour density deficit between the atmosphere andhydrometeor. In addition D/lt [m

3 K kg-1], termed thepsychrometric exhange ratio, increases linearily with Ta(Figure 9 b)) and quantifies the turbulent exhange of massand energy between the atmosphere and hydrometeor.

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