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Estimation of Wind-Induced Losses from a Precipitation Gauge Network in the Australian

THOMAS CHUBB AND MICHAEL J. MANTON School of Earth, Atmosphere and Environment, Monash University, Clayton, Victoria,

STEVEN T. SIEMS School of Earth, Atmosphere and Environment, and ARC Centre of Excellence for Climate System Science, Monash University, Clayton, Victoria, Australia

ANDREW D. PEACE AND SHANE P. BILISH Ltd., , , Australia

(Manuscript received 26 October 2014, in final form 15 June 2015)

ABSTRACT

Wind-induced losses, or undercatch, can have a substantial impact on precipitation gauge observations, especially in alpine environments that receive a substantial amount of frozen precipitation and may be ex- posed to high winds. A network of NOAH II all-weather gauges installed in the Snowy Mountains since 2006 provides an opportunity to evaluate the magnitude of undercatch in an Australian alpine environment. Data from two intercomparison sites were used with NOAH II gauges with different configurations of wind fences installed: unfenced, WMO standard double fence intercomparison reference (full DFIR) fences, and an experimental half-sized double fence (half DFIR). It was found that average ambient temperature over 6-h periods was sufficient to classify the precipitation phase as snow, mixed precipitation, or rain in a statistically robust way. Empirical catch ratio relationships (i.e., the quotient of observations from two gauges), based on wind speed, ambient temperature, and measured precipitation amount, were established for snow and mixed precipitation. An adjustment scheme to correct the unfenced NOAH II gauge data using the catch ratio relationships was cross validated with independent data from two additional sites, as well as from the inter- comparison sites themselves. The adjustment scheme was applied to the observed precipitation amounts at the other sites with unfenced NOAH II gauges. In the worst-case scenario, it was found that the observed pre- cipitation amount would need to be increased by 52% to match what would have been recorded had adequate shielding been installed. However, gauges that were naturally well protected, and those below about 1400 m, required very little adjustment. Spatial analysis showed that the average seasonal undercatch was between 6% and 15% for gauges above 1000 m MSL.

1. Introduction species are threatened by decreases in annual snowpack levels (Nicholls 2005) and projected decreases in pre- Precipitation in the Australian alpine regions is criti- cipitation (Hennessy et al. 2003). Despite these factors, cally important to agriculture in the Murray–Darling precipitation observations in both the Snowy Mountains basin, which accounts for 45% of national irrigated alpine region (New South Wales; see Fig. 1)andinthe production (Worboys and Good 2011). Alpine rain and Victorian Alps are sparse and of poor reliability, with long- snowfall also support major infrastruc- term precipitation measurements limited to just a few ture and a ski tourism industry. A number of vulnerable locations near ski resorts. The climate of the Snowy Mountains received some attention following the Millennium Drought (van Dijk Corresponding author address: Thomas H. Chubb, School of Earth, Atmosphere and Environment, Monash University, Build- et al. 2013) in southeastern Australia. It was the subject ing 28, Clayton VIC 3800, Australia. of a study by Chubb et al. (2011), who performed a de- E-mail: [email protected] composition of wintertime precipitation in 1990–2009 by

DOI: 10.1175/JHM-D-14-0216.1

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FIG. 1. (left) Southeastern Australian topography (colors) and study region (magenta box). (right) Detail of topography and pre- cipitation gauge network in the study region. Where markers are shown with gray, the gauge was installed during the analysis period of 2007–12. The yellow markers show locations where there was an overlapping period between an unfenced NOAH II gauge and a NOAH II in a half DFIR fence, used for cross validation. synoptic type. Precipitation was predominantly due to deformation around the gauge orifice. Wild (1885) ob- cold fronts associated with either cutoff lows (equator- served that a gauge shielded by a fence collected sub- ward of 458S) or lows embedded in the westerly storm stantially more snow than an unshielded one, and Alter track, in roughly equal proportions. They noted that the (1937) was among the first to test the collection effi- topography was of principal importance in determining ciency of a variety of shield designs. His legacy persists the spatial impacts of the drought, with declines on the in the contemporary use of the Alter shield, which western (windward) slopes of the mountains related consists of a ring of wedge-shaped slats surrounding the much more closely to elevation than on the eastern gauge and suspended slightly above the gauge orifice. It slopes. By way of explanation, Fiddes et al. (2015) noted has since been shown that a gauge shielded in this way that the synoptic types affecting eastern slopes pre- can catch up to 50% more precipitation than an un- cipitation were less influenced by the climate drivers of shielded counterpart (Goodison et al. 1981), but this the Millennium Drought. Dai et al. (2013) also identified value depends heavily on the type of gauges used and synoptic types associated with precipitation, but they the conditions in which they are operating. Double were based on a nearby upwind sounding. Two of the fences were found to be even more effective; Golubev classes accounted for more than 70% of the total win- (1986) found that the WMO standard double fence inter- tertime precipitation and were typified by high moisture comparison reference (DFIR) gauge, consisting of a flux and/or high shear. Russian Tretyakov gauge housed in concentric 12- and Accurate measurement of precipitation in mountain- 6-m diameter octagonal fences [see Goodison et al. ous regions is extremely challenging. High spatial vari- (1997), annex 2B], recorded 92%–96% of the reference ability due to orographic effects necessitates the use of bush gauge amount. Yang (2014) recently compared 20 high-density precipitation gauge networks to accurately years of DFIR and bush gauge data collected over 12-h represent precipitation patterns (Frei and Schär 1998). intervals to calculate correction equations to recover A further complication is that different gauge configu- the true precipitation amount from DFIR gauge rations can record quite different amounts at the same observations. location during snow or mixed precipitation (Goodison There is continued interest in gauge intercomparison et al. 1981, 1997; Rasmussen et al. 2012), leading to ar- research. A number of national standard precipitation tifacts in records from inhomogeneous networks. gauges were assessed in the WMO Solid Precipitation Undercatch (Groisman and Legates 1994), or losses Measurement Intercomparison [Goodison et al. (1997), due to wind, have long been recognized as an error and references therein]. One of the main aims of this source for frozen precipitation measurement due to flow project was to establish standard methods of adjusting

Unauthenticated | Downloaded 10/02/21 12:23 AM UTC DECEMBER 2015 C H U B B E T A L . 2621 solid precipitation measurements for gauge undercatch. also requires a humidity measurement) to determine The dominant environmental variable affecting gauge precipitation phase. They found appreciable increases in efficiency was found to be wind speed (measured at the accuracy of phase discrimination compared to gauge orifice height), and temperature was found to be temperature-only schemes, especially as the time in- more important during mixed precipitation because of terval used decreased from daily to subhourly. More higher snowflake fall speeds as melting occurs. More complex algorithms use aerological data to identify the recently, Rasmussen et al. (2012) highlighted the ongo- presence of warm layers where snowflake melting could ing disparity in the performance of different gauges, occur (e.g., Bourgouin 2000) in order to predict the oc- and a second WMO experiment [the WMO Solid Pre- currence of freezing rain, but this approach requires cipitation Intercomparison Experiment (SPICE; Nitu intensive soundings and/or numerical model data. et al. 2012)] is currently being conducted at a number of Once the relationship [often termed the catch ratio sites around the world, including Guthega (GD) in (CR)] between a reference precipitation gauge and the the Australian Snowy Mountains, which is the focus of gauges used in the field have been established, it is this paper. possible to assess the impact of environmental losses A number of factors affect precipitation particle fall over a region and develop an estimate for the seasonal speed and thus the gauge collection efficiency. Rain and precipitation amounts. A number of studies have been mixed precipitation (wet snow) typically have higher fall performed around the globe with this objective, with speeds than dry snow (Yuter et al. 2006). Thériault et al. highly variable results due to the differences in the na- (2012) directly simulated the flow around a Geonor ture of the sites and equipment used: gauge in a single Alter shield and computed collection 2 d In Siberia, application of the regression parameters efficiencies for wet (fall speed $22ms 1) and dry (fall 2 estimated by the WMO intercomparison showed that speed ’ 1m s 1) snowflakes and compared these pre- annual precipitation was underestimated by 10%– dictions with observations of snow crystal types during a 65% (Yang and Ohata 2001). wintertime storm in Colorado. The wet crystal category, d Mongolian annual precipitation amounts should be in fact consisting of a wide range of crystal types, was 17%–42% greater than reported from 31 meteorolog- found to have a higher scatter in the collection efficiency ical stations because of undercatch of snowfall (Zhang because of the wider range of particle fall speeds. et al. 2004). Other losses that influence the amount of pre- d In Alaska, 10 gauges were adjusted by 10%–140% cipitation recorded are wetting losses, which are sys- over a 2-yr period to account for wind-induced losses tematic undermeasurements when volumetric methods (Yang et al. 1998). (i.e., tipping gathered precipitation into a separate d Chinese gauge data were adjusted at 710 meteorolog- measuring container) are used, and evaporative losses, ical stations during 1951–98 by Ye et al. (2004), which occur in the interval between bucket tips or identifying an underestimation of 6%–62% (mean manual gauge readings. Trace precipitation occurs when 19%) for annual precipitation over all gauges. the accumulated amount is less than the increment of d Adjustment of a long-term precipitation dataset for the gauge. For manual observations, this does not con- gauges north of 458N from multiple countries required tribute to the measured seasonal precipitation amount correction factors of 80%–120% in winter months and but may nonetheless be important in low-precipitation around 10% in summer months (Yang et al. 2005). regimes. Determination of the phase of the precipitation gen- In this paper, we seek to test two key hypotheses. The erally requires either manual observation of the gauge first is that a precipitation phase partitioning scheme can contents or specialized equipment, so in practice it is be developed based on the observations available at a often predicted from meteorological variables. The al- gauge intercomparison site in the Snowy Mountains gorithms used may be basic temperature thresholds for region. This site did not have humidity measurements snow, mixed precipitation, and rain, as used by Yang and for the majority of the analysis period, so we used a

Ohata (2001). The wet-bulb temperature Twb is a better temperature-only scheme and tested it using the catch indication of conditions in the immediate vicinity of a ratio between an unfenced (UF) and a fenced gauge. precipitation particle, which cools both itself and the air The second major hypothesis is that an empirical CR around it through evaporation and/or sublimation, and relationship between fenced and unfenced gauges can Michelson (2004) evaluated the mixed fraction be modeled by observations from the site and that this for 20.218,Twb , 2.428C using hyperbolic functions. relationship can be used to adjust precipitation amounts Harder and Pomeroy (2013) estimated the hydrometeor reported by an unfenced gauge in a way that reduces temperature using psychometric energy balance (which the root-mean-square error (RMSE) between the two

Unauthenticated | Downloaded 10/02/21 12:23 AM UTC 2622 JOURNAL OF HYDROMETEOROLOGY VOLUME 16 gauges. We aim to validate this adjustment scheme using using a similar algorithm by SHL staff as follows to pro- independent data before applying it across the network vide the half-hourly dataset used in this paper. The raw to evaluate the impact of installing wind fences through- fluid depth and transducer temperature data were median out the Snowy Mountains region. filtered with a centered 50-min window to eliminate noise Similar analysis has been presented in other studies, and other artifacts. The filtered fluid depth is periodically but this paper is the first to present such work for an compared to a reference depth, and if it is greater by one Australian alpine environment, and there are several (or more) increments of 0.254 mm, a corresponding aspects of this work that are of general interest. First, to number of tips are reported, and the reference depth is our knowledge, the use of catch ratios to evaluate the incremented. If the fluid depth falls below the reference temperature-only partitioning is novel and the analysis depth for a sustained period (e.g., through evaporation), is compelling. Further, we show that the inclusion of a the reference depth is correspondingly reduced. precipitation term in the CR formulation, which is also a In addition to the Alter shields, a large number of the novel approach, results in an improved fit and sub- NOAH II gauges were protected from wind by a double stantially reduces the RMSE in the adjustment scheme. fence. These fences were made to half of the diameter of the standard WMO DFIR fence (hereafter full and half DFIR fences), with the outer fence inscribed in a 6-m 2. Surface meteorological observations in the diameter circle, to facilitate prefabrication and trans- Snowy Mountains region portation by helicopter, as well as to reduce the envi- Snowy Hydro Ltd. (SHL) is the operator of the Snowy ronmental impact within the national park. Mountains Hydro-electric Scheme and has maintained Wetting losses are reduced by the application of a an independent surface meteorological network to in- hydrophobic coating to the wall of the gauge. However, form hydrological inflow estimates. To facilitate the there is a significant surface area (especially when the evaluation of the Snowy Precipitation Enhancement fluid level is low) and some retention and evaporation of Research Project (SPERP; Manton et al. 2011), there moisture is possible. To suppress evaporation, a layer of have been substantial improvements to the observa- oil was maintained above the antifreeze. This technique, tional network. combined with the software algorithms, prevented vir- The data were quality coded and provided as half- tually all evaporative losses. Trace precipitation, on the hourly accumulated values for precipitation, and half- other hand, could fail to be carried over to the next hourly average values for other variables, as soon as precipitation event because of the temperature de- practicable after collection. In this paper, we use aver- pendence of the load cell. Changes in temperature due ages and totals over 6-h intervals that divide each day to the diurnal cycle were sufficient to cause the software into four parts, for an analysis period of the months of algorithm to reset the reference depth periodically, so April–October in the years of 2007–12. that partial increments could be lost. This response was expected to be similar to that experienced because of a. Precipitation gauges evaporation by tipping-bucket gauges. Figure 1 (right) shows the current precipitation gauge 2) TIPPING-BUCKET GAUGES network, which has NOAH II (ETI Instrument Systems Inc. 2008) at locations where snow frequently falls, and a There were a number of different configurations of mixture of heated and unheated tipping-bucket gauges tipping-bucket gauges, with 37 installed in total through- (TBG) throughout the region. All of the NOAH II out the Snowy Mountains region. Some of these are in- gauges in the Snowy Mountains were fitted with the stalled inside heated chambers, others have heated manufacturer’s Alter shield. At many of these sites collectors, and others at lower elevations were not heated other variables are observed, including temperature, at all. In addition to undercatch, these gauges were subject wind speed and direction, atmospheric pressure, and to wetting and evaporative losses, as well as reporting humidity. delays due to buildup of snow in the collectors, but treatment of these impacts is beyond the scope of this 1) NOAH II PRECIPITATION GAUGES paper. For the spatial analysis performed in section 2c,we The NOAH II gauge collects precipitation in a chamber only used tipping-bucket gauges below 1400 m to mini- partially filled with antifreeze, while the pressure at the mize this effect. bottom is monitored by a sensitive load cell. These data b. Other surface meteorological variables were processed by a software algorithm to generate electrical pulses in real time similar to a tipping-bucket In addition to the precipitation gauges, a number of rain gauge. The raw data were subsequently reprocessed other surface meteorological instruments were deployed.

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At most of the sites, at least wind speed and direction and available only about 60% of the time over the six win- ambient temperature were recorded in addition to pre- ters. To establish a more complete and reliable wind cipitation amount. A smaller subset of the sites also re- speed record for the observation period, a composite of ported pressure and humidity, but these variables were these wind speeds, designated WS, was used. WS was not used in this study. available for 82% of the 6-h observation intervals in the For the SPERP, at sites where power was available, analysis periods of April–October 2007–12 and was heated NRG IceFree3 cup anemometers and wind vanes validated against the independent wind speed WSD were deployed, and at other sites either Young 05103 or measured at 10 m. Vaisala WMS301 combination wind monitors were used. On average, winds came from the western sector at 2 A number of other instruments from the original SHL Guthega Dam with an average speed of about 3.2 m s 1 sites were incorporated into the SPERP dataset and have (see Figs. 3a,b). When precipitation was recorded, the been used in this study. In total, wind observations were winds predominantly came from the northwest, with 2 reported at 43 unique sites during the analysis period. an average speed of about 4.3 m s 1. Wind speed was Ambient temperature was reported by Unidata 6507A weakly correlated with precipitation amount, with thermistor sensors at the majority of the new SPERP maximum precipitation rates observed for wind speeds 2 sites, but Vaisala HMP45A humidity–temperature sen- of around 5 m s 1. sors were deployed at a small number of sites instead. A composite of data from the two thermometers at the Some of the original SHL sites used in-house thermo- site provided a robust ambient temperature T that was couple sensors, and others had Vaisala HMP131Y available for more than 99% of the 6-h averaging intervals. humidity–temperature sensors. In total, 47 unique sites The mean temperature over all the 6-h measurement in- reported temperature during the analysis period. tervals was 2.88C, and for those in which precipitation was recorded the mean temperature was 2.38C. c. Guthega Dam intercomparison site d. The Kerries observational site The observational site near Guthega Dam (elevation 1586 m MSL) is the principal subject of this paper and At the Kerries (TK), a site about 13 km to the north of has since been included in the ongoing WMO SPICE Guthega Dam at 1741 m MSL elevation, there were two (Nitu et al. 2012). It is situated on a small plateau about NOAH II gauges installed simultaneously for four of the 5 m above the level of the dam (see Fig. 2). The small winters of the analysis period (see Fig. 2, Table 1). One bluff indicated in Fig. 2 is about 2 m in height and is not of these gauges was unfenced and was removed at the expected to cause substantial vertical wind at the gauge end of October 2010, and the other was deployed for the orifices, but these cannot be ruled out with the available entire period inside a half DFIR fence. There was also a observations. Since 2006, there have been four pre- heated tipping-bucket configuration similar to the one at cipitation gauges at Guthega Dam (see Table 1), in- Guthega Dam, but this was unused in our study. In terms cluding three NOAH II gauges (full DFIR fence, half of precipitation amount statistics, the site was almost DFIR fence, and unfenced), and a Hydrological Services identical to Guthega Dam, with precipitation recorded (HS) tipping-bucket gauge installed in a heated cham- in 34% of nominal observation periods, with a mean ber. Precipitation (Pr . 0.254 mm) was recorded in 35% (nonzero intervals) of 4.34 mm and median of 2.03 mm. of all 6-h intervals during the analysis periods. The mean The Kerries was considerably better protected than (nonzero) precipitation amount was 4.76 mm, and the Guthega Dam. Mean wind speeds at the site were 2 2 median was 2.03 mm. 1.5 m s 1 for all intervals and 1.7 m s 1 for intervals with Two NRG IceFree3 anemometers were installed precipitation. The easterly sectors in Figs. 3c and 3d outside the wind fences at Guthega Dam at 3 m above were probably due to nocturnal drainage flow down a ground level, at the same height as the top of the NOAH gully running in this direction just to the north of the II gauges, and two others were installed within the fence site and were generally not present during intervals structures. These fenced anemometers consistently re- with precipitation. The mean temperature over all the ported lower wind speeds by a factor of 4–5 than their 6-h measurement intervals was 1.08C, and for those in unfenced counterparts, demonstrating the efficacy of the which precipitation was recorded the mean tempera- DFIR fences. We designated the wind speed variables as ture was 0.28C. per the labels in Fig. 2: the wind speed from the ane- e. Other sites with multiple gauges mometer installed beside the half DFIR wind fence is designated WSA, and the one beside the unfenced Two other sites had a period with unfenced and half NOAH II gauge is WSB. Because of maintenance and DFIR fenced configurations of NOAH II gauges in- certain instrumentation issues, each of these was stalled simultaneously, which we used to cross validate

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FIG. 2. (top left) Situation of the Guthega Dam site, with contoured elevation (m MSL). (top right) Instrument layout at Guthega Dam [expanded from box in (top left), legend provided in (bottom right)]. (bottom left) Situation of the Kerries. (bottom right) Instrument layout at the Kerries [expanded from box in (bottom left)]. the CR models developed in this paper. Grey Hill, to the at 1368 m MSL, had 226 nominal intervals. Both of these west of the Main Range in Fig. 1 at an elevation 1624 m sites were relatively protected with mean wind speeds 2 MSL, had 162 intervals where all data were available around 2 m s 1 during intervals where precipitation was and precipitation was recorded. Snowy Plain, to the east recorded.

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TABLE 1. Description of surface meteorological instruments at Guthega Dam and the Kerries. Availability represents the fraction of the 6-hourly data available during April–October 2007–12. Asterisk denotes gauge orifice height.

Variable Instrument Height (m) Comment Availability Guthega Dam

PrA ETI NOAH II 3.0* ETI Alter shield, half DFIR fence 85.3% PrB ETI NOAH II 3.0* ETI Alter shield, no wind fence 87.0% PrC ETI NOAH II 3.0* ETI Alter shield, full DFIR fence 90.5% PrE HS TB3 5.0* SHL Alter shield, no wind fence 85.8% TE SHL (in house) 2.0 Thermocouple sensor, 300-mm screen 96.3% TB Unidata 6507A 1.6 Thermistor, 150-mm screen 88.6% T — — Composite of TB and TE 99.5% WSA NRG IceFree3 3.0 Outside half DFIR fence, to the west 63.8% WSA,F NRG IceFree3 3.0 Inside half DFIR fence 81.6% WSB NRG IceFree3 3.1 Next to unfenced NOAH II 63.1% WDB NRG IceFree3 3.1 Next to unfenced NOAH II 57.0% WSC,F NRG IceFree3 3.0 Inside full DFIR fence 68.8% WSD Vaisala WAA252 10 Well clear of HTBRG hut 88.7% WDD Vaisala WAV252 10 Well clear of HTBRG hut 90.9% WS — — Composite of WSA and WSB 82.1% The Kerries PrA ETI NOAH II 4.5* ETI Alter shield, half DFIR fence 76.2% PrB ETI NOAH II 3.0* ETI Alter shield, no wind fence 50.5% TA Unidata 6507A 3.0 Thermistor, 150-mm screen 97.4% WSA Young 05103 4.8 Outside half DFIR fence, to the northeast 76.5% WDA Young 05103 4.8 Outside half DFIR fence, to the northeast 95.1%

f. Gap filling and spatial interpolation represented by a Fourier series. The accuracy of the technique is determined by the uniformity and accuracy In a number of cases, wind speed and/or temperature of the input data, as well as the choices of the radii of instrumentation were not installed until well after the influence parameters, which determine the convergence installation of the NOAH II gauges. Additionally, there of the scheme in the successive iterations. are a number of extended gaps in the datasets where We used radii of influence of 0.058 and 0.158, or one instrument maintenance was delayed because of logis- and three grid cells, for the two iterations. This means tical difficulties (many of these sites were only accessible that the value determined for any given grid cell was by helicopter in the winter months). most strongly influenced by gauges within 0.058, or about For the catch ratio analysis and evaluation in sections 5 km, and no value was calculated if there was no gauge 4 and 5, only directly measured variables were used. To within 0.158 (15 km). The objective analysis was per- apply the results of our analysis more broadly, we gap formed for each 6-h interval in the analysis period and filled the wind speed and temperature data using a summed for each year to give the total precipitation self-organizing linear output (SOLO) map (Hsu et al. amount for April–October. 2002), a type of artificial neural network (ANN). The drivers used were the best correlated variables of the same type from nearby locations, and we were generally 3. Partitioning of precipitation types for regression able to represent about 90% of the variance of the target analysis variables with the SOLO for wind speed, and more than 95% for temperature. No precipitation data were There are no direct observations of precipitation gap filled. type at Guthega Dam. Measurements of humidity We performed an objective spatial analysis of the onlybegantowardtheendof the analysis period, so precipitation amount from the gauge data over the do- the only measured variable that may be used to cate- main 36.958–35.458S, 147.858–148.908E, with grid spacing gorize the precipitation type is the ambient tempera- of 0.058. The analysis was performed using the NCAR ture. Yang and Ohata (2001) used daily mean air Command Language obj_anal_ic() routine, which is temperature thresholds to define the precipitation essentially a Barnes (1964) successive correction analy- type, with criteria set at T ,228CandT . 28Cfor sis. This spatial interpolation technique is related to snow and rain, respectively, with mixed precipitation kriging and assumes that the underlying data can be between these bounds.

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FIG. 3. Wind speed and direction at (a),(b) Guthega Dam and (c),(d) the Kerries during (left) all 6-h intervals and (right) those in which at least 0.25 mm precipitation was reported.

We defined optimal temperature intervals (defined by A minimum threshold of 4 mm of precipitation at the threshold values, or breakpoints, Tb1 and Tb2) based on reference gauge was used for this analysis, but the sen- analysis of the CR relationship between the NOAH II in sitivity to this parameter was low, with Tb1 only varying the full DFIR fence (the reference gauge; PrC) and the between 0.28 and 0.58C over thresholds of 1–8 mm. We unfenced NOAH II (the comparison gauge; PrB). Or- repeated the analysis using NOAH II in the half DFIR dinary least squares (OLS) linear regression was used to fence as the reference gauge and produced the same evaluate the impact of 6-h average WS on CR for in- result. Using data from the gauge pair at the Kerries tervals T # Tb1, Tb1 , T # Tb2, and T . Tb2. The produced a wider interval for mixed-phase precipitation breakpoints were varied between 238 and 68C with a (Tb1 5 0.28C and Tb2 5 2.68C), but the low range of wind step size of 0.18C, under the condition that Tb1 , Tb2 (the speeds there made it harder to achieve good-quality fits special case Tb1 5 Tb2, or only two intervals, was con- for the analysis. sidered separately). The RMSE was calculated for each There is good physical justification for these break- of the breakpoint pairs (Fig. 4), and the values that point values. Michelson (2004) used a large body of minimized the RMSE overall were Tb1 5 0.48C and wintertime synoptic observations to derive a hyperbolic Tb2 5 1.88C. relationship for the fraction of snow psnow based on

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the precipitation amount to predict CR is also somewhat novel, but we found that it was statistically significant as well as independent of the other predictors. We found that the square root of precipitation amount was a more statistically significant predictor than the simple amount. Optimal predictor combinations were developed by minimizing the Bayesian information criterion (BIC; Schwarz et al. 1978), which prevents overfitting by pe- nalizing complex models. We required all of the pre- dictors to be statistically significant (P , 0.05) with respect to CR. There were a very small number (n , 4) of outliers in the raw CR values used to perform the regression for snow (specifically, CR $ 1.0 for moderate wind speeds). The fits obtained by including these out- liers were judged to be nonphysical for higher wind 2 FIG. 4. Overall RMSE for a set of three OLS linear regression speeds (WS $ 8ms 1). The outliers mostly vanished models for CR using WS as the only predictor, and with two when the precipitation threshold was set to 5.0 mm, but breakpoints T and T defining phase partitions. The values of T b1 b2 b1 in order to retain the sample size we required that CR , and Tb2 for the optimum RMSE are shown. 2 1.0 for wind speeds greater than 4 m s 1. wet-bulb temperature. The function was defined for The following sections discuss the specifics of each of

20.218,Twb , 2.428C and has upper and lower decile the CR relationships developed for the various gauge values of 0.488 and 1.728C, respectively. The agreement pairs considered. All of the CR relationships referred to of the breakpoint analysis with these empirical values is are presented in Table 2. consistent with the hypothesis that the NOAH II gauges a. Unfenced and full DFIR NOAH II gauges perform differently for snow, mixed precipitation, and rain. Based on the 6-h intervals where both gauges were working optimally and the full DFIR recorded more than 0.1 mm of precipitation, the unfenced NOAH II 4. Developing optimal CR relationships between gauge caught, on average, about 48% of the snow re- gauge pairs corded by the gauge in the full DFIR fence and 77% of Catch ratio relationships between various gauge pairs the mixed precipitation. This amounted to a total deficit at Guthega Dam were calculated through OLS re- of 1404 mm over the analysis period. gression for the snow and mixed precipitation temper- Robust catch ratio relationships were found between ature intervals defined above. As a basic check, we first the unfenced NOAH II and the NOAH II in the full verified that the catch ratio for rain was very close to DFIR. Only one outlier was removed from the snow 2 unity for each gauge pair. The 6-h intervals were in- dataset where CR $ 1.0 for WS $ 4ms 1. cluded only if at least 2.0 mm of precipitation for the These relationships are shown numerically in Table 2 reference gauge and valid temperature and wind speed and graphically against wind speed (Figs. 5a, 6a) for data were available for the whole interval. Different some constant values of T (which characterize the thresholds were tested; 1.0 mm affected the fits because temperature intervals), and Pr 5 5.0 mm (which, to- the observed CR values were constrained to simple gether with the fixed values for T, explained the dis- fractions (e.g., 1/2) due to the NOAH II gauge resolution. crepancy between the constant terms above and the y A threshold of 3.0 mm (used in a number of previous intercepts in the figures). The quality of the fits obtained studies) did not show any improvement in quality of fit indicates that the model explains the variance in CR over 2.0 mm. very well for snow, and moderately well for mixed pre- The predictors considered were the 6-h mean tem- cipitation. The quadratic fit for snow had a minimum 2 perature, mean wind speed, the square of mean wind value for WS 5 11.9 m s 1, which is at the extreme of the speed, and the total precipitation amount in the com- range of the wind speeds observed, making it a physi- parison gauge. Previous studies, analyzing 24-h in- cally valid model. tervals, often included daily maximum and minimum The implication of the large Pr0.5 term is clear: the temperatures, but our use of subdaily intervals to re- catch ratio was generally higher for greater precipitation solve the diurnal cycle made this unnecessary. The use of amounts, for both snow and mixed precipitation. The

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TABLE 2. Optimal CR relationships for the gauge pairs discussed in sections 4a–e.

Gauge pair CR model nR2 For snow UF vs full DFIR 0:7153 1 0:1352Pr0:5 1 0:0045WS2 2 0:1068WS 1 0:0212T 271 0.73 UF vs full DFIRa 0:9990 1 0:0034WS2 2 0:1083WS 1 0:0323T 271 0.60 TBG vs full DFIR 0:2544 1 0:1984Pr0:5 2 0:0268WS 259 0.74 Half DFIR vs full DFIR 0:9282 1 0:0492Pr0:5 2 0:0037WS2 2 0:0216T 300 0.43 UF vs half DFIRb 0:6265 1 0:1398Pr0:5 1 0:0032WS2 2 0:0800WS 1 0:0293T 243 0.63 UF vs half DFIRc 0:8254 1 0:0979Pr0:5 1 0:0053WS2 2 0:1167WS 1 0:0178T 482 0.78 For mixed precipitation : UF vs full DFIR 0:5926 1 0:1017Pr0 5 2 0:0401WS 1 0:1034T 140 0.49 UF vs full DFIRa 0:8188 2 0:0413WS 1 0:0992T 140 0.30 TBG vs full DFIR 0:3242 1 0:1494Pr0:5 2 0:0257WS 1 0:0950T 132 0.59 Half DFIR vs full DFIR 0:8807 1 0:0473Pr0:5 2 0:0025WS2 138 0.28 : UF vs half DFIRb 0:5857 1 0:0915Pr0 5 2 0:0200WS 1 0:0843T 122 0.28 UF vs half DFIRc 0:6702 1 0:0858Pr0:5 2 0:0302WS 1 0:0712T 187 0.51 a Pr was omitted from the analysis for comparison purposes. b Referred to in text as GD-only. c Referred to in text as GD1TK. physical explanation for this effect is that higher pre- NOAH II in the DFIR over the analysis period. Statis- cipitation rates are associated with larger snowflake tically significant relationships for CR were found for sizes, and hence greater fall speeds, in accordance with Pr0.5 and WS for both snow and mixed precipitation, but the Gunn–Marshall (Gunn and Marshall 1958) distri- T was significant for mixed precipitation only (see Table bution (analogous to the better-known Marshall– 2 and Figs. 5b, 6b). 2 Palmer distribution for raindrop size; Marshall and At moderate wind speeds (WS ; 5ms 1), the CR Palmer 1948). For snow, the wind speed was the next values for snow and mixed precipitation (see Figs. 5b, 6b) most important factor, with Fig. 5a showing that the were similar to the unfenced NOAH II gauge, but the catch efficiency of the unfenced NOAH II gauge drop- spread in the values was much higher, and the fit provided 2 ped to around 0.3 for wind speeds above 8 m s 1. The by the regression was poorer. At high wind speeds, the coefficient of temperature for the mixed CR was more relationships suggest that CR dropped to zero for snow, than 4 times that for snow, supporting the hypothesis and this is indeed borne out by the observations: zero that temperature had a controlling influence on particle precipitation amounts were common for the tipping- 2 fall speeds in this temperature range. bucket gauge at wind speeds greater than 7 m s 1,while The optimal CR relationships with Pr omitted are the reference gauge recorded at least 2.0 mm. presented in Table 2 for this gauge pair, but not the c. Half DFIR and full DFIR NOAH II gauges subsequent ones. Including Pr0.5 increased the absolute fraction of the explained variance in CR by 13% for snow The raw values of precipitation for snow and mixed and by 19% for mixed precipitation. Furthermore, the precipitation recorded by NOAH II in the half DFIR changes in the other coefficients were small, which in- fence were relatively unbiased, with 90% and 92% for dicates that the effect of the precipitation was nearly in- snow and mixed precipitation relative to the NOAH II dependent of the other effects. Finally, the change in the in the full DFIR fence. This amounted to a total deficit constant term may be reconciled against the precipitation of 329 mm over the analysis period. The CR relation- amount term. For snow, the difference is neutralized by a ships are presented in Table 2 and Figs. 5c and 6c. precipitation amount of 4.95 mm and for mixed pre- As the sole predictor (apart from precipitation amount), cipitation the amount was 5.26 mm, which are close the WS was found to have a statistically significant relationship value of 5.0 mm used for plotting purposes in the figures. with the CR, but WS2 was a slightly better fit. When both were used, the WS term became insignificant, so it was b. Unfenced heated tipping-bucket gauge and full omitted from the above relationships. Temperature was DFIR NOAH II gauge not statistically significant for mixed precipitation. The heated tipping-bucket gauge recorded 55% and The negative coefficient in the WS2 term is at odds with 85% of the NOAH II gauge in the full DFIR fence the CR relationships defined between reference and un- for snow and mixed precipitation, respectively. This fenced gauges in previous studies (e.g., Goodison et al. amounted to a total deficit of 1533 mm compared to 1997), where the turning point represents a flattening of

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FIG. 5. (a)–(d) CR for snow for each of the gauge pairs (indicated by labels) analyzed at Guthega Dam. Points plotted in red are outliers that were omitted for developing the CR models. The dashed lines show the empirically derived relationships with temperature held constant at the indicated values (representing the variance that can be explained by T) and precipitation held constant at 5.0 mm. the CR at high wind speeds. However, the relationships variance R2 of 0.44 for snow and 0.09 for mixed pre- above describe the performance of different fence con- cipitation. The coefficient for WS2 in the relationship for figurations, so it is not necessarily valid to compare them snow was somewhat smaller than in the relationship with the relationships found in previous studies. between the unfenced/full DFIR fence configuration. This result is important because it highlights some This can be explained in terms of the CR relationships vagaries of using an alternative reference standard. The described above. The positive curvature of the CR re- negative coefficient of temperature implies that the lationship between the unfenced NOAH II gauge and gauge inside the half DFIR fence was relatively more NOAH II in the full DFIR fence was offset by the rel- efficient than that with the full DFIR fence for drier atively strong negative curvature of the relationship snow. For both snow and mixed precipitation, the CR between the two fenced gauges. The minimum value for 2 was approximately unity for low to moderate wind the CR relationship for snow occurs at WS 5 12.4 m s 1, speeds, but the efficiency of the half DFIR fence de- which is at the extreme of the observed wind speeds. creased rapidly for higher wind speeds. There was some For mixed precipitation, the CR was higher at mod- indication that the relative performance may level off at erate to high wind speeds than when compared to the CR ’ 0.5 for the highest wind speeds, but there were not reference gauge. This also reflected the choice of refer- enough data available to establish this. ence gauge: we saw above that the efficiency of the NOAH II gauge in the half DFIR fence decreased with d. Unfenced and half DFIR NOAH II gauges wind speed for mixed precipitation as well. The unfenced NOAH II gauge recorded 55% and e. Inclusion of unfenced and half DFIR NOAH II 85% of the NOAH II gauge in the half DFIR fence for gauges from the Kerries snow and mixed precipitation, respectively. This amounted to a total deficit of 1106 mm over the analysis Cross validation of the model presented for unfenced period. Two outliers were removed from the snow and half DFIR NOAH II gauges at other sites with 2 dataset where CR $ 1.0 for WS $ 4ms 1 to obtain the multiple gauges (section 5b) showed that conditions at CR relationships (see Table 2 and Figs. 5d, 6d). Guthega Dam do not represent more sheltered locations For this model (hereafter GD-only), the Pr0.5 term in the Snowy Mountains. The Kerries, on the other 2 also had quite a marked effect for this gauge pair: hand, had a mean wind speed of only 1.4 m s 1 and a 2 omitting Pr from the regression resulted in an explained 95th percentile value of 3.5 m s 1 during snow or mixed

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FIG.6.AsinFig. 5, but for mixed precipitation.

precipitation. The unfenced NOAH II gauge recorded (PrR), by the simple application of the following 92% of snow and 98% of mixed precipitation compared expression: to the NOAH II gauge in the half DFIR during the 5 overlap period. Taken alone, the data from the Kerries PrR Prm/CR, were unsuitable for developing a CR model because of the small range in wind speed, so we combined the data where PRm is the measured precipitation amount and from both the Kerries and Guthega Dam to develop a CR is the empirical catch ratio. Ultimately, this adjust- model we hypothesize to be more generally applicable ment should be done only if it reduces the RMSE or in the Snowy Mountains (see Table 2, Fig. 7). bias. Table 3 contains the RMSE and mean bias before This CR model (hereafter GD1TK) departed from and after adjustment for each of the gauge pairs con- GD-only by having a higher catch ratio for low wind sidered in section 4, both with and without a pre- speeds, driven by the cluster of observations for WS , cipitation term. In addition to the CR fits, we evaluated 2 2.0 m s 1 at the Kerries for snow, and the influence of the performance of a bias adjustment, based on a linear temperature was also diminished. For mixed pre- regression of precipitation amount only, for each cipitation, the temperature coefficient was decreased by gauge pair. about 14% compared to Guthega Dam alone, and the The reduction in overall RMSE for the unfenced and relationship to wind speed was slightly steeper, again full DFIR (unfenced and half DFIR) NOAH II gauge pair was about 52% (49%), but if Pr0.5 was omitted the because of the cluster of low wind speed observations 0.5 from the Kerries. reduction was only about 28% (26%). Including Pr in the CR relationship resulted in an undercorrection of 0.225 mm (0.150 mm), while omitting it resulted in an 5. Evaluation and application of the derived CR average overcorrection of 0.139 mm (0.123 mm). relationships For the unfenced and full DFIR gauge pair, both of the CR adjustments resulted in lower RMSE than the a. Does applying a gauge adjustment improve the bias adjustment. For the unfenced and half DFIR pair, RMSE in comparison to a reference gauge? the CR adjustment omitting the precipitation term The CR relationships developed above permit the resulted in higher RMSE than the bias adjustment, but estimation of the precipitation amount that would have when the precipitation term was included the RMSE been measured by a better-shielded reference gauge was lower than the bias adjustment.

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fences in the Snowy Mountains (or anywhere else in the Australian Alps), so it is not possible to validate the full DFIR model thoroughly. Furthermore, when we apply the adjustments more broadly in section 5c, the use of a half DFIR model allows us to homogenize the network with the smallest number of adjustments. We directly cross validated two adjustments derived for half DFIR fenced versus unfenced NOAH II gauges (GD-only and GD1TK) using independent data from Grey Hill and Snowy Plain, with RMSE and bias of the adjusted precipitation amounts shown in Table 4. Both adjustments resulted in larger overall RMSE at the in- dependent sites. The GD-only model was considerably worse at both sites, with moderate increases in RMSE for both snow and mixed precipitation. For the GD1TK model, the changes in RMSE for Snowy Plain were negligible. There was a modest decrease in RMSE for mixed precipitation at Grey Hill, but a larger increase for snow dominated the overall RMSE. The adjustment performed resulted in a large overcorrection, increasing the mean bias from 20.05 to 0.73 mm. This result is not particularly encouraging, but there were some issues with the cross-validation sites that FIG. 7. CR relationships for (top) snow and (bottom) mixed precipitation for unfenced NOAH II and NOAH II in half DFIR should be discussed. In particular, we believe that Grey fence, with data from both Guthega Dam (cyan points; as in Hill is a poor candidate for a cross validation site. It was Figs. 5d, 6d) and the Kerries (magenta points). The gray lines show the only site at which the CR for the unfenced NOAH II the empirically derived relationships for Guthega Dam only (GD- was higher for snow than for mixed precipitation. It is only; as in previous figures), and the black lines show the re- lationships for the combined data (GD1TK). difficult to evaluate this anomaly because wind speed was only measured at the fenced gauge, but there were no obvious differences in terrain or vegetation that For the heated tipping-bucket gauge, the bias adjust- could account for influences on local wind flow. Addi- ment was only narrowly beaten by the CR adjustment tionally, both sites had relatively low wind, so the mean when Pr0.5 was included, and when it was omitted the bias in the raw data was very low to begin with. It is overall RMSE was actually increased. For the half unfortunate that more exposed, reliable cross-validation DFIR and full DFIR NOAH II comparison, the CR sites were not available. adjustments reduced the RMSE by about 15%, regard- To address the issue of suboptimal cross-validation less of whether precipitation was included, whereas the sites, we also tested the models using a jackknife method bias adjustment had a smaller impact. (Tukey 1958) to develop statistically independent data The mean RMSE of the GD1TK raw data was lower from the intercomparison sites themselves. The method than for Guthega Dam alone, because the precipitation consisted of removing a single interval from the GD- data from the unfenced NOAH II gauge at the Kerries only and GD1TK datasets and deriving the CR re- were relatively accurate because of the low wind speeds lationship with the remaining data and testing this there. The bias adjustment resulted in only a modest against the withheld (independent) data. This was re- reduction in RMSE for the same reason. The CR ad- peated for each interval in which any precipitation was justments, both with and without Pr0.5, resulted in an reported, and RMSE and bias in Table 4 were calculated overall decrease in RMSE. in the same way as previously. We found that the validation of the GD1TK model b. Cross validation of adjustment scheme with data from Guthega Dam resulted in only a very The empirical CR adjustment scheme presented small increase in RMSE compared to the GD-only above requires cross validation before it may be robustly model, whereas the RMSE for the cross validation us- applied to other sites. In this section, we concentrate on ing data from the Kerries increased when using the GD- the unfenced and half DFIR fenced NOAH II gauge only model but decreased using the GD1TK model. pairs, simply because there are no other full DFIR When validated using the combined GD1TK dataset,

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TABLE 3. RMSE (mm) and mean bias (mm) for gauge comparisons in section 5 within the snow and mixed classes. The adjustments tested were bias adjustment of precipitation amounts, CR adjustment omitting precipitation term (CR without Pr), and CR adjustment including precipitation term (CR with Pr0.5). Where the statistic was increased by the adjustment, values are shown in italics.

Snow Mixed Overall Gauge pair Adjustment RMSE Bias RMSE Bias RMSE Bias UF vs full DFIR None 3.304 22.137 1.994 21.228 2.935 21.835 Bias adjustment 2.403 — 1.369 — 2.117 — CR without Pr 2.260 0.112 1.790 0.192 2.116 0.139 CR with Pr0.5 1.547 20.259 1.108 20.157 1.416 20.225 TBG vs full DFIR None 3.429 22.300 2.288 21.573 3.091 22.054 Bias adjustment 2.558 — 1.224 — 2.200 — CR without Pr 3.883 0.451 2.089 0.325 3.385 0.408 CR with Pr0.5 2.489 20.297 1.180 20.242 2.139 20.279 Half DFIR vs full DFIR None 1.139 20.415 1.044 20.396 1.110 20.409 Bias adjustment 1.065 — 0.945 — 1.028 — CR without Pr 0.946 0.007 0.938 0.024 0.943 0.012 CR with Pr0.5 0.945 20.067 0.896 20.080 0.930 20.072 UF vs half DFIR (GD-only) None 2.775 21.900 1.483 20.947 2.420 21.580 Bias adjustment 1.680 — 1.011 — 1.489 — CR without Pr 1.953 0.130 1.392 0.109 1.785 0.123 CR with Pr0.5 1.350 20.153 0.942 20.196 1.228 20.167 UF vs half DFIR (GD1TK) None 2.060 21.197 1.242 20.700 1.864 21.055 Bias adjustment 1.754 — 0.990 — 1.574 — CR without Pr 1.538 0.077 1.110 0.064 1.429 0.073 CR with Pr0.5 1.117 20.111 0.910 20.144 1.062 20.120 the overall RMSE was lower for the GD1TK model. unexposed. Mount Hudson, on the other hand, is the The model coefficients were stable with respect to the second highest and the windiest site. Here, we estimate omission of single data intervals, and varied by less than that an adjustment of about 52% of the total recorded 5% (95% confidence interval). wintertime precipitation is needed to represent the amount that would have been recorded by a NOAH II c. Application of the results to the Snowy gauge shielded inside a half DFIR fence. Mountains network d. Spatial analysis of precipitation amount The results of applying the GD1TK CR relationship to each of the 12 sites with an unfenced NOAH II gauge An objective spatial analysis was performed on the are shown in Table 5. The conditions at the sites are precipitation gauge data from a total of 70 gauges at 61 quite varied, ranging from the relatively warm and calm unique sites in the Snowy Mountains region, using the conditions of the Murray 1 Valve House to exposed sites method described in section 2. The gauges used included on the Main Range of the Snowy Mountains. For all of d 22 unheated tipping-bucket gauges, with elevation up the sites below 1400 m MSL in elevation (the approxi- to 1250 m MSL; mate snow line), the estimated undercatch was 5% or d 15 heated tipping-bucket gauges, with elevation be- less of the total precipitation amount. The mean tem- tween 800 and 1320 m MSL; perature during precipitation at these sites was 48–58C, d 12 unfenced NOAH II gauges; and and snow and mixed precipitation accounted for around d 21 NOAH II gauges in a half DFIR fence. 15%–30% of the total measured precipitation. For sites above 1400 m MSL, about half of the measured The unfenced NOAH II gauge data were adjusted precipitation was snow or mixed (except at Guthega Dam, using the methods described above to estimate the which is in a valley directly downwind from the Main precipitation that would have been recorded had a half Range and may be warmed by foehn winds when pre- DFIR fence been installed. The tipping-bucket gauge cipitation occurs along the Main Range). Although the data were not adjusted, but the effects at lower altitudes Kerries was the equal coldest of the sites on average, it had were judged to be minimal (see Table 5). The resultant the smallest adjustment of the high-altitude sites because gridded dataset was designated the half DFIR analysis. of the light winds there. The adjustments had an impact of To test the overall effect of the wind fences installed in about 9% of the total recorded amounts at Pinnacle the Snowy Mountains region, the objective analysis Mountain and Grey Hill, which were relatively warm and procedure was repeated, but this time applying the

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TABLE 4. Cross-validation RMSE (mm) and bias (mm) for raw data (i.e., no adjustment) and gauge adjustments between unfenced NOAH II gauges and those in half DFIR fences for the GD-only CR model and the GD1TK model. Where the magnitude of the statistic was increased by the adjustment, values are shown in italics.

Snow Mixed Overall Adjustment Site RMSE Bias RMSE Bias RMSE Bias None Snowy Plain 0.520 20.363 0.513 20.248 0.515 20.287 Grey Hill 0.818 20.053 1.145 20.423 0.902 20.137 Guthega Dama 2.775 21.900 1.483 20.947 2.420 21.580 The Kerries 0.836 20.450 0.603 20.244 0.790 20.403 GD1TKa 2.060 21.197 1.242 20.700 1.864 21.055 GD-only Snowy Plain 0.701 0.380 0.587 0.194 0.628 0.258 Grey Hill 1.517 0.980 1.048 0.240 1.424 0.813 Guthega Damb 1.373 20.152 0.970 20.198 1.252 20.167 The Kerries 0.867 0.265 0.825 0.100 0.858 0.228 GD1TKb 1.152 0.053 0.921 20.091 1.091 0.012 GD1TK Snowy Plain 0.532 0.213 0.512 0.094 0.519 0.135 Grey Hill 1.178 0.726 1.021 0.071 1.144 0.578 Guthega Damb 1.402 20.147 0.965 20.181 1.272 20.158 The Kerriesb 0.749 20.073 0.870 20.083 0.778 20.075 GD1TKb 1.129 20.111 0.932 20.146 1.076 20.121 a Denotes an entry from Table 3. b Denotes a cross validation performed by a jackknife method (see text). inverse of the catch ratio calculated to the NOAH II to produce a robust result in repeating the analysis of gauges in half DFIR fences, and leaving the unfenced section 3 with wet-bulb temperature. Second, since NOAH II gauges unadjusted, to create a no DFIR humidity was only measured at a selection of sites, most analysis. The two analyses are compared in Fig. 8. of the phase discrimination in a humidity-aware scheme Differences at low elevations were negligible because would be based on estimates, which is another potential the tipping-bucket gauge data were identical in each source of error. On the other hand, ambient tempera- analysis. Above 1000 m MSL, the mean difference be- ture was directly measured at nearly every one of the tween the analyses was 43 mm per season, or about 6% sites considered in this paper. relative to the no DFIR analysis. The maximum differ- Since T $ Twb (as for hydrometeor temperature), a ence between the two analyses was 249 mm, which is 25% temperature-only scheme could result in misclassification relative to the no DFIR analysis at the same grid point. of snow as mixed precipitation, and of mixed pre- cipitation as rain, but not the reverse. For a given tem- perature, the empirical CR for snow was less than for 6. Discussion mixed precipitation, meaning that such a misclassification would always result in overestimate of CR, and an un- a. Uncertainty due to precipitation phase dercorrection would be applied. Using only ambient classification scheme temperature is therefore a conservative approach and is There are several justifications for using a temperature- more desirable given the assumptions that would need to only criterion in this paper instead of a humidity-aware be made in deriving a networkwide humidity estimate for scheme (e.g., Michelson 2004; Harder and Pomeroy the Snowy Mountains. 2013). First, no humidity measurements were made at b. Uncertainty due to spatial interpolation of Guthega Dam during our analysis period, but a sensor precipitation was installed in 2013 during the reconfiguration of the site for the SPICE. For 224 six-hour intervals in the Regardless of the scheme used, spatial interpolation winter months of 2013/14 with at least 4 mm of pre- of precipitation data can lead to large errors, especially cipitation (the threshold used in section 3), the wet-bulb in mountainous terrain. Aside from the condition of the and ambient temperature were very highly correlated input data, local topography can have a profound effect (R 5 0.99). This suggests that ambient temperature is on precipitation amounts (as we have seen in this paper). indeed an adequate discriminant for precipitation phase, Objective analysis of precipitation amount implicitly at least in an alpine environment during wintertime. assumes that conditions in any grid cell are similar to However, we found that 2 years of data were insufficient those in the next, which is in general not the case, but on

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the scale of about 5 km this is probably not unreasonable for the Snowy Mountains region. In any case, the spatial interpolation scheme for the two analyses was consis- tent, so comparisons between the two were valid. c. The impact of installing wind fences in the Snowy Mountains well as the estimated Interestingly, there was a strong linear relationship between gridpoint elevation and the undercatch for grid points above 1000 m MSL (Fig. 9). We partitioned the gridded data into east and west of the continental divide ) is the expected value of this event P

given that precipitation was recorded. 5 ( (n 85 and 115, respectively) and evaluated the un- E x dercatch for each group separately. The increase in un- dercatch with respect to height was similar for both 2 groups, at 15.5 mm (100 m) 1 in the east and 17.4 mm 2 (100 m) 1 in the west. The R2 values were 0.41 and 0.50, respectively, implying high statistical significance given the number of samples. These relationships reflect the effect of both lower temperatures and increased exposure to winds experienced by the gauges at higher elevations. The greatest precipitation amounts occurred along the catchment boundary (leftmost dark line in Fig. 8). This is also where the greatest absolute ) Total (mm) Snow (mm) Mixed (mm) Adj. (mm) Adj. (%)

), as per the text. ‘‘Adj.’’ stands for adjustment amount. difference between the analyses occurs because of ex- 1 jP 2 posure to winds and a predominance of snow at high

(WS elevation. The secondary maximum for precipitation ) is the expected value (mean) of the variable E

jP amount, located around 36.18S, 142.38E, is not associ- x ( )

E ated with a large difference between the analyses. De-

jP spite the relatively high elevation of the sites in this T (

E region (1500–1700 m MSL), they are relatively pro- 2 tected, with mean wind speeds of 2–3 m s 1 when pre- ) C), and wind speed (m s 8 cipitation was recorded. There is a secondary maximum jP in the difference between the two analyses along the (Pr

E Snowy–Murrumbidgee catchment boundary (rightmost dark line in Fig. 8), where the sites in this region recorded ) 21 P

( mean wind speeds of 3–5 m s during precipitation. E is the event where more than 0.1 mm of precipitation was recorded in a 6-h period,

P d. Comparisons with CR relationships from other studies Goodison et al. (1997) provide specific CR relation- ships for a selection of different gauges compared to the WMO DFIR, which we compare to the relationships derived in this study in Fig. 10 (specifically, the unfenced NOAH II gauge compared to the NOAH II gauge in the full DFIR fence at Guthega Dam). For the purpose of

plotting the values, we set Tmin 5 Tmax 5 Tmean 5258C for snow, and 18C for mixed precipitation. Our results

, and WS are precipitation amount (mm), temperature ( assume the same nominal 5-mm precipitation amount as T for previous figures. 5. Details of precipitation and other variables recorded at the sites of the 10 unfenced NOAH II precipitation gauges in the Snowy Mountains region, as Site Elev (mm) No. obs We cannot exclude the possibility of minor differences in the performance of the NOAH II gauge in the full ABLE

T DFIR fence compared to the WMO standard Tretyakov Murray 1 Valve HouseIsland BendTooma DamThredbo 993Snowy PlainPinnacle MountainGuthega Dam 2873Grey Hill 1221Bald Hill 1221The 0.27 1535 KerriesMount Hudson 1367 1348 3751Charlotte Pass 3883 3.64 1586 3834 0.22 1103 5086 0.27 1624 0.29 4.95 4970 1757 3.43 1651 1741 0.22 0.25 5.09 1758 4.68 0.29 2546 0.59 3.11 4.90 1747 3.95 3834 2446 3.83 4.10 0.30 1739 1.29 0.33 0.29 0.32 4.04 4.08 2777 1.96 0.31 4.95 1.63 2.31 2.28 1.92 2.47 4.12 3.48 2.15 2.22 0.71 2808 4.64 151 5409 0.59 1.08 0.26 5134 0.26 6144 2.03 749 5.61 4.84 1.67 5803 136 243 698 3.42 1948 3772 378 1315 2699 3226 61 990 326 1867 924 15 846 1713 678 1448 529 930 88 931 0.55 767 82 143 467 528 192 495 158 419 1223 2.94 2.65 38 282 9.10 344 3.13 21.09 1095 214 683 5.13 504 9.14 40.58 51.93 6.63 27.00 undercatch of snow and mixedoccurring precipitation. (i.e., Here, the fraction of 6-h intervals where precipitation was recorded), and Variables Pr, DFIR, which have not been compared to our knowledge.

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FIG. 8. (left) Mean April–October half DFIR objective analysis of precipitation gauge data for 2007–12, showing only grid cells where there was no missing data. (middle) As in (left), but for the no DFIR analysis. (right) The difference between the two analyses. The thin contours show terrain elevation at 500, 1000, and 1500 m MSL. The thick lines show the major catchment boundaries.

In spite of this ambiguity, the CR for snow for the NOAH considerably smaller, is the source of much of the inflows II gauge is within 5% of the values for the Tretyakov and to the of Canberra (the national capital). NWS 8-in. gauges reported by Goodison et al. (1997) for These mountains currently have very sparse tipping- 2 wind speeds of 5.0 m s 1, which is close to the average at bucket and manual gauge networks operated by the Guthega Dam during precipitation. Agreement with Australian Bureau of Meteorology (BoM). It would be these two gauges was within about 10% for wind speeds possible to adjust these data in a similar way. However, 2 up to about 7 m s 1. As values greater than this were we found that the RMSE for the tipping-bucket gauge absent from the analysis of Goodison et al. (1997),there adjustment was nearly twice that for the adjustment to is no value speculating on the divergence for higher the unfenced NOAH II gauges. Furthermore, the heated wind speeds. tipping-bucket gauge at Guthega Dam was a nonstandard installation, so further measurements would need to be e. Comparisons with the networkwide impact in other obtained to characterize the BoM gauges. Installation of studies NOAH II gauges (or another standard similarly suited to The no DFIR analysis presented in this paper was a snow measurement) at the existing BoM sites, and at a theoretical exercise to determine the net effect of in- collection of new sites if possible, would permit the stalling wind fences. We found that the magnitude of the adjustment of historical data as well as improving the re- losses of a network with no fences (6% on average over liability of future precipitation measurements in Australia’s winter for elevations above 1000 m MSL, and 15% alpine regions. around the peaks) would be at the lower end of the scale of the results found in previous work by Yang and Ohata 7. Conclusions (2001), Zhang et al. (2004), Yang et al. (1998), Ye et al. (2004), and Yang et al. (2005), among others. In section 3 we showed that despite lacking humidity The results of this study are applicable to the Aus- observations, we were able to partition the precipitation tralian alpine region more generally. The Victorian Alps data into effective phases based on ambient temperature are the continuation of the Great Dividing Range to the thresholds for the purpose of deriving the CR relation- south and are similarly important for hydrological in- ships. The temperature thresholds were chosen by flows to the Murray–Darling basin. The Brindabella minimizing the overall RMSE of a piecewise WS-only Range to the north of the Snowy Mountains, while CR formulation. The analysis was robust to the choice of

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FIG. 9. Mean annual undercatch amount vs terrain elevation from the datasets compared in Fig. 8. Here, only points with ele- vation greater than 1000 m MSL were included, and error bars show one std dev in the annual undercatch amounts. gauge pair at Guthega Dam, but returned a slightly different upper threshold for mixed precipitation at a second site, where the range of WS was low and the linear fits poorer. The thresholds derived by this novel technique are supported by empirical evidence from FIG. 10. Comparison of the derived CR relationships for un- other studies, but an interesting follow-up study would fenced, Alter-shielded gauges presented in Goodison et al. (1997), be to evaluate this against humidity-aware schemes shown in color, to the relationships derived in this study, shown (e.g., Michelson 2004; Harder and Pomeroy 2013) when with black lines. sufficient humidity data have been collected at Guthega Dam. Plain) having little effect on RMSE but moderately re- In section 4 we presented what we believe to be the ducing the mean bias. However, these sites were some- best possible CR relationships between gauge pairs at what flawed in that they both experienced relatively low Guthega Dam, over a wide range of meteorological winds and thus low differences in raw catch amount, and conditions. We found it essential to include a term for the Grey Hill site was unusual in that it experienced a precipitation amount to satisfactorily characterize the lower mean bias for snow than for mixed precipitation. CR. This, to our knowledge, differs from previous In this sense, the neutral results for these sites probably studies, but there is a strong physical justification in the represent a worst-case scenario for validation attempts. link between precipitation rate and particle size (Gunn A second cross-validation analysis used a statistically and Marshall 1958; Marshall and Palmer 1948) and independent dataset derived from the cross-validation hence fall speed. Ultimately, the best model for the sites through jackknifing. Adjustments to this dataset unfenced and half DFIR CR used data from a second resulted in substantial reduction in RMSE. We believe intercomparison site (the Kerries) that together that, taken together, these cross-validation analyses experienced a much wider range of wind speeds. We also support the extension of the CR adjustment scheme to showed that the half DFIR fence provides a similar level the wider Snowy Mountains network. of protection from wind-induced losses to the WMO We applied the CR relationships derived at the inter- standard DFIR for the NOAH II gauges in low to comparison sites to all of the unfenced gauge data to moderate winds, but the performance deteriorates for estimate the undercatch of individual gauges in a range higher winds. of conditions in Table 5 and used the relationships to We cross validated the unfenced and half DFIR homogenize the NOAH II gauge network to account for model using independent data from other sites where a changes in fence installations over 2007–12. To de- short overlap between fenced and unfenced gauges was termine the overall impact of having the half DFIR available. This validation provided mixed results, with fences installed, we also inverted the CR relationship to adjustments at one site (Grey Hill) moderately in- estimate what would have been recorded if no fences creasing the RMSE for snow, and the other (Snowy had been installed. The effects were as expected, with

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