The hotplate outputs data to two files. The previously discussed Qtop and Qbot are two of several recorded variables and both of these are essential for the analysis described here. One of the files is known as the UHP or “user” hotplate file. The UHP file is provided to all YES customers. The second file is the SHP or “sensor” file. The SHP file is proprietary but we were granted access to it by NCAR. Table 1 has the list of all recorded variables and how some of these are symbolized. A complete list of variables (measured and computed) and constants is provided in the Appendix. With the exception of Unix time, all variables in Table 1 are provided as 60 s averages, sampled at 1 Hz (YES, 2011).

Two radiative properties are applied in our analysis of the top plate's power budget (Eq. 3). In the infrared, or longwave, the emissivity of the top plate is the key property. The material used to fabricate the plates is aluminum, which when exposed to air becomes covered with an aluminum oxide layer. Hence, the hotplate emissivity was taken to be that of oxidized aluminum (εh=0.14; Weast, 1975; Sect. E). Furthermore, we made two assumptions: (1) the longwave output (Eq. 3) is the product of εh, the hotplate area (Ah), and the flux emitted by a black body at Th, and (2) the longwave input (Eq. 3) is the product εh, Ah and the downwelling longwave flux (IRd). In a later section, we explain how we derive IRd.

In the visible, or shortwave, the top plate's reflectance (Rh) is the key property. Equation (3) shows how we factored into the power budget the top plate's reflectance, a measured downwelling shortwave flux (SW; Table 1), and Ah. A value for Rh was determined as follows. We exposed the UW hotplate to solar illumination while measuring the solar flux and then shaded the hotplate to establish a baseline for the determination of Rh. During these experiments, there was negligible wind and therefore natural convection dominated forced convection in the budget. The budget equation we used to analyze these measurements has three terms: Qtop, sensible power output, and solar input. In two experiments, the values Rh=0.66 and Rh=0.61 were derived. We apply the average of these (Rh=0.63) in our analysis of measurements from both UW and NCAR hotplates. Because of the oxide layer, the derived reflectance is smaller than the value reported for polished aluminum reflecting “incandescent” light (0.69; Weast, 1975; Sect. E) and significantly smaller than the value for vacuum-deposited aluminum at visible wavelengths (0.97; Hass, 1955).

Ice bulb temperatures at OWL were calculated using temperature, RH, and pressure measurements made within a fully shielded housing (Steenburgh et al., 2014). At GLE and BTL ice bulb temperatures were calculated using the hotplate-derived temperature, RH, and pressure values (Table 1). Because the hotplate temperature sensor is incompletely shielded (Fig. 1), there is concern that its measurement is positively biased by solar heating. We investigated this by differencing hotplate-derived temperatures acquired during precipitation events at OWL and values acquired by the fully shielded temperature sensor operated at OWL. On average, the hotplate values were larger (0.4 ± 0.4 ∘C). We did not attempt to correct for this bias.

Indoor testing was conducted in a high-bay weather balloon hangar and in a laboratory. These facilities are at the University of Wyoming (UW) and are referred to as hangar and lab. During wintertime, and especially at night, the hangar is cold (∼ 0 ∘C); the lab is warm year-round (∼ 20 ∘C). Field measurements (Table 2) were conducted in southeastern Wyoming at the Glacier Lakes Ecosystem Experiments Site (GLE), in southeastern Wyoming near the summit of Battle Pass (BTL), and at the northern Redfield site in western New York (OWL). During both indoor and field measurements, all parameters reported by the hotplate (UHP and SHP variables; Sect. 2.1) were recorded using a custom-built data system.

The accuracy of a hotplate-estimated precipitation rate depends on whether the sensed hydrometeors are rain or snow (R11). We infer the presence of rain or snow using a calculated ice bulb temperature (TIB) (Iribarne and Godson, 1981; chap. 7). Measurements used to derive the TIBs are described in Sect. 3.1. The lower limits on these derived values, assuming the measured RH is overestimated by 5 % (YES, 2011), is no more than 0.4 ∘C colder than the values we report. In instances with TIBs larger than 0 ∘C, we assume the sensed hydrometeors were liquid.

The NOAH-II is a weighing-type gauge manufactured by ETI Instrument Systems Inc. (www.etisensors.com). NCAR operated a NOAH-II at GLE and BTL during 2012, and coauthors (Campbell and Steenburgh) operated a NOAH-II at OWL (December 2013 to January 2014; Campbell et al., 2016). The three NOAH-II gauges were outfitted with Alter shields (Goodison et al., 1998; hereafter G98).

Indoor testing of the UW hotplate was conducted every year from 2011 to 2015; the NCAR hotplate was only tested in 2012. Based on our testing of the UW hotplate, we have no evidence indicating that the calibration changed over the duration of any of the field deployments; however, Wettlaufer (2013) demonstrates that calibration constants did change over the 2011 to 2015 interval and likely in response to servicing conducted twice at YES. In this paper we present calibration constants appropriate for the UW hotplate sensor deployed at GLE (April 2012) and at OWL (December 2013 to January 2014).

During testing, we controlled the hotplate's radiation environment by placing a material with known emissivity (painted-steel sheeting, εs=0.84) above and below the hotplate. The steel sheets were positioned to dominate the hotplate's upward and downward fields of view (Fig. 2); however, the sheets were positioned so that they were not heated by the hotplate. In that case, the sheet temperature (Ts) can be assumed equal to T.

As we have already mentioned, previous work concluded that the hotplate method of determining precipitation can be affected by longwave radiation. In response to that finding, newer versions of the hotplate have a device that measures longwave radiation (pyrgeometer, e.g., Albrecht et al., 1974) (Fig. 1 and Table 1). MIR=IRd-IRu The left-hand side of Eq. (4) represents the longwave measurement (MIR) and the right-hand side has the downwelling and upwelling components contributing to MIR.

Because IRd appears in the top plate's power budget (Eq. 3), and since MIR is the only term in Eq. (4) that is measured, the upwelling component (IRu) must be evaluated. This is possible because the signal from the pyrgeometer is adjusted within the hotplate electronics package to make the source of the upwelling flux a virtual blackbody at the ambient temperature (YES, personal communication, 2012). In that case, IRd can be formulated as IRd=MIR+σ⋅T4, where σ is the Stefan–Boltzmann constant and T is the hotplate-measured ambient temperature. We also use Eq. (6) to calculate the downwelling longwave flux. IRd=εs⋅σ⋅Ts4

Procedures described here were applied during testing conducted indoors (hangar and lab, Sect. 3.2) at two different temperatures and are hereafter referred to as the warm–cold test. We show how values of a warm (Tw) and cold (Tc) ambient temperature, combined with other recorded hotplate variables (Table 1), can be used to derive two calibration parameters in Eq. (3) (Th and γ). In our analysis, the temperature of the steel sheeting (Ts) was assumed equal to the ambient temperature (either Tw or Tc) and IRd was calculated using Eq. (6). By design these tests had negligible forced-convective and latent energy transfers. In that case, Eqs. (7a)–(7b) are the top plate budget equations. 0=Qtop,w-Dh⋅Kx⋅(Th-Tw)⋅γ-Ah⋅εh⋅σ⋅Th4+Ah⋅εh⋅εs⋅σ⋅Tw4+Ah⋅(1-Rh)⋅SWw0=Qtop,c-Dh⋅Kx⋅(Th-Tc)⋅γ-Ah⋅εh⋅σ⋅Th4+Ah⋅εh⋅εs⋅σ⋅Tc4+Ah⋅(1-Rh)⋅SWc The measurements applied in these equations were Tw and Tc, the warm and cold plate powers (Qtop,w and Qtop,c), the warm and cold shortwave fluxes (SWw and SWc), and the constants (Appendix). Values of Th and γ (hereafter referred to as Th/γ pairs) were derived by minimizing departures from zero simultaneously in Eqs. (7a)–(7b). Minimization was conducted using a Newton's method equation solver (Exelis Visual Information Solutions, Inc.); the convergence tolerance was 1⋅10-4 J s-1.

The Nusselt number (Nu=γ+α⋅Reβ), is a component of the sensible power output term in Eq. (3). In this section, we develop a relationship between Nu and Re based on measurements recorded in the field when precipitation was not occurring; in a later section we show how that relationship was applied in the new algorithm.

Conceptually, Nu is a dimensionless representation of the sensible power output. Equation (8a) was used to calculate Nu with measurements (Qtop, T, and SW), a calculated variable (IRd; Sect. 3.5), and constants (Appendix and Table 3). Nu=[Qtop-Ah⋅εh⋅σ⋅Th4+Ah⋅εh⋅IRd+Ah⋅(1-Rh)⋅SW]/[Dh⋅Kx⋅(Th-T)] In the numerator are the terms contributing to the sensible power output, and in the denominator is a term proportional to the sensible power due to molecular conduction.

Conceptually, the Reynolds number Re (Sect. 2) is a dimensionless representation of the wind speed. Equation (8b) was used to calculate Re with a measurement (U) and the constants (Appendix). Re=px⋅Dh⋅U/(Rd⋅Tx⋅μx) Two criteria were used to select a site-specific data subset for the Nu–Re development: (1) no precipitation, and (2) at least 3 h of continuous measurements with a broad range of wind speeds. We fitted the selected Nu–Re pairs using a nonlinear least squares procedure (curvefit; Exelis Visual Information Solutions, Inc.); the convergence tolerance for the relative decrease in chi-squared was 1⋅10-3.

Equilibrium thermodynamics, with the assumptions that ice melts at To = 0 ∘C and vaporization occurs at Th, was used to derive the conversion factor in Eq. (3) (f2). Adopting the temperature criteria from R11 (also see Sect. 2) and a framework from Iribarne and Godson (1981; chap. 7), we formulated the theoretical conversion factors as f2(T,Th)={ρ⋅Ah⋅[Ci⋅(To-T)+Lf(To)+C⋅(Th-To)+Lv(Th)]}-1(T<0∘C)f2(T,Th)={ρ⋅Ah⋅[C⋅(Th-T)+Lv(Th)]}-1(T>4∘C). This formulation is graphed in Fig. 3a (solid line) where we extended Eq. (9b) into the temperature range (0 ∘C < T < 4 ∘C) where the distinction between rain and snow is ambiguous (R11).

We now compare the conversion factor derived using Eqs. (9a)–(9b) with that reported in R11. To be consistent with R11, we assume T=Th=0 ∘C. We find that the ratio of f2 (Eq. 9a) divided by the factor reported in R11 for snow (3.99⋅10-8 m J-1) and the ratio of f2 (Eq. 9b) divided by the factor reported in R11 for rain (4.52⋅10-8 m J-1) are both 0.666. Since these ratios are equal to the area in R11 (Ah=0.008844 m2), divided by the area applied in our calculation (Ah=(π/4)⋅0.1302=0.01327 m2), we conclude that the discrepancy is not due to differing thermodynamic parameters applied in R11 and our calculations (e.g., the latent heat of vaporization); rather it stems from the different values used for the hotplate area. Further, R11 changed their theoretical f2 to an actual conversion factor that was “…lower because of the imperfect heat transfer from the precipitation to the hot plate (losses to the air, e.g.).” We do not find justification for this in R11, nor do we agree with R11's assignment of Ah=0.008844 m2, assuming they were recommending that value for the hotplate sold by YES. Recently, Boudala et al. (2014) addressed the second of these two points, making it clear that Ah=0.01327 m2 is appropriate for the hotplate sold by YES.

In light of the above, the ratio of our f2 (Eqs. 9a–9b with T=Th=0 ∘C) divided by the actual conversion factor in R11 is 0.86 for snow and 0.89 for rain. Since a derived precipitation rate is proportional to f2 (e.g., Eq. 2), we expect the ratio of a precipitation rate from the new algorithm (assuming T=Th=0 ∘C) divided by a synchronous hotplate-derived precipitation rate to be between 0.86 and 0.89. Our expectation hinges on the assumption that the YES algorithm has incorporated R11's surface area and R11's distinction between theoretical and actual conversion factors.

We calculate f2 in the new algorithm two ways: (1) in a comparison to a hotplate-derived accumulation, our f2 is set to 2.66⋅10-8 m J-1 (snow) and 3.01⋅10-8 m J-1 (rain). These values were obtained from Eqs. (9a)–(9b) with T=Th=0 ∘C and are displayed as a dotted line in Fig. 3a. (2) In comparisons to either a NOAH-II accumulation or to a laboratory reference precipitation rate, we evaluate f2 using Eqs. (9a)–(9b) with a Th from Table 3 and with the hotplate-measured ambient T (Table 1). In addition to the step change due to the difference between the latent heats of sublimation and vaporization, our conversion factor has a weak temperature dependence (Fig. 3a, solid line). This is due to the warming discussed in Sect. 2. Also, in Fig. 3a we display the actual conversion factor from R11 (dashed line). Our classification of measurements into snow and rain is discussed in a later section.

In this section, we evaluate a wind-speed-dependent function and use it to account for the top plate's snow particle catch efficiency (E; Sect. 2). The physical processes this function accounts for are (1) snow particle bouncing subsequent to collision with the top plate, followed by transfer away from the top plate by wind, and (2) shearing off of a snow particle after it has landed on the top plate (R11). This conceptual description of catch on the hotplate is different from that used to describe catch by weighing gauges where undercatch results because a subset of snow particles are carried over the gauge by a vertically accelerated flow (Nespor and Servuk, 1999; Thériault et al., 2012). Both R11 and G98 derive catch efficiencies as the ratio of two paired values of liquid-equivalent accumulation, one obtained from the gauge of interest and the other obtained from a second gauge operated inside a Double Fence Intercomparison Reference shield (DFIR).

The snow particle catch efficiency functions applied here are both gauge and location specific. For the UW hotplate (at GLE and OWL), and the NCAR hotplate (at BTL), we apply the function recommended by YES (YES, personal communication, 2012; hereafter Y12). Wind speeds used in the efficiency calculation are the hotplate-derived U. In addition, the hotplate catch efficiency function described by R11 (their Eq. 6) was also applied. This was based on the hotplate U adjusted to the 10 m level with a roughness length zo=0.3 m (G98, their Eq. 4.3.1) and was only used in analyses of measurements made at OWL. The zo we picked corresponds to a surface with “Many trees, hedges, few buildings” (Panofsky and Dutton, 1984; their Table 6.2). This assignment is consistent with the presence of shrubs and trees (Steenburgh et al., 2014) and a two-story barn at the OWL site. The barn was located at the eastern edge of a fallow field, 80 m west of the gauges at OWL. For the NOAH-II gauge, we applied a function developed for an 8 inch (0.20 m; diameter) Alter-shielded gauge (G98; their Eq. 4.7.1). Wind speeds used in that calculation are from the hotplate (at GLE and BTL) or from an anemometer (at OWL) (Campbell et al., 2016). Of course, we are assuming that the function from G98 mimics undercatch by our 12 inch (0.30 m; diameter) Alter-shielded NOAH-II gauge.

In Fig. 3b, we present the three catch efficiency functions (R11 with U adjusted to 10 m, Y12, and G98). In this graph, the wind speed applied in the R11 function is the value plotted on the abscissa multiplied by 2.9. This adjustment corresponds to the lowest installation of the hotplate at OWL and decreases to 2.0 for measurements made after 17 December 201

a.g.l. altitudes of the two hotplate installations are provided in Table 2.

Since the anemometer at OWL was operated at nearly the same height as the top of the NOAH-II gauge (Steenburgh et al., 2014) and the G98 catch efficiency formula (their Eq. 4.7.1) assumes speeds are measured at the height of the gauge opening, a vertical adjustment of the wind speed was not factored into the G98 catch efficiencies.

Results from the warm–cold tests are described here. The derived Th/γ pairs (Sect. 3.6) are in Table 3. The Th values are 42.2 ∘C for the NCAR hotplate deployed at BTL (NCAR/BTL), 52.2 ∘C the UW hotplate deployed at GLE (UW/GLE), and 65.5 ∘C for the UW gauge deployed at OWL (UW/OWL). The first two Ths differ from those presented in Wettlaufer (2013) where, for the NCAR hotplate, he reported agreement with the nominal plate temperature (75 ∘C; R11) and for the UW hotplate (GLE) he reported a larger temperature (Th=109 ∘C). The Th/γ pair reported in Table 3 for the UW/OWL study was evaluated after Wettlaufer (2013) reported his warm–cold test results.

In our analysis of the warm–cold measurements we only used data acquired in the hangar. As we describe below, this may have improved the accuracy of the resultant Th/γ pairs. This is because all data needed to derive a Th/γ pair can be obtained without turning off the hotplate. Wettlaufer (2013) analyzed both hanger and lab data. Both in his work and in ours, the relevant hotplate properties were derived by averaging over a 5 min warm interval and a 5 min cold interval and applying these averages in Eqs. (7a)–(7b). For us the warm–cold temperature pairings are 5.4/-4.3 ∘C (NCAR/BTL), 7.0/-1.1 ∘C (UW/GLE), and 29.5/10.4 ∘C (UW/OWL). Compared with Wettlaufer (2013), our Tws are 15 ∘C colder (NCAR/BTL and UW/GLE experiments only). Using our Th/γ pairs (Table 3) and the first two Tws (i.e., for NCAR/BTL and UW/GLE), we evaluated the term in Eq. (7a) representing natural-convective transfer (Dh⋅Kx⋅(Th-Tw)⋅γ) and compared them with values derived using Th/γ pairs in Wettlaufer (2013; his Table 2). In the NCAR/BTL comparison Tw was set at 5.4 ∘C and in the UW/GLE comparison Tw was set at 7.0 ∘C. Our natural-convective term agrees within ±0.1 W of those derived by Wettlaufer (2013). Also in good agreement is the product of Th and γ. Relative to Wettlaufer (2013), our Th⋅γ product is 6 % larger (NCAR/BTL), and 7 % larger (UW/GLE). We expect that our Th/γ pairs (Table 3), when applied in Eq. (3), will produce a reasonable estimate of the precipitation rate. We test that expectation in the next section.

Error limits on Th and γ in Table 3 were derived by perturbing Qtop,w (i.e., the value acquired in the warm test) by ±0.5 W and repeating the analysis (Eqs. 7a–7b). Our estimate of the Qtop,w error (±0.5 W) came from a comparison of values acquired before and after power to the hotplate was stopped and restarted. These tests were conducted in the hangar and the 10 min warm-up recommended by the manufacturer was adhered to (YES, 2011).

This section compares two time sequences of precipitation rate: one is calculated with the new algorithm; the other is the hotplate-derived value (Table 1). The basis for the comparison is the measurements of artificially produced liquid precipitation made in the hangar. We applied water drops to the NCAR and UW hotplates using a volumetric water pump (Ismatec Inc.; Model 7618). Each of these tests has a drip period (4 min) and a nondrip period (5 min). Drops (4 mm volume-equivalent diameter) were added uniformly to the top plate at a constant volumetric rate. We convert the pump rate to a reference precipitation rate (PREF) and apply the PREF in subsequent analyses

The value of the multiplier that converts the volumetric pump rate (cm3 min-1) to precipitation rate (mm h-1) is 4.51.

Because the drip tests were conducted with the hotplate operating as in Fig. 2, and unventilated, the recorded data were analyzed with Ts=T, in Eq. (6) (Sect. 3.5), and with the sensible power output formulated as Dh⋅Kx⋅(Th-T)⋅γ (Appendix and Table 3). Also, because all of the pumped water is delivered to the top plate, the catch efficiency is E= 1. Hotplate precipitation rates were derived by inputting measurements (Qtop, T, U, and SW) and a calculated variable (IRd; Sect. 3.5) into Eq. (3) and solving for a precipitation rate sequence (P(t)). We symbolize this P(t) as PUW and refer to calculations leading to that sequence as the UW algorithm. Also, we refer to sequences obtained from the UHP file (Table 1) as PYES and refer to that calculation as the YES algorithm.

We now compare values of PUW to synchronous values of PYES. Typically, these rates exhibit a maximum ∼ 3 min after the nondrip-to-drip transition (Fig. 4). We interpret these maxima as overestimates, possibly due to a violation of the steady-state assumption. Also evident, particularly in the PUW sequence, is a minimum. This occurs during the time in which the instrument is relaxing to its rest state; i.e., ∼ 2 min after a drip-to-nondrip transition. The figure also demonstrates that thresholding is applied to the PYES sequence; i.e., the YES algorithm thresholds the output to 0 mm h-1 if values decrease to < 0 mm h-1. This is evident at ∼ 16:11 UTC and at three other times in the PYES sequence. In fact, thresholding is not desired for the drip tests. Thus, the UW sequence is not thresholded in Fig. 4.

Two 1 min averaging intervals are shown in Fig. 4. We set the end of these at the drip-to-nondrip transitions and symbolize the averages as <PUW> and <PYES>. Figure 5 is a compilation of the two tests already discussed plus four additional PREF vs. <PUW> comparisons and four additional PREF vs. <PYES> comparisons.

We now use a linear least squares regression analysis and a regression equation of the form y=a⋅x to derive the ratio of two precipitation rates. In Fig. 5 it is apparent that the regression slope (ratio) derived for the PREF vs. <PUW> comparison does not differ from one by more than ±1 standard deviation. Ratios for the two hotplates (UW and NCAR) and for three drip tests are summarized in Table 4. In the third column (PREF vs. <PUW>), we see that none of the ratios differ from one by more than ±1 standard deviation. In contrast to Fig. 5 and Table 4, we also evaluated intercepts of regressions that were not forced through the origin; none of these differ significantly from zero (results not shown). From the statistical comparisons in Table 4, we conclude that the Th/γ pairs (Table 3) applied in the UW algorithm (Eq. 3) produce a precipitation rate consistent with the reference.

Values of the reference rate and the hotplate-derived rate (<PYES>) are compared as ratios in Fig. 5 and in the fourth column of Table 4. These ratios are seen to deviate systematically from unity and in the direction discussed in Sect. 3.8. In the unforced regressions (not shown) the intercepts are negative, but only one of these differed significantly from zero (NCAR/BTL; intercept =-0.3 ± 0.1). Negative intercepts are expected because PYES is positively offset, by ∼ 0.2 mm h-1 during most of the nondrip periods (e.g., 16:21 UTC in Fig. 4).

The 27 precipitation events are summarized in Table 5. Measurements were made during 2012, at the two southeastern Wyoming field sites (BTL and GLE), and during 2013 and 2014 at the western New York site (OWL). Table 5 and Fig. 6 have event-averaged ambient temperatures (<T>) and event-averaged ambient ice bulb temperatures (<TIB>). Twenty-three of the events have <T>≤-3.3 ∘C and upper-limit temperature (<T> plus two standard deviations) no warmer than -2.3 ∘C. We classified these as snowfall. In addition, we classified four events as rainfall. These had <TIB>≥+2.9 ∘C and a lower-limit temperature (<T> minus two standard deviations) no colder than +2 ∘C.

Figure 7b shows a plot of the Nu–Re fit function with the data used to constrain the function. This result is based on UW hotplate measurements (GLE site) and formulas developed in Sect. 3.7. Fit coefficients (α, β, and γ) are reported in Table 6 for each field site. Hansen and Webb (1992) reported α=0.09 and β between 0.69 and 0.72 for a surface similar to the hotplate (circular with three concentric rings); however, their flow direction was perpendicular to the plate surface. The values of α and β we report may differ from those in Hansen and Webb (1992) because the flow is principally parallel to the plate surface at our field sites. There are two other differences relative to Hansen and Webb (1992): (1) our geometrically averaged Nu (∼ 360) is about a factor of 5 larger, and (2) our Re extends over a much larger range. Finally, we note that compared to Fig. 7b there is an order of magnitude narrower Re range in the NCAR/BTL and UW/OWL Nu-Re plots (not shown).

Figure 7a is a companion to Fig. 7b showing the γ based on the warm–cold test. The error limit on this datum is explained in Sect. 4.1. Since Nu is dependent on the Th derived in the warm–cold test (Sect. 3.6), we expect the Nu-Re function to converge to the warm–cold γ in the limit of small Re. In our assessment of convergence, we evaluated the limiting Nu at the Re corresponding to the minimum U reported in the hotplate data output (0.1 m s-1). This minimum U establishes the left end of the function in Fig. 7b. Convergence of the Nu–Re relationship to within the error limit on the warm–cold γ, at the former's left-most limit, is evident in Fig. 7a–b. Convergence is also evident in the NCAR/BTL and UW/OWL plots analogous to Fig. 7a–b (not shown) and this in spite of narrower Re range in those data sets.

Figure 8 shows budget terms (Eq. 3) for one of the four rainfall events in our data set (OWL-15). The three output terms (sensible, latent, and longwave) and three input terms (top plate, longwave, and shortwave) are shown in Fig. 8a–b. In this section we begin with the latent power output (i.e., P⋅E/f2 in Fig. 8a) and describe how we calculate the rainfall rate. We also contrast that calculation with steps followed in the case of snowfall.

The first step in the calculation is the conversion of the latent power output term (Fig. 8a) to a provisional precipitation rate; this is done by multiplying each element of the term by the corresponding element of f2 (Eq. 9b). This operation is referred to as element-by-element vector multiplication. Thresholding is applied next. Both a 300 s running average of the provisional rate and a 10 s running average of the provisional rate are computed. If the 300 s average exceeds 0.25 mm h-1 and the 10 s average exceeds 0 mm h-1, the rate is stored as the 10 s average; otherwise the rate is stored as 0 mm h-1. We refer to the resultant as PUW, but we note that in Sect. 4.2 the PUW sequences are unthresholded. Both the thresholded and unthresholded sequences are presented in Fig. 8c–d. The thresholded PUW is identical to the unthresholded PUW where the 300 s average exceeds 0.25 mm h-1 and the 10 s average exceeds 0 mm h-1.

In the case of snowfall, the f2 is calculated using Eq. (9a) and applied as discussed in the previous paragraph. Finally, the precipitation rate is derived as the resultant of element-by-element vector multiplication of the thresholded PUW and the reciprocal of the snow particle catch efficiency (Sect. 3.9).

Here we use linear least squares regression analysis with a regression equation of form y=a⋅x to derive the ratio of two measures of liquid-equivalent accumulation for snow. In Fig. 9, these measures are the accumulations derived using the UW and YES algorithms. In the these algorithms the particle catch efficiency function is the one described in Y12 and f2 is 2.66⋅10-8 m J-1 (Sect. 3.8). The data points correspond to measurements made at GLE (UW hotplate), at BTL (NCAR hotplate), and at OWL (UW hotplate). We note that 19 of 23 y axis values are from the same instrument (UW hotplate) and are derived using the same calibration (UW/OWL) used to produce the result shown in the third row of Table 4. Statistical consistency between the ratio in Fig. 9 (0.79 ± 0.05) and the ratio in the third row of Table 4 (i.e., 0.79 ± 0.03 for the PREF on <PYES> ratio) suggest a systematic error in the YES-derived precipitation rates and accumulations. This assertion is reinforced by the three NCAR hotplate points straddling the best-fit line in Fig. 9 and by the ratio reported in Table 4 for the NCAR hotplate (i.e., 0.81 ± 0.03 for the PREF on <PYES> ratio). However, we cannot exclude the possibility that bias in our field-based calibration coefficients (α, β, and γ; Table 6) is the reason for a UW / YES ratio significantly smaller than unity in Fig. 9.

As was discussed in Sect. 4.2 and demonstrated in Fig. 4, during the indoor nondrip periods the PYES sequence is positively offset. A plausible reason for this, and for the ratios < 1 reported in the previous paragraph, is disregard of longwave forcing in the YES algorithm. Since we do not have access to the YES algorithm, we estimated the longwave radiative effect by setting the longwave terms to zero in Eq. (3). After doing this, a larger UW / YES ratio (a=0.83 ± 0.04) was obtained in a plot analogous to Fig. 9. From this modest increase of the UW / YES ratio, we conclude that longwave forcing cannot explain the shift of the best-fit line away from unity in Fig. 9. An even smaller perturbation of the UW / YES ratio was obtained in calculations that set the shortwave term to zero in Eq. (3) (results not shown).

Further evidence for systematic error in the YES values comes from Fig. 10. With the exception that these data are observed for rain at OWL (Sect. 5.1), the comparison in Fig. 10 is similar to Fig. 9. Although the number of points is small, Fig. 10 establishes that our finding of a UW / YES ratio significantly smaller than unity is true for both rainfall and snowfall. In addition, Fig. 11 strengthens this conclusion by showing agreement between values of the UW accumulation and the NOAH-II accumulation when both gauges detected rain.

An additional assessment of snowfall at OWL is presented in Fig. 12a–c. In these graphs the NOAH-II measurements are plotted on the abscissa and different interpretations of the UW hotplate measurements are plotted on the ordinate. For both devices, we plot the ratio of a liquid-equivalent accumulation divided by an event-averaged catch efficiency, and we note that the numerators of these ratios are accumulations that were not corrected for inefficient catch

This comparison was also made using accumulations corrected with a time-dependent catch efficiency (Sect. 5.3), but we found that the fit-line slopes differed by less than ±5 % from those in Fig. 12.

Consistent with the ranking of event-averaged values of E (Table 5), Fig. 12a shows that the hotplate values, derived with the hotplate U and the Y12 catch efficiency function, are smaller (on average) than the NOAH-II-derived values. We also see that the 15 % underestimate in the hotplate (Fig. 12a) reverses to a slight overestimate when using the R11 catch efficiency function (Fig. 12b) and when using the anemometer U with the Y12 function (Fig. 12c). These results do not allow us to specify contributions to the 15 % underestimate (Fig. 12a), coming from the fact that the Y12 function does not use a height-adjusted U, or from the suspected hotplate underestimate of U. Further studies that focus on the development of a hotplate catch efficiency function that is dependent on the local wind speed as opposed to the wind speed at 10 m (R11) and an investigation of the hotplate's determination of wind speed are needed to resolve this issue. Since there is error in the NOAH-II values used in this comparison, there is also a need for characterization of that uncertainty. The latter can propagate from the NOAH-II measurements themselves and from the catch efficiency function we applied to those data (Sect. 3.9).