The transfer functions presented in K2017b were developed for both unshielded and single Alter-shielded automated precipitation gauges by combining observations from the Geonor T-200B3 and OTT Pluvio2 gauges (hereafter referred to as the sensors under test, or SUT), after the authors demonstrated that the unshielded catch from both SUT types were very similar. Using the SEDS, further processing was applied to the SUT data (as justified in Kochendorfer et al., 2017a) using a minimum 30 min threshold defined as the median of the ratio of the SUT accumulation to that of the DFAR for the precipitation event threshold of 0.25 mm. This prevented the results from becoming biased towards the gauge used in the SEDS event selection. For wind speed, K2017b used the wind speed measurements available at each site and applied the log profile law to produce a 30 min average wind speed for both the gauge height (Ugh) and the standard 10 m height (U10m), either increasing speeds to U10m or decreasing speeds to Ugh, depending on which measured wind height speed data was deemed the best at each site. Catch efficiencies (CE) were then calculated for each event as the ratio of the 30 min SUT precipitation accumulation to that of the DFAR over the same period. From K2017b, two functional forms were used to fit the data as follows: 1CE=e-a(U)(1-tan⁡-1bTair+c), and 2CE=(a)e-b(U)+c, where U is wind speed (specifically either Ugh or U10m) in m s-1, Tair is air temperature in ∘C, and a, b, and c are coefficients to fit the data to the model. Equations (1) and (2) listed here are referred to as Eqs. (3) and (4) in K2017b. To reduce the impact of fewer events at higher wind speeds and the potential impacts of blowing snow, the SEDS data were filtered further to remove events with wind speeds higher than 7.2 m s-1 (9 m s-1) at the gauge height (10 m).

The key difference between Eqs. (1) and (2) is the inclusion of temperature dependency in Eq. (1). This allows for a continuous (3D) transfer function at all temperatures without having explicit knowledge of the precipitation phase. This curve is shown in Fig. 2 (red) for both the single Alter-shielded (solid) and unshielded (dashed) gauges at a temperature of -5 ∘C. Equation (2), however, requires an assessment of the precipitation phase (liquid, solid, or mixed), with each phase having unique coefficients. K2017b used temperature to discriminate the phases for Eq. (2) and assumed the following: solid precipitation occurs at Tair<-2 ∘C, liquid precipitation occurs at Tair>2 ∘C, and mixed precipitation occurs at -2 ∘C ≤ Tair ≤ 2 ∘C. The temperature thresholds for phase discrimination in the SPICE analysis are based on the disdrometer measurements of precipitation type from Wolff et al. (2015) and Kochendorfer et al. (2017a). Equation (2) is plotted in Fig. 2 (blue) using the coefficients for snow for the single Alter-shielded (solid) and unshielded (dashed) gauges. For both equations and gauge configurations, unique coefficients were derived for each of the two wind speed measurement heights. The SUT precipitation was adjusted using both Eqs. (1) and (2) by employing the appropriate coefficients, depending on the phase and/or temperature, wind measurement height, and shield configuration. For Eq. (2), precipitation classified as rain (Tair>2 ∘C) was assumed a CE equal to 1. The coefficients used in Eqs. (1) and (2) are detailed in K2017b and are not repeated here. Kochendorfer et al. (2017a, b) examined the use of more complex transfer function forms for adjusting solid precipitation measurements, such as the sigmoid function used by Wolff et al. (2015), but found that the simpler forms had similar bias and RMSE characteristics as the more complex forms.

Following the end of the SPICE project, the performance of the SPICE transfer functions was evaluated as described in K2017b, using the same SEDS data used to develop those transfer functions. As discussed above, the data from all eight sites in Table 1, including data from multiple gauges of the same configuration at each of the sites, were combined to fit the transfer function models. This model, developed by pooling the data from multiple sites, was then applied to each individual gauge at each site. By applying a model developed from data collected at multiple sites to individual gauges at each individual site, the authors maintained some distinction between the model development and the evaluation. The K2017b results were based on four metrics, namely the root mean square error (RMSE), mean bias, Pearson correlation (r), and percentage of events (PEs) between the DFAR and SUT that agreed within a specified threshold (typically 0.1 mm). It should also be noted that the overall performance metrics summarized in K2017b included all precipitation phases, whether adjusted by the transfer functions (i.e. solid and mixed) or not (i.e. liquid).

K2017b showed that the SPICE transfer functions reduced the overall bias in the unshielded precipitation gauges (both Geonor T-200B3 and OTT Pluvio2; all sites combined) from -33.4 % to 1.1 %, but the results varied by site, with CAR and WFJ showing an over-adjustment and HKL, FOR, and XBK showing an under-adjustment. For the most part, the r, RMSE, and PEs were slightly improved after the adjustment, but these also varied by site. K2017b also showed that, in general, the mountainous sites experienced larger errors after the adjustment, with one mountainous site (WFJ) being over-adjusted and the other two (HKL and FOR) being under-adjusted.

The impetus for this extended evaluation was twofold:

The methodology used during SPICE for developing and evaluating the transfer functions used only a subset of the observed data (the SEDS), and although this was a robust methodology for developing transfer functions, it did not provide a comprehensive evaluation of the adjustments under circumstances more typical of users collecting precipitation data in the field where the data are less filtered to remove smaller amounts.

The NAF algorithm removes noise in cumulative precipitation time series by iteratively balancing positive and negative noise and accumulating positive changes exceeding the noise by a user-defined threshold (Δ*; e.g. 0.05 or 0.2 mm, depending on the gauge precision; Smith et al., 2019a) such that the total accumulated positive increases in bucket weight after filtering are forced to equal the total end-of-season bucket weight. The algorithm removes random and systematic diurnal noise but does not account for signal drift (an example of signal drift is a decrease in weight that occurs due to evaporation of water from the gauge bucket). Signal drift can result in estimation errors, which can be mitigated using an iterative manual process, with the NAF output as a first guess. This process is called NAF supervised (NAF-S) and lets the user select the beginning and the end points of the segments within the time series where evaporation is occurring. The process then removes these segments so that they have no impact on the time series. Because there is some user subjectivity in selecting the beginning and end points of the impacted segments, this process is completed by a single user employing predetermined and consistent criteria. Although beyond the scope of the present work, testing NAF and NAF-S on both simulated and observed precipitation time series over an entire winter season, including both noise and evaporation drift, showed the technique to be effective, with low error compared to the control. The end product of the NAF-S filter is a clean, time-consistent 1 min accumulating time series with preserved data gaps (i.e. no gap filling) for each gauge configuration for each season.

To produce accumulation periods consistent with the K2017b validation, the 1 min NAF-S precipitation accumulation time series were resampled to 30 min accumulation amounts via differentiating the bucket weights between the start and end of the 30 min period. The continuity of the time series was maintained, despite data gaps, through the assumption that the gauge continues to accumulate precipitation despite logger or power outages. In the event of missing data, precipitation accumulation during outages was calculated based on the differential bucket weight between the start and end of the outage and recorded as an accumulation at the end of the outage. Although this preserves the total accumulation during the outage, information related to the timing of the events during the outage is not preserved, and the accumulation data need to be flagged. Protocols for adjusting the data for undercatch are noted below.

The 1 min wind speeds (U10m and Ugh, where available) and air temperatures (generally measured at 1.5 m) were averaged over the same 30 min periods as the accumulated precipitation amounts. Site-specific details on the ancillary measurements can be found in the SPICE site commissioning reports (referenced in Sect. 1). If more than 10 min of wind or temperature data were missing in any 30 min period, the data were flagged as missing and were not used in the adjustment procedure.

The resultant time series for each test gauge at each site were adjusted separately using both Eqs. (1) and (2). Each 30 min accumulation was adjusted individually if the following conditions were met: (1) both the start and end bucket weights for the 30 min period were not missing, such that the differential could be determined, and (2) no more than 10 of the 30 min values of either wind speed or temperature were missing. Periods that did not meet these criteria were preserved in the time series but were flagged as being unadjusted and were not included in the validation.

For adjustments using Eq. (1), the predetermination of the precipitation phase was not necessary as the transfer function is continuous with temperature and not directly dependent on the precipitation phase. For the purpose of adjusting precipitation using Eq. (2), the phase is determined by air temperature using the phase regimes outlined in Sect. 1.1 with rain assuming a catch efficiency of 1 (and is therefore not adjusted). The relative total amounts (snow, mixed, and rain), as measured by the DFAR at each site, are shown in Table 1. The same maximum wind speed thresholds for the adjustments were employed here as in K2017b, which were 7.2 and 9.0 m s-1 at gauge height (generally 2 m above ground) and at a 10 m height, respectively. Wind speeds above these thresholds were set at the threshold value to avoid over-adjustment and increased uncertainty in the transfer functions above the wind speed threshold. Figure 2 suggests that Eq. (2) can exceed a catch efficiency of 1 at low wind speeds. There is no obvious physical explanation for the portion of the Eq. (2) catch efficiency function (originally published by K2017b) that is >1.0, and this is related to the empirical fit of the catch efficiency curve to the original SPICE data. For the current assessment, calculated catch efficiencies > 1 were infrequent, and occurrences were automatically set to 1.

The resulting data (https://doi.org/10.1594/PANGAEA.907379; Smith et al., 2019b) include a subset of adjusted and unadjusted 30 min precipitation amounts for each SUT gauge configuration at each site (adjusted using Eqs. (1) and (2), using either Ugh or U10m or both, where available), the 30 min DFAR data, and the accumulated gap-preserved time series for each, with flags identifying the periods that were not adjusted.

Four complementary statistical metrics are used to assess the performance of the transfer functions for adjusting precipitation. These are relative total catch (RTC), root mean square error (RMSE), Pearson correlation (r), and percentage of events (PEs) within 0.1 mm of the DFAR-reported values. RTC is the ratio of accumulated catch of the SUT to that of the reference over the same period and using the same filter or thresholds (i.e. for snow). RTC is expressed as a percentage of the reference precipitation amount and reflects the capability of the transfer functions to adjust seasonal and long-term precipitation totals, with a perfect seasonal adjustment having an RTC of 100 %. Hence, it can be used to assess the improvement in the seasonal bias following the adjustment.

Root mean square error is used to estimate the magnitude of uncertainty in the 30 min unadjusted and adjusted SUT measurements relative to the DFAR. The ideal value of the RMSE is 0 mm, indicating a perfect agreement between the 30 min SUT observations and those from the reference; however, the variability in the magnitude of the RMSE amongst the sites should be interpreted with caution as a small RMSE at a site with low precipitation rates may be more significant than a higher RMSE at a site that has higher precipitation rates. For that reason, the RMSE will be used mainly to assess the relative performance of Eqs. (1) and (2) at each site and the relative performance of the transfer functions for the single Alter-shielded and unshielded gauges.

The Pearson correlation assesses the strength of the linear correlation between the 30 min measurements made with the SUT and the reference DFAR before and after adjustments, using Eqs. (1) and (2). This metric provides an overall indication of the changes in the differences between SUT and reference measurements but does not provide an indication of the changes in the bias or the magnitude of differences.

The PE statistic is the percentage of 30 min events measured by the SUT that differs from the DFAR by less than a predefined threshold (0.1 mm in this analysis) and is calculated as follows: 3PE=nTn×100%, where n is the number of 30 min events considered in the analysis and nT is the size of the subset of n where |DFAR - SUT|<0.1 mm. PE was introduced as a metric for assessing transfer functions in K2017b, with the 0.1 mm threshold based on the measurement uncertainty of the reference configuration as investigated during WMO-SPICE (Nitu et al, 2018). Ideally, applying a transfer function to adjust the systematic bias (undercatch) in precipitation measurements would increase the magnitude of SUT observations to be closer to the reference measurements, thereby increasing PEs. A perfect agreement between the reference and the SUT, within the 0.1 mm threshold, would produce a PE of 100 %. Hence, PE provides additional event-based perspectives on how adjustments impact the bias and uncertainty that are not captured by the other metrics used in the assessment.

The assessment considers the overall performance for all precipitation types combined and for snow alone. In the latter case, the assessment of snow adjustments using Eq. (1) employs the same temperature threshold for snow as K2017b, namely Tair<-2 ∘C. Assessment results are reported for both unshielded and single Alter-shielded gauge configurations, which can be either a Geonor T-200B3 or OTT Pluvio2. Where multiple gauges of the same configuration are present at a site, these gauges are assessed both individually and as a combined data set.

For evaluation purposes, and where possible, the following circumstances are assessed for all precipitation types (including rain, snow, and mixed) and snow only: (a) adjustments using Eq. (1) vs. Eq. (2), (b) adjustments using gauge height vs. 10 m wind speeds, and (c) adjusting single Alter-shielded vs. unshielded gauges. Based on site-by-site evaluations, some insight is provided as to the performance of transfer functions in different environments and under different climate characteristic conditions.

The impact and the performance of transfer functions used for adjusting precipitation can be examined by comparing the accumulation time series for unadjusted and adjusted data to the reference. Figures 3 and 4 show the unadjusted, adjusted (Eq. (1) only), and reference (DFAR) time series of precipitation accumulation for the unshielded and single Alter-shielded gauges at all sites for the 2015/2016 and 2016/2017 winter seasons, respectively. Where more than one gauge with the same shield configuration was present at a site, and where more than one wind speed height was available, results for only one gauge and wind speed height were selected for illustrative purposes.

Figures 3 and 4 show the relative impacts of wind on undercatch for each of the eight sites and the relative effectiveness of the transfer function adjustments on each SUT configuration (shielded and unshielded) for the two winter seasons separately. Note that the season lengths vary by site and season (depending on both the actual length of the winter season and on data availability), and the scale of the vertical axis changes with site and season to show the relative scale of the bias and the adjustment. Gaps in the series represent missing data, with total accumulations during the gap obtained from the bucket weight change (in both the DFAR and the SUT); the gap accumulations were preserved but not adjusted.

The precipitation amounts vary by site and season, but the general trends in the SUT undercatch, compared to the DFAR, are consistent. Accordingly, the impact of the adjustment also appears to be consistent. Without considering precipitation-phase partitioning, unadjusted precipitation (solid lines) relative to the DFAR was always lowest at the windy sites of XBK and HKL. Referring to unadjusted precipitation, unshielded gauges (blue lines) always catch less precipitation than the single Alter-shielded gauges (red lines) at all sites and during both winters. The transfer function (only temperature-dependent Eq. (1) adjustments are shown here) appears to be less effective at the windier sites (wind speeds during precipitation events are shown in Table 2), with a substantial undercatch remaining after the adjustment. Furthermore, precipitation is over-adjusted at some of the less windy sites (CAR, CCR, and SOD).

The RTC metrics for the single Alter-shielded gauges are shown in Table 2 and for the unshielded gauges in Table 3 for Eqs. (1) and (2), combining the data from the two intercomparison seasons (CCR being the exception, since data are only available for 2016/2017). RTC is shown for all precipitation phases and for snow and for both wind measurement heights (U10m and Ugh), where available. If there are multiple gauges per site, the RTC is reported separately for each gauge and for the combined gauge data set. Figure 5 summarizes the snow RTC in the tables for the combined data for both winter seasons. When more than one gauge exists, the Ugh was used for the adjustment for all sites except FOR, which only reported U10m.

The RTC values in Tables 2 and 3 indicate that the unadjusted catch for snow is lower than the unadjusted catch for all precipitation types at most of the sites. The magnitude of the difference depends on the relative amounts of solid and liquid precipitation received during the season and the wind speeds during snow. The biggest difference in the unadjusted RTC values between all precipitation types and snow occurred at sites where more rain occurred during the intercomparison season, as the gauge catch for rainfall is naturally higher (Yang et al., 1998; Smith, 2008) and biases the total catch. At XBK, CAR, FOR, and HKL, removing rain and mixed precipitation from the statistics had a large impact on the RTC, both pre- and post-adjustment, and provided a more realistic metric for assessing how well the transfer functions were performing for the adjustment of snow measurements.

Although the sample size is smaller (fewer unshielded than single Alter-shielded gauges), the unadjusted catch of the unshielded gauges (Table 3) was lower than the unadjusted catch of the single Alter-shielded gauges (Table 2). From the single Alter-shielded RTC in Table 2, focusing on snow, the differences between Eqs. (1) and (2) results were small, varying within 1 % to 2 %. This can also be seen in the combined results in Fig. 5. The difference between Eqs. (1) and (2) was greater for the unshielded gauges (Table 3), with Eq. (1) performing better than Eq. (2) for snow at XBK (+12 %) and HKL (+10 % using Ugh). Equation (2) tended to under-adjust the unshielded gauges more than Eq. (1) at XBK and HKL.

At sites with both wind speed heights available for use in the adjustment (namely XBK, CAR, HKL, and MAR), the data shown in Table 2 for single Alter-shielded gauges suggest that using Ugh reduces the extent of over-adjustment (CAR and MAR) or under-adjustment (XBK and HKL) relative to U10m (i.e. adjustments closer to 100 %). This holds for the unshielded gauge adjustments in Table 3 with the exception of MAR, which shows a large under-adjustment using Ugh as compared to U10m. This may suggest that Ugh wind speeds are biased low at MAR, which is consistent with comments made by Kochendorfer et al. (2017a), who stated that the ground height wind measurement were shadowed in some directions. Although the sample size was small, there is reason to suggest, from an RTC perspective, that Ugh outperforms U10m when used in Eqs. (1) and (2) for adjusting snow measurements. For this reason, where available, the Ugh rather than U10m wind adjustments are shown in Fig. 5 and in subsequent figures.

The differences in RTC for the adjusted measurements from single Alter-shielded gauges versus those from unshielded gauges are mixed. At the windier HKL and XBK sites, Fig. 5 suggests that the adjusted RTC for the unshielded gauge is just as high as, or higher than, for the single Alter-shielded gauge (Eq. (2) at XBK being the exception). The over-adjustments at SOD and CCR are exaggerated for the unshielded gauge, but the unshielded adjustment is closer to 100 % at CAR and WFJ. MAR is an outlier in Fig. 5, possibly due to the potential issue with Ugh, but the U10m adjustment of the unshielded gauge (Table 3; snow) has an RTC closer to 100 % (105 % and 106 % for Eqs. (1) and (2), respectively) than the single Alter-shielded gauge (117 %).

Including the RTC for both wind speed heights but excluding the combined gauge statistics, the adjustment for snow using Eq. (1) increases the mean catch efficiency for the single Alter-shielded gauge from 61 % to 88 % and for the unshielded gauge from 48 % to 92 %.

Table 4 (single Alter-shielded gauges) and Table 5 (unshielded gauges) show the RMSE for each available SUT at each site and the RMSE when multiple SUTs are combined. As with RTC, the metric is provided for both transfer functions and using both wind speed heights where available.

Comparing the RMSE values between Tables 4 and 5, the RMSE values for both the adjusted and unadjusted unshielded gauges are higher than their single Alter-shielded counterparts. However, the RMSE differences between all precipitation phases and those for snow are inconsistent, with RMSE occasionally being lower for snow than for all phases and vice versa. For the single Alter-shielded and unshielded gauges, respectively, 46 % and 36 % of the RMSE values are either lower or the same for snow as compared to all precipitation phases. The differences in adjusted RMSE with wind measurement height are also small. For single Alter-shielded gauges, CAR has a lower RMSE for Ugh, MAR has a higher RMSE for Ugh, and HKL and XBK show similar RMSE values for Ugh and U10m. For unshielded gauges, the RMSE for Ugh is lower than that for U10m at XBK and CAR, and higher at HKL and MAR.

When considering each gauge at each site, the anticipated decrease in the RMSE following the adjustment (whether for all precipitation types or snow only) is not universal. This is illustrated in Fig. 6 which shows the RMSE results for combined SUT snow data sets before and after the adjustment using U10m (where possible). For single Alter-shielded gauges, the RMSE increases with the adjustment at CAR, MAR, SOD, and WFJ (although the increase is small at all sites but WFJ). The decrease in RMSE is small at XBK and CCR. The differences between RMSE results, using Eqs. (1) and (2), for single Alter-shielded gauges are insubstantial (<0.005 mm). These differences are larger for the unshielded gauges, as shown in Fig. 6 (as high as 0.05 mm).

Similar to previous metrics, the single Alter-shielded and unshielded r values are shown separately in Tables 6 and 7, respectively, and are plotted for snow in Fig. 7. In theory, the adjustment using a transfer function should strengthen the linear relationship (increase r) between the adjusted and the reference measurements by removing the nonlinearity associated with wind bias.

For single Alter-shielded gauges, unadjusted r values for all precipitation types range from 0.83 at HKL to 0.96 at CCR. For unshielded gauges, the unadjusted r values for all precipitation types are only slightly lower than their shielded counterparts. The unadjusted r values for single Alter-shielded gauges for snow are generally lower than for all precipitation types, especially at the windy sites of HKL and XBK. The unshielded, unadjusted values for snow follow similar trends to all precipitation types.

The results show that adjusting measurements for all precipitation types with either transfer function has little impact on the r values, with greater variability in r values observed for the unshielded gauges. The impact of adjustments on snow measurements are shown in Fig. 7. Generally, the r values for the single Alter-shielded gauges are improved with adjustment, but the change is small (<0.07). The largest improvements are observed for the HKL and XBK measurement data sets. With the unshielded adjustment, unshielded gauges at most sites also show an improvement in r values with adjustment, with the most significant increases observed for the HKL and MAR data sets.

For both all precipitation phases and snow only (Fig. 7), the differences between r values following the application of Eqs. (1) and (2) are negligible for the single Alter-shielded gauges. For the unshielded gauges, Eq. (2) results in higher r values than Eq. (1), but the differences are very small (<0.03).

For sites with both wind speed measurement heights, the correlations appear to be independent from the measurement height. The only exception is for the unshielded adjustment of snow measurements at MAR, where correlations based on the transfer function application using Ugh are significantly less than those using U10m. This likely results from shadowing effects on the Ugh data.

As shown in Table 8, the PEs for the single Alter-shielded gauges did not generally increase following adjustment, contrary to what was observed in K2017b. Similar to the observed trends for r and RMSE, the change in PEs following the adjustment of the Alter-shielded gauges was small, typically within ±5 %, with the only exception to this being at FOR (+10 % for snow).

The unshielded gauges showed a greater change in PEs following the adjustment (Table 9). For all precipitation, the difference in PEs before and after the adjustment was generally small (MAR and FOR being the exceptions with a 10 % increase), but the change for snow was more substantial. As shown in Fig. 8, PEs for snow were found to decrease by more than 6 % at some sites following the adjustment (namely XBK, CCR, and SOD) and increase by more than 9 % at others (namely CAR, MAR, and WFJ), with changes varying between -8 % and +17 %.

Similar to the other metrics, PEs do not show any consistent advantage to either Eq. (1) or Eq. (2), with differences being less than 2 % (most being less than 1 %). There also does not appear to be any clear or consistent advantage in using Ugh vs. U10m, with differences in PE values generally within 2 %.