Haukeliseter test site is situated on a mountain plateau in southern Norway (59.82∘ N and 7.21∘ E at 991 m a.s.l.), see Fig. 1. All instruments are placed on a 5000 m2 flat area, surrounded by topographic variations up to 20 m in the immediate vicinity and then slowly increasing to the surrounding mountain tops which are between 100 and 500 m higher.

The area is situated between two lakes and the closest mountaintop (distance 1 km) has an altitude of 1162 m a.s.l., located towards the northeast. The mountains to the east are ca. 1250 m a.s.l. at a distance of 2 km. The terrain is more open towards the south and the west, with mountains 4 and 3 km away, respectively.

Precipitation sensors are mounted side by side perpendicular to the prevailing wind from easterly and westerly directions in order to minimize mutual disturbances. The reference configuration at Haukeliseter consists of an automatic precipitation gauge (Geonor T200-BM, 1000 mm, 3 transducers; Geonor AS, Norway) and an Alter wind shield, both centred in an octagonal double fence (DF) construction that effectively minimizes the wind-influence on the precipitation measurements. The DF is similar to the Double Fence Intercomparison Reference (DFIR) of the first WMO intercomparison (Goodison et al., 1998) where it is used with a Tretyakov manual gauge. The combination of the DF and the automated gauge at Haukeliseter also fulfils the specifications for the official DFAR (Double Fence Automated Reference) of the ongoing WMO-SPICE (WMO/CIMO, 2012).

Additionally, measurements of numerous other meteorological parameters are performed to support the analysis of the precipitation data. Air temperature is measured with a pt100 element (1/10 DIN) protected by a standard Norwegian radiation screen, installed at gauge height on a tower close to the DFIR.

Wind is measured by different sensors at several places around the measurement site. Standard 10 m wind measurements are performed at the tower close to the DFIR with an ultrasonic wind sensor from Gill (Windobserver II with extended heating). Three wind sensors are directly mounted to the precipitation gauges for measuring wind at gauge height (Windobserver II at precipitation gauge inside DFIR, and Young Wind Monitor SE at the two closest precipitation sensors – X1 and X2, see layout). In 2013, a Thies Ultrasonic Wind Anemometer 3-D was installed on a separate mast at 4.5 m (gauge height) to allow measurements undisturbed by the precipitation sensor installations (see Sect. 3.1.2).

Several optical precipitation detectors (Thies precipitation sensor) are placed on the two 10 m masts at the site. In the described event selection, one of these sensors (selected because of its stability over the course of the experiment) is used for the event selection, see Sect. 3.1.1.

Furthermore, one forward scatter instrument (Vaisala PWD 21) and two disdrometer type instruments (Thies LPM and Ott Parsivel) are installed on the meteorological mast close to the DFIR, providing additional information on the precipitation type, see Sect. 3.3.3.

Further information about the test site, including an evaluation of the homogeneity and a list of instruments, can be found in Wolff et al. (2010, 2013).

The Haukeliseter test site was chosen because of its significant number of snow events often paired with high wind speeds during the 6 to 7 month-long winters. Solid precipitation is commonly observed between October and May, but can also occur during the summer months. The mean annual air temperature (MAAT, 1961–1990) for the site is 0.6 ∘C. Mean monthly temperatures are below 0 ∘C for the period November to April, with an estimated mean air temperature (1961–1990) of -5.4 ∘C. The estimated, uncorrected annual precipitation (1961–1990) is approximately 800 mm of which more than 50 % is solid precipitation. In a normal winter, the average snow depth reaches approximately 1.5–2.0 m.

Further, 10 years of winter observations from the nearby manual station “Haukeliseter Brøytestasjon” (800 m distance) operating between 1984 and 1995 reported a significant number of snow events with maximum wind speed above 15 m s-1. These observations also contain a frequent occurrence of blowing and drifting snow, a significant number of these below eye-height. The precipitation gauges at Haukeliseter are therefore mounted relatively high – at 4.5 m – in order to minimize the influence of blowing and drifting snow on the measurements.

Data for this study were collected over the course of three winters, from early 2011 until May 2013. Figure 2 shows the monthly precipitation and mean temperature anomaly with respect to the normal period 1961–1990 for all measurement months, based on data from the official nearby meteorological station Vågsli (821 m a.s.l., located 10 km to the east). Months not identified as “measurement months” are used for maintenance and upgrades of the equipment at the test site.

All three months of the first period in 2011 were characterized by a higher precipitation amount than normal. Whereas February 2011 was relatively cold, March and April 2011 were rather warm. April 2011, with a mean temperature of 4.8 ∘C above the normal monthly mean temperature, was registered as the warmest April since 1900 in large areas of southern Norway.

The second winter (November 2011–April 2012) was continuously mild (with the exception of April 2012) and a higher precipitation amount than usual was registered (with the exception of March 2012). In December 2011, more than double of the normal monthly precipitation amount was observed. March 2012 was the warmest March ever recorded in western and eastern Norway. The mean temperature at Vågsli was 6.2 ∘C above the normal monthly temperature.

The third winter was characterized by low temperatures. Whereas during February and March 2013 very little precipitation occurred, April and May 2013 were characterized by very high precipitation amounts.

Catch ratios between standard Geonor configurations and the DF-Geonor for all identified events are calculated. Figure 3 shows the results for the southern Geonor precipitation gauge X2 (see layout in Fig. 1), as this sensor provides the most stable data set. The large amount of scatter visible in panel a (all events), including some very clear outliers, makes it necessary to evaluate the influence of various parameters in more detail.

A few negative catch ratios are visible in panel a, which are mainly due to only small accumulation inside the DF-Geonor and no significant accumulation in the X2-Geonor. For these cases the noise of the transducers dominates the X2-signals. They subsequently vary around zero, thus resulting in negative catch ratios. For panel b an additional threshold is introduced, accepting only events for which the X2-Geonor collected more than 0.1 mm, and thus removing the unrealistic very small or negative catch ratios. About 5 % of the recorded events inside the DF at Haukeliseter show no significant accumulation in the gauges outside.

Since the installations are optimized for minimized influence under prevailing wind directions (installation along a line, see site layout in Fig. 1), shadowing effects on the precipitation measurements are likely for other wind directions. Precipitation measurements by the Geonor X2 will be mostly affected by shadowing for wind directions between 355 and 55∘. Panel c shows all events where these wind directions are removed using data from the wind sensor at 10 m height. The resulting data points show a little less scatter for lower wind speeds. The effect is more visible when considering only snow events. Panels g and h are based on the same data as in panel c, but show only data measured at temperatures below 0 ∘C and below -2 ∘C, respectively.

Variations of both temperature and wind speed during an event are evaluated. Events with a standard deviation smaller than 0.2 ∘C during the event period are shown in panel d, although other thresholds are tested (not shown). It seems most natural to weight wind speed variations by the mean wind speed. The maximum ratio between the standard deviation of wind speed and the mean wind speed is set to 0.2 for the events shown in panel e. The same filters are applied in panel f as for panel e, however only events with mean temperature below -2 ∘C are shown. These latter filter methods for temperature and wind speed variations do not improve the catch ratio data set from Haukeliseter. Removed data points are evenly spread and no significant noise reduction is achieved. Therefore, no thresholds for limiting temperature and wind speed variations are used for the further analysis.

In a further step, the data set is analysed qualitatively in order to get a more detailed understanding of how the catch ratio is influenced by various parameters. For this purpose, the data set is divided into classes for temperature, wind, precipitation type and intensity.

The qualitative analysis indicates a clear temperature dependence of the catch ratio and a non-linear relationship on the wind speed. Precipitation events which are clearly identified as rain or dry snow show two very different catch ratio relationships. It is, however, desirable to develop only one transfer equation considering a continuous transfer from dry snow over mixed precipitation to rain based on data available at standard weather stations: precipitation, wind and temperature.

How well the derived function and associated covariates described the actual catch ratio is evaluated by analysing the residuals. Standardized residuals, which are the original residuals normalized to have zero expectation and unit variances, are plotted in Fig. 10.

No signs of model misspecification can be seen for the wind speed and temperature covariates. Plotting the residuals against the true precipitation, measured in the DFIR, yields a trumpet shape, which may indicate that the noise variance is dependent on the amount of true precipitation. The panel showing the theoretical quantiles of a normal distribution versus the actual sample quantiles reveals that the residuals have a heavier tail than a normal distribution, which also indicates a non-sufficient description of the noise or uncertainty of the adjusted values.

The precipitation events from 13 effective measurement months contain a large range of event average wind speeds. For the first time, an adjustment function can be derived from a sufficient number of events with wind speeds larger than 7–9 m s-1. The derived transfer function is valid for event average wind speeds up to 15–20 m s-1, which occurred frequently at Haukeliseter. The data clearly support the assumption of a stabilization of the precipitation loss for higher wind speeds. It seems therefore possible to apply the transfer function for even higher wind speeds, since an extrapolation beyond the area of validity does not change the catchment efficiency any further.

In this study, wind speed is measured with sensors mounted at 10 m height (WMO standard) as well as at gauge height (4.5 m for all gauges). As described in Sect. 3.1.2, gauge height wind measurements are partly affected by nearby installations and only unaffected measurements are used for the analysis. Both data sets are used and two different versions of the adjustment function are determined, to be used with 10 m or gauge height wind, respectively. The resulting adjusted precipitation amounts, calculated with either version of the transfer function, agree extremely well. That might be different for gauges at another installation height. A lower gauge height, for example, would result in a larger difference between 10 m and gauge height winds. The use of wind data at gauge height is therefore recommended wherever possible.

The developed adjustment function is solely based on winter data. Nevertheless, quite mild events are also part of the analysis (up to ca. 6–7 ∘C monthly average temperature), thus covering all three major precipitation types: snow, mixed precipitation and rain. The results for the analysed warmer rain events are very clear and consistent. Summer precipitation, however, is typically characterized by a larger variety of rain types, covering very light long-lasting drizzle to heavy rain or hail showers. That might create quite different precipitation intensities than those observed during this study. An application for temperatures larger than 3 ∘C is therefore not recommended, until studies evaluating explicitly summer precipitation are available.

Non-systematic scatter can be reduced significantly by means of relevant filters before the Bayesian statistic is applied. The necessity of this method can be confirmed by trying to retrieve the adjustment function based on the unfiltered data set. Some of the derived parameters defining the adjustment function are significantly different and less able to reproduce the real data set. The catch ratios at higher wind speeds, for example, stabilized at a higher value than the adjustment functions based on the filtered data sets suggest.

The scatter, however, is not eliminated completely. The catch efficiency still varies for individual events, especially for mixed precipitation events. Consequently, the resulting adjustment function does not correct the measured precipitation amount perfectly, i.e. adjusting individual events can result in over- or underestimation of the true amounts. An application of the adjustment functions over a longer period, however, should balance out these errors.

Precipitation data sets from operational stations can contain accumulation records not related to precipitation. Wind measurements from wind sensors which are not adequately mounted might lack the necessary quality for a successful use of the adjustment function. This study shows the importance of an extensive quality control of the observations before the application of the adjustment function.

As a matter of course, trace events, i.e. with non-measurable precipitation, cannot be corrected by the presented function. During the course of this study about 5 % of the recorded events (compared to measurements inside the DF) at Haukeliseter showed no significant accumulation in the standard gauges outside the DF. The accumulated sum of these events adds up to 10 % of the observed precipitation at Haukeliseter. These values depend highly on the local climate and are probably very site specific; they may add up to a considerable amount. When correcting precipitation data from a climate perspective, a separate consideration of these trace amounts is necessary, as for example done by Mekis and Vincent (2011).

In Norway, as well as in other countries, the most usual reporting interval at automated weather stations is 1 hour and the adjustment functions are optimized for that time interval. Historically, larger time intervals (12 and 24 h) are widely used. The adjustment function has been applied, successfully, for these longer time intervals for the available data from Haukeliseter in preliminary tests. The length of the precipitation events does not, of course, always match the longer time periods represented by the average wind speed and temperature observations. Precipitation might occur at temperatures and wind speeds quite different from the averages and thus larger uncertainties have to be taken into account when correcting the precipitation loss.

The precipitation event averages of both temperature and wind speed in the present data set cover the climate variations commonly expected in the Norwegian mountains, suggesting that the presented adjustment functions can also be applied to data from other Norwegian sites. However, the influence of other parameters, such as humidity or pressure, has not been studied and no systematic evaluation of the adjustment functions with data from other sites has been performed yet. It is therefore not known to what extent the present adjustment study is valid for sites in other climates and at other altitudes. The co-operation within WMO SPICE, with 20 sites in very different climates, will help to answer this question.

The new adjustment function is based on sufficient data covering low and high wind speeds, thus allowing an extension of the validity beyond 7 m s-1 up to 15–20 m s-1. Furthermore, it is suitable for all precipitation types, hence avoiding discontinuities resulting from the use of different equations for each phase. Comparisons with the old equation set by Førland et al. (1996) do not show significant differences for the adjustment of snow events for wind speeds lower than 7 ms-1 and well below O ∘C. It can easily be seen that the old equation quickly approaches zero as the wind speed grows beyond 7 m s-1, yielding unrealistically large amounts of precipitation. A truncation, where wind speeds above 7 m s-1 are set to 7 m s-1, is therefore commonly applied in Norway. Even then, the framework by Førland et al. (1996) differs significantly from the one presented in this study. Figure 11 shows that, for temperatures close to 0 ∘C and wind speeds above 7 m s-1, the truncated version of the old equation adjusts up to 50 % more precipitation than the new one. This overcorrection is still present for wind speeds below 7 m s-1 and decreases with further decreasing wind speeds. A comparison for temperatures above zero is not performed since this involves a third determinant, intensity, in the old correction method.

It should be mentioned that the results from Førland et al. (1996) are based on a manual reference, with a Tretyakov gauge inside the DF. The aerodynamical characteristics of a Tretyakov are surely different from those of a Geonor/Alter shield configuration as used in this study. However, it can be assumed that the effect of the double fence around these different gauges will dominate the overall aerodynamics of the reference system. Therefore, no large deviations are expected. The possible effect of this difference will probably be quantified during SPICE using data from those sites, which are equipped with both references.

As seen in the residual analysis, the regression noise is not optimally described with Eq. (). There are quite clear indications of heteroscedasticity in the residuals for increasing true precipitation. Heteroscedasticity is not expected to create any bias, but it does indicate that the uncertainty analysis could be inaccurate. Heavy-tailed residual distributions are also noted. This suggests that the residual distribution belongs to another family than the normal distribution, though symmetric around zero. Uncertainty analysis therefore becomes imprecise and adds to the problems caused by heteroscedasticity.

A further, and perhaps more important, source of inaccuracy is how the regression result is used in this study. It is applied in an inverted form to derive the true precipitation from the ratio. The statistical properties of this quantity, which in the Bayesian formulation is a distribution, are not clear. Adding the fact that the noise is subject to misspecification, makes uncertainty analysis about the true precipitation estimate substantially unreliable at this stage.

While it may be sensible to model the distributional properties of the measured precipitation as a function of wind speed, temperature and the true precipitation, the objective is to use this to predict true precipitation given wind speed, temperature and measured precipitation, as formulated in Eqs. () and (). These formulae however, only relate to estimates of R and the measured precipitation, and do not consider the distributional aspects. A multivariate model for true and measured precipitation would allow for expressing one as a distribution of the other, whether true or measured precipitation is of interest. It is also worth noting that even with a normally distributed R as the denominator, the resulting distribution will be the rather unfamiliar reciprocal normal distribution, which is heavy-tailed and bimodal. The bimodality might not be a problem as long as we require a positive R, but the tails are so heavy that the expectation is not available, making it difficult to evaluate bias. If a distribution with heavier tails is considered for the noise terms, such as the t-distribution, even more inflated tails can be expected. Medians are however preserved during monotonic transformations, which should make Eqs. () and () valid as median estimates.

The two aforementioned statistical issues – the distribution of the inversion and specification of the regression noise – are beyond the scope of this study, the main objective of which is to develop an adjustment function for measured precipitation. Further investigations with alternative regression models able to deliver a more reliable framework for the uncertainty analysis are currently in progress.

A thorough evaluation of the validity of the adjustment functions and a quantification of the actual improvement of the precipitation data, require a detailed study of a large number of individual events as well as time series of various lengths, and would also include data from other sites. The data sets from the similarly equipped WMO SPICE host sites will form a unique database for this kind of study and parts of it will surely be performed within the SPICE effort.

At the time of writing, only a very limited set of data that could be used for evaluation is available. Most of the data are already used in the derivation, and thus do not constitute an independent data set. Therefore, only a few preliminary results can be shown here to illustrate the effects of an application of the adjustment functions.

The adjustment function is applied to precipitation data from two individual events, representing a snow and a mixed precipitation event, see Fig. 12. In addition, data from two longer periods of time in March 2011 and March 2012 are analysed. The results are summarized in Table 2. In all four cases a significant improvement is achieved. Differences between the adjusted precipitation amount and the reference value (measured inside DFIR) are both positive and negative, which might indicate that the remaining differences are actually representing the uncertainty of the method. For the two cases where the original difference was 32 %, the adjusted precipitation amounts differed by less than ±10 % from the DFIR measurements. The remaining differences after adjustment of the two cases with the larger original differences (52 and 74 %) are 20 and 16 %, respectively.