Hydrologic measurements are important for both the short- and long-term
management of water resources. Of the terms in the hydrologic budget,
precipitation is typically the most important input; however, measurements
of precipitation are subject to large errors and biases. For example, an
all-weather unshielded weighing precipitation gauge can collect less than
50 % of the actual amount of solid precipitation when wind speeds exceed
5 m s
Precipitation measurements are used by policy makers, hydrologists, farmers, and watershed managers to quantify and allocate the water available for society's needs. Precipitation measurements are necessary for public safety in areas as diverse as avalanche control, flood forecasting, roadway safety, and aircraft de-icing operations. Precipitation measurements are also used to evaluate radar-based estimates of rainfall, to monitor climate change, and help improve climate and weather models. More specifically, monitoring changes in the frequency, intensity, and duration and phase of precipitation is critical for current and future climate research (Barnett et al., 2005; Blunden and Arndt, 2016; Trenberth, 2011; Trenberth et al., 2003). Although precipitation has been monitored for many centuries, the need to accurately measure precipitation will become even more important in the future, as changes in precipitation are predicted to be complex and variable with location, requiring robust and accurate precipitation measurements (Trenberth, 2011). Despite this critical need, precipitation observations are still beset with significant biases and errors (e.g., Adam and Lettenmaier, 2003; Førland and Hanssen-Bauer, 2000; Groisman and Legates, 1994; Scaff et al., 2015; Vose et al., 2014; Yang et al., 2005).
Solid precipitation is particularly difficult to measure accurately, and biases between wintertime precipitation measurements made using different technologies, in different measurement networks, or across different regions can be larger than 50 % (Mekis and Vincent, 2011; Rasmussen et al., 2012; Yang et al., 1999). Previous studies have identified wind effects as one of the primary causes for snow undercatch (e.g., Folland, 1988). This is due to two important factors: (1) the relatively slow fall velocity of snow, and (2) the creation of flow distortions of similar magnitude to the snowfall velocity by the gauge itself as air flows past it. These two factors cause a snowflake trajectory to be significantly deflected by the airflow past the gauge. In particular, the updraft at the leading edge of the gauge can lead to an upward deflection of snowflake trajectories, causing snow to miss the gauge orifice and not be measured. The flow distortion around the gauge increases as the wind speed increases, while snowflake terminal velocity remains the same, causing more snowflakes to be deflected around the gauge. Thus, the amount of precipitation caught in a precipitation gauge relative to the reference or actual amount of precipitation (also referred to as the collection efficiency) decreases with increasing wind speed. The collection of rain in a weighing gauge suffers from this same problem (e.g., Duchon and Essenberg, 2001), but to a much lesser extent due to the order-of-magnitude higher fall velocity of raindrops, allowing them to be subject to only minimal trajectory deflection due to flow distortions around the gauge.
Adjustments, also referred to as transfer functions, are used to correct the gauge undercatch caused by the wind (e.g., Goodison, 1978). Such transfer functions are derived from precipitation test bed measurements, and describe the collection efficiency (also referred to as catch efficiency) for a specific gauge-shield system. These transfer functions determine the catch efficiency as a function of wind speed for different precipitation types (e.g., Yang et al., 1999), or more recently as a continuous function of both wind speed and air temperatures (Wolff et al., 2015).
In addition, to mitigate the deflection and undercatch of snow by weighing
gauges, wind shields are used around the gauge with the goal of slowing the
oncoming flow, and lessening the resulting flow distortions around the
gauge. Prominent among these is the Alter shield (Alter,
1937). This shield consists of vertical slats of
To quantify the impact of the Alter shield and other types of shields (Alter, 1937; Nipher, 1878; Yang et al., 1995), the World Meteorological Organization (WMO) sponsored a solid precipitation intercomparison study for manual precipitation gauges in the early 1990s (Goodison et al., 1998). A significant result of this study was the creation of a reference standard gauge for snowfall. This was determined to be a precipitation gauge embedded within a carefully pruned bush without leaves. The height of the bush was the same level as the orifice of the gauge. A secondary reference was established as the Double Fence Intercomparison Reference (DFIR; Groisman et al., 1991; Yang, 2014). This allowed field sites to establish a standard for snow measurement using a DFIR without having to grow and prune a bush system. A key characteristic of the reference was that the snowfall rate did not significantly depend on the magnitude of the wind.
This earlier WMO study used both the bush gauge and DFIR as references to compare to a variety of gauges with different shielding configurations (Goodison et al., 1998). A key result from this study was that the collection efficiency of the gauge was primarily determined by the type of wind shield used (Yang et al., 1999). Rasmussen et al. (2012) compiled a review of snowfall measurements to date that confirmed this result for automatic weighing gauges and other wind-shield types. These studies confirmed that the weighing gauge collection efficiency for snow, as compared to the abovementioned reference gauge systems, decreased to varying extent with increasing wind speed depending on the type of the shield. In addition, past studies have shown that the collection efficiency for a given wind speed and wind shield/gauge type can vary significantly (Yang et al., 1999; Rasmussen et al., 2012). While functions describing the decrease in collection efficiency could be derived, there was often as much variability at a given wind speed as across the range of wind speeds (Yang et al., 1999). These results revealed that wind speed is not the only factor that impacts the trajectory of a snowflake past a gauge. Since the fall speed of a snowflake is often close to the magnitude of the flow distortion, an obvious candidate was the fall speed of the snow. Using numeric modeling, Theriault et al. (2012) showed that the difference between wet and dry snowfall speeds can lead to significant changes in the collection efficiency of snow by a Geonor weighing gauge with and without an Alter shield. Other factors that impact collection efficiency include airflow turbulence, time dependence of the flow past a gauge (Colli et al., 2015), snow size distribution (Theriault et al., 2012), ice crystal habit, and snow density (Colli et al., 2015).
The performance of weighing gauges with various types of wind shields may therefore be expected to vary by climate region. The previous WMO Solid Precipitation Intercomparison (Goodison et al., 1998) examined solid precipitation from manual gauges at a limited number of field sites. The more recent WMO Solid Precipitation Intercomparison Experiment (WMO-SPICE) expanded the number of climate regimes covered, and used automatic gauges instead of manual (Nitu et al., 2016). This paper examines results from two sites participating in this experiment, and includes several years of measurements that pre-date the WMO experiment. These results include (1) the assessment of various weighing gauge–shield combinations across these sites; (2) a description of the dependence of snow collection efficiency on wind speed, as well as its uncertainty, at two sites with different characteristic climatological conditions; (3) the functional form of the collection efficiency–wind-speed relationship (transfer function); (4) an assessment of whether each climatological site requires a different transfer function, or if a single multi-site function can be used to reduce wind-induced snow undercatch; and (5) quantification of the expected uncertainty of the correction as a function of gauge–shield type and climatological conditions.
The US field site is located just outside of Boulder, Colorado, along the
eastern slopes of the Colorado Front Range (Fig. 1a). The site resides on
top of the Marshall Mesa at 39.949
The Norwegian Haukeliseter test site (abbreviated as NOR) is situated at
59.812
The US measurements used here span from 1 January 2009 to 7 March 2014, and include all seasons. The NOR measurements used here are identical to those used in Wolff et al. (2013), and were recorded only during winter periods as follows: 1 February–30 April 2011; 1 November 2011–30 April 2012, and 1 February–31 May 2013.
To reduce potential sources of uncertainty, all of the precipitation
measurements presented here were recorded using the same model weighing
precipitation gauge (3-wire T200B, Geonor Inc., Oslo, Norway), although
there were differences in the Geonor gauge capacities, with 1000 mm gauges
used at the NOR site and 600 mm gauges used at the US site. The gauge inlets
were all heated using the same type of inlet heaters (described in NOAA
Technical Note NCDC no. USCRN-04-01), with both the upper (exterior) and
lower (interior) sections of the inlet heated to prevent snow melted at the
orifice from re-freezing when it drips into the collection bucket. The inlet
heaters were activated only when the inlet temperature and the air
temperature were both
Present at both the NOR and US sites, the DFIR shield has the largest footprint of any of the shields, and consists of three concentric shields. The outer two shields are octagonal in design, and are made out of 1.5 m tall wood laths, with an outer-shield diameter of 12 m and a middle-shield diameter of 4 m. The DFIR shield has a porosity of 50 %, with 50 % of its surface area open, allowing air to pass though (the other 50 % of its surface area is blocked by the wood laths), and both the outer and middle shields are perpendicular to the ground. For the third innermost shield, an Alter-style shield of standard size and configuration is used. The DFIR shield is described in more detail in the first WMO Solid Precipitation Intercomparison (Goodison et al., 1998).
The two-thirds scale version of the DFIR, hereafter referred to as the small DFIR (SDFIR), was designed for the US Climate Reference Network program and was installed only at the US site. The SDFIR laths are 1.2 m long, the diameter of the outer shield is 8 m in diameter, and the middle shield is 2.6 m in diameter. Additionally, the middle-shield height is 10 cm lower than the outer shield. A standard diameter Alter shield is used as the innermost shield, which is 10 cm lower than the middle shield and located at the same height as the gauge orifice.
Single-Alter shields were installed at both the NOR (foreground of Fig. 1b) and US sites. The single-Alter shield consists of metal laths about 40 cm in length (though some versions of the Alter use slightly longer laths that are 46 cm in length). The laths on the SA shield are typically attached near the top to a circular ring, 1.2 m in diameter, and are allowed to move freely in the wind. The double-Alter shield (DA; Fig. 1d) is a variation of the single-Alter shield and has two concentric shields instead of one (Rasmussen et al., 2001). This shield consists of a standard 1.2 m diameter single-Alter shield surrounded by an additional outer ring of laths measuring 2 m in diameter. Like the single-Alter, the laths on both rings are approximately 40 cm in length, and secured only at the top, allowing them to move freely at the bottom. Drawings of the DFIR, single-Alter shields, and double-Alter shields, and descriptions of their effects on the wind speed at the gauge inlet are available in Rasmussen et al. (2012).
The Belfort double-Alter shield was only present at the US site (Fig. 1e),
and is a modified version of the standard double-Alter shield. The diameter
of the inner shield is 1.2 m and the laths are 46 cm long. The diameter
of the outer shield is 2.4 m and the laths are 61 cm long. Unlike the
standard single- and double-Alter shield laths, these laths do not taper at
the bottom and are only allowed to swing inwards or outwards at a maximum
45
Unshielded gauges (e.g., Fig. 1c) were present at both sites, but due to problems with the unshielded measurements from the NOR site, only the unshielded measurements from the US site were used for the development and testing of transfer functions.
At the US test bed, the air temperature was measured using fan-aspirated
(Model 076B Radiation Shield, Met One Instruments, Grants Pass, OR, USA)
platinum resistance thermometers (Thermometrics, Northridge, CA, USA) mounted
at a height of 1.5 m. Three wetness sensors (Model DRD11A, Vaisala,
Helsinki, Norway), also mounted at a height of 1.5 m, were used to
independently detect precipitation. Wind speed was measured at 1.5 m using a
cup anemometer (Model 014A Wind Speed Sensor, Met One Instruments, Grants
Pass, OR, USA), at 2 and 3 m using propeller anemometers (Model 05103 Wind
Monitor, RM Young, Traverse City, MI, USA), and at 10 m using both a propeller
anemometer (Model 05103 Wind Monitor, RM Young) and a two-dimensional sonic
anemometer (Model 86004 Ultrasonic Anemometer, RM Young). The two
anemometers at 10 m were found to interfere with each other due to wind
shadowing when winds were from the north or the south, and a composite 10 m
wind speed was therefore produced using the ultrasonic anemometer
measurements to replace the propeller anemometer measurements when winds
were from the north (wind directions
At the Norwegian site, air temperature was measured with a 100
Transfer functions have commonly been developed separately for snow, mixed precipitation, and rain (e.g., Goodison et al., 1998; Yang et al., 2005). Another proposed classification scheme involves differentiating between wet and dry snow. In the past, manual observations of precipitation type were recorded and used to develop such transfer functions, but modern automated measurement networks now rarely include such observations. Airport weather stations often include automated precipitation type measurements, but hydrological, meteorological, and climate stations do not typically include precipitation type measurements, and defensible methods to correct wind-induced errors without precipitation-type measurements are therefore needed.
At the US test bed, precipitation type was determined using an unshielded present weather detector (Vaisala PWD22, Helsinki, Finland). Half-hour increments of rain, mixed precipitation, and snow were identified when more than 15 min of any of these precipitation types was detected from the present weather detector measurements, which were recorded every minute. For rain and snow classifications, less than a 5 min total of any other precipitation type was allowed to occur.
At the US site, when the temperature was below
An alternative to using temperature thresholds to differentiate between
different precipitation types is to use a continuous function of both air
temperature and wind speed to describe the catch efficiency
(Wolff et al., 2015). Although the functions produced using such
methods are more complex than a relationship between wind speed and catch
efficiency for a single precipitation type, such an approach is arguably
more convenient because only one equation is needed to determine catch
efficiency for all conditions. More importantly, a continuous function of
temperature may more accurately represent reality, as catch efficiency
varies continuously with air temperature, especially near 0
Following Wolff et al. (2015), the transfer functions developed
here use a continuous
The temperature distribution of 30 min periods classified as snow, mixed, and rain from the US site.
For the US results, the US Climate Reference Network precipitation algorithm was used to determine 5 min accumulations from all of the 3-wire Geonor T200B gauges (Leeper et al., 2015). The algorithm relied upon wetness sensor measurements to detect periods of precipitation, and it calculated the average accumulation of the three wires by inversely weighting the individual wire accumulations using the variance of the individual depths over the last 3 h. This was done to lessen the contribution of noisier wires to the total gauge depth, and thereby decrease the amount of noise in the precipitation measurements. The algorithm was modified for the purposes of this study by increasing the 5 min precipitation resolution from 0.1 to 0.01 mm. The 5 min accumulations were then summed into half-hour periods, with these half-hour precipitation measurements used for the subsequent analysis.
In addition, at the US site, more than 10 min total of any type of precipitation as identified by the present weather detector had to occur within each half hour to be included in the transfer function analyses. Half-hour increments with unrealistic air temperatures or wind speeds were also excluded from the transfer function analyses. For example, half-hour increments with 10 m anemometer measurements affected by ice accumulation were identified by comparing the 10 m propeller anemometer measurements with the 1.5 m cup anemometer measurements.
Errors and biases in the uncorrected 30 min precipitation from gauges under test, estimated using the DFIR precipitation measurements as the standard.
For the NOR results, the methods presented in Wolff et al. (2015) were used
to calculate precipitation accumulation and select 60 min precipitation
periods for analysis. Every minute, gauge depths were determined by
averaging the output of the three wires of each sensor. As an additional
noise filter, 10 min running averages were calculated for the precipitation
gauges and the optical precipitation detector. For the next step, periods
with continuous and clear precipitation signals were selected using the
following criteria:
the precipitation detector signalled precipitation for at least 8 out of 10 min; the accumulation was greater than 0.1 mm per 10 min or greater than 1 mm
for events that lasted longer than 100 min; the resulting precipitation periods were of different lengths, and were
divided into sets of 10 and 60 min events for further analysis.
For the US site, 30 min was selected as the most suitable time interval for the creation of transfer functions, as 30 min averages of air temperature and wind speed are both representative of the field site as a whole and also relatively stationary (e.g., Stull, 1988). A longer time period would be subject to increased mesoscale, synoptic, and diurnal changes in precipitation type, wind speed, and air temperature. Under quiescent conditions, a shorter averaging period would approach turbulent timescales, where the presence or absence of an individual eddy would affect the results, making the results less representative of the entire site. At the NOR site, 60 min periods of precipitation were used following Wolff et al. (2015), with many of the same arguments supporting the 30 min period equally valid for 60 min. Qualitative analyses by Wolff et al. (2015) on 10 and 60 min datasets did not reveal any significant differences between those time intervals. Therefore, the 60 min time period, which is similar to the operational measurement frequency in Norway, was chosen for further analysis by Wolff et al. (2015).
The effects of minimum precipitation threshold on transfer function
development for 30 min periods from the US site.
Catch errors are described well using catch efficiency, described as the
ratio between precipitation accumulated in a gauge under test and the
standard precipitation accumulation (CE
Example transfer function using the sigmoid function to describe the
combined SA catch efficiency (CE) measurements from both the US and NOR sites
as a function of air temperature (
Using the original 30 min SDFIR precipitation measurements, which were
typically nearly equal to the DFIR gauge measurements, it was found that a
minimum threshold for the gauge under test was also required to help select
representative precipitation measurements, rather than a biased
sub-selection of the measurements. This was because both the gauge under
test and the standard DFIR gauge were affected by random measurement error
and random spatial variability in precipitation. In other words, the DFIR
gauge is capable of measuring more than 0.25 mm of precipitation in a
30 min period, even when the actual site-average rate is below this
threshold. Because many solid precipitation events occur near the 0.25 mm
threshold, many such events may be included in the analysis. Without the use
of a minimum threshold for a gauge under test, measured catch efficiencies
from a gauge under test may therefore be biased erroneously low (as a result
of the DFIR gauge being biased erroneously high), and the resultant transfer
function may over-correct the gauge under test. The minimum thresholds for
the gauges under test were determined from Eq. (2), using the entire
multi-year datasets available.
Wolff et al. (2015) tested many sigmoidal-type transfer functions
for the determination of catch efficiency from a single-Alter gauge as a
function of
For the sake of simplicity, an alternative function is proposed, with an
exponential response to wind speed, and with a simple sigmoid (
Comparison of precipitation (
The repeatability or random error of the precipitation measurements used to
develop the transfer functions was estimated using four different sets of
replicate gauge-shield combinations at the US and NOR test beds. This
analysis included both random gauge measurement uncertainty and uncertainty
caused by the spatial variability in precipitation occurring across a field
site. At the US site, there were two SA-shielded gauges and two DA-shielded
gauges recording precipitation measurements throughout the field study.
There was also one DFIR gauge and one SDFIR gauge, which were similar enough
in their catch to be considered identical for the purposes of estimating
measurement uncertainty. At the NOR site, there were two pairs of
near-identical SA-shielded gauges, but the two gauges were on opposite sides
of the DFIR. This limited the amount of data available for comparison
between them, as additional screening for wind directions was necessary. In
addition, two different heating systems were used on the NOR gauges, with
the primary gauge used for the transfer function analysis configured with
the NOAA Climate Reference Network heating system (NOAA Technical Note NCDC
No. USCRN-04-01), and the secondary SA gauge using the standard Geonor
heater system. Figure 5 shows the comparison results for these four sets of
identical or near-identical gauge–shield combinations. The RMSE values were
calculated from differences between the identical gauges, and were <0.15 mm for all gauge-shield combinations. These results include only
snowfall; the precipitation type at the US site was determined using the
present weather detector to classify 30 min periods with more than 15 min of
snow and less than 5 min of other precipitation types as snow, while the
precipitation type at the NOR site was determined using the air temperature,
with snowfall identified when mean
Uncertainty in the transfer functions was estimated by applying the transfer functions to the different gauges under test and then comparing the results to the standard DFIR precipitation measurements. To maintain some independence between the data used to develop the transfer function and the data used to test the transfer function, the uncertainty of the transfer functions was estimated using a 10-fold cross-validation. This model validation technique randomly separated the available measurements of a given shield type into 10 equally sized groups. The transfer function was determined using 90 % of the data (nine groups), then tested on the remaining 10 % of the data (one group). This process was repeated for each permutation of the 10 groups. The coefficients describing the transfer function were based on the entire dataset, but the uncertainty estimates were based on this 10-fold cross-validation. The uncertainty estimated from 10-fold cross-validation and the uncertainty estimated by circularly developing and testing the transfer function on identical data were very similar, but the 10-fold validation was used where possible for more defensible estimates of the transfer function uncertainty.
For the SDFIR-shielded gauge under test, it proved impossible to constrain the sigmoid function for all 10 iterations of the model fitting; therefore, the cross-validation was not used and the uncertainty and the transfer function were circularly determined using exactly the same data. To assess the uncertainty of the two-site transfer function developed for the combined SA NOR and SA US measurements presented in Sect. 4.2, the transfer function was applied to the entire dataset using the 10-fold cross-validation, and it was also applied to the two sites individually. The site-specific results were calculated to assess to what degree a single transfer function was valid for the two individual sites. Because the dataset used to create the transfer function was split into two groups for this two-site validation, 10-fold cross-validation was not used.
Transfer function coefficients for estimated gauge-height wind
speeds. Coefficients for the sigmoid transfer function (Sig; Eq. 3) and the
exponential transfer function (Exp; Eq. 4), as well as the number of periods
available (
Errors in uncorrected precipitation measurements were estimated by comparing
the DFIR-shielded precipitation measurements to the other shielded and
unshielded measurements. Based on the differences between the 60 min
DFIR-shielded accumulation and the SA-shielded accumulation at the NOR site,
RMSE values and biases were calculated (Table 1, NOR SA). The RMSE of the
NOR SA measurements was 0.64 mm (51.6 %) and the bias was
Transfer function coefficients for 10 m height wind speeds.
Coefficients for the sigmoid transfer function (Sig; Eq. 3) and the
exponential transfer function (Exp; Eq. 4), as well as the number of periods
available (
Transfer function results for estimated gauge-height wind speeds. Sigmoid transfer function (Sig; Eq. 3) and exponential transfer function (Exp; Eq. 4) RMSE values and biases described for the US unshielded (UN), single-Alter (SA), double-Altar (DA), Belfort double-Alter (BDA), small DFIR (SDFIR), the NOR single-Alter (SA) gauge, and the combined US and NOR SA results (All SA).
For the US site, precipitation catch efficiencies were described as a
function of
The RMSE and bias in the corrected measurements were then determined for
each transfer function using both the gauge-height wind speeds (Table 4)
and the 10 m height wind speeds (Table 5). This includes the two-site SA
transfer functions and the associated errors determined from the combined
dataset (“All SA” in Tables 4 and 5). In addition, by applying the All SA
transfer functions individually to the NOR and US SA measurements, RMSE
values and biases were estimated separately for the US and NOR SA
measurements using the two-site transfer functions (Tables 6 and 7). This
was done to evaluate site biases and the effects of different climates on
the transfer functions. For example, for the SA gauges at the US site, the
two-site gauge-height wind-speed Exp transfer function reduced the RMSE from
23.6 % (Table 1) to 15.4 % (Table 6) and improved the bias from
The RMSE values of the corrected results reflect the significant residual variability in the corrected catch efficiency. It is worth noting that the RMSE of even the corrected SDFIR measurements was greater than 0.1 mm, indicating that such uncorrectable errors may be due to random measurement error and site variability rather than crystal type and wind-speed effects. That is, even a gauge that is shielded quite similarly to the reference, which likely responds to wind speed and crystal habit similarly to the DFIR, was subject to such errors; in a given half-hour period the SDFIR and DFIR shields are subject to similar hydrometeors and wind speeds, and these hydrometeors presumably behave the same way over each shield. Such uncorrectable errors can therefore be attributed to more random causes, such as measurement noise and the natural spatial variability of precipitation.
Transfer function results for 10 m height wind speeds. Sigmoid transfer function (Sig; Eq. 3) and exponential transfer function (Exp; Eq. 4) RMSE values and biases described for the US unshielded (UN), single-Alter (SA), double-Altar (DA), Belfort double-Alter (BDA), small DFIR (SDFIR), the NOR single-Alter (SA) gauge, and the combined US and NOR SA results (All SA).
Transfer function results for estimated gauge-height wind speeds. The same coefficients determined by the multi-site All SA transfer function (Table 2) were used to correct the results from NOR and US sites. Sigmoid transfer function (Sig; Eq. 3) and exponential transfer function (Exp; Eq. 4) RMSE values and biases are described for the US single-Alter (SA) and the NOR single-Alter (SA) gauge.
Generally, differences between the Exp and Sig functions were small, indicating that the Exp function can be used as a simpler alternative to the Sig function developed by Wolff et al. (2015). For the US site, the transfer function RMSE values were about 0.15 mm (15 %) for all gauges, irrespective of whether the sigmoid function or the exponential function was used (Tables 4 and 5). The errors in the uncorrected data (Table 1) were generally much larger than the errors in the corrected data, with the errors in the uncorrected data dependent upon the efficacy of the shield. For example, using the gauge-height wind-speed transfer functions, the corrected SDFIR gauge RMSE and bias shown in Table 4 were only slightly better than the uncorrected RMSE and bias shown in Table 1, whereas application of the transfer function resulted in a much more significant improvement in the unshielded and SA gauge error (UN and SA, in Tables 1, 4 and 5).
The RMSE values were much larger for the NOR SA measurements than the US SA
measurements. This was due primarily to a generally more noisy gauge at the
NOR site than at the US site. Random measurement error from these
vibrating-wire weighing gauges can be reduced via trial and error by
rotating and remounting the vibrating wires within the gauge and also by
mounting the shield separately from the gauge, but such noise can vary
significantly from gauge to gauge and even from wire to wire within a gauge
equipped with redundant vibrating wires. The NOR site is also windier than
the US site and the undercatch is generally larger, and because of this, one
can expect the RMSE to increase (i.e., a well-shielded gauge that requires
less correction will be less affected by variability in precipitation type
and crystal habit). In addition, blowing snow may have increased the RMSE
values of the NOR results, with 2.6 % of the events occurring wind speeds
greater than 15 m s
The bias found for the NOR SA gauge corrected using the two-site transfer
function is, however, more notable, as the bias should be relatively
unaffected by random measurement noise. For example, the NOR SA measurements
corrected using the gauge-height transfer function had a larger bias
(approximately
For the gauges at the US site, there was no difference in the RMSE or bias
between the 10 m wind speed and the gauge-height wind-speed transfer
functions. However, this is neither surprising nor noteworthy, as the
gauge-height wind speed was estimated based on the 10 m wind speed. It is
notable, however, that the RMSE for the combined US and NOR SA gauge results
was also not significantly affected by the choice of wind-speed measurement
height (Tables 6 and 7). These RMSE values indicate that although the gauge
heights at the US site and the NOR site were significantly different, there
was no significant loss in accuracy when transfer functions were created for
both sites using the 10 m wind speed. There was, however, a more negative
bias in the 10 m wind-speed NOR SA results (e.g., Sig bias
Transfer function results for estimated 10 m height wind speeds. The same coefficients determined by the multi-site All SA transfer function (Table 3) were used to correct the results from NOR and US sites. Sigmoid transfer function (Sig; Eq. 3) and exponential transfer function (Exp; Eq. 4) RMSE values and biases are described for the US single-Alter (SA) and the NOR single-Alter (SA) gauge.
To demonstrate both the importance and the limitations of the transfer
function corrections, the 30 min uncorrected (Fig. 6a) and corrected (Fig. 6b)
SA snow (
To demonstrate further the necessity of the transfer functions and the
effects of errors and variability in the transfer functions, an example
event is shown Fig. 7a. Using the appropriate transfer function and the mean 1 min
Example event from the US site with accumulated precipitation measured
using the Double Fence Intercomparison Reference (DFIR; dark blue), small DFIR
(SDFIR; red), Belfort double-Alter (BDA; yellow), standard double-Alter (DA;
purple), single-Alter (SA; green), and unshielded (UN; light blue) weighing
precipitation gauges. Both the
Wind-speed measurements at gauge-height and at the standard 10 m measurement height both have advantages. The 10 m height wind speed is widely used by national weather services, is designated as the standard wind-speed measurement height by the WMO, and is also less likely to be affected by obstacles such as towers and precipitation gauge shields. The effects of obstacles at gauge height were apparent in both the NOR and US sites, for example (Sects. 3.3.1 and 3.3.2). However, the catch efficiency of a shielded or unshielded gauge is more closely linked to the wind speed at gauge height. If, for example, the wind speed at gauge height is affected by the changing height of the snowpack or by vegetation or other obstacles, this will affect the relationship between the 10 m and gauge-height wind speed, and potentially lead to additional sources of error.
For the present study, in which the 10 m wind speed and a gauge-height wind
speed derived from the 10 m wind speed were both used to create two-site
transfer functions for single-Alter shielded gauges at significantly
different heights, the RMSE of the combined NOR and US transfer function was
relatively insensitive to the different wind-speed heights when tested on
the US, NOR (Tables 6 and 7), or combined datasets (All SA, in Tables 4 and 5).
The only notable change caused by the use of the 10 m wind-speed
versions of the combined transfer function was in the bias calculated from
the NOR SA, which was about
However, based on the argument that catch efficiency is physically more
closely tied to the wind speed at the height of the gauge than at a height
of 10 m, the correction of precipitation measurements using a gauge-height
wind-speed measurement, or an approximation of the gauge-height wind speed,
is more defensible than the use of a 10 m height wind speed. Because
differences in gauge height are common due to the necessity of mounting
gauges and shields well above the highest expected snow depth, even when
only 10 m wind-speed measurements are available they should be adjusted to
gauge height for the application of shielding corrections. For example, at a
gauge height of 5 m, the wind speed affecting the catch efficiency of the
gauge would typically be
Uncertainties and biases associated with the development and application of
a single transfer function for two separate sites within differing climate
regions have been presented. The NOR site was much windier than the US site;
during precipitation events the mean NOR
Such a multi-site transfer function is needed, because site-specific transfer functions can only be developed for sites where a DFIR shield is present. A more broadly applicable transfer function is necessary for real-world precipitation corrections, where the actual or DFIR-shielded amount of precipitation is unknown. In this study, the bias was shown to be minimized at sites in two separate climates using one transfer function that was developed from combined results, and we suggest using this same approach in future studies such as the WMO Solid Precipitation Intercomparison, for which many more sites and climates will be included.
Measurements presented in this study were recorded at two separate sites. Although similar methods were used to analyze the results from each site, the datasets available from each site were not developed exactly the same way. The methods used to determine when precipitation occurred were different, as described in Sect. 3.5.1. In addition, 30 min precipitation accumulations were used at the US site, and 60 min accumulations were used at the NOR site. It is unlikely that this biased the resultant catch efficiencies, because both 30 and 60 min time periods are short enough that representative averages of temperature, wind speed, and precipitation type can be calculated. In addition, as described in Sect. 3.5.1, Wolff et al. (2015) did not detect any significant differences between 10 and 60 min intervals.
The number of events available from each site also differed, with 1156
30 min periods of single-Alter precipitation available for analysis from the
US site, and only 352 60 min periods available from the NOR site. To explore
the effects of a potential bias towards the more numerous US catch
efficiency measurements, a test was performed using approximately one out of
every four US single-Alter measurements. The resultant single-Alter dataset
included 352 NOR measurements and 292 US measurements. Using the gauge-height winds
and the Exp transfer function as an example, there were only
small differences between the resultant transfer function and the original
transfer function created using all of the available US and NOR
measurements. Likewise, the site-specific errors were not significantly
altered by the omission of 3 out of every four US measurements. At the NOR
site the original RMSE of 0.45 mm was unchanged by application of the new
transfer function, and the bias was changed from
Two sites were included in this study to help advance the methods and concepts available for the development and testing of transfer functions using measurements from multiple test beds. The focus of this work was on applying new methods to existing datasets from two sites, rather than on refining the methods used to prepare the precipitation measurements for analysis. The development of a common approach to data processing and event selection is included in WMO-SPICE. Application of the methods presented here to more standardized datasets from several WMO-SPICE sites is currently underway, and will be made available in the WMO-final report and associated publications. In addition to employing standardized methods to prepare the precipitation datasets available for transfer function development, WMO-SPICE also includes more sites with more varied climate conditions, which will be used to better quantify site-specific biases associated with the use of a single transfer function at multiple sites and create more universally applicable transfer functions.
Methods to address the effects of wind and precipitation type on precipitation measurements have been presented, and significant improvements to the measurements have been demonstrated for unshielded gauges and other common gauge–shield combinations. A new adjustment function was used to describe catch efficiency as a function of air temperature and wind speed, and it performed comparably to the more complex function suggested by Wolff et al. (2015). Precipitation measurements from two sites were used to derive and test a single transfer function for the single-Alter shielded measurements, and site biases caused by using one transfer function at more than one site were quantified for the first time. In addition, the remaining uncertainty in the transfer functions used to correct or standardize precipitation measurements has also been carefully described and quantified. Significant errors persisted in the measurements, even after correction for undercatch, with the root mean square error (RSME) reduced by less than 50 % for all wind shields examined. Measurement error, the random spatial variability of precipitation, and variability in the type, size, density, and fall speed of hydrometeors all likely contributed to the errors that remained uncorrected. This is an active ongoing area of research that merits more attention. However, when precipitation measurements are used to help describe water budgets, such variability in the corrected measurements may be relatively unimportant relative to the improvement in the bias, or the total amount of precipitation. In addition, this study indicates that low-porosity windshields like the Belfort double-Alter show great promise in reducing undercatch with a small-footprint, low-maintenance shield.
Significant errors exist in our historical and present-day precipitation measurements. For weighing gauges that are designed to measure snowfall, these errors are affected primarily by shielding, precipitation type, crystal habits, wet vs. dry snow, and wind speed. Such errors affect the measurement of the amount of water in both seasonal and ephemeral snowpack, and therefore affect our ability to quantify the availability of water for communities and ecosystems that rely upon water from snowfall. The results and techniques presented here can be used to help create precipitation records that are traceable to a common standard, ultimately leading to a more constrained and accurate representation of the Earth's hydrological balance.
In this paper, the 30 min precipitation measurements from the US test bed and 60 min precipitation measurements from the Norwegian test bed are available in the Supplement.
The authors declare that they have no conflict of interest.
We thank Hagop Mouradian from Environment and Climate Change Canada for contributing the mapped site locations (Fig. 1a). We also thank Samuel Buisan from the Spanish National Meteorological Agency and Eva Mekis and Michael Earle from Environment and Climate Change Canada for carefully reviewing this manuscript. This work was greatly improved by their comments. Edited by: M. Earle Reviewed by: S. Buisan and E. Mekis