Quantitative evaluation of weighing gauges with different...

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Quantitative evaluation of weighing gauges with different wind 1

shields through error modellings 2

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Soorok Ryu1, GyuWon Lee*1, Rodica Nitu2, EunHa Lim3, and Hye-Lim Kin3 4

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1Department of Astronomy and Atmospheric Sciences, Research and Training Team for 6

Future Creative Astrophysicists and Cosmologists, Center for Atmospheric REmote sensing 7

(CARE), Kyungpook National University (KNU) 8

2Observing Systems and Engineering, Environment and Climate Change Canada, Toronto, Canada 9

3National Institute of Meteorological Sciences, Korea 10

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＊Corresponding author: GyuWon Lee, Department of Astronomy and Atmospheric 15

Sciences, Kyungpook National University, 1370, Sankyuk-dong, Buk-gu, Daegu 702-701, 16

Korea. 17

Phone: +82-53-950-6361, Fax: +82-53-950-6359, E-mail: [email protected] 18

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Abstract 20

The uncertainty of measurement of precipitation using weighing gauges is attributed to 21

several factors specific to the operation of these gauges in the outdoor environment: wetting 22

losses, wind effects, heating losses, as well as due to inherent instrumental noise. In this work, 23

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quantitative error modelling is carried out for two types of automatic weighing gauges with 24

broad operational use (AWGs : Geonor T200-B3, 600 mm and OTT Pluvio2), configured with 25

different wind shield types. The 30 min average data are obtained from the 5 types of wind 26

shields at the Centre for Atmospheric Research Experiments (CARE) near Egbert, Ontario, 27

Canada. 28

Four models are designed to obtain bias and random uncertainties of all gauges studied. 29

The measurement is modelled using the true value, bias, and random uncertainty. The true 30

precipitation value is assumed as a mean value of the two gauges studied, each installed in a 31

Double Fence Inter-comparison Reference (DFIR). In the first model, the bias and 32

uncertainties are function of wind shields and gauges types. The second model assumes the 33

same bias for the same types of gauges but different bias with different wind shields. In the 34

third model, the bias varies with wind speed and air temperature. The forth model is for 35

instrumental uncertainty for each gauge using error propagation equation. Using four types of 36

models, each bias and uncertainties are compared according to different gauges, windshield, 37

and precipitation types. 38

1. Introduction 39

The measurement of precipitation has been the subject of a multitude of studies, but there 40

have been limited coordinated assessment of the ability and reliability of automatic sensors to 41

accurately measure solid precipitation. The most comprehensive study for solid precipitation 42

measurements took place between 1987 and 1993 (Goodison et al. 1998) by the World 43

Meteorological Organization (WMO). In this report, for the solid precipitation, the manual 44

observation due to wind-induced updrafts at the gauge orifice and wetting losses on the 45

internal walls of the gauge, the under catch of precipitation (Groisman and Legates, 1994) 46

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affects the accuracy and quantity of precipitation data. This result identified that the mean 47

wind speed is the major environmental factor that impacted the catchment efficiency of tested 48

instruments. Since this report, an increasing number of automated stations have been 49

providing measurement of precipitation data, including solid precipitation, but little 50

information on the uncertainty of measurement. Some observations for the large variability in 51

the total snow water equivalent (SWE) were carried out over the 2008-2009 using a large 52

number of precipitation gauges and windshield. Some automatic weighing gauges (WG), 53

heated tipping-bucket rain gauges, and present weather sensor detector (PWD) were 54

examined with a Geonor T200-B in DFIR-fence as the reference. The notable result in this 55

study was the poor performance of the heated tipping bucket gauges as compared with WG or 56

the reference (Rasmussen at al. 2012). 57

Given the strong needs for automated solid precipitation data from both the climate and 58

weather communities, intercomparison studies are required. The Commission for Instruments 59

and Methods of Observation (CIMO) of the WMO is organizing a Solid Precipitation 60

Intercomparison Experiment (WMO-SPICE) focused on the performance of modern 61

automatic sensors measuring solid precipitation and their configurations, in a variety of 62

environmental conditions. The aim of the intercomparison is to improve the understanding 63

and reliability of solid precipitation measurement gauges. One of the key objectives of 64

WMO-SPICE is assessing the achievable uncertainty of the measurement systems evaluated 65

during SPICE and their ability to effectively accurately report solid precipitation 66

(WMO/CIMO 2011). For the purpose of these objectives for SPICE, it is necessary to assess 67

the sensitivity, uncertainty, bias, and the magnitude of errors including instruments (sensors). 68

There are many challenges for the measurement of solid precipitation, but only a few 69

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studies considered for different gauge types between many wind shields types. Recently, in 70

Rasmussen at al. (2012), six different shield designs and four different gauges in various 71

combinations are tested at Marshall Field Site test bed to determine the most accurate 72

measure of the water content of solid precipitation using automated snow gauges for long-73

term climate measurements. The collection efficiency of double alter-shielded Geonor, is 74

considered by normalizing as reference is the average of one SDFIR (small DFIR) and one 75

DFIR-shielded Geonor measurement according to 1.5-m height wind speed. They observed 76

the dependency of collection efficiency on shield type from accumulation during the 23-24 77

March 2010, of Geonor gauge in DFIR, SDFIR, double Alter (DA), and single Alter (SA) 78

wind shield. In this study, they didn’t use two SPICE working field references when they 79

compute catch ratios, and didn’t consider quantitative uncertainty errors according to 80

different gauges, wind shields, and precipitation types under consistent environmental 81

conditions. 82

The survey of 2008 (Nitu and Wong 2010) shows that the Geonor T-200B3 gauge with 3 83

transducers and the OTT Pluvio2 gauges were the most widely operational used as weighing 84

type gauges, and they were recommended for use in the SPICE reference, R2 (see section 2). 85

An R2 system using Geonor gauge is labeled as R2G, and the R2 system of Pluvio2 is called 86

R2P. The comparison between two systems are one of the important studies in SPICE, but 87

outside of this study. This paper will present the quantitative uncertainties of two type of 88

weighing gauges with difference wind shields using some reasonable models as reference is 89

the average of R2G and R2P. 90

In the CARE site in Canada, from November 2014, with two types of R2 systems (R2G 91

and R2P), heated two types of weighing gauges with four different windshield types 92

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(including no shield type) are operated. Therefore, this site has almost near perfect conditions 93

for the observation of performance of different weighing gauge types and wind shield types. 94

This paper will provide consistent methodologies about quantification of uncertainty, can be 95

used for assessing the uncertainty of the measurement of solid precipitation. Also, using the 96

data of the CARE site, quantitative uncertainties will be calculated according to different 97

gauges, windshields, and models that can be referenced other sites. 98

The uncertainty can be originated from various sources. Following the classification of 99

Regan et al. (2002), uncertainty can be divided into some classes : inherent randomness, 100

measurement error, systematic error, natural variation, and model uncertainty. In this study, 101

the uncertainties are related with inherent randomness, measurement error, and systematic 102

errors. The measurement of precipitation from each gauge includes inherent randomness, 103

systematic errors, and measurement errors related with various environmental conditions. The 104

purpose of this paper is to provide some methodologies to assess the achievable uncertainty 105

of the measurement system, furthermore, to quantify the uncertainties of each gauge with 106

different wind shields, can be compared with the ones of other sites. 107

The section 2 provides the background information about test site, sensors, and various 108

wind shield types. The descriptions of the way of Quality Control (QC) of data, sampling, 109

and classification of precipitation types, is presented in section 3. In section 4, some 110

methodologies are introduced to quantify the uncertainty of precipitation gauges, including 111

general statistical measures. All estimated uncertainties for all are presented and compared in 112

section 5, for all uncertainty models mentioned in this paper. Lastly, section 6 summarizes the 113

results and provides conclusions. 114

2. Test site, sensors, and wind shields 115

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2.1 CARE site in Canada 116

The CARE (Centre for Atmospheric Research and Experiments) site is located in the 117

town of Egbert, province of Ontario, at 44˚ 17' latitude, 79 ˚ 47' longitude and 251 m 118

elevation and belongs to humid continental climate. The daily average temperature is -8.2℃ 119

in January and total average annual snowfall is 157 cm. The mean wind speed for the period 120

from November to April is 3.5~4.0 m/s (WMO/CIMO 2012). Fig. 1 shows the site layout of 121

CARE site from 20 November 2014. 122

2.2 Wind shields 123

2.2.1 Automatic Double Fence Reference (DFAR) 124

Double Fence Intercomparison Reference (DFIR) is an “octagonal vertical double-fence 125

inscribed into circles of 12 m and 4 m in diameter, with the outer fence 3.5 m high and the 126

inner fence 3.0 m high surrounding a Tretyakov precipitation gauge mounted at a height of 127

3.0 m. In the outer fence, there is a gap of 2.0 m and in the inner fence of 1.5 m between the 128

ground and the bottom of the fences.” (Goodison et al, 1998), and It is recognized as the 129

secondary field reference for the measurement of solid precipitation, and is named R1. For 130

the configuration of the WMO SPICE references, the SPICE IOC adopted the octagonal 131

double fence as same as R1, and using automatic gauges as measuring instruments, as a 132

replacement of the manual Tretyakov gauge. To distinguish R1, the SPICE IOC decided to 133

use the term ‘DFIR-fence’ when referring to the octagonal double fence only, and decided at 134

its meeting in Boulder (CO, USA), in 2012, to refer to the configuration consisting of a 135

DFIR-fence with automatic instruments in the center of the octagonal double-fence as the 136

Double Fence Automatic Reference (DFAR), is named R2. The Fig. 2a and 2b show the R2G 137

and R2P at the CARE site in Canada. 138

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2.2.2 Single Alter shield (SA) 139

The single Alter shield configuration will consist of a single ring of “blades”, also known 140

as slats or fins, mounted on a ring of 1230mm diameter (or approximately 4 feet), centered 141

about the gauge. The height of the blades will be positioned at a height of 20mm above the 142

orifice of the gauge. The single Alter configuration that will be used during the WMO-SPICE 143

is a modified configuration of the design distributed by Geonor, originally designed by the 144

Norwegian Meteorological Institute. This shield is used for the gauges which are part of the 145

SPICE reference systems, i.e. the gauge in the Double Fence Intercomparison Reference, the 146

R2 reference, and the gauge in a single Alter, part of the R3 reference (see Smith. et al., 2012) 147

2.2.3 Canadian double Alter shield (CDA) 148

The double Alter shield (Fig. 2e) has another ring of vertically oriented slats 0.5 meter 149

from the inner ring. 150

2.2.4 Belfort Double Alter shield (BDA) 151

The Belfort Alter Shield (patent pending) consists of closely spaced rectangular metal 152

wind deflectors that are limited in travel by rubber grommets and springs (Fig 2.c-d). 153

Limiting the travel assures uniform wind deflection even in high wind precipitation 154

conditions. Spring loading and noise suppression grommets help reduce wind deflector noise 155

to a minimum while still permitting adequate travel to reduce possible snow accumulation. 156

The Belfort Alter Shield is designed to mount to 3/4 inch, sched. 40, (1 inch OD) pipe that 157

is mounted vertically in the ground with either a 4-foot hoop diameter (inner shield) with 4 158

mounting pipes, or 8-foot hoop diameter (outer shield) with 8 mounting pipes each 159

positioned circumferentially about the Precipitation collector. 160

2.3 Sensors 161

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The two gauges, Geonor T200 and Pluvio2 are recommended for the configuration of the 162

SPICE working field reference system. They operate on different principles, using different 163

sensing elements, data collection, and processing. 164

For the Geonor T200-B3 gauge (Fig. 2f) the bucket content is weighted using a precision 165

load cell with a high-tension vibrating wire (VW) transducer. Under load, the wire vibration 166

frequency is proportional to the weight detected (P), based on a quadratic relation (GU 167

20030829 and Bakkehøi et al., 1985). The signal from a transducer is amplified into a 168

measurable quantity read with an external data logger. This signal is converted into a 169

precipitation amount corresponding to the weight of the bucket content, and this data is used 170

for the analysis of this study. 171

Through internal processing of Pluvio, every 6 seconds, the weight of bucket content is 172

determined with a resolution of 0.01mm. In some output data of the Pluvio2, the Bucket RT 173

(Real Time) is used for this analysis. 174

At the CARE site, heated 6 Geonor T200-B3 and heated 6 Pluvio2 are installed in this 175

2014/15 and 2015/16 winter seasons. Table 1 shows the used models, capacities, and 176

locations of Geonor and Pluvio gauges for analysis in this study. Regardless of Geonor BDA 177

and Pluvio BDA, the used gauges are the same ones in 2014/15 and 2015/16. As seen in 178

Table 1, for Geonor BDA, the data of H4 (name of file prefix), but in 2015/16 season, of H5 179

is used for analysis because Geonor of H4 is not operated in 2015/16 season. Note that the 180

capacity of Geonor of H5 is 1500 mm, so it can affect the results of analysis for BDA. For 181

Pluvio BDA, the data of HN is in 2014/15, and HO is used in 2015/16 season. The two 182

Pluvio gauges of HN and HO are the same models and capacities. 183

For wind speed, the Vaisala NWS425 of Y7 (see Fig. 1) with 30 sec time resolution, and 184

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for temperature, Vaisala HMP155 of D6 is used with 6 sec time resolution. 185

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3. Data 187

The analysis in this paper was constructed from two winter seasons in CARE site. The 188

periods are form 1 December 2014 to 31 March 2015, and 1 December 2015 to 31 March 189

2016. 190

3.1 QC of accumulated precipitation amount data 191

The results in this paper are based on the quality-controlled (QCed) 1min accumulation data 192

of the Pluvio2 and Geonor gauges. For data QC, the SPICE QC methodology (WMO CIMO 193

2014) is used, and it has following three steps: min-max outlier filtering, jump filtering, and 194

Gaussian filtering. All raw data of CARE site for precipitation has 6sec resolution, so, after 195

three steps, the processing for1 min aggregation is applied. For Geonor with 3 wires, the 196

averaged value of QCed 1min 3-wire is used for analysis 197

Fig. 3 shows time series of QCed 1min accumulated precipitations of all Geonor gauges 198

(Fig. 3a) and Pluvio gauges (Fig. 3b) with different types of windshields in 2014/15 and 199

2015/16 winter seasons. In this figure, different color represents different wind shield types. 200

3.2 Data sampling and precipitation types 201

For the uncertainty analysis for the measurement values of different gauges (Geonor and 202

Pluvio), and different wind shield types, a 30min sampling interval is used to obtain all 203

uncertainties of gauges. All analysis is made when all data are greater than or equal to 204

0.5mm/h. For the horizontal wind speed U and air temperature T, they have been averaged 205

over the same precipitation sampling interval of 30min. 206

In this work, using the following temperature condition which is similar to that used in 207

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Yang et al. (1995, 1998), the precipitation types, such as rain, mixed precipitation, and snow 208

are separated. 209

precipitationtypesnow, 2.0 ,

mixedprecipitation, 2.0 2.0rain, 2.0 ,

,

When precipitation types are classified in this way, the numbers of events of rain, mixed 210

precipitation, and snow events, with the 30min precipitation condition P≥0.5mm/h were 120, 211

89, and 91, respectively. 212

4. Method 213

In this study, four kinds of models are used to quantify the uncertainties for different 214

gauges and wind shields. In uncertainty models (Models I ~ III), we assume that the true 215

value or reference precipitation is an average of R2G and R2P. Before introducing some 216

uncertainty models, the following methodology is used based on the recommendations from 217

Standard ASTM D4430-00 (2015). 218

4.1 Statistical measures 219

The statistical measures of the difference of two systems, systematic difference d, 220

operational comparability C, and estimated standard deviation s of the differences, are used. 221

The systematic difference d is the mean of the differences in the measurement by the two 222

systems, is defined as 223

1 ,

where N is the number of measurement dependent on length of data. is measurement 224

value of ith type gauge with jth windshield at time tk, and t is the reference or true data at 225

time tk . The operational comparability is the root mean square (RMS) of the difference 226

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between simultaneous readings from the two instruments measuring the same quantity in the 227

same environment, such that: 228

1 .

The estimated standard deviation s of the difference, is defined as a standard deviation of the 229

set . The relative values (or normalize values) of the three quantities 230

are defined, as the ratio to the average of reference μ t . 231

The quartile statistics are also used to describe the distribution of differences or catch ratios 232

when the mean of R2G and R2P is used as a reference. A box plot is used to display the 233

comparison of quartile statics. 234

4.2 Model I for uncertainty 235

In the first model, simply we assume that the estimated precipitation rate P at time t is 236

composed as: 237

ϵ , 238

where i 1,2 is gauge index for Geonor (i=1) and Pluvio (i=2), and j 1, … ,5 is the index 239

of wind shield types for DFIR-fence(j=1), BDA(j=2), CDA(j=3), SA(j=4), and NS(j=5). 240

is observed precipitation rate at time t, and μ t is reference or true precipitation rate 241

at time t. β is the constant bias of ith gauge with jth wind shield, and ϵ is the 242

instrumental noise of ith gauge with jth wind shield at time t. Then, the constant bias and 243

the error ϵ can be computed as the mean of the difference , and RMS of 244

ϵ , respectively. That is, we assume that the uncertainty σ for 245

gauge i with jth wind shield is RMS value of ϵ . Note that the bias and the 246

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uncertainty σ of the first model are theoretically the same as the ones of systematic 247

difference d and estimated standard deviation s if the same reference is assumed. 248

4.3 Model II for uncertainty 249

The second model is similar to the first model (Model II). With the same gauge and wind 250

shield index, and the same assumption for the true reference μ t , 251

ϵ .

In this model, we define biases for gauge type and wind shields, independently. That is, α is 252

assumed the constant bias due to different gauge types (i=1,2), and β , the constant bias due 253

to different wind shield. Then, the biases α and are only dependent on gauge and wind 254

shield type, respectively. To calculate α , the average of each gauge i for all 255

wind shield types is computed under the condition U < 2 m/s. The condition ‘U < 2 m/s’ is to 256

remove the effect of wind shield types. Then is an average of for all 257

gauges and all wind speeds. The total constant bias dependent on gauge and wind shield can 258

be defined as . Similar to the Model I, the uncertainty σ for gauge i with 259

windshield j can be defined as σ . 260

4.4 Model III for uncertainty 261

The wind bias in the gauge measurement of a snowfall event can vary significantly 262

depending on the wind speed, air temperature, precipitation characteristics, and gauge 263

configuration (Goodison and Yang 1996). This wind bias can be reduced by the choice of 264

wind shield or adjustments for the measurement of precipitation in windy environments. The 265

choice of the wind shield such as DFIR-fence looks effective at reducing wind bias, but it can 266

face the limitations such as size or costs of installation and maintenance. In this reason, the 267

wind bias adjustments for the measurement is necessary to increase the precipitation accuracy. 268

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One of the significantly rising parameter is temperature which include precipitation type. 269

Recently, Wolff et al. (2015) used quantitative analysis and Bayesian statistics to evaluate and 270

choose the model that best describes the data. A continuous adjustment function and its 271

uncertainty are obtained from the measurements of all types of winter precipitation at 272

Haukeliseter site in Norway. 273

The third model is related with a bias adjustment using continuous function of catch ratio 274

dependent on wind speed U and air temperature T. Also, the uncertainty in this model is 275

adjusted one after removing the adjusted bias. The adjustment function is a sigmoid function 276

which do not use such as complex Bayesian analysis in Wolff et al. (2015) instead uses 277

exponential function with inverse of tangent function. 278

If precipitation measurement is composed as P , where is the 279

difference between the measurement P and , then by dividing, ,at both sides, 280

we obtain 281

1 (1) 282

Then, would be a difference error of catch ratio. To approximate the catch ratio which 283

is dependent on U and T, 1 is approximated as the function CR U,T) = 1284

tan , where , , and are constant coefficients in the range [0, 1]. To find 285

the constants, the fitting library function ‘fit’ is used in MATLAB and Statistics Toolbox 286

Release 2011b, The MathWorks, Inc., Natick, Massachusetts, United States. If the catch ratio 287

is approximated as the function , , then the equation (1) will be 288

P, .

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Then, the relative adjusted (by U and T) bias , and relative adjusted uncertainty 289

are , 1 100(%) and 100(%), respectively. In the next 290

section, the uncertainty R will be compared with the ones of other models in section 5. 291

4.5 Uncertainty Model IV 292

The forth model is totally different from Model I, II, and III. The purpose of Model IV is to 293

find instrumental uncertainty when one has no information about true or reference data. This 294

model needs not any assumption about the true value μ t . 295

Let P be any precipitation measurement value of ith gauge at t and μ t be a true 296

precipitation value at t, then we define the uncertainty of P as the standard deviation 297

s . By the property of variance, the variance of difference between two 298

measurements is 299

2 , . 300

The quantities and represent the errors of and gauges, respectively. 301

If the errors and have random noise distributions and have no correlation 302

between them, then, the covariance cov ⋅ will be zero or has very small quantity (see Ciach 303

and Krajewski (1999) for discussion). If and have positive relation, then the 304

covariance values between them is positive, and this results in the uncertainties of P (using 305

this model) is smaller than s μ . Similar appoach is used for a radar-rainfall uncertainty 306

analysis in Habib and Krajewski (2002). 307

The individual uncertainty for each ‘n’ gauges can be approximated by solving n(n-1)/2 by 308

n linear system. For example, for the four measurement values i 1,⋯ , 4 , by denoting 309

and by and , respectively, the uncertainty i 1,⋯ , 4 of 310

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each gauge can be approximated by solving the 6 by 4 overdetermined linear system 311

110010101001011001010011

σ

. (2) 312

In general, if n ( 2 gauges are used, then the matrix size is n(n-1)/2 by n, so a least-squares 313

method can be easily applied to obtain an individual uncertainty. The total uncertainty of all 314

same type instruments can be computed as the averaged value of the right hand side term in 315

the linear system (2) as 316

317

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This model is designed to find an averaged instrumental uncertainty of same type gauge or 319

individual instrumental uncertainty when there is no information about the true data. In this 320

model, actually, the smallest uncertainty will be obtained from the stable measurement data 321

which have small variance compared to the others. 322

5. Results 323

5.1 Statistical errors 324

For analysis, statistical errors of all gauges between the reference data μ are computed, 325

Figs. 4-5 show the scatter plots of Geonor, and Pluvio gauges for rain, mixed precipitation, 326

and snow types in various wind shields: DFIR-fence, BDA, CDA, SA, and no shield. 327

5.1.1 Rain events 328

In the rain events, the measurement values of Geonor gauges are agreed well with the 329

reference value μ. All correlation coefficients are larger than 0.99, and also, all absolute 330

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relative biases not exceed 3%. In Fig. 4, without Geonor BDA, RC and Rs have small values 331

as under 5%. The RC or Rs of Goenor BDA is a little large compared to other wind shields as 332

11%. The reason is probably due to the difference of capacities between Geonor BDA (with 333

600mm) of H4 in 2014/15 and Geonor BDA (1500mm) of H5 in 2015/16 season. The scatter 334

plots of Pluvio gauges are presented in Fig. 5. In all windshield types, Pluvio gauges also 335

have small errors for rain events as Rd and Rs are under 1.1% and under 7%, respectively. 336

Fig. 6a and Fig 7a show quartile statistics of differences and ratios, respectively, of each 337

gauge with different wind shield for rain events. Table 2 and Table 3 are corresponding values 338

of Fig. 6 and Fig.7, respectively. In the results of quartile statistics, in all gauges (Geonor of 339

Pluvio), without Geonor BDA, high agreements with reference value μ are appeared as the 340

IQRs of differences and ratios are under 0.1mm/h and under 1%, respectively. 341

5.1.2 Mixed precipitation events 342

In Fig. 4b, the correlation coefficient decreases to 0.98 at Geonor SA, and this gauge have 343

underestimation as Rd=-10%. For mixed precipitation type, notable result is that, for mixed 344

precipitation type, Pluvio is overestimated 2~7% than Geonor unlike other types. 345

The correlation coefficient of Pluvio has a decreasing to 0.98 at NS, and at this gauge, the 346

Rs has a sudden increasing to 14.4%. In the quartile analysis, the IQR of Pluvio SA is smaller 347

than the one of Geonor SA but, Pluvio NA has a larger IQR than Geonor NA as presented in 348

Table 2 and Table 3. 349

5.1.3 Snow events 350

In the snow events, the measurement values have remarkable differences according to 351

different wind shields. From CDA, Geonors have decreasings of correlation coefficient and 352

relative bias as -0.92 and Rd as -17%, respectively. At NS, Rd is decreased to -42.1% and 353

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RC (Rs) is increased to 52.3% (32.5%). Pluvio also have remarkable decreasing of 354

correlation coefficient and Rd, from CDA, as 0.93 and -21.2%, respectively. At NS, Rd and 355

RC(Rs) are decreased to -43.3% and 55.3%(34.6%), respectively. 356

In quartile statistical analysis, also, obvious changes of errors are appeared according to 357

different wind shields rather than gauge types. Fig. 6c and Fig. 7c show the box plots of 358

distribution of differences and ratios for snow events, respectively, and Table 2(Table 3) 359

shows the corresponding data to Fig. 6c (Fig. 7c). When compared median Q2 for R2G and 360

R2P, R2G is 2% overestimated than R2P (see Table 3). In Table 3, without DFIR-fence and 361

CDA, the IQRs of Pluvio gauges are 2~6% larger than those of Geonor. 362

5.2 Results of Model I, II and III 363

The bias and uncertainty of Model I, II, and III are presented in Tables 4-7. Table 1 shows 364

the relative bias Rβ and relative uncertainty Rσ of all gauges using Model I. As noted in 365

the previous section, the bias and uncertainty using Model I are exactly the same as the 366

systematic difference d and estimated standard deviation s. 367

In Table 5, using Model II, represents the bias for different gauge type, Pluvio and 368

Geonor. To remove wind shield effects, the bias is computed under the condition ‘U < 369

2m/s’, for selecting 30 min sampled sets. The number of events for rain, mixed, and snow 370

are 43, 23 and 15, respectively. In Table 5, R represents bias errors for different wind 371

shield, not gauge type. As results, for Model II, the total bias can be computed as the sum 372

of two biases. This total bias will be compared with β of Model I with uncertainty 373

in Fig. 9. 374

In Model III, the bias is adjusted one using continuous function for catch ratio, dependent 375

on temperature and wind speed. The coefficients a, b and c of catch ratio function, and 376

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theuncertainties are presented in Table 7 for different gauge and wind shield types. 377


In Fig. 9a, for rain events, all bias obtained from Model I and Model II does not drop 379

below -3%, and without Geonor BDA, all uncertainties do not exceed 5%. In this figure, the 380

uncertainty and bias are much dependent on the types of gauges not different Models. In 381

Table 7, the maximum uncertainties of Geonor and Pluvio for Model III are appeared at BDA 382

and NS, as 12.63% and 6.29%, respectively. As a result, in rain events, bias and uncertainties 383

are affected by gauge types and instrumental errors not much wind shields. 384


Similar to the rain events, in mixed precipitation type, the differences are appeared usually 386

for different gauges with different wind shields. In Fig 9, for the mixed precipitation type, 387

about 3% overestimations of Pluvio gauges are obviously observed in the bias. The 388

uncertainties of Model I and II are very similar according to gauge and wind shield types, but 389

the uncertainties of Model III are not. Without the third model, all uncertainties of Geonor 390

gauges are smaller than thouse of Pluvio from BDA to SA. In all models, maximum 391

uncertainty is appeared at Pluvio NS as 16.75% for Model III. 392

Fig. 8 shows the continuous catch ratio function of U and T using Model III. In Fig. 8, the 393

dependence on wind speed and temperature is most obviously appeared at NS. Fig. 10 shows 394

the adjusted bias for fixed temperature T = 5℃ (first row), 0℃ (second row), and -5℃ 395

(third row) by varying the wind speed U obtained from sigmoid catch ration function. In this 396

figure, for fixed T = 0℃ (mixed precipitation) little increasing of bias for Pluvio DFIR is 397

observed as increased wind speed. When U = 5m/s, and T = 0℃ the catch ratios (bias) of 398

Geonor and Pluvio at SA are 0.85 (-15%) and 0.86 (-14%), respectively. Also, at NS, the 399

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ratios Geonor and Pluvio are 0.78 (-22%) and 0.77(-23%), respectively. 400


Unlike the mixed precipitation events, in the case of snow events, the differences of errors 402

for wind shield types look dominant than gauge types. The absolute values of bias and 403

uncertainties are certainly increasing when wind shield is varied from DFIR to NS as 404

presented in Fig 9 and Fig.10. In Model II, 1.38 % underestimation of Pluvio is observed than 405

Geonor as can be seen in Table 5, and this bias is very similar with the ones of Model I. 406

According to Model III, for U=5m/s and T = -5℃ the catch ratios (bias) of R2G and R2P are 407

0.99 (-1%) and 1.01 (1 %), respectively, whereas, in the same condition, the catch ratio (bias) 408

of Geonor NS and Pluvio NS are 0.61 (-39%) and 0.60 (-40%), respectively. Note that the 409

mean average wind speed and average temperature were about 3.7m/s and -8.7℃, 410

respectively, when snow events were observed in this period for analysis. In this averaged 411

condition, the bias for Geonor SA is -21% (using Model III), this value can be compared with 412

the median Q2 as 81% in Table 3. This loss quantity is much smaller than the one of Bratt’s 413

site in Smith (2009) due to the differences of environmental conditions (temperature, wind 414

speed, precipitation character, etc.) and the reference measurement. 415

Without Model III, uncertainties of Geonor gauges are increased with varying the wind 416

shield, from BDA to NS, as about 8.2%, 20.5%, 19.6%, and 32.4%. Similarly, the bias of 417

Pluvio gauges are increased as 11.6%, 19.7%, 23.9%, and 34.5%. Whereas, uncertainties for 418

Model III are much smaller than those of Model I and II: from BDA to NS, uncertainties of 419

Geonor and Pluvio are increased as 7.2% ~ 18.8%, and 8.7% ~19.2%, respectively. This 420

reason is that the bias removed uncertainties are obtained from adjusted bias using wind 421

speed and temperature. 422

20

5.3 Results of Model IV 423

Note that a reference is not defined in Model IV as the other models. To find the 424

instrumental uncertainty, for the same gauge types, same environmental conditions are 425

nedded including same windshield. Thus, to remove the effect of windshield, the wind speed 426

condition ‘U < 2m/s’ is assumed for this analysis. In the same wind speed condition, the 427

uncertainties for this model are compared with the ones of Model II. The uncertainties for 428

Geonor and Pluvio are presented in Fig. 11, using Model II and Model IV, and their values 429

are depicted in Table 8. 430


In the rain events, there are disagreements in uncertainties for different gauge types and the 432

same gauges. But the magnitude of differences between two models are within 2%. 433

Interesting is that the trends of two uncertainties for Geonor BDA are very analogous to each 434

other. So, the result of Model IV appears to have a relation with Model II despite their 435

different assumption about true data. 436


In Fig. 11, in the mixed precipitation events, similar patterns are appeared for the same 438

gauges. Just 2% of difference for Pluvio SA is observed, and without SA wind shield, the 439

uncertainties of Model IV are less than around 2%. Also, similar to the rain events, Geonor 440

BDA for two models have slightly large uncertainties compared to other wind shields. For SA 441

wind shield, in two models, Geonor has larger uncertainties than Pluvio, whereas, the 442

uncertainty for Geonor NS is smaller than the one of Pluvio. 443


In the snow events, the changes of uncertainties are small compared to rain or mixed 445

21

precipitation events, and all values are within 4%. In the snow events, it seems that the effect 446

of wind speed is not removed with the condition ‘U < 2m/s’, because the largest uncertainties 447

are appeared at NS for two gauges. Therefore, when we use Model IV in snow events, the 448

smaller threshold for wind speed is needed for analysis if there are enough number of 449

samples. 450

As results, most uncertainties of Model IV and II are not almost same and the uncertainites 451

ofr Model IV are usually smaller than the ones of Model II. The differences are probably 452

induced from the wrong assumption about covariance (zero assumption) and true data in 453

Model II. If the values and are affected by wind speed, that is, a wind speed condition 454

is not completely removed, then and will have positive relations because 455

is unrelated with wind speed. Also, even though wind speed condition is removed, it is 456

difficult to find which gauge has the nearest true data. Through this model, the smallest 457

uncertainty can be obtained from the gauges which have small variance of difference between 458

other gauges. That is, this model could be useful to find the gauge producing most stable 459

measurement value. 460

6. Summary and conclusion 461

In this study, quantitative evaluation analysis is performed for the data of two kinds of 462

automatic weighing gauges with different wind shields at CARE site, for two winter seasons. 463

For the uncertainty analysis, general statistical analysis for differences and ratios are 464

computed, and then four types of models for bias or uncertainty are applied. From the first to 465

the third model, the reference or true value is assumed as the mean of R2G and R2P. The first 466

model is theoretically the same as ones of general statistical analysis. Using the second model, 467

bias and uncertainties can be calculated according to gauge types and wind shield types. In 468

22

the third model, catch ratios of all gauges are fitted as continuous functions of temperature 469

and wind speed, so using these continuous functions, the bias values are adjusted ones 470

according to wind speed and temperature. When the bias and uncertainties are compared, the 471

values of two models (I and II) were analogous to each other because of their definitions for 472

uncertainty and bias. Whereas the uncertainties for Model III was little smaller than those of 473

Model I and II due to their adjusted biases using temperature and wind speed. 474

The last model suggests an alternative way to calculate instrumental uncertainty without 475

any assumption for true or reference values. This model should be performed to same gauge 476

type with same environmental conditions. Under a small wind speed condition, when the 477

uncertainties are compared with those of Model II, the values of Model IV are around 2% 478

less than Model II, whereas, similar trends were appeared in two models. The discrepancy of 479

uncertainties between them are duo to the assumption of zero covariance for Model IV and 480

assumption for the true data of Model II. Also, the small wind speed condition (U < 2m/s) is 481

not enough to remove different wind shield condition. Nevertheless, under the same 482

environmental condition, for same gauges with same wind shield, this method could be an 483

alternative for finding instrumental uncertainties without reference value. 484

485

Acknowledgements. This work was funded by the Korea Meteorological Administration 486

Research and Development Program under Grant KMIPA 2015-1010. 487

488

23

References 489

ASTM D4430-00 (2015): Standard Practice for Determining the Operational Comparability 490

of Meteorological Measurements, ASTM International, West Conshohocken, PA, 2015, 491

http://dx.doi.org/10.1520/D4430-00R15. 492

Ciach, J. G., and W. F. Krajewski, 1999: On the estimation of radar rainfall error variance. 493

Adv. Water Resour., 22, 585-595. 494

Goodison, B. E., and D. Yang, 1996: In-situ measurements of solid precipitation in high 495

latitudes: The need for correction. Proceedings of the Workshop on the ACSYS Solid 496

Precipitation Climatology Project, WMO/TD-739, WCRP-93, 3-17. 497

Goodison, B. E., P. Y. T. Louie, and D. Yang, 1998: WMO Solid precipitation measurement 498

intercomparison. WMO Instruments and Observing Methods Rep. 67, WMO/TD-872, 499

212 pp. 500

Groisman, P. Ya., and D. R. Legates, 1994: The accuracy of United States precipitation data. 501

Bull. Amer. Meteor Soc., 75. 215-227. 502

Habib, E. and W. F. Krajewski, 2002: Uncertainty analysis of the TRMM ground-validation 503

radar-rainfall products: application to the TEFLUN-B field campaign. Journal of 504

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Nitu, R., and K. Wong, 2010: CIMO survey on national summaries of methods and 506

instruments for solid precipitation measurement at automatic weather stations. WMO 507

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Regan H. M., M. Colyvan, and M. A. Burgman, 2002: A taxonomy and treatment of 509

uncertainty for ecology and conservation biology, Ecological Applications 12, 618-628. 510

Smoth, C., J. Hoover, J. Kochendorfer, and R. Nitu, 2012: Specifications for the WMO-511

24

SPICE Single Alter Shield Configuration, URL : https://www.wmo.int/pages/prog/ 512

www/IMOP/intercomparisons/SPICE/Docs/Specifications%20SPICE%20Single%20513

Alter%20JH.PDF 514

Smith, C. and S. Watson, 2009: An assessment of the double Alter wind shield for reducing 515

wind bias in snowfall measurements made with the Geonor T-200B, CMOS Congress 516

2009, May 31-June 4, Halifax, NS, Canada 517

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First Session and International Organizing Committee for the WMO Solid 519

Precipitation Intercomparison Experiment First Session, Final Report of the First 520

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Intercomparison Experiment Second Session. Final Report of the Second Session, 523

Boulder, United States, WMO, Geneva, 74 pp. 524

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2015: Derivation of a new continuous adjustment function for correcting wind-induced 526

loss of solid precipitation: results of a Norwegian field study, Hydrol. Earth Syst. Sci., 527

19, 951–967, doi:10.5194/hess-19-951-2015. 528

Yang, D., B. E. Goodison, J. R. Metcalfe, V. S. Golubev, E. Elomaa, T. Gunther, R. Bates, 529

T. Pangburn, C. Hanson, D. Emerson, V. Copaciu, J. Milkovic, 1995: Accuracy of 530

Tretyakov precipitation gauge: result of WMO intercomparison. Hydrological 531

Processes 9 (8), 877–895. 532

25

Yang, D., B. E. Goodison, C. S. Benson, S. Ishida, 1998: Adjustment of daily precipitation at 533

10 climate stations in Alaska: application of World Meteorological Organization 534

intercomparison results. Water Resources Research 34 (2), 241–256 535

536

26

Table 1. Used models, capacity, height, and locations of weighing gauges. 537

Sen-sor

Shield 2014-2015 2015-2016

base File prefix

Model, capacity (height)

base File prefix

Model, capacity(height)

Geo- nor

DFIR H2 Geonor T-200B3, 600mm (3m)

H2 Geonor T-200B3, 600mm (3m)

BDA 3B H4 Geonor T-200B3, 600mm (2m)

8 H5 Geonor T-200B3, 1500mm (2m)

CDA 2 H3 2 H3 Geonor T-200B3, 600mm (2m)

SA 9 H6 9 H6

NS 5 H7 5 H7

Pluvio DFIR HR Pluvio2,200cm2, 1500mm(3m)

HR Pluvio2,200cm2, 1500mm(3m)

BDA 4A HN Pluvio2,200cm2, 1500mm(2m)

7 HO Pluvio2,200cm2, 1500mm(2m)

CDA 13C HS 13C HS

SA 13D HT 13D HT

NS 13 HP 13 HP

538

539

27

Table 2. The quartile statistics of P [mm/h] for all precipitation types. 540

Type Gauge Wind shield

DFIR BDA CDA SA NS

Rain [mm/h]

Geonor Q1 -0.03 -0.12 -0.03 -0.03 -0.01

Q2 0.00 -0.03 -0.02 -0.03 -0.01

Q3 0.03 0.05 0.02 0.00 0.04

IQR 0.06 0.17 0.07 0.06 0.09

Pluvio

Q1 -0.03 -0.06 -0.05 -0.05 -0.06

Q2 0.00 -0.02 -0.01 -0.02 -0.02

Q3 0.03 0.02 0.03 0.02 0.02

IQR 0.06 0.08 0.08 0.07 0.08

Mixed [mm/h]

Geonor Q1 -0.07 -0.19 -0.11 -0.20 -0.18

Q2 -0.04 -0.06 -0.06 -0.15 -0.01

Q3 -0.01 0.01 -0.02 -0.06 -0.04

IQR 0.07 0.21 0.09 0.14 0.14

Pluvio

Q1 0.01 -0.06 -0.06 -0.08 -0.15

Q2 0.04 -0.01 -0.01 -0.03 -0.05

Q3 0.07 0.03 0.04 0.02 0.02

IQR 0.07 0.09 0.10 0.10 0.17

Snow [mm/h]

Geonor Q1 -0.03 -0.25 -0.66 -0.70 -1.35

Q2 0.01 -0.13 -0.21 -0.35 -0.72

Q3 0.04 -0.01 0.01 -0.12 -0.17

IQR 0.07 0.24 0.67 0.58 1.18

Pluvio

Q1 -0.04 -0.29 -0.65 -0.83 -1.35

Q2 -0.01 -0.15 -0.31 -0.38 -0.81

Q3 0.03 -0.01 -0.07 -0.07 -0.19

IQR 0.07 0.28 0.58 0.76 1.16

541

28

Table 3. The quartile statistics of the ratio P / for all precipitation types 542


DFIR BDA CDA SA NS

Rain

Geonor Q1 0.98 0.90 0.96 0.95 0.96

Q2 1.00 0.98 0.99 0.98 0.99

Q3 1.02 1.03 1.02 1.00 1.03

IQR 0.05 0.13 0.05 0.05 0.06

Pluvio

Q1 0.98 0.96 0.96 0.95 0.95

Q2 1.00 0.99 1.00 0.99 0.99

Q3 1.02 1.02 1.02 1.01 1.01

IQR 0.05 0.05 0.06 0.07 0.06

Mixed

Geonor Q1 0.95 0.88 0.93 0.85 0.88

Q2 0.98 0.97 0.96 0.91 0.93

Q3 1.00 1.01 0.99 0.95 0.98

IQR 0.05 0.13 0.07 0.10 0.10

Pluvio

Q1 1.00 0.96 0.96 0.94 0.88

Q2 1.02 0.99 0.99 0.98 0.97

Q3 1.05 1.02 1.02 1.01 1.01

IQR 0.05 0.06 0.06 0.08 0.13

Snow

Geonor Q1 0.98 0.89 0.72 0.70 0.47

Q2 1.01 0.93 0.88 0.81 0.63

Q3 1.03 0.99 1.00 0.89 0.80

IQR 0.05 0.10 0.29 0.20 0.33

Pluvio

Q1 0.97 0.86 0.72 0.66 0.43

Q2 0.99 0.93 0.85 0.83 0.63

Q3 1.02 0.99 0.92 0.92 0.78

IQR 0.05 0.13 0.20 0.26 0.35

543

29

Table 4. Relative bias and relative uncertainty of all gauges when using Model I. 544

545

546


DFIR BDA CDA SA NS

β

[%]

Rain Geonor -0.25 -2.91 -0.58 -1.81 -0.32

Pluvio 0.25 -0.80 -0.19 -0.85 -1.14

Mixed Geonor -2.31 -5.54 -5.18 -9.91 -8.34

Pluvio 2.31 -1.28 -1.51 -3.01 -6.88

Snow Geonor 0.39 -7.21 -17.20 -23.22 -41.08

Pluvio -0.39 -9.21 -21.19 -26.13 -43.33

[%]

Rain Geonor 3.43 11.59 3.54 4.60 4.57

Pluvio 3.43 3.83 6.26 4.23 4.19

Mixed Geonor 2.95 9.81 8.93 10.89 12.00

Pluvio 2.95 4.73 6.15 7.98 14.36

Snow Geonor 3.47 8.19 20.52 19.11 32.50

Pluvio 3.46 11.62 19.73 23.96 34.60

30

Table 5. Relative bias of ith gauge and relative bias of jth windshield. 547

548

Table 6. Relative total bias ( β ) and relative uncertainty Rσ of all gauges for model 549

II. 550

551

Types [%] [%]

Geonor Pluvio DFIR BDA CDA SA NS

Rain 0.00 -0.01 0.39 -1.46 0.01 -0.94 -0.34

Mixed -2.73 0.43 1.15 -2.25 -2.20 -5.35 -6.46

Snow -2.19 -3.57 2.88 -5.33 -16.31 -21.79 -39.33


DFIR BDA CDA SA NS

β [%]

Rain Geonor 0.49 -1.37 0.10 -0.84 -0.24

Pluvio -0.49 -2.34 -0.87 -1.82 -1.22

Mixed Geonor -1.58 -4.99 -4.93 -8.08 -9.19

Pluvio 1.58 -1.83 -1.77 -4.92 -6.03

Snow Geonor 0.69 -7.52 -18.51 -23.99 -41.52

Pluvio -0.69 -8.90 -19.89 -25.37 -42.90

[%]

Rain Geonor 3.50 11.65 3.58 1.68 4.55

Pluvio 3.50 4.11 6.27 4.32 4.18

Mixed Geonor 3.02 9.78 8.88 10.98 11.96

Pluvio 3.03 4.74 6.12 8.14 14.30

Snow Geonor 3.46 8.14 20.45 19.02 32.33

Pluvio 3.46 11.56 19.67 23.84 34.41

31

Table 7. Relative uncertainty Rσ and the coefficients , , and of the transfer function 552

for catch ratio: CR T, U 1 tan . 553


DFIR BDA CDA SA NS

a All types

Geonor 0.0021 0.0153 0.0199 0.0254 0.0503

Pluvio -0.0020 0.0111 0.0225 0.0301 0.0534

b Geonor 0.0000 0.0507 0.1874 0.3382 0.2968

Pluvio 0.0000 0.1981 0.2570 0.2377 0.2745

c Geonor 0.0000 0.0000 0.0000 0.2961 0.0014

Pluvio 0.0000 0.0000 0.0000 0.0000 0.0000

Rain Geonor 3.76 12.63 4.35 5.33 7.10

32

554

[%]

Pluvio 3.76 4.90 5.79 5.35 6.29

Mixed Geonor 4.00 11.28 7.51 7.85 12.85

Pluvio 4.00 6.44 8.42 9.78 16.75

Snow Geonor 3.65 7.23 14.55 9.62 18.77

Pluvio 3.65 8.66 13.01 14.38 19.21

All types

Geonor 3.80 10.84 9.41 7.65 13.27

Pluvio 3.80 6.69 9.36 10.13 14.53

33

Table 8. Comparison of Model II and Model IV for relative uncertainty Rσ when U < 2 m/s. 555

The number of samples for rain, mixed, and snow are 43, 23, and 15, respectively. 556

557

558

Gauge Type Model Wind shield

DFIR BDA CDA SA NS

Geonor [%]

Rain Model II 2.86 6.52 3.30 5.25 5.46

Model IV 2.87 7.24 3.83 4.07 4.27

Mixed Model II 2.42 5.05 2.31 4.77 4.81

Model IV 2.70 3.94 1.51 2.58 3.25

Snow Model II 0.61 1.79 2.08 2.05 3.71

Model IV 0.86 1.28 0.96 1.11 2.45

Pluvio [%]

Rain Model II 2.85 3.31 3.92 3.64 3.76

Model IV 2.38 3.04 2.36 2.48 2.41

Mixed Model II 2.42 2.96 2.35 3.08 7.07

Model IV 1.22 2.06 1.44 0.41 5.24

Snow Model II 0.61 1.63 1.78 1.17 3.81

Model IV 0.27 1.75 0.34 0.66 2.65

34

Fig. 1. Site layout of CARE (20 November 2014–present). Green colored bases

represent Geonor gauges and the oranges are Pluvio gauges. The file prefix names for

R2G and R2P are H2 and HR, respectively.

559

560

561

Fig. 2

2015-2

Pluvio

. Photos of

2016 seaso

o in SA, (h)

f 5 types of

n, (d) in 20

Geonor NS

wind shield

014-2015 s

S, and (i) Pl

35

ds. (a) R2G

season (e) P

uvio NS (co

G in DFIR, (

Pluvio in C

ourtesy by E

(b)R2P in D

CDA, (f) Ge

EC).

DFIR, (c) BD

eonor in SA

DA in

A, (g)

36

(a)

(b)

Fig. 3. Time series of QCed accumulation data of (a) Geonor sensors and (b) Pluvio

snesors with different wind shields types in 2014-2015 winter (left) and 2015-2016 winter

(right).

562

563

37

Fig. 4. Scatter plots of Geonor in DFIR-fence (first row), in BDA (second row), in CDA

(third row), in SA (fourth row), and with no shield (fifth row), which are compared with

the average of R2G and R2P.

564

38

Fig. 5. Scatter plots of Pluvio in DFIR-fence (first row), in BDA (second row), in CDA

(third row), in SA (fourth row), and with no shield (fifth row), which are compared with

the average of R2G and R2P.

565

39

(a) Rain

(b) Mixed

(c) Snow

Fig. 6. Box plots of distribution of the difference P-μ, where P is precipitation rate of

Geonor (left) or Pluvio (right) with the different wind shield types, and μ is the mean value

of the two references R2G and R2P.

566

567

40

(a)

(b)

(c)

Fig. 7. Box plots of distribution of the ratio P/μ, where P is precipitation rate of Geonor

(left) or Pluvio (right) with the different wind shield types, and μ is the mean value of the

two references R2G and R2P.

568

569

570

571

Fig. 8.

(right) f

Catch ratio

for all types

os and its si

s to obtain th

igmoid fun

he bias dep

41

ctions of G

endent on U

Geonor gaug

U and T.

ges (left) annd Pluvio ggauges

42

Fig. 9. Comparisons of bias (left) between Model I and II, and comparisons of uncertainty

(right) among Model I, II, and III.

572

573

43

Fig. 10. Adjusted bias functions of all gauges for T =5℃ (first row), 0℃ (second row), and

-5℃(third row) using Model III.

574

44

Fig. 11. Comparison of Model II and IV for uncertainties when U ≤ 2 m/s.

575

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