NOTES AND CORRESPONDENCE. Estimating the Proportion of Monthly Precipitation that Falls in Solid Form

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1 OCTOBER 2009 N O T E S A N D C O R R E S P O N D E N C E 1299 NOTES AND CORRESPONDENCE Estimating the Proportion of Monthly Precipitation that Falls in Solid Form DAVID R. LEGATES AND TIANNA A. BOGART Office of the State Climatologist, University of Delaware, Newark, Delaware (Manuscript received 29 August 2008, in final form 21 April 2009) ABSTRACT In applications where a monthly temporal resolution is employed, an important variable is the proportion of monthly precipitation that falls in solid form. Globally applicable equations for estimating this variable developed by previously published research are reevaluated. A revised equation developed 20 years ago by the lead author for climatological analysis works well for long-term data but not for actual monthly averages. A new equation, therefore, is developed for use with monthly data using an Arctic database of stations above 508N latitude. These two equations have mean absolute fit errors of and , respectively. The data were split into four regions North America, northern Europe, northern Asia, and Greenland and were also evaluated for the effect of elevation or seasonality influences. Results suggest that seasonality also is an important variable, particularly to differentiate between midwinter and transition months (i.e., October and April). 1. Introduction Corresponding author address: Dr. David R. Legates, Office of the State Climatologist, University of Delaware, 212A Pearson Hall, Newark, DE legates@udel.edu In a number of hydrological and climatological applications, data with a monthly temporal resolution are used, either out of convenience or by choice. Assessments of water balances, analysis of long-term climatic trends, and investigations of spatial variability in various climatic variables, for example, often employ monthly averaged observations of air temperature and precipitation. This is because their spatial and temporal resolution tends to be greater owing to data availability; for many nations, monthly totals and averages are more readily available for about twice the number of stations than for daily data. Increased fidelity in both space and time often justifies a researcher to select monthly data over daily data. Monthly averages or totals also are often the period of choice, owing to an emphasis on longer time-scale patterns and trends, because mesoscale phenomena (e.g., individual storm events or the passage of fronts and weather patterns) are smoothed over. Although not always appropriate, monthly averages nevertheless provide a convenient average time scale that preserves the seasonal cycle while removing the higher frequency noise. But missing in this information is the degree to which the monthly precipitation is apportioned into solid and liquid components. The proportion of monthly precipitation that falls in solid form is sensitive to both climate variability and climate change (Huntington et al. 2004). Moreover, it is an important variable for evaluating the hydrologic cycle on a monthly basis (Jaeger 1983; Legates and Mather 1992; Legates and McCabe 2005) and in assessing the gauge undercatch associated with precipitation gauge measurement (Sevruk 1982; Legates 1987; Goodison et al. 1998; Adam and Lettenmaier 2003; Legates et al. 2005; Bogart 2007). In addition, the need for high-quality assessments of snowpack accumulations, particularly in mountainous regions where the complex terrain leads to considerable spatial variability in many climate fields, makes a method for differentiating between solid and liquid precipitation (i.e., snow versus rainfall contributions to the total precipitation) useful. As a result of its importance, the World Climate Research Programme (WCRP) addresses solid versus liquid precipitation issues through its Climate and Cryosphere (CLIC) project. DOI: /2009JHM Ó 2009 American Meteorological Society

2 1300 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 10 Whether precipitation falls in solid or liquid form depends in large part on the surface air temperature, which is why it is often used as a surrogate for estimating the form of precipitation. However, it also is a function of several other parameters, including the timevarying vertical structure of air temperature and humidity (Forland and Hanssen-Bauer 2000). Indeed, Fuchs et al. (2001) have used surface relative humidity as an additional variable to determine the solid proportion of daily precipitation totals. Their analysis shows that as the relative humidity at 2-m height decreases, the proportion of solid precipitation increases slightly. Sevruk (1984) also considered elevation and the proportion of the number of days with snow when assessing snowfall proportion in Switzerland. Unfortunately, humidity variables (e.g., relative humidity, dewpoint temperature, and wet-bulb temperature) are not as widely measured as air temperature and precipitation. Sevruk (1984) found that his best predictor was the proportion of the number of days with snow but as with humidity variables, this variable is not widely measured. Legates (1987) had considered the use of precipitation amount as a second regressor but dismissed it as not providing a significant improvement to prediction. Precipitation anomaly is likely to be a better variable as a surrogate for moisture content, but it would only be helpful when assessing the actual monthly proportion of solid precipitation (rather than long-term averages in which the anomaly is always zero, by definition). Similarly, solar (or possibly net radiation) also may be useful in determining the proportion of precipitation falling in solid form (Daly et al. 2007). However, the lack of consistent measurements of humidity and/or radiation variables at a global scale limits the applicability of any method that relies upon these observations. To enhance the estimation of the proportion of precipitation that falls in solid form, Sevruk (1984) incorporated station elevation and seasonality as additional regressors. Unlike humidity and radiation, these variables are part of the metadata associated with precipitation observations and therefore are readily available. Sevruk (1984) found that station elevation may be a better predictor of the proportion of solid precipitation than air temperature for some stations and some months. For this paper, the use of both air temperature and station elevation (and also station latitude) was problematic as a result of the high degree of collinearity associated with these regressors. Although it is recognized that station elevation may be useful in some regional analyses (e.g., Sevruk s analysis in Switzerland), elevation by itself may not be a perfect predictor, owing to differences between the windward and the leeward side of mountain ranges and north-facing versus southfacing slopes, among others. On the basis of these concerns, air temperature will be considered as a sole regressor but additional variables, such as elevation and seasonality, also will be evaluated to determine their additional contribution to assessing the proportion of precipitation that falls in solid form for assessments of water budgets in the Arctic. Sevruk (1984) concluded that seasonality is the most important characteristic of the snowfall proportion in middle latitudes and derived equations for different times of the year, specifically, December/January, November/ February/March, and April October. These times represent the main winter, winter transition, and nonwinter months in Switzerland, respectively. Although this worked well for the Swiss Alps, stratification by month may not be useful for a globally applicable relationship because the definition of winter, transition, and nonwinter are not commensurate across a variety of disparate climates. Owing to its importance in climatological and hydrological studies and the concerns discussed earlier, the proportion of monthly precipitation that falls in solid form R has been estimated by several researchers solely as a function of air temperature. This paper seeks to examine the various relationships that have been developed to estimate R and to better understand how it relates to surface air temperature. 2. Estimates of R for long-term averages Given that R can be related to the long-term mean monthly air temperature T a, Lauscher (1954) proposed the simple linear relationship ) for T a, 08C ) T a for 08C # T a # 108C, and ) 5.0 for T a. 108C, (1) where T a is given in 8C (see Fig. 1). This curve assumes that rain does not occur when the long-term mean monthly air temperature is below 2108C and that snow does not occur when the temperature is above 108C. Thus, Eq. (1) implicitly assumes that the proportion of solid precipitation is symmetric about freezing; that is, ) when the mean monthly air temperature is 08C. Although probabilities are certainly low, data provided by Cehak-Trock (1957) demonstrated that for a number of stations, snow and rain often occur outside of these limits for mean monthly air temperature (Fig. 1) but that the curve of Lauscher (1954) provided a reasonable fit [i.e., a mean absolute fit error (MAE) of ]. Indeed, Lauscher s curve was recommended for

3 OCTOBER 2009 N O T E S A N D C O R R E S P O N D E N C E 1301 FIG. 1. Fit of equations to estimate by the proportion of R by Lauscher (1954; dotted line) and Legates (1987; dashed line) to air temperature data given by Cehak-Trock (1957; points), which were long-term monthly averages. estimating the proportion of solid precipitation by both Shver (1962) and Sevruk (1984) for computing precipitation gauge measurement bias adjustments. Legates (1987) recognized that a logistic curve would yield a better fit to the data of Cehak-Trock (1957) and developed the equation ) 5 [ (1.35) T a ], (2) which has a mean absolute fit error of (see Fig. 1). Equation (2) is symmetric about 21.68C and ) at 08C. However, the asymmetry about 08C [i.e., ), 0.5] can be explained physically. Long-term mean monthly air temperature includes observations from both storm events as well as from clear-sky conditions and represents a probability distribution of daily air temperatures. As a result of the insular effect of clouds, cloud cover (and hence precipitation potential) is associated with the higher temperatures, which, in turn, are more likely concomitant with precipitation events. Thus, it is likely that the mean monthly air temperature during precipitation is greater than the long-term mean monthly air temperature and thus ), 0.5. It should be noted that an evaluation of the proportion of precipitation that falls in solid form is strongly affected by the undercatch associated with precipitation gauge measurement (see Sevruk 1982; Legates 1987; Goodison et al. 1998). The deleterious effect of the wind is the largest source of gauge undercatch and results in a underestimate of the actual precipitation by about 8% globally (Legates 1987). But more importantly, wind errors are differentially biased toward snow events in that the bias with respect to snowfall is much greater than with rain events [see Goodison et al. (1998) for quantitative assessments of the magnitude of this bias for various precipitation gauge designs]. Although wetting losses (moisture that adheres to the interior walls of the gauge and to the collector during its emptying) are greater for rain than for snow (Sevruk 1982), their effect is much less than the importance of the effect of the wind on snowfall measurement. As a consequence, the water equivalent of snowfall is underestimated considerably more than rainfall such that the proportion of precipitation falling as snow, as estimated from traditional precipitation gauge observations, is therefore an underestimate as well. This is accentuated for months and locations where strong winds are commensurate with higher snowfall totals as compared to months and locations with smaller wind speeds. Here, such biases have not been estimated and removed from the data prior to the assessment of the proportion of precipitation falling as snow. This is useful for our goal of apportioning precipitation into solid and liquid components prior to the application of gauge bias adjustments; however, this bias in our equations (and, indeed, those developed by others where bias adjustments have not be addressed) should be duly noted in studies where gauge measurement bias adjustments are not employed. 3. A revised assessment for use with monthly averaged data The proportion of solid precipitation will first be estimated using air temperature as the only predictor variable for the full pan-arctic region (i.e., poleward of 508N) as well as for four subregions (i.e., North America, northern Europe, northern Asia, and Greenland). Subsequently, the effect of latitude and elevation will be included to determine if these additional variables significantly enhance the prediction of the proportion of solid precipitation. Seasonality will be explicitly considered in these subsequent analyses. a. A reevaluation of R using air temperature only Equation (2) was successfully applied to long-term mean monthly air temperature data to produce a biasadjusted climatology of gauge-measured precipitation (Legates 1987; Legates and Willmott 1990). However, in an evaluation with actual monthly air temperatures (i.e., not long-term means but actual monthly data), significant problems were found with the use of Eq. (2). In

4 1302 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 10 FIG. 2. Proportion of R as a function of actual average monthly T a. Monthly values of R and T a were computed from daily data for for stations poleward of 508N. The solid white line is the logistic fit, and the gray lines are the 95% confidence interval. For the sample size of station months, the MAE was particular, the use of Eq. (2) results in a significant overestimate of monthly values of R for air temperatures between 228 and 208C and a significant underestimate between about 248 and 2228C (Bogart 2007). To seek a remedy, Legates et al. (2005) obtained data for 2709 stations above 508N from the National Climate Data Center s (NCDC) Global Summary of the Day (GSOD) database (version 6, TD9956). These data are derived from a minimum of four synoptic/hourly observations, although many are based on a complete set of 24 hourly observations. The time series spans from 1994 through 2002, and the records are relatively complete; the most notable exception being communication lapses for some stations in The NCDC and the U.S. Air Force Climatology Center have both provided quality control of the data, although a small number of errors may still exist, including rounding errors when the data were converted to metric units. Of the 2709 stations, 950 are located in the former Soviet Union, 454 in Canada, 309 in the United Kingdom, 269 in Sweden, 160 in Norway, 155 in Alaska, 69 in Germany, 59 in Finland, 58 in Poland, 53 in Denmark, and the remainder (173) in other countries (including six Arctic buoy and fixed platform stations). Notice that precipitation is classically divided into three forms solid, liquid, and mixed precipitation although not all countries or observers diligently record mixed precipitation. In keeping with the original definition of R FIG. 3. Comparison of various estimates of the proportion of R using equations developed by Lauscher (1954; dotted line), Legates (1987; dashed line), and Eq. (3) (solid line). used by Sevruk (1982), R here is defined solely as the solid precipitation proportion of the precipitation total, computed as the amount of gauge-measured snowfall divided by the total gauge-measured precipitation. Overall, the number of mixed events was relatively small for most stations, and these mixed events did not comprise a significant proportion of the total number of events. Analysis of these data resulted in station months from which a new logistic regression curve was fit. The revised equation is ) 5 [ (1.5315) T a ], (3) where T a is the mean monthly air temperature given in 8C and provides a mean absolute fit error of (Fig. 2). 1 To compute this equation, weighted regression was used to reduce the influence of the plethora of points at ) 5 0. The data were binned by values of ) into 10 equally spaced categories, and the weights were selected so that each category of 0.1 ) was given equal weight. Thus, the equation was forced to fit the entire distribution of points (Fig. 2) rather than providing a statistical line of best fit to all of the data points, which would give undue weight to low values of ). Equation (3) is symmetric about Cand ) at 08C. Notice that visual inspection of the scatter 1 Notice that this equation is different from that given by Bogart (2007) because of the use of weighted regression in this paper.

5 OCTOBER 2009 N O T E S A N D C O R R E S P O N D E N C E 1303 FIG. 4. Regional assessments of Eq. (3) for (top left) North America, (top right) northern Europe, (bottom left) northern Asia, and (bottom right) Greenland. in Fig. 2 suggests considerable variability around the equation, owing to the dense network of observations. The relatively low mean absolute fit error, however, indicates that approximately half of the data lie within of the line the errors are not uniformly distributed between 20% and 80%, for example. Figure 3 illustrates the relationship between the three equations. The three curves converge near R and T a C while the biggest difference between Eq. (2) and Eq. (3) is and occurs at 2.38C. The reason for the lack of fit of Eq. (2) is that the distribution of air temperatures that comprise a long-term average (i.e., its probability density function) is much wider than for an average for a given month. A long-term average contains months with a greater variety of air temperatures and hence more variability in the solid proportion of the total precipitation. Thus, it is expected that the equation developed from long-term monthly data would overestimate R for high air temperatures and underestimate R for low temperatures. b. Estimation of R using air temperature by region To assess the regional dependence on R, Eq. (3) was refit to subsets of the data for North America, northern Europe, northern Asia, and Greenland. This partitioning resulted in station months for North America, for northern Europe, for northern Asia, and 1077 for Greenland (98 station months at six Arctic buoy and fixed platform stations were not included). Regionally, the equations become ) 5 [ (1.493) T a ] for North America, (4a)

6 1304 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 10 FIG. 5. Comparison of the logistic curves fit to data from each of the four regions. ) 5 [ (1.667) T a ] ) 5 [ (1.461) T a ] and ) 5 [ (1.695) T a ] for for northern Europe, (4b) northern Asia, (4c) for Greenland, (4d) with mean absolute fit errors of for North America [Eq. (4a)], for northern Europe [Eq. (4b)], for northern Asia [Eq. (4c)], and for Greenland [Eq. (4d)]. These equations are shown, along with the data scatter, in Fig. 4. Recall that although the scatter visually appears large, this is due to the large number of station months; the mean absolute fit errors show the data are concentrated much higher near the curve. Regionally, the curves are substantially different from one another. For example, at 08C, the estimate of ) is 0.299, 0.316, 0.381, and for the four regions, respectively. These differences are larger than the margin of error (i.e., the mean absolute error) for the original equation [Eq. (3)] and illustrate that a universal relationship between T a and R for large areas of the Arctic does not likely exist (see Fig. 5). The largest mean absolute fit error, and the smallest value of )at08c, occurs in Greenland where most of the stations are at low elevation along the coast. By contrast, northern Asia has the largest value )at08c and has a larger percentage of continental (noncoastal) stations. Notice, however, from Fig. 5 that the four curves are not substantially different from one another such that to a first approximation, a global relationship could be used. Nevertheless, the evaluation of ) for smaller regions may vary dramatically. c. Correlation of the residuals using elevation and month On the basis of the results of the previous section, it seems plausible that the efficacy of )mightbe enhanced by including elevation as an additional variable and possibly stratifying the computation of )by season (month). Elevation potentially plays a role because the apportionment of snowfall and rainfall amounts can be affected by the altitude of the station, although the slope and azimuth are important as well. Slope and azimuth were not included in the analysis because they are not naturally part of the station metadata. Notice, too, that elevation itself tends to be inversely collinear with air temperature, which may introduce a collinearity problem in fitting the coefficients. Seasonal differences are more likely to be an issue, particularly with stations at lower latitudes. This is because day length is strongly a function of both latitude and time of year, which can affect the mean daily distribution of air temperature but often does not affect the snowfall proportion. A priori, it is expected that the stations included in this analysis should not be adversely affected by seasonality because they are all located above 508N latitude and solar zenith angles during the entire snow season are high. It is expected, however, that seasonality would be a more significant issue for stations in midlatitudes, which is why Sevruk (1984) found season to be an important variable for estimating snowfall proportion in Switzerland. Nevertheless, the influence of elevation and seasonality (month) will be evaluated for each of the four subregions previously mentioned. Correlation of the residuals of Eq. (4) for each of the four regions with station elevation (Table 1) shows that elevation, by itself, does not substantially enhance the efficacy of estimating ). All but one correlation is less than 0.16, and all explain less than 7.5% of the residual variance. At this spatial scale, the differences among slope aspect indicate that elevation alone is not helpful in reducing the uncertainty in ). As a result, it is concluded that the use of elevation as a predictor at the large regional scale is not warranted. However, it is again noted that Sevruk (1984) found elevation may be a better predictor of R than air temperature for small regional analyses (e.g., Switzerland) where the orientation of mountain ranges is more consistent with the prevailing wind direction.

7 OCTOBER 2009 N O T E S A N D C O R R E S P O N D E N C E 1305 TABLE 1. Correlations between the residuals of Eq. (4) and elevation for each of the four regions. North America Northern Europe Northern Asia Greenland January February March April May June July August September October November December An investigation of the coefficients of the logistic equation ) 5 (1 1 bc T a) by month for each of the four regions during the five winter and transition months (Table 2) highlights a trend to the coefficients that appears to hold across most regions. 2 In general, the multiplier (b) tends to increase and the base of the exponential function (c) decreases slightly during the midwinter. Increasing b leads to shifting the curve toward lower (negative) values of R for the same T a, whereas decreasing c increases the spread of the curve around T a 5 0. Thus, during the coldest months, the curve tends to shift left and spread out, which causes the values of R to be lower in the middle of winter than during the transition months for the same T a. This is not unexpected because snows during the transition months tend to be wetter and thus a higher proportion of the precipitation will be snowfall for the same air temperature. The importance of month, particularly during these transition months, is significant enough that it will be incorporated into Eq. (3) and thus a monthly dependency on ) will be explicitly considered. For October April, separate global curves were developed from Eq. (3) to account for the varying distribution of ) by month. These equations are as follows: ) 5 [ (1.808) T a ] (MAE ) for October, (5a) ) 5 [ (1.614) T a ] (MAE ) for November, (5b) 2 May September were deleted from subsequent analysis because more than 90% of the observations had monthly values of R 5 0.0, which would have significantly skewed the coefficients. TABLE 2. Coefficients (b and c) for the logistic equation ) 5 (1 1 bc T a) by month for each of the four regions, where T a is the mean monthly air temperature in 8C. Only winter and transition months are shown because very few observations of snow occurred in the other months. ) 5 [ (1.561) T a ] (MAE ) for December, (5c) ) 5 [ (1.554) T a ] (MAE ) for January, (5d) ) 5 [ (1.546) T a ] (MAE ) for February, (5e) ) 5 [ (1.698) T a ] (MAE ) for March, and (5f) ) 5 [ (1.681) T a ] (MAE ) for April. (5g) These curves are graphically compared in Fig. 6. Notice that the global curves are very much similar for November February, with the transition months of October and April being substantially different. Although Eq. (5) is preferable, Eq. (3) could be used for all months without introducing too much uncertainty. 4. Conclusions North America Northern Europe Northern Asia Greenland October 1.17, , , , 2.08 November 5.59, , , , 1.87 December 7.86, , , , 1.64 January 8.13, , , , 1.63 February 10.98, , , , 1.24 March 6.33, , , , 1.35 April 1.24, , , , 1.70 On the basis of this examination, it is recommended that Eq. (2) be used to estimate the proportion of precipitation falling in solid form when long-term mean monthly air temperatures are used. Equation (3) is more appropriate when actual monthly air temperature averages are employed. The mean absolute fit error (MAE) for these two equations is and , respectively. However, the differences between the months most notably, the transition months versus those from midwinter suggest that separate equations be used for different months [i.e., Eq. (5)].

8 1306 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 10 Grant NNG05GO92H). D. Legates has received funding for the development of precipitation gauge bias adjustment methodologies from the National Science Foundation (NSF Grant ATM ). REFERENCES FIG. 6. Comparison of the logistic curves fit to the monthly subsets of the dataset. Notice that with the continued use of automatic weather stations with daily/hourly observations, equations based on higher temporal resolution (and possibly including mixed precipitation as a third possibility) will yield a better MAE than these monthly relationships. But because more stations exist for which only monthly total precipitation is available, researchers will opt for increased spatial and temporal fidelity that underscores the need for an equation to differentiate between liquid and solid components of precipitation. The efficacy of these equations is limited by the predictive ability of surface air temperature as the sole regressor. In many regional or local applications, results may be enhanced by including other variables, such as atmospheric humidity, latitude, precipitation anomaly (i.e., departure from normal), number of days with precipitation, and/or proportion of days with snowfall. For global or continental-scale analyses, however, air temperature remains as the only variable measured at a relatively high station density. Recall, too, that the dataset used may also be a source of bias because it covers only nine years and focuses only on stations poleward of 508N. Acknowledgments. We acknowledge the extremely helpful comments of three anonymous reviewers. In addition, D. Legates wishes to express his thanks to B. Goodison (Canada), P. Ya. Groisman (Russia), B. Sevruk (Switzerland), and D. Yang (USA) for their discussions regarding solid precipitation measurement and biases. T. Bogart was supported by the Delaware Space Grant College and Fellowship Program (NASA Adam, J. C., and D. P. Lettenmaier, 2003: Adjustment of global gridded precipitation for systematic bias. J. Geophys. Res., 108, 4257, doi: /2002jd Bogart, T. A., 2007: Bias Adjustments of Arctic Precipitation. Publications in Climatology, Vol. 60, Center for Climatic Research, University of Delaware, 36 pp. Cehak-Trock, H., 1957: Der feste Niederschlag im atlantischen Klimagebiet. Arch. Meteor. Geophys. Bioklimatol., 8B, Daly, C., J. W. Smith, J. I. Smith, and R. B. McKane, 2007: Highresolution spatial modeling of daily weather elements for a catchment in the Oregon Cascade Mountains, United States. J. Appl. Meteor. Climatol., 46, Forland, E. J., and I. Hanssen-Bauer, 2000: Increased precipitation in the Norwegian Arctic: True or false? Climatic Change, 46, Fuchs, T., J. Rapp, F. Rubel, and B. Rudolf, 2001: Correction of synoptic precipitation observations due to systematic measuring errors with special regard to precipitation phases. Phys. Chem. Earth, 26B, Goodison, B. E., P. Y. T. Louie, and D. Yang, 1998: WMO solid precipitation intercomparison final report. Instruments and Observing Methods Rep. 67, WMO/ TD-872, 212 pp. Huntington, T. G., G. A. Hodgkins, B. D. Keim, and R. W. Dudley, 2004: Changes in the proportion of precipitation occurring as snow in New England ( ). J. Climate, 17, Jaeger, L., 1983: Monthly and areal patterns of mean global precipitation. Variations in the Global Water Budget, A. Street- Perrott, M. Beran, and R. Ratcliffe, Eds., D. Reidel, Lauscher, F., 1954: Klimatologische Probleme des festen Niederschlages. Arch. Meteor. Geophys. Bioklimatol., 6B, Legates, D. R., 1987: A Climatology of Global Precipitation. Publications in Climatology, Vol. 40, C. W. Thornthwaite Associates, 91 pp., and C. J. Willmott, 1990: Mean seasonal and spatial variability in global surface air temperature. Theor. Appl. Climatol., 41, , and J. R. Mather, 1992: An evaluation of the average annual global water balance. Geogr. Rev., 82, , and G. C. McCabe Jr., 2005: A re-evaluation of the average annual global water balance. Phys. Geogr., 26, , D. Yang, S. M. Quiring, K. F. Freeman, and T. A. Bogart, 2005: Bias adjustment to Arctic precipitation: A comparison of daily versus monthly bias adjustments. Preprints, Eighth Conf. on Polar Meteorology and Oceanography, San Diego, CA, Amer. Meteor. Soc., 5.1. [Available online at ams/annual2005/techprogram/paper_86285.htm.] Sevruk, B., 1982: Methods of correction for systematic error in point precipitation measurement for operational use. Operational Hydrology Rep. 21, WMO Rep. 589, 91 pp., 1984: Assessment of snowfall proportion in monthly precipitation in Switzerland. Zb. Meteor. Hidrol. Rad. Beograd, 10, Shver, Ts. A., 1962: Frequencies in the amounts of precipitation of various forms. Sov. Hydrol. Sel. Pap., 4,