Application of a Comprehensive Bias-Correction Model to Precipitation Measured at Russian North Pole Drifting Stations

Transcription

1 700 JOURNAL OF HYDROMETEOROLOGY VOLUME 3 Application of a Comprehensive Bias-Correction Model to Precipitation Measured at Russian North Pole Drifting Stations ESFIR G. BOGDANOVA, BORIS M. ILYIN, AND IRINA V. DRAGOMILOVA Voeikov Main Geophysical Observatory, St. Petersburg, Russia (Manuscript received 29 May 2001, in final form 29 April 2002) ABSTRACT An improved bias correction is applied to daily precipitation measured at Russian North Pole drifting stations during the period from the early 1950s through The bias-correction method is based on a model accounting for all main systematic errors of precipitation measurement by means of the standard Tretyakov gauge, namely: aerodynamic error; joint effect of wetting, evaporation, and condensation at the gauge collector interior; trace precipitation; and the effect of false precipitation due to blowing snow flux into the gauge. The bias-corrected annual precipitation averaged over the entire period and all drifting stations amounts to 165 mm, which is 28% higher than the measured value. Large errors induced by strong winds are to a certain extent compensated by the false precipitation, the amount of which increases with the wind speed and blizzard duration. Annual mean false precipitation comprises 30% of the total measured precipitation. The validity of the obtained bias-corrected estimates, both for the cold season (solid precipitation only) and for the entire year, is supported by a comparison against estimates of the snow water equivalent (SWE) at the drifting stations. 1. Introduction The World Meteorological Organization (WMO) Solid Precipitation Measurement Intercomparison conducted during (WMO 1998) provided an opportunity to obtain reliable data on cold region precipitation, including solid precipitation. The main achievement of the experimental research has been a comprehensive assessment of the aerodynamic error (wind-induced undercatch) in precipitation measurements for the main types of standard national gauges through comparison (either direct, or by means of intermediate reference gauges) against the most reliable reference precipitation gauge the Valdai Control System (VCS). The Russian standard Tretyakov gauge and the double-fenced [so-called double fence intercomparison reference (DFIR)] gauge were used as the intermediate reference gauges. DFIR data were compared against VCS measurements. Reliability of VCS measurements has been proven by a wide spectrum of multiyear field tests and an original method of objective estimates of the gauge accuracy (WMO 1998; Golubev et al. 1997b). The progress and results of the gauge international intercomparisons were regularly described and discussed in the corresponding WMO publications and other scientific literature containing extensive lit- Corresponding author address: Dr. Boris Ilyin, Voeikov Main Geophysical Observatory, 7, Karbyshev Str., St. Petersburg , Russia. bilyin@main.mgo.rssi.ru erature references on the problem (e.g., WMO 1998; Golubev et al. 1999; Forland et al. 1996; Golubev and Simonenko 1998; Goodison and Yang 1995; Yang et al. 1995). The study by Yang et al. (1995) is entirely devoted to the comparison of measurements by the Tretyakov gauge against those by DFIR. By now, several versions of the method of bias correcting gauge-measured precipitation on daily or shorter (12 or 6 h) timescales have been developed. The algorithms have been adjusted to different national gauges and to specific features of their usage, including parameters necessary for error estimation. In particular, for the Tretyakov gauge, three versions of the bias-correction method were developed: the method of the WMO International Organizing Committee (IOC) (WMO 1998; Yang et al. 1995); the method of a group of experts from Scandinavian countries (Forland et al. 1996); and the method of V. S. Golubev, developed in Russia (WMO 1998; Golubev and Simonenko 1998). The two former versions are based on results of intercomparisons of the Tretyakov gauge measurements against those of DFIR carried out at most stations of the international intercomparison. DFIR errors, in their turn, were obtained from the comparison against the VCS. For the Golubev method, only the results of direct comparisons of the standard Tretyakov gauge against the VCS were used. A comparison of bias-correction results obtained with each of the methods against the VCS data has shown that the magnitudes of the calculated systematic errors are almost equal (Golubev et al. 1999) given the 2002 American Meteorological Society

2 DECEMBER 2002 BOGDANOVA ET AL. 701 ranges of wind speed and air temperature that are characteristic of the Valdai, Russia, climate. However, according to the conditions of the WMO IOC method application (WMO 1998), the correction equations for the wind-induced undercatch of solid precipitation are recommended for wind speeds lower than 6.5 m s 1 at the gauge height, and in the absence of blizzards. No solutions for stronger winds or blizzards are suggested by the WMO IOC to correct solid precipitation measured with the Tretyakov gauge; further investigation is recommended instead. Nevertheless, recent years have been marked with extensive publication of the results of the WMO IOC method application in different regions, mainly those characterized by predominately solid precipitation and strong winds. It is well known that precipitation measurements under such conditions are the least reliable and require major bias correction (e.g., Larson and Peck 1974; Sevruk 1982; Goodison and Yang 1995). Hence, the primary areas of interest have been Alaska (Yang et al. 1998), Greenland (Yang et al. 1999), Svalbard (Forland and Hanssen-Bauer 2000), Siberia, and the Russian Arctic (Yang and Ohata 2001), as well as the North Pole drifting stations (Yang 1999). In all of these studies only three types of systematic errors of precipitation measurements are taken into account: wind-induced undercatch, wetting loss, and loss in the cases when the measured precipitation is less than one-half of the smallest gradation of the measuring device. The latter quantity is recorded as 0.0 or trace, and is ignored in further summations. The wind coefficient is confined to the value corresponding to 6.5 m s 1 of the wind speed at the gauge orifice height and is kept equal to that value for any higher wind speed (Yang and Ohata 2001; Yang 1999). Yang (1999) and Yang and Ohata (2001) corrected precipitation measured with the Tretyakov gauge. Their results have shown such a dramatic increase in the corrected precipitation in the Arctic region, as compared to the measured one, that it raises questions from a climatological perspective. For example, it is difficult to explain why precipitation is so high at the drifting stations in the Arctic Ocean (Yang 1999) under persisting conditions of a stable anticyclonic regime, very low air temperatures, and, correspondingly, low water vapor content for much of the year. Annual mean precipitation obtained by Yang (1999) based on the corrected data from the drifting stations (256 mm) is comparable to that of the northeast coast of Asia [see the map in the UNESCO (1978) world water balance atlas based on the corrected precipitation data]. However, in the central Arctic, where the stations were drifting, air temperature and, accordingly, precipitable water are much lower than over the Chukchi coast. Thus, precipitation in the central Arctic should also be lower. Evidently, the cause of such overestimation is the fact that the applied bias-correction procedure underestimates false precipitation, that is, snow raised from the surface of the snow cover and caught by the gauge during blowing snow or blizzard. (Hereafter, the term blowing snow will be used for the snow lifted from the surface of the snow cover by the wind to a height of 2 m or more above the surface, while the term blizzard will be for a weather condition characterized by high winds and both falling and blowing snow.) For the Arctic climate, snowfalls are typical under strong winds and blizzard conditions throughout almost the entire year. The need to account for the influence of the false precipitation during intensive blizzards was noted as long ago as the early 1970s (Struser 1971; Struser and Bryazgin 1971; Struser and Bogdanova 1975). In these studies, estimates of the measurement error were obtained as functions of wind speed and blizzard duration, and methods were suggested to account for the error in estimates of multiyear annual mean precipitation. In recent years, the formulas suggested earlier by Struser (1971) for estimating false precipitation overcatch by the Tretyakov gauge were refined by Golubev and Bogdanova (1996) and Golubev et al. (1997a; 2000). It was shown (Golubev et al. 1997a), based on daily precipitation corrections over periods of 3 8 yr and different climate conditions (at Russian stations spread from the Arctic coast to the Volga River leftbank steppes, and Bashkiria), that neglecting false precipitation caught by the gauge leads to a significant overestimation of the bias-corrected values. Therefore, when correcting daily precipitation measured with the standard Russian Tretyakov gauge at the North Pole drifting stations, it is necessary to include in the biascorrection model the estimation of false precipitation. 2. Bias-correction model for the Tretyakov gauge The method of bias correction of measured daily precipitation is based on the model developed by V. S. Golubev (Golubev et al. 1999, 1997a,b, 2000; Golubev and Bogdanova 1996; Golubev and Simonenko 1998). The parameters of all formulas given below were obtained experimentally as a result of the Tretyakov gauge measurement comparisons against VCS data, as well as by summarizing numerous studies of snow transport characteristics during blizzards. The full details of the model, including a set of algorithms of necessary calculations, are described in Golubev et al The model allows estimates of the actual amount of precipitation falling from clouds at the observation point by accounting for systematic errors due to aerodynamic features of the gauge, the processes of evaporation, condensation, and wetting in the gauge collector, as well as false precipitation raised by the wind from the snow surface and caught by the gauge during blizzards and blowing snow. The actual amount (mm) of precipitation is given by P K(P P P P ), f1 f2 (1)

3 702 JOURNAL OF HYDROMETEOROLOGY VOLUME 3 TABLE 1. Empirical parameter A 0 as a function of precipitation type and air temperature (reproduced from Golubev and Simonenko 1998). Type of precipitation A 0 Snow Snow and drizzle Mixed precipitation (rain and snow) Drizzle Rain, rain, and drizzle if (t a 2C); if (t a 2C) where K is a coefficient accounting for the influence of the wind on the measured precipitation; P is the measured precipitation (when the measured precipitation is marked as trace, i.e., P0.0 mm); P is the correction for the effects of evaporation, condensation, and wetting of the gauge collector for each measurement, including the situation in which P0.0 mm (trace precipitation); and P f1 and P f2 are corrections accounting for false precipitation caught by the gauge during blizzard and blowing snow, respectively. a. Aerodynamic coefficient The coefficient K is calculated using the formula 2 2 K 1 A 0 U h, (2) where A 0 is an empirical parameter, depending on the aerodynamic features and equilibrium velocity of the falling precipitation particles [the values of A 0 for different types of precipitation and different air temperatures are given in Table 1 (reproduced from Golubev and Simonenko 1998)]; is a coefficient of transfer from air density under the standard atmospheric conditions to the density under the actual conditions; and U h is the wind speed (m s 1 ) at the height of the gauge orifice during precipitation. The coefficient is given by P a/[(273 t a)(pa 0.4e a )], (3) where P a is the atmospheric pressure (hpa) at the station; t a is the air temperature (C); and e a is the partial pressure (hpa) of water vapor. Wind speed U h at the gauge orifice height h (m) is obtained from h hs H hs U U m(a) ln ln, (4) z z h H 0 0 TABLE 2. Values of P for 12-h sums of precipitation at different values of saturation deficit [(100 r)%] on the days when precipitation occurs (reproduced from Golubev et al. 1999). Liquid precipitation [(100 r)%] P (mm) Mixed precipitation [(100 r)%] P (mm) Solid precipitation [(100 r)%] P (mm) where U H is the wind speed (m s 1 ) at the height of the standard wind-measuring device during precipitation; m(a) is a coefficient characterizing the distortion of the logarithmic wind profile due to various obstacles surrounding the precipitation gauge; H is the height (m) of the wind measuring device; h s is the snow-cover depth (m) at the station; z 0 is the roughness parameter of the land surface around the gauge (for continuous snow cover z m; for the grass and patchy landscape, when snow covers less than a half of surroundings, z m). The coefficient m(a) is (WMO 1998) m(a) 1 0.0(A), (5) where (A) is the vertical angle from the rain gauge orifice to the top of the highest of the obstacles located less than 300 m from the gauge in the wind direction (A, degree). b. Bias correction for wetting, evaporation, and condensation To estimate bias correction P (mm) for evaporation, condensation, and wetting of the gauge collector interior, and trace precipitation, Golubev et al. (1999) apply an original approach considering the total effect of the above processes. The P value is estimated as the difference between the VCS data and the Tretyakov gauge measurements corrected for wind-induced undercatch. The analysis of the difference for 12-h precipitation of different types showed its dependence on the value of saturation deficit [(100 r)%], where r is the relative humidity. Mean values of P for liquid, mixed, and solid precipitation per single measurement at different values of the saturation deficit are given in Table 2 and Fig. 1 (both reproduced from Golubev et al. 1999). In Fig. 1, it can be clearly seen that for r values within FIG. 1. Dependence of the integral correction P on the value of saturation deficit [(100 r)%] on the days when precipitation occurs, for 12-h sums of liquid, mixed, and solid precipitation (reproduced from Golubev et al. 1999).

4 DECEMBER 2002 BOGDANOVA ET AL. 703 the interval of 80% 90% (which are of frequent occurrence on the days when precipitation occurs) P values are rather close to corrections for wetting used in practice: 0.1 mm for solid and 0.2 mm for liquid precipitation. However, for mixed precipitation P falls outside of these values, approaching 0.0 mm. When r is greater than 90%, P becomes negative not only for mixed, but also for solid precipitation. The curves at Fig. 1 correspond to the experimentally derived values from Table 2. For further use, the curves are approximated with the formulas given below. Since at relative humidity higher than 95% the statistical significance of the obtained relationship is low, and observed values of r do not exceed 97%, the approximations are not extrapolated beyond the 95% limit, and P is fixed to the values corresponding to r 95% as shown in Fig. 1. As a result, the bias-correction P for wetting, evaporation, condensation, and trace precipitation depends on the type of precipitation and the relative humidity, r (%), on a day when precipitation occurs, as follows. In case of liquid precipitation: ln(100 r) if r 95%, P (6) 0.1 if r 95%. In case of solid precipitation: ln(100 r) if r 95%, P (7) 0.2 if r 95%. In case of mixed precipitation: ln(100 r) if r 95%, P (8) 0.2 if r 95%. c. Calculation of the amount of false precipitation The amount of false precipitation is determined as the product of the false precipitation intensity J f and the blizzard duration f. Equations for determining the intensity of false precipitation caught by the Tretyakov gauge were obtained by L. R. Struser based on V. M. Kotlyakov s formula establishing an empirical relationship between the integral snow flow during a blizzard, the wind speed at 2-m height, the type of blizzard, and the state of snow cover (Struser 1971). Parameters of the Kotlyakov formula determine the values of the coefficients in the formulas for calculation of the false precipitation intensity. In particular, the wind speed threshold values of 4.2, 6, and 8.5 m s 1 correspond to different states of the snowcover surface from which the particles lifted by the wind can reach the height of 2 m. A brief description of the formula deduction is given also by Golubev and Bogdanova (1996). The Struser formulas were refined later (Golubev and Simonenko 1998; Golubev et al. 2000) by introducing the coefficient B h, which accounts for the difference between the real height of the gauge over the snow surface and 2 m, and the coefficient L f, which accounts for the extent to which the wind flow is saturated with suspended snow particles, depending on the length of the blizzard spinup. By the length of a blizzard spinup we understand the distance (in the wind direction) between the gauge and the boundary of the snow catchment area marked with, for example, forest, buildings, bushes, a precipice, an aviation runaway, etc. Below are the formulas for calculation of intensity and amount of false precipitation under various weather conditions and states of the snow cover surface in terms of the Kotlyakov formula (Struser 1971): blowing snow, blizzard, fresh snow, old snow, and snow compressed by wind. The amount (mm) of false precipitation, caught by the gauge during a blizzard ( ) is P f1 J f1 f1, (9) where J f1 is the mean intensity (mm h 1 ) of false precipitation during the blizzard, and f1 is the duration (h) of blizzard: BL (U 4.2 ) h f1 2, Jf1 Kf1U2 1 0 if U 4.2ms ; P f1 2 (10) where U 2 is the wind speed at the height of 2 m above the snow-cover surface. It is calculated using (4), where (h h s ) 2m. Coefficient K f1 characterizes wind-induced undercatch of false precipitation particles during the blizzard: Uh if ta 7.0C, Uh if ta 7.0C; K (11) f1 where and U h are calculated using (3) and (4), respectively, and the coefficient values correspond to the structure of fresh snow at different air temperatures. The coefficient B h accounts for the difference between the concentration of precipitation particles in the blizzard flow at the height of the gauge orifice and at 2 m: 2 2 h h B ln ln s h. (12) h h z z s 0 0 The coefficient L f1 is a measure of the extent to which the blizzard flow is saturated by suspended particles: 3 3 th[2 10 (A)] if ta 7.0C, Lf1 (13) th[3 10 (A)] if t 7.0C; where is the length (m) of blizzard spinup, A is the wind direction, and th is the hyperbolic tangent. The amount (mm) of false precipitation caught by the gauge during blowing snow is P f2 J f2 f2, (14) where J f2 is the mean intensity (mm h 1 ) of false pre- a

5 704 JOURNAL OF HYDROMETEOROLOGY VOLUME 3 cipitation during blowing snow, and f2 is the duration (h) of the blowing snow. The intensity of false precipitation during blowing snow is calculated using one of three formulas in accordance with the state of the snow cover before the beginning of blowing snow. The formula is chosen on the basis of the sequence of occurrence of the observed snowfall, blizzard, blowing snow, and drifting snow. If blowing snow is observed after snowfall and (or) a blizzard, when false precipitation is produced from the fresh snow, then BL (U 4.2 ) h f2 2, Jf2 Kf2U2 1 0 if U2 4.2ms ; (15) L f2 is calculated from (13); Uh if ta 7.0C, Kf U if t 7.0C. If blowing snow is observed after drifting snow and the snow surface has been already compressed by the wind, then BL J (U 6) h f2 f2 2, K f2 U 2 1 Jf2 0 if U2 6ms ; 3 Lf2 th[2 10 (A)]; 2 2 K U. (16) f2 In all other cases (e.g., either liquid or mixed precipitation, or fog, etc., has occurred before the blowing snow, or there hasn t been any precipitation during the preceding day), BL (U 8.5 ) h f2 2, Jf2 Kf2U2 1 0 if U 8.5ms. 2 (17) If in (1) (PPP f1 P f2) 0, then the corrected precipitation P is set equal to 0. Based on the equations described above, a computer code was developed and tested for several stations of the Russian northwest, Arctic coast, and Kamchatka. It was found that under the climate conditions of the Russian northwest, where for the period considered there were essentially no blizzards and the wind speed U h during precipitation was not higher than 8 9 m s 1 the method performed similarly to more trivial schemes that had been developed earlier. All calculated bias corrections quite adequately reflected the influence of the corresponding meteorological parameters and the degree to which the gauges were sheltered by the surroundings. Having applied the above method to the Arctic coast, h h a when bias-correcting precipitation measured under wind speeds higher than 10 m s 1, we encountered difficulties. The difficulties were associated with missing input parameters necessary for calculation of false precipitation using (10) and (15) (17), particularly the parameters characterizing the blizzard condition and the state of the snow-cover surface. Under strong winds, blowing snow and blizzards become less distinct. Moreover, during a strong blizzard, it is practically impossible to determine whether the snow falls from the clouds or is raised from the surface of the snow cover by the wind, or whether both process are occurring simultaneously. To solve this problem, an approach was suggested and substantiated by Struser and Bryazgin (1971). The underlying premise was that the actual intensity (mm h 1 ) of falling precipitation ( J p ) during blizzards at polar stations does not change significantly and can be considered as a constant value close to the long-term monthly mean precipitation under the given climatic conditions. This conclusion was based on analyses of individual snow storm intensities at 22 Arctic land stations for a 12-yr time period ( ) using daily observational data. The approach of Struser and Bryazgin (1971) was employed in our model in the cases when either a blizzard or blowing snow was observed, and the mean wind speed at the anemometer height was higher than 10 m s 1. In such cases, this approach allowed us to use precipitation intensity ( J p ) calculated for wind speeds lower than 10 m s 1. Having multiplied J p by the observed duration of blizzard precipitation p, one obtains the actual amount of precipitation for a certain period of observation (12 h or 1 day). Long-term mean monthly values J p for each particular station are obtained from the formula P 1 n J p, (18) N N p where P is the full-model bias-corrected daily precipitation (mm), p is the duration (h) of precipitation for the same day, n is the number of days with precipitation for the month, and N is the number of years of averaging. In calculation of J p, the only cases included are those in which the mean wind speed at the anemometer height is not higher than 10 m s 1. Accordingly, the algorithm of bias correction includes the condition that in all cases when, during blizzards or blowing snow, the wind speed is higher than 10 m s 1, the corrected precipitation is calculated from the formula n P J. p p (19) In these cases, measured precipitation is not taken into account.

6 DECEMBER 2002 BOGDANOVA ET AL. 705 FIG. 2. North Pole drifting stations monthly locations during (reproduced from Colony et al. 1998). 3. Bias correction of precipitation at the North Pole stations a. Input data A major portion of the input dataset for correcting precipitation measured at the North Pole drifting stations was from the Arctic and Antarctic Research Institute (AARI), St. Petersburg, Russia, daily meteorological archive based on standard observations. The archive contains data for the entire period of the North Pole (NP) drifting station program starting in 1937 (NP-1) and through 1991 (NP-31). Precipitation bias correction was carried out for the period from May 1955 (NP-5) to March 1991 (NP-31). The data for NP-14 from May 1965 through January 1966 were excluded because their reliability was questionable: the measured and corrected precipitation for NP-14 for the period from November 1965 through January 1966 appeared to be 5 times as high as that for NP-13 for the same months under similar meteorological conditions, and 3 times as high as the corresponding multiyear monthly means for the whole region. Monthly mean position and time periods of operation of all NP stations are shown in Fig. 2 (reproduced from Colony et al. 1998) and in Table 3. Colony et al. (1998) and Warren et al. (1999) contain detailed information about the NP drifting station program, as well as a description of precipitation and snow-cover observation methods. The detailed climatic data analyses in those papers were very helpful for this study. The AARI archive contains in particular the following meteorological variables: atmospheric pressure, air temperature, relative humidity, wind speed, snow cover depth, total precipitation, and type of precipitation (distinguishing solid, mixed, and liquid phases). Obviously, application of the above precipitation correction method requires a significant amount of information missing from the archive, namely: 1) total precipitation directly measured with the gauge (P) [the archive contains daily sums (P arch ) already corrected for wetting loss in accordance with the standard procedure]; 2) number of precipitation measurements per day (which could be either one or two, with two measurements per day as the standard); 3) information that distinguishes between a blizzard and blowing snow, and the duration of each event per day; and 4) duration of precipitation per day. b. Missing data and key assumptions To obtain P, it was necessary to subtract from P arch the compensation for wetting loss that had already been introduced in accordance with the standard method of processing the measurements. Due to the fact that the time resolution of the archived precipitation P arch was not finer than that of daily precipitation, the daily totals were used for the calculation of P. In other words, P TABLE 3. Years of operation of NP drifting stations. Station no. Period Station no. Period Station no. Period May 1955 Apr 1956 Jun 1956 Aug 1959 May 1957 Mar 1959 May 1961 Mar 1962 May 1960 Dec 1960 Nov 1961 Apr 1964 May 1962 Apr 1963 May 1963 Apr 1965 May 1964 Apr 1967 May 1965 Jan 1966 May 1966 Mar May 1968 Apr 1970 Mar 1971 Apr 1971 Jun 1971 Mar 1972 May 1968 Sep 1969 Dec 1968 Apr 1969 Sep 1969 Sep 1970 Apr 1971 Sep 1971 Dec 1969 Mar 1973 May 1970 May 1972 May 1972 Apr Oct 1973 Mar 1982 Jan 1976 Nov 1976 Jan 1977 Oct 1978 Apr 1978 Oct 1980 Jun 1981 Mar 1984 Jun 1983 Dec 1984 Jul 1984 Apr 1987 Jun 1986 Dec 1988 Jul 1987 May 1988 Nov 1987 Feb 1991 Jan 1989 Mar 1991

7 706 JOURNAL OF HYDROMETEOROLOGY VOLUME 3 was computed as if precipitation was measured once a day. That is why the total correction for wetting loss subtracted from P arch proved to be less than the amount actually used in the algorithm, and the values of P were somewhat higher than the precipitation actually measured. On the other hand, the total correction P was underestimated to the same extent because it was calculated using (6) (8) and introduced in accordance with the number of days with precipitation, not the number of precipitation measurements. Due to the fact that the standard correction for wetting loss and the value of P are generally rather close (Golubev et al. 1999), such an approximation does not have a significant effect on the amount of the bias-corrected precipitation. Characteristics of the degree of shelter of the gauges [parameters m and l from (4), (5), (13), (15), and (17)] for all NP stations were set equal to 1 and 3000 m, respectively, due to the absence of any obstacles around the gauges. All missing data on the type and duration of blizzards and precipitation were obtained indirectly in accordance with their relationships with other available meteorological variables. Parameters of these relationships were determined based on a multiyear time series for 16 Arctic coastal and island stations available from a 3-h archive of standard meteorological observations for the period (Razuvaev et al. 1995). A detailed description of how these relationships were derived, their statistical justification, and characteristics of accuracy are given by Bogdanova et al. (2002) (see also the appendix herein). In this section, only the corresponding formulas used in the correction algorithm are provided. Total duration (h) of blizzards and blowing snow per day ( f f1 f2 ) is determined only for the days with solid precipitation according to the daily mean wind speed at the anemometer height (at NP stations it was always 10 m): f 1.61UH 3.75, (20) with the obvious restriction, 0 f. The relationship between blowing snow ( f2 ) and total duration of both blizzard and blowing snow ( f ) is obtained from monthly values of U H and P in accordance with the formula f2 UH (21) P f Then, this monthly relationship is used to determine f1 and f2 for individual days of the month. The duration of precipitation for a month p [needed to determine the monthly mean precipitation intensity J p from (18)] is given by t D e 10 a p p a, (22) where D p is the number of days with precipitation during the month, 1.11, and c. The algorithm of precipitation bias correction The bias correction of the precipitation measured at the NP stations was carried out using the following algorithm: 1) The daily value of gauge-measured precipitation (P) was obtained by subtraction of the standard correction for wetting loss (P w ) from the archived daily value of precipitation (P arch ). 2) The value of the aerodynamic coefficient (K) was determined using formulas (2) (5) and the data from Table 1, depending on the daily mean wind speed, atmospheric pressure, air temperature, humidity, snow depth, and the type of precipitation. The value of the coefficient m(a) for the NP stations was set to zero. 3) The value of the bias correction (P) for wetting, evaporation, condensation, and trace precipitation was determined from (6) (8) using relative humidity daily means and depending on the type of precipitation. 4) The amount of the false precipitation ( P f1 and P f2) was calculated only for the days with solid precipitation, a blizzard, or blowing snow [ f 0 from (20)], and the daily mean wind speed U H 10 m s 1. First, from (21) and (22), the duration was determined of the blizzard ( f1 ) and blowing snow ( f2 ). Next, from (10) (13) and (9), correspondingly, the intensity (J f1 ) and the amount ( P f1 ) of the false precipitation during the blizzard (J f1 ) were obtained. Then, from (16) and (14), respectively, the intensity (J f2 ) and amount ( P f2 ) of the false precipitation due to blowing snow were calculated. The choice of (16) was caused by the lack of information on the weather types and, accordingly, the inability to determine the state of the snow cover. 5) Finally, from (1), the bias-corrected amount of precipitation was obtained. 6) For the days with blizzards or blowing snow, solid precipitation, and the mean wind speed U H 10 m s 1, the bias-corrected amount of precipitation was determined from (19). As it took place, the duration of precipitation on that day was assumed to be equal to the blizzard duration. The bias correction of precipitation for all NP stations was carried out in two steps. At the first step, the calculations were carried out for all days with precipitation, except for the days with solid precipitation, blizzards, or blowing snow, and a wind speed higher than 10 m s 1 (algorithm parts 1 5). Based on the results of those calculations, for each NP station and month, the mean intensity of the corrected precipitation was determined from (18). Then, for each month, the weighted mean intensity of precipitation was determined for the entire polar region and, finally, the mean intensity of precipitation was calculated for the cold

8 DECEMBER 2002 BOGDANOVA ET AL. 707 TABLE 4. Summary of bias correction of precipitation measured at NP drifting stations during the period from 1956 (NP-5) through 1990 (NP-31). Year n t a (C) U H (m s 1 ) D p P arch (mm) P (mm) P (mm) P P P (mm) P arch P (mm) Pf1 Pf2 (mm) P f1 + P f2 P Mean season. That value, equal to mm h 1, was used when correcting precipitation by employing (19). At the second step, the calculations followed the full algorithm (parts 1 6), and the results of those calculations are discussed in sections 3d and 4. It should be noted that the bias correction of precipitation was based on (1) on 96% of all days with precipitation at all NP stations, while (19) was used only on 4% of the days. d. Results of bias correction As a result of the calculations, an archive was created of corrected daily precipitation for all NP stations for the period from May 1955 (the start of the NP-5 operation) through March 1991 (the end of the NP-31 operation). Based on these data, the values presented in Table 4 were obtained. The annual totals were calculated by summing up the monthly values averaged over the stations in operation that year and month. In individual years, several stations could be simultaneously in operation (Table 3); therefore, the number of months (n) indicated in the first line of Table 4 is different for different years. If, for a certain year, there was no full cycle of observation, then the data for this year are not included in Table 5. The air temperature (t a ) and wind speed (U H ) for the days with precipitation are given in Table 4 as annual means. Long-term annual and monthly mean characteristics of measured and bias-corrected precipitation are presented in Table 5. These were averaged for the entire data array, so the total number of months (n) included in the averaging, as well as the long-term annual means of the other characteristics, differ somewhat between Tables 4 and 5. In Tables 4 and 5, on the days when formula (19) was used, the amount of false precipitation ( P f1 P f2) was calculated as the residual member of (1), using P obtained from (8) and K taken from (2). Based on Table 5, seasonal cycles were obtained for the long term means of P, P arch, P P P, and P (Fig. 3). P fthe bias-corrected precipitation for the entire year is greater than the measured amount by about one-fourth. Averaged over the whole time period from late 1955 through early 1991, the ratio P/P is equal to 1.28, varying from a minimum of 0.93 (1956) to a maximum of 1.56 (1985). It is evident that, while the aerodynamic

9 708 JOURNAL OF HYDROMETEOROLOGY VOLUME 3 TABLE 5. Seasonal cycle of multiyear mean characteristics of measured and corrected precipitation. Month n P arch (mm) P (mm) P (mm) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec P P P (mm) P arch P (mm) P f1 P f2 (mm) P f1 P f2 P Year coefficient is significant under the observed wind speeds, its impact to a large extent is compensated by false precipitation, which also increases with the wind speed and duration of blizzards and blowing snow. The annual average amount of false precipitation is 38 mm, or 30% of the annual mean precipitation. The maxima of false precipitation were in 1956, 1957, and 1983, and they amounted to mm. Correspondingly, for those years, the measured and bias-corrected precipitation totals were very similar (P/P was about 1). The minimum false precipitation was in 1985 (20.2 mm); that year was also marked with the maximum ratio P/P (1.56). The annual mean value of the correction, accounting for evaporation, condensation, wetting, and trace precipitation (P), is 15.4 mm, or about 12% of P. However, as it has been mentioned above, P was somewhat underestimated because it was introduced into the daily precipitation totals, not into the individual measurements. For this reason, the values of P must be somewhat overestimated as compared to the actually measured precipitation (see the discussion at the beginning of section 3b). The annual cycles of the measured precipitation (P), partly corrected with the standard correction for wetting (P arch ), and the fully bias-corrected (P) precipitation are similar (Fig. 3), so the timing of the annual maximum (July) and the annual minimum (April) are the same. The relative total error of precipitation measurement (P/ P 1) varies throughout the year from 45% 50% in April May to 16% in August. At the same time, the absolute total error (P P) varies throughout the year comparatively insignificantly, averaging about 3.0 mm month 1, with maximum values of about 5 mm in July August and minimum values of about 2 mm in February March. The amount of false precipitation is about one-half of the measured precipitation in winter (October March) and gradually decreases until it disappears in July. The annual cycle of P is clearly different, especially for summer, from that of the standard correction for wetting (P arch P). In summer, under high relative humidity (often approaching 100%), the relative importance of condensation at the interior of the gauge collector increases, and the losses for evaporation and FIG. 3. Seasonal cycle of gauge-measured and bias-corrected precipitation characteristics: P gauge-measured precipitation; P arch P P w ; P P P P f ; P K P; and Py Ky(P g P w ) P t.

10 DECEMBER 2002 BOGDANOVA ET AL. 709 wetting decrease correspondingly. As a result, in June August P often becomes negative. On the contrary, the standard correction for wetting loss during liquid and mixed precipitation is twice as large as that during solid precipitation, so the value of (P arch P) in summer reaches its maximum. The validity of the estimates of the bias-corrected precipitation was verified by their comparison against snow water equivalent (SWE) estimates of Warren et al. (1999) at the same NP stations using the measured snow-cover depth and density for the period comparable to that of ours. According to Warren et al. (1999), for the period from October through May, SWE was equal to 83 mm. In this study, the estimates of the bias-corrected precipitation for that period of the year give 85.6 mm. Warren et al. (1999) assessed the mean annual precipitation in accordance with Colony et al. (1998), who determined the amount of winter precipitation accounting for hoarfrost and rime accumulation, and sublimation loss. To estimate the mean annual precipitation, Warren et al. (1999) added the SWE estimates for the October May season to the gauge measurements for June September. Warren et al. s (1999) estimate of the mean annual precipitation over the Arctic is 164 mm, while in the present study it is 165 mm. Such consistency of the results obtained using the independent methods points to their robustness and reliability. 4. Discussion and conclusions The values of the bias-corrected NP station precipitation that we obtained significantly differ from Yang s (1999) estimates obtained for the NP stations for the period According to Yang (1999), the multiyear annual mean precipitation at the NP stations is 256 mm, while our estimate is 165 mm. Figure 3 compares the bias-corrected precipitation monthly means obtained by Yang (Py) and by us (P) against the gaugemeasured P and archived P arch means. To understand the reason for the differences between P and Py, one should consider the formulas used in the two bias-correction models. Following Golubev, we use formula (1) in this paper. Yang s (1999) formula is Py Ky(Pg P w) P t, (23) where P g is the gauge-measured precipitation, P w is wetting loss calculated using the standard method for NP stations, P t is the trace precipitation, and Ky is a correction coefficient for wind-induced errors. For convenience of further comparison we can replace designations in (23): Py Ky(P P w) P t. (23a) Since in this paper P P w P arch, formula (23a) becomes Py Ky P P. arch t (23b) The comparison of (23) (23b) with (1) shows the following differences of these formulas. 1) In (1), the integral effect of wetting, evaporation, condensation, and trace precipitation is taken into account, using a single integral value of P. In (23), evaporation and condensation losses are neglected, and the way of accounting for trace precipitation is not physically correct. Whatever the assumption on daily or 12-h amounts of gauge-measured trace precipitation, when calculating the corrected precipitation amount P, the value P t should also be multiplied by the wind coefficient; that is, in (23) P t should be placed inside the brackets. It is quite evident that for the same small actual precipitation its significant amount can be measured under weak wind conditions, while only trace precipitation can be found in the gauge collector if the wind is stronger. 2) In (1), false precipitation caught by the gauge during a blizzard or blowing snow is taken into account, while in (23) it is not accounted for at all. (Indirectly, in accordance with the recommendations of the WMO IOC, some false precipitation is taken into account through limiting the aerodynamic coefficient K to its value corresponding to the wind speed of 6.5 m s 1. Evidently, under the given conditions, such measure is not sufficient.) We think this is the main reason for the differences in the two sets of results. Using multiyear means from Table 4, we calculated bias-corrected precipitation values for each month (P c ), having excluded from (1) the effect of false precipitation, that is, Pc K(P P). () The annual value of P c is 229 mm, which is 1.4 times greater than P, and P c is only 10% lower than Py. The 10% difference is presumably due to the difference in accounting for the other errors listed in the previous item. Currently the amount of false precipitation is determined with a large random error, which is so far difficult to objectively assess, but accounting for false precipitation is necessary for correcting a significant part of systematic errors. 3) A comparison of the yearly values of the wind coefficients K (1) and Ky (23b), calculated using the formulas P K(1) and P P P f Py P Ky(b) t, (25) P arch shows that they are very close to each other and equal, correspondingly, to 1.56 and Consequently, systematic differences in calculations of the wind coefficient between the WMO IOC and Golubev methods are insignificant.

11 710 JOURNAL OF HYDROMETEOROLOGY VOLUME 3 4) Intercomparison of results of one or another method application is not sufficient for establishing their reliability, especially if the difference between the results is rather significant. An independent reliable source of the same data is necessary. The comparison of observed precipitation against snow-cover water content during the non-thaw season is a traditional way of investigating and establishing robustness of the both estimates. Thus we believe the consistency between our estimates of Arctic precipitation and the results of Warren et al. (1999) lends support to the validity of the bias-correction method we used and, particularly, the necessity of accounting for false precipitation. The applicability of the complete correction procedure (Golubev et al. 2000; Bogdanova et al. 2001) to the archive of the NP station data became possible due to the following fortuitous features of this archive. The archive includes a sufficiently rich set of supplementary meteorological data (wind, humidity, temperature, and precipitation type) that are required by the procedure implementation. Important and quite often absent parts of metadata and supplementary information (the sites exposure, the lengths of blizzard spinup, and the state of surface) have been reliably assumed due to the specifics of the NP sites location. In other regions where blowing snow and blizzards significantly affect the in situ precipitation measurements (e.g., coastal high-latitudinal regions, ice sheets, tundra, mountain desert, and steppe climatic zones), accounting for the false precipitation is a much more arduous task. On the other hand, our analysis has shown that serious miscalculations may occur in these regions if incomplete precipitation bias-correction schemes are implemented. Acknowledgments. The authors thank Dr. Nikolay Bryazgin of the Arctic and Antarctic Research Institution for very helpful discussions. We are grateful to Prof. John Walsh of the University of Illinois at Urbana Champaign and Dr. Vladimir Kattsov of the Voeikov Main Geophysical Observatory for their valuable comments on the manuscript. The comments of Dr. Pavel Groisman of NOAA, Dr. Daqing Yang of the University of Alaska, Fairbanks, and anonymous reviewers are gratefully acknowledged. This study was supported by the Russian Foundation for Basic Research (Grants and ) and by the National Science Foundation (Grant OPP ). APPENDIX Determination of Data Not Available from the Archive a. Determining precipitation duration When calculating monthly duration of precipitation [in order to determine monthly mean intensity of precipitation using Eq. (18)] a relationship is used between the precipitation duration, on the one hand, and the number of precipitation days, the temperature, and the humidity, on the other hand. Such a relationship was established by Bogdanova (1980), who suggested the formula for calculating multiyear monthly mean duration of precipitation : a+bt 0.01D e (100 r)10, (A1) where is the multiyear monthly mean duration (h) of precipitation, D is the monthly mean number of days with precipitation 0.1 mm, e is the monthly mean partial pressure (hpa) of water vapor, r is the monthly mean air relative humidity (%), t is the monthly mean air temperature (C), and a and b are empirical coefficients. For the averaged climatic conditions, for which the formula (A1) was obtained, a and b When the value of precipitation duration for a particular month is required, rather than the multiyear mean, formula (A1) can be transformed by substituting the monthly mean values of e and t by their values averaged only over the days with precipitation. The factor (100 r) in (A1) was excluded because, for the values of r close to 100%, (A1) produced significant errors. Thus, (A1) was transformed into t D e 10 a p p a, (A2) where p is the duration (h) of precipitation for a particular month; D p is the number of days with precipitation for that month, including the days with traces; e a and t a are, respectively, the partial pressure (hpa) of water vapour and air temperature (C), both averaged over the days with precipitation for the month; and and are constants determined for each particular station from the comparison of the observed monthly values of precipitation duration against those calculated using formula (A2). The coefficients and were determined based on the data analysis from 16 Russian stations situated at the Arctic continental coast and islands (Table A1). Actual monthly values of precipitation duration ( r ) were available from the routine monthly publications of standard meteorological observations. Monthly values of D and e in (A2) were determined using the standard observational data for the corresponding months. Table A1 gives values of and obtained for each station, along with statistical characteristics of the relationship between the actual monthly values of precipitation duration and those calculated using formula (A2): the correlation coefficients R, the root-mean-square deviations of p (from the regression line) calculated using 2 the formula S p (1 R ), the mean values of p for the entire dataset, and the variation coefficients determined from the relationship C S /. The and values averaged over the 16 terrestrial stations (1.11 and 0.07, correspondingly) were used