Snow Nowcasting Using a Real-Time Correlation of Radar Reflectivity

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20 JOURNAL OF APPLIED METEOROLOGY VOLUME 42

Snow Nowcasting Using a Real-Time Correlation of Radar Re¯ectivity with Snow Gauge Accumulation

ROY RASMUSSEN AND MICHAEL DIXON National Center for Atmospheric Research, Boulder, Colorado

STEVE VASILOFF National Severe Storms Laboratory, Norman, Oklahoma

FRANK HAGE,SHELLY KNIGHT,J.VIVEKANANDAN, AND MEI XU National Center for Atmospheric Research, Boulder, Colorado

(Manuscript received 21 November 2001, in ®nal form 13 June 2002)

ABSTRACT This paper describes and evaluates an algorithm for nowcasting snow water equivalent (SWE) at a point on

the surface based on a real-time correlation of equivalent radar re¯ectivity (Ze) with snow gauge rate (S). It is

shown from both theory and previous results that Ze±S relationships vary signi®cantly during a storm and from

storm to storm, requiring a real-time correlation of Ze and S. A key element of the algorithm is taking into account snow drift and distance of the radar volume from the snow gauge. The algorithm was applied to a number of New York City snowstorms and was shown to have skill in nowcasting SWE out to at least 1 h when compared with persistence. The algorithm is currently being used in a real-time winter weather nowcasting system, called Weather Support to Deicing Decision Making (WSDDM), to improve decision making regarding the deicing of aircraft and runway clearing. The algorithm can also be used to provide a real-time Z±S relationship for Weather Surveillance Radar-1988 Doppler (WSR-88D) if a well-shielded snow gauge is available to measure real-time SWE rate and appropriate range corrections are made.

1. Introduction and runway deicing ¯uids is signi®cantly affected by dilution from the water content of snow (Bernadin et Snowstorms affect a variety of human activities such al. 1997; Rasmussen 1999a). In the case of aircraft de- as transportation (aviation and highways), commerce, energy, and communications. Snow accumulating on icing (or anti-icing), accurately measured SWE is need- highways and runways must be cleared to ensure safe ed by pilots and ground personnel to assess whether the operation of surface vehicles and aircraft. The operation snow accumulation on an aircraft wing since deicing/ of aircraft during snowy conditions is a signi®cant safety anti-icing has exceeded the capability of the deicing/ issue because of the rapid loss of lift and increase in anti-icing ¯uid to keep the surface ice free. The Society drag for relatively thin coatings of snow on a wing (25% of Automotive Engineering (SAE) Ground Deicing loss of lift and increase in drag for rough ice coatings Committee produces Holdover Tables that indicate the of only 0.8-mm thickness on the wing), requiring re- amount of time a deicing/anti-icing ¯uid can prevent moval before takeoff. Runways are often treated with ice formation on an aircraft for a given precipitation an anti-icing ¯uid to prevent the accumulation of snow. type, rate, and temperature. The tables are based on Snow on highways must also be removed as quickly as testing of deicing ¯uids at 1 and 2.5 mm hϪ1 liquid possible to ensure safe and ef®cient operations of both equivalent snowfall rates and at various temperatures. commercial and public vehicles. Thus, knowledge of the occurrence of rates less than 1 A key quantity in all of the above applications is the mm hϪ1, between 1 and 2.5 mm hϪ1, or greater than liquid equivalent amount of snow, or snow water equiv- 2.5 mm hϪ1 are critical in the proper use of this table. alent (SWE). For instance, the performance of aircraft Current National Weather Service snow intensities are based on visibility, which has been shown to be a poor indicator of the actual liquid equivalent snowfall rate Corresponding author address: Dr. Roy Rasmussen, NCAR, P.O. Box 3000, Boulder, CO 80307. (Rasmussen et al. 1999b). Thus, the current hourly ME- E-mail: [email protected] TAR (a French acronym that translates as aviation rou-

᭧ 2003 American Meteorological Society JANUARY 2003 RASMUSSEN ET AL. 21

tine weather report) reports of snow intensity do not TABLE 1. Various Z±S and Ze±S relationships from literature (adopt- ed from Gray and Male 1981). Conversion to Z ±S is based on Z ϭ meet this need. e e 0.224Z for melted snow¯akes (Smith 1984). The method of runway and taxiway snow removal also depends on whether the snow is dry and ¯uffy (low Precipitation type ZZe water content) or wet and dense (high water content). Hail 320S 1.6 72S 1.6 The formation of ice on a highway critically depends Graupel 900S 1.6 202S 1.6 on the water content of the snow. Single crystals (Carlson and Marshall 1972) 160S 2.0 36S 2.0 SWE rates at speci®c locations such as an airport or Snow¯akes consisting of the following crystal types: along a highway can be measured using accurate snow (Ohtake and Henmi 1970) gauges with appropriate wind shielding (Goodison Plates and columns 400S 1.6 90S 1.6 1978; Yang et al. 1998; Rasmussen et al. 2001). The Needle crystals 930S 1.9 208S 1.9 Stellar crystals 1800S 1.5 403S 1.5 recent study by Rasmussen et al. (2001) has shown that Spatial dendrites 3300S 1.7 739S 1.7 real-time, accurate snow measurements can be made if Snow¯akes (Imai 1960) the sidewalls of the snow gauges are heated to ϩ2.0ЊC Dry (T Ͻ 0ЊC)* 540S 2 120S 2 and appropriate corrections are made to account for the Wet (T Ͼ 0ЊC) 2100S 2 470S 2 undercatch of snow due to wind effects. In principle, a Snow¯akes (Puhakka 1975) network of these heated and shielded snow gauges could Dry (T Ͻ 0ЊC)* 1050S 2 235S 2 be deployed to cover a wide region, such as a metro- Wet (T Ͼ 0ЊC) 1600S 2 358S 2 politan area or large airport. However, such a network Snow¯akes (Gunn and Marshall 1958) 2000S 2.0 448S 2 is costly to deploy and maintain, and thus an attractive Snow¯akes (Sekon and Srivastava 1970) 1780S 2.21 399S 2.21 alternative is to use radars to estimate liquid equivalent snowfall rate. Radar measures the equivalent radar re- * T ϭ mean air temperature. 1 ¯ectivity, Ze, rather than the SWE rate. Thus, a method to correlate radar re¯ectivity Ze with SWE rates is need- ter weather nowcasting system (Rasmussen et al. 2001) ed. Rasmussen et al. (2001) present a method to perform developed with Federal Aviation Administration (FAA) this correlation in real time using snow gauges on the funding. Section 2 provides a background on the use of ground and radar re¯ectivity measurements from aloft Z±S relationships to estimate snowfall rate and the prob- that will be further described in this paper. lems therein. The real-time technique is brie¯y de- In addition to current SWE rates, nowcasts of SWE scribed in section 3, and an evaluation of the technique rates are important. Forecasts with lead times as short is given in section 4. Conclusions are presented in sec- as 30 min are of value to decision makers, who require tion 5. forecasts of SWE amounts for particular locations, such as the ramps, taxiways, runways, and highway sections. Techniques such as the cross-correlation method (Tuttle 2. Background and Foote 1990; Rinehart and Garvey 1978) enable de- The estimation of liquid equivalent snowfall rate us- termination of the motion of radar echoes. This method ing radar has been studied for the past 50 years by many was adapted to track winter storm echoes by Rasmussen investigators (e.g., Fujiyoshi et al. 1990; Langville and et al. (2001). An evaluation of the technique by Turner Thain 1951; Ohtake and Henmi 1970; Yoshida 1975; et al. (1999) showed it provided reasonably accurate Sekhon and Srivastava 1970; Marshall and Gunn 1952; point re¯ectivity forecasts out to 30 min. Therefore, a Carlson and Marshall 1972; Boucher and Weiler 1985; 30-min forecast of SWE rates could be made if a re- Harimaya 1978). These studies have attempted to relate lationship existed between radar re¯ectivity aloft and the liquid equivalent snowfall rate, S (mm hϪ1), to radar snow gauge accumulation at the ground. Rasmussen et re¯ectivity factor Z (mm6 mϪ3) using a power law of al. (2001) present a method to properly time-lag and the form wind-adjust the re¯ectivity and snow gauge data to Z aS b (mm6 mϪ3 ). (1) achieve this relationship, and they use it to perform a ϭ snow nowcast. In this paper we present a statistical eval- The values of the coef®cient a and exponent b are uation of this technique using data from New York City usually determined through a regression ®t of Z and S 6 snowstorms. for a number of snowstorms, in which Z (ϭ⌺nDm, n is The main motivation for this work is to provide airline number concentration and Dm is the diameter of a melted and airport decision makers with accurate point now- snow¯ake) is calculated from melted snow¯akes (e.g., casts of SWE rates in support of aircraft deicing/anti- Marshall and Gunn 1952). These studies have found icing and runway snow removal operations. The tech- that the values of a and b are highly variable, depending nique is currently being used operationally in the Weath- on various parameters such as the crystal type, degree er Support to Deicing Decision Making (WSDDM) win- of riming and aggregation, density, and terminal velocity (Table 1). 1 In many cases the goal of such studies is to determine Here, Ze is the radar-determined radar re¯ectivity factor that assumes particles with a dielectric constant of water. the so-called climatological Ze±S relationship that can 22 JOURNAL OF APPLIED METEOROLOGY VOLUME 42

from 2230 to 2330 UTC, despite the nearly constant conditions of temperature and liquid equivalent snowfall rate. The snowfall density is high for relatively small snow¯ake (aggregated ice crystals) sizes (3±4-mm diameter) and is very low for large snow¯ake diameters (20±25-mm diameter). This inverse relationship between snow¯ake diameter and snow¯ake density has also been documented by Rogers (1974). His study showed that snow¯ake density varies from 0.005 to 0.5 gcmϪ3. Gunn and Marshall (1958) observed a similar

rapid change in the Ze±S relationship with a change from single crystals to aggregates. Wilson (1975) observed large variations in radar-estimated snow amounts for different storm types as compared with snow gauge measurements.

This variation in the Ze±S relationship can be further FIG. 1. Time series of 15-min average snow density (solid line) analyzed by considering a theoretical relationship be- and liquid equivalent snowfall rate (dashed line) from the NCAR Marshall test site from 13 Nov 1994. Air temperature is Ϫ1ЊC. tween Ze and S for aggregated snow¯akes. The liquid equivalent snowfall rate, S (mm hϪ1) can be written as

ϱ then be used to determine snowfall rate over the domain S ϭ 3.6 ϫ 104 [n(D)V␳ VdD] (mm hϪ1 ), (2) of the radar [Smith (1984) discusses how to convert ͵ st 0 from Z to Ze]. In this paper this method is referred to as the traditional approach. For instance, the Weather where D (cm) is the unmelted snow¯ake diameter, n(D) Surveillance Radar-1988 Doppler (WSR-88D) Precip- (cmϪ4) is the number concentration, V (cm3) is the vol- Ϫ1 itation Processing Subsystem (PPS; Fulton et al. 1998) ume of the snow¯ake, Vt (cm s ) is the terminal ve- 1.4 Ϫ3 uses the relation Ze ϭ 300R for convective precipi- locity, and ␳s (g cm ) is the snow¯ake density. If we 1.2 tation, Ze ϭ 250R for tropical rainfall, and several assume an exponential snow¯ake size distribution (Sek- 2.0 relations for winter precipitation (e.g., Ze ϭ 75S ). hon and Srivastava 1970) with spherical aggregates of

However, because of the wide variety of snow crystal density ␳s, Eq. (2) can be written as types, degrees of riming, aggregation and snow size ␲ distributions in natural clouds, and the possible presence S ϭ 3.6 ϫ 104 of brightband echo, it is not possible to specify one Ze± 6

S relationship that will work for every winter storm. ϱ The Z±S relationships from previous studies (Table 1) ϫ [ND3 exp(Ϫ⌳D)␳ VdD] (mm hϪ1 ), (3) show that the value of the coef®cient a ranges from 160 ͵ 0 st 0 to 3300, while the value of the exponent b ranges from Ϫ4 1.5 to 2.2. Thus, for a given radar re¯ectivity, a wide where N 0 (cm )isthey intercept of the size distribution variation in snowfall rate is observed. A scatterplot of and ⌳ (cmϪ1) is the slope. As mentioned above, snow- snowfall rate (S) versus equivalent radar re¯ectivity fac- ¯ake density decreases inversely with size (Rogers

tor Ze (dBZ) as presented by Fujiyoshi et al. (1990, their 1974). For dry snow¯akes, ␳s,dry ϭ 0.017/D, while for Fig. 1), for instance, shows that snowfall rate ranged wet and/or rimed snow¯akes, ␳s,wet ϭ 0.072/D, where from 0.03 to 3 mm hϪ1 (two orders of magnitude) for D is in centimeters (Rogers 1974). Snow¯ake terminal a radar re¯ectivity of 20 dBZ using 1-min radar and velocity is also nearly constant with size and close to snowfall-rate data. In one of the earliest Z±S studies, 100 cm sϪ1 (Rasmussen et al. 1999b). If we use these Marshall and Gunn (1952) showed a factor-of-10 var- relations in Eq. (3) and assume that snow¯ake terminal iation in the daily value of the coef®cient a (from 46 velocity is constant, the following equations can be ob- to 465). They attributed this variation to changes in tained for dry and wet snow¯akes (in this paper, ``wet'' crystal type. Puhakka (1975) observed storm to storm snow¯akes refer to wet and/or rime snow¯akes): variations in the value of a from 400 to 2150. S 612 NV /3 3 (mm hϪ1 ) An example of the rapid variation of snow density dry snowϭ ␲ 0 t,d ⌳

(and therefore particle type) with time for nearly con- (dry snow, constant Vt) and (4) stant temperature and snowfall-rate conditions is shown 3 Ϫ1 in Fig. 1. In this ®gure, snow density was measured in Swet snowϭ 2592␲NV 0 t,w/3⌳ (mm h ) a pan every 15 min, while the snowfall rate was deter- (wet snow, constant V ). (5) mined by a weighing snow gauge. The crystal types and t

sizes were determined by an observer at the site. Note The equivalent radar re¯ectivity factor Ze for snow- that the snow density changes from 0.12 to 0.03 g cmϪ3 ¯akes can be written as (Smith 1984) JANUARY 2003 RASMUSSEN ET AL. 23

12 Ze,snowflakes ϭ 1.0 ϫ 10 Sdry snowflakes

ϱ Ϫ3 2/5 3/5 Ϫ1 ϭ [1.92 ϫ 10 (NV0 t,d)]Z e,ds (mm h ) (15) ϫ |K |/|22K |[n(D)DdD 6] ͵ sw 0 and (mm6 mϪ3 ), (6) Swet snowflakes where K ϭ (m2 Ϫ 1)/(m 2 ϩ 2), m being the complex Ϫ3 2/5 3/5 Ϫ1 w ϭ [1.46 ϫ 10 (NV0 t,w)]Z e,ws (mm h ). (16) 2 refractive index of water. The value of | Kw | is 0.91± 2 Thus, the Z ±S or S±Z relationship for snow¯akes 0.93. The value | Ks | is a similar quantity but for snow. e e Because of the low density of snow¯akes, the value of depends on the snow¯ake size distribution through the 2 y intercept N 0, whether the snow is dry or wet, and the | Ks | for snow¯akes is determined using a volume mixing ratio for a mixture of ice and air (Battan 1973; terminal velocity of the snow¯akes through Vt. b Bohren and Battan 1980). The Debye (1929) mixing The values of a and b using the Ze ϭ aS relationship for dry snow¯akes are then given from Eqs. (13) and formulation yields the following relationship: Ks ϭ (␳s/ Ϫ3 (14) as ␳i)Ki, where ␳i ϭ 0.92 g cm and Ki ϭ 0.424. Thus, 2 | Ks | ϭ 0.0021 for a typical snow density of 0.10 g bdry snowflakes ϭ 1.67 and (17) cmϪ3, and 0.000 021 for a snow density of 0.01 g cmϪ3. 2 4 2/3 5/3 As a result, | Ks | is at least two orders of magnitude adry snowflakesϭ 3.36 ϫ 10 /(NV 0 t ). (18) smaller than | K | 2 and also varies by two orders of i The corresponding values for wet snow are magnitude. As discussed above, the density for dry snow¯akes can be given as bwet snowflakes ϭ 1.67 and (19)

Ϫ3 4 2/3 5/3 ␳s,dry ϭ 0.017/D (g cm ), (7) awet snowflakesϭ 5.32 ϫ 10 /(NV 0 t ). (20) while for wet and/or rimed snow¯akes The value of the exponent b is a constant and is equal to 1.67 for both dry and wet snow¯akes. Previous stud- ␳ ϭ 0.072/D (g cmϪ3 ). (8) ies (Table 1) have found b to range from 1.5 to 2.21 s,wet for dry and wet snow¯ake aggregates, with an average Using the Debye mixing relation discussed earlier and value of 1.89. Thus, the theoretically derived value of Eqs. (7) and (8), the following equations can be derived 1.67 agrees reasonably well with the observational data. 2 The main unknown is the value of the parameter a. for | Ks | for dry and wet and/or rimed snow: The value of a can vary by a factor of 1.6 because of 2 Ϫ52 |Ks,dry| ϭ 6.15 ϫ 10 /D and (9) wet or dry snow, by a factor of 3 because of variations in terminal velocity from 100 to 200 cm sϪ1, and by a |K |2 ϭ 1.07 ϫ 10Ϫ32 /D . (10) s,wet factor of 5 because of variations in N 0 from 0.05 to 0.005 cmϪ4 (Braham 1990). Thus, speci®cation of the Assuming an exponential snow size distribution and value of a for snow¯akes requires a knowledge of the 2 the previous | Ks | relations, Eq. (6) can be integrated snow¯ake size distribution, whether the snow is rimed to obtain or partially melted, and the mean terminal velocity of the snow¯ake size distribution. In addition, variations 95 6Ϫ3 Ze,dry snowflakesϭ 1.6 ϫ 10 N 0/⌳ (mm m ) (11) of the snow size distribution from exponential can also and add variability. Figure 2a shows the Ze±S relationship for dry and wet Z ϭ 2.81 ϫ 1010N /⌳ 5(mm 6 mϪ3 ). (12) Ϫ1 e,wet snowflakes 0 snow assuming that N 0 varies from 0.005 to 0.05 cm (Braham 1990) and a terminal velocity of 100 cm sϪ1 Combining Eqs. (4) and (5) with Eqs. (11) and (12), for dry snow and 200 cm sϪ1 for wet snow. The curves we obtain show that the observed variation in N0 leads to a factor- of-2 variation in snowfall rate for a given radar re¯ec- Ze,dry snowflakes tivity value. The difference between wet and dry snow ϭ [3.36 ϫ 104 /(NV 2/3 5/3)]S 5/3(mm 6 mϪ3 ) (13) leads to an additional factor-of-2-variation, resulting in 0 t,d a factor-of-4 overall variation. This amount of variation and is very consistent with previous observations such as those by Fujiyoshi et al. (1990). They show even larger Z e,wet snowflakes variability, most likely due to other factors such as mea- 4 2/3 5/3 5/3 6 Ϫ3 ϭ [5.32 ϫ 10 /(NV0 t,w )]S (mm m ). (14) surement error and evolution and/or drift of snow between the height of the radar beam and the snow gauge. Solving for S yields the following two equations for dry The value of the coef®cient a for the curves in Fig. and wet snow: 2a ranges from 57.3 for wet snow with an N0 of 0.05 24 JOURNAL OF APPLIED METEOROLOGY VOLUME 42

Ϫ1 FIG. 2. Relationship between radar re¯ectivity 10 logZe (dBZe) and snowfall rate S (mm h ): (a) theory for dry and wet and/or rimed Ϫ4 Ϫ4 Ϫ4 snow with N0 ϭ 0.05 and 0.005 cm , and (b) theory for dry snow with N0 ϭ 0.005 cm and wet snow with N0 ϭ 0.05 cm , and previous observation-based Ze±S relationships given in Table 1.

Ϫ4 Ϫ4 cm , to 533.5 for dry snow with an N 0 of 0.005 cm . velocity in order to accurately specify a Ze±S relationship. Estimates of the coef®cient a for snow¯akes from the As a result, it is misleading to use only one Ze±S rela- previous studies listed in Table 1 have a range of 90± tionship for a speci®c region or speci®c storm because

739 for Ze±S relations, very similar to the range of the of the dif®culty in predicting the type of snowfall that theoretical values. Figure 2b compares these previous will occur. Passarelli (1978) reached the same conclusion relationships with the current theoretical predictions. As in a theoretical and observational study of snow. He con- shown, nearly all of the previous relationships are con- cluded that ``it is very unlikely that a single Ze±R relation tained within the bounds of the current theoretical for snow will be suitable for any quantitative radar±hy- curves. Thus, both theory and observation show a fac- drometeorological studies of snowfall amounts.'' tor-of-4 variation in SWE rate for a given re¯ectivity Wilson (1975) and Collier and Larke (1978) have value. demonstrated that well-shielded weighing snow gauges Thus, one must know whether the snow is wet or dry, can be used to adjust radar estimates of snow instead the y intercept of the size distribution, and its terminal of using a ®xed Ze±S relationship. In this paper, we present a method to determine the time-varying Ze±S relationship in real time using well-shielded weighing snow gauges and demonstrate a technique to make use of this real-time Z±S relationship to nowcast snowfall.

3. 30-min point nowcast of snowfall rate using a

real-time Ze±S relationship The previous discussion has shown the dif®culty of using a climatological Z±S relationship to estimate SWE rate for 1 h or shorter periods within a storm. In this section we summarize and extend the technique presented in Rasmussen et al. (2001) to 1) determine the

Ze±S relationship in real time using radar and snow gauge data, and 2) make a 30-min forecast of SWE rate based on the extrapolated radar echo motion. The basis for this technique is the observation that radar echo aloft is correlated with snowfall rate at the ground. An example of this correlation from the 10 December 1997 FIG. 3. Time series from 10 Dec 1997 of snowfall rate from a snowstorm in New York City is shown in Fig. 3. A time Geonor snow gauge at LaGuardia Airport in New York City (solid line) and radar-derived snowfall rate for the same location (dashed series of SWE from the snow gauge at LaGuardia Air- line). The radar-derived snowfall rate is lagged by 15 min to account port is compared with a time series of snowfall rate as for particle fall time. derived from the radar re¯ectivity taken directly over- JANUARY 2003 RASMUSSEN ET AL. 25

FIG. 4. Schematic diagram showing the radar beam and gauge geometry and theoretical motion of snow particles from the radar volume to the snow gauge.

FIG. 5. Time series from 10 Dec 1997 of the a (solid line) and b head of the gauge (ϳ900 m above) lagged by approx- (dashed line) coef®cient (exponent) in the Ze±S power law. The terms imately 15 min to allow time for the snow particles to a and b are determined as averages from the radar±snow gauge data fall to the gauge (winds in this case were relatively associated with LaGuardia and Kennedy Airports in New York City. light). The re¯ectivity was converted to snowfall rate 1.5 using the following relation: Ze ϭ 414S . The traces show that SWE rate as measured by the gauge correlates b. Real-time Ze±S and 30-min snowfall rate and fairly well with radar-measured re¯ectivity aloft. This accumulation nowcast forms the basis of the nowcasting technique presented in this paper. The 30-min snow echo motion estimated from TREC The 30-min point nowcast technique for snowfall is used to produce a 30-min liquid equivalent snowfall consists of two steps: 1) a 30-min nowcast of the radar rate and accumulation nowcast at the snow gauge lo- re¯ectivity at a point, and 2) conversion of the 30-min cations. To do this, a real-time calibration between radar nowcast of re¯ectivity into SWE rate using an adjust- re¯ectivity and SWE rate is required. ment procedure based on the radar re¯ectivity aloft and the snow gauge SWE at the ground during the previous 1) REAL-TIME Z ±S ALGORITHM 30±60 min. The details of this procedure are described e next. In the Ze±S equation [Eq. (1) using equivalent radar re¯ectivity], the exponent b is assumed to be a function of temperature. For pure rain events (T Ͼ 5ЊC), the a. 30-min radar re¯ectivity nowcast Marshall±Palmer value of b ϭ 1.6 is used. For snow The 30-min nowcast of re¯ectivity is based on the events (T Ͻ 0ЊC), a value of b ϭ 1.75 is used based Tracking Radar Echoes by Correlation (TREC) tech- on the assumption of constant terminal velocity. This nique (Tuttle and Foote 1990; Rinehart and Garvey value is consistent with published Ze±S relationships in 1978). This technique compares two consecutive radar Table 1 and the theoretical discussion in section 2. For images (typically 5±10 min apart for a WSR-88D, de- mixed events, the value of b is interpolated assuming a pending on the scan strategy) and determines through linear relationship with temperature. a pattern matching technique the most likely direction At each radar scan time, the storm motion at the gauge and speed of motion of 10 km ϫ 10 km re¯ectivity is computed using TREC. An average fall time (tf ) for blocks throughout the radar domain. The assumption is the snow particles from the radar beam height to the made that the future snow echo motion (over the next gauge is computed using 0.9 m sϪ1 for dry snow (T Ͻ 30 min) will be very similar to the previous motion 0ЊC), a mean value based on 3 yr of snow particle fall during the past 12±24 min. A description of the TREC speed measurements at the National Center for Atmo- technique, as applied to winter storms, is given in Ras- spheric Research (NCAR) Marshall snow measurement mussen et al. (2001). An evaluation of TREC perfor- site using a vertically pointing Doppler radar called Pre- mance to nowcast radar re¯ectivity using radar re¯ec- cipitation Occurrence Sensor System (POSS) (Sheppard tivity data from Chicago (Lockport, Illinois) and New 1990). For rain events (T Ͼ 5ЊC), a fall speed of 10 m York City [Fort Dix, New Jersey (KDIX), and Stony- sϪ1 is assumed. For mixed events, the fall speed is as- brook, New York (KOKX)] WSR-88D radars by Turner sumed to vary linearly between these two values of et al. (1999) showed that the 30-min TREC echo now- surface temperature. Future enhancements to the tech- cast consistently beat persistence in terms of probability nique may involve the assignment of terminal velocity of detection at a point for similar false alarm ratio by based on precipitation type from Automated Surface up to 21% for winter storms in these regions. Observing System (ASOS). 26 JOURNAL OF APPLIED METEOROLOGY VOLUME 42

during startup and low-data periods. An example of the variation in a and b based on the real-time algorithm is shown in Fig. 5. Of note is the jump in a from values near 400 before 2200 UTC to values around 1000 after 2300 UTC, indicative of two different regimes of precipitation in this storm.

2) 30-MIN NOWCAST ALGORITHM

Once the real-time coef®cient a is found, the 30-min forecast is made using the following steps:

FIG. 6. Snow gauge catch ef®ciency as a function of 3-m wind (i) Determine the average TREC storm motion vector speed for a Geonor snow gauge in a double Alter shield (upper solid Vtrec for the most current radar scan over the lo- line) and in a single Alter shield (lower solid line). The dashed line cation of the gauge by averaging all of the TREC represents the curve used to correct the single Alter snow gauge data used in this study. vectors over a 20 km ϫ 20 km box centered over the gauge. A large box size is used because of the variation inherent in the TREC vectors. (ii) Determine the time for the snow to fall to the The radar re¯ectivity associated with the precipitation ground from the closest radar elevation scan (typically the 0.5Њ scan for WSR-88D radars) overhead falling into the snow gauge resided tf seconds ago at a of the gauge (tf ). distance (tf ϫ storm speed) upwind of the gauge site (Fig. 4). Storm speed is calculated using a weighted (iii) Based on the fall time tf , determine the most likely sum of the TREC storm motion and the surface wind distance and direction upwind of the gauge from which the snow particles that fall at the airport [(c1Vtrec ϩ c 2Vsurf) ϫ tf ]. Based on the storm speed and direction, a search back in time and upwind in space is originated. This is done using the TREC wind and executed to locate the relevant re¯ectivity region as- the surface wind in a weighted sum [(c1Vtrec ϩ sociated with the snow gauge measurement. This up- c2Vsurf) ϫ tf ], where c1 and c 2 are weights currently wind re¯ectivity is averaged over a 10 km ϫ 10 km set at 0.75 and 0.25, respectively for the New York WSR-88D radars (these weights are likely to square. In this fashion a time series of correlated Ze±S pairs is created. change from site to site because of factors such The Z ±S adjustment procedure is then simple. The as storm type and distance of the radar beam over- e head). At this upstream point, calculate the 0-, coef®cient a in the Ze±S relationship is suitably adjusted to make the radar-estimated and gauge-estimated ac- 5-, 10-, 15-, 20-, 25-, and 30-min forecasts of cumulations equal using the following equation: re¯ectivity based on the TREC storm motion at this location using the re¯ectivity from the lowest b elevation scan. a ϭ (Z 1/b) dt S dt , (21) []͵ e ΋͵ (iv) Centered on the upwind location, average the forecasted re¯ectivity pattern over a 10 km ϫ 10 km where # Sdtis the SWE accumulation from the snow area for each of the forecast times. gauge over the chosen time period. (v) Convert the forecasted averaged re¯ectivity into No attempt is made to adjust the exponent b in real snowfall rate using the calibrated Ze±S relation- time (other than the earlier discussed temperature ad- ship. justment) because the data are too sparse and noisy for (vi) Add tf to the forecast times above to get the actual calibration with 2 degrees of freedom. In addition, both forecast times for snowfall rate at the ground. observations (Table 1) and theory (section 2) show that Thus, the upstream forecasts at 0, 5, 10, 15, 20, its value is nearly constant. Integral quantities were used 25, and 30 min at the upstream radar altitude be- because it was found that the relationship was much come the ground forecasts at 0 ϩ tf ,5ϩ tf ,10 more stable if snowfall rate and re¯ectivity are inte- ϩ tf ,15ϩ tf ,20ϩ tf ,25ϩ tf , and 30 ϩ tf .As grated over time [Fujiyoshi et al. (1990) also found that a result, particle fall time adds additional time to the regression between snowfall rate and radar re¯ec- the forecast. tivity was much more stable if at least a 30-min aver- (vii) Integrate the ground forecast rates over time to aging time was used]. A typical integration time to es- produce an accumulation forecast. tablish the real-time value of the coef®cient a is 30±60 min. The value of a is constrained to be within cli- The technique just described can be shown to be matological limits in order to ensure algorithm stability equivalent to JANUARY 2003 RASMUSSEN ET AL. 27

TABLE 2. Optimal parameter values and associated rmse. Forecast Accumulation Wind Rmse Case site Radar time (s) method Gauges (mm) 10 Dec 1997 LGA KOKX 1800 T ϩ S* All 0.29 EWR KDIX 3600 T ϩ S EWR 0.41 JFK KOKX 1800 TREC All 0.23 21 Mar 1998 LGA KDIX 3600 T ϩ S All 0.19 EWR KDIX 1800 T ϩ S All 0.5 JFK KDIX 1800 None All 0.42 22 Mar 1998 LGA KDIX 3600 T ϩ S LGA 0.18 EWR KDIX 3600 T ϩ S EWR 0.4 JFK KOKX 3600 TREC All 0.24 8 Jan 1999 LGA KOKX 3600 None All 0.20 EWR KDIX 1800 T ϩ S EWR 0.19

*Tϩ S refers to the weighted avarage of TREC and surface winds.

Future snow accumulation real changes in the snow intensity and not to changes in evaporation/growth/melting processes or the wind ®eld. ϭ (Past snow accumulation)

ϫ (Zdt1/b )(Zdt1/b ) . (22) 4. Statistical evaluation of the 30- and 60-min []͵ forecast ΋͵ past liquid equivalent snowfall nowcast The forecast snow amount is based on the previous n- In this section, a statistical evaluation of the algorithm minute snow amount times the ratio of the integral of is presented using a number of cases from New York. the future forecast re¯ectivity raised to the 1/b power The results show that the algorithm consistently beats to integral of the past forecast re¯ectivity raised to the snow gauge persistence in terms of probability of de- same 1/b power. If the re¯ectivity time integral is fore- tection (POD) and false alarm ratio (FAR). This was cast to increase (decrease) over the past re¯ectivity time especially true for cases with strong horizontal gradients integral, then the ratio will be greater (less) than 1.0 of re¯ectivity, such as storms with snowbands. In these and an increased (decreased) accumulation over the past cases, the algorithm beats snow gauge persistence 30- accumulation will be forecast. Thus, the technique is min snow accumulation POD values by up to 25% for equivalent to modifying the snow gauge persistence similar FAR values. For uniform echo cases, snow gauge forecast by the re¯ectivity trend. persistence and the real-time algorithm performed sim- A desirable feature of this technique is that it takes into ilarly, as expected. In the following we describe this account snow sublimation, melting, and growth between evaluation in more detail. the radar beam and the snow gauge as long as these processes are uniform over the calibration and forecast pe- a. Data sources riods. The technique also assumes that the wind ®eld is stationary in time during the calibration and forecast pe- The data used to evaluate the real-time Ze±S algorithm riods. In other words, it is assumed that changes in the were WSR-88D re¯ectivity data from the KDIX and past and future re¯ectivity trends in Eq. (22) are due to KOKX radars and liquid equivalent snowfall rates from

TABLE 3. Number of times the Z±S algorithm exceeded the climatological limits. No. times No. times Forecast lower limit upper limit Date No. volumes site exceeded exceeded Percent 10 Dec 1997 65 LGA 0 0 0 EWR 0 21 32 JFK 0 0 0 21 Mar 1998 29 LGA 0 0 0 EWR 2 0 7 JFK 7 0 24 22 Mar 1998 59 LGA 0 14 24 EWR 0 13 23 JFK 9 0 15 8 Jan 1999 64 LGA 60 0 94 EWR 0 0 0 Totals 587 78 48 (78 ϩ 48)/587 ϭ 0.21 28 JOURNAL OF APPLIED METEOROLOGY VOLUME 42

FIG. 7. Radar re¯ectivity from the (a) KDIX radar (note that the interior label is incorrectly marked ``KOKX'') at 2047 UTC 10 Dec 1997 and the (b) KOKX radar at 2050 UTC 10 Dec 1997. Re¯ectivity scale is the vertical color-coded bar at the right. Superimposed are the TREC storm motion vectors representing 30 min of motion. Location of KDIX and KOKX radars is indicated in yellow. Range rings (km) are centered on LGA. three snow gauges located at LaGuardia (LGA), John ϩ2ЊC to prevent sidewall snow accumulation from F. Kennedy International (JFK), and Newark Interna- blocking the collection ori®ce (Rasmussen et al. 2001). tional (EWR) Airports. These data were collected during The wind correction for undercatch for this particular an operational demonstration of the WSDDM system snow gauge±windshield con®guration was determined for LaGuardia Airport from December 1997 to March from extensive testing at the NCAR Marshall test site 1999 (Rasmussen et al. 2001). The snow gauges used (Rasmussen et al. 2001). The correction factor used in were Geonor gauges with an Alter shield and a sidewall this study is shown in Fig. 6. As shown, gauge under- heater. The sidewall heater maintained the sidewall tem- catch is nearly linearly related to wind speed for wind perature at ϩ2ЊC for ambient temperatures less than speeds up to 8 m sϪ1. JANUARY 2003 RASMUSSEN ET AL. 29

FIG.7.(Continued)

Data from four snowstorms from this period will be the TREC storm motion and surface wind speed to ac- analyzed, representing a variety of storm types. count for snow drift), 3) the minimum allowable a coef®cient, and 4) the ``rain temperature'' (i.e., the temperature above which to set the value of the exponent in b. Parameter optimization the Z±S relationship and the hydrometeor fall velocity to Prior to performing the statistical evaluation of the that of rain). The optimal parameters were determined performance of the real-time Z±S algorithm, key param- by changing one parameter at a time and computing the eters of the algorithm were optimized. These included 1) root-mean-square error (rmse) of the difference between the calibration time (the amount of time over which the the 30-min forecast and the actual gauge accumulation. radar re¯ectivity accumulations are compared with the The optimization yielded the following results: 1) cali- gauge accumulations to adjust the coef®cient of the Ze± bration time is 30 min, 2) weights for calculation of the S relation), 2) wind shear parameter (i.e., how to combine snow drift wind are 0.75 for TREC wind and 0.25 for 30 JOURNAL OF APPLIED METEOROLOGY VOLUME 42

FIG. 8. Radar snow trend plot from 10 Dec 1997 for Newark using the (left) KOKX radar and (right) KDIX radar as the input for the forecast. Dashed yellow line is the re¯ectivity forecast, and solid yellow line is the re¯ectivity veri®cation. Solid orange line is the snow gauge accumulation in millimeters, and dashed orange line is the forecast. The vertical red line represents current time, with past data to the left and forecast data to the right. The orange accumulation curves are zero when they cross the red vertical line. A 1½-h time window is shown. surface wind, 3) minimum a coef®cient is 50, and 4) the location relative to the airport, it was found that EWR rain temperature is ϩ2ЊC. The evaluation that follows is results were best when the EWR snow gauge was used conducted using these values. in tandem with the KDIX radar, and that JFK and LGA Tests were done to determine the best calibration based results were best when using a combination of JFK and on individual gauges or a combination of two or more LGA snow gauges and the KOKX radar (Table 2). gauges. If more than one gauge is used, the calibration The number of times the algorithm hit the climato- is the result of an average of the individual gauge ac- logical limits of the a coef®cient as given above is in- cumulations as compared with the average of radar re- dicated in Table 3. As shown, climatological limits were ¯ectivity accumulations for the sites. Because of the radar reached an average of 21% of the time, showing that

FIG. 9. Newark snow forecasts from 10 Dec 1997 using three different wind schemes to advect the snowfall: (left) no winds (use the overhead re¯ectivity, underforecast), (center) TREC storm motion vector (overforecast), and (right) weighted winds (0.25 surface, 0.75 TREC storm motion, best forecast). JANUARY 2003 RASMUSSEN ET AL. 31

FIG. 10. Radar re¯ectivity from the KOKX radar at 1200 UTC 21 Mar 1998. Re¯ectivity scale is the vertical color-coded bar at the right. Superimposed are the TREC storm motion vectors representing 30 min of motion. Location of the KOKX radar is indicated in yellow. Range rings (km) are centered on LGA. limits to the coef®cient a are required for successful heavy, where light is Ͻ1mmhϪ1, moderate is between application of the algorithm. 1 and 2.5 mm hϪ1, and heavy is Ͼ2.5 mm hϪ1. A hit (H) occurs when the forecast descriptive rate (light, moderate, heavy) veri®es, a miss (M) is an underforecast of c. Scoring methodology the actual rate, and a false alarm (F) is an overforecast Forecasts for each gauge location were evaluated using of the actual rate. Thus, POD ϭ H/(H ϩ M), FAR ϭ F/ probability of detection, false alarm ratio, and critical (H ϩ F), and CSI ϭ H/(H ϩ M ϩ F). success index (CSI; Donaldson et al. 1975). A forecast The evaluation metrics are compared with persistence is issued every radar volume scan (ϳ6±10 min depending forecasts. Persistence is de®ned as the current gauge rate on the volume coverage pattern (VCP)] and is converted (with the gauge ef®ciency wind correction) forecast for from a 30-min accumulation to an hourly rate. Each fore- the next 30 min. Gauge data from the most recent 10 min cast is then assigned a rate of either light, moderate, or are used to determine the rate. Again, rates are de®ned in 32 JOURNAL OF APPLIED METEOROLOGY VOLUME 42

FIG. 11. Same as in Fig. 10 but for the KOKX radar at 1027 UTC 22 Mar 1998. terms of light, moderate, and heavy. This type of persis- JFK gauge data were not available for the 8 January 1999 tence forecast is called gauge persistence. As will be dem- case. Hourly snowfall rates were heavy for a substantial onstrated later, the use of no winds in the forecast is es- amount of time on 10 December 1997 and 21 March sentially a ``radar persistence'' forecast, whereby overhead 1998. The echoes on 10 December 1997 tended to form re¯ectivity data are forecast to remain constant, that is, in small bands. The radar echoes on 21 and 22 March upstream re¯ectivity data are not considered. 1998 also exhibited banding but for shorter time periods. Echoes on 8 January 1999 were fairly uniform. As will d. Case studies be shown later, the echo structures have a direct bearing on how well the WSDDM system performs. Data from four days were analyzed: 10 December 1997, 21 and 22 March 1998, and 8 January 1999. As ECEMBER 1997 mentioned earlier, WSR-88D data from KDIX in New 1) 10 D Jersey and KOKX on Long Island were used, as well as This case had a variety of radar echo intensities and data from the three snow gauges at JFK, LGA, and EWR. shapes providing for a rigorous test of the WSDDM real- JANUARY 2003 RASMUSSEN ET AL. 33

FIG. 12. Same as in Fig. 10 but for the KOKX radar at 1732 UTC 8 Jan 1999. time Z±S algorithm. The choice of radar had a large effect effect on the re¯ectivity forecast. Figure 9 shows EWR on the algorithm performance. As an example, at 2047 forecasts using the three wind schemes discussed in sec- UTC, KDIX was indicating heavy echoes just upstream tion 3. With no winds (re¯ectivity persistence), SWE from EWR (Fig. 7a). However, KOKX indicated little echo values are underforecast. The most accurate forecast in that region as the beam was overshooting the storm results from using the weighted combination of TREC (Fig. 7b). Also, EWR is ϳ30 km closer to KDIX than it and surface wind vectors. is to KOKX, resulting in better sampling of echoes near Note on radar operation: At the onset of the storm, EWR. A comparison of forecasts for EWR using KOKX the KOKX radar was operating in clear-air mode. While and KDIX (Fig. 8) illustrates the dramatic effect of re- the radar may be slightly more sensitive in clear-air ¯ectivity forecast accuracy on the 30-min SWE prediction. mode, the maximum re¯ectivity reported in that mode Although the re¯ectivity forecast and veri®cation using is 28 dBZ; higher values will also be given the value KDIX are not perfectly aligned, the forecast is much more of 28 dBZ. Thus, a forecast based on clear-air re¯ectivity accurate than the KOKX radar forecast. will miss peaks in the echoes over 28 dBZ, causing an The computation of the effective wind has a marked underforecast. Fortunately, the radar was switched to 34 JOURNAL OF APPLIED METEOROLOGY VOLUME 42

FIG. 13. (a) Probability of detection, (b) false alarm ratio, and (c) critical success index for the 30-min forecasts (black vertical bar) and the snow gauge persistence (gray vertical bar) for the indicated cases (dates above the bars), and the average for all the cases (extreme right).

VCP 21 soon after the storm began and only an hour While KDIX provided more complete coverage south- or so of data were affected. west of EWR, both radars saw echoes southeast of EWR equally well. Since echo motion was from the south- southeast, the echoes were equidistant from both radars, 2) 21 MARCH 1998 and thus no appreciable difference between the forecasts Precipitation on 21 March was brief although rates from the two radars was found in this case (not shown). were heavyÐat times exceeding 5 mm hϪ1. A snowband moved across the area that was seen equally well by 4) 8 JANUARY 1999 both radars (Fig. 10). For this reason, only data from KOKX radar are shown in Fig. 10. Thus, the forecast As seen in Fig. 12, radar echoes on 8 January were for EWR using KDIX data was similar to the forecast very uniform with little change in structure with time. using KOKX data. However, as for the 10 December Note that the area of most signi®cance was the northern 1997 case, the WSDDM Z±S algorithm performance edge of the heavier precipitation. was heavily dependent on the wind scheme, with the most accurate scheme being the TREC-surface wind e. Scoring results average (not shown). This section presents the scoring results for the cases described above. Values of POD for both the WSDDM 3) 22 MARCH 1998 real-time Z±S algorithm (W) and gauge persistence 30- Radar echoes on this day were weaker and smaller min forecasts (P) are shown in Fig. 13a. and snowfall rates were mostly moderate (Fig. 11). For all but the 8 January 1999 case, WSDDM Z±S JANUARY 2003 RASMUSSEN ET AL. 35

FIG. 14. Same as in Fig. 13 but for the 60-min forecasts.

algorithm PODs are signi®cantly higher than persistence January case was not scored because rates were not PODs. The average WSDDM Z±S algorithm POD is signi®cant and results would not have been any differ- 0.81 as compared with 0.70 for persistence. There is a ent. Interestingly, the WSDDM Z±S algorithm perfor- much larger difference in FARs (Fig. 13b): the WSDDM mance did not change signi®cantly overall while the Z±S algorithm had an average FAR of 0.09 as compared average persistence CSI dropped from 0.54 to 0.35. with 0.31 for persistence. In general, these results in- While the WSDDM Z±S algorithm rarely overfore- dicate that the WSDDM Z±S algorithm slightly under- casts precipitation, there was a slight tendency to un- forecasts and rarely overforecasts. Persistence resulted derforecast. However, the bulk of the underforecast in large overforecast errors. problem was caused by cases in which echoes increased A comparison of CSIs (Fig. 13c), an indicator of over- in intensity after the forecast was made. The algorithm all skill, shows that the WSDDM Z±S algorithm beats usually takes 10±15 min to adapt to the changes in echo persistence with an average value of 0.73 as compared intensities. For situations in which an echo, especially with 0.54 for persistence. The persistence forecast CSI a band, simply advected over a site without changing, on 8 January is nearly equal to the WSDDM algorithm the forecast tended to be good. CSI. Note that nearly one-half of the nowcasts were Because FAA Terminal Doppler Weather Radars made on 10 December 1997, which was considered the (TDWR) with a ®ner beamwidth (0.5Њ vs 1.0Њ for WSR- most rigorous test for the WSDDM algorithm. For these 88D) are located near major airports, these data will likely events WSDDM had a CSI of 0.70. improve the performance of the real-time Z±S algorithm. The WSDDM Z±S algorithm and persistence scoring The TDWR also provides rapid updates of higher-reso- were also performed for 1-h forecasts (Fig. 14). The 8 lution data very close to the ground (often within 100 m) 36 JOURNAL OF APPLIED METEOROLOGY VOLUME 42 that could mitigate problems caused when the WSR-88D snowfall using a radar and sensitive snow gauges. J. Appl. Me- beam is high above the ground (sometimes overshooting teor., 29, 147±152. Fulton, R. A., J. P. Breidenbach, D.-J. Seo, D. A. Miller, and T. the storm). The advantage in this case is the reduced ver- O'Bannon, 1998: The WSR-88D rainfall algorithm. Wea. Fore- tical distance to calculate snow drift, thereby reducing one casting, 13, 377±395. of the main sources of error in the algorithm. Goodison, B. E., 1978: Accuracy of Canadian snow gage measurements. J. Appl. Meteor., 17, 1542±1548. Gray, D. M., and D. H. Male, 1981: Handbook of Snow: Principles, 5. Summary and conclusions Processes, Management and Use. Pergamon Press, 776 pp. Gunn, K. L. S., and J. S. Marshall, 1958: The distribution with size An algorithm for nowcasting snowfall has been de- of aggregate snow¯akes. J. Meteor., 15, 452±461. veloped that uses a real-time correlation of radar re- Hariyama, T., 1978: Observation of size distribution of graupel and snow ¯ake. J. Fac. Sci., Hokkaido Univ., Ser. 7, 5 (3), 67±77. ¯ectivity with snow gauge data. It was shown that a Imai, J., 1960: Raindrop size distributions and the Z±R relationship. real-time correlation is needed in order to take into ac- Proc. Eighth Weather Radar Conf., Boston, MA, Amer. Meteor. count the natural variations in the Z±S relationships that Soc., 321±326. occur during a storm because of changes in snow crystal Langville, R. C., and R. S. Thain, 1951: Some quantitative measurements of three-centimeter radar echoes from falling snow. type, degree of riming and aggregation, wetness, and Can. J. Phys., 29, 482±490. size distribution. The algorithm was shown to have skill Marshall, J. S., and K. L. S. Gunn, 1952: Measurement of snow in nowcasting snowfall (SWE) out to at least 1 h when parameters by radar. J. Meteor., 9, 322±327. compared with persistence. The algorithm is currently Ohtake, T., and T. Henmi, 1970: Radar re¯ectivity of aggregated snow¯akes. Preprints, 14th Conf. on Radar Meteorology, Tuc- being used in a real-time winter weather nowcasting son, AZ, Amer. Meteor. Soc., 209±210. system called WSDDM to improve decision making Passarelli, R. E., Jr., 1978: A theoretical explanation for Z±R rela- with regard to the deicing of aircraft and runway clear- tionships in snow. Preprints, 18th Conf. on Radar Meteorology, ing (Rasmussen et al. 2001). The algorithm can also be Atlanta, GA, Amer. Meteor. Soc., 332±335. used to provide a real-time Z ±S relationship for WSR- Puhakka, T., 1975: On the dependence of the Z±R relation on the e temperature in snowfall. Preprints, 16th Conf. on Radar Mete- 88D radars if a well-shielded snow gauge measuring orology, Houston, TX, Amer. Meteor. Soc., 504±507. real-time liquid equivalent snowfall rate is available and Rasmussen, R. M., A. Hills, S. Landolt, and C. Knight, 1999a: Results appropriate range corrections are made. of holdover time testing of type IV anti-icing ¯uids with the improved NCAR arti®cial snow generation system. Rep. DOT/ FAA/AR-99/10, U.S. Dept. of Transportation, Federal Aviation Acknowledgments. This research is in response to re- Administration, 36 pp. quirements and funding by the Federal Aviation Ad- ÐÐ, J. Vivekanandan, J. Cole, B. Myers, and C. Masters, 1999b: ministration (FAA). The views expressed are those of The estimation of snowfall rate using visibility. J. Appl. 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