Microphysical modes of precipitation growth determined by

Q J R Meteorol Soc (2003) 129 pp 455ndash476 doi 101256qj01216

Microphysical modes of precipitation growth determined by S-band verticallypointing radar in orographic precipitation during MAP

By SANDRA E YUTERcurren and ROBERT A HOUZE JRUniversity of Washington Seattle USA

(Received 28 December 2001 revised 12 July 2002)

SUMMARY

High-resolution vertically pointing S-band Doppler radar data obtained within orographic rain by theUniversity of Washington Orographic Precipitation Radar (OPRA) at Locarno-Monti Switzerland during theMesoscale Alpine Programme (MAP) Intensive Observing Periods (IOPs) 2b and 8 are examined to characterizethe ne-scale precipitation structure The relative roles of collection of cloud water by raindrops versus collectionof cloud water by ice particles (riming) in the same column are assessed with a one-dimensional (1D) Kesslerwater-continuity model using the observed data characteristics as input

The OPRA data reveal nearly ubiquitous small-scale fallstreaks each lt5 minutes in duration occurring withina wide range of precipitation intensities Periods of higher rain rates gt10 minutes in duration associated withconvective cells evident in coarser-resolution data manifested as increased frequency and intensity of fallstreaksin the OPRA data A subset of fallstreaks had suf cient magnitude in re ectivity to indicate a clear connectionfrom the snow region across the melting layer and into the rain region The small-scale inhomogeneities inmicrophysical structure associated with fallstreaks are likely to be associated with convective overturning in theunstable IOP 2b case In the more stable IOP 8 case shear-driven turbulence near the melting layer evidentin truck-borne and airborne X-band Doppler-radar data shown in companion studies is a likely contributor tofallstreak formation

The vertical pro le of vertical air velocity (w) is critical to understanding the relationship between collectionand riming and their contributions to precipitation ef ciency Characteristics of the w pro le within precipitatingcloud were estimated in both rain and snow using observed radar parameters from the OPRA data In rainre ectivity-weighted fall speed was derived from observed re ectivity and assumptions about the raindrop sizedistribution The derived fall velocity was subtracted from the observed Doppler radial velocity to estimate w inrain regions to within raquo15 m siexcl1 In snow regions a lower bound on peak updraught velocity was estimatedfrom the observed maximum Doppler velocity For the data examined from MAP IOP 2b typical peak updraughtvelocities at Locarno-Monti were between 2 and 5 m siexcl1

These estimated peak updraught velocities were used to construct plausible parabolic pro les of w that werein turn used as input to a 1D Kessler water-continuity model Model output shows local maxima in the rimingrate and mixing ratio of ice within 2 km of the freezing level indicating a favourable environment for graupelformation The location of this layer in the model is consistent with the observed occurrence of graupel in NationalCenter for Atmospheric Research S-Pol radar data in the IOP 2b storm in a companion study The modelled ratesof collection and riming are comparable and both make signi cant contributions to the growth by accretion ofprecipitation within the storm updraughts Within the rain layer liquid-water coalescence (autoconversion andcollection) in updraughts with peak velocities of 5 m siexcl1 can account for up to raquo40 of column-integrated cloudwater

Our analysis of the observational data and the 1D model results con rms and extends previous workindicating that a combination of liquid-water coalescence and ice-phase processes is needed to obtain highprecipitation ef ciencies gt40 in orographic precipitation

KEYWORDS Accretion Fallstreaks Mesoscale Alpine Programme One-dimensional water-continuitymodel Riming

1 INTRODUCTION

Heavy rain of the type that causes ooding in the Alps is produced both quicklyand ef ciently over the lower slopes of the Alpine barrier Cloud water condensed overthe terrain is swept out rapidly by precipitation particles Terminology from water-continuity models describes the modes of rapid precipitation growth by the accretionof liquid cloud water below the freezing level as collection of cloud water by raindropsand the collection of cloud water by ice particles above the 0 plusmnC level as riming (Houze1993) By understanding the relative roles of collection and riming better we expect

curren Corresponding author Atmospheric Sciences Box 351640 University of Washington Seattle WA 98195-1640USA e-mail yuteratmoswashingtoneducdeg Royal Meteorological Society 2003

455

456 S E YUTER and R A HOUZE JR

TABLE 1 CHARACTERISTICS OF THE UNIVERSITY OF WASHINGTON OROGRAPHICPRECIPITATION RADAR (OPRA) DURING MAP

Model Modi ed Raytheon Path nder S-band

Receiver NCARATI PIRAQSignal Processor 50 MHz TI TMS320C50 on PIRAQ boardHost Computer 233 MHz Pentium II MMX 32 MB RAM 4 GB disk DAT CDROMFrequency 3050 MHzAntenna 18 m offset-feed parabolaAntenna Gain 31 dB (estimated)Antenna Height 382 m amslTransmitter Magnetron 2J75B with solid state modulatorPeak Power 60 kW maximum 35 kW minimumBeam Width 43plusmn (estimated)PRF 1000 HzPulse Width 10 sup1s Gates 100Variables Z Vr and spectral width (SW)

Figure 1 The University of Washington Orographic Precipitation Radar OPRA on the roof of the SwissMeteorological Institute Osservatorio Ticinese in Locarno Switzerland The antenna has an offset feed and isset so the radar beam is pointing vertically The radarrsquos electronics display and processing systems are contained

within the small shelter to the left of the antenna

to be able to improve modelling and prediction of heavy orographic rain events and toquantify their precipitation ef ciency

This paper assesses the relative roles of riming and collection in the same columnof precipitating cloud using data from vertically pointing radar obtained during theMesoscale Alpine Programme (MAP Houze et al 1998 Bougeault et al 2001)The University of Washington Orographic Precipitation Radar (OPRA) is a verticallypointing 10 cm meteorological pulsed Doppler radar (Table 1) OPRA was deployed onthe roof of the Swiss Meteorological Institute Osservatorio Ticinese from September toOctober 1999 at Locarno-Monti in Locarno Switzerland in collaboration with Jurg Jossand Urs Germann of the Swiss Meteorological Agency (SMA Fig 1) Approximately365 hours of radar data were obtained during 11 of the MAP Intensive Observation

MICROPHYSICAL MODES OF PRECIPITATION GROWTH 457

5-m

in r

ain

accu

mul

atio

n (m

m)

0

1

2

3

4 (a) 19-20 Sept 1999 (IOP2b)

03 05 2307 09 11 13 15 17 19 21 23 01 03 05 07 09 11 13 15 17 19 21

(b) 20-21 Oct 1999 (IOP8)

0

1

07 09 11 13 15 17 19 21 23 01 03 05 07 09 11 13 15 17 19 21

September 19 September 20

October 20 October 21UTC

UTC

Figure 2 Time series of 5-minute rain accumulations from the Deutschen Zentrum fur Luft and Raumfahrtdisdrometer collocated with the University of Washington Orographic Precipitation Radar during (a) IOP 2b and

(b) IOP 8 (Data courtesy of Martin Hagen)

Periods (IOPs) These data were taken on the lower windward slope of the Alps in aregion of copious autumn rain and should represent precipitation mechanisms critical toAlpine orographic rainfall

Previous studies have assigned a dominant precipitation growth process to particu-lar time periods of data from vertically pointing radar Wuest et al (2000) classi ed thedegree of riming over 30-minute periods using Formvar data of ice particles obtainedconcurrently with data from vertically pointing radar White et al (2001) classi ed theprecipitation growth mechanism in 30-minute blocks of data from vertically pointingradar using the mean vertical pro le of re ectivity and the presence or absence of aradar bright band We approach the problem from a different perspective by addressingthe relative contributions of riming and collection within the same column via verticalvelocity measurements at 1 s time-resolution

The vertical pro le of the vertical velocity of air (w is critical to understandingthe relationship between collection and riming We rst estimate characteristics of thevertical pro le of w using the observed Doppler velocity (Vr data and re ectivity-weighted fall speeds (hVti where subscript t is terminal velocity) derived from observedre ectivity (Z From a pro le of estimated w with height we then use Kesslerrsquos one-dimensional (1D) water-continuity model (Kessler 1969) to assess the relative rates ofaccretion of cloud water in regions above and below the 0 plusmnC level

In this study we focus on data obtained during 19ndash20 September 1999 (IOP 2b)and 20ndash21 October 1999 (IOP 8) The two cases represent contrasting stability and windenvironments at levels below 900 hPa (see Medina and Houze (2003) for a discussionof the synoptic mesoscale settings for these cases and Rotunno and Ferretti (2003)for mesoscale model simulations) IOP 8 was stable and relatively cool compared tothe mean MAP sounding and had weak winds from the surface to 900 hPa IOP 2bwas potentially unstable warmer than the mean sounding and had strong winds at lowlevels In both cases above 900 hPa there were strong south-easterly winds toward the


Alpine barrier The layer of ow toward and over the terrain in IOP 2b was deeper andmore unstable than in IOP 8 The time series of 5-minute rain ratescurren reported by theDeutschen Zentrum fur Luft and Raumfahrt (DLR) disdrometer at Locarno-Monti areshown in Fig 2 During IOP 2b the rainfall was heavier and more variable (mean D 29standard deviation D 55 maximum D 49 all mm hiexcl1 compared to the steadier rainfallin IOP 8 (14 15 and 86 mm hiexcl1 respectively)

2 DATA

The OPRA datadagger consist of vertical pro les of radar re ectivity Doppler radialvelocity and spectral width obtained every second at 150 m vertical resolution to aheight of raquo7 kmDagger Horizontal beam width varies linearly as a function of height from75 m at 1 km to 525 m at 7 km Consecutive 1 s pro les are not independent For typicaladvection speeds of 3 to 10 m siexcl1 the resulting horizontal advection of the precipitationstructures is 3 to 10 m for a 1 s pro le For the analysis in this paper a threshold valueof autocorrelation at rst lag (Bringi and Chandrasekar 2001 Eq 5195) was applied toremove bad Doppler velocity data A more rigorous quality control procedure that willaddress side-lobe echo from the mountains across the Lago Maggiore valley is underdevelopment When present the side-lobe contamination in the OPRA data usuallyoccurs at raquo15 km altitude

Figure 3 shows 45 minutes of OPRA data obtained during IOP 2b on 20 September1999 From 0705 to 0725 UTC a region of heavy precipitation is indicated by the strongre ectivity values in rain and snow The 0 plusmnC level is at raquo35 km altitude Fallstreaksare evident both above the 0 plusmnC level within snow and below within rain A 300ndash500 mdeep layer of enhanced re ectivities is associated with melting particles in the heavyprecipitation After 0725 UTC the convection weakens and lighter precipitation fallsuntil the end time of the plot at 0750 UTC (Figs 3(a) and (c)) During the weakerprecipitation portion of the 45-minute example the layer of enhanced re ectivitiesassociated with the melting of snow is narrower and slightly weaker than during theheavier precipitation periods The high-resolution OPRA data reveal nearly ubiquitoussmall-scale fallstreaks in a wide range of intensities of precipitation Fallstreaks in rainappear to originate in locally intense re ectivity regions within the melting layer andmay connect to a fallstreak in snow descending from above

The high-resolution data obtained by OPRA can be put into the context of thelarger-scale precipitation system by examining data collected by two scanning radarsutilized during MAP the Swiss Meteorology Agency C-band radar at Mt Lema 16 kmsouth-east of OPRA and the National Center for Atmospheric Research (NCAR)S-Pol radar 52 km south of OPRA (Fig 4(a)) Both scanning radars were blocked bytopography from scanning near the surface at OPRArsquos position Figure 4(a) shows themesoscale re ectivity eld at 0718 UTC 20 Sept 1999during the period of heavy rainfallshown in Fig 3 The intense precipitation over OPRA was one of many localized regionsof heavy precipitation associated with the interaction of the large-scale south-easterly

curren Rainfall rates were recorded every minute but are shown as accumulations every 5 minutes to reduce measure-ment uncertainty associated with the small sample volume of the instrument To convert to equivalent mm hiexcl1

multiply the 5-minute accumulation by 12dagger Urs Germann of SMA compared the OPRA re ectivity data to the continuously calibrated SMA Mt LemaC-band radar data He found spatially and temporally coincident samples to be within a few dB of one anotherThis agreement is as close as can be expected considering the differences in sample volume sizesDagger All heights are above ground level unless otherwise indicated


0745 UTC0735072507150705

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

Vr (m s-1)-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

2

1

0

5-m

in r

ain

accu

mul

atio

n (m

m)

0735072507150705 0745 UTC

Time

6

5

4

3

2

1

6

5

4

3

2

1

Hei

ght (

km)

Figure 3 Timendashheight pro les for 45 minutes of 1 s data from the University of Washington OrographicPrecipitation Radar (2700 pro les) from 0705ndash0750 UTC 20 Sept 1999 during IOP 2b (a) radar re ectivity (Z(b) Doppler velocity (Vr (c) 5-minute rain accumulations from the Deutschen Zentrum fur Luft and Raumfahrtdisdrometer The re ectivity data shown are the raw data as observed Heights are amsl The mean surface

rain-rate is 64 mm hiexcl1 and the maximum is 133 mm hiexcl1

ow and the Alps (Frei and Schar 1998 Houze et al 2001) The location of theprecipitation relative to the topography is best shown by the northndashsouth cross-sectionin Fig 4(b) Re ectivity and precipitation maxima are associated with upslope regionsof the topography The operational scan strategy for Mt Lema is optimized to obtainhigh-resolution time data of the near-surface re ectivity and repeats every 5 minutesThe S-Pol radar used a research scan strategy to yield high-resolution spatial data andscanned slower and to higher elevations than the Mt Lema radar A detailed analysisof the NCAR S-Pol radar data for IOPs 2b and 8 including dual-polarization data ispresented in Medina and Houze (2003)


64

56

48

40

32

24

16

8

0

dBZ

46 30deg

46deg

8degE 9degE

10

8

6

4

2

0

Hei

ght (

km M

SL)

625854504642383430262218141062-2

(a) 0718 UTC 20 Sept 1999

(b)

(c)

88deg460deg 88deg461deg 88deg462deg 88deg463deg 88deg464deg

10

8

6

4

2

0

dBZ

LatitudeLongitude

OPRA

Mt Lema

S-Pol

Figure 4 (a) Overlapped horizontal cross-sections of radar re ectivity at 2 km amsl from the Swiss Meteoro-logical Agency Mt Lema C-band radar and the NCAR S-Pol radar for 0718 UTC 20 Sept 1999 The red lineindicates the international border between Switzerland and Italy (b) Vertical cross-section through topography(solid green) and S-Pol radar re ectivity data along a roughly southndashnorth line from S-Pol to the University ofWashington Orographic Precipitation Radar (OPRA) the re ectivity enhancements near the top of the rst andsecond peaks from the left are side-lobe contamination (c) Vertical cross-section through topography (solid green)and Mt Lema radar re ectivity data along line (not shown) from Mt Lema to OPRA In (b) and (c) the location

of OPRA is shown by the red arrow

3 STRUCTURES AND SCALES OF PRECIPITATION VARIATION

It is well known that precipitation varies at small space- and time-scales Waldvogel(1974) examined the minute-to-minute variation of raindrop size distribution (RDSDdrops gt03 mm diameter) characteristics derived from disdrometer data in the contextof vertically pointing C-band radar Joss and Gori (1978) showed that the characteristicsof the RDSD varied with scale and tended to converge toward an exponential characterfor longer time periods of several hundred minutes They hypothesized that precipitation


at the scale of a typical scanning radar volume (raquo1 km3 consisted of a mixtureof rain rates of different intensities Jameson and Kostinski (2000) examined dropsize distribution time series and discussed the clustering of raindrops which couldpotentially physically interact over time periods as short as 2ndash3 s They hypothesizedthat typical observed distributions (usually at least 1 minute in duration) representprobability mixtures of many short-duration spectra Building on this previous workOPRA provides an opportunity to examine the timendashheight variation of precipitation atup to 1 s time-resolution

Gossard et al (1990) describe the ambiguity in interpreting data from verticallypointing radar in terms of several generic structures time-varying horizontal sheetstime stationary vertical shafts and tilted shafts translated over the radar by the horizontalwind Combinations of these structures appear likely in the OPRA data examined withthe melting layer often most similar to a time-varying sheet and fallstreaks most similarto vertical or tilted shafts depending on the vertical wind shear

(a) Fallstreaks and variations in ne-scale structuresFrom the time series of surface precipitation in Fig 2 one can lter out by eye

the higher-frequency variations and observe lsquopulsesrsquo of heavier precipitation tens ofminutes in duration and at least a factor of two greater than the backgroundprecipitationrate These pulses are associated with the movement of locally intense regions withinmesoscale precipitation systems as shown in Fig 4(c)

The re ectivity and Doppler velocity structurescurren associated with some of theseprecipitation pulses can be observed in detail in Figs 3 and 5 for IOP 2b and in Figs 6and 7 for IOP 8 In Figs 3 and 6 the pulses in precipitation intensity are associated withan increase in the frequency and intensity of fallstreaks where individual fallstreaks arelt5 minutes in duration (eg 0705ndash0725 and 0945ndash1030 UTC) The light-rain situationdaggerin Fig 7 exhibits similar fallstreak structuresDagger but at reduced re ectivities compared tothe other examples

A precipitation fallstreak is a manifestation of an inhomogeneity in the microphys-ical structure of the storm To be observed the relative size and number of precipitationparticles within the fallstreak need to be suf cient such that their radar re ectivity standsout as a local maximum from the immediate background re ectivities The temporal andspatial resolution of the observing instrument determine whether a particular spatial-scale inhomogeneity in the microphysical structure can be observed For a discreteprecipitation inhomogeneity to be clearly resolved as a fallstreak the time-resolutionof the data should be less than the time it takes the set of precipitation particles to fallthrough an individual range gatesect and the horizontal resolution of an individual rangegate has to be smaller than the size of the inhomogeneity

Fallstreaks can develop as a result of one of several dynamical processes or theircombination buoyant convective overturning of saturated air associated with discernible

curren Similar to data from other vertically pointing radars the tilt of features in the OPRA timendashheight re ectivityplots is a function of both the horizontal advection speed and the fall speed of the precipitation particles For agiven fall speed the lower the horizontal advection speed of the features over the radar the larger the slope of thefeatures in the graphdagger The apparent lack of relation between the near-surface re ectivities and the rain rates in the light-rain casein Fig 7 is likely to be a result of the larger uncertainty in rain rate associated with a smaller total number ofraindrops per 5-minute sample (Smith et al 1993)Dagger These structures are more apparent when the re ectivity colour-scale is modi ed to better represent the lowerrange of re ectivities (not shown)sect In the OPRA data a raindrop falling at 8 m siexcl1 will take 1875 s to fall through a 150 m range gate


Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

2055 2105 2115 2125

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

5-m

in r

ain

acc

umu

latio

n (m

m)

UTC

2055 2105 2115 2125 UTC2045

2045

0

1

2

3

4

Time

Figure 5 Same as Fig 3 except for 2045ndash2130 UTC 20 September 1999 during IOP 2b The surface rain-ratemean is 223 mm hiexcl1 and the maximum is 492 mm hiexcl1

updraughts shear-driven turbulence and convective overturning within the meltinglayer In a recent combined aircraft and scanning-radar study Hogan et al (2002) relatedshear-driven turbulence in the form of KelvinndashHelmholtz instability near the meltinglayer to raquo1 km-scale microphysical variability associated with embedded convectionwithin a warm-frontal mixed-phase cloud During the unstable IOP 2b storm buoyantconvective overturning is likely to have been the dominant mechanism producingfallstreaks In IOP 8 strong shear was observed near the 0 plusmnC level (Steiner et al 2003)in valley ows Within the stable conditions of the IOP 8 storm fallstreaks probablydeveloped primarily as a result of shear-driven turbulence

In Fig 5 fallstreaks lt5 minutes in duration are discernible except during the heavy-rain period (gt36 mm hiexcl1 from 2100ndash2110 UTC The Doppler velocity measurementof 4 m siexcl1 at 45 km altitude at 2102 UTC represents a lower limit on the updraughtvelocity and is an indirect indicator of convective overturning associated with a partic-ularly vigorous updraught within the storm Vigorous overturning would act to diffusethe signature of individual fallstreaks and make them less distinct The frequency of


Hei

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km)

6

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0955 1005 1015 1025

5-m

in r

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accu

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m)

UTC

06

04

02

00

0945 0950 0955 1000 1005 1010 1015 1020 1025

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time

0945

Figure 6 Same as Fig 3 except for 0945ndash1030 UTC 21 October 1999 during IOP 8 The surface rain-rate meanis 38 mm hiexcl1 and the maximum is 53 mm hiexcl1

fallstreaks and their consistency in appearance over a wide range of rain rates indicatesthat they are an important small-scale precipitation structure in MAP precipitation

(b) Melting layerA distinct melting layer and associated strong gradient in Doppler velocity appears

in Figs 3(b) and 6(b) in terms of rain rates Both these gures also include examplesof fallstreaks in snow associated both with localized enhancements in re ectivity inthe melting layer and with connected fallstreaks in rain Although not readily apparentfrom the colour-scale used the relative decrease in re ectivity from the melting bandto peak re ectivities within fallstreaks 1 km below the melting band is similar (raquo8ndash10 dB) in both gures For example in Fig 3 the local maxima of 42 and 44 dBZwithin the melting layers at 0712 and 0720 UTC are associated with fallstreaks with peakre ectivities 1 km below the melting layers of 34 and 38 dBZ respectively Similarlyin Fig 6 local maxima in the melting layer of 38 and 40 dBZ at 0958 and 1025 UTC areassociated with peak re ectivities 1 km below the melting layer of 30 dBZ

At the higher rain rates in Fig 5 and the lower rain rates in Fig 7 there is someevidence of a melting region (eg at 2120ndash2127 and 0547ndash0554 UTC respectively)


He

igh

t (km

)

6

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2

1

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1

0525 0535 0545 0555

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02

00

0525 0535 0545 05550515

0515

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time


but a distinct melting layer is absent In the light-rain case in Fig 7 this can be easilyexplained by the minimal-to-absent radar echo at altitudes above the 0 plusmnC level andhence a lack of ice particles to melt For the heavy-rain case in Fig 5 the explanation isnot as simple Figure 5 clearly indicates precipitation particles above the freezing levelIce nucleation arguments imply that it is unlikely that all the hydrometeors above the0 plusmnC level are liquid so melting of a portion of the hydrometeors must occur Again apossible explanation is that vigorous convective overturning would inhibit formation ofa narrow well-de ned melting layer As the frozen portion of hydrometeors fell past the0 plusmnC level they would melt over a deeper layer than in Fig 3 and the radar lsquobright bandrsquoenhancements associated with melting particles would be diffused over a greater depth(Yuter and Houze 1995)

4 ESTIMATION OF CHARACTERISTICS OF THE VERTICAL VELOCITY PROFILE INSITUATIONS OF DOMINANT ACCRETIONAL GROWTH

In discriminating situations where growth by accretion is occurring a subjectiverain-rate threshold of 20 mm hiexcl1 is often used based on the physical argument that


vapour deposition processes by themselves cannot produce such high rain rates (Austinand Houze 1972 Churchill and Houze 1984) In the current study we do not need such arigid condition For the purpose of discriminating where dominant growth by accretionis likely to be (as opposed to de nitely) occurring we use as a guideline a rain rate ofraquo10 mm hiexcl1 based on the nding of Steiner et al (1995 their Fig 9) of raquo10 mm hiexcl1

as the highest-frequency rain rate within convective precipitation observed at DarwinAustraliacurren Following this general guideline we focus our analysis in the next sectionson portions of the IOP 2b storm with surface rain rates gtraquo10 mm hiexcl1

(a) Derivation of vertical air velocity in rainThe observed mean Doppler velocity represents the sum of the average air velocity

and the mean re ectivity-weighted fall speed of the raindrops in the resolution volume(Vr D w C hVti) If one knew the size distribution of the raindrops within the radar-resolution volume one could apply an empirical diameterfall-speed relation (eg Gunnand Kinzer 1949 Berry and Pranger 1974) using a suitable temperature and pressure toderive the distribution of fall speeds for the RDSD From that information one couldcompute the mean re ectivity-weighted fall speed for the RDSD within the radar-resolution volume

A basic practical problem with deriving w from Vr data is that the RDSD in theradar-resolution volume is not directly measured Methods are available to estimatesome characteristics of the RDSD from a recording of the full Doppler spectra (egGossard et al 1990 Gossard 1998) However OPRA was able to measure only the meanDoppler velocity values as larger integration times are required to record a reliable fullDoppler spectrum for each range gate

The RDSD can be represented as a gamma distribution following Ulbrich (1983)and Chandrasekar and Bringi (1987) by

dN DN0

m3mDm expiexcl3D dD (1)

where D is drop diameter 3 is the slope of the distribution 3 D 612W=Z1=3 W

is liquid-water content in units of mm3miexcl3 and Z is radar re ectivity with unitsof mm6miexcl3 (Waldvogel 1974) For desired values of rain rate N0 and m (1) canbe iterated to determine the associated value of 3 Speci c forms of the distributionrange from nearly monodisperse (m D 16) to exponential (m D 0) The sensitivity ofestimates of hVti to assumptions regarding the values of N0 and m in (1) is shown inFig 8 assuming a temperature of 10 plusmnC and pressure of 925 hPa (calculation providedby Jurg Joss personal communication) The worst-case uncertaintydagger of raquo15 m siexcl1

associated with the RDSD assumptions is comparable to the uncertainty of aircraft insitu measurements of w

Sets of Z and hVti values were calculated for different sets of assumptions regardingrain rate m and N0 and variations in temperature and pressure These data were then tted to an equation of the form

hVti D b C kZ (2)

curren The rain rates in the Steiner et al (1995) study were derived from 2 km pound 2 km horizontal-resolution radarre ectivity data The differences in spatial resolution and precipitation climatology between the Steiner et alstudy and the current study mean that the rain-rate values are unlikely to be directly comparable and hence areused as a general guidelinedagger In applying the technique errors associated with radar measurements of Vr and the calibration of Z willcontribute additional uncertainty Calibration errors would yield a systematic bias


Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000

9No=8000 m=0No=16000 m=0No=8000 m=1No=8000 m=2No=8000 m=4No=8000 m=8No=8000 m=16

8

7

6

5

4

3

Figure 8 Estimated fall speed Vt as a function of rain rate and varying raindrop size distribution parametersN0 and m (see text) The calculation was provided by J Joss (personal communication)

where Z is in units of dBZ in order to analytically determine the coef cients b and k asa function of m N0 temperature and pressure Turbulence is assumed to be symmetricsuch that over the radar-resolution volume its mean is zero

This method of estimating hVti (Jurg Joss personal communication) was appliedto several samples of OPRA data The lapse rate was assumed to be 6 K kmiexcl1 and thepressure decreased by a factor of exp(z=10) where z is height in km The calculationswere made assuming the RDSD was exponential (ie m D 0) which is consistent withRDSD observations at larger sample sizes approaching the scale of a radar volume (egJoss and Gori 1978) and assigning N0 D 8000 (Marshall and Palmer 1948) For theseparameters the coef cients b and k are de ned as follows where temperature (T is inKelvin and pressure (P in hPa

a D T =P 045 C 03401 (3)k D 04099a C 000558=a (4)b D iexcl015 C 1548a (5)

Figure 9 shows the method applied to OPRA data obtained from 0716 to 0721 UTC20 Sept 1999 The observed Z eld (Fig 9(a)) was used to derive hVti (Fig 9(c)) thatin turn was combined with the observed Vr (Fig 9(b)) to obtain w (Fig 9(d)) Verticalvelocity was estimated at each range gate in each radar data pro le independently (ieno mass continuity constraint was applied)

A statistical representation of the derived w results is shown in Fig 10(a) in termsof a contoured frequency by altitude diagram (CFAD Yuter and Houze 1995) a jointfrequency distribution of w with height An abrupt shift in the modal values of woccurs at 275 km altitude near the bottom of the melting layer indicated by the dashedlines in Figs 10(a) and (b) The method of estimating hVti is valid for the rain regionbelow the melting layer The CFAD shows that the strongest mode of the frequencydistribution of w is near 0 m siexcl1 at all heights within rain (lt27 km altitude) Thisresult is consistent with the frequency distribution of w based on studies of dual-Dopplerdata (eg Yuter and Houze 1995 Braun et al 1997) and indicates that the bias in themethod is small Updraughts lt3 m siexcl1 predominate at low levels The outliers of thedistribution varied between approximately C5 m siexcl1 for updraughts and iexcl6 m siexcl1 fordowndraughts Timendashheight plots of the estimated vertical velocity (Fig 9(d)) indicate


7

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00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)

(b) Doppler velocity

3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720

(c) Fallspeed (d) Vertical air velocity

0716

Figure 9 Example application of methodology to estimate vertical air velocity on 5 minutes of the Universityof Washington Orographic Precipitation Radar data from 0716ndash0721 UTC 20 September 1999 (a) Observed radarre ectivity (Z to 7 km amsl (b) observed Doppler velocity (Vr to 7 km amsl (c) derived fall speed (Vtwithin the rain region and (d) derived vertical air velocity (w within the rain region In (c) and (d) the meltinglayer between 3 and 35 km altitude is included to clarify its position The methods to derive Vt and w are valid forthe rain region below the raquo275 km amsl lower boundary of the mixed-phase region (indicated by the dashed

lines in (c) and (d))

coherent updraught and downdraught structures The results of these simple tests arepromising in that this method of deriving hVti produced physically realistic resultsAn alternate version of the fall speed and derived w elds were also obtained fromthe OPRA data using the Atlas et al (1973) mapping of re ectivity to fall speed ofVt D 26Z0107 These w values yielded a distribution with a physically inconsistentnegative bias (Fig 10(b))

(b) Derivation of vertical air velocity in snowIce crystals of different habits have different mass-to-size relationships and hence

different fall speed relations for the same diameter temperature and pressure Locatelliand Hobbs (1974) measured the fall velocities of a variety of snow particles of differentcrystal habits Hanesch (1999) obtained relations between snow particles and fall speedfor several degrees of riming using 2D-video disdrometer data obtained during the SwissAlpine Melting Layer Measurements campaign in winter 1996ndash97 Both analyses foundthat most naturally occurring snow particles had fall speeds in still air from near 0 to2 m siexcl1 and small graupel (5 mm diameter) had fall speeds of raquo3 m siexcl1

In order to estimate the fall speed of ice from re ectivity a crystal habit andassociated fall speed relation with size would need to be assumed As a rst step a


-5 0 5

05

10

15

20

25

30Hei

ght (

km)

Vertical velocity (m s-1)

-5 0 5

05

10

15

20

25

30 (a)

(b)

Figure 10 (a) Contoured frequency by altitude diagram (CFAD Yuter and Houze 1995) of derived vertical airvelocity w for data obtained from 0704ndash0750 UTC 20 September 1999 The joint frequency distribution is plottedusing a w bin size of 02 m siexcl1 and height bin size of 150 m (b) w derived using the Atlas et al (1973) Z iexcl Vtformula (see text) A discontinuity (dashed line) is present in the plots at raquo275 km amsl where the transition

from mixed phase to rain occurs The derived w values are valid for the rain region below the dashed line

simple method that does not require information about the particle size distributionis used to estimate a lower bound for the vertical air motions in snow The observedDoppler velocity data in snow are split into two groups For Vr gt 0 m siexcl1 the observedDoppler velocity represents a robust underestimate of positive vertical air velocity ForVr 6 0 m siexcl1 the physical interpretation is ambiguous One can examine the statisticsof the underestimated positive vertical air velocities and interpret these velocities ascharacteristics of the vertical pro le of w For example the maximum observed Vr of22 m siexcl1 at 346 km altitude in Fig 11 can be interpreted as a lower limit for maximumupdraught velocities at this altitude for this sample The use of measured Vr within snowand ice regions to estimate w can lead to an underestimate of w in these regions of upto the maximum fall speed of ice particles of raquo3 m siexcl1

Examination of estimated w below the 0 plusmnC level based on derived hVti in rainregions and estimated lower bounds of maximum w above the 0 plusmnC level based onmeasurements of Vr in snow yielded values of between 2 and 5 m siexcl1 for likely peakvertical velocities within typicalcurren updraughts associated with precipitation at Locarno-Monti during IOP 2b These velocities are assumed to occur as the local maximumwithin parabolic pro les of vertical velocity which are in turn used as input to a 1Dmicrophysical parametrization described below

curren The range 2ndash5 m siexcl1 is intended to encompass those updraughts associated with a major portion of theprecipitation accumulation in the IOP 2b storm


0

800 (b) Height = 361 km Max value = 14 m s-1

0

600

(c) Height = 346 km Max value = 22 m s-1

0

600(d) Height = 331 km Max value = 18 m s-1

0

800(e) Height = 316 km Max value = 14 m s-1

2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26

Figure 11 (a) Timendashheight pro les of the University of Washington Orographic Precipitation Radar Dopplervelocity Vr data within the ice region and a portion of the melting layer for 2230ndash2350 UTC 19 September 1999(b) Histogram of Vr values for layers 150 m deep at 361 km (c) (d) and (e) as (b) but at 346 km 331 km and

316 km respectively All heights are amsl

5 RELATIVE ROLES OF DIFFERENT PROCESSES IN PRECIPITATION GROWTH

Precipitation growth by accretion occurs within updraughts By simulating small-scale updraughts typical of those embedded in the baroclinic rainstorms observedin MAP with a 1D parcel model we can determine the altitudes where condensateis available and the preferred layers for different particle growth processes Sincethe small-scale updraughts occur within a broad layer of generally stratiform cloudand precipitation growth occurs both on precipitation particles produced within theupdraught and on pre-existing precipitation particles entrained into the updraught Thesimple 1D parcel model below calculates only the former but its results also indicategrowth processes available to pre-existing particles

(a) Adaptation of the Kessler 1D modelAn estimation of the relative roles of several precipitation processes in the growth

of precipitation was made using a simple 1D column-model calculation (Fig 12) fora precipitating cold cloud following Kessler (1969) Ogura and Takahashi (1971)Ferrier (1988) and Houze (1993 section 36) The following equations describe watercontinuity in terms of the rate of change of the mixing ratios of water vapour (qv cloud


Water Vapo r Cloud Water

Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl

Figure 12 Block diagram of the Kessler 1D model See text for explanation of symbols

water (qc rain (qr and ice (qi in the 1D model

Dqv

DtD iexclCc (6)

Dqc

DtD Cc iexcl Ac iexcl Kc iexcl Kci (7)

Dqr

DtD Ac C Kc iexcl Fr iexcl Gl (8)

Dqi

DtD Gl C Kci iexcl Fi (9)

where Cc is condensation of cloud water Ac is autoconversion (the rate at which cloudwater content decreases due to growth of precipitation by collision and coalescence ofcloud drops) Kc is the collection of cloud water by raindrops Kci is the collection ofcloud water by graupel above the 0 plusmnC level (ie riming) Gl is the glaciation of rain intoice Fr is the fallout of raindrops from the air parcel and Fi is the fallout of ice particles

The parcel is assumed to be saturated with respect to liquid water at all temperatures(ie entrainment and evaporation are ignored) Integration starts at cloud base (z D1 km) where qc D qv D qi D 0 and qv D qvs the saturation mixing ratio The calculationwas performed using an altitude increment of 8 m for altitudes from 1000 to 7000 m Thelapse rate was set to 6 K kmiexcl1 and the temperature at 1000 hPa was set to 291 K basedon Milan soundings for 20 September 1999 The fall speed of rain was set to 6 m siexcl1

and the fall speed for ice was set to a value for graupel of 3 m siexcl1 Once the parcel isabove the freezing level glaciation is assumed to be rapid such that by raquo1 km above thefreezing level all the pre-existing rain has glaciated Rapid glaciation is consistent withdata obtained in several eld studies (eg Yuter and Houze 1995 Zeng et al 2001) Thecalculation is particularly sensitive to the assumptions regarding the glaciation rate andthe fall speed relation of ice particles See the appendix for further details on the modelcalculation

(b) Model resultsThe 1D parcel model permits evaluation of changes in water vapour cloud-water

rain and ice mixing ratios with height and their associated precipitation processes ata snapshot of time near the peak strength of an updraught whose characteristics arederived from MAP observations Several runs of the 1D calculations were made using xed parabolic pro les of vertical air velocity from 1 to 7 km altitude and from 1 to5 km altitude assuming a 0 plusmnC level at 3 km altitude Figures 13 and 14 show thecalculations for maximum w of 2 m siexcl1 for a velocity pro le extending to 7 km altitudeand for maximum w of 5 m siexcl1 within a velocity pro le extending to 5 km altitude


0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc

0 1 2Mixing ratio (gmgm) x 10-3

qi

qr

0

1000

2000

3000

4000

5000

6000

7000

0 42Vertical velocity (m s-1)

Hei

ght (

m)

(a) Vertical Velocity (b) Water Content (c) Processes

Figure 13 (a) Vertical velocity (w) pro le with maximum w D 2 m siexcl1 and updraught top of 7 km agl used asinput to Kessler 1D model (b) Vertical pro le of model output in terms of mixing ratios and (c) vertical pro le

of model output in terms of precipitation process rates See text for explanation

0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)


Figure 14 Same as Fig 13 except for model results using vertical velocity pro le with maximum w D 5 m siexcl1

and updraught top of 5 km

The resulting pro le of mixing ratio and process rate for the different updraughtstrengths are generally similar in shape with the pro le corresponding to the 5 m siexcl1

peak updraught having larger magnitude mixing ratios and rates as expected Othercalculations performed (not shown) using a maximum w of 2 m siexcl1 (5 m siexcl1) and amaximum altitude of 5 km (7 km) showed qualitatively similar results

The simplicity of the calculation limits our ability to make quantitative interpre-tations but some qualitative interpretations can be made At weak-to-moderate verticalvelocities observed in IOP 2b precipitation the layer 2 km thick above the freezing levelcontains local maxima in qi and Kci indicating that this region is a favourable growthenvironment for graupel Medina and Houze (2003) found graupel at these altitudes in


TABLE 2 ESTIMATE OF RELATIVE AMOUNT OF CLOUDWATER CONVERTED TO RAIN WATER IN COLUMN FROM1 TO 3 km A GL BASED ON VARIOUS INPUTS TO 1D

CLOUD MODEL

Maximum vertical Maximum heightvelocity w (m siexcl1 z (km)

Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036

qr and qc are the mixing ratios of rain and cloud waterrespectively

dual polarization radar data obtained by NCAR S-Pol radar in several MAP stormsincluding IOP 2b A comparison of the relative rates of Kc below the freezing level andKci above the freezing level indicates that collection of cloud water by rain and by iceare both important to the growth of precipitation and that neither can be ignored

Precipitation ef ciency is often de ned as the ratio of observed rainfall at the sur-face to computed condensedwater where the latter is deducedusing upper-air soundingsin in ow air and an estimate of lifting (Smith 1979) An estimate of a quantity relatedto precipitation ef ciency can be made by comparing the column-integrated values ofqr and qc eg the area under the curves of qr versus qc in Figs 13(b) and 14(b) Forsimplicity we examine only the region below the freezing level within cloud (1ndash3 kmaltitude) to obtain an estimate of column-integrated rainfall obtained from condensedcloud water The ratio of areas under the qr versus qc curves are shown in Table 2The source terms (autoconversion and collection) in (8) can be described genericallyas liquid drop coalescence Liquid drop coalescence describes processes occurring bothwithin lsquowarm cloudsrsquo ie clouds that are warmer than 0 plusmnC throughout and incapableof supporting ice-crystal precipitation mechanisms and within lsquocold cloudsrsquo extendingabove the 0 plusmnC levelcurren If the assumptions in the 1D model are valid this calculationimplies that liquid drop coalescence in updraughts peaking at 5 m siexcl1 can extract up toraquo40 of the condensed cloud water as rain As previously hypothesized by Browninget al (1975) in order to obtain higher precipitation ef ciencies a combination of bothliquid drop coalescence and ice-phase processes is needed

The pro les in Figs 13 and 14 show the growth of particles formed and grownentirely within the postulated updraughtAn important question is what is the horizontaldistance traversed by hydrometeors growing in and falling out of the updraught cellFor illustration purposes the following calculations assume a horizontal wind speed of10 m siexcl1

An updraught parcel with a w pro le corresponding to Fig 13(a) rising from cellbase to cell top would take 408 minutes to ascend which corresponds to a horizontaldownwind distance of 245 km For a w pro le corresponding to Fig 14(a) the timeto ascend is 129 minutes and the horizontal advection is 77 km Thus the particle-growth processes occurring in the cell all take place in a distance less than the raquo50ndash80 km horizontal-scale of the windward side of the Alps near Locarno A particle (eitherpre-existing or newly formed in the cell) having grown to precipitation size in the cellwould fall from a height of raquo37 km (the height of maximum riming growth) to thesurface in about 10 minutes (assuming a fall speed of 6 m siexcl1 which corresponds to

curren Cold clouds predominated during IOP 2b Our 1D model re ects this observation by including an ice layer Useof the term lsquowarm rainrsquo to describe liquid drop coalescence within cold clouds is a misnomer


raquo6 km downwind distance This distance is also well within the horizontal-scale of thewindward slopes of the southern Alps

6 CONCLUSIONS

The University of Washington OPRA obtained vertically pointing S-band Doppler-radar data at high temporal resolution (1 s) and high spatial resolutioncurren (raquo3 pound 10iexcl3 km3

sample volume near the altitude of the melting layer) at Locarno-Monti during MAPAnalysis of OPRA data obtained during MAP IOPs 2b and 8 indicates that fallstreaksare nearly ubiquitous in a wide range of precipitation intensities Several dynamicalmechanisms can yield small-scale inhomogeneities in the microphysical structure of astorm associated with fallstreaks In unstable environments such as IOP 2b convectiveoverturning was probably the dominant mechanism In more stable environments suchas IOP 8 shear-driven turbulence as observed near the 0 plusmnC level (Steiner et al 2003)probably played a role in fallstreak formation Higher-rain-rate pulses gt10-minutesduration associated with convective cells evident in coarser-resolution scanning radardata manifested as an increased frequency and intensity of fallstreaks each lt5-minutesduration in the OPRA data A subset of the fallstreaks had suf cient magnitude inre ectivity to indicate a clear connection across the melting layer from the snow tothe rain region Terminal velocities of up to raquo8 m siexcl1 were estimated within fallstreaksin the rain region (Fig 9(c))

A distinct melting layer and hence unambiguous evidence of precipitation-sizedice was present in most of the samples of OPRA data obtained during IOPs 2b and 8with surface rainfall amp1 and 36 mm hiexcl1 The width and intensity of the re ectivitieswithin the melting layers varied with surface rain rate However the relative decrease inZ between the local melting-layer maxima and the peak Z in rain 1 km below remainedremarkably consistent at raquo8ndash10 dB for a wide range of surface precipitation rates (egFigs 3 and 6) For high rain rates amp36 mm hiexcl1 neither discernible fallstreaks nor adistinct narrow melting layer were evident (eg Fig 5) Both structures may have beendiffused in the presence of strong convective overturning within the heavy rain

An estimation of characteristics of the vertical air velocity pro le within precip-itating cloud was made both in rain and in snow regions using the observed radarparameters In rain regions re ectivity-weighted fall speed derived from the observedre ectivity with assumptions about the RDSD and an empirical fall speed to diameterrelation was subtracted from the observed Doppler velocity to yield an estimated w Insnow regions a lower bound on maximum updraughtw was estimated from the observedmaximum Doppler velocity Using these methods on data from IOP 2b typical peakvertical velocities within an updraught were estimated to be 2 to 5 m siexcl1

Plausible parabolic vertical velocity pro les with maximum velocities between 2and 5 m siexcl1 were input into a simple calculation based on Kesslerrsquos 1D water-continuitymodel (section 5(b) Figs 13 and 14) These calculations yielded local maxima in qiand Kci within 2 km of the freezing level These conditions constitute a favourableenvironment for graupel formation and their altitude corresponds to the layer wheregraupel was observed in NCAR S-Pol dual polarization radar data during IOP 2b(Medina and Houze 2003)

Studies in the 1950s 60s and 70s indicated that in conditions of deep moist owover a mountain range the total column (ice C liquid drop coalescence) precipitation

curren The OPRA-resolution volume in units of km3 corresponding to a particular range gate can be estimated as thevolume of a cylinder where h is the height agl in km with Volume D 0150 frac14

4 h sin43plusmn2


ef ciencies within deep orographic rain are raquo70 or more (see review by Smith 1979)Browning et al (1975) suggested that a combination of both liquid-water coalescenceand ice-phase processes are needed to obtain high precipitation ef ciencies in oro-graphic precipitation Our 1D model results further indicate the importance of processesboth below and above the freezing level in the ef cient production of precipitation overwindward slopes We nd that the rates of collection and riming are comparable andmake signi cant contributions to the growth of precipitation by accretion within thesmall-scale embedded updraughts (Figs 13 and 14) An estimate of a quantity relatedto precipitation ef ciency based on the 1D model calculation indicates that liquid-watercoalescence (autoconversion and collection) processes associated with updraughts witha peak w of 5 m siexcl1 can yield column-integrated rain water constituting 640 ofcolumn-integrated cloud watercurren These results suggest that within typical small-scaleembedded updraughts associated with MAP storms liquid-water coalescence alone willbe insuf cient to yield the high precipitation ef ciencies often observed in orographicprecipitation

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the work of several people in the successfuldeployment of University of Washingtonrsquos OPRA radar during MAP Grant Graydesigned and built OPRA and oversaw its installation in Locarno Steve Domonkosbuilt OPRArsquos antenna platform Katherine Pearl and Don Kaydk worked on instrumenttesting preparing for eld deployment and instrument installation at Locarno Jurg Jossand Urs Germann of the Swiss Meteorological Agency mentored the OPRA equipmentduring its stay in Locarno and worked closely with the authors on analysis of the dataMel Nordquist and Nancy White of the Eureka CA National Weather Service ForecastOf ce and Clifford Spooner of North Bend WA graciously allowed testing at theirfacilities and watched over the instrumentation David Spencer toiled on a wide varietyof tasks associated with the test deployments in California and Washington CandaceGudmundson edited the manuscript and Kay Dewar worked on the gures Additionallythe authors would like to thank Chih-Chieh (Jack) Chen for his software for the 1Dmodel and Martin Hagen for his disdrometer data This work was supported by NSFgrants ATM-9409988 ATM-9817700 and ATM-0121963

APPENDIX

One-dimensional cloud-model descriptionThe following equations were used in the 1D water-continuity model after Kessler

(1969) Ogura and Takahashi (1971) Ferrier (1988) and Houze (1993 his section 36)With the exception of (A4) Ogura and Takahashi (1971) equations and coef cientswere used Equation (A4) was derived following Ferrier (1988) using a collectionef ciency of unity and using Locatelli and Hobbsrsquos (1974 their Table 1) fall speed forconical graupel of Vti D 12D065

m in m siexcl1 where Dm is the maximum diameter of theparticle in mm

Ac D Qregqc iexcl at (A1)

Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)

curren Calculation of the equivalent quantity related to ice processes is beyond the scope of the current study


TABLE A1 VALUES OF COEF-FICIENTS USED IN 1D WATER-

CONTINUITY CALCULATION

Coef cient Value

Qreg 0001 if qc gt at0 otherwise

at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC

Kci D macr 0qcq09125i (A4)

Fi D qiVti=b (A5)Gl D macrqr (A6)

The value of b for a speci c level i is calculated iteratively from the temperatureand pressure and is used to account for the varying density of air with height Othercoef cient values are given in Table A1

bi D bi iexcl 1[T i curren P i iexcl 1=fT i iexcl 1 curren P ig]1=3 (A7)

REFERENCES

Atlas D Srivastava R C andSekhon R S

1973 Doppler-radar characteristics of precipitation at vertical inci-dence Rev Geophys Space Phys 11 1ndash35

Austin P M and Houze Jr R A 1972 Analysis of the structure of precipitation patterns in New EnglandJ Appl Meteorol 11 926ndash935

Berry E X and Pranger M R 1974 Equations for calculating the terminal velocities of water dropsJ Appl Meteorol 13 108ndash113

Bougeault P Binder P Buzzi ADirks R Kuettner JHouze R Smith R BSteinacker R and Volkert H

2001 The MAP Special Observing Period Bull Am Meteorol Soc 82433ndash462

Braun S A Houze Jr R A andSmull B F

1997 Airborne dual-Doppler observations of an intense frontal systemapproaching the Paci c northwest coast Mon Weather Rev125 3131ndash3156

Bringi V N and Chandrasekar V 2001 Polarimetric Doppler weather radar Principles and applica-tions Cambridge University Press Cambridge UK

Browning K A Pardoe C andHill F F

1975 The nature of orographic rain at wintertime cold fronts Q J RMeteorol Soc 101 333ndash352

Chandrasekar V and Bringi V N 1987 Simulation of radar re ectivity and surface measurements ofrainfall J Atmos Oceanic Technol 4 464ndash478

Churchill D D and Houze Jr R A 1984 Development and structure of winter monsoon cloud clusters on10 December 1978 J Atmos Sci 41 933ndash960

Ferrier B S 1988 lsquoOne-dimensional time-dependent modeling of squall-lineconvection rsquo PhD thesis University of Washington

Frei C and Schar C 1998 A precipitation climatology of the Alps from high-resolutionrain-gauge observations Int J Climatol 18 873ndash900

Gossard E E 1988 Measuring drop-size distributions in clouds with a clear-air-sensing Doppler radar J Atmos Ocean Technol 5 640ndash649

Gossard E E Strauch R G andRogers R R

1990 Evolution of dropsize distributions in liquid precipitation ob-served by ground-based Doppler radar J Atmos OceanTechnol 7 815ndash828


Gunn R and Kinzer G D 1949 The terminal velocity of fall for water droplets in stagnant airJ Meteorol 6 243ndash248

Hanesch M 1999 lsquoFall velocity and shape of snow akesrsquo PhD dissertation ETHZurich

Hogan R J Field P RIllingsworth A JCotton R J andChoularton T W

2002 Properties of embedded convection in warm-frontal mixed-phasecloud from aircraft and polarimetric radar Q J R MeteorolSoc 128 451ndash476

Houze Jr R A 1993 Cloud dynamics Academic Press San Diego USAHouze Jr R A Kuettner J and

Smith R B1998 lsquoMesoscale Alpine Programme US overview document and ex-

perimental designrsquo Available from MAP US Project Of ceUCAR (httpwwwjossucaredujoss psgprojectsmap )

Houze Jr R A James C N andMedina S

2001 Radar observations of precipitation and air ow on the Mediter-ranean side of the Alps Autumn 1998 and 1999 Q J RMeteorol Soc 127 2537ndash2558

Jameson A R and Kostinski A B 2000 Observations of hyper ne clustering and drop size distributionstructures in three-dimensional rain J Atmos Sci 57 373ndash388

Joss J and Gori E G 1978 Shapes of raindrop size distributions J Appl Meteorol 171054ndash1061

Kessler E 1969 On the distribution and continuity of water substance in atmos-pheric circulation Meteorological Monographs Vol 10 No32 American Meteorological Society Boston USA

Locatelli J D and Hobbs P V 1974 Fall speeds and masses of solid precipitation particles J GeophysRes 79 2185ndash2197

Marshall J S and Palmer W M 1948 The distribution of raindrops with size J Meteorol 5 165ndash166Medina S and Houze Jr R A 2003 Air motions and precipitation growth in Alpine storms Q J R

Meteorol Soc 129 345ndash371Ogura Y and Takahashi T 1971 Numerical simulation of the life cycle of a thunderstorm cell

Mon Weather Rev 99 895ndash911Rotunno R and Ferretti R 2003 Orographic effects on rainfall in MAP cases IOP 2b and IOP 8

Q J R Meteorol Soc 129 373ndash390Smith R B 1979 The in uence of mountains on the atmosphere Adv Geophys 21

87ndash230Smith P L Liu Z and Joss J 1993 A study of sampling variability effects in raindrop size observa-

tions J Appl Meteorol 32 1259ndash1269Steiner M Houze Jr R A and

Yuter S E1995 Climatological characterization of three-dimensional storm struc-

ture from operational radar and rain gauge data J ApplMeteorol 34 1978ndash2007

Steiner M Bousquet OHouze Jr R A Smull B Fand Mancini M

2003 Air ow within major Alpine river valleys under heavy rainfallQ J R Meteorol Soc 129 411ndash431

Ulbrich C W 1983 Natural variations in the analytical form of the raindrop sizedistribution J Clim Appl Meteorol 22 1764ndash1775

Waldvogel A 1974 The N0 jump in raindrop spectra J Atmos Sci 31 1067ndash1078White A B Neiman P J

Ralph F M Kingsmill D Aand Persson P O G

2003 Coastal orographic rainfall processes observed by radar during theCalifornian Landfalling Jets Experiment J Hydrometeorol in press

Wuest M Schmid W and Joss J 2000 lsquoCoupling between riming and the dynamics of precipitatingcloudsrsquo Pp 421ndash424 in Proceedings of the 13th internationalconference on clouds and precipitation Reno NV AmericanMeteorological Society Boston USA

Yuter S E and Houze Jr R A 1995 Three-dimensional kinematic and microphysical evolution ofFlorida cumulonimbus Part II Frequency distributions ofvertical velocity re ectivity and differential re ectivityMon Weather Rev 123 1941ndash1963

Zeng Z Yuter S EHouze Jr R A andKingsmill D E

2001 Microphysics of the rapid development of heavy convective pre-cipitation Mon Weather Rev 129 1882ndash1904


TABLE 1 CHARACTERISTICS OF THE UNIVERSITY OF WASHINGTON OROGRAPHICPRECIPITATION RADAR (OPRA) DURING MAP

Model Modi ed Raytheon Path nder S-band

Receiver NCARATI PIRAQSignal Processor 50 MHz TI TMS320C50 on PIRAQ boardHost Computer 233 MHz Pentium II MMX 32 MB RAM 4 GB disk DAT CDROMFrequency 3050 MHzAntenna 18 m offset-feed parabolaAntenna Gain 31 dB (estimated)Antenna Height 382 m amslTransmitter Magnetron 2J75B with solid state modulatorPeak Power 60 kW maximum 35 kW minimumBeam Width 43plusmn (estimated)PRF 1000 HzPulse Width 10 sup1s Gates 100Variables Z Vr and spectral width (SW)

Figure 1 The University of Washington Orographic Precipitation Radar OPRA on the roof of the SwissMeteorological Institute Osservatorio Ticinese in Locarno Switzerland The antenna has an offset feed and isset so the radar beam is pointing vertically The radarrsquos electronics display and processing systems are contained

within the small shelter to the left of the antenna

to be able to improve modelling and prediction of heavy orographic rain events and toquantify their precipitation ef ciency

This paper assesses the relative roles of riming and collection in the same columnof precipitating cloud using data from vertically pointing radar obtained during theMesoscale Alpine Programme (MAP Houze et al 1998 Bougeault et al 2001)The University of Washington Orographic Precipitation Radar (OPRA) is a verticallypointing 10 cm meteorological pulsed Doppler radar (Table 1) OPRA was deployed onthe roof of the Swiss Meteorological Institute Osservatorio Ticinese from September toOctober 1999 at Locarno-Monti in Locarno Switzerland in collaboration with Jurg Jossand Urs Germann of the Swiss Meteorological Agency (SMA Fig 1) Approximately365 hours of radar data were obtained during 11 of the MAP Intensive Observation


5-m

in r

ain

accu

mul

atio

n (m

m)

0

1

2

3

4 (a) 19-20 Sept 1999 (IOP2b)

03 05 2307 09 11 13 15 17 19 21 23 01 03 05 07 09 11 13 15 17 19 21

(b) 20-21 Oct 1999 (IOP8)

0

1

07 09 11 13 15 17 19 21 23 01 03 05 07 09 11 13 15 17 19 21



UTC









2 DATA







0745 UTC0735072507150705

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

Vr (m s-1)-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

2

1

0

5-m

in r

ain

accu

mul

atio

n (m

m)

0735072507150705 0745 UTC

Time

6

5

4

3

2

1

6

5

4

3

2

1

Hei

ght (

km)





64

56

48

40

32

24

16

8

0

dBZ

46 30deg

46deg

8degE 9degE

10

8

6

4

2

0

Hei

ght (

km M

SL)

625854504642383430262218141062-2

(a) 0718 UTC 20 Sept 1999

(b)

(c)


10

8

6

4

2

0

dBZ

LatitudeLongitude

OPRA

Mt Lema

S-Pol















Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

2055 2105 2115 2125

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

5-m

in r

ain

acc

umu

latio

n (m

m)

UTC

2055 2105 2115 2125 UTC2045

2045

0

1

2

3

4

Time





Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

0955 1005 1015 1025

5-m

in r

ain

accu

mul

atio

n (m

m)

UTC

06

04

02

00

0945 0950 0955 1000 1005 1010 1015 1020 1025

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time

0945







He

igh

t (km

)

6

5

4

3

2

1

6

5

4

3

2

1

0525 0535 0545 0555

5-m

in r

ain

accu

mul

atio

n (m

m)

02

00

0525 0535 0545 05550515

0515

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time












dN DN0






hVti D b C kZ (2)



Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000


8

7

6

5

4

3








7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES




















































5-m

in r

ain

accu

mul

atio

n (m

m)

0

1

2

3

4 (a) 19-20 Sept 1999 (IOP2b)

03 05 2307 09 11 13 15 17 19 21 23 01 03 05 07 09 11 13 15 17 19 21

(b) 20-21 Oct 1999 (IOP8)

0

1

07 09 11 13 15 17 19 21 23 01 03 05 07 09 11 13 15 17 19 21



UTC









2 DATA







0745 UTC0735072507150705

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

Vr (m s-1)-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

2

1

0

5-m

in r

ain

accu

mul

atio

n (m

m)

0735072507150705 0745 UTC

Time

6

5

4

3

2

1

6

5

4

3

2

1

Hei

ght (

km)





64

56

48

40

32

24

16

8

0

dBZ

46 30deg

46deg

8degE 9degE

10

8

6

4

2

0

Hei

ght (

km M

SL)

625854504642383430262218141062-2

(a) 0718 UTC 20 Sept 1999

(b)

(c)


10

8

6

4

2

0

dBZ

LatitudeLongitude

OPRA

Mt Lema

S-Pol















Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

2055 2105 2115 2125

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

5-m

in r

ain

acc

umu

latio

n (m

m)

UTC

2055 2105 2115 2125 UTC2045

2045

0

1

2

3

4

Time





Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

0955 1005 1015 1025

5-m

in r

ain

accu

mul

atio

n (m

m)

UTC

06

04

02

00

0945 0950 0955 1000 1005 1010 1015 1020 1025

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time

0945







He

igh

t (km

)

6

5

4

3

2

1

6

5

4

3

2

1

0525 0535 0545 0555

5-m

in r

ain

accu

mul

atio

n (m

m)

02

00

0525 0535 0545 05550515

0515

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time












dN DN0






hVti D b C kZ (2)



Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000


8

7

6

5

4

3








7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES





















































2 DATA







0745 UTC0735072507150705

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

Vr (m s-1)-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

2

1

0

5-m

in r

ain

accu

mul

atio

n (m

m)

0735072507150705 0745 UTC

Time

6

5

4

3

2

1

6

5

4

3

2

1

Hei

ght (

km)





64

56

48

40

32

24

16

8

0

dBZ

46 30deg

46deg

8degE 9degE

10

8

6

4

2

0

Hei

ght (

km M

SL)

625854504642383430262218141062-2

(a) 0718 UTC 20 Sept 1999

(b)

(c)


10

8

6

4

2

0

dBZ

LatitudeLongitude

OPRA

Mt Lema

S-Pol















Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

2055 2105 2115 2125

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

5-m

in r

ain

acc

umu

latio

n (m

m)

UTC

2055 2105 2115 2125 UTC2045

2045

0

1

2

3

4

Time





Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

0955 1005 1015 1025

5-m

in r

ain

accu

mul

atio

n (m

m)

UTC

06

04

02

00

0945 0950 0955 1000 1005 1010 1015 1020 1025

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time

0945







He

igh

t (km

)

6

5

4

3

2

1

6

5

4

3

2

1

0525 0535 0545 0555

5-m

in r

ain

accu

mul

atio

n (m

m)

02

00

0525 0535 0545 05550515

0515

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time












dN DN0






hVti D b C kZ (2)



Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000


8

7

6

5

4

3








7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES




















































0745 UTC0735072507150705

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

Vr (m s-1)-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

2

1

0

5-m

in r

ain

accu

mul

atio

n (m

m)

0735072507150705 0745 UTC

Time

6

5

4

3

2

1

6

5

4

3

2

1

Hei

ght (

km)





64

56

48

40

32

24

16

8

0

dBZ

46 30deg

46deg

8degE 9degE

10

8

6

4

2

0

Hei

ght (

km M

SL)

625854504642383430262218141062-2

(a) 0718 UTC 20 Sept 1999

(b)

(c)


10

8

6

4

2

0

dBZ

LatitudeLongitude

OPRA

Mt Lema

S-Pol















Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

2055 2105 2115 2125

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

5-m

in r

ain

acc

umu

latio

n (m

m)

UTC

2055 2105 2115 2125 UTC2045

2045

0

1

2

3

4

Time





Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

0955 1005 1015 1025

5-m

in r

ain

accu

mul

atio

n (m

m)

UTC

06

04

02

00

0945 0950 0955 1000 1005 1010 1015 1020 1025

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time

0945







He

igh

t (km

)

6

5

4

3

2

1

6

5

4

3

2

1

0525 0535 0545 0555

5-m

in r

ain

accu

mul

atio

n (m

m)

02

00

0525 0535 0545 05550515

0515

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time












dN DN0






hVti D b C kZ (2)



Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000


8

7

6

5

4

3








7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES




















































64

56

48

40

32

24

16

8

0

dBZ

46 30deg

46deg

8degE 9degE

10

8

6

4

2

0

Hei

ght (

km M

SL)

625854504642383430262218141062-2

(a) 0718 UTC 20 Sept 1999

(b)

(c)


10

8

6

4

2

0

dBZ

LatitudeLongitude

OPRA

Mt Lema

S-Pol















Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

2055 2105 2115 2125

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

5-m

in r

ain

acc

umu

latio

n (m

m)

UTC

2055 2105 2115 2125 UTC2045

2045

0

1

2

3

4

Time





Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

0955 1005 1015 1025

5-m

in r

ain

accu

mul

atio

n (m

m)

UTC

06

04

02

00

0945 0950 0955 1000 1005 1010 1015 1020 1025

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time

0945







He

igh

t (km

)

6

5

4

3

2

1

6

5

4

3

2

1

0525 0535 0545 0555

5-m

in r

ain

accu

mul

atio

n (m

m)

02

00

0525 0535 0545 05550515

0515

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time












dN DN0






hVti D b C kZ (2)



Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000


8

7

6

5

4

3








7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES





























































Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

2055 2105 2115 2125

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

5-m

in r

ain

acc

umu

latio

n (m

m)

UTC

2055 2105 2115 2125 UTC2045

2045

0

1

2

3

4

Time





Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

0955 1005 1015 1025

5-m

in r

ain

accu

mul

atio

n (m

m)

UTC

06

04

02

00

0945 0950 0955 1000 1005 1010 1015 1020 1025

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time

0945







He

igh

t (km

)

6

5

4

3

2

1

6

5

4

3

2

1

0525 0535 0545 0555

5-m

in r

ain

accu

mul

atio

n (m

m)

02

00

0525 0535 0545 05550515

0515

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time












dN DN0






hVti D b C kZ (2)



Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000


8

7

6

5

4

3








7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES




















































Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

2055 2105 2115 2125

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

5-m

in r

ain

acc

umu

latio

n (m

m)

UTC

2055 2105 2115 2125 UTC2045

2045

0

1

2

3

4

Time





Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

0955 1005 1015 1025

5-m

in r

ain

accu

mul

atio

n (m

m)

UTC

06

04

02

00

0945 0950 0955 1000 1005 1010 1015 1020 1025

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time

0945







He

igh

t (km

)

6

5

4

3

2

1

6

5

4

3

2

1

0525 0535 0545 0555

5-m

in r

ain

accu

mul

atio

n (m

m)

02

00

0525 0535 0545 05550515

0515

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time












dN DN0






hVti D b C kZ (2)



Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000


8

7

6

5

4

3








7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES




















































Hei

ght (

km)

6

5

4

3

2

1

6

5

4

3

2

1

0955 1005 1015 1025

5-m

in r

ain

accu

mul

atio

n (m

m)

UTC

06

04

02

00

0945 0950 0955 1000 1005 1010 1015 1020 1025

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time

0945







He

igh

t (km

)

6

5

4

3

2

1

6

5

4

3

2

1

0525 0535 0545 0555

5-m

in r

ain

accu

mul

atio

n (m

m)

02

00

0525 0535 0545 05550515

0515

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time












dN DN0






hVti D b C kZ (2)



Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000


8

7

6

5

4

3








7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES




















































He

igh

t (km

)

6

5

4

3

2

1

6

5

4

3

2

1

0525 0535 0545 0555

5-m

in r

ain

accu

mul

atio

n (m

m)

02

00

0525 0535 0545 05550515

0515

UTC

14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 dBZ

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Vr (m s-1)

Time












dN DN0






hVti D b C kZ (2)



Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000


8

7

6

5

4

3








7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES


























































dN DN0






hVti D b C kZ (2)



Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000


8

7

6

5

4

3








7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES




















































Rain rate (mm hr-1)

Mea

n te

rmin

al f

all

spee

d (m

s-1

)

01 05 10 50 100 500 1000


8

7

6

5

4

3








7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES




















































7

6

5

4

3

2

1

(a) Reflectivity44

14

40

36

32

28

24

20

1618

22

26

30

34

38

42

7

6

5

4

3

2

1

00153045607590105

-15-30-45-60-75-90-105

dBZ Vr (m s-1)


3

2

1

0716 0718 0720

8280

787674

7270686664626058

Vt (m s-1)

01234567

-1-2-3-4-5-6-7

w (m s-1)

3

2

1

0718 0720


0716








-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES




















































-5 0 5

05

10

15

20

25

30Hei

ght (

km)


-5 0 5

05

10

15

20

25

30 (a)

(b)







0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES




















































0


0

600


0


0


2230 2245 2300 2315 2330 2345 UTC

Num

ber

of p

ixel

s5

4

3

Hei

ght (

km)

(a) Vr

Vr (m s-1)

-46 -42 -38 -34 -3 -26 -22 -18 -14 -1 -06 -02 02 06 1 14 18 22 26









Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES





















































Rain

Ice

Cc

Ac

Kc

Kci

Fr

Fi

Gl



Dqv

DtD iexclCc (6)

Dqc


Dqr


Dqi








0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES




















































0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

KcFr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)




0

1000

2000

3000

4000

5000

6000

7000

Fi

Kci

Gl

Kc

Fr

Cc

Ac

0 05 1 15Rate (s-1) x 10-5

0

1000

2000

3000

4000

5000

6000

7000

qc


qi

qr

0

1000

2000

3000

4000

5000

6000

7000


Hei

ght (

m)









CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES





















































CLOUD MODEL


Pqr

macr Pqc

2 5 0152 7 0135 5 0405 7 036









6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES





















































6 CONCLUSIONS








4 h sin43plusmn2



ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES





















































ACKNOWLEDGEMENTS


APPENDIX





Kc D Qqcq0875r (A2)

Fr D qrVt=b (A3)





Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES






















































Coef cient Value


at 00005macr 002macr 0 3066Q 219

Vt 3 m siexcl1

Vti 6 m siexcl1

For T lt 0 plusmnC





REFERENCES



















































































Documents

Microphysical modes of precipitation growth determined by