2. Dthan 2.5 dBZ enhancement of Z , though Z increased by 7.5 dBZ or more in 4% of the cases. O Connor et al. (2004) also found that the exponential distribution reasonably describedstratocumulus

Q J R Meteorol Soc (2004) 130 pp 2891ndash2918 doi 101256qj03187

Reflectivity and rain rate in and below drizzling stratocumulus

By KIMBERLY K COMSTOCKlowast ROBERT WOOD SANDRA E YUTER andCHRISTOPHER S BRETHERTON

Department of Atmospheric Sciences University of Washington USA

(Received 29 September 2003 revised 6 July 2004)

SUMMARY

Ship-based radar measurements obtained during the East Pacific Investigation of Climate 2001 stratocumulus(Sc) cruise are used to derive characteristics of the rainfall from drizzling Sc Reflectivity to rain rate (ZndashR)relationships are determined from shipboard raindrop-size distribution measurements obtained from observationsusing filter-paper and compared to ZndashR relationships derived from aircraft probe data from below north-eastAtlantic drizzling Sc and stratus A model for the evaporation and sedimentation of drizzle is combined withreflectivity profiles from a millimetre-wavelength cloud radar to derive information on the mean raindrop radiusand drizzle drop concentrations at cloud base and to show how ZndashR relationships change with height belowthe cloud base The ZndashR relationships are used in conjunction with shipborne C-band radar reflectivity data toestimate areal average precipitation with uncertainties at cloud base and at the surface In the Sc drizzle ZndashRrelationship Z = aRb (where a and b are constants) the estimated exponent b = 11 to 14 is lower thancommonly observed in deep convective rain (b = 15) Analyses indicate that variations in Sc rain rates andreflectivities are influenced both by fluctuations in drizzle drop concentration and in mean radius but that numberconcentration contributes more to the modulation of rain rate in Sc Rain rates derived using the scanning C-bandradar are found to be spatially variable with much of the accumulation originating from a small fraction of thedrizzling area The observations also suggest that rain rate in marine Sc is strongly dependent on cloud liquid-water path and inversely correlated with cloud droplet concentration

KEYWORDS Drizzle Drop-size distribution Marine boundary layer Stratus ZndashR relationship

1 INTRODUCTION

Stratocumulus (Sc) clouds play an integral role in the earthrsquos climate systemLarge regions of Sc exist off the west coast of continents in the subtropics (Klein andHartmann 1993) The low warm Sc clouds reflect a substantial amount of incomingsolar radiation but have only a small effect on the net outgoing long-wave radiationcompared to the sea surface The substantial areal extent and persistence of Sc cloudsmake them important to global climate (eg Slingo 1990) Philander et al (1996)found that the presence of low-level stratus was also crucial to the positioning of thePacific intertropical convergence zone north of the equator Sc drizzle is associatedwith latent heating in the clouds and is a primary means of removing water from themarine boundary layer (MBL) that could otherwise condense into cloud A portionof the drizzle evaporates this cools the sub-cloud layer stabilizes the MBL againstturbulence and could potentially decouple the cloud layer (eg Turton and Nicholls1987) Significant below-cloud evaporation was observed at times during the secondLagrangian experiment in the Atlantic Sc Transition Experiment (ASTEX Brethertonet al 1995) but few of the studies focusing on Sc have examined the evaporation ofdrizzle In this paper we estimate drizzle both at cloud base and at the surface usingship-based radar observations This dataset from EPIC (Eastern Pacific Investigationof Climate 2001) Sc provides an unprecedented opportunity to quantify the meancharacteristics and spationdashtemporal variability of drizzle and its relation to MBL andcloud characteristics in a subtropical stratocumulus regime

The EPIC Sc cruise in October 2001 (Bretherton et al 2004) was an extensiveexamination of the Sc region near Peru (20S 85W) As in the TEPPS Sc cruise(Yuter et al 2000) off the coast of Mexico EPIC Sc used a scanning C-band radar

lowast Corresponding author Department of Atmospheric Sciences University of Washington Box 351640 SeattleWA 98195 USA e-mail kcomstockatmoswashingtoneduccopy Royal Meteorological Society 2004

2891

2892 K K COMSTOCK et al

aboard the National Oceanic and Atmospheric Administration (NOAA) ship the RonaldH Brown (RHB) to obtain areal information on the structure of the drizzling ScDuring EPIC Sc the RHB was also equipped with a NOAA Environmental TechnologyLaboratory (ETL) vertically pointing millimetre-wavelength cloud radar (MMCR) amicrowave radiometer and a suite of other instruments for sampling the ocean andatmospheric boundary layer We use the C-band radar data from EPIC Sc in conjunctionwith a derived relationship between radar reflectivity (Z) and rain rate (R) to obtain arealaverage drizzle statistics MMCR data are used to examine below-cloud evaporation ofdrizzle The radar data used in this study are unique because of the shiprsquos location withinthe south-east Pacific Sc region the sample duration of several days and the large areasampled by the scanning radar

Previous field studies of drizzling Sc have used aircraft radar and in situ data toestimate rain rates along and near the flight track (eg Austin et al 1995 Vali et al 1998Stevens et al 2003) and surface-based vertically pointing radar to obtain profiles ofprecipitation characteristics (eg Miller and Albrecht 1995) Because no in situ clouddata were available for this campaign data obtained on 12 flights in the north-eastAtlantic between 1990 and 2000 aboard the UK Met Office C-130 aircraft (Wood 2005)are used for verification and comparison of our techniques and results

The data used in our analysis are described in section 2 and the procedure forobtaining ZndashR relationships is outlined in section 3 Section 3 also includes an ex-amination of below-cloud evaporation of drizzle using an evaporationndashsedimentationmodel In section 4 the effect of evaporation on the parameters in the ZndashR relationshipsis discussed Also in section 4 reflectivity and rain rate are each expressed as functionsof drizzle drop number concentration and mean size and these are used as additionalmeans to estimate the exponent b in the ZndashR relationship Z = aRb where a and b areconstants We show that all of our datasets and methods yield similar ZndashR relationshipsfor Sc drizzle In section 5 the ZndashR relations are applied to EPIC and TEPPS C-bandradar data to estimate rainfall amounts their probability distribution at cloud base andthe quantity of rainfall reaching the surface We also determine an empirical relationshipamong rain rate liquid-water path and droplet concentration that will be useful in thedevelopment of model parametrizations of drizzle

2 DATA

(a) Filter-paper data samplesFilter-paper treated with a water-sensitive dye (methylene blue or lsquometh bluersquo) is

a time-tested but labour-intensive technique for observing rain drop-size distributions(DSDs) Filter-paper DSD samples were taken aboard the RHB because ship vibrationsinterfere with disdrometer measurements and the shiprsquos rain-gauges were not sensitiveto small amounts of drizzle (Yuter and Parker 2001) During EPIC Sc the 238 cmdiameter filter-paper was exposed to precipitation for a timed duration (up to 2 minutes)and the drops were counted and categorized by hand into eight evenly spaced binsbetween 01 and 08 mm radius establishing a DSD for each sample The preparationand collection of filter-paper samples is described by Rinehart (1997) The range ofresolvable drop sizes is assumed to be sufficient to determine a ZndashR relationshipThe minimum detectable drop size is 01 mm radius During the EPIC Sc cruise33 samples were collected during 23 separate drizzle episodes When possible twosamples were collected in sequence to check the consistency of the DSD Six filter-paper samples were also analysed from the TEPPS Sc cruise

REFLECTIVITY AND RAIN RATE 2893

(b) Samples from aircraft in situ microphysicsAircraft DSD data were collected on 12 flights in and below drizzling Sc clouds off

the coast of the UK The UK Met Office C-130 aircraft was equipped with a ParticleMeasuring Systems (PMS) Inc Forward Scattering Spectrometer Probe which countedcloud drops between 1 and 235 microm radius and categorized them in 15 evenly spacedbins The PMS 2D-C optical array probe counted drops in 32 size categories between125 and 400 microm radius Post-processing by linear interpolation produced combinedDSDs from the two instruments (Wood 2005) On constant-height in-cloud flightssamples were averaged over about 10 minutes corresponding to 50ndash100 km on lsquosaw-toothrsquo flights data were averaged over the entire flight Exponential curves were fittedto the collected data and extrapolated to determine the expected number of drops withradii between 400 microm and 17 mm as these occur in small quantities and are poorlysampled by the optical array probe In 80 of the cases corrections produced a lessthan 25 dBZ enhancement of Z though Z increased by 75 dBZ or more in 4 of thecases OrsquoConnor et al (2004) also found that the exponential distribution reasonablydescribed stratocumulus drizzle

(c) Data from C-band and millimetre cloud radarsRadar data in this paper are from a 6-day observational period during EPIC Sc

16ndash21 October 2001 inclusive at 20S 85W This period was characterized by per-sistent Sc sometimes continuous and other times broken with intermittent drizzlethroughout One of the two meteorological radars aboard the RHB the horizontallyscanning C-band radar has a 5 cm wavelength with 095 beam width (Ryan et al 2002)It provided a reflectivity volume of 30 km radius every 5 minutes throughout EPIC ScThe C-band lower reflectivity limit is about minus12 dBZ at 30 km sufficient to detectdrizzle but not non-precipitating clouds The upper limit is significantly higher thanany reflectivity found in drizzle Appendix A discusses the calibration scan strategyand the interpolation procedure applied to the C-band data The calibration uncer-tainty is plusmn25 dBZ Quality-controlled C-band three-dimensional (3-D) reflectivity wasaveraged between 05 and 2 km and subsequently treated as a 2-D dataset This verticalaveraging was to circumvent uncertainties in radar pointing angles during volume scansthat produced uncertainties in the altitude corresponding to individual radar returns(see appendix A) Because the cloud thickness was typically less than the 500 minterpolated resolution and data below 500 m were contaminated by sea clutter verticalaveraging did not significantly degrade reflectivity information

The NOAA ETL 86 mm wavelength vertically pointing MMCR has a 05 beamwidth and obtained a profile every 10 s during EPIC Sc Its minimum detectablereflectivity is approximately minus60 dBZ the maximum depends on the distance fromthe radar but it is about 20 dBZ near cloud top during EPIC (Moran et al 1998)Uncertainties in MMCR data are outlined in appendix A An example of C-band andMMCR data during EPIC Sc is shown in Bretherton et al (2004 their Fig 6)

(d) Data from additional shipboard instrumentationA shipboard ceilometer provided cloud-base heights with 15 m vertical resolution at

15 s intervals Hourly cloud-base heights were computed using the median value duringeach hour to eliminate the influence of spuriously low readings caused by drizzle

Continuous observations were made of the vertically integrated cloud liquid-water content (ie the liquid-water path LWP) using a microwave radiometer (Fairallet al 1990 Bretherton et al 2004) Data contaminated due to wetting of the radome


surface by drizzle were removed There was also a broadband short-wave radiometer orpyranometer aboard the RHB (Bretherton et al 2004)

3 COMPUTATION OF ZndashR RELATIONSHIPS FOR DRIZZLE AT CLOUD BASE ANDTHE SURFACE

Rain rates can be determined along aircraft flight paths using in situ DSD measure-ments but current remote-sensing technology does not enable rain rate to be measureddirectly Remote-sensing techniques can measure radar reflectivity and radar reflectivi-ties are converted into rain rates using a ZndashR relationship traditionally of the form

Z = aRb (1)

where Z is the independent variable and a and b are constants Currently there are veryfew ZndashR relationships published for drizzle Reported slopes b in the literature varywidely from 10 (Vali et al 1998) to 15 (Joss et al 1970)

(a) ZndashR relationships for drizzle from DSDsThe derivation of ZndashR relationships from DSD data usually has fewer sources of

uncertainty than other methods (eg radarndashrain-gauge comparisons) because the dataused to calculate both Z and R are obtained from the same volume of the atmosphere atthe same time However short duration DSDs are typically not accurately sampled overthe full range of relevant drop sizes (Joss and Gori 1978 Smith et al 1993)

For the filter-paper DSDs R and Z were estimated for each sample followingRinehart (1997) Aircraft Z and R were determined from the exponentially extrapolatedDSDs as outlined in Rogers and Yau (1989) The relationship for terminal velocity usedin these calculations is a function of drop radius temperature and pressure using thespherical best-number approach summarized in Pruppacher and Klett (1997)

Coefficients a and b can be obtained by least-squares regression of the logarithmof (1) log Z = log a + b log R (eg Doelling et al 1998) If the correlation between Zand R is not close to unity the values of a and b will vary depending on whether log Zor log R is treated as the independent variable (eg Campos and Zawadzki 2000) As wewant to minimize errors in rain rate we consider log Z to be the independent variablein all subsequent linear regressions and rearrange the above terms to obtain

log R = 1

b(minuslog a + log Z) (2)

Because values of log a are approximately normally distributed in our datasets theone standard deviation (σ ) values of log a corresponding to the 16th and 84th percentilevalues of a can be used as error bounds on the ZndashR relationship (Doelling et al 1998)

Using this procedure the surface ZndashR relationship for the EPIC filter-paper datais Zsfc = 57R11

sfc with the estimated error bounds Zsfc = 38R11sfc and Zsfc = 86R11

sfc TEPPS filter-paper DSDs are also well described by this relationship For the aircraftdata the resulting cloud-base relationship is ZCB = 32R14

CB bounded by a values of 17and 61lowast A table of statistics for each dataset is presented in appendix B Filter-paperand aircraft data are plotted in Fig 1

lowast If log R is considered the independent variable the ZndashR relationship is unchanged for the filter-paper but theresulting aircraft relationship is ZCB = 14R12

CB


105

104

103

102

101

100

101

30

20

10

0

10

20

30

R [mm hr 1]

Z [

dBZ

]

MMCR Aircraft EPIC sfc MMCR ZR Aircraft ZREPIC sfc ZR

Figure 1 Reflectivity Z versus rain rate R for cloud-base millimetre-wavelength cloud radar (MMCR)-derived data (circles) cloud-base aircraft data (squares) and surface EPIC filter-paper data (triangles)ZndashR relationship lines are shown for MMCR ZCB = 25R13

CB (solid) aircraft ZCB = 32R14CB (dashed) and

filter-paper Zsfc = 57R11sfc (dash-dot) Arrows are sketched to represent evaporation between cloud base and

the surface See text for details

We do not expect the ZndashR relationships from the cloud (aircraft) and surface(filter-paper) data to be the same because the data sources differ significantlyAlso significant evaporation occurs below the cloud affecting the DSD and thereforethe ZndashR relationship this will be discussed in the following sections

In this paper we find b = 11ndash14 For deep convective rain b sim= 15 (Smith and Joss1997 Doelling et al 1998 Steiner and Smith 2000) Other published ZndashR relationshipsfor drizzle include Z = 150R15 (Joss et al 1970) and Z = 10R10 (Vali et al 1998)Joss et al acquired surface DSDs with a disdrometer but assumed the exponent in theZndashR relationship a priori to be 15 based on relationships available at that time forrain Although we find a similar ZndashR relationship for EPIC filter-paper DSDs when weassume b = 15 the Joss data may have been contaminated with ice within the cloudwhich can alter the size distribution Vali et al used aircraft data from marine stratus offthe Oregon coast The small sample volume of the instrument (similar to the aircraftinstrumentation described in subsection 2(b)) did not permit detection of any dropswith radii larger than about 018 mm Because larger drops have a disproportionateeffect on reflectivity (simD6 where D is drop diameter) compared to rain rate (simD4)neglecting them introduces errors in the ZndashR relationship Appendix B shows the effectof extrapolation on the ZndashR relationship

(b) ZndashR relationships for drizzle from MMCR vertical profiles of reflectivityBecause drizzle drops are smallmdashrain rate and radar reflectivity in Sc are dominated

by drops with radii in the range 20 lt r lt 400 microm (Wood 2005)mdashtheir evaporationbelow cloud base will change the ZndashR relationship This has important implications forestimation of precipitation To evaluate this effect we use an evaporationndashsedimentation


model that modifies the DSD (and thus Z and R) with distance beneath the cloudWe estimate the drizzle drop number concentrations ND and the mean radii r of theDSDs by comparing MMCR reflectivity profiles with model results This process yieldsanother cloud-base ZndashR relationship (from MMCR Z and model-derived R) as well asrelationships between cloud-base Z and below-cloud R

(i) Sedimentationndashevaporation model Evaporation of drizzle below cloud baseThe sedimentationndashevaporation model simulates the evaporation of drizzle drops belowcloud base It does not include the effects of coalescence or break-up but these effectsare of little consequence below cloud for the sizes and concentrations of drizzle dropsin Sc (Pruppacher and Klett 1997) The model provides steady-state solutions for apopulation of sedimenting drops evaporating into a sub-saturated environment belowcloud base with an imposed relative-humidity gradient of 036 kmminus1 based on EPICobservations The DSD at cloud base is prescribed and is represented by an exponentialdistribution truncated at a lower size limit r0 shown to be a good fit by Wood (2005)

NCB(r) = ND

r minus r0expminus(r minus r0)(r minus r0) (r gt 20 microm) (3)

where r is the mean radius of the truncated exponential distribution at cloud baselowast andr0 = 20 microm is the smallest drizzle drop size Drops smaller than r0 are cloud dropswith insignificant terminal velocities and negligible contributions to radar reflectivityIncluding the small drops can result in instabilities in the model because their evapora-tion rates are large Model details and a discussion of the limitations of the techniqueare presented in appendix C

The following function provides a reasonable parametrization of the model-predicted rainfall rate as a function of height above the surface z for a truncated-exponential DSDdagger

R(z)

RCB= c(χ) = exp(minuskχ(r z)) (4)

where χ = (zCB minus z)(r)2515 is a normalized height coordinate RCB is rain rate atcloud base ie where z = zCB A single value of constant k = 320 microm375mminus15 wasfound to be appropriate for the temperatures pressures and vertical relative-humiditygradients observed during EPIC Sc (see appendix C)

The model can be used to estimate changes to the ZndashR relationship as the drizzleevaporates For the range of cloud-base mean radii observed in drizzling Sc the model-predicted reflectivity can be further parametrized

Z(z)

ZCBasymp

(R(z)

RCB

)q

(5)

where q asymp 075 for our simulations of drizzle evaporation Reflectivity decreases moreslowly with distance below cloud base than does the precipitation rate because thedominant contributions to the reflectivity are from larger more slowly evaporatingdroplets than those that dominate the rain ratelowast For a non-truncated exponential the ratio of mean volume radius rvol to r is 6(13) = 18 For an exponentialtruncated at radius r0 the ratio rvolr is lower than this and increases with the ratio rr0 For r0 = 20 micromr = 30 microm corresponds to rvol = 34 microm and r = 50 microm corresponds to rvol = 67 microm Aircraft measurements(Wood 2005) find rvol at the cloud base between 31 and 53 microm consistent with this rangedagger The authors note that our evaporationndashsedimentation model can be solved analytically by separation of variablesto yield solutions having a Weibull-type distribution from which a linear combination of solutions could beused in theory to match the prescribed boundary conditions at the cloud base However the incorporation of theexponential distribution boundary condition at z = zCB would lead to unwieldy mathematical solutions


Figure 2 Terminal-velocity relationship with drizzle drop radius from Pruppacher and Klett (1997) (actualsolid line) and single power law used to fit the velocity relationship (dashed line) for simplifying calculations

The value of q is primarily a function of the relationship between terminal velocityand drop size but it also depends on the form of the assumed DSD and on the relation-ship between evaporation rate and drop size The exponent may be somewhat differentin other types of rain-producing systems such as deep-convective or midlatitude rainApproximately q = (3 + d)6 where d is the exponent in the relationship betweenterminal velocity ωT and drop size

ωT(r) = ATrd (6)

with AT = 22 times 105 mminus04sminus1 and d = 14 (for r in m and ωT in m sminus1) This relation-ship shown in Fig 2 provides a reasonable fit to the terminal-velocity relations givenin Pruppacher and Klett (1997) for the size range 20 lt r lt 400 microm This single powerlaw in (6) simplifies the solution of the sedimentationndashevaporation equations and testsindicate that results do not appreciably differ from those obtained using a more complexform The exponent d here is different from that for rain (eg Rogers and Yau 1989)because it is optimized to drops of smaller size

Combining (4) and (5) gives

Z(z)

ZCB= exp(minusqkχ(r z)) (7)

To show that the parametrization (7) is consistent with independent in situ datawe plot aircraft estimated reflectivity data against χ in Fig 3 No in situ cloud micro-physical measurements were made during EPIC Sc but we consider Sc clouds suffi-ciently universal in nature for the UK results to serve as a test of the numerical modelRelative-humidity gradients are similar to those in EPIC Sc (within plusmn10) Althoughthe observed values are somewhat scattered due to sampling uncertainties and variablecloud-base heights the model parametrization (7) does not seem unduly biased andrepresents the observations well


001 010 100Z(z)ZCB

-0020

-0015

-0010

-0005

0000

- [

m1

5

m-3

75]

AircraftParametrization

Figure 3 Profiles of radar reflectivity Z below cloud normalized with the maximum value ZCB versus thenormalized height variable χ = (zCB minus z)(r)2515 Circles represent aircraft data from the UK Met Officeflights in North Atlantic Sc with estimated error bars The dashed line shows the evaporationndashsedimentation

model parametrization using (7) See text for details

(ii) MMCR-based estimation of cloud-base drizzle parameters and a ZndashR relationshipThe MMCR cloud-base reflectivity and profiles below cloud base are combined with theparametrization from the sedimentationndashevaporation model to estimate the parametersof the drizzle DSD at cloud base The latter is assumed to be a truncated exponentialfunction To avoid contributions from cloud liquid water no profile with a maximumreflectivity less than minus20 dBZ was used We averaged the acceptable profiles over10 minutes because this is short enough to capture the spatial variability of drizzleobserved during EPIC and long enough to ensure that the profile would be verticallycoherent with respect to the falling of drizzle drops We approximate cloud base asthe height with maximum reflectivity in the MMCR profile in order to simplify theexponential fit (7) The mean height of the maximum reflectivity is consistent with thecloud base derived from the ceilometer Figure 4 shows three example MMCR profilescompared with parametrization (4) and the cloud bases for cases of light and heavydrizzle

For each 10-minute mean MMCR reflectivity profile we solve for r in (7) usingthe Z(z)ZCB profile between cloud base and 400 m Only data in this height range areused to ensure that (7) is a good approximation and to avoid problems associated withthe saturation of the MMCR at low levels

Once r is known ND is derived using the observed cloud-base radar reflectivityZCB = 26M6 where M6 is the 6th moment of a truncated exponential distributionThe moments Mn of order n of this distribution can be expressed using an integralrecurrence relation as

Mn(r0 r ND) = NDn(r minus r0)n

nsumi=0

(r0

r minus r0

)i 1

i (8)


-40 -30 -20 -10 0 10radar reflectivity [dBZ]

0

500

1000

1500

hei

ght

[m]

cloudbase

NO DRIZZLE

LIGHT

DRIZZLE

HEAVY

DRIZZLE

MMCR

Eqn 4

Figure 4 Ten-minute mean profiles of millimetre-wavelength cloud radar (MMCR) reflectivity with the modelparametrization (4) and ceilometer cloud-base heights Profiles are representative of typical conditions with nodrizzle light drizzle and heavy drizzle during EPIC Peak reflectivity occurs at cloud base during drizzling periods

but somewhat higher in non-drizzling periods

Once r and ND are found any of the moments of the truncated exponentialdistribution can be obtained through (8) For example the rain rate at cloud base is

RCB = 4πρw

3ATMd+3(r0 r ND) (9)

where AT and d are from (6) (the approximation for the terminal velocity of drizzledrops) and ρw is the density of water For non-integer values of d we interpolate (8) tofind Md+3 Figure 5 shows time series of ND and r and their median fitting uncertaintiesfrom the model based on MMCR data during EPIC Sc The range of variations in r issmall (40 plusmn 20 microm) compared to ND which fluctuates over four orders of magnitude

A ZndashR relationship is computed as described in subsection 3(a) from cloud-baseRCB estimated using (9) and MMCR ZCB

ZCB = 25R13CB (10)

with uncertainty bounds in a of 11 and 54lowast Figure 1 shows MMCR ZCB and RCB valuestogether with (10)

(iii) Effect of evaporation below cloud bi-level ZndashR relationships Cloud-base ZndashRrelationships can be applied to the cloud-base radar data to determine the amountof drizzle falling out of the clouds but how much drizzle reaches the surfaceThe evaporationndashsedimentation model predicts drizzle rates at any level below the cloudby modifying the inferred cloud-base DSDs from the MMCR data From the model-derived rain-rate profiles we can estimate lsquobi-levelrsquo ZndashR relationships that relate cloud-base reflectivity to below-cloud rain rates

To explore what we expect a bi-level ZndashR relationship to look like we use (4) andassume the ZndashR relation obeys a power law ie ZCB = aRb

CB at cloud base which leads

lowast Using log(R) as the independent variable would yield an alternative relationship ZCB = 11R11CB


median error

(a)

(b)

Figure 5 Time series of (a) 10-minute cloud-base drizzle drop concentration ND(zCB) and (b) mean cloud-basedrizzle drop radius r(zCB) derived using millimetre-wavelength cloud radar reflectivity profiles (dots) Lines show

3-hourly mean values Median error bars in each plot represent uncertainties in ND and r Time is UTC

to

ZCB = a

(R(z)

c(χ)

)b

(11)

Taking the logarithm of (11) and using the definition of c(χ ) gives

log ZCB = log a + blog R(z) + kχ(r z) (12)

It is apparent from (12) that there is not necessarily a simple power-law relationshipbetween Z at cloud base and R below cloud This is not surprising because evap-oration changes the size distribution and affects reflectivity and rain rate nonlinearly(see section 4(a)) From our data it is reasonable to expect that the departure from lin-earity increases with increasing distance from the cloud base or increasing evaporation

The range of rain rates is limited in the MMCR 10-minute average dataset and is in-sufficient to fully define a non-power-law ZndashR relationship for all rain rates of interesthence instead we define a piecewise linear function Only profiles with below-cloud rainrates greater than 1 times 10minus4 mm hrminus1 are used because of the large scatter and insignifi-cant accumulation associated with lower rain rates (see subsection 5(b)) The relation isestimated by assuming a linear relationship between log ZCB and log R(z) below cloudas in (2) Where this ZndashR line intersects the cloud-base ZndashR line it must follow thelatter for higher reflectivity values because in an evaporative environment there cannotbe more precipitation below cloud than at cloud base The log R(z) data are obtained byusing the model to sedimentevaporate the MMCR estimated cloud-base DSD Model-derived surface rain rates and several bi-level ZndashR relationships are shown in Fig 6


106

104

102

100

102

20

15

10

5

0

5

10

15

20

25

30

R(z) [mm hr 1]

ZC

B [

dBZ

]

Cloud BaseCB 250m CB 500m CB 900m CB 900m R

Figure 6 Bi-level relationships of radar reflectivity Z and rainfall rate R from the evaporationndashsedimentationmodel at various levels at the cloud base (ZCB = 25R13

CB) 250 m below cloud base (ZCB = 35R(zCB-250)1)

500 m below cloud base (ZCB = 75R(zCB-500)09) and 900 m below cloud base which is the average

distance to the surface (ZCB = 302R09sfc ) Circles represent model-derived rain rates at 900 m below cloud

base Relationships were calculated using R(z) 10minus4 mm hrminus1 although they are plotted for lower rainrates here See text for details

Increasing the distance below cloud increases the rain rate at which the bi-leveland cloud-base ZndashR relations intersect ie the maximum rain rate at which measurableevaporation occurs between cloud base and the specified level The average cloud baseduring EPIC was around 900 m (Bretherton et al 2004) so the lsquosurfacersquo (CBndash900 m)bi-level ZndashR relation is

ZCB = 302R09sfc (13)

with uncertainty bounds in a of 159 and 571Although the derived bi-level ZndashR relationships may not be precise descriptions of

the sub-cloud rain-rate behaviour our results show an important trend in the relationshipbetween cloud-base reflectivity and below-cloud rain rates For low rain rates at cloud-base it is essential to consider the evaporation below cloud base when relating rain rateand reflectivity at different levels (Li and Srivastava 2001)

(iv) Potential sources of error in the derived drizzle parameters Two categories of un-certainty lead to errors in the derived drizzle parameters The first category discussedin appendix A is related to possible saturation of the MMCR Periodic MMCR satura-tion means that there are no high values of reflectivity to constrain the MMCR-derivedZndashR relation This may lead to poor estimates of rain rate for the highest reflectivityvalues that are measured by the C-band radar The second source of error discussed inappendix C arises from simplifying assumptions made in the method of estimation ofdrizzle parameters from the MMCR reflectivity profiles


An important assumption made in the model is that vertical air motions have negli-gible effect on the profiles of rain rate and reflectivity and on their dependence upon themean radius of the drizzle drops at cloud base It is well understood (eg Nicholls 1987)that the terminal velocity of drizzle drops is comparable to the vertical ascentdescentrates for turbulent eddies and that this motion has an important effect on the productionof drizzle by recirculating small drizzle drops within the cloud It is less certain howthis may impact the rain-rate profiles below cloud where many of the smaller dropshave evaporated Because our method uses 10-minute mean profiles the mean verticalmotion over this period will be negligible because the typical duration of a eddy of scale1000 m as it passes over the ship is about 2 minutes However a non-zero correlationbetween r and vertical wind at smaller scales would alter the profile (4) leading tooverestimates in rain rate These errors are estimated to be smaller than those associatedwith the uncertainty in C-band radar calibration (see appendices A and C)

4 UNDERSTANDING THE PARAMETERS IN THE ZndashR RELATIONSHIP

(a) Expected changes in ZndashR relationships due to evaporationThe ZndashR relationships for the surface and cloud base differ in part because of the

nature of the DSD collection but the main source of difference is due to evaporationbelow cloud base From the cloud-base and surface ZndashR lines shown in Fig 1 wesee that a increases significantly from cloud base to the surface while the exponentdecreases slightly Parcels with higher rain rates tend to be less affected by evaporationthan parcels with lower rain rates as represented by arrows in Fig 1 Some surface Zvalues in Fig 1 are greater than the cloud-base values primarily because filter-papersamples are nearly instantaneous while cloud-base samples are horizontally averaged(see also MMCR uncertainties in appendix A)

(b) Mathematical derivation of b

We can understand the cloud-base ZndashR relationship in terms of the joint proba-bility density function (pdf) of drizzle drop concentration ND and mean drizzle dropradius r Figure 7 shows scatter plots of pair-wise correlations among MMCR-derived10-minute averaged ND r and cloud-base rain rate RCB obtained as in subsec-tion 3(b)(ii) The correlation coefficients between the logarithms of these variables are072 (ND R) minus058 (ND r) and 014 (r R) the latter of which is not significantWe can now use this information to derive an expression for the value of the exponent bin the ZndashR relationship at cloud base ZCB = aRb

CB Relating Z and R to the momentsof a truncated exponential DSD

ZCB = α1M6

RCB = α2Md+3(14)

where α1 and α2 are constants with values of 26 and 43πρwAT from (9) respectively and

M is from (8) Using a power-law fit to (8) over the estimated range 25 lt r lt 60 micromwe obtain

M6 asymp ND(r)β1

Md+3 asymp ND(r)β2(15)

where β1 asymp 98 and β2 asymp 65 if r0 = 20 microm Without truncation of the exponential sizedistribution ie r0 = 0 we would obtain β1 = 6 and β2 = 3 + d (and (15) would beexact)


(a) (b)

(c)

Figure 7 Correlations between (a) drizzle drop concentration ND and rain rate R (b) drizzle drop meanradius r and R and (c) r and ND for parameters at cloud base derived by millimetre-wavelength cloud radar

Correlations greater than 035 are significant at the 95 confidence level

The parameters log a and b in the ZCBndashRCB power law (2) can be consideredoptimal least-squares values obtained from the regression of log RCB on log ZCBTogether (14) and (15) express ZCB and RCB in terms of ND and r We can deduceexpressions for log a and b in terms of the fluctuations in these two DSD parametersif they have a bivariate log-normal joint pdf with a correlation coefficient rlog ND log r The solution for the least-squares value of b at cloud base is

b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND

+ 2β1rlog r log NDσlog rσlog ND

1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r

are the variances of the logarithms of ND and r which indicatethe respective degrees of variability of the size distribution parameters (see appendix Dfor derivation) Thus the exponent is determined by the relative amount of variance inND and r (see also Doelling et al 1998) Note that the degree of correlation betweenlog r and log ND rlog r log ND does not greatly affect b and the correlation betweenlog R and log Z rlog R log Z is typically close to one The two limiting cases (assumingfor the moment that log Z and log R are perfectly correlated and there is no correlationbetween log r and log ND) are b = 1 (precipitation rate variations are dominated byvariations in ND σ 2

log ND σ 2

log r) and b = (β1β2) = 151 (precipitation rate variations


TABLE 1 VALUES OF DROP SIZE DISTRIBUTION PARAMETERS ANDTHEIR VARIABILITY

Parameter Value (EPIC MMCR) Value (Aircraft) Units

σlog ND 0787 0628 Noneσlog r 0082 0161 None

Median ND 235 times 104 254 times 104 mminus3

Median r 393 345 micromrlog R log Z 092 091 Nonerlog r log ND minus058 minus044 None

See text for details

TABLE 2 RELATIVE CONTRIBUTIONS TO VARIANCEIN RAINFALL RATE R AND RADAR REFLECTIVITY Z

Contribution to variance of R to variance of Z

from ND 062 062from r 029 066from rlog ND log r minus049 minus074Sum 042 054Observed 042 056


are entirely modulated by variations in r σ 2log r σ 2

log ND)lowast Equation (16) couches the

ZndashR exponent b as a physically significant parameter related to whether variability(in time or space) in drizzle droplet number concentration or in the size of the drops hasmost influence over variability in the precipitation rate A similar relationship is showngraphically in Steiner et al (2004) based on modelled DSD data Relevant quantities forthe estimation of b for both MMCR-derived and aircraft data are given in Table 1

Distributions of ND and r calculated from the MMCR data are approximately log-normal Log-variances for the MMCR-derived size-distribution parameters (Table 1)lead to a theoretical value (16) of b = 124 This is intermediate between the limitingvalues indicating that precipitation rate variability is controlled by variability in both NDand r There is much greater variability in ND but because of the stronger dependenceof Z on r (compared to R) r also impacts the fluctuations in radar reflectivity and to alesser degree in rain rate The aircraft data were characterized by higher variation in r which led to a larger theoretical b of 141

To better understand the relative contributions of ND and r to variances in R and Zthe variance equation for log Z or log R can be written σ 2

log(Z or R)= σ 2

log ND+ β2σ 2

log r

+ 2βrlog ND log rσlog NDσlog r where rlog ND log r is a correlation coefficient and β is eitherβ1 (for Z) or β2 (for R) Results given in Table 2 indicate that the values of β1 and β2are appropriate because the sum of the terms is very close to the observed variance inthe MMCR-derived time series These are not always equal because (15) is not exactVariability in ND contributes more than r for R but for Z both contribute more equallyThe negative correlation between ND and r reduces the variance in R and Z

lowast In the classic MarshallndashPalmer formulation (Marshall and Palmer 1948) their N0 (our NDr) is taken to bea constant This implies that σlog r = σlog ND and rlog r log ND = 1 The value of rlog R log Z also equals one for aMarshallndashPalmer distribution Inserting those values into (16) with the definitions for β1 and β2 for untruncateddistributions b = (1 + β1)(1 + β2) = (1 + 6)(1 + 3 + d) For rain d = 067 (Gunn and Kinzer 1949) so thetheoretical exponent b equals the expected value of 15


16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface

Figure 8 Estimated areal average rain rate from C-band radar data for the cloud base and surface frommillimetre-wavelength cloud radar-derived cloud-base and bi-level relationships of radar reflectivity and rain rate(ZndashR) for 6 days during EPIC Sc Shading represents C-band calibration uncertainties of plusmn25 dBZ Time is UTC

5 IMPLICATIONS

(a) Estimation of drizzle amount from radar dataPrevious sections have described methods to obtain relationships between observed

radar reflectivity and precipitation at cloud base and below These relationships cannow be applied to determine the amount of rainfall during the EPIC Sc and TEPPSSc cruises To obtain area-averaged cloud-base rain rate we apply the MMCR-derivedZndashR relationship (10) to the C-band data in order to take advantage of the C-bandradarrsquos superior areal coverage The resulting area-averaged rain-rate time series duringEPIC Sc is shown in Fig 8 The surface drizzle rate derived from the bi-level ZndashRrelationship (13) is also shown The effect of the plusmn25 dBZ calibration uncertainty onthe estimated rain rates is illustrated This is the largest source of error in the rainfallestimation The ZndashR relationship uncertainties are not shown they are of the samemagnitude as the calibration uncertainties Average reflectivity is determined usingC-band data interpolated to 500 m by 500 m pixels Because precipitation rates arescale-dependent a different spatial resolution may yield somewhat different results

For each ZndashR relationship derived in this study the average rainfall rate is com-puted for the days on which it drizzled during EPIC and TEPPS Sc in order tomake a fair comparison between rain rates in the north-east and south-east Pacific Scregions lsquoDrizzle daysrsquo are defined as having a daily areal average rain rate (AARR)of gt01 mm dayminus1 or a daily average conditional rain rate (ACRR) gt 5 mm dayminus1The conditional rain rate describes the pixel rain rate if and only if it is raining AARRsand ACRRs and uncertainties are presented in Table 3

Our best estimate of the mean AARR during the 5 drizzle days in EPIC Sc is about07 mm dayminus1 at cloud base with a total uncertainty envelope of 02ndash23 mm dayminus1About 02 mm dayminus1 reached the surface (uncertainty range 01ndash06 mm dayminus1) On thetwo TEPPS drizzle days there was much less precipitation about 02 mm dayminus1 at cloudbase (within the range 01ndash05 mm dayminus1) and 01 mm dayminus1 (004ndash02 mm dayminus1) atthe surface

During TEPPS we expect the C-band calibration uncertainty to be in the samerange as for EPIC The TEPPS region was synoptically different from the EPIC Scregion with a more decoupled MBL and higher cloud bases at times (as much as 200 m)so the surface rain rates may be slightly overestimated Drizzle occurred less frequentlyduring TEPPS but when it was drizzling the cloud-base rain rates are comparable to


TABLE 3 AVERAGE AREA AND AVERAGE CONDITIONAL RAINFALL RATES FOR EPIC AND TEPPS

EPIC TEPPSDaily areal averagerain rate (AARR) ZndashR minus25 dBZ 0 dBZ 25 dBZ minus25 dBZ 0 dBZ 25 dBZ

MMCR-derived minus (CB) Z = 11R13 07 13 23 02 03 05

MMCR-derived (CB) Z = 25R13 04 07 13 01 02 03MMCR-derived + (CB) Z = 54R13 02 04 07 01 01 02

bi-level minus (Rsfc ZCB) Z = 159R09 01 03 06 01 01 02

bi-level (Rsfc ZCB) Z = 302R09 01 02 04 00 01 01bi-level + (Rsfc ZCB) Z = 571R09 00 01 02 00 01 01

Daily average conditionalrain rate (ACRR)





MMCR is millimetre-wavelength cloud radar CB is cloud base sfc is surface R is rain rate and Z radarreflectivity Average rain rates in mm dayminus1 are given for mean ZndashR relationships ZndashR uncertainties and C-bandcalibration uncertainties (minus25 0 +25 dBZ) on EPIC Sc drizzle days (17ndash21 Oct 2001) and TEPPS Sc drizzledays (2ndash3 September 1997) Best estimates from (10) and (13) are in bold Only values of R 1 times 10minus4 mm hrminus1

are used to compute daily rain rates See text for further details

those from EPIC (see ACRRs in Table 3) Even with the uncertainties it is clear that asubstantial amount of evaporation of sub-cloud drizzle is occurring in both the north-eastand south-east Pacific Sc MBLs

(b) The spatial pdf of cloud-base drizzle rateAs in deep convective rainfall (eg Doelling et al 1998) the spatial pdf of drizzle

rate is strongly skewed such that a large percentage of the rain rate in drizzling Scfalls from only a small fraction of the area This may lead to considerably differentdynamical feedbacks than if the drizzle fell evenly throughout (through spatially patchyevaporative cooling in the sub-cloud layer and latent warming in the cloud layer)We examine spatial cloud-base rain-rate pdfs using the C-band radar data from EPIC ScThe C-band radar has far better sampling statistics than the MMCR and gives truespatial variability information For each C-band horizontal scan the MMCR-derivedZndashR relationship (10) is used to estimate rainfall at each pixel and a pdf of rain rateis obtained All of the pdfs are then composited As illustrated in Fig 9(a) the pdfof the drizzling area has a significant tail which indicates that a considerable amountof rain is associated with only a small fraction of the area For example as shown inFig 9(b) 50 of the drizzle accumulation is contributed by rain rates greater than037 mm hrminus1 but it originates from only 5 of the drizzling area Drizzle was detectedby the C-band in only 41 of the total area so that 90 of the accumulation whichcomes from 68 of this drizzling area corresponds to only 28 of the total areaThe intermittency is considerable Because most of the drizzle during EPIC evaporatedand rates of 004 mm hrminus1 can lead to local sub-cloud cooling rates of several K dayminus1it is possible that evaporating drizzle could result in downdraughts with subsequentdynamical response that may locally enhance cloud thickness and drizzle production(Jensen et al 2000)


(a) (b)

Figure 9 (a) Composite probability density functions of drizzling area (solid line) and total accumulation(dashed line) for each rain rate at cloud base R(zCB) Data are taken from the C-band radar using the relation(10) derived from millimetre-wavelength cloud radar (b) The total rainfall accumulation and the correspondingdrizzling area for the given rain rates (eg 25 of the rain comes from 010 lt R(zCB) lt 037 mm hrminus1 and this

corresponds to 17 of the drizzling area)

(c) Estimation of rain rate from cloud-drop concentration and liquid-water pathModel simulations (eg Nicholls 1987 Baker 1993 Austin et al 1995 Khairout-

dinov and Kogan 2000) observations (eg Bower et al 1992) and simple physical argu-ments (Tripoli and Cotton 1980) show that the production of drizzle depends stronglyupon both the cloud liquid-water content and the cloud droplet concentration with highliquid-water content and low droplet concentration leading to stronger drizzle produc-tion During EPIC Sc the cloud droplet concentration Nd (note that this is different fromdrizzle drop concentration ND used previously) was estimated during the daytimeusing the observed LWP and cloud transmission measurements from the pyranometer(Dong and Mace 2003 Bretherton et al 2004) Linear interpolation of the daytime Ndwas used to estimate values during the night Because of the coarseness in Nd estima-tions and to reduce the sampling uncertainties all the values (RCB LWP and Nd) areaggregated into 3 h means Air advects about 75 km in a 3 h period during this timepatches of thicker and thinner cloud may advect overhead resulting in considerable LWPvariability Thus these estimates should be regarded as appropriate for mean quantitiesaveraged over (75 km)2 regions Tests show that RCB is reasonably well parametrizedas a function of LWPNd (Fig 10)

RCB = 00156(LWPNd)175 (17)

with LWP in g mminus2 Nd in cmminus3 and RCB in mm hrminus1 The correlation between rainrates derived in subsection 3(b)(ii) and parametrized from (17) is 077 If only LWP isused to estimate the rain rate the correlation falls to 060 suggesting that there is some


01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]

R(zCB)=00156(LWPNd)175

Figure 10 Three-hourly mean cloud-base rain rate R(zCB) derived from the millimetre-wavelength cloudradar plotted against the ratio of the mean cloud liquid-water path LWP to the droplet concentration Nd withuncertainties The parametrization described in the text is shown by the dashed line Uncertainties in LWP areassumed to be 25 g mminus2 which affects the computation of Nd as well A conservative estimate of combined

uncertainty in rain rate is 60

important modulation of the rain rate by changes in droplet concentration (see Fig 7 inBretherton et al 2004) However our data are not sufficient to establish the statisticalsignificance of the RndashNd relationship Our results are in general qualitative agreementwith those of Pawlowska and Brenguier (2003) whose data support a near-quadraticdependence of RCB upon liquid-water path and an inverse dependence upon clouddroplet concentration Further observational datasets are necessary to quantify theserelationships more accurately

6 CONCLUSIONS

Observations from field campaigns in different Sc regimes were used to obtainrelationships between rain rate and radar reflectivity in drizzle for the surface andcloud base The impact of evaporation below cloud base on Z R and their relationshipwas explored with a sedimentationndashevaporation model and MMCR reflectivity profilesSeveral independent datasets yield an exponent b of 10ndash11 near the surface and13ndash14 near the cloud base in the relationship Z = aRb for drizzle These exponentsare lower than the accepted value of 15 for deep convective rain Our suggested ZndashRrelationship at Sc cloud base is Z = 25R13

For exponential or truncated-exponential DSDs we relate b to the relative variabil-ity of ND and r (time series of ND and r are shown in Fig 5) Variations in rain rateare mainly driven by variations in ND while fluctuations in ND and r contribute equallyto variations in reflectivity Understanding the microphysical mechanisms underlyingthe variability of ND and r will require careful modelling studies and further analysesof aircraft data The maximum size that a drizzle drop may reach is constrained bythe combination of weak updraughts (almost everywhere lt1 m sminus1) and limited cloudthickness (almost always lt500 m) This may have some important consequences forthe observation of MBL drizzle from space-borne cloud radar and deserves additionalattention


Evaporation below cloud base has a significant effect on drizzle DSDs and there-fore ZndashR relationships The coefficient a increases with distance below cloud baseas evaporation of the small drops leads to an increased mean drop size This makes thederivation of sub-cloud rain rate profiles using only reflectivity difficult Remote-sensinginstruments such as surface-based radar and satellite radar (eg CloudSat Stephenset al 2002) may need to use different ZndashR relationships to determine precipitationamounts at various vertical levels where significant changes in the DSD are expected totake place Bi-level ZndashR relationships that were derived for predicting surface rain ratefrom cloud-base reflectivity show that for low rain rates it is important to account forevaporation below cloud

Although our radar retrievals of the rainfall amount in the Pacific Sc regions areuncertain to within a factor of three it is possible to say that area-averaged drizzle ratesare highly variable that sub-cloud evaporation recycles a large fraction of the drizzlebefore it reaches the surface and that drizzle is spatially highly inhomogeneous Arealaverage drizzle rates frequently exceed 10 mm dayminus1 at cloud base especially in the latenight and early morning when Sc is usually thickest Our best estimate for the EPIC Scregion during 5 days in October 2001 was 07 mm dayminus1 on average or between 02and 23 mm dayminus1 within the range of conservative radar calibration uncertaintiesThe amount of precipitation reaching the surface is usually significantly less than theamount falling out of the clouds during EPIC the average was 02 mm dayminus1 (rangingfrom 004 to 06 mm dayminus1 with uncertainties) Like deep-convective rain most of thedrizzle accumulation comes from a small fraction of the precipitating area

Drizzle rates in Sc are dependent on both the LWP and the cloud droplet concentra-tion Nd (eg Austin et al 1995) A linear relationship was found between the derivedrain rate and (LWPNd)

175 during EPIC Sc The inverse relationship between rain rateand cloud-drop concentration is consistent with previous findings but more observationsare needed to establish the uncertainties in this relationship

ACKNOWLEDGEMENTS

The authors wish to thank Christopher Fairall Taneil Uttal Duane Hazen andPaquita Zuidema of NOAA ETL for providing MMCR data and information We arealso grateful to the crew of the NOAA RHB for their assistance in collecting EPIC dataand to the UK Met Office for supplying aircraft DSD data This research was fundedby NSF grant ATM-0082384 NASA grants NAG5S-10624 and NNG04GA65G and aNDSEG fellowship

APPENDIX ARADAR CALIBRATION SCAN STRATEGY AND DATA PROCESSING

(a) MMCR calibration and comparison with C-band dataAfter the EPIC cruise the MMCR was calibrated to within about 1 dBZ (NOAA

ETL 2002 2003 personal communications) Two potential sources of error remainin the MMCR data Mie scattering and saturation Drops of radius greater than about300 microm scatter in the Mie regime rather than the Rayleigh regime Figure A1 showsZMieZRayleigh as a function of mean radius at the MMCR 86 mm wavelength In Scdrizzle the mean radius of drizzle drops is typically 80 microm or smaller (lt10 error)calculated from our data The largest mean drop size obtained by surface filter-papersampling during EPIC Sc was about 350 microm radius (this is likely to be an overestimatebecause the detection threshold was 200 microm) so the errors will be at most +20 or


Figure A1 Ratio between Mie-scattering reflectivity and Rayleigh-scattering reflectivity for drop-size distribu-tions with a mean radius of 0ndash400 microm

minus50 of the MMCR reflectivity The larger mean sizes mostly occur well below cloudwhen the small drops have evaporated No MMCR data are used below 400 m so errorsare expected to be smaller than the range stated above These errors will only occurwhen the drizzle rate is significant and we expect them to account for a small fractionof the total error in cloud-base rain rate derived from the MMCR

The reflectivity value at which the MMCR saturates increases with increasingheight (ie range) Saturation is about 17 dBZ at mean cloud base and 20 dBZ nearmean cloud top (D Hazen 2003 personal communication) Hourly averaged cloud-baseMMCR reflectivity is plotted with hourly area-averaged reflectivity from the C-bandradar (discussed in the following sections) in Fig A2(a) The C-band reflectivity datain this plot is lsquothresholdedrsquo at 17 dBZ Because their time and space resolutions differthe comparison between the two instruments cannot be exact however the two timeseries track each other fairly well

Figure A2(b) shows the ratio of non-thresholded to thresholded hourly area-averaged C-band reflectivity The curve signifies the reflectivity peaks that the MMCRmay be underestimating Comparison between the MMCR maximum reflectivity dataand the thresholded C-band data yields a consistent result that indicates a relativecalibration offset between the C-band and MMCR that is small and positive (ie theC-band reflectivity is greater than that from the MMCR)

(b) C-band calibration scan strategy and quality controlWe estimate that the C-band absolute calibration is within plusmn25 dBZ In addition to

the above comparison that shows C-band data are consistent with the MMCR two otherindependent comparisons were performed with radar data from the first leg of the EPICcruise immediately prior to EPIC Sc Radar data were compared to TRMM precipitationradar data and no apparent biases were found (Petersen et al 2003) Mapes andLin (2005) estimated divergence profiles from the C-band radar data using severalassumptions to compute moisture convergence Using different ZndashR relationshipsthey found that the calibration offset was likely to be in the range 20 to 27 dBZOur estimation of plusmn25 dBZ is consistent with this result


16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)

Figure A2 (a) Time series of hourly-averaged millimetre-wavelength radar (MMCR) cloud-base reflectivity(dashed) and hourly area-averaged C-band radar reflectivity (solid) A threshold of 17 dBZ was imposed on theC-band reflectivity (shown here C-band 17 dBZ) (b) Time series of the ratio of C-band actual hourly area-

averaged reflectivity (Z) to C-band thresholded reflectivity Time is UTC See text for details

The C-band radar scan strategy for EPIC Sc was designed to obtain high-resolutiontemporal and spatial data of the mesoscale structure of drizzling Sc Constraints onthe radar sampling were the small size of the features of interest a cloud-top heightless than 15 km and a radar echo depth of 500ndash1000 m These constraints combinedwith the 095 beam width of the C-band radar antenna limited volumetric observationsof research quality to within 50 km radius of the ship and the minimum usableelevation angle to 1 Due to erroneous values in the signal-processing software themaximum range of the volume and RHI scans was reduced to 30 km The centrepiece ofEPIC Sc C-band scan strategy was an 11 elevation-angle volume scan every 5 minutesVolume scans were interspersed with vertical cross-sections six times an hour and long-range surveillance scans every 30 minutes

Over 3100 radar volume scans were obtained during EPIC Sc An automatedquality-control algorithm originally developed for TEPPS was fine-tuned to removequestionable echoes in the recorded reflectivity data

(c) C-band antenna stabilization and interpolation of data to a 2-D gridScanning radar observations from a ship requires antenna stabilization to maintain

the antenna pointing angle at the requested elevation with respect to the horizon indepen-dent of the motion of the ship On the RHB a Seapath Inertial Navigation Unit providesthe SIGMET Inc RCP02 antenna controller with information to perform the antennastabilization and to remove the ship motion from the recorded radial velocity data


There is usually a lt04 discrepancy between the requested angle and the antennapointing angle There were some concerns about potentially larger pointing-angleerrors during EPIC Sc impacting the interpolated reflectivity maps consequently forthe purposes of this paper the reflectivity values were averaged between 05 and 2 kmto yield a 2-D dataset that circumvents this issue

The 3-D polar coordinate volume scan data were interpolated to a 2-D Cartesianhorizontal grid utilizing the National Center for Atmospheric Research AtmosphericTechnology Divisionrsquos REORDER software with Cressman (1959) interpolationREORDER uses the beam by beam recorded pointing angle and is well suited to dataobtained from moving platforms The interpolated Cartesian grid has 500 m spacing inthe horizontal and extends to 60 km diameter The weight (W ) of a particular radar rangegate in deriving the grid point is calculated as follows (Oye and Case 1992)

W = L2 minus l2

L2 + l2 (A1)

where l is the distance between the centre of the polar coordinate gate and the centre ofthe Cartesian grid point and L is the radius of influence

L2 = dX2 + dY 2 + dZ2 (A2)

where dX dY and dZ were set to be a function of range from the radar a delta azimuthof 06 and a delta elevation of 15 Data below 500 m altitude are not used in theinterpolation due to potential sea clutter contamination The interpolation weights (A1)peak at 500 m altitude and decrease with increasing altitude

APPENDIX BSTATISTICS FOR ZndashR RELATIONSHIPS

Table B1 compares ZndashR relationships of the form Z = aRb derived from differentstratocumulus datasets Cloud-base and surface ZndashR relationships will differ partlydue to differences in data sources For example considerable sampling limitations foraircraft data result in poor sampling of the largest drops These are estimated usingexponential extrapolation as discussed in section 2(b) The primary effect of this in theZndashR relation is a smaller exponent b shown in Table B1

APPENDIX CSEDIMENTATIONndashEVAPORATION MODEL

(a) Model formulationFor a drizzle drop larger than about 20 microm radius the evaporation rate below cloud

base is linearly proportional to the degree of subsaturation and inversely proportionalto its radius (Pruppacher and Klett 1997) The constant of proportionality is a fairlyweak function of temperature T and pressure p and it is assumed to be constantfor the conditions of this study (T = 286 K p = 900 hPa) We model profiles of thesize distribution N(r z) of a population of sedimenting evaporating drops via theequilibrium relationship

ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)


TABLE B1 STATISTICS FOR ZndashR RELATIONSHIPS OF THE FORM Z = aRb

1 EPIC filter-paper Aircraft Aircraft MMCR(surface) (cloud) no extrapolation (cloud base)

2 Best exponent b 11 14 11 133 Mean a 57 32 22 254 p16th a 38 17 18 115 p84th a 86 61 28 546 Cumulative bias 106 099 112 0837 Average bias 107 112 103 117

Rows in the table represent1 Datasets used The columns here are EPIC (Eastern Pacific Investigation of Climate

2001) Sc filter-paper UK Met Office aircraft in cloud Aircraft without using exponentialextrapolation to estimate large drop concentrations cloud-base parameters derived fromMMCR (millimetre-wavelength cloud radar)

2 The best exponent b from linear least-squares regression rounded to the nearest tenth3 Mean value of a from least-squares regression4 16th percentile value of a from 10log aminusstdev(log a)5 84th percentile value of a from 10log aminusstdev(log a)6 Cumulative bias for all drop size distribution (DSD) samples in the datasetsum

Restsum

Rcalc where Rest is estimated from the ZndashR relationship and Rcalc iscalculated from the DSD for each sample

7 Average bias (1N)sum

(RestRcalc) where N is the total number of DSD samples in thedataset (for further discussion see Hagen and Yuter 2003)

where ωT(r) is the terminal velocity of a drop of radius r (eg Hall 1980 his Eq (29)retaining only evaporationcondensation and vertical advection terms with no timedependence) We use an exponential distribution truncated at a lower radius of r0 =20 microm in (3) as the cloud-base boundary condition Leg- and level-averaged droplet-size distributions in Sc are described well by an exponential distribution (Wood 2005)

We assume that RH is unity at cloud base and decreases linearly below cloud basewith a rate 036 kmminus1 the median gradient from rawinsonde profiles during EPIC ScDeviations from this RH profile will alter evaporation rates necessitating differentvalues of k in (4) as illustrated in Fig C1 One standard-deviation values of dRHdzare 026 and 046 kmminus1 these lead to a RMS fractional error in RCB of only 11 at anyone time We did not find a strong correlation between drizzle and the value of dRHdzso errors in RCB will tend not to be correlated with RCB Because the ZndashR relationshipis nearly linear introducing a random uncorrelated error in dRHdz leads to only smallchanges in the ZndashR relationship

We use a single power-law terminal-velocity relationship in the model (see (6))Ventilation coefficients are taken from Pruppacher and Klett (1997) and increase almostlinearly from approximately unity at r = 20 microm to 52 at r = 500 microm Finally weassume that the drops are falling below cloud in still air ie there are no turbulentmotions Turbulent motions are responsible for the growth and development of thedrizzle DSD within cloud (Nicholls 1987 Baker 1993 Austin et al 1995) No directobservational evidence exists to show how the sizes and concentrations of drizzle dropsare correlated with vertical wind fluctuations in the cloud-base and sub-cloud regionsThere may be considerable errors associated with the still-air assumption This isaddressed below in subsection (b) but requires more investigation both in observationsand models

We calculate N(r z) numerically by solving (C1) as a function of height belowcloud for the temperature range 270ndash290 K and for cloud-base mean radius r from30ndash80 microm which covers the range of MMCR observations We then calculate the


00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078

increasing stratificationsuppressed evaporation

Median dRHdz for EPIC

Figure C1 Values of k in (4) (given as kes in figure) as a function of relative-humidity gradient below cloud(dRHdz) The median RH gradient for EPIC corresponds to k = 320 microm375mminus15 The curve represents a fit to

results from the sedimentationndashevaporation model (diamonds) for different RH gradients See text for details

precipitation rate normalized with its cloud-base value as a function of distance belowcloud base The rate of decrease in rain rate with height is lower when the meanradius is larger because larger drops fall faster and evaporate more slowly A goodparametrization of the model results is provided in (4)

Results from the sedimentationndashevaporation model are presented in Fig C2which shows normalized profiles of rain rate RRCB against the height parameterχ = (zCB minus z)(r)2515 that best collapses the different model conditionsThe parametrization of (4) is also shown and clearly represents a good fit to themodel results over the range of cloud-base mean radii typical in drizzling Sc cloudsFigure C2(b) shows the relationship between RRCB and ZZCB together with theparametrization expressed in (5)

(b) Sources of error and considerationsThe spread in observational values is a result of two main factors (i) there is

considerable spatial variability in the cloud-base height (ii) turbulent mixing in thecloudndashsub-cloud layer can alter the drizzle drop profiles The latter was also noted byNicholls (1987) who compared sub-cloud DSDs with the results of a numerical modelNichollsrsquo model assumes still air beneath cloud base and results in drop concentrationsdecreasing faster with height below base than those measured However we find thatthe simple sedimentationndashevaporation model can reproduce fairly well the observeddecrease in precipitation rate below cloud base

Vali et al (1998) present the only observations published to date of correlationsbetween radar reflectivity and vertical wind from three cases of marine stratusScIn the sub-cloud region these correlations are of the order minus025 The correlations arenegative because in the sub-cloud layer there is a positive gradient of reflectivity with


00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)

Figure C2 Results from the sedimentationndashevaporation model (a) profiles of normalized rain rate RRCBagainst the normalized height parameter χ from the model (thin lines) together with the analytical parametrization(thick solid line) in (4) (b) RRCB plotted against normalized radar reflectivity ZZCB from the model (thin lines)together with the analytical parametrization (thick solid line) The key in (a) also applies to (b) but similarities are

such that many lines are effectively superimposed See text for details

height and a downward turbulent transport of drizzle drops from the more reflectivecloud layer The correlations result in profiles of R that decrease less rapidly withheight (for a given ensemble mean r) than profiles with no correlation Thereforeusing a still-air value of k (see (4)) to derive r results in an overestimate if negativecorrelations between reflectivity and vertical wind are neglected We simulate theeffect of such a negative correlation between reflectivity and vertical wind using anensemble of 100 realizations of the sedimentationndashevaporation model with a rangeof updraughts and downdraughts A constant vertical-wind standard deviation σw =06 m sminus1 is used which is representative of turbulence in relatively deep cloud-toppedMBLs Observations from the MMCR suggest that in time-scales less than an hourthe standard deviation of the radar reflectivity is approximately 5ndash10 dBZ The modelsize distributions are initialized to give an ensemble of parcels with these statisticalproperties We also assume that the updraughtsdowndraughts are coherent through thedepth of the sub-cloud layer Using these ensembles the approximate overestimate ofr depends upon the magnitude of r decreasing as r increases with errors of 30 15and 5 for r = 40 55 and 75 microm respectively These overestimates in r propagate tooverestimates in RCB of 67 35 and 12 respectively and corresponding underestimatesof Rsfc of a similar magnitude These errors while non-negligible are somewhat lowerthan the uncertainties associated with the C-band calibration (see appendix A)

APPENDIX DDERIVATION OF AN EXPRESSION FOR b

We define u = log ND and v = log r to be normally distributed with standarddeviations σu = log ND and σv = σlog r respectively We wish to find the least-squaresoptimal value of the exponent b in the relationship ZCB = aRb

CB where log(ZCB) =u + β1v and log(RCB) = u + β2v from (14) and (15) Taking the logarithm of the ZndashRrelationship with log(ZCB) as the independent variable as in (2) the optimal value of b


is given by (eg Press et al 1992)

b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2

v + 2β1σuσvrlog ND log r

σ 2u + β2

2σ 2v + 2β2σuσvrlog ND log r

12

which results in the expression given in (16)

REFERENCES

Austin P Wang Y Pincus R andKujala V

1995 Precipitation in stratocumulus clouds Observations and modelingresults J Atmos Sci 52 2329ndash2352

Baker M B 1993 Variability in concentrations of cloud condensation nuclei in themarine cloud-topped boundary layer Tellus 45B 458ndash472

Bower K N Choularton T WBaker M B Blyth ANelson J and Jensen J

1992 lsquoMicrophysics of warm clouds measurements and discussionrsquoP 133 in Proceedings of the 11th international confer-ence on clouds and precipitation Montreal Canada Interna-tional Association of Meteorology and Atmospheric PhysicsToronto Canada

Bretherton C S Austin P andSiems S T

1995 Cloudiness and marine boundary layer dynamics in the ASTEXLagrangian experiments Part II Cloudiness drizzle surfacefluxes and entrainment J Atmos Sci 52 2724ndash2735

Bretherton C S Uttal TFairall C W Yuter S EWeller R ABaumgardner DComstock K and Wood R

2004 The EPIC 2001 stratocumulus study Bull Am Meteorol Soc 85967ndash977

Campos E and Zawadzki I 2000 Instrumental uncertainties in ZndashR relations J Appl Meteorol39 1088ndash1102

Cressman G P 1959 An operational objective analysis system Mon Weather Rev 87367ndash374

Doelling I G Joss J and Riedl J 1998 Systematic variations of ZndashR relationships from drop size distri-butions measured in northern Germany during seven yearsAtmos Res 47ndash48 635ndash649

Dong X and Mace G G 2003 Arctic stratus cloud properties and radiative forcing derived fromground-based data collected at Barrow Alaska J Climate16 445ndash460

Fairall C W Hare J E andSnider J B

1990 An eight-month sample of marine stratocumulus cloud fractionalbedo and integrated liquid water J Climate 3 847ndash864

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

Hagen M and Yuter S E 2003 Relations between radar reflectivity liquid water content andrainfall rate during the MAP-SOP Q J R Meteorol Soc129 477ndash493

Hall W 1980 A detailed microphysical model within a two-dimensionaldynamic framework Model description and preliminaryresults J Atmos Sci 37 2486ndash2507

Jensen J B Lee SKrummel P B Katzfey Jand Gogoasa D

2000 Precipitation in marine cumulus and stratocumulus Part IThermodynamic and dynamic observations of closed cellcirculations and cumulus bands Atmos Res 54 117ndash155

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

Joss J Schram K Thams J Cand Waldvogel A

1970 lsquoOn the quantitative determination of precipitation by radarrsquoScientific Report 63 Eidgenossische Kommission zumStudium der Hagelbildung und der Hagelabwehr ZurichSwitzerland

Khairoutdinov M F andKogan Y L

2000 A new cloud physics parametrization in a large-eddy simulationmodel of marine stratocumulus Mon Weather Rev 128229ndash243


Klein S A and Hartmann D L 1993 The seasonal cycle of low stratiform clouds J Climate 61587ndash1606

Li X and Srivastava R C 2001 An analytical solution for raindrop evaporation and its applica-tion to radar rainfall measurements J Appl Meteorol 401607ndash1616

Mapes B E and Lin J 2005 Doppler radar observations of mesoscale wind divergence inregions of tropical convection Mon Weather Rev in press

Marshall J S and Palmer W M 1948 The distribution of raindrops with size J Meteorol 5 165ndash166Miller M A and Albrecht B A 1995 Surface-based observations of mesoscale cumulusndashstratocumulus

interaction during ASTEX J Atmos Sci 52 2809ndash2826Moran K P Martner B E

Post M J Kropfli R AWelsh D C andWidener K B

1998 An unattended cloud-profiling radar for use in climate researchBull Am Meteorol Soc 79 443ndash455

Nicholls S 1987 A model of drizzle growth in warm turbulent stratiform cloudsQ J R Meteorol Soc 113 1141ndash1170

OrsquoConnor E J Hogan R J andIllingworth A J

2004 Retrieving stratocumulus drizzle parameters using Doppler radarand lidar J Appl Meteorol in press

Oye D and Case M 1992 lsquoREORDERmdashA program for gridding radar data Installation anduser manual for the UNIX versionrsquo Available from NCARATD Boulder CO USA

Pawlowska H and Brenguier J-L 2003 An observational study of drizzle formation in stratocumulusclouds for general circulation model (GCM) parameteriza-tions J Geophys Res 108 803ndash821

Petersen W A Cifelli RBoccippio D JRutledge S A and Fairall C

2003 Convection and easterly wave structures observed in the easternPacific warm pool during EPIC-2001 J Atmos Sci 601754ndash1773

Philander S G H Gu DHalpern D Lambert GLau N-C Li T andPacanowski R C

1996 Why the ITCZ is mostly north of the equator J Climate 92958ndash2972

Press W H Teukolsky S AVetterling W T andFlannery B P

1992 Numerical recipes in Fortran The art of scientific computingSecond edition Cambridge University Press CambridgeUK

Pruppacher H R and Klett J D 1997 Microphysics of clouds and precipitation Second edition KluwerAcademic Publishers Dordrecht the Netherlands

Rinehart R E 1997 RADAR for meteorologists Third edition Rinehart PublicationsGrand Forks North Dakota USA

Rogers R R and Yau M K 1989 A short course in cloud physics Third edition ButterworthndashHeinemann Oxford UK

Ryan M Post M J Martner BNovak J and Davis L

2002 lsquoThe NOAA Ron Brownrsquos shipboard Doppler precipitationradarrsquo In Proceedings of the sixth symposium on integratedobserving systems Orlando Florida January 2002American Meteorological Society Boston USA

Slingo A 1990 Sensitivity of the earthrsquos radiation budget to changes in lowclouds Nature 343 49ndash51

Smith P L and Joss J 1997 lsquoUse of a fixed exponent in lsquoadjustablersquo ZndashR relationshipsrsquoPp 254ndash255 in Preprints of the 28th conference onradar meteorology Austin Texas American MeteorologicalSociety Boston USA

Smith P L Liu Z and Joss J 1993 A study of sampling variability effects in raindrop size observa-tions J Appl Meteorol 32 1259ndash1269

Steiner M and Smith J A 2000 Reflectivity rain rate and kinetic energy flux relationships basedon raindrop spectra J Appl Meteorol 39 1923ndash1940

Steiner M Smith J A andUijlenhoet R

2004 A microphysical interpretation of the radar reflectivityndashrain raterelationship J Atmos Sci 61 1114ndash1131

Stephens G L Vane D GBoain R J Mace G GSassen K Wang ZIllingworth A JOrsquoConnor E JRossow W B Durden S LMiller S D Austin R TBenedetti A and Mitrescu C

2002 The CloudSat mission and the A-Train Bull Am Meteorol Soc83 1771ndash1790


Stevens B Lenschow D HVali G Gerber HBandy A Blomquist BBrenguier J-LBretherton C S Burnet FCampos T Chai SFaloona I Friesen DHaimov S Laursen KLilly D K Loehrer S MSzymon Malinowski PMorley B Petters M DRogers D C Russell LSavic-Jovcic V Snider J RStraub DMarcin Szumowski JTakagi H Thornton D CTschudi M Twohy CWetzel M andvan Zanten M C

2003 Dynamics and chemistry of marine stratocumulusmdashDYCOMS IIBull Am Meteorol Soc 84 579ndash593

Tripoli G J and Cotton W R 1980 A numerical investigation of several factors contributing to theobserved variable intensity of deep convection over southFlorida J Appl Meteorol 19 1037ndash1063

Turton J D and Nicholls S 1987 A study of the diurnal variation of stratocumulus using a multiplemixed layer model Q J R Meteorol Soc 113 969ndash1009

Vali G Kelly R D French JHaimov S Leon DMcIntosh R E andPazmany A

1998 Finescale structure and microphysics of coastal stratus J AtmosSci 55 3540ndash3564

Wood R 2005 Drizzle in stratiform boundary layer clouds Part I Vertical andhorizontal structure J Atmos Sci in press

Yuter S E and Parker W S 2001 Rainfall measurement on ships revisited The 1997 PACS TEPPScruise J Appl Meteorol 40 1003ndash1018

Yuter S E Serra Y L andHouze R A

2000 The 1997 Pan American climate studies tropical easternPacific process study Part II Stratocumulus region BullAm Meteorol Soc 81 483ndash490


aboard the National Oceanic and Atmospheric Administration (NOAA) ship the RonaldH Brown (RHB) to obtain areal information on the structure of the drizzling ScDuring EPIC Sc the RHB was also equipped with a NOAA Environmental TechnologyLaboratory (ETL) vertically pointing millimetre-wavelength cloud radar (MMCR) amicrowave radiometer and a suite of other instruments for sampling the ocean andatmospheric boundary layer We use the C-band radar data from EPIC Sc in conjunctionwith a derived relationship between radar reflectivity (Z) and rain rate (R) to obtain arealaverage drizzle statistics MMCR data are used to examine below-cloud evaporation ofdrizzle The radar data used in this study are unique because of the shiprsquos location withinthe south-east Pacific Sc region the sample duration of several days and the large areasampled by the scanning radar

Previous field studies of drizzling Sc have used aircraft radar and in situ data toestimate rain rates along and near the flight track (eg Austin et al 1995 Vali et al 1998Stevens et al 2003) and surface-based vertically pointing radar to obtain profiles ofprecipitation characteristics (eg Miller and Albrecht 1995) Because no in situ clouddata were available for this campaign data obtained on 12 flights in the north-eastAtlantic between 1990 and 2000 aboard the UK Met Office C-130 aircraft (Wood 2005)are used for verification and comparison of our techniques and results

The data used in our analysis are described in section 2 and the procedure forobtaining ZndashR relationships is outlined in section 3 Section 3 also includes an ex-amination of below-cloud evaporation of drizzle using an evaporationndashsedimentationmodel In section 4 the effect of evaporation on the parameters in the ZndashR relationshipsis discussed Also in section 4 reflectivity and rain rate are each expressed as functionsof drizzle drop number concentration and mean size and these are used as additionalmeans to estimate the exponent b in the ZndashR relationship Z = aRb where a and b areconstants We show that all of our datasets and methods yield similar ZndashR relationshipsfor Sc drizzle In section 5 the ZndashR relations are applied to EPIC and TEPPS C-bandradar data to estimate rainfall amounts their probability distribution at cloud base andthe quantity of rainfall reaching the surface We also determine an empirical relationshipamong rain rate liquid-water path and droplet concentration that will be useful in thedevelopment of model parametrizations of drizzle

2 DATA

(a) Filter-paper data samplesFilter-paper treated with a water-sensitive dye (methylene blue or lsquometh bluersquo) is

a time-tested but labour-intensive technique for observing rain drop-size distributions(DSDs) Filter-paper DSD samples were taken aboard the RHB because ship vibrationsinterfere with disdrometer measurements and the shiprsquos rain-gauges were not sensitiveto small amounts of drizzle (Yuter and Parker 2001) During EPIC Sc the 238 cmdiameter filter-paper was exposed to precipitation for a timed duration (up to 2 minutes)and the drops were counted and categorized by hand into eight evenly spaced binsbetween 01 and 08 mm radius establishing a DSD for each sample The preparationand collection of filter-paper samples is described by Rinehart (1997) The range ofresolvable drop sizes is assumed to be sufficient to determine a ZndashR relationshipThe minimum detectable drop size is 01 mm radius During the EPIC Sc cruise33 samples were collected during 23 separate drizzle episodes When possible twosamples were collected in sequence to check the consistency of the DSD Six filter-paper samples were also analysed from the TEPPS Sc cruise














Z = aRb (1)






log R = 1








CB


105

104

103

102

101

100

101

30

20

10

0

10

20

30

R [mm hr 1]

Z [

dBZ

]













NCB(r) = ND




R(z)




Z(z)

ZCBasymp

(R(z)

RCB

)q

(5)





ωT(r) = ATrd (6)



Z(z)




001 010 100Z(z)ZCB

-0020

-0015

-0010

-0005

0000

- [

m1

5

m-3

75]








nsumi=0

(r0

r minus r0

)i 1

i (8)



0

500

1000

1500

hei

ght

[m]

cloudbase

NO DRIZZLE

LIGHT

DRIZZLE

HEAVY

DRIZZLE

MMCR

Eqn 4




RCB = 4πρw




ZCB = 25R13CB (10)







median error

(a)

(b)



to

ZCB = a

(R(z)

c(χ)

)b

(11)






106

104

102

100

102

20

15

10

5

0

5

10

15

20

25

30

R(z) [mm hr 1]

ZC

B [

dBZ

]








ZCB = 302R09sfc (13)












ZCB = α1M6

RCB = α2Md+3(14)



M6 asymp ND(r)β1




(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES


















































































Z = aRb (1)






log R = 1








CB


105

104

103

102

101

100

101

30

20

10

0

10

20

30

R [mm hr 1]

Z [

dBZ

]













NCB(r) = ND




R(z)




Z(z)

ZCBasymp

(R(z)

RCB

)q

(5)





ωT(r) = ATrd (6)



Z(z)




001 010 100Z(z)ZCB

-0020

-0015

-0010

-0005

0000

- [

m1

5

m-3

75]








nsumi=0

(r0

r minus r0

)i 1

i (8)



0

500

1000

1500

hei

ght

[m]

cloudbase

NO DRIZZLE

LIGHT

DRIZZLE

HEAVY

DRIZZLE

MMCR

Eqn 4




RCB = 4πρw




ZCB = 25R13CB (10)







median error

(a)

(b)



to

ZCB = a

(R(z)

c(χ)

)b

(11)






106

104

102

100

102

20

15

10

5

0

5

10

15

20

25

30

R(z) [mm hr 1]

ZC

B [

dBZ

]








ZCB = 302R09sfc (13)












ZCB = α1M6

RCB = α2Md+3(14)



M6 asymp ND(r)β1




(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES









































































Z = aRb (1)






log R = 1








CB


105

104

103

102

101

100

101

30

20

10

0

10

20

30

R [mm hr 1]

Z [

dBZ

]













NCB(r) = ND




R(z)




Z(z)

ZCBasymp

(R(z)

RCB

)q

(5)





ωT(r) = ATrd (6)



Z(z)




001 010 100Z(z)ZCB

-0020

-0015

-0010

-0005

0000

- [

m1

5

m-3

75]








nsumi=0

(r0

r minus r0

)i 1

i (8)



0

500

1000

1500

hei

ght

[m]

cloudbase

NO DRIZZLE

LIGHT

DRIZZLE

HEAVY

DRIZZLE

MMCR

Eqn 4




RCB = 4πρw




ZCB = 25R13CB (10)







median error

(a)

(b)



to

ZCB = a

(R(z)

c(χ)

)b

(11)






106

104

102

100

102

20

15

10

5

0

5

10

15

20

25

30

R(z) [mm hr 1]

ZC

B [

dBZ

]








ZCB = 302R09sfc (13)












ZCB = α1M6

RCB = α2Md+3(14)



M6 asymp ND(r)β1




(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES






































































105

104

103

102

101

100

101

30

20

10

0

10

20

30

R [mm hr 1]

Z [

dBZ

]













NCB(r) = ND




R(z)




Z(z)

ZCBasymp

(R(z)

RCB

)q

(5)





ωT(r) = ATrd (6)



Z(z)




001 010 100Z(z)ZCB

-0020

-0015

-0010

-0005

0000

- [

m1

5

m-3

75]








nsumi=0

(r0

r minus r0

)i 1

i (8)



0

500

1000

1500

hei

ght

[m]

cloudbase

NO DRIZZLE

LIGHT

DRIZZLE

HEAVY

DRIZZLE

MMCR

Eqn 4




RCB = 4πρw




ZCB = 25R13CB (10)







median error

(a)

(b)



to

ZCB = a

(R(z)

c(χ)

)b

(11)






106

104

102

100

102

20

15

10

5

0

5

10

15

20

25

30

R(z) [mm hr 1]

ZC

B [

dBZ

]








ZCB = 302R09sfc (13)












ZCB = α1M6

RCB = α2Md+3(14)



M6 asymp ND(r)β1




(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES








































































NCB(r) = ND




R(z)




Z(z)

ZCBasymp

(R(z)

RCB

)q

(5)





ωT(r) = ATrd (6)



Z(z)




001 010 100Z(z)ZCB

-0020

-0015

-0010

-0005

0000

- [

m1

5

m-3

75]








nsumi=0

(r0

r minus r0

)i 1

i (8)



0

500

1000

1500

hei

ght

[m]

cloudbase

NO DRIZZLE

LIGHT

DRIZZLE

HEAVY

DRIZZLE

MMCR

Eqn 4




RCB = 4πρw




ZCB = 25R13CB (10)







median error

(a)

(b)



to

ZCB = a

(R(z)

c(χ)

)b

(11)






106

104

102

100

102

20

15

10

5

0

5

10

15

20

25

30

R(z) [mm hr 1]

ZC

B [

dBZ

]








ZCB = 302R09sfc (13)












ZCB = α1M6

RCB = α2Md+3(14)



M6 asymp ND(r)β1




(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES








































































ωT(r) = ATrd (6)



Z(z)




001 010 100Z(z)ZCB

-0020

-0015

-0010

-0005

0000

- [

m1

5

m-3

75]








nsumi=0

(r0

r minus r0

)i 1

i (8)



0

500

1000

1500

hei

ght

[m]

cloudbase

NO DRIZZLE

LIGHT

DRIZZLE

HEAVY

DRIZZLE

MMCR

Eqn 4




RCB = 4πρw




ZCB = 25R13CB (10)







median error

(a)

(b)



to

ZCB = a

(R(z)

c(χ)

)b

(11)






106

104

102

100

102

20

15

10

5

0

5

10

15

20

25

30

R(z) [mm hr 1]

ZC

B [

dBZ

]








ZCB = 302R09sfc (13)












ZCB = α1M6

RCB = α2Md+3(14)



M6 asymp ND(r)β1




(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES






































































001 010 100Z(z)ZCB

-0020

-0015

-0010

-0005

0000

- [

m1

5

m-3

75]








nsumi=0

(r0

r minus r0

)i 1

i (8)



0

500

1000

1500

hei

ght

[m]

cloudbase

NO DRIZZLE

LIGHT

DRIZZLE

HEAVY

DRIZZLE

MMCR

Eqn 4




RCB = 4πρw




ZCB = 25R13CB (10)







median error

(a)

(b)



to

ZCB = a

(R(z)

c(χ)

)b

(11)






106

104

102

100

102

20

15

10

5

0

5

10

15

20

25

30

R(z) [mm hr 1]

ZC

B [

dBZ

]








ZCB = 302R09sfc (13)












ZCB = α1M6

RCB = α2Md+3(14)



M6 asymp ND(r)β1




(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES







































































0

500

1000

1500

hei

ght

[m]

cloudbase

NO DRIZZLE

LIGHT

DRIZZLE

HEAVY

DRIZZLE

MMCR

Eqn 4




RCB = 4πρw




ZCB = 25R13CB (10)







median error

(a)

(b)



to

ZCB = a

(R(z)

c(χ)

)b

(11)






106

104

102

100

102

20

15

10

5

0

5

10

15

20

25

30

R(z) [mm hr 1]

ZC

B [

dBZ

]








ZCB = 302R09sfc (13)












ZCB = α1M6

RCB = α2Md+3(14)



M6 asymp ND(r)β1




(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES






































































median error

(a)

(b)



to

ZCB = a

(R(z)

c(χ)

)b

(11)






106

104

102

100

102

20

15

10

5

0

5

10

15

20

25

30

R(z) [mm hr 1]

ZC

B [

dBZ

]








ZCB = 302R09sfc (13)












ZCB = α1M6

RCB = α2Md+3(14)



M6 asymp ND(r)β1




(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES






































































106

104

102

100

102

20

15

10

5

0

5

10

15

20

25

30

R(z) [mm hr 1]

ZC

B [

dBZ

]








ZCB = 302R09sfc (13)












ZCB = α1M6

RCB = α2Md+3(14)



M6 asymp ND(r)β1




(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES













































































ZCB = α1M6

RCB = α2Md+3(14)



M6 asymp ND(r)β1




(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES






































































(a) (b)

(c)




b = 1

rlog R log Z

1 + β2

1σ 2log r

σ 2log ND


1 + β22σ 2

log rσ2log ND


12

(16)

where σ 2log ND

and σ 2log r


log ND σ 2


















log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES





















































































log(Z or R)= σ 2

log ND+ β2σ 2

log r




16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES






































































16 17 18 19 20 21 220

4

8

12R

[m

m d

ay1 ]

Day in October 2001

Cloud Base Surface


5 IMPLICATIONS
























(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES























































































(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES






































































(a) (b)





RCB = 00156(LWPNd)175 (17)



01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES






































































01 10 100LWPN d [g m-2 cm3]

0001

0010

0100

R(z

C

B ) [

mm

hr

-1 ]





6 CONCLUSIONS








ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES










































































ACKNOWLEDGEMENTS













16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES













































































16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES






































































16 17 18 19 20 21 20 10

0

10re

flec

tivi

ty [

dBZ

]C bandMMCR

16 17 18 19 20 21

10

12

14

16

18

20

Day in October 2001

(a)

(b)










W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES








































































W = L2 minus l2

L2 + l2 (A1)


L2 = dX2 + dY 2 + dZ2 (A2)







ωT(r)partN(r z)

partz= minus part

partr

(N(r z)

Dr

Dt

) (C1)








Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES












































































Restsum









00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES






































































00 02 04 06 08dRHdz [km-1]

0

200

400

600

kes

sed-evap model

kes=704(dRHdz)078











00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES






































































00 02 04 06 08 10R(z)RCB

-0015

-0010

-0005

0000

- [

m-1

5

m-3

75 ]

Sed-evap model

r = 35 m__

r = 45 m__

r = 55 m__

r = 65 m__

r = 75 m__

00 02 04 06 08 10R(z)RCB

00

02

04

06

08

10

Z(z

)Z

CB

Parametrization

(a) (b)









b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES







































































b = 1

rlog Z log R

σlog Z

σlog R

= 1

rlog Z log R

σ(u+β1v)

σ(u+β2v)

= 1

rlog Z log R

σ 2

u + β21σ 2


σ 2u + β2


12


REFERENCES



























































































































Documents

2. Dthan 2.5 dBZ enhancement of Z , though Z increased by 7.5 dBZ or more in 4% of the cases. O Connor et al. (2004) also found that the exponential distribution reasonably describedstratocumulus