March 25, 2004 1Z, Z and Z-R Relationships 22222)2ln(1024 RCRcPGPtrηηπτθφλ== z425λκπη= ∑=VolumeUnitDz6 Radar equation for distributed targets Radar reflectivity Radar reflectivity factor (mm6/mm3) Combining these equations, we can write: 22RzcPr=, and rearrange to get: 23RPczr= c3 is the so-called radar constant. It has units mm6/m3 mW-1 km-2 . The radar reflectivity factor z has a tremendous dynamic range so it is convenient to express it on a decibel scale with a reference z = 1 mm6/m3 =)m/mm(1)m/mm(log10363610zZ with units dBZ Using this, we can write )(log2010323RPCZRPczrr++== where Z is measured in dBZ, C3 = 10log10(c3), Pr is measured in dBm, and R is in km. Marshall-Palmer DSD. 21.01.4−−==ReNNDoDλλ No = 8000 m-3 mm-1 R = rainrate in mm/h D = drop diameter in mmMarch 25, 2004 2Given a DSD one can compute a Z-R relationship. In practice, empirical relationships are used: iprelationsh MPor Palmer -Marshall 2006.1RZARZb== There are many relationship in use. The table below is from the NOAA ROC: Table 1. Z-R RECOMMENDATIONS RELATIONSHIP Optimum for: Also recommended for: Marshall-Palmer (z=200R1.6) General stratiform precipitation East-Cool Stratiform (z=130R2.0) Winter stratiform precipitation - east of continental divide Orographic rain - East West-Cool Stratiform (z=75R2.0) Winter stratiform precipitation - west of continental divide Orographic rain - West WSR-88D Convective (z=300R1.4) Summer deep convection Other non-tropical convection Rosenfeld Tropical (z=250R1.2) Tropical convective systems Sample Z-R relationships measured in Iowa (note the X-Y axis are switched between the graphs). 10010110210310410510610-210-1100101102103Reflectivity Z (mm6/m3)Rainrate R (mm/hr)Parsivel DataZ= 21 4 R1.7 5Sample: 1-minute integration interval Sample: 5-minute integration
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