Assign7 Radar Problems – solution

63. Assign7 Radar Problems – solution#

Reference: Stull Chapter 8

Answer the following questions in a Jupyter notebook, using a function to define the radar equation.

  1. Suppose a Nexrad radar (Stull p.~246) is receiving a signal with returned power Pr = -58 dBm. Using the radar equation find the precipitation rate under the assumption that there is no attenuation and that it is a rainstorm (i.e. liquid water) 100 km away from the radar.

  2. Now keep everything the same, but make the mistake of guessing that it’s a snowstorm, which means that K2=0.208 and we use the snowfall Z-RR relation of \(Z=2000*RR^2\). What is the new incorrect precip rate?

  3. Now assume it’s rain, but make the mistake of guessing that there’s a factor of La=2 attenuation between the target and the rainstorm. What is the new precip rate?

Nexrad coefficients:

    #coefficents for nexrad
    R1=2.17e-10#range factor, km, Stull 8.25
    Pt=750.e3 #transmitted power, W, stull p. 246
    b=14255 #equipment factor, Stull 8.26

import numpy as np
from numpy import log10
from numpy.testing import assert_almost_equal

63.1. Question 1#

Q1: Suppose a Nexrad radar (Stull p.~246) is receiving a signal with returned power Pr = -58 dBm. Using the radar equation find the precipitation rate under the assumption that there is no attenuation and that it is a rainstorm (i.e. liquid water) 100 km away from the radar.

63.1.1. Question 1 answer#

63.1.1.1. Radar functions#

Here is the radar equation: Stull 8.28

def finddbz(Pr,K2,La,R,R1=None,Pt=None,b=None):
   """calculate dbZ using Stull 8.28
      with Pr the returned power in Watts
   """
   dbZ=10.*log10(Pr/Pt) + 20.*log10(R/R1) - \
       10.*log10(K2/La**2.) - 10.*log10(b)
   return dbZ

and here is the rain rate equation: Stull 8.29

def findRR_rain(dbZ):
   """
    find the rain rate in mm/hr using Stull 8.29
    dbZ:  reflectivity in dbZ referenced to 1 mm^6/m^3
   """
   #given that for rain Z=300*RR**1.4
   #a1_rain=(1/300.)**(1/1.4) = 0.017
   #a2_rain=1/1.4  = 0.714
   Z=10**(dbZ/10.)
   a1_rain=0.017  
   a2_rain=0.714  
   RR=a1_rain*Z**a2_rain
   return RR

and here are the Nexrad radar constants from Stull p. 246, converted into a dictionary called nexrad

# stull p. 246 sample appliation
# given

#coefficents for nexrad
R1=2.17e-10#range factor, km, Stull 8.25
Pt=750.e3 #transmitted power, W, stull p. 246
b=14255 #equipment factor, Stull 8.26

nexrad=dict(R1=R1,Pt=Pt,b=b)

63.1.1.2. Set coefficients for problem 1#

We’re assuming -58 dBm so need to convert that to watts. Range is 100 km, no attenuation.

K2=0.93  #stull p. 245
Pr=10**(-5.8)*1.e-3  #dBm=-58, convert from mWatts to Watts
La=1  # no attenuation
R=100.  #km

63.1.1.3. Question 1 dbZ#

dbZ=finddbz(Pr,K2,La,R,**nexrad)
print(f"calculated dbZ is {dbZ=:6.1f} referenced to 1 mm^6/m^3")

calculated dbZ is dbZ=  45.3 referenced to 1 mm^6/m^3

63.1.1.4. Question 1 rain rate#

RR=findRR_rain(dbZ)
print(f"calculate rain rate is {RR=:6.1f} mm/hour")

calculate rain rate is RR=  29.1 mm/hour

63.2. Question 2#

Now keep everything the same, but make the mistake of guessing that it’s a snowstorm, which means that K2=0.208 and we use the snowfall Z-RR relation of \(Z=2000*RR^2\). What is the new incorrect precip rate?

63.2.1. Question 2 answer#

63.2.1.1. Radar functions#

def findRR_snow(dbZ):
   """
    find the rain rate in mm/hr Environment Canada's relation for snow
    dbZ:  reflectivity in dbZ referenced to 1 mm^6/m^3
   """
   #given that for snow Z=2000*RR**2. 
   a1_snow=0.02236   #(1/2000.)**(1./2.)
   a2_snow=0.5   #RR=(1/2000)**(1./2.)*Z**(1/2.)
   Z=10**(dbZ/10.)
   RR=a1_snow*Z**a2_snow
   return RR

63.2.1.2. Assume K2 for snow#

K2=0.208 #p. 245
dbZ=finddbz(Pr,K2,La,R,**nexrad)
RR=findRR_snow(dbZ)

63.2.1.3. Q2 dbZ assuming snow#

print(f"calculated dbZ is {dbZ=:6.1f} referenced to 1 mm^6/m^3")

calculated dbZ is dbZ=  51.8 referenced to 1 mm^6/m^3

63.2.1.4. Q2 RR assuming snow#

print(f"calculate rain rate is {RR=:6.1f} mm/hour")

calculate rain rate is RR=   8.7 mm/hour

63.3. Question 3#

Now assume it’s rain, but make the mistake of guessing that there’s a factor of La=2 attenuation between the target and the rainstorm. What is the new precip rate?

63.3.1. Question 3 answer#

63.3.1.1. Assume K2 for liquid, la=2#

K2=0.93 #p. 245
La=2.
dbZ=finddbz(Pr,K2,La,R,**nexrad)
RR=findRR_rain(dbZ)

63.3.1.2. dbZ assuming attenuation#

print(f"calculated dbZ is {dbZ=:6.1f} referenced to 1 mm^6/m^3")

calculated dbZ is dbZ=  51.3 referenced to 1 mm^6/m^3

63.3.1.3. Rain rate assuming attenuation#

print(f"calculate rain rate is {RR=:6.1f} mm/hour")

calculate rain rate is RR=  78.4 mm/hour
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