Zdr Bias Determination for S-Pol in PECAN

Why a Bias Correction?

Zdr is the difference between the two co-polar reflectivities (Zdr = dBZH - dBZV). Since each of the two co-polar reflectivites is known only to (optimistically) the nearest half dB, there is a potential for a large bias in Zdr. The bias can be determined through measuring Zdr in light rain while the radar is pointed vertically. Under such conditions, all rain or snow should appear spherical, on average, and the Zdr values measured should also be zero dB (note: the antenna is rotated while pointing vertically to remove any effects due to particle alignment or non-zero canting angles). Note that this technique presumes a uniform distribution of hydrometeor acccross the main radar beam.  Also, the removal of bias does not remove random statistical Zdr errors. 

Bias in the measured Zdr can be removed in real-time using a constant bias correction obtained from vertical pointing measurements. For PECAN, changes to the radar system at the start of the experiment impacted the ability to apply a uniform correction for the entire project.  

For the first time an alternative technique was used to determine the Zdr bias for PECAN quality controlled data. The technique, termed the crosspolar power technique, uses the principle of radar reciprocity. The technique uses crosspolar power measurements, solar scans and estimates of S-Pol's antenna temperature. See Hubbert (2017) for details of this technique. For the PECAN data set it was determined that there was a high correlation between antenna temperature and Zdr bias and since the temperature of S-Pol's antenna was continuously monitored, the Zdr bias was corrected as a function of temperature. The bias dependency is close to 0.01 dB/degC.  The figure below shows the Zdr bias correction factor used for PECAN data as a function of time. 


Table of Vertical Pointing Determinations

Vertical pointing determinations were made on targets of opportunity when the radar was staffed (i.e., not in "remote operations"), and when such scanning would not intefere with critical project objectives.  This is the complete table of vertical pointing scans.  Note that in general, four rotations were considered to be adequate to obtain reliable statistics, so during some episodes of vertical pointing, multiple sets of determinations were made.

Date     Time     ngates    mean    mode  median std_dev  Dixon
                                                          Determination
20150523 144208   101200  -0.243  -0.230  -0.241  0.11                            
20150530 011525    26984  -0.306  -0.353  -0.304  0.22
20150530 012751     1305  -0.281  -0.835  -0.289  0.46
20150601 174824        2     n/a     n/a     n/a   n/a
20150603 203733        1     n/a     n/a     n/a   n/a
20150604 011119    41004  -0.279  -0.262  -0.282  0.22
20150604 194958
20150604 201409      633  -0.273  -0.369  -0.301  0.29
20150608 193939      170   0.067  -0.069  -0.071  0.69
20150611 002814   206051  -0.083  -0.063  -0.084  0.12
20150611 043654   226652  -0.103  -0.153  -0.104  0.14
20150614 201513    89849  -0.145  -0.161  -0.147  0.14
20150614 201916    42726  -0.142  -0.151  -0.145  0.18
20150614 205054    21035  -0.140  -0.159  -0.146  0.22
20150626 082812    95962   0.012   0.014   0.011  0.16
20150626 083215    94395  -0.002  -0.001  -0.003  0.16
20150627 163516      n/a     n/a     n/a     n/a   n/a
20150702 140332   106781   0.012   0.009   0.011  0.14
20150702 140734   106183   0.038   0.022   0.037  0.12
20150702 141137   110529   0.002  -0.025   0.000  0.11
20150702 141540   113391   0.002  -0.000   0.001  0.10
20150702 141942   130199   0.019   0.003   0.017  0.09
20150702 142345   131870   0.028   0.010   0.027  0.09
20150702 142748   110740  -0.016  -0.048  -0.018  0.09
20150702 143151    88742  -0.039  -0.034  -0.041  0.09
20150702 143553    78235  -0.027  -0.048  -0.028  0.09
20150702 143956    92678  -0.027  -0.048  -0.030  0.10
20150702 144359    70395  -0.024  -0.026  -0.024  0.11
20150702 144801    45872  -0.024  -0.040  -0.024  0.13
20150702 145204    13419  -0.031  -0.022  -0.027  0.16
20150702 184343    87869  -0.016   0.011  -0.016  0.15
20150702 184745    96915  -0.020  -0.065  -0.022  0.14
20150702 185148    91227  -0.015  -0.045  -0.018  0.15
20150702 185551    89517  -0.013  -0.050  -0.015  0.18
20150702 185954    39869  -0.019  -0.021  -0.020  0.20
20150706 160425    40873   0.009   0.006   0.002  0.20
20150706 160827    44068   0.016   0.014   0.015  0.21
20150706 161230    49661   0.013  -0.006   0.011  0.20
20150706 161633     6345   0.007  -0.050   0.003  0.18
20150706 163848   112328  -0.011  -0.026  -0.012  0.14
20150706 164250   102455  -0.008   0.018  -0.010  0.17
20150706 164653    73017  -0.006  -0.071  -0.008  0.21
20150706 165056    56530  -0.008  -0.022  -0.011  0.21
20150708 191935    65436   0.045  -0.024   0.043  0.25
20150708 192338    62341   0.045   0.001   0.041  0.27
20150708 192741    63077   0.040   0.057   0.038  0.26
20150708 193143    66764   0.041   0.085   0.039  0.25
20150708 193546    65706   0.049   0.032   0.047  0.26
20150708 193949    66449   0.041   0.116   0.038  0.28
20150714 002947    96567   0.154   0.144   0.152  0.15
20150714 003350    98705   0.153   0.161   0.150  0.14
20150714 003753    52402   0.152   0.158   0.151  0.14
20150714 010414   120482   0.137   0.138   0.136  0.12
20150714 010816   121310   0.138   0.158   0.136  0.13
20150716 032309   131917   0.023   0.030   0.023  0.12
20150716 032712    92912   0.030   0.033   0.029  0.13
20150716 150422       73     n/a     n/a     n/a   n/a
20150716 181455        1     n/a     n/a     n/a   n/a

 

There are multiple techniques within EOL/RSF for computing Zdr bias from vertical pointing. Each technique may use a slightly different data stream, or apply different screening criteria to the input data. All techniques produce results that are within a few hundredths of a dB of each other. Shown in the table, above, are the results by both Rilling and Dixon. The Dixon computation referenced in the table uses a reprocessing of the vertical pointing time series data, and (perhaps) incorporates too much data near the radar; LDR thresholds are fairly restrictive. Full results for the Dixon work are available.

The Rilling results use the following criteria:

  • Minimum range = 3.0 km (avoid differential T/R tube recovery near radar)
  • Max range = 15.0 km
  • Eliminate LDR > -20.0 dB (remove most wet ice, i.e, the bright band)
  • Eliminate H pwr < -100.0 dBm (avoid areas subject to noise power correction)
  • Eliminate H pwr > -47.0 dBm (stay away from receiver saturation)
  • Eliminate RHOHV < .96 (use reliable signal, only)

Within the table provided, above, a given set of results was ingored if there were too few points used in the computation, or if the distribution was highly skewed (the mode was not approximately the same as the mean). When computing an average bias, generally only one determination was used from a given set of runs, to avoid biasing results toward a sequence that had many repeat attempts.

Histogram Output

Matlab Code

Zdr histograms were generated using Matlab code. The code reads uncorrected field data directly from disk, applies appropriate spatial and gross signal quality filtering, and generates plots.

Example Plot

Additional Plots

Histograms for almost all vertical pointing attempts may be found here.

References

  • Gorgucci, E., Scarchilli, G and Chandrasekar, V.: A procedure to calibrate multiparameter weather radar using properties of the rain medium. IEEE Trans. Geosci. Remote Sens., 17. 269-276, 1999.
  • Rilling, R.A., J. Lutz, M. Randall and S. Ellis, 2001: Calibration of Zdr for an S-band polarimetric radar. 11th Symposium on Meteorolical Obs. and Inst., Amer. Meteor. Soc., P1.8
  • Hubbert, J.C., V.N. Bringi and D. Brunkow, 2003: Studies of the polarimetric covariance matrix: Part I: Calibration methodology. J. Atmos. and Oceanic Technol., 20, 696-706.
  • Hubbert, J., F. Pratte,M. Dixon, R. Rilling, and S. Ellis: 2006, Calibration of Zdr for NEXRAD. IGARSS- 2006, Denver, CO.
  • Hubbert, J.C., F. Pratte, M. Dixon and R. Rilling, 2007: Differential Reflectivity Calibration for NEXRAD. Interim Report Prepared for NEXRAD Product Improvement Program NWS, Office of Science and Technology
  • Hubbert, J. C., 2017: Differential reflectivity calibration and antenna temperature. J. Atmos. Oceanic Technol., https://doi.org/10.1175/JTECH-D-16-0218.1.
  • Frech, M, J.C. Hubbert 2020: Monitoring the differential reflectivity and receiver calibration of the German polarimetric weather radar network, Atmospheric Measurement Techniques, Copernicus, V13, pp 1051-1069, URL: https://amt.copernicus.org/articles/13/1051/2020/