Correction of Zdr Bias

S-Pol IHOP_2002, Oklahoma Panhandle
May/Jun 2002

Differential Reflectivity (Zdr) is a residual of two large quantities of limited absolute accuracy. The accuracies of the larger quantitiies (the H and V polarized system-derived reflectivities) is a function of system calibration and signal statistics. If the H and V reflectivity calibrations are stable, there is likely to be a bias in Zdr due to the inaccuracies of those reflectivity calibrations; under such circumstances, it is possible to apply a bias correction to Zdr, even if there is a relatively large uncertainty in the absolute calibration of the H and V subsystems.

Note that high accuracy in Zdr is desired when Zdr is applied to precipitation accumulation estimates. For precipitation estimates, a change of 0.3 dB in Zdr will result in a 17% change in estimated accumulation (as estimated from typical Z/Zdr algorithms).

For IHOP_2002, analysis indicates that there was a bias of -.08 dB in Zdr, and that this bias was stable throughout the field experiment. Variations in the bias estimate were small, on the order of .02 dB.

In light of the bias and the stability of that bias, ATD applied a bias correction of +.08 dB to Zdr for the entire period of the IHOP_2002 experiment. Details of the techniques used and individual bias analyses are provided.

Technique

To estimate Zdr bias, we require a well-characterized, non-biased, system-independent data set for analysis. Such a data set can be obtained from viewing rainfall at vertical incidence.

For purposes of Zdr bias estimation, there is no consistent axial asymmetry in raindrop shape when viewed from directly below. In the case of a strongly sheared environment, there might arguably be preferential orientation of a collection of hydrometeors. Fortunately, preferential orientation effects can be reliably removed by rotating the vertically pointing antenna in azimuth and averaging results over several rotations. It may also be surmised that ice crystals can serve for bias determination; experience with frozen hydrometeors shows that this is indeed the case, but that there is somewhat greater variablility in results (larger standard deviation in the Zdr spectrum, and somewhat greater variability introduced into the inter-case mean).

Antenna rotation is important for a second reason: neutralization of side-lobe effects. The antenna 90-degree side lobes can show a significant bias in Zdr when the antenna is pointed vertically. This bias is typically evident at a certain azimuth, and typically shows a repetition pattern with a 45 or 90 degree azimuthal periodicity (periodicity is dependent upon feedhorn strut location, as evidenced in the radar's antenna pattern). Under the best circumstances, rotation of the antenna, combined with sufficient averaging time (i.e., number of rotations), cancels out bias due to clutter. (For documentation of S-Pol 90° sidelobes, see S-Pol Sidelobe Artifacts)

Practical Considerations

• light precipitation at the radar
• precipitation-sized hydrometeors extend vertically for 5 to 10 kilometers
• radar dish not too wet from previous precipitation
• signal power return is not too great

• data collection period of 2 minutes or greater
• antenna is slowly rotated while looking vertically
• clutter filter is OFF (although clutter filter effects are generally acceptably small)

Every attempt is made to process appropriate cases in a very consistent way. Vertical-pointing scans are transferred to a data processing system. A script is used to drive the SOLO analysis package, performing parameter thresholding and general data selection, on through production of a histogram of Zdr values for qualifying data. The only operator interaction is in the definition of a broad boundary in order to time-window the data and to eliminate obvious artifacts.

Table 1 summarizes the automatic thresholding criteria applied to vertical pointing data. Note that original criteria used in the field during TRMM-LBA were different from the criteria detailed in the table. These modifications were made to bring procedure into conformance with enhancements introduced during MAP (Sep/Oct 1999). For TRMM-LBA, there is no substantive difference between early Zdr bias estimates and current Zdr bias estimates.

In Table 1, if two conditions are shown for the same threshold parameter, the more restrictive condition is used. In most cases, when two conditions are listed, the second condition indicates criteria that are specific to S-Pol, and may be adjusted for other radars or other S-Pol projects.

TABLE 1. Vertical Pointing for Zdr Bias Determination: threshold criteria

Description	Exclusion Condition	Reason
eliminate data when received power is too high	DM > -45.0 dBm	avoid regions of non-linear receiver response
	DM > -70.0 dBm	restrict data to a portion of receiver response that is most likely to be used during operational data collection; this limit is dictated in part by S-Pol automatic gain control (AGC)
eliminate data in regions of weak signal	DM < -105 dBm (flexible criteria)	limit variablity due to poor signal statistics
eliminate bright band and regions of wet hydrometeors	LDR > -13.0 dB	Zdr can have a very wide distribution in these regions
avoid regions close to radar	range < 1.2 km	eliminates regions of TR tube recovery, and selects data in far-field, only
	range < 3.0 km	eliminates regions of differential TR tube recovery, a special issue for the S-Pol receiver configuration
remove data above the atmosphere	range > 14.0 km	also eliminates inadvertant inclusion of S-Pol test pulse

Analysis

For IHOP_2002, only 5 separate events of vertical pointing were logged. Of these, one was considered to be unsuitable for use. Within the 5 events, subsets were occasionally deliniated and processed separately. These subsets provide an indicator of the short-term consistency of the procedure and results. All events are listed in Table 2. Each independent event is separated by a horizontal line; within each event, any subsets are shown on their own line. For determination of gross conclusions, subsets are first combined to provide a single set of event values. Within the table, links are provided to images of the data (time section of received power, DM, and Zdr, both raw and thresholded: ZDR or TZDR, respectively), or the histogram produced in the analysis.

TABLE 2. Determined values of Zdr Bias, by event.

Date	UTC	Zdr Bias mean sdev #pts	Zdr Test Pulse,dBm	Comment
020524	0122	-.05 0.31 14888	n/a	interesting side-lobe pattern in raw Zdr
020526	2346 2351	-.07 0.23 59091 -.08 0.20 30845	n/a n/a
020526	2346 2351	-.07 0.23 59091 -.08 0.20 30845	n/a n/a
020526	2346 2351	-.07 0.23 59091 -.08 0.20 30845	n/a n/a
020526	2346 2351	-.07 0.23 59091 -.08 0.20 30845	n/a n/a