Determination of Bias in Zdr

S-Pol TRMM-LBA, Brazil 1999

Importance of Bias Determination

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.

Since S-Pol is a research radar system, particular attention is given to ensuring the accuracy of all parameters. Every effort is made to minimize the error in Zdr, with the goal of obtaining accuracies of .2 dB, or better.

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 upper portion of receiver response, as selected by S-Pol automatic gain control (AGC)
eliminate data in regions of weak signal	DM < 100 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 TRMM-LBA, about 16 separate events of vertical pointing were logged. Of these, one was considered to be unsuitable for use, and three others were marginal. Within the 16 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 shows column entries for date and time, and Zdr bias statistics (mean value, standard deviation, and number of points). In addition, a correction to the determination is shown, as well as the final bias determination for each event. Test pulse information is included for completeness (actually, this has yet to be compiled), and a comment.

The correction to the bias determination comes about due to the fact that the determinations were made in log-space. The mean of the log distribution differs from the mean of the equivalent linear distribution by one-half the square of the standard deviation; when the distribution is well-behaved (as virtually all these are), a simple correction to the log-determined mean is appropriate.

The Results Section follows Table 2.

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

Date	UTC	Zdr Bias mean sdev #pts	Log Correction	True Zdr Bias (dB)	Zdr Test Pulse,dBm	Comment
990120	1810	-.01 0.21 33479	.02	0.01	n/a
990122	1847	-.06 0.22 4411	.02	-.04	n/a	fair case, only
990130	0330	-.07 0.29 10880	.04	-.03	n/a
990130	1754	-.02 0.33 5456	.05	0.03	n/a	fair case, only
990201	2121	-.08 0.32 9678	.05	-.03	n/a
990203	1400	-.08 0.24 14155	.03	-.05	n/a
990211	1206 1209	-.03 0.36 5039 -.03 0.39 3208	.06 .07	0.03 0.05	n/a n/a	fair case, only fair case, only
990212	1719	-.05 0.23 12628	.03	-.02	n/a
990215	2036	-.06 0.17 19447	.01	-.05	n/a
990216	2219	-.05 0.34 20882	.06	0.01	n/a
990218	0428	-.04 0.28 21177	.04	0.00	n/a
990219	1300	n/a n/a n/a	n/a	n/a	n/a	bad data (sys problems)
990226	0308 0313 0339 0344 0400 0404 0420 0424	-.05 0.35 38070 -.06 0.33 32900 -.03 0.31 23102 -.03 0.29 21638 -.04 0.33 26811 -.03 0.30 22633 -.03 0.29 24081 -.03 0.30 21378	.06 .05 .05 .04 .05 .045 .04 .045	0.01 0.00 0.00 0.01 0.01 0.02 0.01 0.02	n/a n/a n/a n/a n/a n/a n/a n/a
990226	0450 0454	-.04 0.31 25256 -.04 0.30 26525	.05 .04	0.01 0.00	n/a n/a
990227	1020 1024	-.03 0.33 10406 -.01 0.38 6858	.05 .07	0.02 0.06	n/a n/a
990228	2120	-.06 0.11 16917	.01	-.05	n/a

Results: Zdr Bias for TRMM-LBA

• Within a single event, Zdr bias determinations are very reproducible
• Over the project period, Zdr bias is stable to within +/- .05 dB of zero
• Final, absolute accuracy of corrected Zdr is well within the goal of +/- .2 dB.

• There is an increase in the standard deviation of the bias estimate when comparing liquid hydrometeors with ice.
• Zdr bias computations must be adjusted for log-averaging when doing computations in log space.