**Calibrating differential reflectivity**

**on the WSR-88d**

**PART II**

National Severe Storms Laboratory Report

prepared by: Dusan S. Zrnic, Valery M. Melnikov, John K. Carter, and
Igor Ivic

April 2007

NOAA, National Severe Storms Laboratory

120 David L. Boren Blvd, Normal, Oklahoma 73072

**Calibration of Z~DR~, simplification of the procedure**

The purpose herein is to describe a simplified, but more robust, version
of calibration procedure proposed by NSSL in the report by Zrnic et al.
(2005). Elimination of few steps reduces the number of error sources.
Critical element in the calibration procedure are also identified. A
quick description of input and output points taken directly from that
report (but slightly embellished), follows.

The block diagram in Fig. 1 captures the gist of the KOUN radar with
points labeled 1 to 4 that are relevant for the subsequent discussion.
The single line arrow

Fig. 1 Diagram of the KOUN system with crucial points for calibrating
Z~DR~.

connects Transmitter to the Power Splitter (PS) and corresponds to the
waveguide on KOUN which goes from the transmitter to the pedestal. Block
arrows indicate two channels H and V as well as direction of signal
flow. The H and V signals are simultaneously transmitted and received.

Point 1 represents coupler for transmitter power measurement. Point 2
represents two couplers above the elevation rotary joints for power
measurements. Point S is the sun's radiation flux at the antenna
(outside of the radome). Point 3 corresponds to calibration couplers
near the input to the low noise amplifiers (LNAs). Between the coupler
and the LNA are the waveguide filter (bandwidth \~ 16 MHz) and the
receiver protector. A variable attenuator (under computer control) is
connected to a signal generator (or noise generator) for calibrating
automatically the receiver. This is standard on the WSR-88D and it is
crucial for maintaining calibrated Z~DR~. Point 4 represents output of
the digital receiver, that is digital I, Q values of both H and V
components; from these one computes various powers, noises, and
differential reflectivity. Absolute values of these powers do not
matter, the ratios do matter.

The premise behind the procedure is to partition calibration into parts
which are constant (time invariant) and parts which can vary with time.
The time invariant part is measured once to establish the constant bias
valid for the full dynamic range. The slowly varying part (see Appendix
C) is tracked over the full dynamic range from volume scan to volume
scan analogous to the AGC calibration in the Legacy system.

Bias between any two points is denoted with the symbol Δ~ij~, where the
first subscript (i) is the input point and the second (j) is the output.
Although Δ~ij~ = Δ~ji~, some of the bias can be easily measured only in
one direction because of the placement of couplers which restrict signal
flow. Hence, in general the signal flow direction both during
measurement and actual operation is from the port indicated by the first
index.

**1. BIAS MEASUREMENT PROCEDURE**

In this section we describe what was established so far (April, 2007),
and list the organization which made the measurement. NSSL's
measurements are from the report and more recent verifications; they
were made on the KOUN with the Sigmet's dual polarization system. NCAR's
measurements are from the presentation to the TAC in October 2006 and
were made on the S-Pole radar.

*Established facts*:

1\) The Sun is a good calibration source for the receiver path (NSSL,
NCAR).

2\) The time varying part of the path drifts slowly; but, occasionally
on the KOUN (WSR-88D) it exhibits sudden shifts of about 0.8 dB. These
are caused by differenced in the LNA attributed to temperature controls
in the housings of the two units.

3\) There is coherent leakage associated with the internal signal
generator, and it affects measurement of the bias at SNRs smaller than
about 30 dB.

4\) Uncertainty in the differential reflectivity bias from the sun
measurement is 0.023 dB (NCAR) and 0.028 dB (NSSL). Mean value is zero.

5\) Uncertainty in the values from the couplers is \<0.1 dB, (NSSL).

6\) The two (H, V) transfer gains of the receivers are linear over the
whole dynamic range (NSSL).

The simplified procedure calls for two sets of measurements and
continuous calibration at the end of volume scans.

**1.1 *TRANSMISSION CHAIN*** - FIRST SET

a.1) Point 1 to point 2:

Differential reflectivity in the transmission chain must be measured at
the time of retrofit.

Deviation from 0 is the bias Δ~12~. (1.1)

**ISSUE 1:** What is the accuracy (bias) and precision (standard
deviation about the mean of this measurement)?

***Recommendation and discussion:*** The V channel in the transmission
path should be constructed of the same components as on the existing H
channel. That way the differential attenuation between the two will be
minimized. The bias Δ~12~ should be recorded at the time of retrofit for
the particular radar site. If it is larger than 0.1 dB consider adding
it in the total correction. But do the measurement again. If it is less
than 0.1 dB ignore it at the time of retrofit, because it might be a
measurement error. It should be possible to deduce the error from the
data later. Two major reasons for the bias are 1) an extra waveguide
switch in the H channel (see the appendix A, and Zrnic et al. 2005), and
2) the dual rotary joint. Using a single azimuth rotary joint and
placing the power splitter above it would eliminate cause 2). If the
dual rotary joint is used we recommend measuring bias on all the dual
rotary joints prior to installation. Cause 1) can be eliminated if one
gives up the option of transmitting single H polarization, which is what
we recommend.

***Desirable measurement:*** The coupling losses of the two couplers. If
these are measured with an accuracy of 0.03 dB, then the bias Δ~12~
should be accounted for. If the accuracy is about 0.1 dB then larger
bias should be corrected and smaller ignored.

***Rationale for possibly ignoring this bias**:* The total specified
attenuation from the splitter (excluding the 3 dB division and \< 0.2
loss through the splitter) to point 2 of the H channel is 0.48 dB
(Appendix A). In the V channel of the KOUN configuration it is 0.43 dB.
The difference of 0.05 dB is within acceptable error.

a.2) Point 2 to outside of radome:

This is more involved and round about because it is deduced from
measurements in the receiving chain; see the report by Zrnic et al.
2005.

The bias is denoted with Δ~2S~. (1.2)

***Recommendation:*** Ignore this bias in the transmitter chain.
Rationale: the total attenuation in the H channel from above the El
rotary joints to the outside of the radome is 0.3 dB. According to the
adaptation data (Appendix A) it is comprised of:

-Loss through the coupler = 0.1 dB (the couplers in the H and V channels
are the same so the losses should be the same). Thus the difference
should be an order of magnitude smaller.

-Loss from the coupler to the antenna = 0.1 dB.

-Loss through the radome = 0.1 dB.

The difference in attenuation between the H and V channels must be
significantly less than 0.3 dB, likely few hundredths of dB, and can be
ignored. The total loss in the channel for the horizontal path (H) from
the splitter (excluding 3 dB split and 0.2 dB pass through loss) to
outside of radome is 0.68 dB. In the vertical channel (V) it is 0.63 dB.

**ISSUE 2:** What is the actual bias?

**1.2** **RECEIVER CHAIN** - SECOND SET

The procedure requires permanent connection of the internal generators
to the input of the LNA in the V channel. The existing line that goes to
the H channel must be split, one end reconnected to the LNA of the H
channel and the other to the LNA of the V channel, as done on the KOUN.

b.1) Point 3 to point 4: Use the internal generator, split the output,
and apply to both couplers. (If there is coherent leakage in the
circuits between the generator and the LNAs, the internal noise
generator should be used at low values of SNR, see Zrnic et al. 2005.
Such leakage was measured on the KOUN.) Change attenuation (of the
internal attenuator, on the WSR-88D this is under computer control) in
steps of 2 dB over the whole dynamic range. Generate the curve of Δ~34~
(Z~DR~) vs power P~hk~, as in Fig. 2, where P~hk~ is the value of
attenuated power in the horizontal channel at the output of digital
receiver and k is the setting index. This power is in units internal to
the digital receiver (i.e., digital numbers which are uniquely related
to the input powers at the antenna -- but that relation is immaterial
for computing the bias!). Ideally this bias curve should have the value
of 0 dB over the whole dynamic range;

deviation is the ***non calibrated bias*** Δ~34~(P~hk~). (1.3)

![](media/image1.png){width="6.0in" height="4.306299212598425in"}

Fig. 2 Bias Δ~34~ curve (black thick line). The red line is obtained
from a least squares fit over the interval between -10 and -50 dB, and
extrapolated to lower values. The calibration point from the Sun is at
-79 dB. The final calibration is the gray line obtained by adjusting
(raising) the red line to the level indicated with the calibration from
the Sun.

This is ***not calibrated*** because it contains the part from the
generator to the point 3 as well as the difference in the gains of the
two channels (point 3 to point 4).

Note that the bias in Fig. 2 is constant at output powers between -10 dB
and -50 dB. In general there could be a trend in this bias, so we
recommend checking and fitting a line if needed. Indications are that it
will not be the case!! Nonetheless the bias graph should be plotted at
each site for inspection. The line is extrapolated to the low values of
power and to the high values. At low values we have verified that the
extrapolation is accurate, the deviation from the line in Fig. 2 is
caused by coherent leakage (Zrnic et al. 2005). At high values
saturation occurs and the bias in Z~DR~ could be few tenths of dB. This
is of no practical consequence because the reflectivity at saturation is
so high and would be a sufficient indicator of strong hail, or heavy
rain/hail mixture; occurrence of saturation is generally rare.

**ISSUE 3:** Is the bias measured with the internal noise generator
equal to the bias measured with the internal signal generator? On the
KOUN this was the case. If it is not, use the value inferred from the
noise generator to adjust the one from the signal generator. (Frequency
spectrum of noise is similar to the one from the weather signal).

b.2) Immediately after b.1: Use sun scan and record differential
reflectivity bias

Δ~S4~(P of sun) (1.4)

This is the calibrated bias (at one power level, that of the sun's
radiation, yellow circle in Fig. 2) from the outside of the radome to
the output of the digital receiver. It is the standard, the one that
will calibrate (1.3).

b.3) Repeat b.1, and if the change is less than about 0.03 dB at the
power (output of digital receiver) of the sun (i.e., at P~hk~ = Psun)
then keep the curve (1.3). Otherwise offset the curve (vertically up or
down) so that at the power of the sun the bias is given by (1.4). Label
the new curve Δ~34CAL~(P~hk~) i.e., it should be used for bias removal
(gray line in Fig. 2). NOTE, this curve is calibrated (compensated) for
all the biases including the Generator to 3 and S to 3! Clearly the
offset Δ~C~ is

Δ~C~ = Δ~S4~(P of sun) - Δ~34~(P~hk~ = Generator power = sun power).
(1.5)

{Δ~34CAL~(P~hk~) = Δ~34~(P~hk~) + Δ~C~}

The change in calibration should be tracked by performing automatically
1.3) at the end of each volume scan. (Amen).

c\) *Calibration*

At the end of volume scan the correction Δ(P~hk~) should be

Δ(P~hk~) = Δ~C~ + Δ~34~(P~hk~) + Δ~12~ , if Δ~12~ ≤ 0.1 (1.6a)

Δ(P~hk~) = Δ~C~ + Δ~34~(P~hk~) , if Δ~12~ \> 0.1 (1.6b)

To summarize:

Δ~12~ is the bias due to the possible differences in the transmission
chain, it is measured once. On the KOUN this bias is about -0.06 to
-0.09 dB (see the Appendix A), and the bias from the Elevation rotary
joints to outside the radome is 0.06. Thus the two almost cancel, or is
it a coincidence? It is highly likely that the total bias on
transmission on other WSR-88D radars will be similar; in which case the
uncertainty in measuring it would be larger than its value.

Δ~C~ is the offset bias of the receiver. It contains all the inherent
biases and uncertainties. It is completely determined from the sun scan
and the internal generator. Further, its uncertainty could be made
arbitrarily small. It is non intrusive.

Δ(P~hk~) is the bias over the dynamic range of the receiver. It must be
updated at the end of volume scan. It contains the variable part due to
the difference in receiver gains.

Δ~2S~ is the bias on transmit between the coupler above El joints and
outside of the radome. It is ignored because it is likely about 5 times
smaller than the total loss along the H or V path.

The major uncertainty is in the measurements of transmitter power at the
two couplers above the elevation rotary joints. Some further inquiry
into this issue is in order.

For example measurements of losses through several couplers should be
made to determine the accuracy (i.e., is it better than the stamped 0.1
dB values).

The knowledge obtained by performing the measurements as in the report
and Zrnic et al. (2005) paper was crucial in making this recommendation.
Further, the details on how to measure the bias constituents reported
herein are also contained in the aforementioned papers.

**Appendix A -- Losses in the Transmission chain**

Losses specified in the adaptation data of the KOUN are discussed
herein, and related to the Z~DR~ bias. Description of measurement and
detail configuration of the radar are in the report by Doviak et al.
(2002). A power splitter and at least one waveguide switch are needed
for two modes of operation: simultaneous H,V, (SHV) and H only. The
simplified diagrams from Zrnic et al. 2005, are in Fig. A.1a and A.1b.
On the KOUN this functionality is accomplished with two switches as in
Fig. A.1a. Clearly the H channel contains one more switch than the V
channel. This certainly contributes to the bias in differential
reflectivity of 0.1 dB measured from the splitter to the output of the
two circulators (Doviak et al. 2002). If the one switch configuration
(Fig. A.1b) is adopted, the H wave would pass through that switch while
the V would not thus unbalancing the system.

***Recommendation:*** Give up on the single (H) polarization mode. That
way there is no need for the waveguide switch. The bias of Z~DR~ on
transmission would be reduced and it would be easier to house the dual
polarization microwave circuits in the pedestal.

a\) b)

Fig. A.1 a) Configuration for transmission of simultaneous H and V
signals on the KOUN radar; S~1~ and S~2~ are four port microwave switch
and SP is the power splitter. The lines within the switch indicate which
input ports are connected and the switch rotates 90^o^ into its second
position. Simultaneously activating both switches changes the SHV mode
(in the figure) to H only mode. The circulators and receiver channels
are not shown, but would connect to the H and V lines. b) Same as in a)
except one switch accomplishes the actions of the two switches in a).

The losses of various components on the KOUN are indicated in the
following table.

**TABLE: Losses from the Transmitter to the feed horn; H channel**

  ----------------------- -------------------------------- ---------------
  TR-17                   Arc Detector                     0.05

  TR-18                   Harmonic filter                  0.15

  TR-19                   Circulator                       0.2

  TR-20                   Spectrum Filter                  0.2

  TR-21                   Excess Loss                      0.05

  TR-22                   Coupler -- straight through      0.05

  TR-24                   Wave guide switch at Transmitter 0.05

  TR-25a                  Wave guide to Switch at Pedestal 1.6

  S~1~                    Wave guide switch                0.05

  SP                      Splitter                         \<0.2

  S~2~                    Wave guide switch                0.05

  TR-25b                  Circulator                       0.2

  TR-26                   AZ rotary joint                  0.1

  TR-27                   Wave guide to EL joint           0.08

  TR-28                   EL rotary joint                  0.05

  TR-29                   Coupler through                  0.1

  TR-31                   Wave guide to feed horn          0.1
  ----------------------- -------------------------------- ---------------

The TRs followed by numbers represent elements in the transmission path
for horizontal polarization as listed in the adaptation data (values are
in black font). The S~1~ and SP are common to both channels (all in
black fonts are) and the S~2~ is unique to the az channel (it is in red
font); these are not in the adaptation data. Rather, they have been
measured or specified (values in orange, Doviak et al. 2002). The TRs in
blue font are separate and mostly identical components in the H and V
channel. The attenuation through the splitter (apart from the 3 dB split
power) is from specifications and would be present in both channels. The
splitter is made with machines under computer control and thus is very
symmetrical, therefore no bias is expected.

The TR-25 (1.8 dB loss) from the adaptation data is split into 1.6 dB up
to the switch S~1~ and 0.2 through the circulator because we have
modified the path by adding the circuit in Fig. A.1a. Adaptation data
indicates 0.2 dB loss through the circulator in the shelter close to the
transmitter (hence we took the same value for the one in the pedestal).

Measurements from the point T (into the switch S~1~) to the output of
the circulator (connected at the H and V arrows in fig. A.1a, but not
shown) indicate the loss in H is 3.4 dB and in V it is 3.3 dB (Doviak et
al. 2002). Clearly the excess loss (above the 3 dB by the splitter) is
0.4 in H and 0.3 in V channel.

It is instructive to compare the losses of the H and V powers in the
parts of the channels that are physically separate. Thus from S~2~ to
the feed horn the loss in H channel is 0.68 dB. In the V channel it is
0.63 dB (because there is one switch less for the wave to traverse). The
difference between the two is - 0.05 dB (i.e., the gain in H is -0.05 dB
with respect to V). It is difficult to directly verify this bias, but
our measurement (above the elevation rotary joints, see Appendix B), of
\~ -0.06 is consistent with the adaptation data and partial measurements
made earlier (Doviak et al. 2002).

**Appendix B - Measurements above the rotary joints**

To check consistency of previously estimated bias in power splitting
above the El rotary joints several of measurements were made in Nov
2006. In the first set two power meters were connected to the couplers
above El rotary joints and the transmitter was repeatedly turned on and
off fifteen times. The results (in dB) follow.

*Measurement 1:*

[TRANSMITTER]{.underline} [HORZ]{.underline} [VERT]{.underline}

7.07 10.47 10.82

7.07 10.46 10.82

7.10 10.50 10.86

7.09 10.49 10.85

7.10 10.50 10.86

7.11 10.51 10.87

7.08 10.48 10.85

7.12 10.52 10.88

7.11 10.51 10.87

7.12 10.52 10.88

7.12 10.53 10.88

7.10 10.50 10.86

7.13 10.54 10.89

7.13 10.54 10.89

7.11 10.52 10.87

Test made by Richard Wahkinney and Mike Schmidt, Nov 17, 2006. HORZ and
VERT indicate powers above the EL rotary joints in the horizontal and
vertical channels, and the left column is the power of the transmitter.
The mean difference is: Mean = -0.3573 dB; The difference in couplers is
-0.3 dB (i.e., P~hc~ -- P~vc~ = -0.3 dB), after taking it out we obtain
the correct mean of -0.0573 dB; SD = 0.0059 dB.

*Measurement 2:*

The second set of measurements produced the following results:

RADAR XMTR CHANGES 2

11/21/2006

[TRANSMITTER]{.underline} [HORZ]{.underline}

7.09 10.49

7.16 10.55

7.18 10.58

7.17 10.57

7.18 10.58

7.18 10.58

7.18 10.58

7.20 10.60

7.18 10.58

7.20 10.60

[TRANSMITTER]{.underline} [VERT]{.underline}

7.19 10.98

7.20 10.98

7.17 10.95

7.19 10.98

7.18 10.97

7.19 10.98

7.20 10.99

7.18 10.97

7.20 10.99

7.19 10.97

Test made by Richard Wahkinney, Mike Schmidt, and Mark Benner. This test
is using one power meter at the transmitter and one power meter at the
couplers above the El rotary joints. We disconnected the meter at the
antenna port between each measurement. Transmitter ON for 25 seconds and
OFF for approximately 1 minute. Mean = -0.3880 dB, take out -0.3 dB
(couplers), true mean = -0.088 dB and SD = 0.0042 dB. The mean values
from both measurements agree very well with the -0.06 measured in 2005
(Zrnic et al. 2005).

*Measurement 3:*

One more measurement was made on April 4, 2007 by Schmidt, Wahkinney,
and Zrnic. This time we took several readings but chose to compute the
bias from those in which the digital readout of the transmitter power
was very stable (several seconds of no change in value). The measured
bias was -0.67 dB (if coupling loss stamped on the coupler is used).
Note that the measured value of coupling loss differs by 0.04 dB from
the stamped value; its inclusion produces a bias of -0.71 dB. This is
clearly a very stable and repetitive outcome.

At that time the total loss (H channel) from the transmitter coupler to
the coupler above the EL rotary joint was measured to be 5.61 dB
(including 3 dB in the splitter). Our adaptation data indicate 5.43 (it
is 2.43 dB without the splitter). The difference 0.18 dB could be due to
some values that were taken from manufacturer's specifications but not
measured or measurement error. Still, for absolute measurements this
accuracy is very good.

***Conclusion:*** The manufacturer's stamped values of coupling loss (on
the KOUN radar) are good to 0.1 dB. For the one time calibration at
upgrade make a measurement with a single power meter above the elevation
joints (switch between measurements) but monitor the power of the
transmitter (and adjust accordingly the bias).  Ignore this bias if it
is \< 0.1 dB.

***Recommendation:*** Verify that the couplers are calibrated to better
than 0.1 dB. If this is not so, then it is desirable to measure the
coupling loss.

**Appendix C - Variation of the bias with time**

The automatic procedure to calibrate the receiver chain has been
implemented on the Research RDA. It can be activated at the end of
volume scans or used in a computed control mode. Herein the results from
a measurement over several hours are presented (Fig. C.1).

![](media/image2.wmf){width="5.995138888888889in" height="3.6in"}

Fig. C.1 Variable bias measured on March 22-23, 2007. Time 0 min
corresponds to about 4:30 pm local time.

For most of the measurement the variation in the bias is insignificant
(400 to 1000 min). The change of about 0.025 dB occurs between 6:30 and
8:30 pm local time. This is caused by temperature change at sunset.
There is no change in the morning hours (end of measurement is at about
9 am), because there was little temperature change at sunrise; the skies
were overcast with thick clouds.

**Appendix D - Verification of bias**

An indirect verification of the bias correction is presented herein. It
is done on data from drizzle that occurred on Feb. 6, 2005.

![](media/image3.jpeg){width="6.0in" height="2.7874015748031495in"}

![](media/image4.jpeg){width="6.15625in" height="3.432638888888889in"}

Fig. D.1 Vertical cross section of reflectivity factor field (top) and
differential reflectivity (bottom). Data enclosed in the rectangle are
used to obtain Z~DR~.

The Sun scan was used for absolute calibration, and the bias in the
transmitter path was ignored. On this day the bias from the SUN was
computed to be 0.65 dB negative. So 0.65 dB was added to all the values
of Z~DR~ in the figure. Histogram was obtained from the region enclosed
with the rectangle in Fig. D.1 (0.5 to 2.5 km in height and 0 to 35 km
range); it is displayed in Fig. D.2.

![](media/image5.jpeg){width="6.0in" height="4.0653543307086615in"}

Fig. D.2 Histogram of differential reflectivity. The absolute
calibration made with the sun scan is indicated. The mean value of the
histogram is 0.01 dB and the peak is at 0.04 dB.

Considering that drizzle was observed at the radar, that the
reflectivity of the data in the histogram is between about 10 and 23 dB,
we would expect that peak (or mean) to be somewhere between 0 and 0.1
dB. The extremely good match with intuitive expectation could be a
coincidence. The KOUN is the only one polarized WSR-88D. Thus, we have
no other samples to compare it with. Comparison with other radars brings
more unknowns and uncertainties because the hardware is quite different.

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