EPIC 2001: Calibration
This document describes the calibration of the Aeronomy Lab profilers during the TRMM LBA program. The calibration technique was essentially the same during the EPIC campaign.
CALIBRATION OF PROFILER REFLECTIVITIES USING DISDROMETERS
Absolute radar calibration is difficult to achieve. With scanning radars, it is possible to put a known target into the observing volume of the radar and perform a direct calibration of the radar. With a profiler, since the antenna beam is fixed, direct calibration using a known target is not a practical option. Indirect calibration done by careful measurement of all of the individual terms of the radar equation can be done, but the overall accuracy of this results in an uncertainty of 1 to 3 dB in the calibration. We have found that the 915 MHz profiler's calibration remains stable to within .4 dB over long periods of time. This allows the use of one calibration value to be used for an entire data set. This makes these instruments very useful, since they don't have calibration drifts that require continual measurement in order to get good data.
For TRMM work, the data from the radar are converted to reflectivity using the procedure described in the pdf document "Aeronomy Laboratory Precipitation Data Products" 
. The conversion of the raw radar data to absolute reflectivity requires the accurate determination of the profiler radar constant (PRC). For the real-time data displays and the preliminary data sets, we used the PRC determined by the indirect calibration of the profiler (PRC=26.9). To refine the calibration for the final data set, we rely on measurements made with a collocated disdrometer to calibrate profiler reflectivites in precipitation. The Joss-Waldvogel (JWD) impact disdrometer manufactured by Distromet is utilized for this purpose. The same JWD has been used for each of the TRMM Ground Validation Field Campaigns. Historically, the JWD has been used for calibration of radar reflectivities and more recently has been intercompared with profiler reflectivities. For example, in their analysis of observations from TOGA COARE, Tokay et al (1999) intercompared observations from a 915 MHz profiler at Kapingamarangi and a collocated JWD to study the classification of tropical convective cloud systems (Williams et al., 1995). While at Kapingamarangi, the profiler and disdrometer were operated independently, for the TEFLUN field campaigns a special effort was made to integrate the JWD data into the profiler data stream.
This document is written specifically to explain how the profiler reflectivities are calibrated in the TRMM Ground Validation Field Campaigns. It is important that users of the profiler observations in these campaigns have an understanding of how the calibrations were made and some of the limitations inherent in the approach that has been adopted. Improvements in calibration may be obtainable when second-order effects are taken into account. Second-order calibration involves profiler and disdrometer instrumentation issues. However, it is important to recognize that the quality of the calibration is inherently limited by time-space ambiguities of the profiler and disdrometer intercomparisons. This document is based largely upon a paper by Gage et al. (2000) which will appear in the forthcoming Special Issue of Journal of Applied Meteorology devoted to TRMM.
Calibration of profiler reflectivities
For the purposes of TRMM, we calculate reflectivity from the disdrometer drop sizes and use the calculated reflectivity as a reference for the profiler reflectivity. When the drop-size distribution, N(D), is known, radar reflectivity can be calculated as an integral over the drop-size distribution weighted by the sixth power of drop size, D. Other precipitation parameters can also be calculated from the drop-size distribution but these are not considered here. Disdrometers are therefore useful tools for calibration and validation of radar observations although they only provide information for a very small volume just above the surface.
The JWD is an impact disdrometer that produces a voltage when a drop strikes the surface of its 50 square centimeter styrofoam cone. The voltage output is calibrated to provide a measurement of the momentum transfer of drops which is related to their size. The JWD has a dead time immediately following the impact of a drop and in heavy rain this can lead to undercounting of raindrops (Williams et al., 2000b). An impact disdrometer determines drop-sizes based on the momentum transfer that occurs on the sensor head when a drop impacts the sensor. It is assumed that the momentum is entirely due to hydrometeor terminal fall velocities in still air assuming drops are spherical. The momentum of individual drops is related to the size of the drop.
For calibration of the profiler we compare the profiler reflectivities at the lowest fully recovered height with the disdrometer calculated reflectivities. The disdrometer provides the distribution of drops in twenty bins with one minute resolution. Disdromet provides standard software for calculating reflectivities from the number of drops in these twenty size bins. In order to optimize the utility of the disdrometer as a calibration tool for the profiler we have fully integrated the JWD into the profiler system so that the profiler and disdrometer are synchronized. The JWD disdrometer is capable of binning drop-sizes in 127 bins. The Aeronomy Laboratory has written software in order to provide a more complete drop-size distribution that utilizes the full 127 bins in the JWD and calculates reflectivities over this distribution. The new Aeronomy Lab software provides 10-second time resolution of the drop-size distributions.
To calibrate the profiler using the JWD we first compare the time series of reflectivities observed using the two platforms. The distribution of reflectivities from the two platforms are then compared. Because of the TRMM PR threshold of detectability of 17 dBz, we only use reflectivities greater than 15 dBz to create the distribution of reflectivity differences. The mean reflectivity difference provides us with a number that can be used to adjust the profiler radar constant to yield the desired calibration of the profiler.
Profiler calibration in TRMM LBA
Figure 1 contains two panels. The top panel shows a time-height cross section of uncalibrated reflectivities measured by the 915 MHz profiler on 15 February 1999. The bottom panel compares time series of uncalibrated reflectivities observed at 307 m with near surface JWD reflectivities obtained near the profiler location. It is obvious from Figure 1 that the reflectivities seen by the two instruments are highly correlated.
By comparing the two sets of reflectivities we choose the value of the profiler radar constant (PRC) that gives the best overall fit in a statistical sense to the disdrometer reflectivities. This requires an approximate 3 dB upward adjustment in the radar constant for TRMM LBA. The default (uncalibrated) value of the PRC used for TRMM LBA was 26.9. The calibrated value determined by intercomparing with the JWD disdrometer is given by 53.67. This results in a nearly 3 dB increase in the profiler reflectivities.
Figure 2 compares calibrated 915 MHz profiler reflectivities with JWD reflectivities observed during TRMM LBA at the Ji Parana municipal airport. Panel a shows the distribution of 915 MHz profiler reflectivities observed at 307 m above the surface. The profiler reflectivities are compared to JWD reflectivities in a scatter plot in Panel b. Panel c contains the distribution of JWD reflectivities observed near the surface at the profiler site. Note that the disdrometer reflectivities have been truncated to exclude reflectivities less than 15 dBz. Observations between 27 January and 1 March 1999 are included in this figure.
The scatter diagram in Figure 2 shows that with PRC equal to 53.67 the curve fit to the points plotted in Figure 2 crosses the diagonal line at about 30 dBZ. For reflectivities less than 20 dBz profiler reflectivities exceed JWD reflectivities by about 1 dBz. For reflectivities in the range of 20 - 40 dBz profiler reflectivities agree within about 1 dBz. Above 40 dBz the profiler reflectivities are less than the JWD reflectivities by 1-2 dBz.
Figure 3 compares the difference between calibrated 915 MHz profiler reflectivities at 307 m and JWD reflectivities observed during TRMM LBA at the Ji Parana municipal airport. Panel a shows the distribution of reflectivity differences. The reflectivity differences are plotted in Panel c as a function of JWD reflectivity. Panel c contains the distribution of JWD reflectivities observed near the surface at the profiler site. The data used in this figure are essentially the same as Figure 2.
Figure 3 shows the same information as Figure 2 but it is easier to see the reflectivity dependent bias between profiler and JWD. This reflectivity dependent bias is a robust feature of these comparisons. Below we consider the instrumental and physical factors that may be responsible for this bias.
Limitations of the calibration based on JWD disdrometer
There are a number of issues that arise in the use of the JWD for calibration of the profiler. Most of these are related in one way or another to the space-time ambiguities between the two platforms and the assumptions used in obtaining the drop-size distributions and reflectivities from the JWD.
The quality of the calibration can be judged in part by examining the differences between profiler reflectivities and JWD reflectivities as a function of JWD reflectivities as shown in Figure 3. When this is done for TEFLUN B, TRMM LBA and KWAJEX we find a reflectivity dependent bias. The bias is in a sense that JWD reflectivities increase relative to profiler reflectivities as JWD reflectivities increase. The amount of this increase for TEFLUN B and KWAJEX is about 4 dBz over the JWD range from 15 dBz to 50 dBz. When similar comparisons are made for TRMM LBA we find a difference of 3.5 dBz over the same range of reflectivities.
Reflectivity distributions seen in the field campaigns peak near or below about 30 dBz. Most reflectivities observed fall in the range of 10 dBz to 40 dBz. The mode of the distribution is close to 30 dBz for TEFLUN B and below 30 dBz for TRMM LBA and KWAJEX. The calibration is applied so that the average reflectivity difference between the calibrated profiler and disdrometer is near zero at 30 dBz. For TEFLUN B and TRMM LBA the profiler reflectivities are within about ± 1 dBz of the corresponding disdrometer values for the range of 20 to 40 dBz. For reflectivities exceeding 40 dBz the profiler reflectivities are biased low with respect to the JWD reflectivities by an amount that exceeds 1 dBz and grows with increasing JWD reflectivity.
For KWAJEX the profiler reflectivities are within about ± 2 dBz of the corresponding disdrometer values in the range of 20 to 40 dBz. For reflectivities exceeding 40 dBz the profiler reflectivities are biased low with respect to the JWD reflectivities by an amount that exceeds 2 dBz and grows with increasing JWD reflectivity.
The reflectivity dependent bias seen in Figures 2 and 3 is likely due to a combination of many factors including instrumentation and sampling by spatially separated measurements. Below some of the factors that contribute to the reflectivity dependent bias are explored.
Instrumental contributions to a reflectivity dependent bias
Profiler instrumental effects
Ideally the profiler will have a
linear response function. This is to say that the output power values
will be linearly proportional to the input signals received from the atmosphere. There are known non-linearities in the profiler signal processing (Time-Domain
Averaging filter). Tests show that these non-linearities are being
properly accounted for in the data processing. We have explored the
possibility that the profiler is behaving in a non-linear fashion. Tests of the profiler in the laboratory indicate that until the dynamic
range of the system is exceeded that the output power is linearly proportional
to the input power level. Other tests in the laboratory and observations
in the field indicate that the system is in the linear response range of
the system for the observed reflectivities at 327 m.
The profiler calibration technique
relies on the fact that the noise power received by the radar is constant
(to within about .3 dB) as a function of
time. By making a good measurement
of the noise power, the received signal power can be absolutely calibrated,
as discussed in "Aeronomy Laboratory Precipitation Data Products". This assumption is valid except during periods when the sun passes through
the antenna beam. During these periods, the reflectivity can be underestimated
by up to 6 dB. The solar passage affects a very small part of the
data set, and is not corrected for in the data.
We have also compared the 915 MHz and 2835 MHz profiler reflectivities and observe the same reflectivity dependent bias when the profiler data are separately compared to the JWD. We have observed that the 2835 MHz reflectivities are influenced by wet radome or wet dish effects. These cause a decrease in the 2835 MHz reflectivities under heavy rain conditions. We do not observe this effect in the 915 MHz data.
Disdrometer instrumental effects:
Undercounting of small drops by JWD
The JWD is known to undercount small
drops due to two effects. First, in heavy rain there is a dead time following
the impact of large drops before the disdrometer can detect the next drop.
Second, the JWD is very sensitive to noise in the environment. In order
to avoid spurious counts in a noisy environment the JWD has a variable
noise threshold that in effect will mask the counts of small drops. Depending
on the noise level of the environment drop sizes of a few tenths mm up
to drop sizes of 1 mm and even larger may not be counted. In the
TRMM field campaigns TRMM LBA appears to have been the quietest installation
for the JWD. The noisiest installation by far was on Legan where
the JWD was located within a 100 meters of a very noisy generator. The
site was so noisy that it was hard to hold a conversation outside the profiler
container. At TEFLUN B a generator was also used but it was a smaller and
quieter unit.
Undercounting of small drops in heavy rain should not have much effect on the reflectivities calculated from the JWD disdrometer. However, the undercounting in very light rain is likely to cause a significant underestimation of reflectivities. Thus, it is likely that for small JWD reflectivities the JWD reflectivities will be less than profiler reflectivities.
Comparison of JWD and 2DVD disdrometer
reflectivities
Disdrometer effects could well introduce
calibration uncertainties of second order. To investigate this possibility
we have intercompared profiler, JWD and 2DVD reflectivities. A 2DVD
disdrometer was collocated with the profiler and JWD for TEFLUN B, TRMM
LBA and KWAJEX but the JWD is used here for the calibration since the 2DVD
data set is much smaller and not as continuous as the JWD data set. The
2DVD is an optical device that has two orthogonal beams of light in horizontal
planes displaced about 6 mm in the vertical. To be counted a drop must
pass through both beams of light. The 2DVD gives an estimate of the size
of the drop and its shape as well as its fall velocity. Over the
range of JWD reflectivities 10 - 50 dBz the JWD reflectivities increase
relative to the 2DVD reflectivities by about 2 dBz. Thus a substantial
portion of the reflectivity dependent bias may be attributed to the disdrometer.
In determining drop-sizes from an impact disdrometer, such as the JWD, it is assumed that there is zero air motion so that the momentum imparted by the falling hydrometeors is entirely due to terminal fall velocity in still air. In the presence of downward vertical motions the JWD may be overestimating drop sizes as a consequence of momentum imparted by air motions. This could account for some of the differences between JWD and 2DVD measurements since the 2DVD measures drop sizes directly. Another difference is that the JWD assumes spherical drops and the 2DVD measures the shape of the drops.
Possible physical causes of a reflectivity dependent bias
Sample volume differences between
profiler and disdrometer
In making comparisons between profiler
reflectivities and reflectivities calculated using disdrometers there are
obviously many issues that arise not the least of which is the time-space
ambiguities that result from comparing a ‘point' measurement at the surface
with a volume measurement at several hundred meters above the surface. Actually the collecting area of the JWD is about 50 square centimeters
while the collecting area for the 2DVD is about 100 square centimeters. The observing volume of the disdrometers is determined by the fall velocity
of raindrops and for drops falling at 7 meters per second would be close
to 1m^3 for a 30-second sample while the volume observed by the 2DVD
is about 2.1 m^3. The volume observed by the profiler with
a nominal 100 m pulse length is about 7.8 x 104 m^3 at 300 meters and 8.6
x 105 m^3 at 1 km. Thus there are roughly five to six orders of magnitude
difference in the observing volume for the disdrometers and profilers. Under these circumstances especially under convective conditions it is
remarkable that the reflectivities calculated from the drop-size distributions
of the disdrometer agrees as well as they do with the reflectivities observed
by the profiler.
Height difference in measurements
between profiler and disdrometer.
The quality of the agreement of
the disdrometer and profiler depends in part on the height separation of
the two instruments. Profiler comparisons with disdrometers are best
made at the lowest profiler heights that are fully recovered. At close
ranges, the received signals exceed the dynamic range of the profiler. It takes 2 to 3 pulse lengths for the system to recover and have the desired
linear response. For 105 meter range gates the second or third range gate
is in the vicinity of 307 m and 412 m, respectively. Note, however, that
velocity information can be valid even at the lowest range gates where
the receiver is not fully recovered.
A lag correlation of time series of profiler and JWD reflectivities was performed for TEFLUNA and it was determined that the best correlation occurred with a one minute lag (one minute was also the time resolution of the time series) of the disdrometer values compared with the profiler observations. This is consistent with an average fall velocity of 7 meters per second for hydrometeors falling from 412 meters to the surface. A fall velocity of 7 meters per second is consistent with the terminal velocity of a drop in the size range of 2 to 2.5 mm and agrees with observations for stratiform rain reported in Cifelli et al. (2000).
Effect of decorrelation of reflectivity time series
Reflectivities are highly variable
from one sample to the next and depend on the spatial separation of the
measurement volumes. The variability will be greater for reflectivities
obtained in small measurement volumes such as obtained by the disdrometer.
Some of the variability will be smoothed out in the larger measurement
volume of the profiler.
Consider the time series of reflectivities measured by the disdrometer and a simultaneous time series of reflectivities from profiler observations at several range gates above the disdrometer. A scatter plot of simultaneous reflectivities measured by these instruments will provide a good indication of how well correlated these measurements are. If perfectly correlated, as a time-series of observations compared to itself, the observations will lie on a diagonal with no scatter. With increasing decorrelation between the two time series there will be increased scatter and a reflectivity dependent bias as discussed next.
The effect of decorrelation on the scatter plot will be an increase in scatter around the diagonal and possibly an effective rotation of the locus of points with respect to the diagonal. Without loss of generality, consider a Gaussian distribution of reflectivities. When the disdrometer values are at the high end of the distribution and there is increasing decorrelation with the profiler values, a given large disdrometer reflectivity is increasingly likely to be associated with a smaller profiler reflectivity. For similar reasons a small disdrometer reflectivity is increasingly likely to be associated with a larger profiler reflectivity. The net effect of decorrelation is to rotate the locus of points in the scatter plot relative to the diagonal obtained for perfect correlation in the sense described above. This rotation of points rmay account for some of the reflectivity dependent bias observed in our comparisons.
Effect of horizontal advection and wind shear
An important mechanism for decorrelation
of vertically separated samples is vertical wind shear. Rain shafts that
are oriented close to vertical will be sheared and tilted off vertical
by vertical shear of horizontal wind so that high reflectivities can be
observed at the surface while low reflectivities are observed a few hundred
meters above the surface and vice versa. The greater the separation between
the disdrometer and the profiler the greater this effect will be.
Effect of drop-size spectra variations with altitude
Tokay et al. (1999) show vertical
profiles of reflectivity for stratiform and convective rain. To first order
reflectivities below the melting layer are nearly constant with altitude
for stratiform precipitation while reflectivities increase with decreasing
altitude for convective rain. Under convective conditions the average increase
in reflectivity is about 2 dB/km. Presumably, this change in reflectivity
is accompanied by a change in drop-size distribution. As drops fall they
tend to collect smaller drops and through coalescence the drop-size distributions
evolve with more larger drops at lower heights. At least under convective
conditions it appears likely that as much as two-thirds dBz of the
reflectivity dependent bias could be due to this effect when comparing
profiler observations at 400 meters with surface disdrometer measurements.
Effect of non-spherical drops
While smaller drops tend to be spherical,
larger drops are likely to be deformed. The shape of falling raindrops
is discussed by Beard (1976). According to Beard oblate spheroids
are the dominant shape for large drops. The theory for backscattering
from nonspherical hydrometeors is reviewed by Battan (1973) and in Doviak
and Zrnic (1993, second edition, chapter 8). Reflectivities of the deformed
drops will depend on the magnitude of the deformation, the orientation
of the drops and the incident angle of the radar beam and its polarization. Figure 8.1 of Doviak and Zrnic shows a photograph of different drops, showing
that the drops are flatter as the drop size increases.
Conventional weather radars observe hydrometeors from the side, and by the use of horizontal and vertical polarizations, can measure the effects of this flattening of the drops. The horizontal polarization (horizontal E-field) can have reflectivities 3 dB or more above the vertical polarization. For vertically pointed radars, the E-field is always horizontal. This means that the equations that are used to calculate the reflectivities from non-spherical drops need to be the appropriate equations, as discussed in section 8.5 of Doviak and Zrnic.
As mentioned earlier, the JWD assumes spherical drops. This will give a reflectivity that is different from that of an oblate spheroid. Further work needs to be done to bring the formulations and assumptions together so they are consistent.
Summary
The calibration of profiler reflectivities that has been performed for TRMM determines the unique radar constants that provide the best overall fit to the disdrometer reflectivities for each field campaign. Several issues impacting calibration have been raised and discussed in relation to a reflectivity dependent bias that is found when comparing the profiler and disdrometer reflectivities. It has been noted that significant differences (at the 1-2 dBz level) are obtained from collocated JWD and 2DVD disdrometers. Until these differences are understood and fully resolved there will be some uncertainty in the absolute calibration of the profiler. The reflectivity dependent bias is thought to be primarily due to differences in sampling provided by the profiler and disdrometer.
Instrumentation changes in TRMM LBA that affect the profiler calibration
Between TEFLUN B in Florida and TRMM LBA in Brazil the instruments were essentially the same with the exception that the voltages were adjusted in TRMM LBA to the values that should have been used in TEFLUN B. The effect of this change was to make the profiler appear as it had in TEFLUN A in Texas before the 12-bit A/D converter was added to the profiler.
During TEFLUN A and TEFLUN B we learned that the 2835 MHz profiler gave similar results to the 915 MHz profiler with two important differences. The 915 MHz profiler was more sensitive to clear air and the S-band profiler reflectivities were decreased relative to the 915 MHz profiler reflectivities whenever the 2835 MHz profiler dish was wet, especially during heavy rain. Since otherwise the two profilers measured similar reflectivities, it was decided to only provide one set of reflectivities for the TRMM LBA archive. The 915 MHz reflectivities were chosen because they are not affected by the wet dish problem. However, in the event of a failure of the 915 MHz profiler the 2835 MHz profiler reflectivites are substituted in the archive.
References
Beard, K.V., 1976: Terminal velocity and shape of cloud and precipitation drops aloft, J. Atmos. Sci., 33, 851-864.
Cifelli, R.C., C.R. Williams, W.L. Ecklund, D.K. Rajopadhyaya, S.K. Avery, K.S. Gage and P.T. May, 2000: Drop-Size distribution characteristics in tropical mesoscale convective systems, J. Appl. Meteorol., in press.
Doviak, R.J. and D.S. Zrnic 1993: Doppler Radar and Weather Observations, Academic Press, 562 pages.
Gage, K.S., C.R. Williams, and P.E. Johnston, W.L. Ecklund, R. Cifelli, A. Tokay and D. Carter: 2000: Doppler radar profilers as a calibration tool for scanning radars, J. Appl. Meteorol., in press.
Tokay, A., D.A. Short. C.R. Williams, W.L. Ecklund and K.S. Gage, 1999: Tropical Rainfall Associated with Convective and Stratiform Clouds: Intercomparison of Disdrometer and Profiler Measurements, J. Appl. Meteor. 38, 302-320.
Williams, C.R., A. Kruger, K.S. Gage,
A. Tokay, R. Cifelli, W.F. Krajewski, and C. Kummerow, 2000: Comparison
of simultaneous rain drop size distributions estimated from two surface
disdrometers and a UHF profiler. Geophys. Res. Lett., in press.
Table 1: Profiler Parameters used in TRMM LBA
| Parameters | 3 GHz Profiler | 1 GHz Profiler |
| Frequency | 2835 MHz | 915 MHz |
| Wavelength | 10.6 cm | 32.8 cm |
| Peak Power | 5 Watts | 500 Watts |
| Antenna | 1.2 meter shrouded dish | 3 meter shrouded array |
| Beamwidth | 5 degrees | 5 degrees |
| Height Resolution | 60 and 105 meters | 105 and 255 meters |
| Max. Height sampled | 10.6 km | 18 km |
| Max. Radial Velocity | +/- 20 ms-1 | +/- 20 ms-1 |
| Spectral Points | 256 | 256 |
| Dwell Time | 30 seconds | 30 seconds |
| Recording | Full spectra | Full spectra |