This web page is linked to by the main ROOF web page, at ROOF, and is devoted to a description of the calibration of the Water Vapor Radiometer, WVR, used during the ROOF observation project.

First Strategy for Deriving Cloud Liquid Burden

The WVR raw data files include solutions for cloud liquid burden, Lz, as well as path delay (approximately 6.1 times the water vapor burden).  The real-time analysis program that generated the WVR raw data files are thought to have been designed for use in Madrid, Spain (site altitude of 2100 feet).  Because the ROOF site is at a lower altitude (200 feet), where the pressure broadening of the 22.2 GHz water vapor line is greater, the Madrid retrieval coefficients will mistakenly lead to larger Lz values than true.  This is borne out by the following plot.

Figure 1. This is a plot of the real-time solutions for cloud liquid content during the entire 26-day ROOF observing period. It contains erroneous values due to radome water effects and variations of water vapor altitude distribution.

At no time did the real-time solutions for Lz goe below zero.  The average value is 40 mirons, which is consistent with the use of Madrid RAOBs for generating retrieval coefficients for Lz. This is not an insurmountable problem, since the pressure level for cloud droplets does not affect their emission at microwaves.  In other words, correcting for the ROOF site being at a different pressure altitude can be acchieved merely by subtracting the observed 40 micron bias.  A greater problem is to remove the effect of water on the radome, which will be dealt with first.

The WVR raw data files contain tip-curve calibrated values for TB1 and TB2 at zenith, TB1Z and TB2Z, plus TB2 measured at 30 degrees elevation and converted to a zenith equivalent, TB2ZE.  The difference between the zenith measured TB2 and TBZE provides a means for determining when radome water was present, since water typically accumulates only at the top of the radome (zenith location).   The next figure shows difference between the two versions of TB2.

Figure 2.  Plotting the difference between the two versions of TB2 (the actual zenith measurement of TB2 and TB2ZE, the zenith equivalent TB2 based upon the 30 degree elevation measurement).  The difference is close to zero when the radome is dry, but departs upward when it has an accumulation of liquid water (at the zenith location).  One major event is present, during June 2.

Figure 3.  Zoom version of the main event on June 2, showing the parameter "TB2,zenith - TB2,30_degrees,zenith_equivalent."  At the arrow symbol I wiped the radome dry, after which the parameter is close to zero.  At June 3.73 I inadvertently disconnected power to the WVR, and during its warm-up there were irregularities in the plotted parameter.

Theoretically, TB1Z should be less affected by radome water because liquid water has a frequency-squared spectral index at the WVR frequencies.  In other words, radome water affects TB2Z about twice as much as it affects TB1Z.  I have correlated TB2ZE and TB1Z with the real-time Lz solution for times known to be free of radome water, and then used TB1Z and TB2ZE to calculate Lz for all data.  This permits a solution for Lz that is much less affected by radome water.  I'll call this liquid burden "LIQmodel."  I determined that LIQmodel = -116.4 -4.7484 * TB1Z + 15.07706 * TB2ZE, where TB1Z and TB2ZE.   LIQmodel is plotted in the next (and subsequent) figure(s).

Figure 4.  This cloud liquid solution is based on TB1Z and TB2ZE.  The June 2 stratus cloud event exhibits a 200 micron peak instead of the uncorrected 1000 micron peak shown in Fig. 1, implying that most of the high Lz values in the real-time solutions for June 2 were due to radome water.

Figure 5.  The blue trace is LIQ for times logged as CLR.  The first CLR measurements occurred June 2, after the major cloud episode of June 2.

In this figure the gaps in the "CLR LIQ" (blue) trace exist where clouds were present, and in all cases the "all LIQ" (red) trace is higher than the interpolated "CLR LIQ" (blue) trace.  The difference between these two traces is an improved estimate of true LIQ value, unaffected by variations in the water vapor altitude distribution.  The fact that the blue trace is always positive must be caused by the real-time analysis program's use of retrieval coefficients that are based on conditions that exist at a site that is at a higher elevation than the ROOF site (where pressure broadening of the water vapor line is less, and where TB2 would have a lower value than at a sea level site, unless clouds were present).  The positive offset could be accounted for if the real-time program uses retrieval coefficients were for Goldstone Tracking Station, at 4000 feet ASL.  In this situation it is acceptable to perform a simple "offset correction" to the real-time LIQ values.

The scale factor change to the real-time LIQ values should be small, and will be unrelated to the fact that an offset calibration was needed.  Any scale factor change will be related, instead, to the fact that the temperature of the clouds for ROOF were, on average, different from the temperature of the simulated clouds in the retrieval procedure.  At the present time I do not know if this difference is significant.

Figure 6.  Final version of calibrated cloud liquid burden, produced by subtracting teh CLR LIQ (blue) trace in the previous figure.

This plot of overhead cloud liquid burden incorporates a correction for dew accumulation on the radome, as well as a correction for the effect of variable (and unkown) water vapor altitude distribution. What is unknown is whether the ROOF cloud temperatures were approximately the same as those upon which the retrieval coefficients are based.  It is thought that RAOBs from Madrid were used to derive the retrieval coefficints, so it is quite likely that the ROOF cloud temperatures are different from the clouds generated from the Madrid RAOBs.  Therefore, another strategy will be developed for deriving cloud liquid burden that is appropriate to the ROOF conditions.

Another Strategy for Deriving Cloud Liquid Burden

Another strategy will be described for deriving Lz.  It was used with an averaged data set, made to be 1/3 the size (to fit my spreadsheet) consisting of averages of 3 WVR cycles.  To review the analysis of Fig.2, above, recall that the WVR files contain two versions for TB2: 1) TB2Z, the value of TB2 actually measured at the zenith, and 2) TB2ZE, a value for TB2 measured at 30 degrees but converted to a zenith equivalent.  During dry radome conditions both versions of TB2 should be the same.  The following figure shows the difference between the two versions of TB2 (using the 3-cycle average data) and a plot of cloud cover fraction at the Santa Barbara Airport, 2 miles away.

Figure 7.  TB2Z minus TB2ZE for only clear weather conditions (green) and cloud cover fraction at nearby Santa Barbara Airport.  The data have undergone a 3-cycle block averaging.

This figure is essentially the same as Fig. 2.

During clear weather conditions TB1 and TB2 should depend only on the profile of vapor with altitude.  If the shape of vapor distribution with altitude were the same at all times, and only the mixing ratio of water vapor at each altitude varied in synchrony with all other altitudes, then TB2 versus TB1 would form a straight line.  The following figure shows a correlation of ROOF data TB2ZE with TB1Z for clear weather conditions only.

Figure 8.  Correlation of TB2ZE with TB1Z for only clear weather conditions.  The thick black line is a "fit" to the data.

This correlation is consistent with theoretical calculations for sea level sites.  The introduction of cloud liquid water would increase TB2 at the rate of 4.4 K/100 microns, and increase TB1 at the rate of 2.0 K/100 microns.  In other words, the effect of adding cloud liquid is to produce a scatter of points to the upper-right of the cloudless location, as shown in the next figure.  (For WVR afficionados, the slope of the fitted equation implies that when TB1 and Tb2 are high, associated with large water vapor burdens, the altitude distribution is water vapor is increased more at low altitudes than at high altitudes, with the "alpha" parameter varying from 0.50 at low Vz to alpha = 0.45 for high Vz; this is a credible scenario.)

Figure 9.  Same as previous figure except that all weather conditions are included.  The data above the thick black fit line are produced by clouds.

In this figure the track of points going to the upper-right are due to cloud liquid droplets.  The set of points near the top that extend to the upper-left, beyond the border (to low TB1 values) is associated with the June 2 radome water event, and is probably caused by uneven accumulation of water along the top of the radome, which would produce incorrect radome corrections to TB1 (based on the TB2Z and TB2ZE difference).  This problem is a limitation of a WVR for which the two channels (20.7 and 31.4 GHz) view the sky through different parts of the radome.

The lowest TB1 data (19 K) correspond to a vapor burden of about 1.0 cm, whereas the highest TB1 data (44 K) correspond to a vapor burden of 2.9 cm.  Considering the theoretical responses of TB1 and TB2 to changes in vapor burden and cloud liquid burden (Vz and Lz), I derive that:

    TB1Z [K] = 6 + 13.3 * Vz [cm] + 1.98 * Lz [microns]
    TB2Z [K] = 10 + 5.59 * Vz [cm] + 4.37 * Lz [microns]

Alternatively, it is possbile to solve for Lz from TB1Z and TB2Z:

    Lz [microns] = 28.26 * TB2 -11.88 * TB1 - 211

Using this equation yields a solution for Lz shown in the next figure.

Figure 10.  Cloud liquid burden for the ROOF period (red trace), based on TB1Z corrected for radome water effects and TB2ZE (which is unaffected by radome water effects), using the above equations for Lz, and cloud cover at nearby Santa Barbara Airport (green trace).

The virtue of this figure's Lz trace over the one presented earlier (in Fig.'s 4 to 6) is that an appropriate scale factor has been used that corresponds to a typical temperature for the ROOF clouds of 10 C (whereas the previous solutions for Lz were based on Madrid coefficients, and clouds at a different temperature).  The Lz equation for ROOF conditions produces Lz values that are almost twice as large as those produced by the Madrid coefficients (which could be explained by the clouds in Madrid being at higher altitudes and thus colder by about 25 C).

This solution for Lz(t) can be improved using the same concept that was applied to Fig. 5 to produce Fig. 6; namely, by creating a table of CLR condition Lz values and subtracting an interpolation of this table from the individual solutions for Lz.  To do this right requires that the "Observer Log" be codified for use by programs, specifically, to indicate sky Cloud Cover, CC, so that Lz for CC=0 is used in the correction table.  The Observer's Log has been entered into a spreadsheet, and the following graphs show some of what was logged.

Figure 11.  Temperature (red, blue and red), pressure (green) and cloud cover (black) during the first half of the ROOF observing period.  Temperature was recorded using a cheap indoor/outdoor thermometer until June 5 (located within a foot of my bedroom window).   From June 5 to June 14 two quality digital thermometers (Taylor and Radio Shack products) was used in identical white boxes placed two yards from the ROOF room, one to the west (in an orange tree) and one to the east (above an oleander bush); the lower of the two readings is plotted here (they were usually within 0.4 C of each other).  Starting June 11 an IR radiometer was pointed to the horizon for the measurements, and these are plotted (red trace).  The IR radiometer has an applicable range of approximately 11 km, so some of the flux that led to reading was due to tree emission at a distance of 1 or 2 km.  Barometric pressure is from a hiker's watch, calibrated to agree with the ROOF altitude and the Santa Barbara Airport readings.

Figure 12.  Same as above, except for the second half ot the ROOF onserving period.

There is a great deal of uncertainty in the accuracy of the temperature readings in these two figures.  Measurements made June 7 showed that a horizontal gradient of at least 3.3 C per 1000 feet existed in the eastward direction from the ROOF site along a horizon view.  I used a digital thermometer at the end of a 14-foot pole at a location 1000 feet east of the ROOF site, and measured air that was cooler by 3.3 C; if I could have hoisted the pole higher I probably would have measured an even greater gradient, given that the vertical gradient was negative over the 14 feet above the ground.  Just two yards east of the ROOF site I measured a difference of 0.8 C over a horizontal distance of only 6 feet.  I conclude that the ROOF location, being a mobile home residence, close to other such residences, must create a "heat island." Further, the gold course 100 to 1200 feet east of the ROOF site is in a hollow (creek bed) that can be the site for downslope air in the evening.  Even the IR radiometer has serious limitations since its applicable range is so great.  The ideal surface temperature measuring unit for a site that is not located on flat ground is an IR radiometer with an applicable range that approximates the applicable range of the MTP's high frequency channel #3, which is 323 meters (1060 feet).  Alas, commercial IR radiometers are designed to operate in the clear window 8 - 14 microns, so a special design would be required to achieve the desired applicable range.  These uncertainties will be referred to in the data analysis section of this web site.

Using the times when I logged zero cloud cover, it was possible to create a table of LIQ corrections.  These corrections were subtracted from the TB1/TB2 solutions to produce the following figure.

Figure 13.  Cloud liquid burden for the ROOF period (red trace), based on TB1Z corrected for radome water effects and TB2ZE (which is unaffected by radome water effects), using equations for Lz that apply to the ROOF site, and corrected for LIQ bias (due to water vapor altitude distribution changes) by subtracting interpolated LIQ solutions for times when the sky was logged to be CLR.  Cloud cover recorded at the ROOF site is shown by the green trace.

This figure's LIQ values are much closer to the zero line during clear weather conditions, which is the result of forcing them to zero at times when I logged CLR for the sky condition and interpolating in between these times.  The standard deviation of LIQ during CLR conditions is 4 microns!  The cloud cover data is from the observing log, and correlates quie well with the meteograms for the Santa Barbara Airport (2 miles away), as can be seen by comparing the cloud cover traces in this figure with that for Fig. 10.  In general, it was slightly less cloudy at the ROOF site than at SBA.
 
 
 
 
 

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This site opened:  July 5, 2001.  Last Update:  July 18, 2001