Field data report for the First Radiobrightness Energy Balance Experiment (REBEX-1), October 1992-April 1993, Sioux Falls, South Dakota John F. Galantowicz Radiation Laboratory Department of Electrical Engineering and Computer Science The University of Michigan Report RL-913 February, 1i95

Abstract We describe the experimental apparatus, methodology, and measurements from the first Radiobrightness Energy Balance Experiment (REBEX-1), conducted from October, 1992 through April, 1993 near Sioux Falls, South Dakota. Three microwave radiometers measured the apparent radiobrightness of a grassy site at 19, 37, and 85 GHz. Augmenting these data were measurements of sky radiobrightnesses, terrain and sky infrared radiometric temperatures, net and global radiation, soil temperatures, soil heat flux, rainfall, air temperature, relative humidity, and wind speed. We also acquired 100 images of the radiometer observation area over the course of the experiment using a video camera and digitization hardware. We report the experiment log, the microwave radiometer calibration record, known errors in the data, summary and monthly plots of the data, the video images of the site, and snow depth and soil moisture data. We also describe post-experiment corrections to the microwave radiometer calibrations and radiobrightness data.

11.

Contents 1 Introduction 1 2 Apparatus 1 2.1 Installation....................................... 10 3 Observations 16 3.1 Experiment log....................................... 16 3.1.1 Summary of experiment conditions..................... 25 3.2 Microwave radiometer calibration record......................... 25 3.3 Soil moisture sample data................................. 29 3.4 National Weather Service data................ 31 4 Radiobrightness processing and analysis 33 4.1 Editing radiobrightnesses for out of range values.................... 33 4.2 Editing sky radiobrightnesses for reflector position errors......... 33 4.3 37 GHz calibration correction for day 403........................ 34 4.4 Estimating actual sky radiobrightnesses......................... 36 4.5 85 GHz recalibration for days 347-403........................ 39 4.6 Alternative calibration parameterization......................... 41 4.7 TAP sensitivity to rl estimates............................ 42 A REBEX-1 summary graphs A-1 B REBEX-1 monthly graphs B-1 C Video images of the REBEX-1 site C-1 D REBEX-1 day to calendar date conversion chart D-1 111

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1 Introduction The Radiobrightness Energy Balance Experiments (REBEX) are a series of field studies designed to track the microwave radiometric response of terrain to antecedent weather. The purpose of REBEX-1 was to examine the link between radiobrightness and land-atmosphere energy fluxes in the northern Great Plains through the course of wintertime freezing and spring thaw. REBEX-1 ran from October, 1992 through April, 1993, making 17200 observation cycles encompassing vegetation senescence, snowpack formation, soil freezing, and thaw. The study site was on the grounds of the EROS Data Center (EDC), U. S. Geological Survey, near Sioux Falls, South Dakota at 43043/ N latitude and 96030' W longitude. The purpose of this report is to describe the experimental apparatus and installation, record information from the experiment log, present the complete set of acquired data in graphs and tables, and examine errors in the data. 2 Apparatus REBEX-1 had two major instrument subsystems: the Tower Mounted Radiometer System (TMRS), with microwave radiometers constructed specifically for REBEX, and the micrometeorological subsystem (MMS), a collection of commercially available instruments for monitoring local weather conditions. Table 1 lists the specifications of the TMRS microwave radiometers. The radiometers simulated the observation angle, bandwidths, and three of the four frequencies of the spaceborne Special Sensor Microwave/Imager (SSM/I), a Defense Meteorological Satellite Program instrument. TMRS measured both terrain apparent radiobrightnesses and sky radiobrightnesses at 19, 37, and 85 Frequency (GHz) 19.35 37.0 85.5 Wavelength in air (mm) 15.5 8.1 3.5 IF bandwidth (MHz) 10-250 100-1000 100-1500 Mixer operation Double-sideband Polarization Horizontal Integration time 6 s Antenna 3 dB beamwidth 100 Incidence angle 530 (terrain brightnesses) Nominal zenith angle 450 (sky brightnesses) Table 1: Microwave radiometer specifications. 1

GHz. We manually calibrated the microwave radiometers at the beginning of tile experiment using ambient and liquid nitrogen temperature microwave absorbers (Eccosorb). In addition, the system automatically executed gain recalibration of the radiometers during the experiment using internal noise reference sources (matched microwave loads). Section 3.2 discusses radiometer calibration in detail. Table 2 lists the specifications of each MMS instrument along with the parameters measured. The Infrared Temperature Transducer-hereafter referred to as an IR radiometer-produced a temperature output computed from a 150 field-of-view thermal infrared radiometric measurement and an assumed target emissivity of 0.95. The IR radiometer and the other MMS instruments were factory-calibrated. We were unable to confirm most of these calibrations independently. We checked the soil thermistor calibration and signal conditioning circuitry by immersing the probes in an ice water bath. All thermistor channels reported the ice bath temperature to be 273.15 K to within 0.1 K. We confirmed rain gage and anemometer operation by manually actuating switch closures in each. During the experiment, nighttime global radiation values were between 0 and 2 W/m2 and the maximum relative humidity value was 101.5%, providing indirect confirmation of the calibration accuracy of the pyranometer and humidity probe, respectively. Figure 1 shows the interior of the small heated trailer (1.5 m x 2.4 m floor dimensions) on site that sheltered the data acquisition and experiment control electronics. A line running from EDC to a circuit breaker box in the trailer provided 120 VAC power. An Apple Macintosh II computer controlled all aspects of the experiment and provided a modem link to our offices in Ann Arbor, Michigan. A custom designed program called FluxMon-operating in the HyperCard software development environment-managed data acquisition from all devices except the video camera, automatically controlled power to the instruments and heaters, and provided a graphical interface for control parameter adjustment and manual radiometer calibration. FluxMon communicated with the IR radiometer via formatted character strings transmitted through one of two Macintosh serial ports. A National Instruments NB-MIO-16 board with an AMUX-64T multiplexer provided 32 differential analog to digital conversion (ADC) channels and a TTL (transistor-transistor logic) 2

Instrument Model Parameters Accuracy Range REBS Net Radiometer Q-6 Net radiation 1 N/A N/A Eppley Black and White Pyranometer 8-84 Global radiation (shortwave)' ~1.0% 0-1400 W/m2 Thornthwaite Soil Heat Flow Disk 610 Soil heat flow at 2 cm depth N/A N/A Met-One Anemometer 014A Wind speed at 10 m height' ~1.5% or 0.11 m/s 0.447 45 rn/s Texas Electronics 525 Rainfall ~1.0% 0-5.1 cm/hr Tipping Bucket Rain Gage Vaisala Relative Humidity Probe HMP35AC Relative humidity ~2% RH over 0-90% RH 0-100% RH ~3% RH over 90-100% RH Campbell Scientific Thermistor 107 Air temperature at 1.8 m I0.2 K 240 —321 K Campbell Scientific Thermistor 107B Soil temperatures at 2, 4, 8, |~0.2 K 240-321 K 16, 32, and 64 cm depths Everest Interscience Infrared 4000ALCS Thermal IR surface and ~0.5 K 243 —373 K Temperature Transducer I sky temperatures Both instantaneous and experiment cycle average values of these parameters were recorded. Table 2: Micrometeorological instruments and parameters. N/A indicates data not available.

Figure 1: Interior of the trailer on site sheltering data acquisition and device control electronics and the Macintosh computer running the FluxMon HyperCard stack which controlled the experiment. counter/timer channel. NB-DIO-24 and NB-TIO-10 boards provided TTL input/output and additional counter/timer channels. All of the boards fit into internal NuBus expansion slots in the Macintosh. Figure 2 shows the TMRS housing at the top of the REBEX tower. The tower-based electronics were divided into five modules: one each for the 19, 37, and 85 GHz radiometers, one for the IR radiometer and video camera, and one in the back of the housing's center compartment for the electrical bus. In addition, a motor and screw drive mechanism in the center compartment positioned the door for sky brightness measurements during each experiment cycle. Figure 3 shows the 85 GHz radiometer module. The 19 and 37 GHz radiometers have similar component layouts. In each radiometer module, a mixer down-converted the RF signal to IF, two amplifiers boosted the signal, and a bandpass filter selected the bandwidth. Three 12.2 m coaxial cables carried the IF signals from the tower to the trailer. Section 3.2 has more detailed radiometer information. The three radiometer modules differed only in the frequencies of their RF (radio frequency) and

19 GHz Radiometer 37 GHz Radiometer <__ __./ Video Camera 85 GHz Radiometer Infrared Radiometer /1~~ ~~ ~~Door & Sky Reflector Figure 2: The TMRS-1 radiometer housing.

Figure 3: The 85 GHz radiometer. The 19 and 37 GHz radiometers have layouts which are comparable component by component. IF (intermediate frequency) components and in the voltage level of the regulators for their local oscillators. The radiometers contained five regulators: one each for the two amplifiers and the local oscillator and two for the RF switch driver. The radiometers were interchangeable on the housing power bus and could be rotated to achieve any combination of polarizations. Two fans in each radiometer circulated air inside and outside the component compartment for even temperature distribution. Two multiconductor cables ran from the trailer to the housing's center module containing the trunk of the housing power bus. The center module had DC voltage regulators that conditioned power for the microwave radiometers and five relays that switched power to each of the microwave radiometers, the IR radiometer, and the fans. There was one regulator for each radiometer local oscillator and one for the fans. Unregulated DC power from- the trailer supplied these regulators as well as those in the radiometer modules and the IR radiometer. The multiconductor cables also carried power for the housing door motor, TTL signals for running the door, the relays, and the RF antenna-reference load switch drivers, duty-cycle controlled 120 V power for the radiometer heaters, leads for the three thermistors in each radiometer (one each on the antenna, the reference load, and 6

4~. 19 GHz Radiometer 37 GHz Radiometer Video Camera 85 GHz Radiometer |l iHi~ Infrared Radiometer Door & Sky Reflector Figure 2: The TMRS-1 radiometer housing. 5

' ~ Figure 3: The 85 GHz radiometer. The 19 and 37 GHz radiometers have layouts which are comparable component by component. IF (intermediate frequency) components and in the voltage level of the regulators for their local oscillators. The radiometers contained five regulators: one each for the two amplifiers and the local oscillator and two for the RF switch driver. The radiometers were interchangeable on the housing power bus and could be rotated to achieve any combination of polarizations. Two fans in each radiometer circulated air inside and outside the component compartment for even temperature distribution. Two multiconductor cables ran from the trailer to the housing's center module containing the trunk of the housing power bus. The center module had DC voltage regulators that conditioned power for the microwave radiometers and five relays that switched power to each of the microwave radiometers, the IR radiometer, and the fans. There was one regulator for each radiometer local oscillator and one for the fans. Unregulated DC power from the trailer supplied these regulators as well as those in the radiometer modules and the IR radiometer. The multiconductor cables also carried power for the housing door motor, TTL signals for running the door, the relays, and the RF antenna-reference load switch drivers, duty-cycle controlled 120 V power for the radiometer heaters, leads for the three thermistors in each radiometer (one each on the antenna, the reference load, and 6

the heat siInk), and the serial communications lines to tile IR radiometer. Separate 120 \ power and 75 Ohm coaxial cable lines for the video camera ran directly to the IR radiometer and video camera module. Trailer-based electronics provided an interface between TMIRS/MMS instruments and the Macintosh's data acquisition and control boards. For each radiometer, a square law detector converted the IF signal from the tower to AF (audio frequency, in this case 0-20 kHz). AF amplifiers in a temperature controlled compartment then conditioned these signals for ADC by the NB-MIO-16. Leads from the TMRS and MMS thermistors were tied to bridge circuits designed to scale the bridge output voltage to the input range of the NB-MIO-16. We used thermistors for all temperature measurements because of their accuracy and ease of use. Debouncing circuits conditioned anemometer and rain gage switch closure signals for the counters and instrumentation amplifiers conditioned the rest of the MMS signals for ADC. The NB-MIO-16 digitized the signals from all of the instruments with voltage outputs-the microwave radiometers, the internal radiometer thermistors, and most of the MMS instruments. The NB-MIO-16 sampled the AF radiometer signals separately on three ADC channels at 40 ksamples/s for 6 seconds. FluxMon then calculated radiometer output values in instrument counts depending on which of two possible radiometer modes was activated-total power mode or Dicke mode. In total power radiometer (TPR) mode, we calculated radiometer outputs by simply averaging each data stream. In Dicke radiometer mode, a 1250 Hz TTL signal generated by the NB-MIO16 counter/timer modulated the RF input between the antenna and the internal reference load. This TTL signal also triggered ADC sampling, synchronizing it to the RF input modulation. We calculated the Dicke-mode radiometer output values by first numerically demodulating the data streams and then averaging. During automatic radiometer operation, FluxMon used TPR-mode for gain recalibration measurements off the internal reference loads and Dicke-mode for brightness measurements. Section 3.2 describes radiometer calibration and measurements in more detail. The NB-DIO-24 provided digital TTL input and output lines. These controlled power relays for the radiometers, the radiometer heaters, the radiometer fans, the humidity probe, and the 7

motor that opened and closed the radiometer housing door. The input lines read signals fronm three microswitches indicating the door's position-fully opened. fully closed, or opened to the sky reflection position. The NB-TIO-10 counter/timer channels generated TTL square wave signals for setting radiometer heater power levels. FluxMon determined heater duty cycle settings approximately once per minute and reset the timer channel outputs based on a ten second total period. Counter channels counted switch closures from the anemometer and rain gage. FluxMon calculated wind speed based on number of switch closures and elapsed time since the last counter reset. Each closure of the rain gage switch was equivalent to 0.254 mm (0.01 in) of rain. Figures 4 and 5 show the trailer boxes containing interface and power electronics, respectively. The power box contained 12 V regulated and 14 and 20 V unregulated DC power supplies. These provided power to bridge circuits in the interface box through voltage regulators. The 12 V regulated supply provided power for the radiometer housing door motor. The power box also contained three 120 VAC zero-switching relays for radiometer temperature control. FluxMon automatically switched off the heaters during radiometer thermistor readings because of noise from the 120 VAC heater lines. In order to monitor site conditions throughout the experiment, the TMRS radiometer housing was equipped with a black and white video camera that observed roughly the same area as the radiometers. A SuperMac VideoSpigot NuBus board enabled manual acquisition of video stills through the Macintosh. We acquired still images of the site by establishing control over the Macintosh via phone lines and Timbuktu/Remote software. Typically, after digitizing an image using SuperMac ScreenPlay software, we transferred the image file and the latest experiment data files to our Michigan office. Timbuktu/Remote software also enabled remote control of the experiment from Michigan. We frequently used this feature to analyze problems and change control software during the experiment. The 9600 baud Hayes modems used during the experiment were capable of transmitting a replica of the remote Macintosh's screen in about 30 seconds and downloading a 235520 byte video image in about 5 minutes. Appendix C contains copies of the video images taken of ti site during the experiment. 8

Figure 4: Trailer-based data acquisition interface electronics. I~~~~~~~~~- S' 1L7p-~~L,L:~~~~~~~~.E<,) * - zl 8 Ift~~b:*EfE.'.'~ --- ^v*E it~:::::::)l.....~ ~~~:::::::;::::::::: t )i*i;ii~ —— * ---— a —-— @ —* *A.':~LI as~=..............:.:'''.'...... l,.,~~.H..":'':.',,.'............,'' ___ ~~~~~~~~~~,,,,..,,,,.',.,.', t __~~ ~1I~~~~~ ~~~ *.r~ ~rr~ Flgure 5: ralle~~,r-bsdpwrsppyeeto1 Ij:+iJI~li,~ ~~~~~~r~~ ~I~t' L ~IC~*L~::;-:::

2.1 Installation Figure 6 shows the EDC site as seen from the east. The TMRS radiometer housing is positioned atop the REBEX tower. The housing was attached to the 9.14 m (30 ft) aluminum tower via a winched shuttle. We installed and calibrated the radiometers with the housing lowered and left it at full height during all experiment cycles. The housing was made from aluminum sheet welded to a tube frame and the bottom hinged door was stainless steel. Figure 7 shows the housing with its back cover removed, revealing the housing power bus, the protruding door motor mechanism, and the housing's center module. The bracket mounting the housing to the shuttle permits rotation of the housing into a vertical position for servicing and module removal. System installation by two workers required approximately two eight-hour days. We connected the three pre-assembled 3.05 m (10 ft) tower sections, slid on the shuttle assembly, and attached the guys and the anemometer to the top of the tower. We fixed the tower's hinged steel base in place using four galvanized steel pipes inserted through the base into the ground and topped with threaded caps. The pipes served only to keep the base from slipping and were not held in the ground strongly enough to keep the tower vertical. We raised the tower by locking the guy opposite the hinged side of the tower base to a vehicle's hitch and simultaneously lifting the tower by hand while towing the guy. The other two guys were attached to their earth screw anchors during the tower raising. The orientation of the tower was such that the radiometers observed an area 570 south of west, as shown in the plan view of the site in Figure 8. Figure 8 shows the distribution of the other instruments to the southeast of the tower. The mounts for the net radiometer, pyranometer, rain gage, and air temperature and humidity probe were simple galvanized steel pipes. The anemometer was attached to the top of the tower at a height of 10 m. We planted the poles for the net radiometer, pyranometer, air probes, and rain gage into the ground as far away from the trailer as cabling lengths would allow. We were careful to leave the region of terrain in the fields of view of the radiometers undisturbed through the installation process. We chose to observe an area to the southeast of the trailer and the MMS instruments so that wintertime prevailing winds from the northwest would not cause snow drifts on the site. We 10

Radiometer Housing Anemometer Guy Wire / I Radiometer Observation Area,,0 T,. 3(. (4 m x 2 m)!''' Tower Net Radiometer RE- s fo, Pyranometer \ Trailer Soil Temperature Probes (Buried) _oe (uid Air Temperature & Soil Heat Flow Relative Humidity Probes Disk (Buried) Figure t' View of the'EBE-1 site from the a st..,,1.1,.0F,...- - -;,.-,...,.:.N-.0....; -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,~~ 11

Figure 7: View of the radiometer housing with its back cover removed. Inserted into the housing are (from the far side) the 85 GHz radiometer, the IR radiometer and video camera module, the center 12

Guy wire Trailer.........i..,Air temperature &:................. relative humidity Guy wire 7W' *I~Ifl Tower 57~ /. Guy wire Rain gage 0 rNadioeter S Pyranometer radiometer Soil 12 m temperature probes (buried) Soil heat flow disk (buried) Snow / Radiometer gage observation area 4m Figure 8: Plan view of the REBEX-1 site. 13

To video camera 53.3 cm Light grass 14.0 cm Dens grass 450 Figure 9: Graduated PVC pipe with alternating 1.27 cm (0.5 in) black and white stripes used for gaging snow depth from video stills of the REBEX-1 site. made a graduated 5.1 cm (2 in) diameter PVC pipe with alternating 1.27 cm (0.5 in) black and white stripes and installed it into the ground within the video camera field of view (Figure 9). The tube was set at a 450 angle to the ground so that the broad side faced the video camera. Using images acquired from the video camera, we were able to make estimates of snow depth on the site almost daily (see Appendix C). We buried the soil heat flow disk at 2 cm depth below the soil surface and the soil temperature thermistors at depths of 2, 4, 8, 16, 32, and 64 cm. This procedure is shown in Figure 10. We chose an undisturbed area of ground under which to install the temperature probes. Because the soil was obscured by grass roots and litter, identifying the surface was possible to within only about 0.5 cm. The temperature probes themselves were 1 cm in diameter. We made six 18 inch long horizontal holes in the side of a trench using a pointed aluminum rod forced through a T-shaped guide with pre-drilled holes at the appropriate probe depths. We then inserted the probes into the holes and back-filled the trench. We installed the soil heat flux disk under a separate undisturbed area by cutting into the sod and soil with a knife and inserting the disk horizontally. 14

Figure 10: Insertion of the soil temperature probes. At the time we took this picture, we had already inserted the probes in the side of the trench and refilled it, burying the 64, 32, and 16 cm probe cables. Cables leading to the 2, 4, and 8 cm deep probes protrude from the side of the trench. 15

3 Observations 3.1 Experiment log The following is a condensed version of notes from the TMRS log book plus subsequent observations inferred from the data. All dates are given as day numbers from January 1, 1992 (day 1). For example, January 1, 1993 is day 367 since 1992 was a leap year. A REBEX-1 day number vs. calendar date chart is given in Appendix D. All times are Universal Time (UT) which is six hours ahead of Central Standard Time (CST) at the site. While the experiment was operational, FluxMon initiated measurements at pre-set timesinitially at every 10 minute mark of the hour and then later every 15 minutes. Data sets were time stamped at the end of each experiment run which lasted approximately 5 minutes. We acquired video images via the telephone link infrequently at first but then almost every day when there was snow on the ground. Setup of the experiment began on day 269 and installation was completed by day 271. Several equipment failures forced a delay in experiment commencement until day 279, when data taking began at 1805 UT. Chief among these were the failures of the IR radiometer and one of the three microwave radiometer IF detector units and general electrical bus noise. Rewiring the infrared temperature transducer onto an independent DC power supply circuit resolved that failure and rewiring one of the 85 GHz circuits resolved the DC problems. We had no spare IF detector units and we decided to use the two remaining detectors in the 19 and 37 GHz radiometers and place the faulty diode with the 85 GHz radiometer. Although the 85 GHz output was unusable, we left the 85 GHz radiometer installed to monitor the performance of the complete electrical system. This was the configuration when the experiment began. Over the course of the experiment, cold weather periodically affected instrument performance. The rain gage was not heated and so did not record snowfall accurately, if at all, and only worked reliably in warm weather. Dew, frost, and snow interfered with operation of the net radiometer and pyranometer, covering the instrument domes and blocking radiation. A heavy frost in early February, 1993 apparently caused the seizure of the anemometer lasting from day 404 to 409. 16

Day 279 1710 UT: With FluxMon controlling temperatures in the radiometers to 323 K and in the AF amplifiers to 313 K, we took complete hot/cold source calibration data for the 19 and 37 GHz radiometers. 1810 UT: FluxMon initiated acquisition of the first data set. During this and the following measurement set we established the quality of the calibrations by holding microwave absorber material in front of the radiometers for later comparison of the measured radiobrightnesses to the physical absorber temperature. See Section 3.2 for more details on calibration checks. Observed that the grass canopy was thick and alive at this point. Day 287-290 Took samples of soil and grass for moisture calculations on day 287 at 2100 UT, day 288 at 1400 and 2100 UT, day 289 at 1400 and 2100 UT, and day 290 at 1400 UT. Day 288 Rechecked radiometer calibration during the 1743 and 1753 UT measurement cycles. 1830 UT: Recalibrated the 37 GHz radiometer because of an observed negative bias in radiobrightness of more than 1 K. 1934 UT: Regular measurements resumed. 2030 UT: Extended the delay between measurements to 15 minutes. Day 289 Computer clock stopped at 0934 UT and did not resume until 1318 UT when we manually disturbed the computer keyboard or mouse. Similar clock stoppages occurred several times during the course of the experiment and were resolved by manual means each time. The problem seemed to be attributable to a suspension of normal computer timekeeping interrupt generation when large data streams were collected from the microwave radiometers by the NB-MIO-16. The problem was resolved in later implementations of the software by performing a query of the system clock after each large data acquisition run. 17

After the clock stoppage, the radiometers reached temperature stabilization at 1500 UT and we performed calibration checks at 1644, 1658, and 1703 UT. There was patchy frost in the morning, with periodic snow flurries and, later in the day, light rain. Day 295 Cleared up a problem interpreting the string returned by the IR radiometer. IR radiometer data had some missing points up to this time as a result. Day 296 1900 UT: Trailer temperature rose above that of the temperature-controlled AF amplifier compartment, corrupting microwave radiometer data until day 297 at 0200 UT. Day 298 1900 UT: Trailer temperature exceeded maximum as on day 296. Day 300 0300 UT: Clock stoppage occurred as on day 289. Day 301 1700 UT: Cleared clock stoppage. 2130 UT: Restarted experiment after temperature stabilization. Day 307 First significant snowfall occurred. Snow depth was not uniform over the site because of grass cover pockets and clumps. 2100 UT: Took samples of soil for moisture calculations. Day 308 1720 UT: Stopped experiment in order to a install new IF detector unit for the 85 GHz radiometer. Day 309 0030 UT: Installed 85 GHz radiometer detector unit and recalibrated all three radiometers. 1630 UT: Calibrated 85 GHz radiometer again and found that the calibration 18

parameters had changed from their 0300 UT values. We left the radiometer running under the assumption that faulty data might be edited out if the radiometer were bimodal with distinct calibrated and uncalibrated states. The subsequent calibration drift was monotonic, however, until day 347 at 1118 UT. At that time TPR gain parameter measurements indicate an apparently spontaneous change in operating state. Although we performed no manual recalibration of the radiometers until day 403, we have attempted to calibrate for days 347 through 403 using calculated sky brightnesses as discussed in Section 4.5. Day 311 0415 UT: Clock failure occurred as on day 289. 1527 UT: Cleared clock failure. Day 330 1715 UT: The computer hung during a telephone session. Day 331 1730 UT: Rebooted computer and restarted experiment. Noted that some IR radiometer sky data was missing. Later analysis showed that this missing data corresponded to temperatures below -9.9 F when the number of characters in the string returned by the radiometer exceeded the available space in the format. This was not resolved until day 394. Day 338 1520 UT: The computer hung during a telephone session. 1730 UT: Rebooted computer and restarted experiment with temperatures controlled. Day 350 1850 UT: Radiometer housing door failed when door did not close completely, stopping the experiment. 1910 UT: Resolved problem and restarted experiment. 2230 UT: Door failed again, stopping the experiment. 19

Day 351 1805 UT: Implemented a software solution to the door failure problem by putting a timer on the motion. If the timer expired before the door was completely closed, the door would be left in whatever position it had reached at that time. A negative side effect of this solution was that sky measurements made in the experiment cycle following an incomplete door closure were made while the door remained in the incorrect position. We discovered this circumstance on day 415 when it became clear that extraordinarily high sky brightnesses were tied to experiment cycles when the door was nearly closed. These high values were later edited out of the data as discussed in Section 4.2. The door failures were found after the experiment to be the result of wear in the screw-drive mechanism. Day 357 0515 UT: Clock failure occurred as on day 289. 2045 UT: Restarted experiment under temperature control. Day 362 Radiometer data was clearly out of range beginning at 0950 UT. 2121 UT: Restarted the experiment after rebooting the computer. Day 366 Noted that radiometer heaters were running at approximately 23% of full power with outside air temperatures at 252 K. Day 380 1935 UT: Rebooted computer. 2230 UT: Restarted experiment under temperature control. Day 393 1130 UT: Clock failure occurred as on day 289. 20

Figure 11: The pyranometer on day 401 with frost on the dome obscuring the sensor. Day 394 2330 UT: Restarted experiment under temperature control. Fixed problem with IR radiometer regarding temperatures below -9.9 F (mentioned on day 331). Day 401 Returned to Sioux Falls for last maintenance trip. Noted that snow was up to 28 cm deep in places with less on top of grass tufts. 1750 UT: Stopped experiment to analyze the 85 GHz radiometer using test electronics built for operating it inside the trailer. Rewiring the link between the IF coaxial cable, the detector unit, and the AF amplifier eliminated noise and drift observed in the radiometer output. In order to make observations of frozen ground uncovered by snow, we cleared the snow off of the radiometer observation site (Figure 12) and the area over the soil temperature probes. The area below the net radiometer was not cleared. At this time there was a dense fog which coated exposed objects with ice and probably led to the failure of the anemometer, which did not rotate from day 404 at 0549 to day 409 at 0533 UT. 21

Figure 12: The radiometer observation area after snow removal on day 401. A cold fog has coated the grass blades with ice. Day 402 0300 UT: Recalibrated radiometers, checked calibration, and started experiment. Day 403 Checked calibration again at 1448 and 1504 UT before leaving Sioux Falls. Noted a great variability in radiobrightnesses and offsets from measured Eccosorb temperatures. Since when these measurements were made the absorber temperature was still 2.5 K warmer than the air temperature, the errors may be attributable to temperature gradients in the absorber and not to calibration error. A general practice should be made of equalizing the absorber and air temperatures before performing or checking calibration and keeping the absorber out of the sun and wind if possible. See Section 3.2 for more details on calibration checks. 22

Day 407 Missed several measurements due to rebooting. Measurement cycles missed were 14501620 UT and 1720-1835 UT. Light snow which fell beginning in the morning ended the period of observations of frozen ground without snow cover. Day 412 2230 UT: Clock failure as on day 289. Day 413 1650 UT: Restarted experiment under temperature control. Day 414 0730 UT: Door failed to open properly, stopping experiment. Day 415 1903 UT: Restarted experiment with temporary fix for door motion problem. 2305 UT: Completed software correction used in positioning door for sky measurements. This door failure was similar to the incomplete closures which began on day 351. Software installed at that time required the door to close completely for the following cycle's sky measurement to be made properly. If the door did not close completely after an experiment, then the following sky measurement would be made with the door in whatever position it had previously reached. After the correction at 2305 UT, the door opened either to the sky measurement position or to the ground observation position at the beginning of every experiment. Missed sky brightnesses were then clearly distinguishable since they had values very close to the ground brightnesses. Day 422 2210 UT: Macintosh hung. Day 423 1505 UT: Rebooted computer and restarted experiment before radiometer temperatures had stabilized. 23

Day 438 1305 UT: Clock failure as on day 289. Day 440 1650 UT: Restarted experiment after temperatures stabilized. Day 455 1120 UT: Clock failure as on day 289. 2307 UT: Restarted experiment after temperature stabilization. Day 457 0620 UT: Clock failure as on day 289. Day 458 1710 UT: Restarted experiment after temperatures stabilized. Day 459 1805 UT: Computer hung while we were trying to make a telephone connection to it. Day 461 2105 UT: Restarted experiment under temperature control. Day 465 1508 UT: Computer hung during telephone session. 2219 UT: Restarted experiment under temperature control. Day 471 1950 UT: Last complete measurement. Attempted to check calibration at 2024 and 2028 UT but radiometer electronics in the trailer had been disturbed during the disconnection of the MMS equipment. A sudden drop in radiometer gain at this point as determined by the internal load calibration indicated that this disturbance had invalidated the calibrations. 24

3.1.1 Summary of experiment conditions Table 3 summarizes hardware problems that lasted for significant portions of the experiment and divides the experiment into seven time periods by general site condition. More detailed descriptions of most entries can be found in the experiment log above, under either the first or last day of each entry. The experiment itself lasted from day 279 to day 471. Days Site coverage conditions 279-306 No snow, green grass cover, unfrozen ground 307-315 Snow cover 316-337 No snow, dormant grass cover, unfrozen ground 338-401 Snow cover 403-407 Snow cover cleared manually exposing frozen ground 408-452 Snow cover 453-471 Mostly snow free, dormant grass cover Days Hardware problems 279-295 IR radiometer: Some data missing due to serial communications error 295-394 IR radiometer: Data drop-outs of temperatures less than 249.9 K (-9.9~F) 279-309 85 GHz radiometer: Not installed due to missing IF detector 309-347 85 GHz radiometer: Installed but malfunctioning 347-403 85 GHz radiometer: Functioning but not manually calibrated 403-471 85 GHz radiometer: Functioning and calibrated 350-471 TMRS housing door: Frequently fails to open to sky reflection position 415-471 TMRS housing door: Frequently fails to close past sky reflection position 404-409 Anemometer: Not spinning due to frost Table 3: Summary of REBEX-1 site coverage conditions and hardware problems. 3.2 Microwave radiometer calibration record Complete manual calibration of the microwave radiometers required TPR-mode and Dicke-mode measurements (in ADC instrument counts) of (i) a microwave absorber soaked in liquid nitrogen (LN2) and (ii) an absorber at ambient temperature. TPR measurements of the internal reference noise sources also made at calibration time established a baseline value for radiometer gain drift corrections. The radiometers were always under computer-controlled temperature stabilization during calibration-that is, FluxMon automatically measured temperatures and set radiometer heater duty cycles about once every minute. The calibration data acquisition procedures built into FluxMon also triggered measurements of the radiometer internal reference load and antenna temperatures with each data sample. A thermistor embedded in the ambient temperature absorber gave its tempera25

Reference Temperature controlled noise source radiometer box (on tower) (matched load) Standard gain Intermediate frequency Bandpass horn antenna Isolator Mixer amplifiers filter Latching N ferrite circulator Local pcirculator 1Switch driver oscillator 10.2 m IF coaxial cable Trailer a e Counter/timer themperature controlled w 8 o 40 kHz sampling aahgeWCounlter/timer t lifr dctor Comput r Figure 13 is a block diagram showing the components of the microwave radiometers, all of whic included estimates of transmission line losses from the antenna to the receiver and from the reference load to the receiver. We arbitrarily defined the receiver as beginning at the output port (port 1) of the RF switch, a latching ferrite circulator. We formulated the following forward radiometer equation for the radiometer output signal: VD = CsD (L TAP + (1 r Tpa - Dof(1) L21 L21 temperature being measured, La is transmission line loss from the antenna to the receiver, a is the 26

Parameter 19 GHz 37 GHz 85 GHz r - 0.9 0.9 0.9 L21 1.1001 1.034854 1.13186 L31 1.18 1.034982 1.13494 Table 4: Estimated loss parameters. the Dicke-mode gain and offset parameters, respectively. We calculated apparent radiobrightness by inverting (1): TAP- L21 C VD ( - r) Tpa + Doff) (2) r/l Cs D L21 C,D and Doff were found through a two point Dicke-mode calibration: D 1 VDO (TAP17Tl + (1 - 771 )Tpal) - VD1 (TAPO 71 + (1 - /71)Tpa) (3 Do~ff = L (3) L21 VDO- VD1 VDo C8D - TAPor7L/L21 + (1 - 771)TpaO/L21 - Doff where subscripts 1 and 0 indicate data from the ambient and LN2 temperature sources. We estimated values for L21, L31, and r1, listed in Table 4, from manufacturers specifications. Precise radiometric measurements require a calibration curve established at a time as close as possible to the time of measurement. This is because radiometer outputs are sensitive to gain variations. The TMRS radiometers were most vulnerable to gain drift through the inevitable change in IF coaxial cable temperature and the commensurate change in loss through the cable. These cables were directly exposed to weather over most of their 12.2 m lengths. IF and AF amplifiers were also subject to gain drift over the seven month length of the experiment. By using the parameterization in (1), gain variation may be isolated to the parameter CoD. Reference load temperature and RF transmission line losses and temperatures are then the primary determinants of the radiometer offset parameter, Doff, and we assume these terms to be constant. To track gain drift, FluxMon automatically made TPR-mode measurements of the internal reference loads and their temperatures during each experiment cycle. Assuming that receiver noise temperature and DC offsets remained constant, we calculated a reference load gain parameter, CsREF: VnEEF Tref /L31 + Trec () 27

where VREF is the TPR-mode output in counts when switched to the reference load. Trcf is tihe temperature of the reference load, L31 is transmission line loss from the reference load to the receiver. and Trec is the TPR-mode receiver noise temperature parameter which includes DC offsets ill tile AF amplifier. We determined T,,rec during each manual calibration using LN2 and ambient temperature absorber data: Trec - 1 VANTO(TAPlr71 + (1 - rii)Tpal) - VANT1(TAP077 + (1 - 1)TpaO) (6) L21 VANT1 - VANTO where the parameters are defined as in (3) except that VANT is the TPR-mode output in counts when the RF switch is set to the antenna input. Dicke-mode and TPR-mode gains differ due to the differing mismatches and losses in the antenna and reference load transmission lines. The RF components preceding the receiver are passive and their losses and mismatches are constant. Provided that internal radiometer temperatures and, consequently, Trec are stable, the ratio of CsD to CREF will remain constant in time. That is, relative gain variation in the TPR reference load radiometer can be used to track variation in Dickemode gain using the relationship: CsD (t) _ CsREF(t) (7) CsD(O) CsREF(O) where t indicates the time of the experiment cycle and t = 0 is the calibration time. Figure A-9 in Appendix A is a graph of the TPR gain factors, CSREF, measured during each experiment cycle using (5). In each experiment cycle, FluxMon calculated CsD from CsREF using: csD(t) = CsREFO(t) CREF () (8) CsREF(O) We manually calibrated the microwave radiometers and changed the calibration parameters accordingly on the dates listed in Table 5. We also checked calibration accuracy by placing an absorber in front of the radiometer during regular experiment cycles. Table 6 gives the results of these tests. We calculated radiometric resolution as the standard deviation of error terms. We did not include the day 403 1448 and 1504 UT calibration checks in the radiometric resolution calculations because the Eccosorb temperature was more than 3 K over the ambient air temperature at that time. The discrepancy suggests that there was a temperature gradient between the Eccosorb surface and the 28

Radiometer J Day [ Time Doff Trec C. D/C, REF 19 GHz 279 1800 272.552 146.796 0.91918 309 1600 271.099 84.4456 0.91065 403 0100 270.710 68.48 0.91162 37 GHz 279 1800 310.754 2.76098 0.93106 288 1900 310.055 -10.00 7 0.93520 309 1600 309.465 -53.472 0.93452 403 0100 303.357 -38.874 0.94690 85 GHz 309 1600 292.432 225.183 0.91427 403 0100 276.149 122.348 0.92667l Table 5: Calibration parameters used during REBEX-1 from day indicated to day of next calibration. Some 37 and 85 GHz parameters were later modified. See Sections 4.3 and 4.5. thermistor embedded in it. For these times, Table 6 compares the 19 GHz apparent brightness to the Eccosorb thermistor temperature and the 37 and 85 GHz brightnesses to air temperature as approximations to actual emitting temperatures. In the future, the Eccosorb should be shielded from wind and direct sunlight and should not be brought into direct contact with the surface of the heated radiometers. 3.3 Soil moisture sample data We took soil samples from the REBEX-1 site on five days in October and November, 1992, using an 8.255 cm (3.25 in) diameter cylindrical coring tool. A 6.35 cm (2.5 in) high bit screwed on to the end of the coring tool, holding in place a set of rings which lined the cylinder. From the top of the bit, we inserted rings of 2, 2, 2, 8, 2, and 8 cm heights. To take samples, we drove the coring tool into the soil to a depth of 12.35 cm. We twisted the tool to break the soil at the bottom of the bit and extracted the core. We then sliced off the soil extending from the bottom of the bit, unscrewed the bit from the cylinder, and removed the core from the cylinder surrounded by the bit and the three lowest 2 cm rings. We sliced between the rings and between the bottom ring and the bit with a knife to make three samples of 2 cm thickness. We then slid the soil remaining in the bit into a 4 cm ring and removed the excess from the bottom. The soil samples then spanned 0-2, 2-4, 4-6, and 6-10 cm depths. We usually took grass samples before coring by cutting the grass over the sampling position as close to the soil horizon as possible. We first dried the grass and most of the soil samples in a 709C oven until the mass had reached a 29

19 GHz 37 GHz 85 GHz Day Time TECCO TAP A TECCO TAP A TECCO TAP A 279 1813 296.7 296.9 0.2 296.7 297.0 0.3 296.7 295.1 -1.1 296.7 296.3 -0.4 1823 297.4 297.6 0.2 297.4 297.6 0.2 297.4 296.8 -0.6 297.4 297.3 -0.1 288 1743 279.9 281.2 1.3 279.9 278.0 -1.9 279.8 280.0 0.2 279.8 277.9 -1.9 1753 279.9 280.2 0.3 279.9 278.6 -1.3 279.8 280.2 0.4 1854 281.8 281.8 0.0 281.8 280.6 -1.2 281.2 280.3 -0.9 281.2 279.9 -1.3 1903 80 80.8 0.8 1913 281.1 281.7 0.6 281.1 280.5 -0.6 281.5 281.7 0.2 281.5 281.2 -0.3 289 1644 278.1 278.5 0.4 278.1 276.8 -1.3 278.3 278.5 0.2 278.3 276.4 -1.9 1658. 277.6 277 -0.6 1703 277.9 279.3 1.4 277.9 277.2 -0.7 277.9 278.3 0.4 277.9 277.3 -0.6 403 0238 273.4 273.5 0.1 273.4 273.7 0.3 273.4 272.9 -0.5 273.7 274.5 0.8 273.7 273.9 0.2 273.7 273.4 -0.3 0243 273.3 273.3 0 _ 273.3 272.5 -0.8 273.6 274.3 0.7 273.6 273.8 0.2. 1448 272.3 271.7 -0.6' 269.82 266.2 -3.61 269.82 271.3 1.5 272.7 273.3 0.61 269.82 269.0 -0.81 269.82 271.4 1.6 1504 273.0 271.2 -1.8' 269.82 267.7 -2.11 269.82 271.4 2.' 273.2 273.0 -0.21 269.82 268.7 -1.1' 269.8 268.6 -1.21 Average A 0.24 -0.61 -0.53 Radiometric resolution 0.61 0.82 1These data were not included in radiometric resolution calculations as noted in the text. 2Air temperature used in place of measured Eccosorb temperature. Table 6: Calibration check results. TEcco is the temperature of the Eccosorb target at the time the TAP were measured. There is insufficient data to calculate 85 GHz radiometric resolution. 30

constant value. The drying time was 9 days for the grass samples and 3- 3.5 days for the soil samples. We then dried all of the soil samples at 1050C for an additional 24 hours. as is the usual practice. We calculated soil and grass moisture gravimetrically as a mixing ratio to dry matter using: Mwet - Mdry (9) Mdry - Mtare where w stands for gravimetric moisture content, Mwet is the measured mass of the wet sample, Mdry is the measured mass of the dried sample, and Mtare is the container (tare) mass. To calculate volumetric moisture content, we first estimated the soil bulk density by taking the maximum ratio of dry soil mass to core volume. By this method, we found a bulk density of 0.972 gm/cm3. We calculated volumetric moisture content, 9, as: = WPb (10) Pw where Pb is the soil bulk density, and Pw is the density of water. The soil and grass data are given in Table 7. 3.4 National Weather Service data To augment data obtained by TMRS and MMS during REBEX-1, we acquired two data sets from the National Weather Service: the October, 1992 through April, 1993 monthly Local Climatological Data (LCD) for Sioux Falls, SD and selected Radiosonde/Rawinsonde Observations and the LCD's from Huron, SD. The LCD's include daily summaries of snow depth, which could only be roughly estimated from REBEX-1 video stills, and precipitation, which was unavailable from the REBEX-1 rain gage during cold weather. The LCD's also give reports of sky cover, ceiling, and weather at six times per day. We used this data in conjunction with the Huron rawinsondes to determine when the sky was cloud free and to calculate the clear-sky downwelling radiobrightnesses discussed in Sections 4.4 and 4.5. The rawinsonde data set includes atmospheric profiles of pressure and temperature from ground level to about the 10 mbar level and dew point and relative humidity to the height at which dew point falls to about -500C. 31

Day Time Depth Tare Wet Dry Dry Gravimetric Gravimetric \:olumetric M ass Mass Mass MI ass Moisture Moisture Moisture I lay[Ti I (700C) (105~C) (700C) (1050C) (1050C) 287 2100 Grass 12.26 22.1-7 18.12 - 0.69 0-2 cm 8.99 152.12 115.75 113.01 0.341 0.376 0.365 2-4 cm 9.00 110.85 85.75 84.69 0.327 0.346 0.336 4-6 cm 8.99 100.67 78.77 77.89 0.314 0.331 0.322 6-10 cm 9.04 260.40 204.55 201.81 0.286 0.304 0.295 288 1400 Grass 12.24 20.59 17.88 - 0.48 0-2 cm 9.02 126.17 96.90 95.65 0.333 0.352 0.342 2-4 cm 9.00 122.15 95.07 93.89 0.315 0.333 0.324 4-6 cm 9.03 124.04 97.36 96.25 0.302 0.319 0.310 6-10 cm 9.03 237.95 186.79 184.42 0.288 0.305 0.296 2100 Grass 12.26 26.91 22.06 - 0.49 - 0-2 cm 9.00 141.10 108.73 107.27 0.325 0.344 0.334 2-4 cm 8.98 127.36 98.42 97.15 0.324 0.343 0.333 4-6 cm 9.02 119.24 92.39 91.34 0.322 0.339 0.330 6-10 cm 9.00 223.16 172.34 171.02 0.311 0.322 0.313 289 1400 Grass 12.23 35.72 25.64 - 0.75 0-2 cm 8.97 117.81 90.37 89.15 0.337 0.357 0.347 2-4 cm 9.03 121.19 93.93 92.59 0.321 0.342 0.332 4-6 cm 9.01 130.73 101.51 100.32 0.316 0.333 0.324 6-10 cm 9.05 234.07 182.88 180.42 0.294 0.313 0.304 2100 Grass 12.29 25.84 20.68 0.62 0-2 cm 9.06 138.99 108.36 106.72 0.308 0.330 0.321 2-4 cm 9.02 126.34 98.38 97.00 0.313 0.333 0.324 4-6 cm 9.08 129.38 101.55 100.21 0.301 0.320 0.311 6-10 cm 8.99 239.31 188.64 185.78 0.282 0.303 0.295 290 1400 Grass 12.27 32.30 24.89 0.59 0-2 cm 9.08 101.61 81.06 79.95 0.285 0.306 0.297 2-4 cm 9.07 120.95 95.31 93.92 0.297 0.319 0.310 4-6 cm 9.02 123.04 97.71 96.48 0.286 0.304 0.295 6-10 cm 8.99 227.72 181.01 178.08 0.272 0.294 0.286 307 2100 0-2 cm 7.25 125.74 89.38 - 0.443 0.431 2-4 cm 7.20 127.98 - 94.87 - 0.378 0.367 4-6 cm 7.22 133.84 - 100.37 - 0.359 0.349 6-10 cm 1 7.20 1233.01 - 1 176.43 - 0.334 0.325 Table 7: Soil moisture sampling data. Masses are in grams and include tare mass. Drying was first done at 700C then at 1050C. 32

4 Radiobrightness processing and analysis In the following sections we describe post-experiment processing of the radiometer data. The analysis covers deletion of out of range values, identification of sky brightnesses corrupted by reflector positioning errors, 37 GHz radiometer calibration errors on day 403, estimation of actual sky brightnesses, 85 GHz recalibration for days 347-403, an alternative calibration parameterization, and radiobrightness sensitivity to rll assumptions. 4.1 Editing radiobrightnesses for out of range values Both terrain and sky radiobrightnesses exhibited occasional out of range values, typically near 296, 320, and 332 K for the 19, 37, and 85 GHz radiometers, respectively. The spurious points occurred singly in either the sky or terrain measurement and were not accompanied by spurious TPR gain factor readings. The out of range values occurred about once every other day in each instrument. The spurious radiometric measurements were always greater than the corresponding infrared surface temperatures, so we could easily identify them as non-physical. We manually deleted these values from the data set. 4.2 Editing sky radiobrightnesses for reflector position errors Sky radiobrightness measurements suffered from two major sources of error during REBEX-1incorrect sky reflector position and inadequate reflector size. We discuss errors from the latter in detail in Section 4.4. Motion of the TMRS housing door-which also served as a sky reflectorbecame erratic on day 351 due to wear in the screw drive mechanism. At that time, only door closures were affected, with incomplete closures occurring periodically and usually in groups. At the same time we began seeing high sky brightness measurements but did not tie them to the door problems until day 414. From day 351 to 414, if an experiment cycle began when the door was not completely closed, FluxMon would make sky measurements without moving the door from its current, partially closed position. Many flawed sky brightnesses from this period were greater than the concurrent terrain brightnesses and could be easily identified. However, the sporadic occurrences of sky-brightening clouds or precipitation make sky brightness inherently highly variable, 33

complicating the job of weeding out faulty data. Since terrain brightnesses are a conlbinationI of emitted radiation and reflected radiation from the sky. it is possible to use terrain brightness variation as an indicator of sky brightness validity. For example, if sky brightness junlps by 100 I fronm one measurement cycle to the next, we would expect terrain brightness to increase by 10 K if the reflectivity were 10%. We chose to manually edit out sky brightnesses in the day 351 to 414 period using the following criteria: sky brightnesses were deleted when they exceeded terrain brightnesses or when a sudden, large change in sky brightness was not accompanied by a commensurate change in terrain radiobrightness. When the data were ambiguous, we chose to remove the points rather than risk using bad data. In most cases, a group of removed points would include at least one very high value, or a group of low values would be bounded by large jumps not mirrored in the terrain brightnesses. It is likely that faulty data remain, however, since zenith angles between 120 and the the nominal sky measurement angle of 450 were possible and would have yielded cold sky brightnesses that were indistinguishable by our criteria from valid 450 measurements. The door mechanism failed in a new way on day 414 when it would not open completely. Software changes at this time eliminated the need for subjective editing of sky measurements. During the sky measurement, the reflector was either in the correct sky measurement position or fully open. Erroneous sky measurements were close to terrain measurements and easily identified. From day 414 to the end of the experiment, we deleted a sky measurement set if both its 19 and 37 GHz sky brightnesses were greater than 0.95 times the respective terrain brightnesses. We checked this criterion against the data from before day 350 and found no matching points, indirectly confirming that no valid points from days 414-471 were removed. 4.3 37 GHz calibration correction for day 403 Following the experiment, we recognized that the 37 GHz radiometer physical antenna temperature (Tpa) values recorded during the day 403 calibration were erroneous. Since no modifications had been made to the system following this calibration, we assumed that the erroneous value persisted through the end of the experiment. Physical antenna temperature affects apparent radiobrightness 34

Radiometer Day Time Dff Trec CSD/CREF 37 GHz | 403 | 0100 305.936 -41.7428 0.93759 | Table 8: Corrected calibration parameters for the period from days 403 to 471. calculations only when it changes from its value at calibration time. Over the course of the experiment, the range of 37 GHz physical antenna temperature was approximately 9 IK. This variation is modified by the factor of (1 - rlj)/L21 in (2) so the error could have a maximum effect of about. 0.9 K on TAp. We did not save the physical antenna or reference load temperatures used in the calculation of TAP during the experiment. In order to correct the 37 GHz calibration for the period from day 403 to the end of the experiment, we estimated these temperatures using outside air temperature. We followed this procedure to correct the 37 GHz data: * Using data available from calibrations on days 279, 288, and 309, we performed linear regressions between the 37 GHz T,,ref and Tpa and air temperature. * We calculated T,,ref and Tp,, for each experiment cycle after the day 403 calibration using the factors from the linear regression. * Using the erroneous Tpa value (282.73 K), the original calibration factors from day 403, and CsREF values saved from each experiment cycle, we estimated the radiometer output, VD, for each experiment cycle after the day 403 calibration by applying (1). * We used the raw calibration data from the day 403 calibration with the estimate for the correct TAP to calculate a new set of calibration factors (Doff, Trec, and CsD/CsREF). * We calculated VREF for each experiment cycle by using the original Tre, value and solving (5). * We calculated new C,REF and TAp values for each experiment cycle from (5) and (2) using the new calibration factors and previously estimated Tref and Tpa. The corrected calibration parameters are listed in Table 8. Of the approximately 5700 experiment cycles between day 403 and the end of the experiment on day 471 the largest correction by this procedure was -0.914 K and the smallest was -0.124 K. The average correction was -0.538 K. 35

4.4 Estimating actual sky radiobrightnesses High REBEX-1 sky radiobrightnesses suggest that these measurements were corrupted lwhen radiation from the terrain reached the radiometers. As seen in Figure 2, the 19 and 83 GHz radiometers were close to the edges of TMRS housing door. Although we specified the size of the door to accommodate 10~ field-of-view main antenna beams we did not account for side lobes and near-field diffraction effects. Sky brightnesses are used to calculate terrain emission from apparent radiobrightness and modeled terrain reflectivity. Since reflectivity is usually small, in most cases an approximate sky brightness will introduce only second order errors in terrain emission calculations. We have therefore attempted to estimate sky radiobrightnesses from the available flawed sky and terrain measurements. To make a sky brightness estimate, we hypothesized that for each radiometer the sky reflector had a fixed efficiency, 77rf 1, such that: TRFL = r7rf TSKY + (1 - tlrf I)TTER (11) where TRFL is sky brightness measured with the reflector, TSKY is actual sky brightness, and TTER is apparent terrain radiobrightness. The hypothesis suffers from some obvious flaws since it assumes that radiation corrupting the sky measurement originates from the same area and at the same incident angle as TTER. If we assume that the radiation source corrupting the sky measurements is of terrestrial origin, then TTER is at least a valid surrogate. If, however, the corrupting source is either emission by the TMRS housing components-including the reflector itself which at times was wet or ice covered-or radiation from angles near the horizon, then TTER is at best the same order of magnitude as the source and the estimate of TSKY will be invalid. The 37 GHz radiometer is most likely to fall into this second category since it was positioned near the center of the TMRS housing and did not have direct line of site to the terrain except at high incidence angles. We made estimates of 1rf I for each radiometer by calculating TSKY from Huron, SD rawinsonde data using radiative transfer. (See Section 3.4 for a description of the data.) Rawinsonde profiles from Huron were available twice daily at 1100 and 2300 UT. We selected 20 profiles corresponding 36

to clear sky periods as reported in both the Sioux Falls and Huron LCD's. Ts),K' is the sum of TDN, the downwelling radiobrightness from the atmosphere, and cosmic radiation attenuated by the atmosphere. Calculation of TDN is based on solution of the equation of radiative transfer [1]: dB -+B=J (12) dr where B is brightness (W/m2sr) and J is the effective total source function at a point r in direction i, dr is incremental optical depth defined as dr = c,dr, (13) and ICe is the total extinction coefficient. At 19, 37, and 85 GHz, the atmosphere is scatter-free in the absence of clouds and precipitation, cK, = cg, the coefficient for absorption by atmospheric gases, and J = Ja, the isotropic absorption source function. Using the Rayleigh-Jeans approximation to Plank's blackbody radiation law, we can express Ja in terms of air temperature, T(r): 2k Ja(r) = AfT(r) (14) where k is the propagation constant, A is wavelength, and Af defines the bandwidth. (In general, k is a function of r but in the atmosphere we can assume that it is a constant.) Similarly, we can use Rayleigh-Jeans to define apparent radiometric temperature, TAp, in terms of B: B(r)ri = Af TAp (r). (15) Solving for downwelling apparent radiometric temperature, TDN, at the surface from zenith angle 0 in a plane-stratified atmosphere, we have: TDN(O) = secoj Kg(z')T(z')e-r(O'z')secedz? (16) where r(0, z') =] g(Z)dz (17) and z is vertical height in the atmosphere. Oxygen and water vapor are the predominant absorbers in the microwave region so Kg(z) is a function of temperature, pressure, and atmospheric water 37

19 GHz 37 GHz 85 GHz 7rfl 0.701 0.723 0.636 Number of samples 20 20 T a 0.02 0.06 0.12 Percent TSK' < 0 8.1 17.7 0.1 Table 9: Reflector efficiencies from (20), the number of clear sky profiles used, and the standard deviation of r/rf I. Also shown are the percentage of TSKY values from (21) that were less than zero. vapor content. We used the semi-empirical formulations in [1] to calculate Kg and then integrated (16) numerically over the range of altitudes available in the Huron atmospheric profiles. Before integrating, we increased the vertical sampling density of the rawinsonde data by 20 times using cubic spline interpolation. Without the denser data, the non-linearity of (16) produced erroneous results when tested with a Huron atmospheric profile modified to be isothermal. We calculated TSKY for each of the 20 profiles using: TSKY = TDN + TCOS/L(O) (18) where Tcos is the cosmic background radiation (2.7 K) and L is the atmospheric loss at zenith angle 0: L(O) = e'(0,oo) sec. (19) Inverting (11) for 7rfll, we have: TRFL - TTER TSKY - TTER We calculated r/rfl using all 20 clear sky points for the 19 and 37 GHz radiometers and only the last seven for the 85 GHz radiometer, which was not calibrated until day 403. Table 9 gives the resultant reflector efficiencies. Next we applied the following equation for estimated sky brightness, TSKY, to the entire REBEX-1 data set: TSKY = (TRFL - (1 - rlrfI)TTER)/rrflI (21) For each radiometer there were a percentage-given in Table 9-of TSKY values less than zero, a non-physical result. This percentage was greatest at 37 GHz, confirming that the reflector efficiency hypothesis expressed by (11) was least applicable to the the 37 GHz radiometer. TSKY and TRFL are graphed in Figures A-3 through A-5 of Appendix A. Figure A-4 shows that the negative 37 GHz 38

7'SK' values are mostly concentrated in the fall and spring. In summary. tile user of TSKy data should be aware of these problems and treat the data set as a first order approximation to the true sky brightnesses. 4.5 85 GHz recalibration for days 347-403 As discussed in the experiment log (Section 3.1), the 85 GHz radiometer was unused from the beginning of the experiment until day 309 when we installed a new IF detector unit and calibrated the radiometer. The instrument quickly drifted out of calibration as seen in the TPR gain factor plot (Appendix A, Figure A-9). On day 347 the TPR gain factor data reveal an apparent transition to a functioning state. Since we do not have an explanation for either the initial drift or the day 347 transition, we cannot conclude that the day 309 calibration remained valid after day 347. In this section we describe a means of determining a calibration set for this period. We previously described the forward radiometer parameterization for Dicke-mode output in (1): VD=CsD (TAPj!+ ( 122pa_- Doff ) (22) and the TPR-mode reference load parameterization was previously used in (5): VREF = CsREF( ef + Trec). (23) L31 Before recalibrating the radiometer, we first evaluated (22) and (23) to recover the radiometer outputs originally measured during each experiment cycle. The 85 GHz radiometer took data from days 347 to 403 using the day 309 calibration parameters given in Tables 4 and 5. The remaining terms in (22) and (23)-the temperature variables Tpa and Tref -were derived from air temperatures using the method described in Section 4.3. Having recovered VD and VREF, we needed a new calibration set for the day 347-403 period to recalculate TAP. We assumed that the ratio CsD(O)/CsREF(O) in (8) remained constant between this period and the day 403 calibration, and CsREF could be found for each experiment cycle by inverting (23) once Tre was found. Of the remaining parameters-Doff and Trec, —the data in Table 5 shows that Tre9 varied between calibrations more than Doff for the 19 and 37 GHz 39

radiometers. Consequently, we chose to use Doff from the day 403 calibration in recalibrating the day 347-403 data, leaving T,re to be determined. From day 347 through 403, the only possible calibration sources were the eleven sky brightnesses, TSKY, calculated from clear-sky Huron rawinsondes as described in Section 4.4. The inefficient sky reflector-also described in Section 4.4-complicated the calculation of Trec using these TSKI'. We can solve for Trec by inverting the TPR-mode reference load parameterization, (23): VREF Tref Trec = CREF T _ (24) CsREF L31 where (from (8)): CREFr(O) CsREF = CsD C.D(O) (25) To calculate Trec from (24), we must find CD using TSKY values from the Huron rawinsondes. We begin with the hypothesized formulation for reflector-measured sky brightness, (11): TRFL = rlrflTSKY + (1- Trrfl)TTER. (26) For each rawinsonde-estimated TSKY, we have Dicke-mode measurements of TRFL and TTER from the coincident experiment cycles that we can use in (22): VRFL= CsD (JL TRFL + L )Tpa - Doff) (27) L21 L 21x VTER = CsD (- TTER + 1 )Tpa - Doff. (28) Solving (26), (27), and (28) for CD, we have: VRFL - (1 - 7rf l)VTER =71?7rfl TSKY /L21 + (1 - 11)77)rflTpa/L21 - 77rfl Doff and we can then calculate Trec from (24) and (25). The average Trec for the eleven rawinsondes was 116.359 K with values ranging from 92.195 to 139.247 K. Trec was 122.348 K in the day 403 calibration (Table 5), for a difference of 6 K. For comparison, the 19 and 37 GHz Trec's changed by -16 and 14.6 K, respectively, between their day 309 and 403 calibrations. Table 10 summarizes the revised 85 GHz calibration parameters. We used the new calibration parameters and the 85 GHz radiometer outputs-from (22) and (23)-to 40

Radiometer Days Doff I Trec | CSD/CREF i 85 GHz 347-403 276.149 | 116.359 0.92667 I Table 10: Revised 85 GHz calibration parameters for days 347-403. calculate TTER, TRFL, and TSKY data for days 347-403. Plots of these parameters appearing in Appendices A and B use the recalibrated data only. Figure A-9 of Appendix A shows both tile original and recalculated TPR gain factor, CREF, between days 347 and 403. The day 347-403 recalculated CREF values are on average somewhat higher than those after day 403 but there is some crossover. The user should consider the recalibrated 85 GHz data to be approximate and of lesser reliability than the 19 and 37 GHz data over the same interval. 4.6 Alternative calibration parameterization In the REBEX-1 calibration parameterization we used approximate values for the transmission line loss factors, L21 and L31, and ignored the effects of mismatch differences between the antenna and reference load radiometer transmission lines. Because radiometer output is linear in apparent radiobrightness, only two parameters need be determined through calibration in order to make an immediate radiobrightness measurement of some unknown source. In this case a very simple parameterization for the radiometer equation, (1), could be used, for example: V = ATAp + B (30) where A differs from the gain parameter, C8D, in (1) by constant terms only while B includes variable gain, physical antenna temperature, and receiver noise terms. We used the parameterization in (1) instead of (30) because in practice each of the terms in B can be treated separately. This effectively isolated the most variable factor-gain-into one term so that it could be corrected through experiment-time TPR reference load measurements. It was not necessary, however, to include the loss parameters L21 and L31 in the parameterization. L21 may be eliminated from the Dicke-mode calculations in (2) through (4) by redefining C/D = C8D/L21 and D'1f = Doff L21. Since L21 is constant, it has no time-varying effect on CSD, that is, the ratio CsD(t)/CsD(O) in (7) will remain the same despite the transformation. L2l and L3l may be similarly removed from the TPR calibration equations (5) and (6). Because the transmission lines for the antenna and 41

Radiometer Day] Time ID'f T,'f CI D/CREF 19 GHz 279 1800 299.982 161.896 0.9635 309 1600 298.227 96.678 0.96266 403 0100 297.097 72.500 0.96763 37 GHz 279 1800 321.333 2.62806 0.93155 288 1900 320.862 -10.3558 0.93532 309 1600 320.196 -55.563 0.93704 403 0100 316.599 -41.7428 0.93759 85 GHz 403 0100 313.057 139.472 0.92653 Table 11: Alternative calibration parameters. reference load were at nearly the same temperature as the reference load itself, self emission by the transmission lines compensated for loss of signal from the load. Consequently, the alternative parameterization: VREF CsREF = (31) Tref + Trec is a better model of the TPR reference load mode of the radiometer, although the (false) assumption is made that Trec is the same for the antenna and reference load radiometer modes. We may justify this assumption-made in this and the original calibration-by taking (31) to be an index of gain variation but not a true radiometer equation for the TPR reference load mode. The effect of the alternative calibration on the other calibration equations is simply as if the values of L21 and L31 parameters were set to unity, so these equations will not be restated here. The alternative calibration parameters were calculated from each set of manual calibration data and the results are listed in Table 11. Applying the alternative calibration changed the calculated value of TAP by at most 0.016 K. Its advantage is simplicity and the elimination of arbitrary constants. 4.7 TAP sensitivity to rlp estimates To examine the sensitivity of TAP to p71, we recalibrated and recalculated 37 GHz TAp using alternative HI values of 0.95 and 0.85. We used data from day 403 to day 471. With 71 = 0.95, the average deviation from the 0.9 case was -0.024, the maximum deviation was 0.165, and the minimum deviation was -0.253. With 771 = 0.85, the average deviation from the 0.9 case was 0.028, the maximum was 0.283 and the minimum was -0.184. These deviations are less than the radiometric resolution of about 1 K which justifies the initial assumption of rit = 0.9. 42

References [1] Ulaby, F. T., Moore, R. K., Fung, A. KI., Microwave Remote Sensing: Active and Passive. Vol. I, Addison Wesley, 1981. 43

44

A REBEX-1 summary graphs The graphs in Figures A-i through A-9 summarize the measured parameters as well as several derived parameters from the entire period of REBEX-1. The parameters are 19, 37, and 85 GHz terrain apparent radiobrightnesses, reflector-measured sky radiobrightnesses, estimated sky radiobrightnesses (see the main text for a description of the estimation process), thermal infrared sky temperature, global radiation, net radiation, wind speed at 10 m, soil temperatures, heat flux in the soil, relative humidity, rainfall, thermal infrared surface temperature, air temperature, terrain radiobrightness spectral gradients, TPR gain factors, estimated 85 GHz TPR gain factor (for the uncalibrated period discussed in the main text), and snow depths. For these figures we have edited out terrain and sky radiobrightness data known to be flawed, removing points which were either out of range or taken when the internal radiometer temperatures drifted from their design values. We have also removed sky radiobrightnesses and IR sky temperatures which were in error due to incorrect reflector positioning. The the main text of this report describes in detail terrain position errors and the editing methodology applied to the sky data. Because of the communications error described in the experiment log, the IR radiometer sky data also contains additional incorrect points but these have not been removed here. We calculated the terrain radiobrightness spectral gradients, Sg, shown in Figure A-8 using: S (, f2) - TTER(f2)- TTER(fl) (A-1) f2 - fl where fi and f2 are radiometer frequencies and fi is less than f2. A-1

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B REBEX-1 monthly graphs The graphs in Figures B-1 through B-14 present monthly compilations of most of the physical parameters measured during REBEX-1. Each month from October, 1992 through April, 1993 is covered by two sets of graphs in consecutive figures. The parameters graphed in the first set for each month are terrain apparent radiobrightnesses, reflector-measured sky radiobrightnesses (no corrections applied), global and net radiation, and wind speed at 10 m. The parameters in the second set for each month are subsurface soil temperatures, vertical heat flux at 2 cm depth in the soil, relative humidity, rainfall, air temperature, and thermal infrared surface temperature. Some terrain and sky radiobrightness data have been edited out as discussed in Appendix A. B-1

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C Video images of the REBEX-1 site In this section we present the collection of video still images of the REBEX-1 site. We acquiredd each image by first establishing interactive control of the on-site Macintosh computer through phone lines and Timbuktu/Remote software. We then used VideoSpigot's ScreenPlay software to display and capture to file an image of the radiometer observation area. Since the video camera had a fixed f-stop, the quality of the images varies with time of day and available sunlight. Each of the images is identified by a REBEX-1 day number label. Refer to Appendix D for a calendar date to REBfEX-1 day conversion chart. C-1

It % - -. -Ioo 0o?4 PI 0 m o3 P r ~ ~ ~ ~ rs P - ~ 14 Y q - ~ r Q < l a~l l _ 19 B — to p Cn | 8sp~ sl |e g~ l' c Cl Cl I" _ ~~~~~~~~~~~~~~~~~~~~I

~~~~~~~~~~~~~~~~~~~~~t- | | l~~~~~~~ | CrS | |i S~S f| "h | ~~~~~,L | | E | |I )r - | m5~'W ezwi Lr:: ~! t..1 -_u s~~~~ ~ ~ ~ E,, =X r Xs a E sa s;3 J z _. ~B% | | E ~,~ ~s.~s r,~ner* | _ S 5 s = = B B;-:i a~~~ * = dt C | __.! ~~~~~~~~~~~~~~~~~~~~~~'P N N N |;i *~~~ "~ s s az s s w~~~~~~~~~~~~~~~~~~~~~:i ~ R i s E..~~~~~~~~~~~~~~~~~~~~~~~~~ | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s —s- Far*l S - = | N i | 1|1 | | 3 _ i _ _~~~~~~~~~~~~~~~~~~~~~~~~~~r | l | - - - a _ __~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~b Figure C-3: Day 311. -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~: ___~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...I _.*.,~~;~8~ _~~~~~~~~~~~~~~:"*C:' -~~~~~C

Figure C-5: Day 313. _=~~~~, -..{: "':: x _._ z 2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a:.:'..';W'.IL..-...'.''...>'..'_E~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I:~::jm.Xa Figure C-6: Day 314.~~~~~~~~~~~~~~~r I r E ~ ~:ilB C-4

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Figure C-9: Day 317. _ _~~~~~~~~~~~~~~~~~~~~~~~~~ _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ _ -~~~~~~~~~~~~~~~~~~~~~~~~~~~i i~~p _LS- s~s P l C~i~ r~yi2TYQ i~~~~~~I ss d E g!~~: 14d~~,! c~~~~~~~~ E:2 R,::.!s~o! B |! ~~rL:~:~:~~~~ ~ 1111 i 3 | |1:' ~ |. I. B b -LNe~~C::::s~~~~~~~~~~~::~~~~~~!~~ 8a:~~~~:i ~:s I~::: ~::::~ii~xd ~a - g | ~ l~Y~ ~e sp~ PSWYIG~:: i~~xFgur C-0:Da 38 C-6~~~~~~~~~~~~~~:

Figure C-13: Day 321. Figure C-14: Day 322. C-8

Figure C-15: Day 323. Figure C-16: Day 324. C-9

Figure C-17: Day 325. Figure C-18: Day 326. C-10

Figure C-19: Day 327. Figure C-20: Day 328. C-11

Figure C-21: Day 329. Figure C-22: Day 330. C-12

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Figure C-25: Day 334. Figure C-26: Day 335. C-14

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Figure C-29: Day 338.~~`iy~ _ D~~~~~~s~s~~P 1Y I~ b h -a ~. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~!~~~~~~~~~~~. f; I: ~~~~~~~~~~~~~~~~~~~~~~~~~~~ K 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~:~I ~~~~~~~ Ij;'rt~eE < prl ". i: _~~:~:r~: -?i~g ~~i7 Figure C-30: Day 339 i~:Pe~~:-~R~~1Rse C-16 ~ ~:

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Figure C-35: Day 344.~~~~~~~~~~~~~~~~~~~~~~~~~~*1-.-r ~ ~'~t- ~`' - H- -- _CN fI ~ Z "4Sc.n i_ m |-' E; l 1!1W ~~rA -~ ia~ Jw - I~ A _~~~~~~~_ ~~~~~~~~~~~~9-k?.`` ~ ~A_+,.......,,x., i..... >. A,.,, _ ~~~~~~~~ — P EI' _ _ = _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' _~~~i~"~ ~~ ~~ +b~J~~:: _,..:',?,Be Figure ~ ~ L-;~lj~~~,~ 3~"t,~~~~~ C-36:"Ta Day 345.:T~ ~ ~~-1

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Figure C-49: Day 359. Figure C-50: Day 361. C' 26

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--,~~).:L.-a..?.;B::i~r~~:. 8..!.. ~ C.:..9.3.~ ~.:j~,,,hr~~....:...::... S~~~iue C-57a: D 2 ay S~u!2=2; 374.i3'~ 7 i",,, mi.-* ".-a.= ~. E'"L = Z;e 3'G~~UIh I<YP*..E== =2=! R fflP.-., S`K; Ds-a 4ua~- A S K.'-~e 4:.<e-zl~;. ~.:;~zi-____ Figure 58' D ay _ 7 5 S:i~k~;~r-30 V:L; ~-:~~~. a 5~~~~~~~~~~ a~~~~~~~~~~~~~~~~~~~~~~~.rr;:~x~.~ij: c~::::::::::::L~il~; ~~;~ z ~~~~~~~~~~~~~~~~~~~~~~~~~rs ~~~~~~~~atliih _ -4~~d~~ _~~~r~~ S IC~~~~~~~~~~~~~~~~i;X I m r.,,..SSS:~-9L.-: _-_ ~: C::r.21: _m 1 ~~~:: Ei~a 2iir90 n~~$.._........g~~~~~r:?::>X. _ r ills 1 _ ___ l~~~~~~~~~Y~ _g~~~v.; 111111:5b::.;r.-.,'..y,::~" ~C. ~.=NR_.;.-.~-:~ IS~': _ ~*.;v:~ao~ ~~~.,V.i~c:~d~:~.. EFXDX>F,- S.. ~ ~ ~ -K ~^~-__:~~~~` at.:8: Sv _~~~~~~! _! _jciji~~ _: ~~ __ _ _i ~ _~~~;:~ S:i_ Figure~~~~~~~.;' C-58:: Day 375.r?~; ~ ~ ~ -3

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Figure C-65: Day 386.! _ | ||| E 2 S _, w ~ fi"_ N E;: C e.s# _s- C-gs: Da 38. |i 2 iS li I _4

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3.~ ~:~c 4:~:lj~.:~-..:~.c* ~~~i., A-..F 1~:6bj -~~~~~~~~.:: L: ~ ~ ~ ~Q- --------- ~ca: ~ ~ ~:~-;X~Figure C-71: Day 401.~. ~*~. ~~*

~ ~~~~~~~~~~~~~~~., ~~w ~P~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,,.::..~c.~:~f~~~ an~~ ~ re ~~h~ - d.: ~is~rai E:La. T _0~C~~n' _~ Figure C-73: Day 404.a~~~~r a u ~~~~~~~~~~~~~a n ~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~:ri~L | 1Id _ ~~~7(:.;~: ~~~~~ ~1 ~gl| ~.~.~:;:~- ":3:~:11 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ rm rr r~:~~~~~::~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~ (~~~~~~~~~~~~~~~~~~~~~~~~s ~ ~ ~ ~ ~:~.~::::' -~~~~~~~~~~~j46~~~-: ~ ~~~~aP~~be~~~' U 3-~~~~_ | _s~~~~~~~~~~~~~~~~~~~~~~~~s~ Figure~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i~ C-74 Da 405.~n;d ~~:~i~:~::;r~~::::r d C-38

Figure C-75: Day 409...... ~!:'~ii'ii~i!ii!!~!il i:i:iii3 iiiiiiiiiiiiiiiiii:iiiiii:iiiii:iiiiiiiliiii -!ii:i:i i-............ ~'""~'""'"'"'"'"'"'"'"'"''~'~'~"~"~"~~:"~~:~:~. ~~~~~~i ~ili: ~*".. ~-'::!:~:~:~.~!::!::!::]: ~.~?~:!::~:!:.?~: ~?:::?~:]:i:~.:~::~i::~.i::.'.:~:!:~:::'.::: ~.. ~2.'.'?....:..::.i~!~:ii~::i::~-~.......:.~.~............ ~................... a~11~'"'"' "'""'"'"'""'~'~""~ "'"'~~"'~~~~~~~i~!! i~:i?:ii::i::?i............ ~'"'~' ~.............~ ~'~~'~'~'""~~'~'"~:'~:~'~:~~~ii~ ~'~'*~'.".'~::i:::'~]:]9 ~i~.::i]~ ~.. ====================================================== ~'~i~:;~::~:,.~.'.-~!~i:~..:..'~.:~ i~i::~:]l!~t~.:~...~;~ ~:~.~ ~:~!~:~!~.~i~..'41 i!'""~-~?..'.~:~i ~.,:~ %~:. i:~....... ~.~,::...~. ~...~:~i~i~::::~.~::.::...~i~i..:~:.~:~S:~e.:~...~i~;~:.~:~i:i:....~ ~.!-::~'.~.~: -.';~::~..~.-:. ~:..j~;~::'~ii~:::.~.~..'-:~ ~~~~.~~..~ ~. ~.~~~~!~............. ~.~."::~.~::-:..'.'.. ~- ~.:.:.~....~:::.:.~:::.::.~::::::.~':e~~:-:~:::::~:~':~~'~:~.~ ~::.~ ~.~..'.:~'.C~.~.~i~Z..:i~!~'~'-~. ~'. ~.~..:':..~:~.~:~:!~ii:.,.~..~..,..~.~:~: ~:.:.~.::~:~.~.~.~.:...~::...:~::~.~..... ~.:~.~';:.~5~. ~-;~i!!'.'~!~ili~i~!~!ii!:~:i?~!i~i!!ii!ii!iiiii:~ ~.~:.~:.~-~:~:q~:~. ~.~:~'!~:~.. ~..~:~..~.:~ ~-~....~.:::~ ~:~.!~:~!.~::~.~:.~.~.....~:i~.~:~-'.~.~:~i~.~i:..:~ ~:.~.~ ~.~:i'.."~z:'~!:'.-"~.~.~:::::::'~:!:~i::'~ ~ ~ ~:...::::i:~:!:!:i~:~:.:.:.::iii~':!~.~:~!:~i~!i~;~i~i!;!i!i~!ii~.!~:!i~i~!i!ii~:~:~!i~:~i~:.~iii:~i.2.....:..~ii:..~:g.:~::~i~i~:::~:!:~....:.:~.~...~ ~.~.~...:....~;~.~~..~.... ~~~~~:'~:~.:::::::::::::: ~: ~::~..~:~: ~:'-:~:.~-: ~-~.::~.:~..~::~;:::.::~::.~.~'z~..'~:~.~2~:~:~:~'~'~.~:::~'~:~':~?~.....~:%::::'~'::::::::i:~:.;~i~.:~:~..::~:~:~:!~:~:~:~:~:~; ~::.s!:~:~:~:~:~:~:~:~:i:~:~:~:.~:::~..~..~.~.~:::..:~:i::~::!:!:....~:!:~.i::~::~:!~..~:~!~.~:.~.~.~i~i:~.~.~!:~.~i~ i iiii~iii''~'"'-~' ~'' ~:':' ~-:-~~~~~zq~-~:~~........ ~"~'~"~'~~'~:~~~ ~" "~ ~~~ ~,~:~.~.~..~.~'~,~'~.:..~,::"",'~:,.'~.~;.~.~;~.~;~".~%..: ~:~"~ ~.~.~..:.~ ~..... ~ ~i~?~:ii!11i'"-" ~"'~'~~ ~ ~::.~:....~j..'.~:~.:.~....~.. ~...~i:i.~:~~'~'~ -~"~.~.'~.~.~~.~.~...~~.:..:~.-:...._~..:~..............~.~..~'.:~.:~.~:~?~":~..~. ~ ~. ~.~~~.:..~:~::~:.~:~i~:~'~' ""-~.~~~....~~.~-~:~ ~:~:.~:~:::.:~:~..~:i~Ili~.~i-.::~~ ~.~. ";~'.~:::t.~ ~;;:~.'.:~:~:::.~::.'-'~'~;~'. e~...':~..~!~;~..i~.~....z~.-.~..!.~.. ~:~i"~. ~'.~-~::'"?~'~" i~z~'~:~.~..:~.~L~' ~":: ~:.......:~~~~-:~ ~ ~:~.............~.~...~ ~.~... ~.~. ~:.~.~ Figure C-76' Day 412. C-39

:~: 9hi; ..~-.c.. X~:\c" -.i ~Yr-r+r; :a-~-y:;Ei~:~ois#ir~-~82.,~;r~ i:j: I ~ ~;1Zt*iYhlPI~;~*"-~~~~.~~x::*ITYie~cra, .. ~~~l-r.- ~~ii "~ —-- —' - —-' I I F:L;..~- lt. ~ r-~rr~v 90cX-':$ ~.~ :(~.~`:yi.;L,~..~u--*~.::'*+. ~~G1,1 ~ ~~ —~~:-:~~...., )~g"Ci~pti::.6b~P ~,:::huahP riP ~.~-p:.-.:.:d~; -*, "~ i;:~-grs " c-..::~ ...I' ~-~-::-s-~ ~~jei~' ~ ~:,i.up.~.i ~ ~-e: ~~~-.:~.~-.~ " ?1 ~~~sc~. i~;-~ - iCf: 2~:~j-~" r.~.~.~;~ ii -: n:~:~j.:n i~~~'j~;c j" g: st: i~s~:SC::::~.f~: ~": -.:~~~~;! i::i R1 isr.3477~i e::: fli~"":~~-:~~: 4::;V::n:~::~:w:-,;-~~~ -~:::~:~~::~.-~ ~:xrrr,,:9 ~:J .~.~...,,.. ~.u c:~:~:~a::~:: z :~~~ -~~~:i:l::I:`:''::::: i :i8 ~~:.:Y: ~:~' s~:~.: -: Ij:~:~::;:i~:~:2:2.~:i~.~:~:~:~:~T:-: ~:-::~:~::X~:i~r. ""."." ~~r~~-~2~.::::::~::;:I.:"'::is~:W:~::~:.:::::: ;:-~1::;;~~:-~:::~: ~:~:~:~:~:~~:~.I..Z..~.,S.J-~: j~ 2;obbi ~:~.~.~.~.~.~.9~:~1~:e:,-z:":c,::::i::::jY~:2~L::~- : 6).x ) iT':~::~l~l~:i~i9i-:~:-2:~:~i;~:h~i X~:~:iiiX i:l:::::::(j: :j.:.:.~'`,:~ps;;~:;~;~:~-~;~;: w ~~~~~-; n:~c ir ""P:-TSJ:~ i:~:~:~;:~: :.~ ~;~ i~arijic::;:ua;~: ~7~snx~s~:,:j:ii2:,,~:~: :; i, ~s s:y::-s iw~.~:~:~:~ iiii,rxi:;j::~:~I:~:~:-~~~.~~~:~:~:~: jiiSifG'.'. P:::8~t: ~:~i :~:~:~x B c:r:. 55.:.s~.~; T.~;~i~.~..~zzz.~2.~. Figure C-77: Day 413. :~r~l;r.z ii::pi ::::: ikSI'S:::::I~' 7rGii:.:,, i::~:~s:1:~:~:~: s~ o:~:~ o:i :::j::::T -— -ASICI — sLYsla~lsL —-YYI(C~ _IPII I -- -— -1LQII-~ — iCGjiAl::;:.... ~~ .~.~:~:::~: ii gbr Is~"l""""""""""""""" - 6sF i: iti 55.:~ ~:~:':'~:I ~:~:~~:~:; ~,;~;t ~::~;~:~:.~ .Ss iiiiii ~:::~~:,. :.:::..:::::.:: .sC~1 lij::: E i; i:,;ii:dPB ---------— q$r- I IX,gai#Po I e- -818BBsllRllPBB_b -P1Sm i-if:3~BlsBj:::::: ::::::~IPi:1.:,:3: X 3~::::333:~:~::~: \'''''':::2:::::.~.c. :;r::::::J "" ipeii Ices;iPz~,~Ilgk'Dsssees:~,,.-,, -, ,, 8LIIBBdBBBWS;"a"5:.:.:.:,, ~'~' ri:L:::::i:i:i':~8i:i:i:::i:::::;:~:::ld r~ii::i,~. iiii ii x:~:~:~:~:~:~:~:~:~:~:~:::::i:i::::::i:Zk:::. ~i x ~: wiiiiiiiii:siiigii: ~:~~:~~rrV~~~XAMN.III*mBIIIIIIX~~ -II1I 1 IWR~PARL?;~.r.. ~;~i.: i:;:::::j~:::::::::!: x;::::~:*a:,,:I::::::::::a::~..~.~..~.~.~.~.~.;~.~.~.~.~.~.~; Pz r. 3:::::::::::i::: ~1::i::::::::::::P'~'~: ::! "5:::~:;::::i2i::2~:~:~:~:~::(:::xax~~-~rr~~:55555 :::::::;:::::ss::~jx~=::~;r il::::~::~:::::;;;:::P j::i.:::~r~::i:~ww~:~~:~:::::::::::I:~:r:iii:i::~:r~: $kiiiiP I~~:~":"::::::::::::#:"::::z~W;~Jrh~~~~~~'; Y: ~-.-r:so:~ ~~- ~~,:e::s;i:.r~:~:~r:~~:c~;~~ —:::;:::::~::5~:~: ~.s:~::~'2~Y-i'''''-`"Vrrl'LLIY Rlisll -AT --- -- III- -I —--— C~ s 'i" ~~; "'::~:S~SAiOPhWe-*I re -- R-.. —,,,,,,,:sst.:;it:~:~:;,pm,, — nm -~ nrrraarnm~laa~R~~s';:Z:~i:~:~:55' i:9:::::::::.ns.~.~....:;.. ~~~~; Figure C-78: Day 414. C-40

~.Q;nsL~~..: _; R....;.-.. ~.pc~-.~B.:~ri b, l _s - C.fi x~T i:;i.-z.* ~~iu ~ 1*-~.~~-;;~: -|3 _: ~:~~ Figure~~~~~~~~~~~~~~~~~~::Y`~~ C-80 Day 419. C -41..~p.;.-; j.:~P Y.~u~~'u~:rv~~ ~~-r..''

:~ i E I - = | N IS N _ N _ _ _' ___i~o~.:'~:~.~ ___..~ __r Aa-~~~X:~' ~~jC aC~rC ~ _N_ __"''~ ~~~~C:T:~ _-:~ ~J~k~~i i~;::= =: iS: = =G~~~~~~~~~~~~~~~~~~~~~~~~~~~-~~~:~:'' r~f: ~~ EI: S A_ ~: =~~~~ ~-~~ ~~~~ _ = S Evz:~ ____~~;:~~~ __ s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- -=: _... _=~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. _ s = | =F~~ ~ ~:i~~: _F_~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~... A__~~~~~~~~~~~~~~~::::~'~-~~" =_~~i _l~i i:~ Figure C-82: Day 421.:~.~~~~:~ir~~C-4

~~~~~:~Fgr C-8: D a 423.* ~- - | | | l j,.:~-::i::~i~: ===== -'. -TI C. ~L~A ~ C~~ ~~ ~~~~1~pt!....:.' s.': r ~,.........A_...........:~....~........~'~~,~,~'-~~w'~.~'.~~.:~~~~~.~ -*a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Figure C-84: Day 425. C-43 S~~~~~~~~~~~ | | ~ | - | | ~~~~~~~~~~ | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l~ c~~~:: ~~ ~~~I - _| s~: ~5 I - _ _| | l - - - lo~~~~~~~~~~~~~~~~~~ - | -S,5 = a!~:~::~~i~;:::~:~:~~::~:::: r | | E~~~~~~~~~ ~-:~s~s ~~2 n: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i~~~~~~~~~~~~~~~~~~~~~~ i~....iz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I 2 | ~~~~~~~~~~~si~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - I ~~:~~~:~~~~~~~::~~~~~~~~::~~~~:~~~:~~~:~~~~I~~~:~~~-~~~:~~~i~~~' WC~~~~~: ~ ~ _ | ~~.~~~:i`::~~~~~~~:::::~~~~~~~i~~~:~~~/~~~~~~~Zl~~~~ic % ~~~~~~~:~~~P ~ ~ ~ ~ _ | Il Figure C-83: Day 423.~~~~~~~~~~~~~~~~~~r An_ -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~p -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.s _Y~ Figure C-84: Day 425.~~~~~~~~~~~~~ C-43~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sz

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Figure C-87' Day 430. Figure C 88 Day 432 C-45

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sE~~~~~~~~~~~~I...... "'....~. Figure C-91' Day 440.'i::' -....::~:i. q " ma~P ~rl,~:~:'spiglli 6~iU:l,[Qp~ E E

Figure C-93: Day 444. - _ _ a D S X S U s S i E E | | g | | | | | B i g E X E E g |. | 1E 10! I Z:l g S - | | | ~ ~ | | i - | | | | S.ZS g S S S S S S d d d E -| m S m i 2 SgE M _ as s am ~ a 5 asP WC OES z { S S S E E | | | | Z | X f R f X 50 I _ - 2 m@ m m 3s -! 2 ffi X B w I g a B11 1|911 13?1a 511 1111 I 11111 f 1 1 S g g g I - | AB " - - I i8 " u - S - R | g S S E S S S I | E.X; XO: X I Rll m X S i i | | | | | | | R S S | | | R S S S E E E | i i S g | | | S |. | | | X E E N. s | S g | | | N | | | | E B g i E | i | | g g W E X S, M i - - i S S I, - W, a E E E E | s | l | | S E g g | | | | | | 2_s ^ De, _ D S ~s S - - S, S S ox ellul 91 S:0 X# 11 1111! 10 | Yl 3hE S aB 5, Z x 2 1E1 11110 1 lBlli 1 1111 l 1 | | OX5>R Ab 0 >E I C9 9U X - - - - s | l - | | 1 XXO Xll MD X#CO 1i1111. IYfflXlb >31 91 IRYI 111 S 1 EBBlEI a, SESI 8 D, s s Xl 11111 W. 111 I M 111 | | - | | |, E | I Cl - 1. 11S l - aa 3t i8a a 8 5 B E _ * s a 19 _IIIP liig 1D s. _ s | e 3 111111 R | _i M i - i _i i fi I fi | i _ - # - - I _ s s 58 _ I C_ - S _ _ _ D S - - - - -- - - -- - - w - w - - - - - - - Figure C-94: Day 449. C-4%

Figure C-95: Day 452. - ~ P 16: ak~~ c ~ ~ ~ - r~p -~~~~~~~~~~~~~~~~~~~ i~~~~~~~~~~~~~~~~~g r~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:: | ~~~~~~~~~~~~~~~~~~~~s ~~~~~~~iFgr -9:Dy48 C-49~ ~ ~ ~~~~::

Figure C-97: Day 470. C-50

D REBEX-1 day to calendar date conversion chart Use the following chart to convert REBEX-1 day numbers to calendar date. The REBEX-1 day number is equivalent to Julian day for 1992 dates and is 366 plus the Julian day for 1993 dates (1992 was a leap year). We calculated fractional day-used in the graphs in Appendices A and B by adding time of day to the day number. For example, 1200 UT on January, 1 1992 becomes fractional day 1.5. 1992 1993 OCT NOV DEC JAN FEB MAR APR 1 275 306 336 367 398 426 457 2 276 307 337 368 399 427 458 3 277 308 338 369 400 428 459 4 278 309 339 370 401 429 460 5 2791 310 340 371 402 430 461 6 280 311 341 372 403 431 462 7 281 312 342 373 404 432 463 8 282 313 343 374 405 433 464 9 283 314 344 375 406 434 465 10 284 315 345 376 407 435 466 11 285 316 346 377 408 436 467 12 286 317 347 378 409 437 468 13 287 318 348 379 410 438 469 14 288 319 349 380 411 439 470 15 289 320 350 381 412 440 4712 16 290 321 351 382 413 441 472 17 291 322 352 383 414 442 473 18 292 323 353 384 415 443 474 19 293 324 354 385 416 444 475 20 294 325 355 386 417 445 476 21 295 326 356 387 418 446 477 22 296 327 357 388 419 447 478 23 297 328 358 389 420 448 479 24 298 329 359 390 421 449 480 25 299 330 360 391 422 450 481 26 300 331 361 392 423 451 482 27 301 332 362 393 424 452 483 28 302 333 363 394 425 453 484 29 303 334 364 395 454 485 30 304 335 365 396 455 486 31 305 366 397 456 1First day of experiment. 2Last day of experiment. Table D-l: REBEX-1 day to calendar date conversion chart. D-1

UNIVERSITY OF MICHIGAN 3 901 5 03466 39821111111111111 3 9015 03466 3982