Improved calibration of infrared radiometers for cloud temperature remote sensing

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1 Improved calibration of infrared radiometers for cloud temperature remote sensing Joseph A. Shaw, MEMBER SPIE Leonard S. Fedor National Oceanic and Atmospheric Administration Wave Propagation Laboratory 325 Broadway Boulder, Colorado Abstract. We discuss errors and uncertainties in calibrating infrared radiometers to measure the temperature of clouds in the earth s atmosphere. Many of the points we make apply to any radiometric temperature-sensing application where the target temperature is less than the ambient temperature. Dominant uncertainties and errors are due to ambient radiance reflected from the blackbody-simulator source, thermal fluctuations in the radiometer, and imprecise voltage measurements. Our improved technique removes, reduces, or accounts for these errors and uncertainties. The resulting calibration uncertainty is ±0.8 C for a radiometer with a 10-V output range. We verified this accuracy by comparing cloud-base temperatures measured by ground-based IR radiometers, in situ (radiosonde) sensors, and other remote sensors on the ground and on satellites. We made these comparisons for spatially uniform blackbody clouds that filled the field of view of our ground-based radiometers. Subject terms: radiometric calibration; radiometry; remote sensing; clouds. Optical Engineering 32(5), (May 1993). 1 Introduction Remote sensing of temperatures less than the ambient calibration temperature with an infrared (IR) radiometer requires consideration of factors that are negligible in other radiometry applications. These factors affect radiometric temperature measurements of any cold object, but we discuss them in terms of calibration for cloud-temperature remote sensing. Several research fields benefit from accurate remote sensing of cloud temperatures or remote identification of clear and cloudy conditions. These include earth-space radiowave propagation, 1 climate and atmospheric radiation, 2,3 and aircraft icing. 4 In the past, we have used our IR radiometers primarily as qualitative cloud detectors. However, having an improved absolute calibration, we can now use the radiometrically measured cloud temperatures quantitatively and understand their uncertainty. Paper received Aug. 8, 1992; revised manuscript received Dec. 10, 1992; accepted for publication Dec. 11, This paper is a revision of a paper presented at the SPIE conference on Atmospheric Propagation and Remote Sensing, April 1992, Orlando, Florida. The paper presented there appears (unrefereed) in SPIE Proceedings Vol Society of Photo-Optical Instrumentation Engineers /93/$2.00. Several recent papers demonstrate ongoing interest in improving radiometer calibration in a variety of applications. 5,6 Fraedrich 5 noted that it is important to perform a detailed error analysis even with an established calibration technique. Doing so encourages refinement and improvement of the calibration technique. Lorenz 6 discussed the calibration and related problems of operating airborne, chopper-stabilized IR radiometers to measure earth-surface temperatures. He showed that periodic in-flight calibrations of airborne radiometers are necessary. Conversely, we show that once calibrated carefully, our ground-based radiometers can operate unattended for weeks or months, providing highly accurate cloud-temperature measurements. We must consider calibration-source emissivity more carefully than Lorenz did because cloud temperatures are usually colder than earth-surface temperatures. An important concern of Lorenz s that is common to our application is chopper-temperature stability. We calibrate our cloud-temperature radiometers by viewing a blackbody-simulator source whose temperature is varied from 20 to about -65 C. At these temperatures, small amounts of reflected ambient radiance can be significant com /OPTICAL ENGINEERING / May 1993 /Vol. 32 No. 5

2 INFRARED RADIOMETERS FOR CLOUD TEMPERATURE REMOTE SENSING pared to the target radiance. Therefore, accurate calibration requires that the source emissivity be accounted for carefully. Other problems unique to this type of cold calibration include frost buildup and thermal gradients in the blackbodysimulator source and convective cooling of the radiometer s chopper and detector. Atmospheric variability causes other uncertainties in cloud sensing. We discuss some of these effects briefly, but we focus our discussion primarily on analysis of the radiometer calibration and verification of the calibration using data collected in winter-storm studies during February-March 1991 in eastern Colorado. After removing, reducing, or accounting for a number of errors and uncertainties, we calculated our calibration uncertainty to be ±0.8 C. Comparisons of cloud-base temperatures measured by radiometers with those measured by radiosondes at laser-determined cloud heights verify this calibration accuracy for blackbody clouds that fill the radiometer s field of view. Previously, Snider 7 had to remove a systematic error of 1.13 C from cloud-base temperatures measured with one of our radiometers to achieve rms differences of about 1.2 C in a similar comparison. The same type of bias has been evident in data from several radiometers in a variety of locations and conditions; the magnitude of the bias increases at lower cloud temperatures. We now have identified the source of this error as ambient radiance that is reflected into the radiometer s field of view during calibration from an imperfect blackbody-simulator source. We used path-integrated liquid measurements from a microwave radiometer to identify blackbody clouds when comparing radiometric and in situ cloud temperatures. This helped distinguish between radiometer calibration errors and temperature differences due to optically thin clouds that have an effective radiating temperature lower than their physical temperature. This works only for liquid clouds; an independent method of verifying the optical thickness of ice clouds is still needed to refine our understanding of the lower temperature range of our radiometer calibration. IR images from satellites also help verify calibrations and indicate the utility of ground-based sensors in aiding the interpretation of satellite data. In the rest of this paper we describe our calibration technique and quantify its dominant uncertainties and error sources, from which we calculate a total calibration uncertainty. We then present experimental verification of this uncertainty by comparing our radiometric cloud temperatures with those from in situ sensors (radiosondes), other groundbased remote sensors, and satellites. 2 Instrument Description The radiometers we use for sensing cloud temperature are single-channel chopper-stabilized mid-infrared systems (modified Barnes PRT-5). Figure 1 is a diagram of the optical head. The radiometer s full-angle field of view is 2 deg and the optical bandwidth is limited by a filter with half-power wavelengths of and µm. We use these filters instead of the more common 8- to 14-µm filters to reduce the effect of atmospheric absorption and to equalize the responses from liquid and ice. At the front of the optical head is a temperature-controlled cavity enclosing a hyperimmersed bolometer detector, a 10-mm-diam f/2.8 IrTran-2 lens, an optical bandpass filter, Fig. 1 Optical head of our cloud-sensing infrared radiometers. FOV is field of view; C, chopper; F, filter; L, lens; and Det, detector. and a gold-coated chopper. The rotating chopper causes the detector to view radiation alternately from the radiometer optics cavity and the external source. The detector output is an ac voltage, proportional to the difference in emission from these two sources. Thus, by subtracting the emission of the temperature-controlled optics cavity from the measurement, the chopper provides a stable reference that enables absolute calibration. 3 Calibration for Radiometric Temperature Sensing Radiometric temperature sensing requires association of the radiometer s output with an object temperature. The easiest way to do this is by filling the radiometer s field of view with a blackbody-simulator source at a known temperature. We derive a calibration equation for target temperature as a function of radiometer output voltage by recording voltages while the temperature of a blackbody simulator is varied. This removes the need for detailed analysis of the component transmittances and responsivities. We fill the radiometer s field of view with the calibration source to avoid angular-response variations, and we have not seen evidence of any polarization sensitivity. As with most IR calibrations, 8 a limitation of this technique is that calibration sources are not ideal blackbodies. Clouds are also not perfect blackbodies, so we must consider carefully the radiative properties of the calibration sources we use and the clouds we measure. Figure 2 illustrates the equipment we use for calibrating our cloud-sensing radiometers. This figure represents the blackbody-simulator source by a conical cavity; this is a common, though not necessary, geometry. The radiometer head points into the source cavity, whose temperature is measured by a thermocouple. We vary the source temperature by setting the blackbody simulator in a bath of alcohol and dry ice. We begin with the alcohol at ambient temperature (typically 20 C) and add dry ice in increments that lower the bath temperature by about 4 C. We continue this process to about -65 C which is the cooling limit for dry ice in the alcohol bath. Though liquid nitrogen could extend our calibration down to clear-air or cirrus brightness temperatures (about -70 to -105 C), the radiometers discussed here have bolometer detectors and are not well suited to measuring such cold temperatures. We have a more sensitive instrument that is designed for such measurements. 9 OPTICAL ENGINEERING / May 1993 / Vol. 32 No. 5 / 1003

3 SHAW and FEDOR Fig. 2 Equipment we use for calibrating our cloud-sensing radiometers. We place a blackbody-simulator cavity in a bath of alcohol and dry ice and vary the calibration temperature from 20 to -65 C. We purge the cavity with N 2 gas to avoid frosting the cavity walls. VM1 and VM2 are precision voltmeters for measuring the thermocouple and radiometer voltages. Fig. 3 Calculated radiometric temperature error that results from ignoring the source emissivity during calibration. This curve was calculated using a source emissivity of and an ambient temperature of 20 C. 4 Calibration Error Analysis Though conceptually simple, our calibration technique includes several sources of serious, though somewhat subtle, errors. The most significant errors arise from imperfect simulation of a blackbody source, undesired thermal fluctuations in the detector cavity, and imprecise measurement of temperatures and voltages. 4.1 Blackbody-Simulator Emissivity Despite the effort that is expended to achieve uniformly high emissivity in blackbody simulators, emissivity effects still are often the dominant calibration errors in cloud radiometry. At cloud temperatures (typically <0 C), even very small percentages of reflected ambient radiation from the warm laboratory cause a significant error. This problem is compounded by our lack of a low-background calibration facility. To calculate the magnitude of this error, we considered the detected radiance as the sum of two components: (1) the radiance emitted by the blackbody simulator and (2) the radiance emitted by the ambient surroundings that is reflected from the cavity to the detector. Thus, the spectral radiance detected by a radiometer at ambient temperature T a, viewing a blackbody-simulator source with emissivity ε and temperature T bb, is A typical calibration might have an ambient temperature of 293 K (20 C) a blackbody simulator with an emissivity of 0.963, and a temperature of 263 K (-10 C). For these parameters, the blackbody spectral radiances at our µm center wavelength are L bb = 514.1µWcm -2 sr -1 µm -1 and L a = 871.8µWcm -2 sr -1 µm -1. Then, from Eq. (l), the detected spectral radiance is L d = 527.4µWcm -2 sr -1 µm -1. Solving Planck s equation for the equivalent black- body temperature T eq corresponding to the detected radiance L d results in T eq = K. Thus, the radiometer detects a signal equivalent to blackbody radiation at K, whereas the calibration source is actually at K. Thus, with no correction for source emissivity, the incorrectly calibrated radiometer will indicate a temperature that is colder than the actual target temperature (in the above example, it would indicate K when subsequently viewing a blackbody target with a temperature of K). Figure 3 is a plot of the calculated radiometric temperature error as a function of target temperature for a calibration using a blackbody simulator that is assumed perfect, but that in fact has a emissivity. The error at the ambient temperature (20 C) is zero because the reflected ambient radiation compensates for the lower cavity emissivity. The error grows with decreasing target temperature because the reflected ambient radiation becomes increasingly large relative to the target radiance. In Colorado, optically thick winter-storm clouds have base temperatures in the range of 0 to -20 C; summer clouds vary from about 0 to 20 C. We see evidence of optically thick ice clouds with temperatures down to at least -30 C. Optically thin clouds, in either season, appear to be very cold ( -30 C) because the measured temperature results from the combined cloud and clear-sky radiances. Thus, correcting for a calibration-source emissivity less than one is especially important for winter clouds and optically thin clouds. 4.2 Correcting for a Blackbody-Simulator Emissivity Less Than One We estimated the emissivity of our conical calibration sources using Bedford and Ma s calculations of integrated cavity emissivity as a function of cavity dimensions. 10 For our cones, which have a 42-deg apex angle, this technique predicts a integrated cavity emissivity. This low value is not surprising, considering the large cone angle / OPTICAL ENGINEERING / May 1993 / Vol. 32 No. 5

4 INFRARED RADIOMETERS FOR CLOUD TEMPERATURE REMOTE SENSING In our improved calibration technique, we use the calculated calibration-source emissivity and measured temperatures in Eq. (1) to calculate the equivalent blackbody radiance, from which we solve the Planck function to find an equivalent blackbody temperature for each calibration point. Associating the radiometer s output voltage with the equivalent blackbody temperature, rather than with the physical cavity temperature, removes the emissivity-induced error in the calibration equation. This correction is adequate because we calibrate in the same temperature-controlled room in which the radiometer operates. In addition to correcting for emissivity, it would be useful to use a blackbody simulator with higher emissivity We recently constructed two inner-cone cavities 13 for calibrating an IR spectroradiometer. 9 These cavities have integrated emissivities of at least 0.99 and could remove much of the calibration uncertainty caused by the low emissivity of our old cones. Similarly, adding to the old cones a black annular lid 10 that reduces the cavity aperture by half would increase the cavity emissivity from to If this were done, the emissivity-induced error shown in Fig. 3 would be reduced from 1.3 to 0.3 C at a target temperature of -10 C. However, in both these cases, it would be difficult to cool the cavity lids with our present alcohol-bath technique. We are considering various options for improved calibration sources to reduce the magnitude of error that might result from incorrectly accounting for the source emissivity. 4.3 Blackbody-Simulator Temperature Uniformity One of the most important characteristics for simulating a blackbody is temperature uniformity. Maintaining temperature uniformity in our blackbody-simulator cavity becomes increasingly difficult at lower temperatures. A blackbody simulator only partly immersed in cold alcohol will radiate at a temperature somewhere between that of the cold alcohol and that of the warm air. Bartell showed that in a case like this, the cavity emissivity appears to be greater than one. 14 In our alcohol-bath technique, we must take great care to immerse enough of our cavities into the alcohol to minimize thermal gradients. The top of our old blackbody-simulator cones flare out to form a flange that rests on the top of the container that holds the alcohol bath. An improvement would be to use a cavity that has thermally nonconductive walls above the alcohol-air interface and conductive walls below. Construction of such a device would prove challenging but worthwhile for reducing calibration uncertainty. 4.4 Temperature Fluctuations in the Chopper Cavity As long as the chopper-cavity temperature is stable, all measurements are referred to the same reference. However, if the chopper-cavity temperature changes, the output is no longer referred to the same absolute reference. Lorenz identified this as a dominant problem with airborne IR radiometers. 6 A related problem is temperature variations of the chopper blade itself. Because the chopper reflectivity is not exactly equal to one (it is 0.99), it emits energy that can also become significant in measurements of cold targets. As long as the chopper temperature is unchanged from calibration to operation, this effect is accounted for in our calibration. If, on the other hand, the chopper temperature varies during calibration or operation, the measurement reference is altered. Fig. 4 Chopper-cavity temperature drift measured (a) without and (b) with purge gas flowing for a blackbody-simulator cavity temperature of -40 C. At temperatures below 0 C, frost will form on the surface of the blackbody simulator and alter the source radiance. To avoid this, we purge the cavity of water vapor by sealing the blackbody-simulator cavity and radiometer head together and purging the system with nitrogen gas. During calibration measurements at cold temperatures, the radiometer optical head is physically very near the cold blackbody simulator, and the chopper cavity begins to cool. If the purge gas is flowing during these measurements, the choppercooling problem is aggravated by convection. Figure 4 shows chopper-cavity temperature deviations measured while the cone was in a -40 C alcohol bath. Curve (a) in Fig. 4 is without gas flowing, and curve (b) is with gas flowing. For curve (a) in Fig. 4, we sealed the blackbody simulator and radiometer head together, purged them with nitrogen gas for 30 s, and then placed them in the cold alcohol with the gas turned off. This new technique slows down the chopper cooling enough that accurate calibration measurements are possible. Calibration measurements must not be taken too soon after placing the blackbody simulator into the alcohol. It is equally important to wait long enough to avoid temperature gradients on the blackbody simulator, but not to wait so long that the chopper cavity is cooled excessively. Between measurements at successive temperature increments, the radiometer optical head must be allowed to warm up to avoid cumulative cooling. Our practice is to wait for about 30 s after immersing the cone in the alcohol bath before taking data, but to avoid taking data after the blackbody simulator has been in the alcohol for about 2 min. We then allow the optical head to warm up for several minutes while the alcohol bath is coming to a new colder equilibrium temperature with the newly added dry ice. Curve (a) in Fig. 4 indicates that the chopper-cavity temperature fell 0.35 C in 2 min, when gas was not flowing. With gas flowing [curve (b)], the chopper cavity cooled more than 3 C in 2 min. These data were collected with an alcohol OPTICAL ENGINEERING / May 1993 / Vol. 32 No. 5 / 1005

5 SHAW and FEDOR temperature of -40 C. The chopper cavity will cool less rapidly at warmer alcohol temperatures and more rapidly at colder alcohol temperatures. 4.5 Voltage-Measurement Errors Given that adequate accuracy is achieved in blackbody simulation, the next significant issue is the precision of radiometer and thermocouple voltage measurements. This is important during both calibration and operation. The best way to avoid voltage-measurement errors is to use the same highquality voltage sensor during both calibration and operation of the radiometer. With our present equipment, we can measure radiometer output voltage with roughly 3-mV precision. We measure the thermocouple voltage, which indicates the physical temperature of the blackbody-simulator cone, with about 3-µV precision. For high SNR, these measurement uncertainties must be small compared to the signal voltages. At the outset of this work, one of our radiometers had a 1-V full-scale output-voltage range, while the others had 10-V ranges. In other words, for the same target temperature, the 10-V range produced a signal 10 times larger than that from the 1-V range. With the 1-V range, the uncertainty in the radiometer voltage measurement corresponds to a temperature uncertainty of up to 1.0 C; however, with the 10-V output range, the same voltage-measurement uncertainty corresponds to a temperature uncertainty of only about 0.1 C. We now operate all our cloud-sensing radiometers with 10-V output ranges. 4.6 Total Calibration Uncertainty With careful attention to detail in the described calibration technique, radiometric measurements of blackbody temperature in a controlled environment with the described radiometers have an uncertainty of ±0.8 C. This number is the rms sum of standard deviations that we estimated or calculated for each error source. Our uncertainties are estimates based on calibration experience and laboratory experiments for the technique described in this paper. All are achievable with proper attention to detail. Blackbody-simulator temperature uncertainty results from temperature nonuniformity and imprecise thermocouplevoltage measurement; these produce a combined uncertainty of σ bb ±05 C. Output-voltage measurements with the old 1-V range typically resulted in a temperature uncertainty of σ 1 ±0.8 C; this has been reduced to a level corresponding to the fluctuations in the voltage itself, σ 10 ±0.1 C, by converting all the radiometers to a 10-V output range. The effect of a cavity emissivity less than one can be accounted for and the resulting systematic error removed. Uncertainty in both the ambient temperature and the blackbody-simulator cavity emissivity produce an emissivity-correction uncertainty σε that increases from 0 at ambient temperature to ±0.5 C at target temperatures down to about -20 C; below this, the correction and its associated uncertainty increase. Our experience so far with emissivity correction suggests that the cloud-temperature uncertainties increase to about 3 or 4 C at temperatures near -60 C. This still is much better than the 7 to 10 C errors that result from not considering source emissivity. Quanti- tative verification of the uncertainty at very cold cloud temperatures is not possible yet because we cannot verify the optical thickness of ice clouds. Chopper-cavity cooling may result in errors of σ ch ±0.4 C if the cavity is purged before, not during, calibration measurements. Though this resembles a systematic error, it is actually random because, for a constant source temperature during a 2-min calibration measurement sequence, it results in time-evolving radiometer output voltages that are dependent on the alcohol and radiometer temperatures. Combining these effects, the total standard deviation of our calibration uncertainty for the old 1-V range is and for the 10-V range is 5 Additional Uncertainties in Cloud-Temperature Measurements Since clouds are not ideal blackbodies and the atmosphere is not a controllable laboratory environment, the uncertainty in remote measurements of cloud-base temperature can exceed that of a laboratory measurement with a controlled source. The purpose of this paper is not to discuss the details of atmospheric effects on remote cloud-temperature measurements. Rather, the object is to understand and minimize the calibration uncertainty for cloud-sensing radiometers. However, we will discuss briefly in this section some important considerations for atmospheric measurements. 5.1 Cloud Uniformity and Atmospheric Transmittance Clouds do not usually have spatially uniform emissivity or temperature. When a radiometer sees partly through a cloud, a broad area of a nonuniform cloud, or cloud and clear sky together, it integrates radiance over an unknown distribution of emissivity and temperature, weighted by the angular responsivity of the radiometer. Measurements of emission from optically thin clouds are particularly difficult to interpret. These effects are all critical to the interpretation of radiometric data, but it is not possible to assign a single value to their uncertainty. Rather, the user should consider them carefully when collecting or interpreting radiometric data. Cloud radiance is altered or sometimes obscured by the atmosphere between the cloud and the radiometer. The 10-µm window spectral region in which our radiometers operate is not perfectly transparent. Absorption within the radiometer s bandwidth (9.95 to µm) is due primarily to water vapor. A common 8- to 14-µm filter would cause greater errors due to increased absorption by ozone, etc. We often operate our radiometers in the semi-arid plains of eastern Colorado where the humidity is usually low. To verify our calibration accuracy, we measured stratus clouds because they are usually uniform optically thick targets. We modeled this type of cloud, with cloud-base height of about 1006 / OPTICAL ENGINEERING / May 1993 / Vol. 32 No. 5

6 INFRARED RADIOMETERS FOR CLOUD TEMPERATURE REMOTE SENSING 1 km, using the MODTRAN computer code. 16 Varying the relative humidity between the ground and the cloud from 0 to 100% produced a brightness temperature variation of only 0.5 C. (We determined the equivalent measured brightness temperature by integrating the calculated radiance across the filter s spectral responsivity.) Thus, for low-level clouds, humidity has a surprisingly small effect. For high clouds in moist air, humidity becomes much more important. 5.2 Contamination of Radiometer Optics During some field experiments in the past, the optics of our radiometers have collected dust, rain, and other contaminants. The result is a bias that increases at colder source temperatures (as the interfering radiance becomes a larger fraction of the received radiance). To avoid this problem, we house our radiometers in containers that have a vertical viewing port. A fan blows air (1200 ft 3 /min) through the container and out the port to keep rain, dust, and other contaminants from falling on the optics. Without this protection, biases up to 25 C have developed during several weeks of remote operation. With our protective housing, our radiometers operate unattended for several months with no apparent degradation. 5.3 Verification of Actual Cloud-Base Temperature Uncertainty in verifying actual cloud temperatures does not affect the accuracy of radiometric measurements, but rather reduces our ability to verify correct calibration. We usually determine an actual cloud-base temperature from a radiosonde measurement of temperature at the cloud-base height. We measure cloud-base height with a laser ceilometer, which calculates range from the transit time of a laser pulse reflected from the cloud. Uncertainty arises because we do not know for sure if the laser beam is reflected from particles at exactly the same height as the optically thick layer that determines the radiometric temperature. Uncertainty in the temperature measurement at that height also exists. Our experience suggests that the uncertainty of an actual cloudbase temperature is about ±0.5 to ±1.0 C for a uniform optically thick cloud. Therefore, improving the accuracy of radiometric cloud-temperature measurements beyond this uncertainty will be difficult to verify. 6 Experimental Verification of Calibration Accuracy During the spring of 1991, we participated in the Winter Icing and Storms Project (WISP) for studying the atmospheric conditions involved in aircraft icing. 4 We operated nearly identical IR radiometers for cloud-base temperature sensing at Stapleton Airport near Denver, Colorado, and about 35 km southeast, at Elbert, Colorado. Stratus clouds that occurred during February-March 1991 proved to be excellent targets for field-testing the radiometer calibration because they were often spatially uniform over large distances, and their high liquid water content made them nearly ideal infrared blackbodies. The emissivity 17,18 of thick stratus is in the range of 0.98 to 0.99, while the 1 to 2% of ambient radiance reflected from the low-lying cloud is from nearly the same temperature, resulting in essentially blackbody radiance at the cloud-base temperature. We have verified that our radiometric and in situ (radiosonde) measurements of cloud-base temperature, for blackbody liquid clouds over Stapleton Airport, differ by an amount that is less than or equal to the calculated calibration uncertainty. At the Elbert field site, where we did not have a laser ceilometer to determine cloud heights, we compared the radiometric cloud temperatures with those from Stapleton and also compared them with satellite measurements of cloud-top temperature. When the ground-based and satellite radiometers both viewed optically thick stratus clouds, the cloud-top temperatures were slightly cooler than our measurements of cloud-base temperature, as was expected. Even though we did not have enough information from Elbert to verify its radiometric cloud temperatures as completely as we did for the Stapleton radiometer, we are confident that the Elbert radiometer s data are at least as good as those from Stapleton. This is because, at that time, the Stapleton radiometer was still operating with the 1-V output range, while the Elbert radiometer had a 10-V range. Both radiometers were calibrated using the same technique and the same equipment, and both were operated in similar environments. Also, prior to and following the WISP 1991 campaign, experiments with both radiometers showed that both instruments consistently measure nearly equal temperatures of laboratory sources and clouds over a common site, though the Elbert radiometer showed smaller deviations because of its lower output-voltage uncertainty. The following subsections give details of the calibration verifications. 6.1 Verification Using Radiosondes and Ground- Based Sensors Figure 5 shows radiometric cloud-base temperatures from Stapleton, with and without the correction discussed in Sec. 4 for calibration-source emissivity. Using the emissivity correction with otherwise well-calibrated measurements brings them within 1.0 C of the actual temperature of uniform optically thick clouds. Most important, however, is that the radiometric temperatures become randomly distributed around the actual temperatures. Without the emissivity correction, the radiometric temperatures are always colder than the actual temperatures, indicating a systematic error. To identify blackbody clouds for creating Fig. 5, we used measurements of integrated liquid from a colocated zenithviewing microwave radiometer. 19 When the microwave radiometer measures at least 0.1 mm of liquid, the clouds are infrared blackbodies. This is a useful criterion that tells us when we can interpret our IR brightness temperatures as actual cloud-base temperatures. Without such independent knowledge, verifying the calibration accuracy of IR radiometers with real cloud measurements would be impossible. In Fig. 6 we plotted the difference of the measured IR brightness temperature and the radiosonde cloud-base temperature against integrated liquid measured by the microwave radiometer. It is clear that when the liquid is at least 0.1 mm, the clouds are consistently black and the radiometric temperature agrees with the radiosonde with deviation less than ±1.0 C. We also occasionally see blackbody clouds that have very little or no liquid. These are evidently ice clouds, for which we do not yet have an independent method of determining optical thickness. Development of such a technique will help us better understand the uncertainties of temperature measurements for cold clouds. OPTICAL ENGINEERING / May 1993 /Vol. 32 No. 5 / 1007

7 SHAW and FEDOR Fig. 5 Radiometric cloud-base temperatures from the Stapleton radiometer, before (open circles) and after (solid circles) correction for calibration-source emissivity, versus actual temperatures of uniform optically thick clouds. Fig. 7 Time series of (a) IR brightness temperatures from groundbased radiometers and satellites in degrees Celsius, (b) cloud-base height in meters, and (c) liquid water content in millimeters for March 14-16, 1991, at Stapleton. In (a), the solid dots are from the groundbased radiometers calibrated by us; the crossed circles are from the VAS satellite sensor; and the stars are from the AVHRR satellite sensor. The AVHRR measurement at 1008 UTC on March 15 is indicated by an arrow. Fig. 6 Difference between radiometric and in situ cloud-base temperatures versus integrated cloud liquid. When the integrated liquid is greater than 0.1 mm, the clouds become black in the infrared and the radiometric temperatures agree within the calibration uncertainty with the in situ temperatures. 6.2 Verification Using Satellites and Ground-Based Sensors At Elbert, because we did not have a ceilometer to determine cloud-base heights, we could not determine actual cloud-base temperatures. When we calibrated the two radiometers, we tested them briefly for consistency by pointing them both at the same source, using both laboratory sources and clouds. The two radiometers agreed within 0.4 C (which is the un- certainty difference due to the different output-voltage ranges). To test the calibration during the WISP observation period, we compared measurements from Elbert and Stapleton when both sites were covered with uniform stratus clouds. We used satellite images to verify that both sites were indeed covered with uniform stratus clouds. Figure 7 shows IR brightness temperatures, cloud-base heights, and microwave radiometer liquid measurements at Stapleton for March 14-16, The IR brightness temperatures plotted with solid dots are from the ground-based radiometer; those plotted with crossed circles are from channel 8 (10.4 to 12.1 µm) of the Vertical Atmospheric Sounder (VAS) aboard the National Oceanic and Atmospheric Administration (NOAA) geostationary GOES-East satellite; and those plotted with stars are from channel 4 (10.3 to 11.3 µm) of the Advanced Very High Resolution Radiometer (AVHRR) aboard the polar-orbiting TIROS-N satellite. The VAS IR temperatures start out much warmer than those from the ground-based radiometer because VAS sees the warm earth through optically thin clouds, while the ground-based radiometer sees the cold atmosphere through the clouds. The satellite measurements near 0900 Universal Time Coordinated (UTC) on March 14 are much colder than the ground-based radiometric temperatures because of cold 1008 / OPTICAL ENGINEERING / May 1993 /Vol. 32 No. 5

8 INFRARED RADIOMETERS FOR CLOUD TEMPERATURE REMOTE SENSING cirrus clouds between the stratus cloud and the satellite. This occurred again several times (e.g., 0700 to 1600 UTC on March 15) as cirrus floated in and out of the satellite radiometer s field of view. We verified that cirrus clouds were in the VAS beam during these times by looking at AVHRR images. The l-km spatial resolution (near the ground) of the AVHRR allowed us to see the stratus cloud-top temperatures between cirrus patches around Denver, whereas the 8-km resolution of the VAS encompassed cirrus much more often. The AVHRR image taken at 1008 UTC on March 15 showed stratus clouds over the entire Denver and Elbert measurement area and cirrus over Elbert. The AVHRR measured cloud-top temperatures of -9.5 C over Stapleton [arrow in Fig. 7(a)] and C over Elbert. The ground-based radiometers measured nearly equal temperatures, -9.0 C at Stapleton and -9.8 C at Elbert. A Stapleton radiosonde at 1100 UTC measured about -8.6 C at the cloud-base height determined by the laser ceilometer. Near the same time, the VAS measured a cloud-top temperature of -20 C due to combined stratus and cirrus radiance in its field of view. These comparisons demonstrate several points. First, the ground-based radiometers at two spatially separated field sites agree with each other within the calculated calibration uncertainty when they view uniform stratus clouds. Second, the ground-based radiometers agree within the calculated calibration uncertainty with radiosonde-measured cloud-base temperatures. Third, the ground-based radiometers seem to agree just as well with satellite radiometer measurements of the temperature of thin layers of stratus cloud, if the satellite s field of view is not partially filled with higher cold clouds. Fourth, the large fields of view of some satellite sensors easily enclose spatially nonuniform scenes, making interpretation of their data difficult. 7 Conclusions Uncertainty arises in radiometric cloud-base temperature measurements because of calibration uncertainties and atmospheric effects. Infrared radiometer calibration accuracy is limited primarily by inadequate simulation of a blackbody source, thermal fluctuations, and imprecise voltage measurements during calibration. Large biases can result from reflected ambient radiation when a blackbody simulator with emissivity less than one is used at low temperatures. Also, purge gas flowing during a cold calibration convectively cools the radiometer s chopper cavity, causing calibration errors up to about 3 C in 2 min. We have calculated the uncertainty for an improved radiometer calibration technique that accounts for the calibration-source emissivity, reduces convective cooling of the chopper cavity, and minimizes voltage-measurement uncertainties. The total calibration uncertainty is 0.8 C for a radiometer with a 10-V output range. We verified this by comparing radiometric temperature measurements of blackbody stratus clouds with cloud temperature measurements from radiosondes at laser-determined cloud heights. We also compared measurements from two ground-based radiometers at different locations, first with each other and then with radiometric measurements of the same clouds from satellites. Atmospheric effects add errors, but it is difficult to quantify these effects because so many factors contribute to their variability. We have discussed briefly some important atmospheric effects, including atmospheric transmittance and cloud uniformity, that can affect IR radiometric measurements. We calculated the maximum effect of humidity variations on ground-based radiometric measurements of stratuscloud temperature to be 0.5 C. Humidity effects will be much more significant for higher colder clouds. Because the actual cloud-base temperature can be verified only to within about ±1 C, calibration improvements beyond what we have described would be difficult to verify. Development of improved methods for verifying radiometric cloud measurements and for sensing the optical thickness of ice clouds are both areas that require further research. An improvement to our calibration technique that would reduce both the effort and the potential errors would be to use a blackbody simulator that has higher emissivity and thermally nonconductive walls above the alcohol-air interface in our cooling bath. Acknowledgments We appreciate all the people from the NOAA Wave Propagation Laboratory who helped with this paper: Judith Schroeder and Ed Westwater offered many helpful discussions, Mark Jacobson designed and built the protective enclosures in which we operated the radiometers, and he did the output voltage conversion, and Sharon Kirby helped prepare the manuscript. We also thank the reviewers for their helpful comments. This work was supported by the Federal Aviation Administration and by the Department of Energy s Atmospheric Radiation Measurement program. References E. R. Westwater, J. B. Snider, and M. J. Falls, Ground-based radiometric observations of atmospheric emission and attenuation at 20.6, 31.65, and 90.0 GHz, IEEE Trans. Antennas Propag. 38(10), (1990). V. E. Derr, R. S. Stone, L. S. Fedor, and H. P. Hanson, A parameterization of shortwave transmissivity of stratiform water clouds based on empirical data and radiative transfer theory, J. Atmos. Sci. 47(23), (1990). K. Sassen, R. Rauben, and J. B. Snider, Multiple remote sensor observations of supercooled liquid water in a winter storm at Beaver, Utah, J. Climate Appl. Meteor. 25, (1986). B. B. Stankov, E. R. Westwater, J. B. Snider, and R. L. Weber, Remote measurement of supercooled integrated liquid water during WISP/ FAA aircraft icing program, J. Aircraft 29(4), (1992). D. S. Fraedrich, Methods in calibration and error analysis for infrared imaging radiometers, Opt. Eq. 30(11), (1991). D. Lorenz, Accurate airborne surface temperature measurements with chopper-stabilized radiometers, J. Atmos. Oceanic Technol. 8(6), (1991). J. B. Snider, Radiometric observations of cloud liquid water during FIRE, in Proc. IGARSS 88 Symposium, IEEE, pp (1987). C. L. Wyatt, Radiometric Calibration: Theory and Methods, Academic Press, Orlando, FL (1978). J. A. Shaw, J. H. Chumside. and E. R. Westwater. An infrared spectrometer for ground-based profiling of atmospheric temperature and humidity. Proc. SPIE (1991). R. E. Bedford and C. K. Ma, Emissivities of diffuse cavities: Isothermal and nonisothermal cones and cylinders, J. Opt. Soc. Am. 64(3), (1974). F. O. Bartell and W. L. Wolfe, Cavity radiators: An ecumenical theory, Appl. Opt. 15(l), (1976). F. O. Bartell, New design for blackbody simulator cavities, Proc. SPIE 308, (1981). R. E. Bedford, C. K. Ma, 2. Chu, Y. Sun, and S. Chen, Emissivities of diffuse cavities: 4, Isothermal and nonisothermal cylindro-innercones, Appl. Opt. 24(18), (1985). F. O. Bartell, Cavity emissivities greater than one, Proc. SPIE 520, (1984). OPTICAL ENGINEERING / May 1993 / Vol. 32 No. 5 / 1009

9 SHAW and FEDOR 15. C. M. R. Platt and G. L. Stephens, The interpretation of remotely sensed high cloud emittances, J. Atmos. Sci. 37(10), (1980). 16. A. Berk, L. S. Bernstein, and D. C. Robertson, MODTRAN: A moderate resolution model for LOWTRAN7, GL-TR , USAF Geophysics Laboratory, Hanscom AFB, MA (1989). 17. G. Yamamoto, M. Tanaka, and S. Asano, Radiative transfer in water clouds in the infrared region, J. Atmos. Sci. 27(3), (1970). 18. P. Chylek and V. Ramaswamy, Simple approximation for infrared emissivity of water clouds, J. Atmos. Sci. 39(1), (1982). 19. D. C. Hogg, M. T. Decker, F. O. Guiraud, K. B. Earnshaw, D. A. Merritt, K. P. Moran, W. B. Sweezy, R. G. Strauch, E. R. Westwater, and C. G. Little, An automatic profiler of the temperature, wind, and humidity in the troposphere, J. Climate Appl. Meteor. 22(5), (1983). Joseph A. Shaw received the BS degree (cum laude) in electrical engineering from the University of Alaska, Fairbanks, in At the university he was involved in research investigating the electromagnetic effects of the aurora borealis on electric power systems. He studied electromagnetics and applied optics at the University of Utah, Salt Lake City, and received the MS degree in electrical engineering in He presently IS studying for a PhD from the OptIcal Sciences Center at the University of Arizona. He has been employed at the Wave Propagation Laboratory of the National Oceanic and Atmospheric Administration in Boulder, Colorado, since His research is in infrared and optical remote sensing and propagation. Recent work focuses largely on infrared spectroradiometric techniques for atmospheric remote sensing. He is a member of Phi Kappa Phi, the Optical Society of America, SPIE, and the IEEE Antennas and Propagation Society. Leonard S. Fedor received the BS degree in physics from San Diego State College in 1961 and the MS degree in meteorology from the Massachusetts Institute of Technology in He is currently a research physicist at the Wave Propagation Laboratory in Boulder, Colorado. For the past 30 years he has been involved in research of various aspects of remote sensing of the environment. These studies have included electromagnetic wave propagation, motions of Ionospheric irregularities, sea state, sea ice, and atmospheric water content. He is a member of Commission F of the International Radio Science Union (of which he is also the current secretary), the IEEE Geoscience and Remote Sensing Society, the American Geophysical Union, and Sigma Xi / OPTICAL ENGINEERING / May 1993 /Vol. 32 No. 5

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