An Improved Calibration Method for a Chopped Pyrgeometer

Transcription

1 96 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 An Imroved Calibration Method for a Choed Pyrgeometer FRIEDRICH FERGG OtoLab, Ingenieurbüro, Munich, Germany PETER WENDLING Deutsches Forschungszentrum für Luft- und Raumfahrt, Institut für Physik der Atmoshäre, Wessling, Germany 29 January 1999 and 26 May 1999 ABSTRACT An imroved calibration method for a choed yrgeometer is resented. The choed yrgeometer is a system of two radiometers (target radiometer and reference radiometer) modulated by a common choer. One radiometer measures the temerature of the choer by modulating an internal blackbody source. A reviously used calibration method needs two stes. The first ste is the measurement of the ratio of the resonsivities for the two radiometers; the second ste is the calibration of the target radiometer against a blackbody source. The first ste is based on the assumtion of a thermal steady state during the measurement of (tyically) a few minutes. Further investigations have shown that this assumtion is too idealistic. The errors introduced to airborne measurements by neglecting thermal unstabilities during ratio measurement are calculated using a numerical model of the instrument. To overcome these roblems a new calibration method is resented, which also erforms the calibration in two stes. The first ste is the calibration of the target radiometer using an isothermal instrument; that is, the temerature of the choer is known and, most imortantly, the whole measurement takes only a few seconds, which rovides sufficient thermal stability. In a second ste, the calibration of the reference radiometer is done with the hel of the reviously known resonsivity of the target radiometer. The exerimental data of a calibration due to the new scheme are discussed. 1. Introduction In the article of Lorenz et al. (1996) a choed yrgeometer has been resented, which consists of two radiometers using the same choer. One radiometer, called a target radiometer, measures the radiation coming from the atmoshere by comaring it with the radiation of the black choer. The other radiometer, called a reference radiometer, measures the radiation of the choer by comaring it to an internal reference blackbody of known temerature. The rincile of the instrument is described by a air of linear equations for the two radiometer oututs U 1 and U 2 as given in Lorenz et al. (1996): U Rc(T ) and (1) E1,TAR 1BCHO 1,TAR 1,B,CHO 2BREF 2BCHO 2,B,REF 2,B,CHO U Rc(T ), (2) Corresonding author address: Dr. Peter Wendling, DLR, Institut für Physik der Atmoshäre, D Wessling, Germany. eter.wendling@dlr.de where U 1, U 2 are the outut voltages of target radiometer 1 and reference radiometer 2; B REF, B CHO are the blackbody radiances of reference source/choer in W m 2 sr 1 ; E 1,TAR is the measured irradiance of target in Wm 2 ; R 1, R 2 are the instrumental constants of target radiometer 1 and reference radiometer 2, for examle in V (W m 2 ) 1 ; 1 is the solid angle of target radi- ometer ( 1 ); 2 is the solid angle of reference radiometer; c 1 (T 1 ), c 2 (T 2 ) are the temerature correction factors due to temerature-deendent yroelectric resonsivities (T 1, T 2 are the corresonding detector temeratures); i,b,ref, i,b,cho are the sectral correction factors for the target radiometer (i 1) and the reference radiometer (i 2) at temerature T REF and T CHO ; and index B refers to blackbody radiation; and 1,TAR is the sectral correction factor for target irradiance. Due to the modulation scheme, the outut of the radiometers is roortional to the difference of two indeendent radiation terms. Each radiation term contains a sectral correction factor that reflects a nonideal sectral characteristic of the receiver (filter and detector). One of the radiation terms, the choer radiation, is common to both equations. The calibration of the instrument has to establish two resonsivities, which are not straightforward, since the 2000 American Meteorological Society

2 JANUARY 2000 NOTES AND CORRESPONDENCE 97 temerature of the choer is not generally known when an uncalibrated instrument is used. Thus, rocedures are needed to establish a secial thermal situation of the instrument, which allows one to find out the desired resonsivities. 2. The calibration as resented by Lorenz et al. (1996) The calibration resented in the article of Lorenz et al. (1996) is erformed in two stes: measurement of the ratio q (R 1 )/(R 2 2 ), called a q measurement, and the calibration of the target radiometer using a blackbody at different temeratures. The q measurement is based on Eq. (10b) of Lorenz et al. (1996): c2 c2 U1 A qlu 2, (3) c c 1 1 where c 1, c 2 are the temerature correction factors, as exlained in Eqs. (1) and (2), A is a constant, and l ( 2,B,CHO )/( 1,B,CHO ). The q measurement is erformed by measuring U 1 and U 2 with the radiometer head on a blackbody source at a constant temerature and the choer drifting in temerature after having been cooled, as described in the aer. As shown by Lorenz et al. (1996), Eq. (3) is valid if the following quantities are constant during the q measurement: the target irradiance E 1,TAR ; the temeratures T 1, T 2 of the two detectors; the temerature T REF of the internal reference blackbody, and the sectral correction factors. The validity of these assumtions will be discussed below. As an alternative to the derivation given in Lorenz et al. (1996), Eq. (3) can be obtained from Eqs. (1) and (2) by substituting R 2 by q and eliminating B CHO without the restriction of assuming any hysical arameter to be constant during the measurement; this aroach more clearly shows the influence of all hysical quantities and leads to c2 c2r1 c2lr1 U1 E1,TAR BREF qlu 2. (4) c 1 1,TAR 2,B,REF The first and second terms on the right-hand side of Eq. (4) reresent the factor (c 1 /c 2 ) A of Eq. (3), which has been assumed to be constant as a necessary condition to derive q from a linear regression. a. Discussion of required constancy of hysical arameters In a first ste we now discuss the constancy of hysical arameters within the first two terms of the righthand side of Eq. (4) during a q measurement. In a second ste, an error analysis is resented on the basis of a numerical model. FIG. 1. Sectral correction factors for three tyes of domes, according to Fig. 5 of Lorenz et al. (1996). 1) Silicone dome, 2) Reading-tye dome, and 3) 01B K7 tye dome for a blackbody source. The index i of the sectral correction factor (ordinate) refers to either target 1 or the reference 2 detector. The sectral correction factors for the two radiometers (indexes 1 and 2) and valid for blackbody radiation are shown in Fig. 1. Assuming a temerature change of 10 K at the choer during the q measurement l ( 2,B,CHO )/( 1,B,CHO ) will change by about 1% since the correction factor of the target radiometer (index 1) increases by 0.5% (curve 3 of Fig. 1), whereas the correction factor of the reference radiometer (index 2) decreases by 0.5% (curve 1 of Fig. 1), going from 300 to 290 K. If the target radiometer is equied with another tye of dome (curve 2, Fig. 1) the change in l becomes negligible since both correction factors change aroximately in the same way. This means that deending on the otical materials used in the two radiometers one may have to consider the changes in l. Since the temerature of the choer is not measured and not accessible from the formalism (B CHO has been eliminated), assumtions have to be made for the time rofile of the choer temerature to erform a first-order correction. The changes in 1,TAR and 2,B,REF are negligible (0.05%) since the temerature drifts of the corresonding sources are much smaller (T 1 K) as comared to the choer. The changes in the two temerature correction factors c 1 and c 2 are negligible (0.05%) since the temerature drift of the detectors is small (0.2 K) and the correction factors are in the order of 0.2% K 1. The change of the target radiance E 1,TAR during the measurement of q can be held negligible (0.1%) by setting the radiometer head on a blackbody source at constant temerature. The temerature of the reference blackbody T REF, however, will show a drift since there is some thermal interaction between the cold/hot choer and the reference blackbody. Measurements show that this temerature drifts u to 1 K during a q measurement, which corresonds to a change of B REF of 1.3% at 300 K. Therefore, the assumtion of thermal steady state during q measurement in Lorenz et al. (1996) is too idealistic and may result in considerable errors of the calibration arameters q and R 1.

3 98 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 In rincile a temerature stabilization of the reference blackbody could solve this roblem. The additional system increases the costs and is not useful for the urose of atmosheric flux measurement. These roblems can be avoided using the new calibration scheme. b. Model calculations To demonstrate the errors mentioned above, a simlified model of the calibration rocedure (q measurement and calibration of R 1 ) has been rogrammed including the errors introduced to a tyical airborne measurement of the downward flux. The simlifications in the model are as follows. 1) All sectral correction factors are constant (1), and 2) the temerature correction factors c 1 and c 2 are constant (1). As mentioned in section 2a, only the sectral correction factors forming l ( 2,B,CHO )/( 1,B,CHO ) can show the changes that have to be considered. On the basis of reasonable assumtions (time rofile of choer temerature), these changes can be established with sufficient accuracy if needed, so they are not considered in the model. The changes to the temerature correction factors c 1 and c 2 are negligible, as ointed out above. Thus the model reflects errors introduced by neglecting temerature drifts of the reference blackbody during q measurement. The logical structure of the model calculation is demonstrated in the following stes: 1) Model the q measurement R Assume a model value of q and R 1 ; R define a series of temerature values for T REF and T CHO describing the temerature drifts of the reference source and the choer as observed during a tyical q measurement; R calculate the corresonding model radiometer oututs U 1 and U 2 using the model values of q and R 1 and Eq. (1) above and Eq. (5c) of Lorenz et al. (1996), R1 BREF BCHO U2 c2 ; and (5) q 2,B,REF 2,B,CHO R determine the measured value of q, q m from the linear regression of Eq. (3). 2) Model the R 1 calibration according to Eq. (11) of Lorenz et al. (1996): 1 U1 U2 E1,TAR BREF l q R l (6) c c 1 2 1,TAR 2,B,REF R Perform the model calibration of R 1 assuming three calibration irradiances E 1,TAR, as used in a tyical calibration, and take the corresonding temeratures T CHO and T REF, as can be found from exerimental data; FIG. 2. Absolute error of an airborne downward flux measurement of 30 W m 2 as a function of the difference between temeratures of the reference source and the choer; model results for two temeratures (210 and 230 K) of the reference source are shown. R calculate the corresonding model radiometer oututs U 1 and U 2 using Eqs. (1) and (5) and the model values R 1 and q; and R determine the measured value of R 1, R 1m from Eq. (6) using q m. 3) Model an atmosheric measurement, Eq. (6) of Lorenz et al. (1996): U1 lqu2 BREF E l (7) cr cr 1,TAR 1,TAR ,B,REF R Assume a model target irradiance E 1,TAR that is tyical for airborne measurements; R assume a value for T REF and a temerature difference between T REF and T CHO as a model variable studying various flight situations, one can find lausible sets for these quantities; R calculate the true radiometer oututs U 1 and U 2 for the measurement in the atmoshere using Eqs. (1) and (5) and the model values R 1 and q; R determine the measured value of E 1,TAR, E 1,TAR,m with Eq. (7) using R 1m and q m ; and R note the difference E 1,TAR,m E 1,TAR leads to the absolute error shown in the grahs below. Figures 2 and 3 show the absolute error for atmosheric downward fluxes of 30 and 90 W m 2 caused by neglecting the changes of T REF during q measurement as art of the calibration. The two curves in each grah corresond to the two temeratures of the reference source, which have been chosen as being reresentative for measurements of radiation fluxes at uer-troosheric levels. The simulations show for this case a ositive error of the atmosheric measurement, on the order of 1to4Wm 2, deending on the thermal situation of the instrument. Since the thermal situation of the instrument can raidly change during the various flight conditions, this error will roduce changes on the calculated fluxes that look like an instability of the instrument. Thus, one of the most imortant advantages of the choed yrgeometer, its radiometric stability in-

4 JANUARY 2000 NOTES AND CORRESPONDENCE 99 FIG. 3. Absolute error of an airborne downward flux measurement of 90 W m 2 as a function of the difference between temeratures of the reference source and the choer; model results for two temeratures (220 and 240 K) of the reference source are shown. herent to the modulation rocess, is lost to a certain extent. It must be clearly ointed out that the errors resented here are introduced only by assuming a steady-state condition during q measurement, thus neglecting the drift of the reference temerature that occurs during actual measurement. In the aer of Lorenz et al. (1996) some results have been resented of the re-eucrex Intercomarison Camaign of 1992 where five yrgeometers (two Eley yrgeometers, two Foot yrgeometers, one choed yrgeometer) have been flown simultaneously on three airlanes. Results of a boxlike attern flown at an altitude of 6.1 km MSL have been analyzed. The results of all five instruments for measurements along the legs and the changes between the legs of the flight box show that the choed yrgeometer rovides a radiometric stability that is at least as good as that of the Foot yrgeometers. Another significant finding was the fact that the choed yrgeometer yields the smallest flux values of all five instruments throughout the four legs of the box. The difference was about 10 W m 2 as comared to the average value (90 W m 2 )ofthe other four instruments. The model calculation resented above would redict a decrease of the measured flux values in the order of 1 W m 2 [ Fig. 3: (T CHO T REF 0), T REF 230 K] for the choed yrgeometer if the new calibration method would have been alied, thus creating a somewhat greater difference to the findings of the other instruments. Since calibration sensitive comonents (detector, dome, etc.) of the choed yrgeometer used for the re-eucrex measurements have been changed in the meantime, it is not ossible to aly the new calibration to the original instrument. 3. The new calibration method To demonstrate the new calibration method, Eqs. (1) and (2) are rewritten as follows: U1 E1,TAR BCHO R1 R1BT and (8) c (T ) 1 1 1,TAR 1,B,CHO U2 BREF B CHO R R 2 2 2B R. (9) c (T ) 2 2 2,B,REF 2,B,CHO Since 2 is a constant system arameter we rewrite R 2 R 2 R 2 2. The basic idea of the new calibration is to calibrate the target radiometer in the first ste by erforming the measurement of each calibration oint (blackbody temerature) within a short time san (tyically a few seconds) in order to maintain the desired isothermal conditions of the instrument during that rocess. If the resonsivity of the target radiometer is known, the calibration of the reference radiometer is straightforward, as shown below. a. Calibration of the target radiometer As is obvious from Eq. (8) the target radiometer can be calibrated with a blackbody source if the temerature of the choer is known during calibration. This can be achieved if the radiometer head is in an isothermal condition during the measurement of a calibration oint; then the choer temerature equals the reference temerature, which is measured by PT100 (accuracy: 0.15 K, 50C T 50C). In this case B T can be calculated since B CHO and E 1,TAR are known blackbody radiations and 1,TAR and 1,B,CHO are sectral correction factors derived for the known temeratures of the radiators. The rocedure to achieve an isothermal radiometer head during target radiometer calibration is as following. In a thermally quiet laboratory the radiometer head (switched off) is ut under a rotection box for some hours to reach isothermal conditions. After that, the box is removed and the head is switched on and ositioned on a blackbody source. These activities can be erformed in less than 10 s; thus isothermal conditions are maintained during that time with sufficient accuracy. Immediately after correct osition on the blackbody, a signal of the target radiometer can be registered (time constant of the radiometer signals is on the order of 0.1 s) for a few seconds. During that time the signal of the reference radiometer begins to drift away from zero since the temerature of the choer slowly drifts toward the temerature of the calibration blackbody source, thus creating a radiometric difference B R [Eq. (9)] between choer and reference source. Therefore, the signal of the reference radiometer can be used to indicate roer isothermal conditions during the measurement and to establish an error value; this signal can be maintained at less than 10 mv throughout the measurement, corresonding to a T of 0.1 K (300 K blackbody). The whole rocedure is reeated for each calibration oint.

5 100 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 FIG. 4. Examle of a calibration of the target radiometer; the hatched line is the linear regression of the measured data oints (crosses). Each of the three calibration temeratures contains between 8 and 11 samles. The grah (Fig. 4) of a target radiometer calibration due to Eq. (8) shows three calibration oints that corresond to three temeratures of the calibration blackbody source (280.4, 300.3, and K) and the corresonding linear regression. Each of the three calibration oints contains n (n 10) samles (1-s samling interval) registered during the first n seconds after ositioning the radiometer head on the calibration blackbody source; the oints are too close together to be resolved in the lot. The linear regression line shows a zero offset of about 4 mv, corresonding to a T of 0.2 K (300-K blackbody), which is consistent with the accuracy of a PT100. This offset can be exlained as follows. The radiometric measurement comares the radiation of the reference source with that of the calibration source (both related to the choer radiation). On the other hand, the calculation of the radiometric terms in Eqs. (8) and (9) is based on the measurement of two indeendent temeratures (calibration blackbody and reference source). For the urose of demonstration we assume that the calibration blackbody, the choer, and the reference source are at the same temerature, that is, isothermal conditions are valid. In this case both radiometer signals will be zero. The temerature measurements at the two sources, however, will show some difference due to systematic errors of the PT100 sensors. Consequently, the radiometric evaluation will redict a FIG. 6. Outut signals of target radiometer U 1 and reference radiometer U 2 during calibration of the reference radiometer. radiometric difference B that is somewhat different from zero. Thus the observed offset is due to a more or less unavoidable difference between the measured temerature and the real radiometric temerature of the two sources. If we assume a constant error in the absolute temerature measurement over the range of interest, the sloe of the linear regression rovides the correct resonse; the offset is constant and can be omitted in subsequent data evaluation. Figure 5 shows the deviation of the individual samles of the three calibration oints from the regression line, where 1 mv corresonds to a T of 0.05 K (300- K blackbody). Since the sign changes between the samle grous of highest and lowest calibration temerature to the grou of the intermediate temerature, the calibration shows a small nonlinearity on the order of 0.1 K(0.15% of the 300-K blackbody); this nonlinearity may be due to small errors in sectral correction factors or errors caused by deviations from a flat sectral emissivity over a wide sectral range (1 100 m) of the black radiating surfaces (reference source and choer). b. Calibration of the reference radiometer The calibration of the reference radiometer is now straightforward because R 1 is already known. One brings the radiometer head to a nonisothermal condition, for examle, by warming the choer with hot air, and FIG. 5. Offset of the individual samles from the linear regression line shown in Fig. 4. The calibration temerature is shown near the corresonding set of samles. FIG. 7. Examle of calibration of the reference radiometer; the solid line is the linear regression on the measured data oints. Since the choer temerature drifts, a continuous series of calibration oints exists along the linear regression.

6 JANUARY 2000 NOTES AND CORRESPONDENCE 101 uts the radiometer head on a calibration blackbody, which is conveniently at ambient temerature. The choer temerature will drift toward ambient and create varying outut signals for both radiometers. The evaluation of the measurement is as follows. Using Eq. (8) one can calculate the choer radiance B CHO for each measurement samle of the target radiometer outut U 1 because R 1 and all other quantities are known. The choer radiation now can be used in Eq. (9) to calculate B R and erform a linear regression to find R 2. The rocedure to calibrate the reference radiometer is somewhat similar to the q measurement discussed above. The imortant difference, however, is that no assumtions are necessary of a thermal steady state of various radiometer comonents since all dynamic quantities, including the temerature of the reference source, are known and can be correctly used in the formalism. Figures 6 and 7 show an examle of the reference radiometer calibration. The blackbody calibrator is at ambient temerature in this case. Before starting the measurement, the choer is warmed to achieve nonzero oututs in both radiometers. During the measurement the signals of the two radiometers are drifting toward zero (Fig. 6) since the choer slowly drifts to ambient temerature. The lot for calibration (Fig. 7) according to Eq. (9) shows the data oints and the linear regression. The measurement starts with a temerature difference between choer and reference source of about 7 K, which corresonds to the data oints at high values of B R. The data oints taken for the calibration cover 140 samles (1-s samling interval); after that eriod the further change of the temerature difference (now 1.3 K) gets slower, thus additional information gain is low. The arameters of the linear regression show a nonzero y intercet of the regression line of 17 mv, which corresonds to a T of 0.15 K of a 300-K blackbody. The nature of this offset is the same as discussed above for the target radiometer. 4. Conclusions The calibration of the choed yrgeometer as roosed by Lorenz et al. (1996) has been analyzed. This calibration scheme (q measurement) requires the validity of various assumtions on the thermal condition of the instrument during the calibration rocedure. It could be shown that one of the assumtions that is, the stability of the reference temerature during the q measurement is too otimistic and leads to systematic errors in the calibration constants and consequently to systematic errors of measured atmosheric fluxes. The new calibration method is based on the assumtion of isothermal conditions over a short eriod of time (a few seconds) to erform the calibration of the target radiometer. This condition can be established quite simly and can easily be verified using the signal of the reference radiometer. The formalism of the new calibration method is more transarent since it does not need further assumtions of the instruments thermal behavior. The rocedures of the calibration are somewhat easier (10-s registration time for one calibration oint) and offer additional information (signal of reference radiometer) about the required isothermal conditions during target radiometer calibration. The main effort, however, is to avoid a systematic error, which is art of the revious calibration scheme. The instruments built so far have been secially designed for airborne use. A develoment of a cheaer instrument mainly designed for ground-based measurements is currently under way. Therefore, the authors exect wider use of the instrument in the community within the next few years. The new calibration is a ste forward to imrove the accetance of the instrument. REFERENCE Lorenz, D., P. Wendling, P. Burkert, F. Fergg, and G. Wildgruber, 1996: The choed yrgeometer: A new ste in yrgeometry. J. Atmos. Oceanic Technol., 13,

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