Accurate Radiometric Measurement of the Atmospheric Longwave Flux at the Sea Surface

Transcription

1 SEPTEMBER 2000 PASCAL AND JOSEY 1271 Accurate Radiometric Measurement of the Atmospheric Longwave Flux at the Sea Surface ROBIN W. PASCAL Ocean Technology Division, Southampton Oceanography Centre, Southampton, United Kingdom SIMON A. JOSEY James Rennell Division, Southampton Oceanography Centre, Southampton, United Kingdom (Manuscript received 16 November, in final form 1 November 1999) ABSTRACT The errors in pyrgeometer measurements of the atmospheric longwave flux at the sea surface due to differential heating of the sensor dome relative to the body and to shortwave leakage through the dome are evaluated. Contrary to the findings of Dickey et al., repeatable laboratory calibrations are obtained for the error due to differential heating of the sensor. The magnitude of the error due to this effect under typical seagoing conditions is shown to be up to 20 W m 2 from measurements made with a precalibrated standard radiometer, for which the dome and body temperatures were recorded, during a research cruise in the North Atlantic in late spring. The error due to shortwave leakage is found to be similar in magnitude and to lead to a combined bias in the longwave flux of up to 40 W m 2 under conditions of strong insolation. The error is reduced when averages are taken over a full diurnal cycle but remains at a typical level of 5 7 W m 2 in the weekly mean flux. The differential heating of the radiometer is shown to be primarily dependent on the incident shortwave radiation, moderated slightly by the cooling effects of airflow over the dome. An empirical correction is developed for the differential heating error as a function of the shortwave flux and relative wind speed. Measurements of the longwave flux during the cruise from the standard radiometer and a second radiometer employed in the normal mode without logging of the component temperatures are compared. Application of the empirical correction for differential heating to the second radiometer together with that for shortwave leakage leads to a reduction in the difference relative to the standard radiometer from to W m 2.Itis suggested that this correction may be usefully employed as an alternative to recording component temperatures in future studies, particularly long-term buoy deployments, to improve the accuracy of the measured longwave flux. 1. Introduction The net flux of longwave radiation between the ocean and the atmosphere is a significant component of the total heat exchange in many regions of the World Ocean. The upwelling component from the sea surface is typically greater than the downwelling flux from the atmosphere resulting in monthly mean net longwave losses from the ocean in the range W m 2 (e.g., Josey et al. 1999). Each of these components is significantly larger than their difference, typical values lying between 300 and 400 W m 2. There is thus the potential for small fractional errors in measurements of the components to generate significant uncertainty in the net heat exchange. In this paper we focus on the errors associated Corresponding author address: Robin Pascal, Ocean Technology Division, Southampton Oceanography Centre, Empress Dock, Southampton SO14 3ZH, United Kingdom. robin.w.pascal@soc.soton.ac.uk with measurement of the downwelling longwave flux at sea that are not as yet well determined (Katsaros 1990; Breon et al. 1991; Dickey et al. 1994). Long-term measurements of the downwelling longwave have recently become more commonplace with the deployment of moored buoys equipped with radiation sensors for periods of up to two years in several experiments (e.g., Moyer and Weller 1997; Weller et al. ). The instrument that has been most widely used for such measurements is the Eppley precision infrared radiometer (or pyrgeometer). We present a detailed evaluation of the performance of the Eppley sensor using measurements obtained in the laboratory with a purpose-built calibration facility and at sea during a research cruise along a meridional section at 20 W in the North Atlantic. The main sources of error in the measured longwave will be shown to be differential heating of the sensor dome and body, and shortwave leakage through the dome filter; each of which can lead to typical errors in the measured longwave of about 10 W m 2 under conditions of moderate insolation American Meteorological Society

2 1272 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 Contrary to the analysis of Dickey et al. (1994), who suggested that the error introduced by the dome body temperature difference could not be reliably corrected, we will show that repeatable calibrations for this term can be obtained and hence that improvements in the accuracy of the measured flux by of order 10 W m 2 are possible. In addition, we consider the contribution due to direct transmission of shortwave radiation through the dome and find that repeatable correction terms for this effect can also be obtained. Alados-Arboledas (1988) considered the effects of insolation on radiometer performance but did not attempt to isolate the contribution due to differential heating from that due to shortwave leakage and claimed that the latter effect was negligible. We will show that the contribution due to shortwave leakage is significant and similar in magnitude to that arising from differential heating. Finally, we investigate the dependence of the increase in dome temperature on the incident shortwave radiation and relative wind speed, and attempt to develop an empirical correction for differential heating that may be used as an alternative to recording the component temperatures in order to improve the accuracy of the measured flux of longwave radiation. The usefulness of the correction is evaluated by comparing measurements of the longwave flux during the cruise from our standard radiometer, which has had the differential heating error explicitly corrected, and a second radiometer for which the correction was made empirically. In the next section we outline the relevant theory concerning pyrgeometer operation. The results from the laboratory calibrations are presented in section 3 and from the research cruise in section 4. Finally, we discuss the significance of our results and make some suggestions regarding future longwave measurements in section Theory The theory describing the operation of the Eppley pyrgeometer has been discussed in detail elsewhere (e.g., Albrecht and Cox 1977; Dickey et al. 1994; Fairall et al. ) and we present only a brief treatment here. A schematic representation of the instrument is shown in Fig. 1. It consists of a dome housing a thermopile plate that is connected to an aluminium body. The interior surface of the dome is coated with a vacuumdeposited interference filter that in principle transmits radiation in the longwave range (4 50 m) and reflects incident shortwave, the transition from complete opaqueness occurring between 3 and 4 m. In practice the filter is not completely effective and a small proportion of the shortwave may be transmitted. The output voltage of the thermopile is proportional to the net gain of radiation at its surface. The temperatures of the cold junction (which is approximated by that of the sensor body at a location close to the junction) and the dome are measured using thermistors; they may be logged if FIG. 1. A schematic diagram of the Eppley pyrgeometer showing the key components. required, although this is not the case in the normal mode of operation. Considerable confusion has arisen in the literature regarding the correct form of the pyrgeometer energy budget equation. Recently, Fairall et al. () have clarified the situation, noting the incorrect inclusion in earlier studies of a factor representing the thermopile plate emissivity. They derive the following fundamental radiometer calibration equation [their Eq. (11), with slightly modified notation], LW E/ o Ts k ( Td Ts ), (1) where LW is the downwelling longwave radiation; E is the thermopile output voltage; o, the fundamental radiometer sensitivity constant; k, a coefficient for the dome body temperature difference correction;, the Stefan Boltzmann constant ( Wm 2 K 4 ); T s, the temperature of the upper plate of the thermopile; and T d the temperature of the dome. The third term on the right-hand side is a correction for the additional longwave flux arising from the dome plate temperature difference. In the normal mode of operation a battery compensated circuit gives an output equivalent to the first two terms on the right-hand side and no correction is made for the effect of differential heating. In practice, as T s cannot be measured directly, it is determined from the temperature of the cold junction (T c, also referred to as the body temperature), and the temperature difference across the thermopile, T, using Ts Tc T Tc E, (2) where the factor relates the temperature difference across the thermopile to its output voltage. Fairall et al. () adopt an Eppley calibration value for to determine the longwave flux from a combination of (1) and (2). They also develop the following approximate form of (1), their Eq. (22), by expanding the fourthorder sum obtained by substituting (2) and retaining leading order terms

3 SEPTEMBER 2000 PASCAL AND JOSEY LW E/ Tc k ( Td Tc ), (3) where is the calibrated radiometer sensitivity, which they take from the Eppley calibration and we determine using the procedure described in section 3. The advantage of using (3) is that k and can be easily calibrated, while use of (1) requires the adoption of the Eppley supplied value for. Fairall et al. () note that the difference between the longwave flux computed from the exact (1) and approximate (3) forms of the equation for a large sample of observations made with a radiometer during the Tropical Ocean and Global Atmosphere Coupled Ocean Atmosphere Response Experiment is less than 1 W m 2. We have taken (3) as our basic equation as the results noted above indicate that use of this form of the equation, in preference to (1), will not lead to errors greater than about 1 W m 2 in our analysis. However, to ensure that this is the case we have carried out several test calculations with (1) that are reported in the next section. In addition we have included a term, as suggested by Dickey et al. (1994), to allow for the possibility of an energy flux due to shortwave leakage through the dome. Thus, the final form of our energy budget equation is LW E/ Tc k ( Td Tc ) SW, (4) where is a shortwave correction factor and SW is the downwelling shortwave flux. We note that there has been some discussion over the processes responsible for the flux associated with the dome body temperature difference. Albrecht and Cox (1977) originally suggested that it is a purely radiative flux and defined k to be the ratio of the dome interior emissivity to its transmissivity from exterior to interior. However, Foot (1986) notes that if this is the case the value for k of about 4 found by Albrecht and Cox (1977) is roughly four times greater than that to be expected from the radiative characteristics of the dome material; he suggests that the difference is due to additional contributions from conduction and convection between the dome and plate. In the present study we do not attempt to separate these various processes but rather focus on the question of whether k is a constant of the system or dynamic (i.e., varying between calibrations), as suggested by Dickey et al. (1994). 3. Calibration procedure a. Instrument sensitivity and dome body temperature difference correction coefficient Calibrations of the instrument sensitivity and the dome body temperature difference correction coefficient k were carried out for a set of four Eppley pyrgeometers using a purpose-built facility consisting of a spherical blackbody mounted in a stirred water cooled bath with an external aperture, shown schematically in Fig. 2. The blackbody cavity consists of a 19-cm-diameter copper sphere which has a 3.5-cm aperture and FIG. 2. A schematic diagram of the pyrgeometer calibration facility. a thickness of approximately 2 mm. The inner surface of the sphere is coated with optical black paint (NEX- TEL-Velvet-Coating ) with an emissivity of The temperature of the sphere is assumed to equal that of the water, which is measured at a distance of 2 mm from the blackbody outer surface using a precision Automatic Systems Laboratories F25 thermometer to an accuracy of C. The geometry of the dome increases its effective emissivity from that of the paint to a value of (T. Nightingale 1999, personal communication), which we take be equal to 1 for our calculations. The radiometer dome is exposed to the blackbody interior via the aperture, which prevents radiative interference from the sensor body. The calibration unit was installed within a constant temperature laboratory, which allowed the sensor body temperature to be kept stable while achieving significant dome to body temperature differences. The temperatures of the dome and body were recorded using a circuit supplied by Dave Hosom of Woods Hole Oceanographic Institute. Two of the four pyrgeometers (31170 and 31172) were obtained from Eppley in April 1997; the other two (27960 and 27225) are older instruments dating from February 1990 and September 1988, respectively. Calibrations were obtained for each pyrgeometer between January and March and repeat calibrations of the sensitivity were made in July. In the intervening period pyrgeometers and were deployed on the research cruise described in section 4. The calibration procedure is a modified version of that suggested by Albrecht and Cox (1977) in which and k are separately determined. In the calibration for, the temperature of the bath, and hence blackbody, is first stabilized, the radiometer is then mounted such that the dome is inside the blackbody and measurements of E and the component temperatures are recorded when the dome and body temperatures are equal. The procedure is repeated for a range of blackbody temperatures within approximately 10 C of the ambient room temperature. The temperature range for the calibration was restricted partly to avoid the possibility of condensation

4 1274 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 TABLE 1. Calibrated values of the instrument sensitivity, obtained for each of the radiometers on four repeat runs [units: V/(W m 2 ) 1 ]. Also listed are the mean sensitivity over the four runs with its standard error and the instrument sensitivity originally supplied by Eppley. TABLE 2. Calibrated values of the dome body correction coefficient k obtained for each of the radiometers on three repeated runs. Also listed are the mean value for k over the three runs with its standard error and the shortwave leakage factor. Sensor Run 1 Feb Run 2 Feb Run 3 Mar Run 4 Jul Mean value Eppley value Sensor Run 1 Jan Run 2 Jan Run 3 Mar Mean k value Shortwave leakage factor forming on the radiometer dome and the inner surface of the blackbody. With the requirement that the dome and body temperatures are equal, the third term on the right-hand side of Eq. (4) is zero, the fourth term may be ignored as there is negligible shortwave leakage into the cavity, and the equation may be rearranged to give E ( T 4 bb T 4 c ), (5) where T bb is the blackbody temperature and LW has 4 been replaced by T bb. Values for may then be de- 4 termined from the slope of a plot of E against ( T bb T 4 csensitivities ). obtained using the above procedure for each of the sensors on four separate calibration runs are given in Table 1 and an example of the calibration data for sensor is shown in Fig. 3. In each case there are only minor differences between the repeat runs for each sensor, indicating that the thermopile response may be reliably calibrated. The mean sensitivity for each sensor over the ensemble of runs and the original values supplied by Eppley are also listed in Table 1. The newly calibrated values tend to be close to those from Eppley with the exception of sensor 27225, which is approximately 10% higher. In the calibration for k, the radiometer is mounted inside the blackbody over a longer period, typically several hours, and the bath temperature is slowly reduced from approximately 10 C greater than the ambient room temperature to about 10 C below ambient. The dome temperature adjusts rapidly toward the blackbody value, while the body temperature remains closer to that of the room, allowing a wide range of dome body temperature differences to be obtained. As is now known, values for k may be obtained from Eq. (4) expressed in the form E/ ( Tc Tbb) k ( Td Tc ), (6) that is, k was determined from the slope of E/ ( Tc Tbb) plotted against ( Td Tc). The k coefficients obtained for each sensor on three separate calibration runs are listed in Table 2 together with the mean values. An example of the calibration data is shown in Fig. 4 for sensor It is clear from the listed values that repeatable calibrations for k can be achieved as the experiments were conducted over a period of three months. For three of the sensors considered the standard error of the mean was of order 1%, while for the fourth (which was the oldest sensor in the sample) it was slightly greater than 10%. These results suggest that, contrary to the findings of Dickey et al. (1994), k is in fact not highly specific to the particular calibration run and is instead a constant characteristic of the instrument, within a relatively narrow error range, that might usefully be applied to improve the accuracy of longwave measurements. In their calibration procedure, Dickey et al. (1994) considered only a small range FIG. 3. Sensitivity calibration data obtained on each of the four runs for sensor Run 1 ( ), run 2 ( ), run 3 (square), and run 4 (diamond). FIG. 4. Dome sensor temperature difference coefficient calibration data averaged over three runs for sensor Error bars indicate 2 standard error limits.

5 SEPTEMBER 2000 PASCAL AND JOSEY 1275 FIG. 5. Time series of the longwave flux from the blackbody (dotted line) and of that measured by the radiometer before (dash dot line) and after (dashed line) correction for differential heating using Eq. (3) for one of the calibration runs with sensor 31170, left-hand y- axis scale. The difference, LW (1) LW (3), in the corrected time series obtained with Eqs. (1) and (3) is also shown (solid line) right-hand y-axis scale. in the relative values of T d and T c. In addition, the contribution of the E/ term was apparently neglected when they attempted to determine a value for k. The magnitude of this term was typically of the order of 50 Wm 2, and it appears likely that its neglect has contributed to their conclusion that reliable values for k could not be determined. Time series of the longwave flux from the blackbody and of that measured by the radiometer before and after correction for differential heating are shown in Fig. 5 for one of the calibration runs with sensor Prior to correction for the dome body temperature difference, the measured and blackbody determined longwave fluxes are noticeably different, afterward they are seen to be in good agreement. Note that we have checked that use of the approximate energy budget Eq. (3) rather than the exact form (1) does not significantly influence our results by carrying out comparison calculations for several of the calibration runs with both equations. A value for of 694 K V 1 has been adopted following Fairall et al. (). The difference in the corrected time series obtained with the two approaches for the calibration run with sensor is also shown in Fig. 5, the rms difference is just 0.3 W m 2. Similar results were obtained from the other test comparisons. b. Shortwave leakage We now consider the error in the pyrgeometer measured longwave flux due to shortwave leakage through the dome. Dickey et al. (1994) estimated a generic value for of , based on typical values of the dome transmissivity and reflectivity, which they applied in an analysis of longwave measurements from various long-term buoy deployments. Given that their stated uncertainty (which reflects differences in the dome characteristics between sensors) in this parameter can result in an error in the measured longwave of order 10 W m 2 under conditions of strong insolation, it is important to obtain an individual value of for each sensor. Calibrated values for were determined from measurements of the downwelling atmospheric longwave and shortwave radiation made at the Southampton Oceanography Centre (SOC) over periods of typically 30 min. on days with no cloud cover. The technique is similar to that of Alados-Arboledas et al. (1988), who considered the combined effects of differential heating and shortwave leakage on measurements made with a single pyrgeometer at a meteorological station in Granada, Spain. The experimental setup used in our analysis consisted of a Kipp and Zonen radiometer, which measured the shortwave radiation, placed in close proximity to the pyrgeometer for which the value was to be determined. The pyrgeometer was equipped with the same circuit used in the laboratory calibrations for recording the dome and body temperatures in order to allow the effect of differential heating to be separated from that due to shortwave leakage. The error in the longwave measurements due to differential heating was corrected prior to carrying out the calibration using the mean value for k specific to each sensor. Alados- Arboledas et al. (1988) did not record the component temperatures in their analysis and so were unable to resolve these two effects. Each sensor was fitted with a 38-mm nonreflective cardboard disc mounted on a wire at a distance of 175 mm from the dome to enable blocking of the direct component of the solar radiation. Alternate measurements were made with both sensors shaded and then fully illuminated at intervals of order 5 min. In this way pyrgeometer measurements were obtained under both strong (direct and diffuse) and weak (diffuse only) insolation over a short period in which the downwelling longwave flux has little variation (the typical rms variation of the longwave over each sampling period was of order 2 W m 2 ). The mean pyrgeometer measured flux was averaged separately over the periods of blocked and unblocked insolation and differences were taken from the mean over the entire calibration run. A value for could then be determined from the slope of a plot of the differences against the mean shortwave in each period, with data being combined from several calibration runs. An example plot is shown in Fig. 6 for sensor for which a value of was determined, where the error range is that for the slope of the least squares fit to the calibration data. The complete set of values is listed in Table 2. We note that is likely to contain some wavelength dependence and that the radiative transfer within the dome is likely to involve additional reflection and transmission back out of the dome of a proportion of the incident shortwave. However, we have not attempted to quantify these effects at this stage as our aim has simply been to develop an empirical correction for the integrated effects of shortwave leakage, which may be employed to correct the measured longwave signal.

6 1276 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 FIG. 6. Shortwave calibration data from four calibration runs for sensor Here LW is the difference of the measured longwave from the mean over each calibration period. Error bars represent the standard error of the mean longwave difference. For the four sensors considered ranged from to 0.024; that is, the calibrated values for shortwave leakage were all smaller than the value of estimated by Dickey et al. (1994) from typical dome characteristics. This result suggests that Dickey et al. (1994) have overcorrected for the effects of shortwave leakage in their analysis of buoy data. Despite the reduction in magnitude, the range in that we find remains significant in the sense that under conditions of strong insolation (1000 W m 2 ) a variation in the signal measured by different radiometers of up to 20 W m 2 is to be expected due to differences in shortwave transmission. In addition there will be an error due to the differential heating effect, the magnitude of which under typical sea-going conditions will be quantified in the following section. Note that by separating the contributions due to differential heating and direct transmission of solar radiation we have been able to show that there is a significant source of error arising from the latter effect. Alados-Arboledas et al. (1988) found that the net effect of insolation on pyrgeometer operation was to introduce an additional flux equal to of the incident shortwave. This factor represents the combined effects of differential heating and shortwave transmission and is thus not directly comparable with the values for obtained here. In fact, Alados-Arboledas et al. (1988) suggested that the additional flux was due entirely to differential heating and that the effect of direct shortwave transmission was negligible. Our results show that this is not the case and that there is a significant component due to shortwave leakage. We note that this finding is in contrast to the theoretical estimate by Olivieri (1991) of 1 2 W m 2 for the maximum error due to shortwave heating (a factor of 10 smaller than the values we obtain). However, results from a recent study by Payne and Anderson (1999) support our conclusion. The latter authors find distinct evidence for leakage of shortwave radiation through the domes in a test study of several radiometers (Fig. 10 in FIG. 7. Example time series of the atmospheric longwave radiation measured at the SOC over a 2-h period between 1025 and 1225 UTC 22 Jul with each of the four calibrated sensors employed in the sequence 31172, 31170, 27960, and their paper) with a signal which is similar in magnitude to that found in our analysis. They suggest that this may be due in part to pinholes in the dielectric coating of the domes. The estimate of Olivieri (1991) neglected the possibility of direct transmission due to inconsistencies in the dome coating and we suggest that this is the reason that our values and those of Payne and Anderson (1999) are significantly higher. Finally, we consider an example time series of the atmospheric longwave radiation measured at the SOC over a 2-h period on 22 July (see Fig. 7). Each of the four calibrated sensors was employed in sequence and corrections for the effects of differential heating and shortwave leakage were made using the mean k and values from Table 2. In comparison, the time series of uncorrected data clearly shows large excursions in the measured longwave both within the deployment period of a particular sensor and at the points of transition between sensors. After correction there is a marked reduction in the amount of variability in the signal, the rms variation of the corrected data being 5.0 W m 2 in comparison with 8.6 W m 2 for the uncorrected. 4. Research cruise measurements In this section, we quantify the typical impact on measurements of the atmospheric longwave flux of the dome body temperature difference and shortwave leakage effects discussed above using measurements from a research cruise. We then examine the factors affecting the dome body temperature difference and develop an empirical parameterisation of the associated longwave error. Finally, a comparison is made between the longwave flux measured by a radiometer for which the differential heating effect has been explicitly corrected using recorded component temperatures and that measured by a second radiometer, which was operated in the normal mode and corrected using the empirical parameterisation. a. Cruise and sensor details The measurements discussed here were obtained on board RRS Discovery between 24 April and 31 May

7 SEPTEMBER 2000 PASCAL AND JOSEY 1277 b. Variation of the radiative fluxes and related variables during the cruise FIG. 8. Ship track during the Chemical and Hydrographic Atlantic Ocean Section cruise experiment, 24 Apr 31 May. during the Chemical and Hydrographic Atlantic Ocean Section (CHAOS; Smythe-Wright ) cruise experiment. The cruise was primarily directed along a meridional section at 20 W from the Cape Verde Islands to Iceland, the track is shown in Fig. 8. A wide range of meteorological conditions were experienced with periods of strong insolation under clear skies in the subtropics and heavily overcast weather at higher latitudes. Various meteorological sensors were deployed at several locations on the ship foremast. Downwelling longwave radiation measurements were obtained using two of the laboratory calibrated Eppley pyrgeometers mounted at the top of the mast, 15 m above the deck, in order to have an unobstructed field of view. The first (31170, referred to as sensor 1 hereafter) was instrumented with the same circuit used for the calibration, which recorded the dome and body temperatures and thermopile output voltage; the second (27960, sensor 2 hereafter) was operated in the normal mode. Measurements of the shortwave flux were obtained from two Kipp and Zonen solarimeters, while the wind speed and direction were recorded using an ultrasonic anemometer; each of these instruments was mounted on the foremast platform, 13 m above the deck. Data were logged at a 5-s sampling rate and averaged over 1-min. intervals. Visual estimates of the total cloud amount were made at hourly intervals during daylight throughout the cruise Time series of the downwelling longwave flux from sensor 1 before and after correction for differential heating and shortwave leakage, using values for k and of 2.60 and 0.011, respectively, are shown in Fig. 9; the data have been averaged over 10-min. intervals for clarity. Note that the value of k used for the cruise analysis was an intermediate value which differs slightly from our final calibration value of 2.57 listed in Table 2. However, the difference between the two values is not significant and does not impact on our results. Also shown are the dome body temperature difference and the maximum flux recorded by the two shortwave sensors, the maximum being taken in order to avoid problems of shadowing of one or other of the sensors that occurred at intermittent intervals. The downwelling longwave flux lies in the range W m 2, with a trend toward lower values as the cruise progressed and cooler air masses were encountered. Within a particular day variations of up to 80 W m 2 were experienced primarily associated with variations in cloud cover. During the period May (Julian day ), the cloud base was low and the skies nearly continuously overcast; under these conditions the daily variation in the flux was as small as 5 W m 2. The dome body temperature difference showed a strong diurnal variation with peak daytime values being of order 1.3 C. The difference is clearly correlated with the shortwave flux for which peak values were about 1100 W m 2. At night, when we would expect the dome and body temperatures to be equal, an offset of 0.13 C in the dome temperature relative to the body value is observed, which persisted throughout the cruise. Postcruise laboratory calibration indicated that this offset remained in a constant temperature environment. We recorded the dome and body temperatures of the sensor in a constant temperature laboratory over a period of several hours and found that the dome was persistently cooler than the body by 0.13 C. A comparison (not shown) of the dome and body nighttime temperatures with the dry bulb temperature measured by a psychrometer mounted nearby indicated that the offset is in the dome temperature, which is persistently low relative to the psychrometer value. Hence, we have increased the dome temperature by 0.13 C prior to correcting the longwave flux for differential heating of the sensor. Given the strong variation in the longwave flux on short timescales that is evident in Fig. 9a it is difficult to appreciate from the plot the difference in the corrected and uncorrected longwave values. Time series of the longwave error introduced by differential heating and the combined error due to differential heating and shortwave leakage presented in Fig. 9d show this more clearly. Peak values for each term approach 20 W m 2.As each is driven by the shortwave flux they can combine to produce errors of up to 40 W m 2 in the uncorrected

8 1278 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 FIG. 9. Time series for the CHAOS cruise of 10-min averaged values of (a) measured downwelling longwave, uncorrected (gray line), corrected (black line); (b) dome body temperature difference; (c) shortwave flux; (d) downwelling longwave error due to differential heating (gray line) and combined error due to differential heating and shortwave leakage (black line). longwave under strong insolation, although values in the range W m 2 are more typical in the midlatitude conditions experienced toward the end of the cruise. As an example of the variation within a particular day, 1-min means of the uncorrected longwave, the longwave corrected for differential heating and the longwave corrected for differential heating and shortwave leakage are shown in Fig. 10 for 15 May (Julian day 135). The hourly record of cloud cover for this day indicates that there was typically less than 2/8 cover during daylight, as indicated by the relatively smooth sinusoidal variation in the shortwave flux. Without correction the longwave flux appears to increase from about 287 W m 2 at 0700 UTC to 305 W m 2 at 1200 UTC before falling away again in the late afternoon. The FIG. 10. Time series of 1-min mean uncorrected (U), differential heating corrected (D) and fully corrected (F) downwelling longwave and the shortwave flux (S) measured during the CHAOS cruise on 15 May (Julian day 135).

9 SEPTEMBER 2000 PASCAL AND JOSEY 1279 TABLE 3. Weekly mean values for the uncorrected and corrected longwave flux, and the errors due to differential heating and shortwave leakage for sensor during the CHAOS cruise (units: W m 2 ). Interval Latitude range Uncorrected longwave Corrected longwave Dome body correction Shortwave correction 24 Apr 1 May 1 8 May 8 15 May May May N N N N N FIG. 11. Scatterplot of 1-min averaged daytime values of LW Eff against incident shortwave (units: W m 2 ). corrections for differential heating and shortwave leakage remove this trend and the fully corrected curve has less high frequency variation than the uncorrected one. The high-frequency variation may be quantified to some extent by considering the standard deviation of the longwave within 20-min intervals during daylight. The mean standard deviation obtained in this way is 1.5 W m 2 for the uncorrected flux which is more than twice the value of 0.7 W m 2 for the fully corrected curve. The errors arising from these effects in the mean longwave averaged over periods of a day or longer are of course somewhat smaller because of the inclusion of nighttime values. Weekly mean values for the various longwave estimates are listed in Table 3, together with the latitude range covered. The differential heating and shortwave leakage terms were typically of the same order combining to produce an error in the weekly mean of between 5 and 7 W m 2 depending on latitude with the greatest values in the subtropics. Finally, we note that the mean daytime error due to the combined effects of differential heating and shortwave leakage during the cruise was 8.3 W m 2.By comparison the mean error that would have been obtained had we corrected by a factor equal to of the incident shortwave as suggested by Alados-Arboledas et al. () is 12.1 W m 2. Thus use of their factor would have led to overcorrection of the measured flux by about 50%. c. Parameterization of the longwave error due to dome body temperature difference We now investigate in greater detail the parameters affecting the longwave flux error due to differential heating of the sensor. Our aim is to produce an empirical expression that may be usefully employed in future studies to correct differential heating effects (given knowledge of the k coefficient for the instrument being used) without the need for the dome and body temperatures to be logged. To this end, we define an effective longwave error, LW Eff ( T 4 d T 4 c ); (7) that is, LW Eff is the longwave error to be expected for a sensor with a k coefficient of 1. Note from the k values listed in Table 2 that the actual longwave error will typically be 2 3 times greater than LW Eff. The time series discussed in the preceding section lead us to expect a strong dependence of LW Eff on the incident shortwave and this is evident in a scatterplot of the 1-min. averaged daytime values for these variables shown in Fig. 11. The slope of the distribution of LW Eff with respect to SW increases as SW increases and the following empirical expression was obtained by making a quadratic least squares fit to the data, LW Eff asw bsw 2, (8) with a and b There is a strong correlation (r ) between the measured values for LW Eff and those predicted using (8); that is, virtually all of the observed variance in LW Eff can be explained as a result of shortwave heating. In addition to the influence of the shortwave flux we might also expect the relative wind speed to affect the differential heating of the dome relative to the body. Albrecht and Cox (1977) noted that cooling due to airflow over the dome can significantly reduce the differential heating effect in aircraft deployed sensors at high wind speeds. However, the relative wind speeds expe-

10 1280 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 rienced on a ship are typically are much lower than those for aircraft measurements and so one might not expect a strong cooling effect in our data (the mean and standard deviation of the relative wind speed during the cruise was ms 1, with a peak value of 22.0 ms 1 ). In order to determine whether wind cooling does play a role we took the ratio of the observed LW Eff values to those predicted by the simple relationship (8) and regressed the resulting normalised values on the relative wind speed u. An approximately linear reduction in the longwave error with increasing wind speed was observed such that LW Eff (c du)(asw bsw 2 ), (9) where c 1.32 and d Scatterplots of the predicted against observed LW Eff obtained with Eqs. (8) and (9) are shown in Fig. 12. Inclusion of the wind speed dependence is seen to improve the fit for high values of LW Eff, although it has only a minor impact on the overall correlation; r 2 increases from 0.92 to Note that measurements made when the relative wind direction was at an angle greater than 45 to the bow have been excluded from the above analysis as previous studies have shown that under such conditions distortion of the airflow by the ship structure can lead to significant variations in the wind speed between sensors located at different positions on the foremast (Yelland et al. ). d. Application of the empirical correction to the second radiometer We now consider whether the empirical correction for differential heating, together with that for shortwave leakage, can be used to improve the accuracy of measurements made using the second radiometer on the cruise which was operated in normal mode, that is, without the dome and sensor temperatures being logged. In order to do this, we reference the signal from sensor 2 to that from our standard sensor 1, for which the effects of differential heating have been explicitly corrected using the recorded component temperatures as described in section 4b. A time series of the difference between the corrected longwave flux from sensor 1 and the uncorrected flux from sensor 2 is shown in Fig. 13. A strong diurnal signal is evident due to a combination of the effects of differential heating and shortwave leakage in the uncorrected signal from sensor 2. In addition, there is a gradual drift evident in the nighttime values throughout the cruise such that the signal from sensor 2 reads low relative to that from sensor 1 by about 10 Wm 2 toward the end of the period considered. The longwave flux measured by sensor 2 was empirically corrected for differential heating [using Eq. (9) with the measured shortwave and relative wind speeds and a k value of 2.32] and then for shortwave leakage using the calibrated value for of Note that the k value used for sensor 2 in the cruise analysis differs slightly from the final figure of 2.35 listed in Table 2; FIG. 12. Scatterplots of the predicted against observed LW Eff obtained using an empirical fit that depends on (a) incident shortwave and (b) incident shortwave and relative wind speed (units: W m 2 ). this difference does not significantly modify our results. Time series of the difference between the flux from sensor 1 and that measured by sensor 2 after each of these corrections are also shown on Fig. 13. It is clear that the application of the corrections for the two effects removes much of the diurnal signal between the sensors. The laboratory calibrations suggest that the long-term drift reflects a tendency in the longwave flux obtained from sensor 2 with the original Eppley calibration to underestimate the true value at fluxes less than about 340Wm 2, which occurred toward the end of the cruise.

11 SEPTEMBER 2000 PASCAL AND JOSEY 1281 FIG. 13. Time series of the difference between corrected longwave flux from sensor 1 and the longwave flux from sensor 2 before correction (U), after correction for differential heating (D), and after correction for differential heating and shortwave leakage (F) (units: W m 2 ). The drift may be removed using a simple linear adjustment derived by requiring agreement of the nighttime value measured by sensor 2 with that from sensor 1. With this adjustment the mean difference in the longwave (sensor 1 sensor 2) is W m 2 after correction for differential heating and shortwave leakage compared to Wm 2 before. Thus, by applying the empirical correction we have been able to reduce the difference between the longwave flux measured by the radiometer operated in the normal mode and that from the standard radiometer for which the effects of differential heating were explicitly corrected. These results suggest that the empirical correction may be used as an alternative to recording radiometer component temperatures to improve the accuracy of pyrgeometer measurements. 5. Discussion We have examined the major sources of error in radiometer measurements of the atmospheric component of the longwave flux at the sea surface. These are the additional longwave flux which arises from differential heating of the sensor dome relative to the body and the transmission of shortwave radiation through the dome filter. Results from an evaluation of a set of four Eppley precision infrared radiometers carried out with a purpose-built calibration facility have been presented which provide new insight into the characteristics of these errors. In an earlier analysis, Dickey et al. (1994) suggested that reliable corrections for the error induced by differential heating were not possible as this was a dynamic process; that is, the magnitude of the error associated with a given temperature difference was not a fixed characteristic of the sensor. In contrast, we have found that corrections for this term are possible and have obtained repeatable calibrations for the k coefficient that characterizes it. Typical values for k were in the range , although a somewhat smaller value of 1.4 was found for the oldest sensor in the sample. The longwave error due to differential heating thus varied by up to a factor of 2 between the sensors considered. We have also calibrated the error associated with shortwave leakage and find values for the proportion of radiation transmitted,, that range from to There is some indication, see Table 2, that k increases as decreases suggesting that those sensors in which the filter is most effective at screening shortwave are likely to exhibit the strongest differential heating effects. Further calibrations with a larger sample of sensors are required before the significance of this trend can be established. The calibrated values for were all smaller than that of estimated by Dickey et al. (1994) from typical dome characteristics, which suggests that they have overcorrected for the effects of shortwave leakage in their analysis. The magnitude of the errors due to these two effects was quantified under typical open ocean conditions during the CHAOS cruise that took place in the North Atlantic from April to June. The terms were found to be similar in magnitude and combined to produce a positive bias in the longwave flux under conditions of strong insolation of up to 40 W m 2. Care must therefore be taken in the use of buoy data for forcing models which rely on accurate descriptions of the diurnal cycle of the heat flux. When averages over periods greater than a day are taken the bias is reduced but remains at a typical level of 5 7 W m 2 with the largest errors occurring at lower latitudes in our analysis because of the increased shortwave flux. An error of this magnitude is significant for analyses that attempt to verify by comparison with shipborne radiometer measurements the empirical longwave formulas used in climatological analyses (Josey et al. 1997). Alados-Arboledas et al. (1988) found that the net effect of insolation on pyrgeometer operation was to introduce an additional flux equal to of the incident shortwave. This factor represents the combined effects of differential heating and shortwave transmission and is thus not directly comparable with the values for. However, a comparison of the mean measured error during the cruise due to

12 1282 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 these effects with the value obtained using the factor suggested by Alados-Arboledas et al. (1988) shows that the latter leads to an overcorrection of the daytime downwelling longwave by an order of 50%. In order to correct for differential heating we have used a circuit that enables the temperatures of the radiometer dome and body to be recorded for our standard radiometer. In the normal mode of radiometer operation such measurements are not available. However, we find that the differential heating effect is primarily dependent on the incident shortwave radiation, moderated slightly by the cooling effects of airflow over the dome, and have developed an empirical relation that may be used to correct this source of error as an alternative to recording the dome and body temperatures. Measurements of the longwave flux during the cruise from the standard radiometer and from a second radiometer employed in the normal mode were compared. Application of the empirical correction for differential heating to the second radiometer together with that for shortwave leakage leads to a reduction in the difference relative to the standard radiometer from to Wm 2. In conclusion, we reiterate our main findings which are that reliable corrections to radiometer measurements of the atmospheric longwave flux for errors introduced by differential heating and shortwave leakage are possible. If neglected these errors can lead to a positive bias in the measured longwave of up to 40 W m 2 under conditions of strong insolation. The error due to differential heating can be corrected empirically given measurements of the shortwave flux and relative wind speed without the need to record the radiometer dome and body temperatures. We suggest that such a correction should be made in future analyses if the component temperatures are not logged in order to improve the accuracy of the measured longwave flux. Acknowledgments. We are grateful to Dave Hosom of Woods Hole Oceanographic Institute for supplying the electrical circuit that enabled us to record the temperatures of the radiometer dome and body; Tim Nightingale of the Rutherford Appleton Laboratory, United Kingdom, for the calculation of the effective emissivity of the calibration blackbody; and to Charles Clayson, Gwyn Griffiths, Elizabeth Kent, Peter Taylor, Margaret Yelland, and the two referees for useful comments on the manuscript. We would also like to acknowledge the assistance provided by the officers and crew of RRS Discovery during the CHAOS cruise. REFERENCES Alados-Arboledas, L., J. Vida, and J. I. Jimenez, 1988: Effects of solar radiation on the performance of pyrgeometers with silicon domes. J. Atmos. Oceanic Technol., 5, Albrecht, B., and S. K. Cox, 1977: Procedures for improving pyrgeometer performance. J. Appl. Meteor., 16, Breon, F.-M., R. Frouin, and C. Gautier, 1991: Downwelling longwave irradiance at the ocean surface: An assessment of in situ measurements and parameterizations. J. Appl. Meteor. 30, Dickey, T. D., D. V. Manov, R. A. Weller, and D. A. Siegel, 1994: Determination of longwave heat flux at the air sea interface using measurements from buoy platforms. J. Atmos. Oceanic Technol., 11, Fairall, C. W., P. O. G. Persson, E. F. Bradley, R. E. Payne, and S. A. Anderson, : A new look at calibration and use of Eppley Precision Infrared Radiometers. Part I: Theory and application. J. Atmos. Oceanic Technol., 15, Foot, J. S., 1986: A new pyrgeometer. J. Atmos. Oceanic Technol., 3, Josey, S. A., D. Oakley, and R. W. Pascal, 1997: On estimating the atmospheric longwave flux at the ocean surface from ship meteorological reports. J. Geophys. Res., 102 (C13), , E. C. Kent, and P. K. Taylor, 1999: New insights into the ocean heat budget closure problem from analysis of the SOC air sea flux climatology. J. Climate, 12, Katsaros, K. B., 1990: Parameterization schemes and models for estimating the surface radiation budget. Surface Waves and Fluxes. Vol. II, Remote Sensing, G. L. Geernaert and W. J. Plant, Eds., Kluwer Academic Publishers, Moyer, K. A., and R. A. Weller, 1997: Observations of surface forcing from the subduction experiment: A comparison with global model products and climatological datasets. J. Climate, 10, Olivieri, J., 1991: Measurement of longwave downward irradiance using a PIR pyrgeometer. WMO Tech. Doc. 453, 26 pp. [Available from WMO, 41, Avenue Giuseppe-Motta, 1211 Geneva 2, Switzerland.] Payne, R. E., and S. A. Anderson, 1999: A new look at calibration and use of Eppley Precision Infrared Radiometers. Part II: Calibration and use of the Woods Hole Oceanographic Institution Improved Meteorology Precision Infrared Radiometer. J. Atmos. Oceanic Technol., 16, Smythe-Wright, D., : RRS Discovery Cruise 233, 23 April 1 June. CHAOS Southampton Oceanography Centre Cruise Rep. 24, 86 pp. [Available from Southampton Oceanography Center, Empress Dock, Southampton SO14 3ZH, United Kingdom.] Weller, R. A., M. F. Baumgartner, S. A. Josey, A. S. Fischer, and J. Kindle, : A one-year record of atmospheric forcing from the Arabian Sea. Deep-Sea Res., 45, Yelland, M. J., B. I. Moat, P. K. Taylor, R. W. Pascal, J. Hutchings, and V. C. Cornell, : Wind stress measurements from the open ocean corrected for airflow disturbance by the ship. J. Phys. Oceanogr., 28,