A new formula for determining the atmospheric longwave flux at the ocean surface at mid-high latitudes

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. C4, 3108, doi: /2002jc001418, 2003 A new formula for determining the atmospheric longwave flux at the ocean surface at mid-high latitudes S. A. Josey James Rennell Division, Southampton Oceanography Centre, European Way, Southampton, UK R. W. Pascal Ocean Engineering Division, Southampton Oceanography Centre, European Way, Southampton, UK P. K. Taylor and M. J. Yelland James Rennell Division, Southampton Oceanography Centre, European Way, Southampton, UK Received 27 March 2002; revised 23 October 2002; accepted 24 October 2002; published 2 April [1] The accuracy of two empirical formulae used in recent climatological studies to estimate the atmospheric longwave flux at the ocean surface from ship meteorological reports has been evaluated using research cruise measurements from the northeast Atlantic. The measurements were obtained with a pyrgeometer and corrected for differential heating of the pyrgeometer dome and shortwave transmission through the dome. The formulae tested were from Clark et al. [1974] and Bignami et al. [1995]; neither was capable of providing consistently reliable estimates of the longwave flux. Clark overestimated the mean measured longwave of Wm 2 by 11.7 Wm 2, while Bignami underestimated by 12.1 Wm 2. A new formula is developed that expresses the effects of cloud cover and other parameters on the longwave through an adjustment to the measured air temperature. The air temperature is adjusted by the amount necessary to obtain the effective temperature of a blackbody with a radiative flux equivalent to that from the atmosphere. A simple parameterization of the adjustment in terms of the total cloud amount gives longwave estimates that have an improved mean bias error with respect to the measurements of 1.3 Wm 2. The new formula is still biased under overcast, low cloud base conditions. However, by including a dependence on dew point depression in the formula, this bias is resolved, and the mean error reduced to 0.2 Wm 2. The new formula has been tested using measurements made on two subsequent cruises and found to agree to within 2 Wm 2 in the mean at middle-high latitudes. INDEX TERMS: 3339 Meteorology and Atmospheric Dynamics: Ocean/atmosphere interactions (0312, 4504); 3359 Meteorology and Atmospheric Dynamics: Radiative processes; 4215 Oceanography: General: Climate and interannual variability (3309); 4504 Oceanography: Physical: Air/sea interactions (0312); KEYWORDS: longwave, climatology, air-sea interaction, formula Citation: Josey, S. A., R. W. Pascal, P. K. Taylor, and M. J. Yelland, A new formula for determining the atmospheric longwave flux at the ocean surface at mid-high latitudes, J. Geophys. Res., 108(C4), 3108, doi: /2002jc001418, Introduction [2] The downwelling radiative flux from the atmosphere at infrared wavelengths (usually referred to as the longwave flux) lies typically in the range Wm 2 and forms an important component of the heat exchange across the ocean-atmosphere interface. Small fractional errors in the magnitude of this term can have a significant impact on the net longwave flux across the interface which is given by the difference in the upwelling component from the sea surface and the downwelling one from the atmosphere and typically represents a net cooling by the ocean of Wm 2. A number of empirical parameterizations of the net Copyright 2003 by the American Geophysical Union /03/2002JC longwave flux in terms of the air-sea temperature difference, atmospheric humidity and cloud cover have been determined over the years and used in climatological analyses of ship meteorological reports. Recently, the formula of Clark et al. [1974, hereinafter referred to as Clark] was used in the production of the Southampton Oceanography Centre (SOC) global air-sea flux climatology [Josey et al., 1998], while that of Binami et al. [1995, hereinafter referred to as Bignami] was chosen by Lindau [2001] for an analysis of fluxes over the Atlantic Ocean. [3] In an earlier study, Josey et al. [1997, hereinafter referred to as JOP] evaluated the atmospheric component of several longwave formulae using data collected over a number of research cruises. They found that the Bignami formula underestimated the atmospheric longwave by 27 Wm 2 when averaged over all the cruise measurements. In 5-1

2 5-2 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX contrast, the Clark formula was found to agree with the observations to within 1 Wm 2, and on the basis of this analysis the Clark formula was selected for the SOC flux climatology. However, subsequent advances have taken place in our understanding of longwave radiometer errors, in particular those caused by radiative heating of the dome and shortwave transmission through the dome [Fairall et al., 1998; Payne and Anderson, 1999; Ji and Tsay, 2000; Pascal and Josey, 2000]. Each of these effects leads to an additional source of radiation in the pyrgeometer and consequently an overestimate of the downwelling longwave. Thus, the question arises as to whether similar conclusions regarding the applicability of the bulk formulae would be obtained with a set of longwave measurements in which these effects have been corrected. We address this question in the present study. [4] Pascal and Josey [2000] analyzed pyrgeometer measurements made on a research cruise in the Atlantic Ocean [Smythe-Wright, 1998] and demonstrated that routine corrections for dome heating and shortwave leakage are possible. They found that corrections for the pyrgeometer errors lead to a typical reduction in the measured daily averaged atmospheric flux during the cruise of about 5 Wm 2. The measurements used in the earlier analysis of JOP were not corrected for either the dome effect or shortwave leakage. In the present study we use the corrected cruise dataset of Pascal and Josey [2000] to determine whether the conclusions of JOP with regard to the performance of the Clark and Bignami formulae still hold when tested with more accurate measurements. The cruise took place from April to May 1998 and spanned the latitude range 20 N 63 N in the Atlantic Ocean [Smythe-Wright, 1998]. As the measurements used in the analysis of JOP for the North Atlantic were confined to latitudes north of 35 N, we now also have the opportunity to test the performance of the formulae over a greater latitude span than previously. [5] Following our evaluation of the Clark and Bignami formulae we develop a new atmospheric longwave parameterization in which the combined effects of cloud cover and other relevant parameters on the atmospheric longwave are expressed in terms of an adjustment to the measured air temperature. The air temperature is adjusted by the amount necessary to obtain the effective temperature of a blackbody with a radiative flux equivalent to that from the atmosphere. We will show that a significant reduction in the bias and scatter between estimates and measurements of the atmospheric longwave is possible with the new formula, and verify that this remains the case when the comparison is extended to include independent measurements from two more recent cruises. [6] We are aware that precise estimates of the downwelling longwave flux at a given time require a detailed treatment of the radiative transfer processes in the atmosphere which necessarily involves a sophisticated modeling approach [e.g., Mlawer et al., 1997]. Some progress can be made toward obtaining accurate daily mean estimates of the longwave flux using relatively simple models. In particular, Lind and Katsaros [1982] showed that daily averaged atmospheric longwave flux estimates with a typical error of about 5 Wm 2 are possible using a model which employs effective cloud emittances, estimated cloud base temperatures and boundary layer water vapor effects determined from a combination of surface observations and synoptic charts. Such an approach unfortunately requires information which is not routinely included in voluntary observing ship meteorological reports. [7] Our goal is to obtain reliable estimates of the longwave flux on a monthly timescale, for inclusion in climatological analyses of the air-sea heat exchange, using the information which is routinely available in the ship meteorological reports. The regularly reported variables of relevance to the longwave exchange comprise only the total cloud amount, the air temperature and humidity, and the sea surface temperature. Thus, we are not able to use more complex model based analyses, such as that advanced by Lind and Katsaros [1982]. Instead we seek to obtain a reliable empirical parameterization of the longwave flux in terms of the routinely reported variables and aim to obtain monthly mean estimates of the longwave flux which are accurate to within 5 Wm 2. The achievement of this goal would represent an important step toward obtaining net heat flux estimates with the accuracy of 10 Wm 2 that is required for large scale climate research projects, in particular the Climate Variability and Predictability Programme (CLIVAR). [8] In the following section, we describe the observational dataset that we employ for our analysis. In section 3, we evaluate the performance of the Clark and Bignami formulae using the corrected pyrgeometer measurements. In section 4, we develop a new parameterization of the atmospheric longwave flux and demonstrate using research cruise measurements that it is capable of providing better estimates than either Clark or Bignami at middle-high latitudes. Finally, we summarize the key results and discuss their significance with respect to obtaining a balanced set of climatological net heat fluxes. 2. Observational Data Set [9] Our primary observational dataset consists of measurements of the atmospheric component of the longwave radiation and surface meteorological conditions made during a research cruise in the northeast Atlantic with RRS Discovery. The measurements were made between 24 April (Julian day 114) and 31 May (Julian day 150) 1998 during the Chemical and Hydrographic Atlantic Ocean Section (CHAOS) [Smythe-Wright, 1998] experiment. The ship track is shown on Figure 1, the core of the cruise consisted of a meridional section roughly along 20 W from 20 to 63 N. [10] Atmospheric longwave measurements were obtained throughout the cruise from an Eppley precision infrared radiometer (pyrgeometer) for which the spectral range of the transmitted radiation is 4 50 mm. Corrections were made for differential heating of the radiometer dome and shortwave leakage as described by Pascal and Josey [2000]. The pyrgeometer (reference number 31170) was mounted on a platform situated close to the top of the foremast of the ship, 15m above the foredeck. Observations were made every 5 seconds and recorded as 1 minute means. The pyrgeometer was calibrated both before and after the cruise and no significant drift found in the calibration values [Pascal and Josey, 2002]. Measurements of the air temperature and humidity were obtained from a foremast mounted psychrometer; of the sea surface temperature from a trailing

3 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX 5-3 Figure 1. Ship track during the Chemical and Hydrographic Atlantic Ocean Section cruise experiment, 24 April to 31 May thermistor and of the atmospheric pressure from a Vaisala sensor in the ship laboratory (for further details of the sensors, see Smythe-Wright [1998]). Visual estimates of the total cloud amount, and the apparent amount of cloud at low, medium and high levels, were made at intervals of typically 1 hour by several of the research scientists on board throughout the cruise; 590 observations were made in total. [11] The large latitude span covered during the cruise enabled a wide range of meteorological conditions to be experienced with periods of strong insolation under clear skies in the subtropics and heavily overcast weather at higher latitudes. Histograms of the key meteorological variables are shown in Figure 2, the sample consists of ten minute averaged values centered on the time of each cloud observation. The dry bulb temperature ranged from 7.4 to 22.2 C ; the SST from C and the vapor pressure from 7.5 to 21.6 mbar. The measured atmospheric longwave varied from 272 to 398 Wm 2. Summary statistics for the amount of cloud cover are given in Table 1, note that these have been subdivided according to the cloud level (low, medium, or high). The level with the greatest cloud amount at the time of observation is referred to hereafter as the dominant cloud level. Overcast, low level cloud conditions formed the largest proportion of the dataset, reflecting a long interval between Julian days 138 and 144 during which a persistent layer of stratocumulus was present. Despite this period, observations were made under a wide range of cloud amounts, with typically greater than 20 observations in a given total cloud amount category. [12] In addition to the primary dataset, we have also employed for validation purposes independent measurements collected during two more recent research cruises. Further details of these data sets will be given in section Evaluation of the Clark and Bignami Parameterizations 3.1. Details of the Formulae [13] The net longwave flux, Q L, across the ocean-atmosphere interface is given by Q L ¼ Q LS ð1 a L ÞQ LA ; ð1þ Figure 2. Histograms of the surface meteorological variables and atmospheric longwave flux during the CHAOS cruise.

4 5-4 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX Table 1. Observation Frequency of Different Cloud Amounts Subsetted by Number of Octas and Cloud Layer a n = 0/8 n = 1/8 n = 2/8 n = 3/8 n = 4/8 n = 5/8 n = 6/8 n = 7/8 n = 8/8 Fog Low Medium High Total a Note that the final row is the sum over the first three except for the special case of n = 0/8 for which the total represents the number of occasions on which clear sky conditions were recorded. where Q LS is the emitted radiation from the sea surface, Q LA is the downwelling radiation from the atmosphere, and the coefficient (1 a L ), where a L is the longwave reflectivity, takes account of the component of the downwelling radiation reflected from the sea surface. The formula of Clark provides empirical estimates of Q L from the reported meteorological variables as follows: Q L ¼ es SB T 4 s 0:39 0:05e 1=2 1 ln 2 þ 4esSB T 3 s ð T s T a Þ ð2þ where T s and T a are the sea surface and dry bulb air temperatures in degrees Kelvin; e is the vapor pressure in millibars; n is the fractional cloud cover; e is the emissivity of the sea surface, taken to be 0.98; s SB is the Stefan- Boltzmann constant ( Wm 2 K 4 ), and l is a latitude dependent cloud cover coefficient (see Table 3 of JOP). The atmospheric component is not explicitly defined in the Clark formula so for our analysis we follow the approach of Katsaros [1990], in which this term is obtained from equation (1) as the residual between the upwelling and net longwave flux, Q LA ¼ es SBT 4 s Q L ð1 a L Þ where a L is taken to be and Q LS has been replaced by es SB T s 4. In contrast, Bignami developed the following explicit parameterization for the atmospheric longwave using measurements made over the Mediterranean Sea, ð3þ Q LA ¼ s SB T 4 a ð 0:684 þ 0:0056e Þ 1 þ 0:1762n2 ; ð4þ which we have used to obtain direct estimates of Q LA in our evaluation Evaluation Against Research Cruise Measurements [14] Estimates of the atmospheric longwave flux obtained from the reported total cloud amount according to the Clark and Bignami formulae have been compared with the measured flux averaged over a 10 minute interval centered on the time of each cloud observation. Scatterplots of the estimated versus measured longwave are shown in Figure 3 and summary statistics for the comparison in Table 2. A large amount of scatter is evident in the estimated longwave flux obtained with both formulae relative to the measured values, the root mean square (RMS) error for Bignami is 20.8 Wm 2 and for Clark is 18.0 Wm 2. In addition, significant offsets are present. Consideration of the distribution of estimates with respect to dominant cloud height indicates that for fluxes greater than about 300 Wm 2 the Bignami formula performs best when estimating the longwave flux under conditions of predominantly medium level cloud. In contrast, the Clark formula provides more reliable estimates under low level cloud conditions. This difference in performance has been quantified by subsetting the full dataset for predominantly low and medium level cloud conditions. Under predominantly medium level cloud, the mean longwave estimated with Bignami (337.0 Wm 2 ) is close to that measured (339.9 Wm 2 ) while Clark (358.7 Wm 2 ) overestimates by nearly 20 Wm 2. For low cloud, the Clark estimate (355.1 Wm 2 ) is the closer of the two to the mean measured longwave (347.6 Wm 2 ), as Bignami (330.0 Wm 2 ) now underestimates by 17.6 Wm 2. Figure 3. Scatterplot of estimated versus measured atmospheric longwave for (a) Clark and (b) Bignami. Symbols: x, predominantly low level cloud; +, medium level cloud; open square, high level cloud; triangle, clear sky conditions.

5 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX 5-5 Table 2. Comparison of Estimated and Measured Atmospheric Longwave During the CHAOS Research Cruise a Mean MBE RMSE r 2 Measured Clark Bignami J J a Tabulated values are the mean, the mean bias error (MBE), root mean square error (RMSE), all with units Wm 2, and the correlation coefficient squared (r 2 ). The latter three statistics have been determined in each case with respect to the measured values; the sample contained 590 estimates. [15] For the full dataset, the mean atmospheric longwave obtained with Bignami is Wm 2, underestimating the measured value of Wm 2 by 12.1 Wm 2. By comparison the Clark formula has an offset which is similar in magnitude but opposite in sign, overestimating by 11.7 Wm 2. In the analysis of JOP, the agreement of the Clark estimates with the observations was much closer, the mean bias error with respect to the combined cruise dataset being 0.7 Wm 2. In contrast, the offset found with the Bignami formula was somewhat greater, 26.5 Wm 2, in the earlier study. The difference in performance of the two formulae in the present study reflects the combined effects of (a) the greater range of subtropical latitudes sampled during the CHAOS cruise, as it is at these latitudes that Bignami performs well and Clark poorly, and (b) the radiometer error corrections, which serve to reduce the measured atmospheric longwave flux, favoring Bignami over Clark. Time series of the measured atmospheric longwave, together with the ship latitude, and of the difference in measured and estimated longwave flux throughout the cruise are shown in Figure 4. Note that for clarity of presentation the difference time series shows daily averages of the available estimates. The figure demonstrates that the Bignami formula provides more reliable estimates during the early part of the cruise in the subtropics, while Clark becomes more accurate in the latter part at higher latitudes. 4. Development of a New Atmospheric Longwave Formula 4.1. Parameterization of the Longwave Flux in Terms of an Air Temperature Adjustment [16] The results of the previous section have demonstrated that neither the Clark nor the Bignami formula is capable of providing consistently reliable estimates of the atmospheric longwave over the latitude range considered. In this section we develop an alternative form for the atmospheric longwave parameterization in which the contributions from the various meteorological parameters are separate terms. Our aim is to produce a more simple and accurate formula than the complicated previous parameterizations such as Clark(2) for which it is difficult to isolate the contributions to the longwave flux from the different meteorological variables. We start by characterizing the downwelling longwave by an effective blackbody temperature, T Eff, such that, Q LA ¼ s SB T 4 Eff Given that our observed variable is T a instead of T Eff,we then write T Eff as the sum of T a and a temperature adjustment, T a, which includes the effects of cloud cover, atmospheric humidity and other, as yet unknown, variables on the downwelling longwave, such that, ð5þ Q LA ¼ s SB ðt a þ T a Þ 4 ð6þ T a is thus the difference between the measured air temperature and the effective temperature of a blackbody which emits a radiative flux equivalent to the atmospheric longwave. The problem of obtaining a reliable estimate for Q LA then becomes one of parameterizing the dependence of T a on cloud cover, vapor pressure and any other relevant variables. In order, to be able to separate out the contribution from each variable we write, T a ¼ fn ðþþge ðþþhx ð7þ Figure 4. Time series of (a) measured longwave (solid line) and ship latitude (dashed), and (b) the daily averaged difference Q LA, of the estimated from the measured longwave for Clark (dash-dot), Bignami (dotted), J1 (dashed), and J2 (solid).

6 5-6 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX Figure 5. Variation of measured temperature adjustment T a with (a) total cloud amount, (b) vapor pressure, and (c) dew point depression. Symbols as Figure 3. where, f(n), g(e) and h(x) represent the functional dependence of T a on cloud cover, vapor pressure and possible other, as yet undetermined, relevant variables (specified by x). We take an empirical approach to the determination of these parameters, selecting them according to how strongly they are correlated with T a as discussed in the next section Dependence of the Air Temperature Adjustment on Meteorological Variables Variation of T a With Total Cloud Amount and Vapor Pressure [17] Values of T a for each of the 10 minute averaged longwave measurements have been calculated according to (6); they range in size from 0.6 K to 20.2 K. The variation of T a with cloud amount and vapor pressure is shown in Figure 5 for the full dataset. There is a clear dependence on the total cloud amount (r 2 = 0.67), with the magnitude of the adjustment increasing with decreasing cloud amount. In contrast there is no obvious variation of T a with vapor pressure, although any dependence may be masked by the dominant effect of cloud cover variations at this stage. Thus we attempt to parameterize the dependence on cloud amount first and then examine whether there is a residual relationship between T a and vapor pressure. Note that we have used vapor pressure rather than specific humidity as a measure of near surface humidity in our analysis for consistency with the earlier Clark and Bignami parameterizations. The relative values of the two variables vary slightly (by ±1% during the CHAOS cruise) as a result of variations in the atmospheric pressure but this effect is of negligible importance for our analysis. [18] The distribution of points at a given cloud fraction in Figure 5a indicates that T a becomes more negative as the height of the dominant cloud layer increases. However, we have restricted our analysis to the total cloud amount rather than parameterizing the dependence of T a on the amount of low, medium and high cloud. This choice is dictated by the frequency of reporting of the different cloud variables in the standard ship meteorological reports. Although there is the opportunity for information on the height of the cloud base to be reported, in practice the number of total cloud amount reports significantly exceeds those containing cloud height information. Thus, if a longwave formula is to be useful for climatological analyses, in which maximization of the sampling rate is a major concern, it is preferable for it to be formulated in terms of the total cloud fraction. Finally, we note that in the formulation of (7) we have implicitly assumed that the cloud cover and atmospheric surface layer humidity (as measured by the vapor pressure) contributions

7 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX 5-7 [20] T a varies more rapidly with cloud amount at high rather than low cloud fractions suggesting a quadratic dependence on cloud amount as adopted by Clark and Bignami. We have parameterized this dependence with the following least squares fit to the cloud fraction averaged values, T a ¼ an 2 þ bn þ c; ð8þ where a = 10.77, b = 2.34, and c = Substituting (8) into equation (6), we obtain the following empirical formula for the atmospheric longwave flux (referred to as J1 hereafter), Q LA ¼ s SB T a þ an 2 4 þ bn þ c ðj1; 9Þ Figure 6. Variation of T a, averaged by cloud amount, with total cloud cover. Crosses indicate the mean value of T a in each cloud fraction class (i.e., 0/8, 1/8 etc.) and the error bars show the standard error. Solid line indicates the quadratic fit in equation (8). can be regarded as independent. We believe that this is a reasonable assumption as investigation of the CHAOS dataset has shown that cloud cover and surface layer vapor pressure are uncorrelated (r 2 = 0.00) even when the observations are restricted to only those in which low cloud cover was dominant Parameterization of T a Dependence on Total Cloud Amount [19] The mean variation of T a with total cloud fraction is shown in Figure 6; the crosses indicate the mean value of T a in each cloud fraction class (i.e., 0/8, 1/8 etc.) and the error bars show the standard error. Under clear sky conditions the temperature of the equivalent blackbody is about 19 K cooler than the measured air temperature. As the cloud fraction increases the difference decreases such that T a is of order 4 K for full cloud cover. Note, that the magnitude of the error is relatively small for overcast conditions because of the large number of observations for which there was complete cloud cover. Estimates of Q LA have been obtained for each cloud observation using the above equation. The difference between these estimates and the measured values is shown as a time series in Figure 4. In addition a scatterplot of the measured and estimated values is shown in Figure 7a, with summary statistics for J1 being listed in Table 2. Comparison of Figure 7a with Figure 3 shows that the J1 formula provides a better fit to the observations than was possible with either the Clark or Bignami formulae despite the omission of any dependence on surface layer humidity. The mean bias error is reduced to just 1.3 Wm 2 and the RMS error to 14.7 Wm 2 although the level of correlation (r 2 = 0.77) is marginally smaller than that found for Clark (r 2 = 0.80). We note that during the interval of low cloud, overcast conditions from Julian day 140 to 145, the time series reveals that J1 persistently underestimates Q LA by about 15 Wm 2, indicating that further improvements may be possible. [21] We have investigated whether there is a significant residual dependence on surface layer humidity that should be included in the longwave parameterization by taking the ratio, R ME1, of the measured longwave to that estimated using (9). The distribution of points in Figure 8a which shows the variation of R ME1 with vapor pressure provides no indication for a residual dependence, at least for values less than about 21 mbar. We are unable to rule out the Figure 7. Scatterplot of estimated versus measured atmospheric longwave for (a) J1 and (b) J2. Symbols as Figure 3.

8 5-8 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX Figure 8. Variation with vapor pressure of the ratio of the measured to estimated longwave for (a) J1 and (b) J2. Symbols as Figure 3. possibility that water vapor in the atmosphere provides a significant additional source of downwelling longwave flux at higher humidities and note that in the analysis of Bignami there is evidence for such a dependence at vapor pressures greater than about 23 mbar (see their Figure 6). However, under the conditions encountered in our analysis at middlehigh latitudes it appears that the atmospheric longwave flux is not strongly influenced by variations in surface specific humidity Parameterization of T a Dependence on Dew Point Depression [22] Can we further improve the accuracy of the J1 longwave estimates by making use of information provided by meteorological parameters not yet employed in the analysis? The temperature adjustment in the formula reflects to some extent the difference between the average temperature of the cloud base for a given total cloud fraction and that of the surface layer. We note that the bias in the J1 estimates under overcast low level cloud conditions noted above are consistent with the parameterized value of T a being too high. A simple estimate of the temperature of the cloud base for low level clouds is provided by the dew point temperature, T Dew, of the air in the surface layer. Air which is displaced adiabatically from the surface layer will become saturated at T Dew as a result of the cooling associated with upward vertical motion [e.g., McIlveen, 1992] and thus have the potential to condense and form a cloud layer. Hence, we have explored using the difference between T Dew and T a, commonly termed the dew point depression, D = T Dew T a, as an indirect measure of variations in the cloud base temperature in our parameterization of T a as detailed below. For this purpose, values of T Dew and D have been calculated at the time of each cloud observation using the following formula [Henderson-Sellers, 1984]: T Dew ¼ 34:07 þ 4157= ln 2: =e : ð10þ Although this approach might only be expected to prove useful for low level clouds we believe it is worth exploring for all cloud types given the typical paucity of reported information regarding cloud height and types in the ship meteorological reports. We note that for the CHAOS cruise dataset the mean and standard error of D for predominantly low level cloud is 3.1 ± 0.1 K; for medium level, 4.5 ± 0.1 K; and for high level, 5.2 ± 0.2 K. [23] In order to investigate whether use of the dew point depression can lead to an improved T a (and hence Q LA ) parameterization, we have calculated the difference, T 0 a, of the temperature adjustment determined from the measured longwave and that estimated using (8): T 0 a ¼ T a Measured an 2 þ bn þ c : ð11þ The variation of T a 0 with D is shown in Figure 9. T a 0 falls below zero for values of D less than about 4 K indicating that the value of T a determined from the measurements is more negative than that estimated using (8). At the other end of the range, for dew point depressions of order 0.5 K, i.e., air which is close to saturation, T a Measured is about 3 K less negative than that estimated using (8). A least squares fit to the data in Figure 9 gives the following relationship, T 0 a ¼ 0:84ðD þ 4:01Þ: ð12þ Using this fit we have revised (8) such that our estimate of the temperature adjustment becomes T a ¼ an 2 þ bn þ c þ 0:84ðD þ 4:01Þ; ð13þ and thus obtain the following modified empirical formula (hereinafter referred to as J2) for the atmospheric longwave: Q LA ¼ s SB T a þ an 2 4: þ bn þ c þ 0:84ðD þ 4:01Þ ðj2; 14Þ We find that use of the modified formula results in a reduction in scatter between the measured and estimated values for Q LA, see Figure 7b and Table 2. The RMS error is reduced from 14.7 Wm 2 with J1 to 11.6 Wm 2 with J2 and there is a corresponding increase in the level of correlation from r 2 =0.77tor 2 = In addition, the mean bias error with the revised formula is reduced to 0.2 Wm 2. The time series of the difference between the measured and J2 estimated atmospheric longwave (solid line, Figure 4) shows that the inclusion of the dew point depression dependence results in a significant improvement relative to J1 in the interval from Julian day 140 to 145. We have again tested for a residual dependence on surface layer

9 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX 5-9 where the emitted radiation from the sea surface is taken to be close to blackbody. Following Katsaros [1990], we suggest values for e = 0.98 and a L = to be used with this formula. Given that the formulation of the upwelling flux from the sea surface is the same in all of the formulae considered, we suggest that by virtue of the inclusion of a more reliable atmospheric flux term equation (13) will provide more accurate estimates than either Clark or Bignami of the net longwave flux. We note that when compared with the earlier more complex parameterizations such as Clark (equation 2) the new formula enables the effects of different meteorological variables on the longwave to be more easily determined as they are separate terms. Figure 9. Variation with dew point depression of the difference, T 0 a, of observed T a from the value estimated using (6). Values are averaged over one degree intervals in D, solid line indicates least squares fit in equation (12). humidity by taking the ratio of the measured values for Q LA to those estimated with J2, but still find no evidence for a relationship, see Figure 8b. [24] In the analysis presented above we have introduced the dew point temperature depression as a secondary adjustment. We have, for completeness, also explored the direct use of D as the leading variable in the T a parameterization, instead of cloud cover. A scatterplot of T a against D is shown in Figure 5c which should be compared with Figure 5a. T a is seen to be correlated with D but the level of correlation (r 2 = 0.32) only explains about half as much of the variance in T a as that which can be accounted for by cloud cover variations (r 2 = 0.67). Hence, we have focused on developing a parameterization (J2) in which cloud cover is the leading term in the temperature adjustment. [25] To summarize this section, by using a newly developed parameterization a significant improvement in the accuracy of estimated values of the atmospheric longwave flux has been possible relative to those obtained with the earlier formulae of Clark and Bignami. The new parameterization is expressed in terms of the surface temperature adjustment necessary to obtain the effective temperature of a blackbody which emits a radiative flux equivalent to the atmospheric longwave. The temperature adjustment is found to vary strongly with total cloud amount and to have a secondary dependence on the dew point depression. Other factors are likely to influence the downwelling flux, for example, the amount and type of cloud at different vertical levels. However, our goal is to obtain climatological estimates of the air-sea heat exchange using ship meteorological reports. Hence, we have considered only those parameters likely to have a bearing on the downwelling longwave which are routinely available in large ship data sets. [26] For completeness, we combine equations (1) and (14) to obtain the following formula for the net longwave flux: Q L ¼ es SB T 4 s ð 1 a LÞs SB T a þ an 2 4; þ bn þ c þ 0:84ðD þ 4:01Þ ð15þ 4.3. Evaluation of New Formula Using Independent Cruise Measurements [27] In the preceding section we developed two versions (J1 and J2) of a new formula for the atmospheric longwave flux using an extensive set of measurements from the CHAOS cruise. We now evaluate the performance of the new formula using measurements from two more recent cruises. Our focus is on the middle-high latitudes, however measurements within the Tropics were also obtained on the second of the cruises considered and we briefly discuss how the new formula performs at such latitudes with reference to ongoing research. We note that the evaluation data sets are necessarily limited to those available at the time of our analysis and do not contain as extensive a set of measurements as were available from CHAOS. Ideally we would like to be able to carry out a more detailed evaluation using data sets with a greater range of meteorological and cloud conditions but this is not possible at the present time RRS Discovery Cruise 253 [28] Our first validation dataset consists of measurements made from 4 May to 18 June 2001 during a Marine Productivity research cruise [Allen, 2001, hereinafter referred to as D253] in the northeast Atlantic with RRS Discovery for which the ship track is shown in Figure 10a. The cruise consisted of both coarse and fine scale surveys carried out in the Iceland basin. The meteorological sensors employed were similar to those used during CHAOS and the measurements were logged using a newly developed stand alone system. Note that following the installation of the sensors and logging system in port, meteorological research scientists did not take any further part in the cruise. Measurements of the longwave flux were obtained with two Eppley radiometers (reference numbers and 31171) the first of which was the same one used in our earlier analysis. Both radiometers were corrected for the effects of dome heating and shortwave leakage and were found to be in good agreement throughout the cruise; the mean and standard deviation of the longwave difference between the two sensors was 2.2 ± 1.2 Wm 2. In the following analysis, comparisons of the estimated atmospheric longwave are made with respect to the average of the measurements made by the two sensors; we take the difference of 2 Wm 2 between them to be indicative of the likely sensor error. [29] Estimates of the atmospheric longwave were obtained using each of the four parameterizations considered earlier : J1, J2, Clark and Bignami. As cloud observations were not made by scientists on the cruise, estimates of

10 5-10 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX Figure 10. Ship track during (a) the D253 research cruise and (b) the AMT research cruise. the total cloud cover required for the longwave parameterizations were obtained from the ship meteorological logbook which contains observations made by officers on the bridge at six hourly intervals (at 0000, 0600, 1200 and 1800 GMT). We note that cloud observations of this sort are typical of those used in ship based climatological analyses [e.g., Josey et al., 1998; Lindau, 2001], and we are therefore able to test the longwave parameterizations using the same type of cloud data that would generally be used. Summary statistics for the amount of cloud cover are given in Table 3 and these indicate a relatively large proportion of overcast or nearly overcast conditions which is typical of this region. Note that there is insufficient information in the logbook reports to determine which cloud level (i.e., low, medium or high) is dominant so we have not subdivided the cloud estimates according to this variable. Histograms of the key meteorological variables are shown in Figure 11, the sample consists of 118 ten minute averaged values centered on the time of each cloud observation. The dry bulb temperature ranged from 0.7 to 11.4 C; the SST from 4.9 to 13.4 C and the vapor pressure from 4.4 to 12.3 mbar. The measured atmospheric longwave varied from 243 to 364 Wm 2. Thus, the conditions are typical of those obtained in the northern half of the latitude range sampled during CHAOS. [30] We have compared the ten minute average values of the measured atmospheric longwave centered on the time of each cloud observation with the estimated values. The results of the comparisons are encouraging and demonstrate that the inclusion of the dew point depression term in J2 leads to a significant improvement in the accuracy of the estimates. Scatterplots of the measured versus estimated longwave are shown in Figure 12 and summary statistics for the comparison are given in Table 4. Considering the newly developed formulae first, the version in which the temperature adjustment is solely a function of cloud cover, J1, has some tendency to overestimate the longwave at the low end of the range and underestimate at the high end. Inclusion of the dew point depression term in J2 reduces this tendency leading to an improved fit between the measured and estimated longwave. The mean bias error with J2 is 1.7 Wm 2, thus we have been able to obtain agreement of the measured and J2 estimated longwave to within 2 Wm 2 which is at the level of uncertainty in the sensor measurements noted above. With regard to the earlier parameterizations, the Clark formula performs significantly better than was found to be the case with the CHAOS dataset, overestimating the longwave by just 3.1 Wm 2, and there is no clear distinction between its performance and that of J2. By comparison, Bignami shows very poor agreement underestimating the longwave by 25.6 Wm 2. We discuss variations in the performance of Clark and Bignami further in the next section in the context of results from the second cruise comparison RRS James Clark Ross Cruise 52 [31] The second cruise took place on RRS James Clark Ross from 11 September to 17 October 2000 along the Atlantic Meridional Transect shown in Figure 10b, we refer to this cruise below by the acronym AMT. Our main aim in this section is to use a subset of observations from this cruise to test the performance of the new longwave param- Table 3. Observation Frequency of Total Cloud Amount Subsetted by Number of Octas for the D253 and AMT Research Cruises n = 0/8 n = 1/8 n = 2/8 n = 3/8 n = 4/8 n = 5/8 n = 6/8 n = 7/8 n = 8/8 Total D AMT

11 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX 5-11 Figure 11. Histograms of the surface meteorological variables and atmospheric longwave flux during the D253 cruise. Figure 12. D253 cruise scatterplot of estimated versus measured atmospheric longwave for (a) J1, (b) J2, (c) Clark, and (d) Bignami.

12 5-12 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX Table 4. Comparison of Estimated and Measured Atmospheric Longwave During the D253 Research Cruise a Mean MBE RMSE r 2 Measured Clark Bignami J J a Tabulated values are the mean, the mean bias error (MBE), root mean square error (RMSE), all with units Wm 2, and the correlation coefficient squared (r 2 ). The latter three statistics have been determined in each case with respect to the measured values; the sample contained 118 estimates. eterizations under conditions similar to those encountered during CHAOS. With this in mind we focus on data from the cruise obtained at latitudes greater than 20 from the Equator that have been subdivided into two bands, N/S and N/S, that roughly represent the mid latitudes and the subtropics, respectively. Note that in order to increase the number of observations available for the comparison, measurements from both the Northern and Southern Hemisphere have been included in a given latitude band as indicated by the notation N/S. In addition, we briefly discuss results obtained for the latitude range 20 S 20 N but reserve a detailed analysis of longwave exchange in the Tropics for a subsequent paper. [32] The instrumentation employed during AMT was similar to that used for D253, for full details see Yelland and Pascal [2000]. Measurements of the longwave flux were again obtained from two Eppley radiometers (31170 and an older sensor, 27225) corrected for the effects of dome heating and shortwave leakage. In the following analysis, comparisons of the estimated atmospheric longwave are made with respect to sensor as an accurate calibration of the older sensor following replacement of a resistor in the sensor circuitry was not available at the time of the cruise. In contrast to D253, cloud observations were made by the research scientists on AMT at hourly intervals following the same procedure as adopted for CHAOS. A total of 250 observations were made at latitudes greater than 20 from the Equator. Summary statistics for these observations are given in Table 3 which shows that there were a greater proportion of low-medium cloud fractions than was the case with D253. Note that the bridge officers were also requested to make hourly observations of the cloud cover during the AMT cruise so that an evaluation could be made of the typical difference between cloud observations made by different sets of observers. A sample of 164 matching observations of the total cloud amount was obtained. The mean difference (scientist - bridge officer) of the estimated total cloud cover for this sample was 0.01 with an RMS difference of 0.15, i.e., a typical observation might differ by 15% but the overall bias was less than 1%. Estimates of the cruise mean longwave obtained using J2 with both the scientist and bridge officer observation sets differed by 0.7 Wm 2 which suggests that our results are not biased as a result of systematic differences between observers. In the remainder of our discussion we present results obtained using the cloud observations made by the scientists on the AMT cruise. [33] Histograms of the key meteorological variables, averaged over 10 min intervals centered on the cloud observation times, are shown in Figure 13. The dry bulb temperature ranged from 6.3 to 24.2 C; the SST from 6.4 to 24.9 C and the vapor pressure from 6.8 to 27.0 mbar. The measured atmospheric longwave varied from 248 to 418 Figure 13. Histograms of the surface meteorological variables and atmospheric longwave flux during the AMT cruise.

13 JOSEY ET AL.: FORMULA FOR ATMOSPHERIC LONGWAVE FLUX 5-13 Wm 2. These conditions are broadly similar to those obtained toward the lower end of the latitude range sampled during CHAOS. [34] Comparisons between the measured and estimated longwave have been carried out as before for the various longwave parameterizations. Values for the mean bias error in the latitude bands N/S and N/S are presented in Tables 5 and 6 with corresponding scatterplots in Figures 14 and 15. In the N/S band, the best agreement in the mean is found with the J2 formula which provides estimates that agree with the measured longwave to within 1 Wm 2, the mean bias error being 0.7 Wm 2. Comparison with the scatterplot for J1 shows that the inclusion of the dew point depression term has again lead to an improved fit of the estimated to the observed values. There is still a tendency for J2 to overestimate the longwave at the low end and underestimate at the high end which may indicate that a stronger dew point depression adjustment should be developed in future studies as more extensive data sets become available. The results obtained with the Clark and Bignami formulae show a shift in bias relative to that found for D253. The Clark formula overestimates the atmospheric longwave by 13.0 Wm 2 in the mean; while Bignami underestimates by 7.1 Wm 2. This change toward better agreement of the measured longwave with Bignami relative to Clark between the D253 and AMT cruises is consistent with the latitude dependent shift in performance of these formulae noted earlier for the CHAOS comparison in section 3.2. [35] In the N/S band, J2 performs less well with a mean bias of 8.5 Wm 2, and better agreement is obtained with J1 for which the difference is 6.4 Wm 2. In both cases the correlation between the estimated and measured longwave is somewhat weaker than that found previously (Figure 15 and Table 6). In contrast, Bignami shows good agreement with the observations with a difference of 1.3 Wm 2, while the bias obtained with Clark has increased to 17.8 Wm 2. The poorer performance of J2 in the N/S band suggests that further research with a more extensive dataset is required to refine the formula at such latitudes. In addition, a preliminary analysis of measurements from the AMT cruise in the Tropical Band 20 S 20 N, indicates that J2 typically underestimates the atmospheric longwave in this region by about Wm 2 and that there is a possibility that this bias is related to an increased contribution from water vapor at high specific humidities. We are in the process of developing an extensive dataset of measurements from a number of cruises in Table 5. Comparison of Estimated and Measured Atmospheric Longwave During the AMT Research Cruise for the N/S Latitude Band a Mean MBE RMSE r 2 Measured Clark Bignami J J a Tabulated values are the mean, the mean bias error (MBE), root mean square error (RMSE), all with units Wm 2, and the correlation coefficient squared (r 2 ). The latter three statistics have been determined in each case with respect to the measured values; the sample contained 122 estimates. Table 6. Comparison of Estimated and Measured Atmospheric Longwave During the AMT Research Cruise for the N/S Latitude Band a Mean MBE RMSE r 2 Measured Clark Bignami J J a Tabulated values are the mean, the mean bias error (MBE), root mean square error (RMSE), all with units Wm 2, and the correlation coefficient squared (r 2 ). The latter three statistics have been determined in each case with respect to the measured values; the sample contained 128 estimates. the Indian Ocean with which we will investigate this possibility and hope to be able to improve our ability to estimate the longwave at low latitudes. [36] To conclude this section, we summarize our main results. We have found from the evaluations against D253 and AMT that the new J2 parameterization is capable of providing accurate estimates of the atmospheric longwave at middle-high latitudes when tested against two independent cruise data sets. These estimates are an improvement on those obtained with the Clark and Bignami parameterizations, each of which showed strong biases with respect to one of the cruise data sets considered. The Clark formula performed well in the D253 comparison but had a positive bias of greater than 10 Wm 2 when compared with the AMT measurements. The reverse was found to be the case for Bignami which was biased by greater than 20 Wm 2 for the D253 comparison but was in reasonably good agreement with AMT. By comparison, longwave estimates obtained with J2 agreed to within 2 Wm 2 in the mean with measurements from D253 and to within 1 Wm 2 with the subset of AMT cruise measurements at latitudes greater than 35 from the Equator. Thus, on the basis of these comparisons, the new parameterization J2 appears to be more suitable than either Clark or Bignami for use in climatological estimates of the longwave at middle-high latitudes. Further analyses of observations collected on future research cruises at middle-high latitudes are however required to fully substantiate our results. 5. Summary and Discussion [37] The accuracy of atmospheric longwave flux estimates obtained using two empirical formulae from the literature has been tested using pyrgeometer measurements made on a research cruise (CHAOS) in the northeast Atlantic in spring The measurements spanned a wide range of meteorological conditions from the subtropics to high latitudes and were corrected for the effects of differential heating of the pyrgeometer dome and shortwave leakage. Neither of the two formulae tested were found to be capable of providing reliable estimates of the atmospheric longwave flux over the full range of latitudes. The formula of Clark et al. [1974] overestimated the cruise mean measured longwave flux of Wm 2 by 11.7 Wm 2, that of Bignami et al. [1995] underestimated by 12.1 Wm 2. [38] These results are significant for the general goal of producing a balanced description of the climatological net