Corresponding author: D. Paynter, Geophysical Fluid Dynamics Laboratory, 201 Forrestal Rd., Princeton, NJ 08540-6649, USA. (firstname.lastname@example.org)
 A newly formulated empirical water vapor continuum (the “BPS continuum”) is employed, in conjunction with ERA-40 data, to advance the understanding of how variations in the water vapor profile can alter the impact of the continuum on the Earth's clear-sky radiation budget. Three metrics are investigated: outgoing longwave radiation (OLR), Longwave surface downwelling radiation (SDR) and shortwave absorption (SWA). We have also performed a detailed geographical analysis on the impact of the BPS continuum upon these metrics and compared the results to those predicted by the commonly used MT CKD model. The globally averaged differences in these metrics when calculated with MT CKD 2.5 versus BPS were found to be 0.1%, 0.4% and 0.8% for OLR, SDR and SWA respectively. Furthermore, the impact of uncertainty upon these calculations is explored using the uncertainty estimates of the BPS model. The radiative response of the continuum to global changes in atmospheric temperature and water vapor content are also investigated. For the latter, the continuum accounts for up to 35% of the change in OLR and 65% of the change in SDR, brought about by an increase in water vapor in the tropics.
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 In a previous study [Paynter and Ramaswamy, 2011] (referred to here as PR2011), we detailed the construction of an empirical water vapor continuum, termed the BPS continuum, from the measurements of Baranov and Lafferty , Baranov et al. , Paynter et al.  and Serio et al.  in selective spectral regions between 240 and 8000 cm−1. The BPS water vapor continuum also utilized the experimental errors associated with these studies, in order to estimate the upper and lower limits of the continuum. In spectral regions where experimental data is missing or inadequate, the BPS water vapor continuum makes use of data from the MT CKD 2.5 [Clough et al., 2005] continuum. BPS should not be viewed as either an alternative or update to MT CKD, but instead, as an attempt to use the aforementioned measurements to improve our understanding of water vapor continuum radiative transfer. Most results presented in this paper that were calculated using BPS are contrasted to those obtained using MT CKD 2.5, in order to highlight the differences between the two. We should stress that throughout this paper when we refer to the continuum we are referring to the water vapor continuum only; we do not consider the continuum of other absorbers (CO2, O2, etc.).
 In PR2011, the BPS continuum was benchmarked in three standard atmospheres (Tropical (TRO), Midlatitude-Summer (MLS) and Sub-Artic-Winter (SAW)) against the commonly used MT CKD [Clough et al., 2005] (versions 1.1 and 2.5) and CKD [Clough et al., 1989] (version 2.4) models. In the longwave, the continuum is generally well constrained and the models show good agreement with each other. It was found that the difference between using the upper and lower limits of the BPS model was never more than 1.5% of total OLR or SDR. However, in the shortwave, the uncertainty is found to be quite significant. For example, in a TRO atmosphere the continuum could contribute as much as 6%, or as little as 2%, to the absorption of shortwave radiation by water vapor.
 Here, we build upon these findings and investigate both how uncertainties in the continuum and the choice of continuum formulation influence global clear-sky radiative transfer. The main aim is to investigate how our current understanding of the water vapor continuum spectra affects radiative transfer in a wide array of atmospheres. In doing so, we hope to draw a picture of how variations in water vapor and temperature profiles impact the contribution of the continuum. We also show how the continuum influences the radiative response to changes in water vapor and temperature and, therefore, can analyze the importance of the continuum in a warming atmosphere. Finally, we investigate the effects of the overlap between the water vapor continuum and the CO2 spectra upon the radiative forcing that is caused by increased atmospheric CO2, similar to work by Kiehl and Ramanathan . Unlike previous studies, where the effects of the continuum upon atmospheric dynamics were investigated using General Circulation Models (GCMs) [e.g., Collins et al., 2002, 2006; Schwarzkopf and Ramaswamy, 1999; Zhong and Haigh, 1999], here we concentrate upon the instantaneous radiative effects of the continuum. However, we intend to expand upon this and explore the consequences of these results using a General Circulation Model in future investigations.
 In this paper we focus on the instantaneous effects of the continuum upon three atmospheric quantities; outgoing longwave radiation (OLR), longwave surface downwelling radiation (SDR) and shortwave absorbed radiation (SWA). Accurate knowledge of all three quantities is important to fully understand the Earth's radiation budget. Longwave is defined here as 1 to 3000 cm−1, with only terrestrial radiation considered; and shortwave is defined as 1000 to 16,000 cm−1, with only solar radiation considered. For all calculations presented, clear-sky conditions are assumed and the effects of scattering neglected. In the case of shortwave calculations, the variations in both atmospheric path length and incoming solar flux with latitude and season are taken into account using Gaussian-weighted zenith angles, as described inPaynter . A calculation performed for a single day in the middle of a season is assumed to represent the seasonal average.
 We have compared the BPS model, and its associated uncertainties (see Table 1 of PR2011 for more details on BPS), to MT CKD 2.5 and, in some cases only, to CKD 2.4. In Figure 1, the continuum coefficients for the foreign (Figure 1a) and self-continuum (Figure 1b) models are presented for reference. The temperature dependence coefficients (discussed later in this section) for BPS, MT CKD and CKD are also given (Figure 1c: note that those for MT CKD and CKD are identical).
 A line by line (LBL) radiative transfer code was used to calculate the fluxes. This code is described in detail in PR2011 and is based on the Reference Forward Model (RFM) (A. Dudhia, Reference Forward Model version 4: Software User Manual, 2005, http://www.atm.ox.ac.uk/RFM). The European Centre for Medium-Range Weather Forecast 40 Year Re-Analysis (ERA-40) [Uppala et al., 2005] specific humidity, ozone (for OLR and SDR calculations only) and temperature fields were used to construct the vertical profiles which were inputted into the LBL radiation code. Typically, these vertical profiles contain 22 layers that extend up to the 1 mb pressure level. The surface temperature, albedo and geo-potential ERA-40 fields were also used to define the surface conditions.
 To create average seasonal climatologies, the ERA-40 data used was split into four seasons, March–April–May (MAM), June–July–August (JJA), September–October–November (SON), December–January–February (DJF), and averaged over the full 1957 to 2002 period. To improve computational time, the ERA-40 data was also averaged to create 10° grid boxes. This gives a global total of 648 vertical profiles for each season.
 For OLR and SDR calculations, the following prescriptions of greenhouse gases were assumed: CO2 (380 ppmv), N2O (280 ppbv) and CH4(1700 ppbv), corresponding to approximate present-day values. All gases were assumed to be uniformly mixed throughout the atmosphere and to have the same mixing ratios globally. Only the water vapor absorption was considered for SWA calculations and the reasons for this are discussed inSection 3.2.3.
 The change in flux due to the continuum is defined as the difference between the flux when calculated with and without the continuum included. Likewise, the change in flux due to an individual component of the continuum is calculated as the flux difference with and without that component included. For example, the change in flux due to the self-continuum is the difference between the flux calculated with all absorbing gases (H2O, CO2 etc.) and both the self and foreign continua included and the flux calculated with all absorbing gases, but only the foreign continuum.
 We wish to strongly emphasize that while the BPS model is based upon experimental data in numerous spectral regions, most measurements of the self-continuum in the atmospheric windows were conducted at temperatures above those typically found in the atmosphere. This is important, as it is well known that the self-continuum has a strong temperature dependence. Although potential problems associated with this were discussed inPR2011, it is important to highlight this again in order to put the current results into context.
 In the 800–1200 cm−1 and 2000–3400 cm−1 window regions, measurements [Baranov and Lafferty, 2011; Baranov et al., 2008] were made between 310 and 363 K. PR2011showed that, when fitted to the measurement data, the simple exponential form of temperature-dependence used by MT CKD,
(where Csis the self-continuum coefficient, T is temperature, T0 is some reference temperature and σ the temperature dependence coefficient), provides a reasonable approximation of the observed temperature dependence. This fitting has resulted in different temperature dependence coefficients than those used in MT CKD, as can be seen in Figure 1c. Unfortunately, at present, it is necessary to use such empirical forms of temperature dependence to estimate the self-continuum at atmospheric temperatures. This is due to the absence of lower temperature measurements, coupled with an incomplete understanding of the physical processes that cause the continuum (seeShine et al.  for a summary).
 In the 4000–5000 cm−1 and 5600–7000 cm−1shortwave windows, the BPS self-continuum is based upon the measurements byPaynter et al.  at 351 K. The lack of measurements at other temperatures has resulted in extrapolations to lower temperatures using the temperature dependence given by MT CKD (rather than fitting the MT CKD form of temperature dependence to the measurement data, as discussed in the previous paragraph). Due to the larger continuum measured at 351 K by Paynter et al.  than predicted by MT CKD, using the MT CKD temperature dependence applied to the Paynter et al.  measurements at 351 K results in the BPS continuum being larger than MT CKD at atmospheric temperatures (Figure 1) in these window regions.
 The Paynter et al.  measurements also provided upper and lower limits of the continuum at 351 K. The upper and lower limits of the BPS continuum at other temperatures were obtained by applying the MT CKD temperature dependence to these limits. Thus, they are representative of how this uncertainty may propagate to lower temperatures. However, these limits may not completely capture all uncertainty in the continuum, as at present BPS assumes no uncertainty in the continuum temperature dependence coefficient. This is more of a concern in the shortwave windows between 4000 and 7000 cm−1, where the lowest measurement temperature of 351 K is notably higher than atmospheric temperatures.
 It is thus apparent that the upper and lower limits of the BPS continuum should not be viewed as the absolute upper or lower limits of the continuum. This is because, first, an assumption is being made about how uncertainty in continuum measurements at higher than atmospheric temperatures propagates down to atmospheric temperatures. Second, in the spectral regions where the BPS continuum contains no experimental data and MT CKD continuum coefficients are used (e.g., above 8000 cm−1), the uncertainty assumed is, by definition, a broad estimate (generally this is a ±50% uncertainty, see Table 1 in PR2011).
 Since PR2011, Ptashnik et al.  have repeated the Paynter et al.  measurements at 351 K and also made measurements at higher temperatures (up to 472 K) in the 2000–3400 cm−1, 4000–5000 cm−1, and 5600–7000 cm−1 window regions. These measurements were in very good agreement with Paynter et al.  at 351 K. All measurements up to 472 K by Ptashnik et al.  show a larger continuum in the latter two windows than predicted by MT CKD 2.5. These two findings increase our confidence that at 351 K and above, the continuum is larger than predicted by MT CKD and also makes the lower limit of the BPS continuum at 351 K less likely.
Ptashnik et al.  also conducted a measurement at 293 K. This suggests a continuum within the shortwave window between 4000 cm−1 and 5000 cm−1 that is comparable with the upper limit of the BPS prediction. However, there is still considerable uncertainty associated with these measurements. We discuss the possible implications of the Ptashnik et al.  results in Section 3.2.3.
 Clearly far more work is required to obtain a comprehensive description of the continuum in the shortwave and (to a lesser degree) the longwave, especially at atmospheric temperatures. Accordingly, the BPS continuum, and its associated upper and lower limits, should be viewed as a useful tool for assessing the impact of the continuum upon radiative transfer, but a tool which is based on certain assumptions and limited by experimental constraints. The aim of this paper is therefore not to provide a definitive value of the continuum contribution to global clear-sky radiative transfer. Instead, it is to investigate the radiative transfer of the continuum and ascertain how this changes with varying atmospheric conditions.
3. Results and Discussion
3.1. Seasonal Variation and Global Radiation Budget
 OLR, SDR and SWA have been calculated for the each of the 648 MAM profiles and spatially averaged to produce global quantities (Table 1) without any continuum. We subsequently calculated the contribution of the BPS, MT CKD 2.5 and CKD 2.4 continuum models (also Table 1) to OLR, SDR and SWA. For globally averaged values, there is a reasonable agreement between the continuum models across all three quantities, with no more than 1 Wm−2 variation between them.
Table 1. The March–April–May (MAM) Globally Averaged Reduction in OLR and Increase in SDR and SWA due to Various Continuum Models (All Wm−2)a
Additionally, OLR, SDR and SWA with no continuum included are presented, along with the seasonal globally averaged WVC (kgm−2), surface temperature (SFC Temp, K) and upwelling surface radiation (SFC LWUP, Wm−2).
MT CKD 2.5
 We also investigated how the contribution of the continuum varies with season. This variation was found to be small and similar to that seen for water vapor lines. Hence, we do not report these findings in detail here. Furthermore, we found the MAM climatology to be a reasonable approximation for the annual average (within 0.1% for global OLR, SDR and SWA) and thus have only considered this climatology for the remainder of this section.
 An estimate of how uncertainty in the continuum might affect the global radiation budget was obtained using the upper and lower limits of the BPS model. It should be re-stated that the upper and lower limits of the BPS continuum are estimates that are subject to the limitations discussed inSection 2 (i.e., the uncertainties are extrapolated from higher temperatures and broad estimates of uncertainty are assumed where no measurement data exist). Accordingly, the results obtained for radiative transfer, here and elsewhere, should also be viewed as estimates. The results in Table 2 show that globally uncertainties in the continuum, as estimated by the BPS model, lead to a 1 Wm−2 uncertainty in OLR, 1.9 Wm−2 uncertainty in the SDR and 2.1 Wm−2 in the SWA. While not negligible, these are much smaller than the uncertainty levels associated with the global radiation budget. For example, there is a 5–15 Wm−2range of accuracy in OLR and SDR for both the Clouds and the Earth's Radiant Energy System (CERES) and the International Satellite Cloud Climatology Project (ISCCP-FD) satellite data quoted inTrenberth et al. .
Table 2. The Clear-Sky Globally Averaged Reduction in OLR and Increases in SDR and SWA (All Wm−2) due to the Total Continuum (Self and Foreign) and Both the Self and Foreign Continua for MAM ERA-40 Climatology
MT CKD 2.5
 A review [Wild, 2008] of the General Circulation models (GCMs) used in the 4th Assessment Report of the Intergovernmental Panel on Climate Change showed there to be considerable variation among the models for OLR, SDR and SWA. For OLR there is a range of 9 Wm−2 across the models, with a standard deviation of 2.8 Wm−2. For SDR and SWA, the ranges are 21 Wm−2 and 15 Wm−2 respectively, with respective standard deviations of 5.6 Wm−2 and 3.7 Wm−2. It is also suggested that GCMs (on average) underestimate SWA by 6 Wm−2, and SDR by 5.6 Wm−2, compared to observations [Wild, 2008]. Therefore, it is clear that the uncertainty due to the continuum is smaller than both the range between the GCMs and the biases that they exhibit relative to observations. In the case of SWA though, the inclusion of a larger self-continuum, say nearer the upper limit of BPS, might somewhat help to reduce the difference between models and observations.
3.2. Variation With Atmospheric Conditions
 We now turn our attention to how the radiative transfer of the continuum, and the associated uncertainties related to this, vary with atmospheric conditions. The motivation for this work comes from the large variation in the continuum contribution, in both the longwave [Clough et al., 1992; Firsov and Chesnokova, 2010; Kratz, 2008] and shortwave [Paynter and Ramaswamy, 2011; Ptashnik et al., 2011, 2004], depending upon the composition of the atmosphere. Here we hope to quantify the nature of this variation more clearly than previously, by providing an analysis of the how the continuum contribution varies with the 648 MAM climatology profiles.
 We discuss OLR, SDR and SWA in turn and present two types of figure for each flux. The first type (Figures 2, 4 and 6) plots flux as a function of both latitude and longitude and the second (Figures 3, 5 and 7) shows flux as a function of both the vertically integrated water vapor column (WVC) and surface temperature. We stress that while the radiative response due to the continuum in the atmosphere is directly determined by the temperature and water vapor profiles, both WVC and surface temperature provide an excellent proxy for predicting the behavior of the continuum. Thus, we present the results in this manner to give a clear picture of how the continuum contribution varies between different sorts of atmospheres. Figures 2a, 3a, 4a, 5a, 6a, and 7a show the flux calculated with no continuum, Figures 2b, 3b, 4b, 5b, 6b, and 7b show the contribution of the BPS continuum, Figures 2c, 3c, 4c, 5c, 6c, and 7c and Figures 2d, 3d, 4d, 5d, 6d, and 7d show the contribution of the self and foreign components respectively, Figures 2e, 3e, 4e, 5e, 6g, and 7e show the difference between BPS and MT CKD 2.5 and Figures 2f, 3f, 4f, 5f, 6h, and 7f show the range between the upper and lower limits of the BPS model. In Figure 1, the global WVC (Figure 1d) and surface temperature (Figure 1e) for the MAM climatology are shown, in addition to the continuum coefficients (Figures 1a–1c) that were discussed in Section 2. These figures provide a useful reference for the forthcoming discussions.
 The clear-sky OLR calculated for atmospheres with H2O, CO2, CH4, O3 and N2O lines, but no continuum included is shown in Figure 2a. This shows a markedly different global pattern than the reduction in OLR caused by the BPS water vapor continuum (Figure 2b). In fact, the reduction in OLR due to the BPS continuum is largely proportional to WVC, reaching a maximum in the humid Indonesian Warm Pool, while OLR without the continuum does not exhibit such variation between the midlatitudes and the tropics. This is demonstrated more clearly by plotting OLR (Figure 3a), and the reduction in OLR due to the continuum (Figure 3b), as a function of WVC.
 Breaking the contribution of the continuum down into the self and foreign components (Figures 2c and 3c and Figures 2d and 3d, respectively) reveals that the reduction in OLR (and subsequently its behavior as a function of WVC) in most atmospheres is predominantly due to the self-continuum. Indeed, the foreign continuum contribution to OLR (Figure 3d) is largely insensitive to WVC value once the value is greater than ∼15 kgm−2and thus exhibits a different geographical pattern to the self-continuum (Figure 2d), which is more comparable to that seen for the spectral lines of atmospheric molecules (i.e., for H2O, O3, CO2 as shown in Figure 2a). This similarity between the geographical pattern of the OLR contribution of spectral lines of atmospheric molecules and that of the foreign continuum is due to the foreign continuum contribution occurring in spectral regions where it overlaps strongly with water vapor lines (i.e., within the rotational and bending band of water vapor). This is discussed in more detail in Section 3.2.4.
 In most atmospheres, there is a small (less than 1 Wm−2), but notable, difference in the OLR between models that use the BPS continuum and the commonly used MT CKD 2.5 model. This difference is illustrated geographically, and as function of WVC, by Figures 2e and 3e respectively. We discuss these results in Section 3.2.2 after first outlining the differences for SDR.
 The range of OLR values calculated using the lower and upper estimates of the BPS continuum (Figure 2f) reveal that up to a 3 Wm−2 estimated uncertainty results from the continuum in the tropics and that this steadily reduces to zero as latitude increases. The percentage uncertainty in OLR estimated from the upper and lower limits of the BPS continuum increases steadily with increased WVC (Figure 3f). This is because as WVC increases, the continuum makes a larger fractional contribution to the OLR. The upper and lower limits also exhibit a similar behavior and thus the percentage contribution (which is the range between the upper and lower limits divided by the OLR including the continuum) also increases with WVC.
 SDR, computed without the water vapor continuum (Figure 4a) has a stronger latitudinal variation than OLR. In addition, although the continuum contributes more to SDR than to OLR [Clough et al., 1992], the total and self-continua (Figures 4b and 5b and Figures 4c and 5c, respectively) behave in a largely similar manner. However, for large WVCs, the sensitivity of SDR to WVC is reduced and this occurs because the bottom layer of the atmosphere becomes saturated in most of the window regions.
 Although the variation in SDR, as a function of WVC, is much smaller for the foreign continuum (Figures 4d and 5d) than for the self-continuum, it shows a more complex relationship, with SDR initially increasing rapidly and then steadily falling off. Thus, we generally see the largest contribution at high latitudes, with an exception being the dry atmospheres present over the western USA and the Mongolian desert. The reasons for this are discussed further inSection 3.2.4.
 The difference between BPS and MT CKD is also more complex for SDR than for OLR (Figures 4e and 5e). When WVC is less than ∼10 kgm−2, the differences between these models are observed to be proportional to WVC (Figure 5e). However, as WVC increases, these differences are influenced more by the lower atmosphere temperatures (not shown; but the surface temperature shown by the color of the circles in the figures provides a useful proxy for the lower atmosphere temperature) than by WVC. Geographically, the differences between the models are largest in the midlatitude oceans, even though these are not the regions with the greatest WVC.
 In the drier, colder atmospheres present at high latitudes, the variations in SDR between MT CKD and BPS occur because of the larger BPS foreign continuum coefficients in the 240–590 cm−1 region, as measured by Serio et al. . These coefficients have the most influence in atmospheres with low WVC. Hence, in Figure 5f the largest estimated percentage uncertainty occurs in very dry atmospheres. However, the minimum uncertainty is also in very dry atmospheres. This is because both the water vapor lines (Figure 5a) and the foreign continuum (Figure 5d) contribution to SDR are very sensitive to the water vapor content of the atmosphere when WVC is less than 5 kgm−2. Interestingly, the WVC value at which the SDR is most sensitive to changes in WVC occurs at a lower WVC values for the foreign continuum than for the lines. It follows that as WVC values increase between 1 and 5 kgm−2 the percentage contribution of the continuum to total SDR decreases.
 However, in atmospheres with larger WVCs, the self-continuum becomes more significant and the differences between theBaranov et al. self-continuum coefficient measurements and MT CKD 2.5 in the 800–1200 cm−1 window become important. Baranov et al.  measured a stronger continuum between 311 and 361 K (measurements were not made at lower temperatures), but estimated it to have a weaker temperature dependence (Figure 1c). As a result, the BPS continuum coefficients are greater than those for MT CKD 2.5 at temperatures above ∼305 K, but less at temperatures below ∼305 K. This explains why MT CKD predicts a larger SDR than BPS (i.e., most atmospheres are normally colder than 305 K) and also why the difference in SDR for atmospheres with the same WVC is greater if the surface temperature is colder (hence the larger differences seen for the ‘colder’, but fairly humid, atmosphere over the midlatitude oceans). A similar argument can be made for the difference in OLR between MT CKD and BPS (Figure 3e), although the differences for atmosphere with the same WVC are smaller, partially due to less variation in emission temperatures.
 In some tropical regions, the BPS continuum suggests a 6 Wm−2 uncertainty in SDR (Figure 4f), which corresponds to a maximum of 1.7% of the total SDR (Figure 5f). However, the percentage uncertainty in the contribution of the continuum to SDR is largest in the driest atmospheres (Figure 5f). This is because in these atmospheres the overlap with water vapor lines has the smallest effect on the foreign continuum contribution to SDR. However, as WVC increases, the self-continuum contribution increases more rapidly than that of the water vapor lines and becomes a larger fraction of the total SDR. As a result, the percentage uncertainty increases (Figure 5f). The value then decreases once WVC is above 40 kgm−2. Similar to the continuum SDR leveling out with increasing WVC, this decrease can also be explained by saturation of the lower atmospheric levels. The upper limit of the BPS continuum becomes less sensitive to WVC at smaller WVC values than the lower limit of BPS. Therefore, the difference between the SDR predicted by the upper and lower BPS continua reduces as WVC increases, which in turn results in the percentage uncertainty in SDR, as estimated by the BPS continuum, also decreasing.
 The analysis of SWA is presented in Figures 6 and 7. In contrast to the longwave analysis, the SWA analysis is performed for water vapor only conditions, as the overlap with gases other than water vapor has far less effect on the contribution of the continuum in the shortwave than in the longwave. In addition, a zero surface albedo and a fixed solar zenith angle of 60° are assumed for the SWA analysis. This allows SWA to be analyzed as a function of WVC, without being biased by the complicated effects of albedo and changes in zenith angle. However, it also means that the results in Figure 6 are not particularly indicative of the actual spatial pattern of the global response in SWA. We discuss this later in this section when we investigate the seasonality of continuum SWA. The day fraction is assumed to be 1, with the solar irradiance incident being 420 Wm−2 (i.e., that between 1000 and 16,000 cm−1).
 The geographical distribution of the SWA of water vapor lines, and the additional increase in SWA due to the continuum, are shown in Figures 6a and 6b respectively. In common with the OLR and SDR results, the foreign continuum contribution to SWA levels out as WVC increases (Figure 7d), while the self-continuum contribution increases almost proportionally with WVC (Figure 7c). These figure panels also show that the relative contribution of the foreign continuum to the total continuum is larger for SWA than for either OLR or SDR and, as a result, there is less decrease in SWA with increasing latitude (Figure 6b).
 The CKD 2.4 foreign continuum is larger than that of MT CKD 2.5 or BPS in much of the 3000–16,000 cm−1 region (Figure 1a). The Paynter et al.  foreign continuum measurements in the shortwave bands (<8000 cm−1) used in BPS are generally in good agreement with MT CKD 2.5. However, there is still considerable uncertainty associated with these measurements and no measurements above 8000 cm−1. Thus, we briefly explore the impact of the larger CKD 2.4 foreign continuum. In Figures 6e and 6f, the geographical contributions of the self and foreign continua of CKD 2.4 are shown respectively. Likewise, Figure 7 shows the self (Figure 7c) and foreign (Figure 7d) continuum contributions of the BPS (circles) and CKD 2.4 (triangles) models, each as a function of WVC. The global SWA pattern of the self-continuum is fairly similar between these two models, but BPS SWA is about twice as large in magnitude as CKD 2.4 SWA and there is a noticeable fall-off of the latter with increasing WVC (Figure 7c). This fall-off does not occur for the BPS continuum. These differences arise because the BPS model has larger continuum coefficients between the major water vapor bands than CKD 2.4. For the foreign continuum (Figure 7d), the geographical patterns are also similar between BPS and CKD 2.4, but due to the larger CKD coefficients within the major water vapor bands, the absorption increases more rapidly at lower WVCs and levels out at a higher SWA value for CKD 2.4 (1.6 Wm−2 for CKD 2.4 versus 1.0 Wm−2 for BPS).
 We now turn our attention back to exploring the differences between MT CKD and BPS. Between 3000 and 8000 cm−1MT CKD predicts stronger self-continuum coefficients than BPS near the edge of the water vapor bands, whereas BPS predicts a larger continuum between them. Accordingly, the greatest differences in SWA between BPS and MT CKD occur for the most humid atmospheres, where the contribution is greatest from between the bands and is least near the band edges, which are saturated (Figures 6g and 7e).
 The two main areas of uncertainty, as estimated by the BPS model, in water vapor continuum SWA are within the bands for the foreign continuum and in the weak absorbing areas between the bands for the self-continuum [Paynter et al., 2009]. In general, the former causes more significant errors in very dry atmospheres, where the largest numbers of micro-windows (the gaps between spectral lines) within the bands are not saturated, whereas the latter is more important for errors in the most humid atmospheres. This explains the ‘tick-like’ shape of the estimated percentage uncertainty in water vapor SWA due to the continuum as a function of WVC (Figure 7f). In absolute terms, the uncertainty in the self-continuum dominates and the greatest uncertainty in SWA (about 4 Wm−2) is centered in the tropics (Figure 6h). However, we remind the reader of the discussion in Section 2 about the present limitations of the BPS model uncertainty estimates in the shortwave windows. Thus, these uncertainty limits provide a guide to the influence of variation in the continuum within the window regions rather than hard upper or lower limits.
 As also noted in Section 2, recent self-continuum measurements in the atmospheric windows between 2000 and 9000 cm−1 by Ptashnik et al. estimate a larger self-continuum at atmospheric temperatures than BPS. These measurements are mainly at non-atmospheric temperatures above 350 K, with the exception of one measurement at 293 K. With their measurement data, and using zonal averaged ERA-40 data,Ptashnik et al.  predicted 0.74 Wm−2 SWA in addition to that predicted by MT CKD 2.5, with a maximum zonal difference of 1.5 Wm−2 occurring in the tropics. This is larger than the 0.4 Wm−2 (peaking at 0.8 Wm−2 in the tropics) extra absorption predicted by BPS, but less than the 1.0 Wm−2 (peaking at 2.1 Wm−2) predicted by the upper limit of BPS.
 In the 4000–5000 cm−1 window, the Ptashnik et al.  measurement at 350 K and the Paynter et al.  measurements at 351 K (from which BPS is derived) are in good agreement. However, there is a difference between the predicted continua at atmospheric temperatures, because the BPS continuum uses the MT CKD temperature dependence to estimate the continuum at lower temperatures, whereas Ptashnik et al.  use the difference between their 350 K and 293 K measurements. The larger continuum at 293 K measured by Ptashnik et al.  compared to that estimated by BPS suggests a stronger temperature dependence of the continuum within this window than the MT CKD temperature dependence presently used by the BPS continuum. Ptashnik et al.  also estimated temperature dependence in the neighboring 2000–3400 cm−1 window, using the ratio between their 350 K and 293 K measurements, and found a similar temperature dependence to the 4000–5000 cm−1 window. However, in the 2000–3400 cm−1 window, the continuum estimated by BPS at 293 K is in better agreement with the Ptashnik et al.  measurement than in any other window. This is because, in this window only, the BPS temperature dependence coefficients are derived from the Baranov and Lafferty  measurements between 310 and 360 K and these suggest a stronger temperature dependence than does MT CKD. Accordingly, the BPS temperature dependence in the 2000–3400 cm−1 window is stronger than elsewhere (Figure 1).
 In the windows between 5600 and 8500 cm−1Ptashnik et al.  used the temperature dependence suggested by their measurements between 350 K and 400 K (the 293 K measurement does not exist here). Although this is weaker than the dependence in the <5000 cm−1 windows, it is still stronger than that used in BPS. In the 5600–6900 cm−1 window, BPS continues to apply the MT CKD temperature dependence to the Paynter et al.  351 K measurements, but in the 7500–8500 cm−1 window the BPS continuum is not based on any measurements and is the same as MT CKD. Thus, in both windows between 5600 and 8500 cm−1 BPS estimates a smaller continuum with a weaker temperature dependence than do Ptashnik et al. .
 However, the 293 K Ptashnik et al.  measurement has large uncertainties associated with it within the window regions and measurements were not made by Ptashnik et al. at any other near atmospheric temperatures. These experimental uncertainties, coupled with a lack of a reliable theory of the self-continuum temperature dependence, mean that a considerable uncertainty in our knowledge of the self-continuum at atmospheric temperatures still persists (D. J. Paynter, manuscript in preparation, 2012). We therefore consider the BPS estimate of the self-continuum and its associated uncertainties to be reasonable, but caution that, in light of thePtashnik et al.  data, the continuum SWA may well be nearer the upper limits of the BPS continuum.
 The fact that zero albedo and a fixed zenith angle of 60° have been assumed means that the global picture in Figure 6 is not realistic. To address this we have investigated how the seasonal flux changes in zenith angle, WVC and albedo influence the impact of the continuum in the shortwave. In Figure 8, we show spatial plots of the seasonal WVC values alongside the BPS continuum SWA. In the case of the MAM climatology, as expected, the continuum contribution in the tropics is increased compared to when a fixed zenith angle is assumed, while in the extra tropics and high latitudes it is decreased. However, similar to the fixed zenith angle analysis, a steady increase in SWA can be observed in the tropics due to the self-continuum, along with a decreased fall-off at high latitudes compared to the WVC. This is because the foreign continuum is less sensitive to changes in water vapor than the self-continuum.
 The continuum SWA in JJA is characterized in the tropics by the maximum self-continuum SWA following the northward progression of the largest values of WVC. It is also notable that the combination of increased zenith angle and WVC causes more SWA continuum absorption in the northern mid (due to the self and foreign continua) and high (foreign) latitudes compared to in MAM. DJF sees a southward shift in the continuum SWA, with a large increase appearing over Antarctica.
 It can also be seen that, despite the higher sensitivity of the continuum to changes in WVC in the tropics, the effects of zenith angle coupled with albedo actually cause the largest seasonal variations in continuum contribution at high latitudes.
3.2.4. Spectral Analysis
 In this section we attempt to offer some insight into why the radiative contribution of the water vapor continuum changes with WVC. In Figure 9 we show the contributions of the self and foreign continua, as functions of wave number, for each of the 648 atmospheres in the MAM climatology. WVC values are represented by different colored points in this figure. The spectral variation in the contribution of the continuum for standard atmospheres (MLS, SAW etc.) has been discussed in detail elsewhere [e.g., Clough et al., 1992; Paynter and Ramaswamy, 2011; Ptashnik and Shine, 2003]. We focus here on how the behavior of the continuum in different spectral regions leads to the relationships with WVC and temperature that was observed in the preceding figures.
 From the integrated (over wavenumber) response shown in Figures 3, 5 and 7, it is apparent that the self-continuum contribution to OLR, SDR and SWA increases almost directly with WVC. This is because the largest changes in transmittance caused by the continuum occur in the spectral regions where there is little overlap with other absorbers (i.e., in the atmospheric windows between 800 and 1200 cm−1, 2000–3400 cm−1, 4000–5000 cm−1, etc.). In these regions, the continuum optical depths are typically not great enough to saturate any particular atmospheric layer, even for a large WVC. Thus, the change in transmittance, as a function of WVC, due to the continuum lies somewhere between that which can be described for strong and weak water vapor lines. It is this change in transmittance, brought about by increasing water vapor, which produces the proportionality between WVC and the self-continuum contribution to OLR (Figure 9a), SDR (Figure 9c) and SWA (Figure 9e) that is observed at most wavenumber in the window regions (as can be inferred by the smooth color gradient).
 In the rotational band (∼1 to 600 cm−1), the addition of the foreign continuum causes a largely similar reduction in OLR for all atmospheres once WVC is greater than ∼8 kgm−2 (Figure 3d). Within this spectral region we can assume that the foreign continuum optical depth is much less than that of the water vapor lines near the line centers and thus its contribution is limited to the micro-windows. Once a WVC value of ∼8 kgm−2is reached, most of the micro-windows in the rotational band are saturated in the lower/middle troposphere. As a result, the influence of the foreign continuum is confined to the micro-windows in a few layers near the tropopause [Clough et al., 1992]. Within these micro-windows the foreign continuum can essentially be viewed as increasing the height at which a micro-window becomes saturated. However, in the upper troposphere, the change in water vapor as a function of temperature is largely the same for all profiles. Accordingly, we would expect the change in emission temperature (and thus OLR) due to the inclusion of the foreign continuum to be similar for all profiles with saturated lower/middle troposphere. In the longwave atmospheric window between 800 and 1200 cm−1, where the optical depth of water vapor lines is small, we see a foreign continuum response to increasing WVC similar to that observed for the self-continuum. However, this is lower in magnitude due to the smaller foreign continuum coefficients (seeFigures 1a and 1b). Also, the change in the contribution of the foreign continuum with WVC is less than that of the self-continuum, as the scaling of the foreign continuum optical depth is linear with water vapor partial pressure and not quadratic (as is the case for the self-continuum).
 For SDR, as a result of the increased saturation of micro-windows in both the pure rotational and primary bending bands in the lowest layer of the atmosphere, the foreign continuum contribution lessens once WVC reaches a particular value (Figure 9d). This explains the trend seen in Figure 5d, where the continuum contribution increases as a function of WVC in dry atmospheres, but eventually decreases as WVC further increases and the micro-windows become saturated. This decrease is partially counteracted by the opposite relationship that occurs between 800 and 1200 cm−1, where the contribution of the foreign continuum increases with WVC. However, due to overlap with the self-continuum, the foreign contribution, as a function of WVC, levels out at higher column amounts in the window.
 The SWA of the foreign continuum is also affected by saturation within the water vapor bands and thus a decrease with increasing WVC is seen within some of the stronger water vapor bands (i.e. <8,000 cm−1 in Figure 9f). However, at the edge of the water vapor bands, and within the weaker bands (i.e., above ∼10,000 cm−1), SWA is seen to increase with WVC. Thus, overall, as WVC increases these two effects almost cancel each other out; this leads to little change in SWA of the foreign continuum once WVC is above 10 kgm−2 (Figure 7d).
3.2.5. Heating Rates
 So far our attention has been focused on fluxes at the top and bottom of the atmosphere. It is also possible that some of the differences between BPS and MT CKD, as well as the uncertainty estimates associated with the BPS continuum, could alter the distribution of radiative energy in the atmosphere in ways not captured by this analysis. In the longwave, the heating rate pattern of the continuum in standard atmospheres has been previously discussed in some detail [Clough et al., 1992; Paynter and Ramaswamy, 2011; Schwarzkopf and Ramaswamy, 1999]. Accordingly, we will limit our discussion to the nature of the global response and the differences between MT CKD and BPS.
 Longwave cooling is shown in Figure 10, which has a similar layout to Figures 2, 4 and 6, but shows zonal averaged cooling rates. In the longwave, the self-continuum greatly increases the cooling rate in the lower troposphere between 20° south and 20° north, by up to 1 K/day (Figure 10c). Contrasting this to the line-only case (Figure 10a), it can be seen that the continuum is responsible for ∼33% of the cooling in the lower troposphere. This cooling is highly coupled to the amount of water vapor in the atmosphere, and thus dramatically decreases with both altitude and latitude. It is notable that, despite its strong dependence upon WVC, the self-continuum makes an important contribution to atmospheric cooling (i.e. >0.1 K/day) at nearly all latitudes, with exception of those above 70°. In the tropics and midlatitudes the self-continuum also leads to some cooling in the middle troposphere, in addition to that seen nearer the surface.
 The inclusion of the foreign continuum leads to a cooling in the upper troposphere and a warming below. This is similar to the results seen by others [Schwarzkopf and Ramaswamy, 1999] and implies that, unlike the self-continuum, the foreign continuum redistributes energy in the atmosphere; the variation in cooling with latitude is also far less than that observed for the self-continuum. This follows on from the discussion inSection 3.2.3 about why the foreign continuum contribution is much less sensitive to WVC.
 In terms of OLR and SDR our analysis shows that in the midlatitudes and tropics the self-continuum has a greater influence on both the uncertainty and the differences between MT CKD and BPS than the foreign continuum. However, a similar result is not seen with respect to the cooling rates. Even in the most humid regions, the differences between BPS and MT CKD are less than 0.1 K/day. This value is generally comparable to the uncertainty as estimated by the BPS model seen in the upper troposphere caused by the foreign continuum. This may be explained by the argument that the increased thermal mass of the lower troposphere makes it more stable to changes in flux compared to the upper troposphere. Correspondingly, the uncertainty in the lower troposphere is also smaller than that seen in the upper troposphere.
 In the shortwave (Figure 11), we observe that the water vapor line heating rate (Figure 11a) is fairly constant throughout the middle and lower troposphere. This is brought about by the increasing contribution of weaker bands [Ramaswamy and Freidenreich, 1991] compensating for the decreasing contribution of the stronger bands in the lower atmospheres. The shortwave continuum, similar to the longwave, is split between the foreign continuum contribution in the middle/upper troposphere (Figure 11d) and the larger self-continuum (Figure 11c) contribution in the lower troposphere, although the contribution of self-continuum is much smaller than in the longwave case. Accordingly, it can only be seen as contributing meaningfully to the heating rates between 30° north and 30° south.
 Unlike in the longwave, in the shortwave it is the self-continuum which dominates the differences between MT CKD and BPS (Figure 11e), as well as the uncertainty as estimated by the BPS model (Figure 11f). This demonstrates that the self-continuum between the bands in the 4000–5000 cm−1 and 5600–7000 cm−1 regions plays an important role in determining the lower atmosphere heating rates within the tropics.
3.3. Changes in Temperature and Water Vapor
 This section describes how the contribution of the water vapor continuum is affected when either WVC or temperature are increased. The response to an idealized, uniform 3 K rise in temperature is investigated, with a water vapor increase brought about by holding the relative humidity constant at all levels of the atmosphere during this temperature change. To understand the role of each, we have investigated the impact of a change in water vapor while keeping temperature constant and vice versa. Like in the previous section for the shortwave calculations, a zenith angle of angle of 60° and a zero albedo are assumed. By holding relative humidity constant we do not capture the effects of a small WVC increase in a warm climate or a large WVC in a cold climate.
3.3.1. Water Vapor
 In Figure 12, the changes in flux are presented as functions of the change in WVC (with temperature held constant). Figure 12a shows the reduction in OLR without the continuum and demonstrates that the sensitivity of OLR to an increase in WVC levels out for larger changes, which occur in the most humid atmospheres. The reduction in OLR due to the continuum is shown in Figure 12b and demonstrates that the continuum is almost as significant as the water vapor lines for changes in WVC. Here, the uncertainty in flux resulting from the uncertainty in the continuum is also plotted and remains small for all changes in WVC.
 The sensitivity of SDR (Figure 12d) to changes in WVC means that, once the change in WVC is greater than 3 kgm−2, the continuum actually contributes more than the water vapor lines alone (Figure 12c). For changes below 6 kgm−2, the response of the continuum is largely proportional to the change in WVC, although this levels out for higher column changes. This is because in humid atmospheres the lowest level of the atmosphere is saturated in many spectral regions (which, due to their higher temperatures, experience the largest change in WVC).
 The SWA response of the continuum (Figure 12f) also largely increases in proportion to the change in WVC and in all atmospheres is smaller than the response of the lines alone. However, for the largest water vapor changes, it does account for ∼20% of the increase in SWA. In this case, because of the large difference between the upper and lower limits of the BPS continuum we have plotted the change in SWA due to both. As noted earlier, the measurements of Ptashnik et al.  suggest that this lower limit estimate is now fairly unlikely, with the continuum being nearer to the upper estimate instead. If this were the case, then the continuum could account for 40% of the increase in SWA due to water vapor observed in tropical atmospheres.
 In this section, we raise the surface and atmospheric temperatures uniformly by 3 K, but keep WVC constant. Without the continuum, the change in OLR as a function of surface temperature is almost linear (Figure 13a; note in Figure 13 the x axis represents surface temperature). The effect of the continuum upon the change in flux resulting from a 3 K rise in temperature is smaller than the effect of the water vapor change described above.
 The continuum affects the longwave response to a change in temperature in two ways (which we will here term the first and second effects). The first effect occurs because inclusion of the continuum in the radiative transfer calculations can cause a change in the altitude from which radiation is emitted to either the surface or top of the atmosphere. For instance, consider the radiation emitted by two layers of the atmosphere which have the same optical depth but different temperatures. It follows from Planck's law that when the temperature of each layer is increased by 3 K, there will be a larger change in flux emitted by the warmer layer than by the colder layer. Hence, by virtue of the continuum altering the altitude, and thus the temperature at which radiation is emitted to either the surface or to space, it also alters the change in flux brought about by a 3 K temperature increase. Assuming a normal lapse rate, this means that the continuum will result in a smaller increase in OLR (i.e., an increased altitude of emission), but a larger increase in SDR (i.e., decreased altitude of emission), compared to the case where it is not present.
 The second effect occurs through the temperature dependence of the continuum, which causes a change in optical depth and thus a change in the emission level. The self-continuum coefficients have a strong inverse temperature dependence, while the foreign continuum coefficients are only sensitive to changes in the water molecule number density and thus also have a slight inverse temperature dependence. This leads to the opposite of the first effect occurring, because the continuum optical depth will decrease with increasing temperature, resulting in an increase in OLR, but a decrease in SDR compared to when the continuum is not present.
 Our results show that the first effect is clearly dominant and that the continuum appears to slightly lessen the increase of OLR (Figure 13b). The largest decreases occur in the warmest and most humid atmospheres and this provides convincing evidence that the continuum causes emissions to occur from colder layers in the atmosphere (than would be the case if there were no continuum), making the change in the Planck function smaller.
 Generally a similar situation exists for SDR (Figures 13c and 13d), where the effect of the continuum is greatest in the warmest and most humid atmospheres. In these cases, the continuum causes emissions to occur from warmer layers in the atmosphere, making the change in the Planck function larger (i.e., the first effect is most influential). However, in the midlatitudes, the second effect appears to win out, causing a small (i.e. <2%) decrease in how much SDR rises. This is most pronounced over hot, but relativity dry, areas (such as the Sahara Desert). In these regions, due to its squared dependence on vapor pressure, the self-continuum optical depth is much smaller than in the tropics, which diminishes the first effect. Conversely, the second effect is increased, because the smaller optical depth of the continuum means that the transmittance function is now more sensitive to changes in the optical depth of the continuum.
 Overall, it can be concluded that while in most cases the first effect dominates the second effect, for both SDR and OLR the presence of the continuum does not significantly alter the atmospheric response to a temperature increase.
 In the shortwave, the changes in absorption due to temperature changes are solely a function of the molecular properties of the gases present. Although complex, these are normally very small and, accordingly, the SWA exhibits a weak temperature dependence without the continuum (Figure 13e). The self-continuum has a stronger temperature dependence than the other absorbing gases, but still only produces a relatively weak change in SWA due to temperature changes (Figure 13f). This change is greatest in the most humid and warmest atmospheres, where the self-continuum is strongest.
3.4. The Continuum and CO2
 There are overlaps between the CO2 and water vapor (lines and the continuum) spectra and these are most significant in the 500–800 cm−1 region. Kiehl and Ramanathan  (KR1982) showed that the self-continuum reduces the SDR considerably due to a doubling of CO2, as it is reabsorbing most of the additional downwelling flux. Due to increased water vapor content, this effect was observed to be greater at the tropics than at higher latitudes. However, when calculating OLR, the continuum was shown to have a much lesser effect, since most of the emission from CO2 is above that of the continuum.
 It is of interest to perform a similar experiment using the BPS continuum (self and foreign) and, more importantly, to see how uncertainty in the continuum affects the results. This analysis is presented in Figure 14. Figures 14a and 14c show the changes in OLR and SDR respectively, due to a doubling of CO2, when only the overlap with water vapor lines is taken into account. Figures 14b and 14d respectively show the additional changes in OLR and SDR when the overlap with the BPS continuum is taken into account.
 We cannot compare our results directly to those in KR1982, as they were presented for averaged cloudy conditions and used the Roberts et al.  continuum model. However, we observe a similar response to that in KR1982, as described above.
 The uncertainty as estimated by the BPS continuum results in up to a ±3% uncertainty in the change in OLR due to a doubling of CO2. The greatest impact of this uncertainty is observed in the most humid atmospheres (Figure 14e). Although a ±3% uncertainty is smaller than the expected accuracy of CO2 radiative forcing, as calculated by GCM radiation codes [e.g., Collins et al., 2006], it is comparable to that expected from LBL calculations. The same calculation performed for SDR reveals an estimated uncertainty of up to ±15% (Figure 14f). The effects of the uncertainties in the continuum upon O3, CH4 and N2O forcings have also been investigated, but were found to be very small (i.e. <1%) and therefore are not reported here.
 This paper has analyzed the influence of the water vapor continuum upon both longwave and shortwave radiative transfer, using ERA-40 data to simulate a range of typical atmospheres found on earth. For these atmospheres we show that the self-continuum contribution to the OLR, SDR and SWA is almost proportional to WVC. In contrast, the foreign continuum contribution to OLR and SWA remains fairly constant once WVC reaches ∼10 kgm−2and, in the case of SDR, actually decreases as WVC increases. An interesting by-product of this analysis is that we demonstrate that the contribution of the BPS continuum, as well as its associated uncertainty and its differences from MT CKD 2.5, can be estimated to a reasonable degree of accuracy (∼ within 10%) for any atmosphere, provided that the surface temperature and WVC are known. As we have continually stated throughout the paper, uncertainty in the SWA between the bands is a major problem. One positive aspect of our analysis is that, regardless of what model was chosen to represent the self-continuum, the response as a function of WVC was found to be very similar. This suggests that even if the continuum coefficients are larger than those estimated by BPS, the effect of this would not lead to unpredictably large levels of additional absorption.
 In addition, the range of values obtained between the upper and lower limits of the BPS continuum suggest that both global and regional energy budgets can be slightly affected by uncertainty in the continuum. Uncertainty in the continuum, as estimated from the range between the BPS upper and lower limits, results in a globally averaged 1 Wm−2 uncertainty in OLR, with a maximum value of 3 Wm−2 (∼1% of OLR) occurring in tropical regions. SDR is marginally more affected by uncertainty in the continuum and we calculate a globally averaged value of 1.9 Wm−2, with a maximum of 6 Wm−2 (∼2% of total SDR). For SWA, the globally averaged uncertainty is 1.3 Wm−2, with a maximum estimated value of 3.6 Wm−2 (∼6% of total water vapor SWA). As highlighted in Section 3.1, these uncertainties are relatively small compared to those associated with GCMs or satellite measurements, but are large in comparison to the impact of uncertainty in other spectral data used in radiative transfer calculations. For instance Kratz  showed less than 0.3 Wm−2 variation in both SDR and OLR between HITRAN 2004 and 2000 (although these calculations were only performed for SAW and TRO standard atmospheres). However, as we stated in the methodology section, these uncertainty values should be viewed as estimates. The lack of continuum measurements for all atmospherically relevant spectral regions and temperatures means that it is still not possible to place hard upper or lower limits upon the continuum. Therefore, presently we are forced to estimate how measurement uncertainty propagates to these unmeasured temperatures and spectral regions. This highlights that the community needs to strive to make high quality measurements of the continuum, in both the longwave and shortwave, at all atmospherically relevant temperatures.
 There is a substantial influence by the continuum upon the changes in SWA, OLR and SDR in a warming climate. In idealized experiments we investigated the radiative impact of the continuum when temperature and water vapor were increased independently. For the change in water vapor we show a globally averaged 0.35 Wm−2 reduction in OLR for every additional kgm−2 increase of water vapor in the atmosphere. The increase in SDR (1 Wm−2 per kgm−2) due to the continuum is stronger than the increase in OLR, but this tapers off for large changes in WVC. The SWA response is weakest at 0.15 Wm−2 per kgm−2. In the SWA case, the uncertainty as estimated by the BPS model is almost as large as the response, but for the longwave variables, the effect of uncertainty was nominal. This highlights the importance of reducing uncertainty in the shortwave continuum if we are to quantify the shortwave response to a warming climate.
 The authors wish to thank three anonymous reviewers for their detailed comments, which have helped to considerably strengthen the paper. They also wish to thank Jenni Paynter for help proofing the manuscript on numerous occasions. D.J.P. received funds from the Princeton AOS Postdoctoral and Visiting Scientist Program.