Instantaneous surface Cloud Radiative Forcing (CRF) in the 7.5–13 μm region is observed for the first time, using a thermal infrared camera. The sampling of clear sky and cloudy radiances from images of broken cloud fields allows cloud cover, CRF and effective cloud emission to be directly calculated, all within a consistent field of view. Analysis of 1300 images taken over more than two months in Central England shows that surface CRF is a nonlinear function of cloud cover, with daytime forcings larger and less linear than those at night. This nonlinearity is caused both by the increase in cloud optical thickness and the more frequent occurrence of low altitude (warm) cloud as the cloud cover increases. Even for nearly complete cloud cover, effective cloud emission remains significantly less than that of widely assumed homogeneous, optically thick cloud. Possible clear sky sampling errors associated with traditional methods of measuring CRF are also investigated.
 The radiative impact of clouds on the Earth's surface is an important factor in determining the climate. It can be quantified in terms of the surface Cloud Radiative Forcing (CRF), which is the change in radiative flux occurring when clouds are introduced into a clear atmosphere [Ramanathan et al., 1989]. During the day, the total CRF is the sum of a longwave (LW), terrestrial component (CRFLW), which warms the surface, and a shortwave solar component, which has a cooling effect. At night, the absence of sunlight means that all forcing is provided by CRFLW. Several studies in recent years have observed surface CRFLW, showing significant and consistent nonlinearity as a function of cloud amount (c), despite their differing methods and climatologies [Shupe and Intrieri, 2004; Dong et al., 2006; Town et al., 2007]. The study by Dong et al.  expresses this relationship as CRFLW = 61.6c1.71 Wm−2, and a similar analysis of results of Shupe and Intrieri  gives CRFLW = 55.2c1.49 Wm−2. These results indicate that climate sensitivity to clouds is greater for high c values than for low values. It is perhaps an unexpected result - if clouds are assumed to be optically thick and radiating at a constant temperature, then the LW flux emitted by the cloud field (Fcl) would simply be the fraction, c, of the flux observed when the cloud totally covers the sky (Fc). Against a clear sky flux Fs the surface CRF arising from this ‘black plate’ assumption would be:
If (Fc − Fs) remains independent of cloud cover, a linear relationship between cloud amount and CRF would thus be produced. Model cloud schemes may also have problems capturing the nonlinearity and magnitude of CRFLW, because they use gridbox-averages of cloud optical thickness to calculate fluxes. This produces an overestimate of the average shortwave cloud albedo [Cahalan et al., 1994], and by inference the LW cloud emissivity as well. Hence an ‘effective emissivity’, similar to the shortwave ‘effective optical thickness’ suggested by Cahalan et al.  should be considered.
 No explanation of the observed nonlinearity between CRFLW and cloud amount has so far been suggested. There are difficulties in measuring CRFLW – extensive time averaging is employed and the clear sky flux Fs must be inferred either from monthly averages of fluxes on separate clear days, or from the use of radiosonde profiles and a radiative transfer model. In this study, we directly measure instantaneous CRF in the 7.5–13 μm region for the first time. We identify two main contributions to nonlinearity, and show significant differences between CRF during the day and the night.
 Automated cloud detection using single images from an infrared camera has been demonstrated previously [Shaw et al., 2005; Thurairajah and Shaw, 2005]. This ability is extended by Smith and Toumi  (hereinafter referred to as ST08), allowing hemispherical cloud cover and radiative fluxes to be measured directly. Images are taken covering an 80 × 60° field of view, extending from 10° past the zenith at the image top to the horizon at the bottom, and giving pixel brightness temperature accuracies of ±0.1 K (full calibration and experimental details are given in ST08). A dataset of over 17,000 images has been collected at the UK Meteorological Office Research Site in Cardington, Bedfordshire, with the camera facing in an easterly direction between 16 February and 27 April 2007. Apart from breaks during periods of rain and short maintenance checks, images were taken every five minutes. Since ST08, the threshold cloud transmittance value for identifying cloud has been changed from 0.5 to 0.7. This gave greatest agreement with cloud fraction estimates from an operating ceilometer at the site after approximating horizontal cloud fraction by taking 15-minute averages of cloud cover [Kassianov et al., 2005].
 As part of the cloud detection process two bounding brightness temperature curves are inferred, representing the variation of clear sky (Ts(θ)) and optically thick cloud (Tc(θ)) with zenith angle (see ST08). These are converted via the Planck function into radiance curves (Is(θ) and Ic(θ) respectively) which can then be integrated over the hemisphere to provide instantaneous Fs and Fc values. Similarly, all the individual pixel radiances can be summed and weighted by angle to provide the cloudy flux, Fcl. A further metric measurable from the images and of use for the CRF discussion is effective cloud emission, ɛeff. Effective emission is defined here as the fractional emittance of a cloud field relative to its maximum emittance (i.e. the fitted curve Ic(θ)), averaged over all the cloudy pixels. For a total number of cloudy pixels Np, each at zenith angle θp and radiance Ip, ɛeff is therefore calculated as:
In a similar way to the cloud detection method, this calculation has only been carried out for pixels at zenith angles up to 80°, beyond which clear/cloudy radiances become hard to distinguish (see ST08). ɛeff is a measure of mean cloud emissivity, but unlike a true emissivity it is sensitive to temperature changes in the cloud field as well as variations purely in optical thickness.
 Some final considerations have been made in order to select the most reliable images for the analysis. First, if the difference between Is(θ) and Ic(θ) is small, the image is either fully clear or fully cloudy. A threshold difference of 5 Wm−2 sr−1 was chosen as giving greatest agreement with the ceilometer data and accounting for pixel noise. The cloud detection process is therefore reliable for low, liquid water clouds, but may not detect all higher cirrus clouds which emit less against the background sky (this will be discussed in conclusion). Second, it is especially important that areas of higher, thin cloud are not mistaken for clear sky, introducing an error into the Is(θ) curve fitting process. For this reason, the cloud transmittance threshold was used to select images with cloud cover from one to seven oktas (0.125 < c < 0.875), and <5% uncertainty in the fitted zenith sky radiance. The analysis thus involves 1300 images. Finally, Is(θ) curve fitting is biased towards the minimum brightness temperatures at all angles, so all pixel radiances are equal to or greater than the curve values. This creates a positive forcing value even for totally clear images (CRFclear), which has been calculated for all clear images in the dataset as 4.7 Wm−2 on average, with a standard deviation of 1.9 Wm−2. For each CRF value calculated from a cloudy image in the dataset, the clear sky in view is (1 − c), and so we subtract 4.7(1 − c)Wm−2.
 Conversion from 7.5–13 μm CRF to CRFLW would require knowledge of the atmospheric water vapour content and cloud liquid water path in each pixel's view. Direct comparison with previous studies is therefore difficult, however an Antarctic study by Town et al.  showed that surface CRF across the 8.3–9.1 μm and 10.5–12.5 μm bands accounted for about one third of the total LW monthly mean.
 Surface CRF in the 7.5–13 μm region is plotted as a function of c for all images in Figure 1 (left). As with Dong et al. , a least squares fit is applied to give a geometric relationship of CRF = 32.3c1.37 Wm−2, with 1-σ uncertainties of 0.7 Wm−2 and 0.05 in the magnitude and exponent respectively. We conclude that cloud forcing does depend on the presence of cloud in a nonlinear way, although not as much as is found by Dong et al.  or Shupe and Intrieri . The large dataset and lack of time averaging allow our CRF measurements to be categorised by time of day. In Figures 1 (right) and 1 (middle), images are divided into 7 am–7 pm and 7 pm–7 am periods, representative of local daytime and night time, respectively. Significant differences are apparent, with average day forcing, CRF = 37.5(1)c1.48(6)Wm−2, greater and less linear than average night forcing, CRF = 26.9(8)c1.28(7)Wm−2 (values in brackets indicate 1-σ uncertainties in the final decimal place).
 The role played by variation of cloud altitudes in determining the overall relationship between surface CRF and c can be investigated. Low cloud typically exerts a greater forcing at the surface than high cloud, because of its greater temperature contrast against the clear sky. Each image was determined to contain low cloud if the change in fitted cloud brightness temperatures from horizon to zenith (Tc(90°)–Tc(0°)) was <10 K. (This value was selected by modelling brightness temperatures using SBDART [Ricchiazzi et al., 1998], inserting cloud layers with an optical thickness of 50 at an altitude of 2 km into model mid-latitude summer and winter atmospheres [Anderson et al., 1986]). As a result, low cloud is found in 76% of images. It is found to be more frequently associated with large cloud cover, whereas images in the dataset containing high altitude clouds show a frequency approximately independent of c. To quantify the impact of this change in relative frequencies on forcing, Figure 2 (left) shows CRF versus c for images containing low cloud only. The resulting fit of CRF = 37.5(7)c1.12(4)Wm−2 is still significantly nonlinear, but less so than the all cloud analysis. Hence the inclusion of all clouds contributes around 0.25 to the exponent of nonlinearity describing CRF in this study. When low cloud is separated into day and night (Figures 2 (middle) and 2 (right), respectively) the CRF for the low cloud is less during the night (33.5(9)Wm−2) than during the day (40.0(8)Wm−2). Also, the nonlinearity exponent of 1.24(7) for the night time low cloud is comparable to that for all clouds (1.28(7), cf. Figure 1 (right)) whereas the daytime low cloud gives a relatively linear 1.10(4). High altitude clouds thus have more of an influence on daytime average CRF than they do at night.
 Another contributing mechanism to the relationship between CRF and c is variation in cloud emission, quantified by ɛeff. Using equation (2), ɛeff has been plotted against c for the overall dataset, and divided into day and night images (Figure 3). Clear increasing trends are apparent, to which lines of least squares linear regression have been fitted as a first order approximation. Solid lines show fits to all values in the plot, and dashed lines show regression to low cloud only. Despite small uncertainties shown in brackets, little difference is apparent between values of ɛeff for the two sets (although low cloud always shows slightly higher emission). Interestingly, none of the plots show expected convergence to ɛeff = 1 at c = 1, with the fit for the overall dataset being ɛeff = 0.32(1)c + 0.52(1), giving a correlation (r) coefficient of 0.40.
 ɛeff affects CRF in the following way: consider the black plate assumption described at the beginning of the chapter. Equation (1) showed that this results in a linear CRF with cloud amount, provided the mean (Fc − Fs) is independent of c. However, Figure 3 demonstrates that the cloud layers in reality are neither uniform nor black. Instead, they thicken optically as they grow in extent. The impact of this emission increase on CRF can be approximated by modulating Fc by ɛeff. CRF is then a function of cɛeff, or c(0.32c + 0.52) for the overall dataset. By least squares fitting this yields a non-linear relationship equivalent to CRF = 0.83c1.27(Fc − Fs). This is only an approximation, because our calculation of ɛeff does not include the zenith angle weighting involved in calculating fluxes. Daytime cloud, where ɛeff = 0.35(1)c + 0.52(1), has a higher emission and a steeper gradient than night time cloud, where ɛeff = 0.31(1)c + 0.48(1), implying that clouds during the night tend to be less homogeneous and optically thinner (Figure 3). Despite this, both lines give rise to similar nonlinearity exponents (<1.27) when applied to the black plate assumption.
 The increased emissivity with cloud amount is in agreement with top-of-atmosphere infrared studies by Luo et al.  and Barker and Wielicki  despite differences in spatial resolution (4 km and 60 m respectively, compared to several metres or less in this study). We observe a smaller gradient, probably because the data are sensitive to the cloud threshold [Barker and Wielicki, 1997], and in our case pixels are only included if their ɛeff > 0.3. Confirmation that cloud altitude and emission are the main two sources of nonlinearity can also be inferred from the study of Stubenrauch et al. . These cloud emission and altitude effects have now, for the first time, been directly related to the observed nonlinearity in surface CRF.
 Finally, the average difference between fluxes from optically thick cloud and clear skies (Fc − Fs) is investigated. The previous black plate assumption held this to be independent of c, but systematic changes in Fs with c are a known potential source of error [e.g., Sohn et al., 2006] for all CRF studies in which clear sky is sampled at different times or places to cloud measurements. Our method simultaneously infers Fc and Fs, making it more reliable than previous methods and allowing us to quantify their associated error. Figure 4 shows a plot of all clear sky fluxes (triangles) and optically thick cloudy fluxes (crosses) as a function of cloud cover. Least squares linear regressions give Fs = 1.32(2)c + 58.83(1)Wm−2 and Fc = 4.05(1)c + 108.23(1)Wm−2, indicating a slight increasing trend with cloud cover, but very little divergence in (Fc − Fs). This trend in Fs with c is consistent with the fact that clear sky fluxes and cloud amounts are both dependent on the concentration of water vapour in the atmosphere, however the total change in Fs is small (1.3 Wm−2, or 2%). Fractional errors for broadband measurements are likely to be smaller still, suggesting that sky variation is a negligible error source. The larger increase in Fc can be explained by the association of high c with low cloud.
 This study shows the applicability of thermal infrared cameras to surface cloud radiation research. A set of 1300 images taken in Central England between 16 February and 27 April 2007 reveals the following: (1) Instantaneous surface CRF in the 7.5–13 μm region follows the form CRF = 32.3c1.37 Wm−2, where c is cloud cover. This significantly nonlinear behaviour is in agreement with previous broadband LW studies [Shupe and Intrieri, 2004; Dong et al., 2006; Town et al., 2007]. (2) The causes of deviation from linearity in CRF are found to be two-fold: first, large cloud amounts tend to be associated with the presence of low clouds, which exert a larger surface CRF than higher clouds. Secondly, emissivity increases with cloud cover, and this is quantified using an ‘effective cloud emission’ parameter, ɛeff. Our relative insensitivity to high (cirrus) cloud may have reduced our measured ɛeff slope for all clouds and our fitted exponent for average CRF, but it does not affect results given for low cloud only, nor the evidence for CRF nonlinearity being due to these two causes. (3) Linear regression yields ɛeff = 0.32c + 0.52 on average, meaning that ɛeff only reaches 0.84 (0.85 for low cloud) even for total cloud cover. These values could be applied to LW model cloud schemes as the equivalent of the shortwave ‘effective optical thickness’ [Cahalan et al., 1994]. (4) Significantly greater average forcing is found for local hours of daytime due to optically thicker cloud emitting with a greater contrast in flux against the background sky compared to that at night. Daytime forcing is also less linear because of the greater influence of cloud at higher altitudes.
 We thank the staff at the UK Met Office in Cardington for their assistance and Matthew Shupe for providing the SHEBA results contained in his 2004 paper. This work was funded by the UK Natural Environment Research Council, grant NER/S/E/2004/12134.