Changes in atmospheric relative humidity in concert with temperature changes in a future climate may have large consequences for the water vapor feedback, the hydrological cycle, and its interaction with weather systems. This study contributes to the basic understanding of the relationship between temperature and humidity by investigating the processes leading to synoptic-scale covariations of the two variables close to the ocean surface. Daily data from in situ observations between 10°S and 50°N and global ERA-Interim reanalyses are used. Correlations between temperature and both specific and relative humidity are calculated. The results from the two data sets appear to be greatly consistent. They show strong anticorrelation between temperature and relative humidity (RH) in the inner tropics with minimum correlation coefficients below −0.8. In midlatitudes, there are large areas where the correlation coefficient of temperature and RH is positive and greater than 0.6. The anticorrelation in the tropics is found to be related to convective precipitation, which, on the one hand, leads to local temperature decrease due to vertical mixing and reduction of solar radiation by clouds. On the other hand, rainfall is associated with an increase in boundary layer RH. Over the midlatitude ocean, daily temperature variations are mainly controlled by meridional transport, as shown with the help of backward trajectories. Moreover, advection of cold air typically goes along with vertical moisture transport, either due to large-scale subsidence or turbulent mixing, causing a reduction of near-surface RH. All together, this dynamical effect induces the positive temperature-RH correlation.
 Variations in atmospheric water content close to the ocean surface have important consequences for atmospheric circulation and climate. For example, they trigger or suppress moist convection [Sherwood, 1999; Bretherton et al., 2004; Zelinka and Hartmann, 2009] and influence air-sea interaction [Lorenz et al., 2010] and, in this way, the moisture supply for the atmospheric water cycle in general. However, the processes causing such humidity variations on different timescales are often complex and not yet fully understood. A widely applied approach for addressing this issue is to analyze the covariability of atmospheric moisture content with air or sea surface temperature [e.g., Stephens, 1990; Dai, 2006]. By this means, variations of humidity can be linked to temperature changes, which can be measured and often also explained in a more straightforward way. Moreover, understanding this covariability is essential for assessing humidity changes and, by this, the water vapor feedback and hydrological cycle in a warming climate [e.g., Willett et al., 2007; Sherwood et al., 2010; Lorenz et al., 2010].
 To first order, the constraint on saturation humidity given by the Clausius-Clapeyron equation (i.e., an approximately exponential increase of saturation vapor pressure with temperature) dominates the temperature-humidity relationship in observations [e.g., Trenberth et al., 2005; Dai, 2006] and also in GCM simulations of future climate scenarios [Manabe and Wetherald, 1975; Held and Soden, 2006]. This constraint is particularly strong if temperature changes are large [Lu, 2007] and water availability is not a limiting factor. This suggests that relative humidity (RH) over the ocean should remain relatively constant on long timescales [Manabe and Wetherald, 1967]. Nevertheless, it is important to understand the processes leading to deviations from this first-order relationship, perceptible in terms of RH fluctuations. Long-term changes of RH are crucial for estimating the magnitude of future climate warming (see again Sherwood et al. ). On short, synoptic timescales, RH variations may, for example, affect the formation of fog or change surface evaporation patterns.
 Several types of observations have been used to investigate covariability of humidity and temperature over the ocean. Stephens  found a close Clausius-Clapeyron like relationship between precipitable water obtained from satellite retrievals and sea surface temperature on a monthly timescale. Deviations from this relation were shown to reflect large-scale atmospheric transport patterns. Gutowski et al.  followed a similar approach but used daily satellite observations and near-surface temperatures from analysis data. They focused on the first-order relation assuming constant RH. Sun and Oort  found a negative correlation between interannual variations of tropical mean temperature and RH on different vertical levels in the troposphere based on gridded radiosonde data. However, the strength of this correlation may have been overestimated owing to the sparse spatial sampling and the analysis procedure [Bauer et al., 2002]. Dai  analyzed a comprehensive data set of surface observations and found a strong relationship between temperature and specific humidity on an interannual timescale but only weak temperature-RH correlations.
 In this study, correlation analysis will be employed to temperature (T) and humidity time series close to the sea surface. The analysis will be restricted to oceanic data, since over land the limited water availability likely leads to additional complexities. In addition to in situ observations, ERA-Interim reanalysis data will be used for obtaining a more complete picture in time and space, covering the major part of the global oceans. The analysis of T-RH covariability will be emphasized in order to detect deviations from the first-order Clausius-Clapeyron relation. Furthermore, unlike in most of the studies cited above, the focus here will be on relatively short-term, daily variations. In this way, the influence of synoptic-scale weather processes on T-RH correlation can be explored in a more straightforward way than by analyzing temporal averages over extended periods. All together, the main objective of this study is the identification of atmospheric processes leading to daily covariations of temperature and RH over the sea.
 In section 2, data and methods are described that are used in this study. Section 3.1 presents the results of the correlation analysis. The most important processes related to the emerging correlation patterns in the tropics and midlatitudes are investigated and discussed in sections 3.2 and 3.3, respectively. Section 3.4 contains a short note on the influence of ocean evaporation on temperature-humidity covariability. Finally, section 4 summarizes the conclusions of the study and presents a brief outlook on future research opportunities.
2. Data and Methods
 Two types of data are used for the correlation analysis performed in this study, in situ observations and atmospheric reanalyses. Air temperature and dew point temperature close to the ocean surface as well as sea level pressure observations have been obtained from the ICOADS Release 2.5 data set [Woodruff et al., 2010], a collection of quality-controlled marine surface observations. This quality control includes the elimination of unphysical data, referring to predefined physical limits for each variable, and outliers (data with a deviation of more than 4.5 standard deviations from a 2-degree grid box climatology have been rejected). Measurements during the years 1989 to 2007, the overlap period between ICOADS 2.5 and the ERA-Interim reanalysis (see below) have been taken into account. A large part of the ICOADS data set consists of observations from ships and drifting buoys, which do not refer to a fixed location in space and could thus not be used for the time series analysis. In order to avoid any transport effects and obtain strictly Eulerian correlation coefficients, no gridding of the data has been performed, but time series at certain locations, as provided by fixed platforms like moored buoys and ships, have been extracted from the data set. A maximum deviation of 0.01° in longitude and latitude has been allowed for two measurements to be attributed to the same position. Since the data set is archived in a chronological way (and not with respect to measurement position), finding sufficiently long time series at fixed locations is rather costly. Hence no complete rearrangement of the data, but only a limited selection of time series has been performed. Specific and relative humidity have been calculated for the selected data following Dai . Daily averages of specific humidity (q), RH and T have then been computed by first averaging measurements between 00:00 and 06:00 UTC, 06:00 and 12:00 UTC, 12:00 and 18:00 UTC, and 18:00 and 00:00 UTC and afterward calculating the mean of these four values. Only days with at least one observation in each 6-hourly time window have been kept for further analysis. All time series have been checked visually in order to exclude gross inhomogeneities in the data. The daily values have been grouped according to the season of observation, i.e., four groups with measurements in December to February (DJF), March to May (MAM), June to August (JJA), and September to November (SON) have been compiled. Finally, Pearson correlation coefficients between daily T and q as well as T and RH time series have been calculated separately for each season. In addition, Spearman rank correlation coefficients have been computed in order to check if the results depend on specific statistical characteristics of the data distributions.
 In Figure 1 the geographical positions of the selected observation sites are shown. Most of them are located close to the North American and European coast over the North Atlantic. There are a few stations over the North Pacific off the United States and Japanese coast and five stations in the tropical Pacific and Indian Ocean region. No measurements are available over wide regions of the global oceans, e.g., in the Southern Hemisphere extratropics and over the central Pacific. In order to obtain a more complete spatial coverage, reanalysis data will be employed (see below). The colors in Figure 1 indicate the minimum number of daily observations in each seasonal group (i.e., min(nDJF, nMAM, nJJA, nSON), where, e.g., nDJF is the number of observations in DJF available at the site). At almost all extratropical sites (all sites north of 23.5°N), there is data for more than 200 days in each season. The number of tropical observations is more limited, there are four stations with less than 200 and one of them with less than 50 observation days per season at minimum.
 Marine observations of temperature and humidity may contain certain biases and errors, for example, owing to changes in instrumentation, solar heating effects or just measurement errors [Dai, 2006; Berry and Kent, 2009]. In addition to the quality checks performed by Woodruff et al. , a consistency check for the calculated RH values has been applied here, omitting all data with RH smaller than 0% or larger than 100%. No corrections of systematic errors have been attempted, on the one hand because correction methods of marine observations are complicated and designed more for preserving long-term changes with monthly means (for example, the correction of solar heating effects proposed by Kent et al. , which was used by Dai ). On the other hand, it is assumed that such errors are less likely to affect covariations within the data and thus the results of the present correlation analysis. Moreover, most of the possible systematic effects (e.g., changes of observation level) probably have a small magnitude compared to the day to day variability of the observations. Finally, a potential effect of outliers would be much greater for the Pearson than for the Spearman correlation statistics and would thus lead to deviations between the two methods.
 As a second data set, ERA-Interim reanalyses [Dee et al., 2011] of the European Centre for Medium-Range Weather Forecasts (ECMWF) are employed. These data are available from 1989 with a temporal resolution of 6 hours and a spectral resolution of T255 in the horizontal. For the period 1989–2009, ERA-Interim surface pressure and T and q on the lowest model level (about 10 m above the surface) have been interpolated to a 1° horizontal grid covering the global oceans, and RH has been computed. The lowest model level data are used instead of 2 m values because they are less influenced by assumptions on the vertical profiles of these parameters made in the boundary layer parameterization of the ECMWF model and because most ocean observations are taken at heights of around 20 m above surface [Berry, 2009]. Daily means of the variables have been calculated from five 6-hourly dates between 00:00 UTC and 00:00 UTC on the following day, reducing the weight of the 00:00 UTC data by a factor of 2. The data has been grouped according to season as described above. Pearson correlation coefficients have then been calculated separately for each season between T and q as well as T and RH time series at every grid point, taking all data in the reanalysis period into account. The computation of Spearman correlation coefficients is hardly feasible in this case due to the huge amount of data. Furthermore, monthly climatologies of all variables have been compiled at each grid point by averaging data in the specific month over the whole time series. Therewith, correlation coefficients have been computed between the complete daily and monthly averaged time series with monthly climatologies (i.e., the seasonal cycle) subtracted.
 The major advantage of the reanalyses compared to the direct measurements is their global coverage. The 4D-Var data assimilation system applied to produce the ERA-Interim data set makes use of a large amount of observations, including not only the fixed marine platforms described above but also data from moving ships. This variational assimilation approach is, as we think, the most physical way to obtain spatially distributed time series with high resolution and without averaging measurements in space. In spite of the good agreement of ERA-Interim with observational data sets on longer timescales [Simmons et al., 2010], the reanalyses may suffer from biases and errors, in particular in data-sparse regions over remote oceans. The data set might contain inhomogeneities owing to changes in the assimilation of different observation types and in the observations themselves. On the basis of the same arguments as outlined above for the measurement errors, these problems are thought to be of minor importance for the present correlation study. However, the quality of reanalyses is also sensitive to model errors to a certain extent, and this model may overestimate or underestimate specific processes in the atmosphere. This might lead to spurious correlations between temperature and humidity. Because of this, a combination of correlation results from direct observations and reanalysis, as pursued in this study, is thought to be the best way for overcoming drawbacks of both datasets.
 It should be noted that using statistical tests for determining the significance of correlation coefficients does not appear to be very useful here, since all time series analyzed in this study are relatively long. This is particularly the case for the reanalysis data but also for most of the observations. Therefore almost every correlation signal would be identified as statistically significant, and the test would not add much information. Hence the following analysis will be restricted to a quantitative investigation of correlation coefficients.
 For the analysis of processes potentially leading to T-RH correlations, some additional data will be taken into consideration in sections 3.2, 3.3, and 3.4. In section 3.2, precipitation estimates from the TRMM multisatellite precipitation analysis [Huffman et al., 2007] are used. Daily adjusted merged-infrared rain estimates for JJA 1999, available with a horizontal resolution of 0.25°, have been received. In order to obtain precipitation time series representative for three surface measurement sites over the western tropical Pacific and one over the western Atlantic, the data have been averaged over 4 times 4 grid boxes enclosing the respective locations. These averaged time series are again used for calculating correlation coefficients; therefore errors in the absolute rain amounts and in particular problems with the exact quantification of light rain events should not affect the analysis. Furthermore, precipitation and surface latent heat flux data have also been obtained from ERA-Interim short-term forecasts. Forecast steps between 6 and 18 hours have been used, omitting the first 6 h of each forecast because of potential model spin-up. Daily averages on a 1° horizontal grid have been calculated as described above.
 In section 3.3, results from kinematic backward trajectory calculations are employed. These trajectories have been computed using the tool LAGRANTO [Wernli and Davies, 1997] based on 6-hourly fields of three-dimensional wind velocity and other variables from the ERA-Interim reanalysis. Pressure, temperature, humidity, and potential temperature have been tracked along the trajectories. They have been started from the lowest three vertical levels of the reanalysis grid at the locations of four observation sites every 6 hours during MAM 2000 (respectively MAM 2004 for one of the sites) and calculated 3 days backward in time. Daily means of trajectory parameters have been obtained by averaging all 6-hourly trajectory data of a specific day using the same weights as for the other ERA-Interim variables. It should be noted here that LAGRANTO does not have a parameterization for turbulent boundary layer fluxes and simulates only the large-scale part of atmospheric transport as resolved by the ERA-Interim wind fields.
3. Results and Discussion
3.1. Correlation Pattern
 First of all, correlation results from observational data are examined. Figure 2a shows the Pearson correlation coefficients r between daily time series of T and q during DJF at the observation sites. Reddish (green-to-blue) colors indicate a positive (negative) correlation between the variables. At the extratropical sites, r is always larger than 0.6 and in most cases exceeds 0.8. In contrast, r at the five tropical sites over the Indian and western Pacific Ocean is much smaller in magnitude and mostly negative, with values between −0.4 and 0.2. In Figure 2b, the correlation between T and q is shown for the months JJA. Also in this season, r is strongly positive in the extratropics. Only at some sites over the western North Atlantic, it is smaller than 0.6. In the tropics, r is also positive, but, with a maximum slightly above 0.4, lower than at most extratropical sites. For MAM and SON, correlation patterns of T and q (not shown) are similar to those in DJF and JJA, with large positive values of r in the extratropics and values closer to zero in the tropics.
 In order to investigate deviations from the first-order T-q relationship, the DJF correlation between T and RH is shown in Figure 2c. Again, a strong difference between sites in the extratropics and in the tropical Pacific/Indian Ocean region can be observed. For the latter, r is negative and smaller than −0.6 in most cases. In the extratropics, r is mostly larger than 0.2, with maxima greater than 0.6 over the North Atlantic. There is only one extratropical site north of Japan with a negative correlation. In JJA, correlation coefficients between T and RH (Figure 2d) in the tropics are of the same magnitude as for DJF. In the extratropics, however, r is reduced, and most of the values are between −0.2 and 0.2. There are slightly more positive correlations close to Europe, and r is between −0.2 and −0.6 at some sites in the Gulf of Mexico and south of Japan. The T-RH correlation patterns in MAM and SON (not shown) strongly resemble the pattern in DJF (Figure 2c), with strong negative correlation in the Pacific/Indian Ocean region and larger values of r in the extratropics than in JJA.
 There are very little differences between the Pearson correlation coefficients shown in Figure 2 and Spearman correlation coefficients obtained from the same time series (not shown). This indicates that the results do not depend on specific properties of the statistical distribution of the data and that the influence of outliers is relatively minor (see again section 2).
 For obtaining temperature-humidity correlations in regions without long time series of in situ observations, ERA-Interim reanalyses are applied. Since it is not a priori clear how well these reanalysis data represent daily temperature and moisture variations over the ocean, they are first compared to observations. In doing so, it should be kept in mind that both data sets are not totally independent, since (parts of) the observations may have been assimilated in the reanalysis procedure. Figure 3a shows the Pearson correlation coefficient between daily temperature time series from measurements and ERA-Interim at the observation sites. All days with measurements at a specific site have been taken into account, and the reanalyses have been bilinearly interpolated to the measurement locations. Values of r are greater than 0.8 at most extratropical sites and larger than 0.6 everywhere else. In Figure 3b, correlation coefficients between RH from measurements and reanalysis are displayed. Slightly lower values as for T are obtained at some sites, but all except for three are still larger than 0.6. The smallest correlation emerges at the tropical site north of New Guinea where the number of observations is lowest (cf. Figure 1) and may thus be partly attributed to the rather limited statistics. Overall, daily variations of T and RH at the measurement sites are relatively well represented in the ERA-Interim data set. The performance of the reanalysis is better for T than for RH, which can be explained by the smaller spatial variability of T and by the larger susceptibility of humidity to measurement errors. Moreover, correlation coefficients in the tropics typically are slightly lower than in the extratropics, most probably owing to the greater importance of small-scale, convective atmospheric structures in the tropical boundary layer, which are not explicitly simulated, but have to be parameterized in the ECMWF model.
Figures 4a and 4b show the correlations of T and q from ERA-Interim data in DJF and JJA, respectively. An overall similar pattern with high positive values larger than 0.8 in middle and high latitudes of both hemispheres and lower values in the tropics can be observed in both seasons. Negative correlations occur in the inner tropics, with minima on the order of −0.4 in the western Pacific and Indian Ocean region in DJF. The patterns of r compare well to the correlation results obtained from measurements (cf. Figures 2a and 2b), also with regard to some regional features (e.g., the JJA correlation minimum in the Gulf of Mexico). Only the slightly negative values over the Indian and western Pacific Ocean in JJA appear to be somewhat too low compared to the results based upon in situ observations.
 The ERA-Interim correlation coefficients of T and RH time series in DJF and JJA are shown in Figures 4c and 4d, respectively. Again, there is a large difference between inner tropics, where r is strongly negative, and the extratropics, with positive r values in wide regions. The minimum of r in the tropics is below −0.8 in both seasons, but the negative values reach further to the north in JJA, in particular over the western North Pacific and North Atlantic. In the extratropics, there is a stronger seasonal cycle in r, with minima in the summer season of the respective hemisphere. In the Southern Hemispheric midlatitudes, there are huge areas with r greater 0.6 during JJA. The maximum correlation in the Northern Hemisphere does not occur in the winter season, but in MAM, as shown in Figure 4e. Absolute maxima of r with values larger than 0.8 occur close to the Antarctic coast during JJA. However, these values have to be interpreted with care due to the presence of sea ice in this region (which affects air-sea moisture fluxes within the reanalyses) and because spatial coverage with observations is very poor [Willett et al., 2008], which in turn means that ERA-Interim data are less well constrained. A small band with negative correlation coefficients occurs along many coast lines in the extratropics, e.g., in the Mediterranean during JJA. As before, there is a good correspondence between the correlation results from reanalyses and in situ observations (see again Figures 2c and 2d) regarding the general geographical pattern and the seasonal variability. There are certain regional features common to both data sets, e.g., the strong seasonal cycle of r in the Gulf of Mexico and south of Japan, and the anomalously small values over the Sea of Japan in DJF. The only noteworthy, but still relatively small difference occurs again over the tropical western Pacific, where r from ERA-Interim tends to be slightly more negative compared to the observation results.
 In order to investigate how these relationships differ over different timescales, Figure 5a shows the correlation between daily T and q from the reanalysis data for the whole year (i.e., not separated into different seasons). Calendar month averages (calculated over the whole time series at each grid point) have been subtracted from the daily data before computing r. The spatial pattern strongly resembles the seasonal results shown before. In Figure 5b the correlation of monthly aggregated time series of T and q is shown (again with the seasonal cycle removed). The pattern is similar as for the daily correlation, but the value of r in tropical and subtropical regions is generally larger. Figures 5c and 5d show the corresponding daily and monthly correlations between T and RH. Again, the spatial pattern in Figure 5c is resembling the seasonal results, with negative correlation in the inner tropics and positive values in the midlatitudes. The maxima of r in the Southern Hemisphere are larger than in the Northern Hemisphere. This indicates that this general pattern is robust and does not strongly depend on the specific data treatment. Also, the monthly correlation pattern looks similar to the daily coefficients, albeit more noisy and with slightly reduced absolute values of r (i.e., the other way round than for the T-q-correlation, where monthly values are larger, see above). This shows that the processes determining the daily covariations of T and RH may not be equally important for but still influence the variability on monthly timescales.
 In summary, the results presented in this section show that there is a strong positive relationship between daily variations of T and q over the vast majority of the global oceans. This positive correlation corresponds to the first-order constraint given by the Clausius-Clapeyron equation (see section 1). Only in the tropics, there are regions where this first-order effect is less dominant and T-q correlations are smaller. This result is in agreement with the thermodynamic arguments given by Lu , who showed that the Clausius-Clapeyron constraint is stronger the larger the temperature variation (simply due to the strong nonlinearity in the equation). Here, this leads to greater values of r in the extratropics where the daily temperature variability is much larger than in the tropics. The fact that correlation coefficients between T and q are larger on monthly than on daily timescales indicates that the influence of the Clausius-Clapeyron constraint is stronger when timescales are longer, in agreement with the strong constraint found, e.g., by Dai . In order to quantify the deviations from the first-order relationship, correlations of T and RH have been analyzed. Strong anticorrelation between the two variables has been found in the inner tropics (the region with a weak T-q relationship). In the extratropics there are large areas with positive values of r. This positive correlation is weakest in the summer season of the respective hemisphere. Both correlation and anticorrelation signals are robust, and there is a very good agreement between results from reanalysis and in situ observational data. Sections 3.2 and 3.3 deal with the identification of the most important atmospheric processes related to the anticorrelation of T and RH in the tropics and the correlation of the same quantities in midlatitudes, respectively.
3.2. Processes in the Tropics
 The region with most pronounced anticorrelation between T and RH coincides with the intertropical convergence zone (ITCZ), not only by spatial extent but also with respect to seasonal variability. This gives a strong indication that the anticorrelation may be related to the precipitation intensity, which is by far higher within the ITCZ than in any other oceanic region. Also, the seasonal cycle of r in the Caribbean and over the Philippine Sea corresponds to the seasonal cycle of precipitation, which has a maximum in JJA in these regions [cf. Xie and Arkin, 1997]. Therefore TRMM rain estimates have been used to complement the statistical analysis in the tropics. Three observation sites in the western Pacific with almost complete data in the period JJA 1999 and strong anticorrelation between T and RH have been selected for this additional investigation (see Table 1). Furthermore, a site in the tropical western Atlantic without pronounced anticorrelation has been selected as reference. Precipitation time series at the four sites have been constructed as described in section 2. The results of the intercorrelation between T, RH and precipitation (RR) for JJA 1999 are shown in Table 1. Spearman rank correlation coefficients ρ have been calculated to account for the non-Gaussian statistical distribution of the precipitation data. The correlation between RH and RR is positive and in the same order of magnitude as the anticorrelation between T and RH at the three Pacific sites. T and RR are anticorrelated, with absolute values of ρ slightly smaller than for T-RH. This indicates that the relationship of both T and RH with daily precipitation intensity is crucial for their anticorrelation. At the reference station, both correlation coefficients with RR have a smaller magnitude, and ρ is closer to zero for T-RR than for RH-RR. This suggests that the influence of precipitation on temperature, or vice versa, is limited at this Atlantic site.
Table 1. Spearman Correlation Coefficients ρ Between T, RH, and Precipitation During JJA 1999 at Four Observation Sitesa
RR denotes precipitation.
 In order to explore the influence of precipitation in the reanalysis data set, composites of T and RH for days with and without precipitation (using 1 mm/d as threshold) have been produced for each season. It should be noted that the ERA-Interim precipitation applied here is not a real analysis variable but is obtained from short-term forecasts (see section 2), which might introduce small inconsistencies. Figure 6 shows the temperature difference between precipitation and nonprecipitation days for JJA in units of the daily standard deviation of T. In this way, the influence of RR on T can be quantitatively assessed in comparison with other local factors (which does not, as for the correlation coefficients, a priori indicate that this is also the direction of physical causality, though). Oceanic grid points where daily RR never exceeded 1 mm in JJA are masked in grey. There is a large area in the inner tropics with negative T anomalies, corresponding very well to the region of strong anticorrelation of T and RH (cf. Figure 4d). Positive T anomalies occur close to the Antarctic continent and in some tropical and subtropical regions where T-RH correlations are mostly weak. RH anomalies on precipitation days are positive for most oceanic regions, except for some coastal areas, the Mediterranean Sea and the western parts of the Arabian Sea and the Bay of Bengal (not shown). This composite analysis gives another strong indication that the negative T-RR relationship within the ITCZ is key to the anticorrelation between T and RH. The only other oceanic region where the occurrence of precipitation may significantly impact T-RH correlations appears to be the Southern Ocean close to the Antarctic coast. However, the presence of sea ice certainly plays a role there, as mentioned above, and more complex feedbacks than analyzed here may have to be considered for fully understanding the near surface T-RH relation.
 Most probably, the physical mechanisms leading to a positive relationship between RH and precipitation over the tropical oceans are twofold. On the one hand, an increase of boundary layer humidity typically precedes intense convective precipitation in the tropics and contributes to the initialization of the convection [Sherwood, 1999; Zelinka and Hartmann, 2009]. On the other hand, precipitation also triggers RH increase near the surface through saturated downdrafts in convective systems and the evaporation of hydrometeors. The negative T-RR relation is likely not caused by T variations, since for the initialization of convection a positive near-surface T anomaly would be more favorable than a negative one. Instead, the vertical mixing induced by convective events, associated with transport of cold air from above into the boundary layer, and the cooling radiative effect of clouds cause a T decrease close to the ocean surface. All together, the results from this section indicate that these physical linkages are the main reason for the anticorrelation of T and RH in the tropics.
3.3. Processes in the Midlatitudes
 Advection is known to be an important driver of daily temperature variability in the midlatitudes. In order to investigate its effect on the covariability of T and RH observed here, backward trajectories from selected measurement sites have been calculated (see section 2). Two sites over the eastern North Atlantic and one over the western North Pacific with almost complete daily time series in MAM 2000 have been chosen (see Table 2). In addition, the same reference site over the tropical Atlantic as for the analysis in section 3.2 has been investigated, but, owing to the lack of data in 2000, MAM 2004 has been taken as analysis period. The trajectory position 48 h before arrival at the observation site has been used as indicator for the air parcel origin; shifting this time to 24 h or 72 h before arrival does not substantially influence the results presented below. The correlation coefficients given in Table 2 show that the average trajectory latitude 48 h before arrival lat48 anticorrelates with both T and RH at the midlatitude stations. The absolute values of the correlation coefficients are in the same order as for T-RH, only at the second station they are slightly lower. In contrast, at the more southerly reference station where the T-RH correlation is weak, there is no strong relationship between lat48 and the other variables, especially RH.
Table 2. Pearson Correlation Coefficients r Between T, RH, and Trajectory Latitude 48 h Before Arrival (lat48) at Four Observation Sitesa
For the first three sites, the reference period is MAM 2000 and for the fourth it is MAM 2004.
 This trajectory analysis confirms that advection and more specifically the latitudinal displacement of air masses strongly influences daily variations of T, but also RH, and thereby the T-RH correlation in midlatitudes. For T, this effect can easily be explained by the meridional T gradient over the midlatitude oceans, leading to equatorward transport of cold and poleward transport of warm air masses. However, for RH there is no such strong meridional gradient. Climatologically, RH is even slightly larger to the north than to the south of the Atlantic measurement sites analyzed here [Dai, 2006]. However, there is a vertical RH gradient, with lower values further aloft [Sherwood et al., 2010]. Hence the negative RH-lat48 correlation might be explained if air masses usually descended when advected from the north but stayed closer to the surface when coming more from the south. This is the case for the site in the western Pacific, as shown in Figure 7. For producing Figure 7, the backward trajectories have been clustered according to the observed RH at the measurement sites. In Figures 7a and 7b all trajectories are displayed that were started at 12:00 UTC on the 30 driest and most humid days, respectively, during the 3-month period analyzed here, with colors indicating the pressure along the trajectories. Figures 7a and 7b show shows that air masses were advected from the northwest during all dry days, whereas there was much less latitudinal displacement on the moist days, in agreement with the correlation results given above. The air parcels typically descended about 100 hPa during the 72 hours prior to arriving at the site on the dry days, but the pressure values of most of the humid trajectories remained high during the 3 days before their arrival.
 For the observation sites in the west Atlantic, no such clear difference in vertical displacement could be detected in the trajectories, as shown exemplarily in Figures 7c and 7d. A more complex mechanism likely caused the low RH values during equatorward transport there. As shown in Figure 8a, the air parcels arriving at the observation site at 12.4°W, 48.7°N on dry days were heated during the last 48 h of transport, while there was less heating along the moist day trajectories. This heating was likely due to turbulent boundary layer fluxes, which are particularly strong if a cold air mass from the north is transported over the warmer sea surface. A destabilization of the air mass caused by the heating from below is evident from the 12:00 UTC vertical profiles of potential temperature at the observation site shown in Figure 8b. On moist days (blue lines), the air column above the site was relatively stable, a well mixed boundary layer reached only 20–50 hPa above the surface. On the contrary, this well mixed layer had a thickness of about 100 hPa on dry days (red lines). In the latter case, more air from aloft with lower RH is thus vertically transported to the surface by turbulent mixing.
 The results from this section show that advection of different air masses mainly triggers the positive T-RH correlation over the extratropical oceans. Transport of air from higher latitudes is associated with the formation of cold near-surface temperature anomalies and subsidence of relatively dry air from aloft, both due to large-scale and turbulent fluxes. The relative importance of these fluxes varies for different sites. This may also explain the seasonal cycle of the T-RH correlations, since the extratropical baroclinicity, which is an important prerequisite for the mechanism outlined above, is strongly reduced during the summer season. In contrast to the conclusion by Lu , dynamical effects do not destroy but rather enhance the positive correlation between temperature and atmospheric moisture content in the case of daily variations in the midlatitudes studied here.
3.4. Evaporation From the Ocean
 Another potential driver of variations in near-surface humidity, in particular in the subtropics and midlatitude storm track regions, is evaporation from the ocean. In order to investigate its impact on T-RH covariability, the correlation between surface latent heat flux and RH from ERA-Interim data has been computed. Figure 9 shows this correlation for JJA, the pattern is similar in other seasons. Over most of the global oceans the correlation coefficients are positive, meaning that low RH is related to enhanced ocean evaporation (since fluxes from the ocean into the atmosphere are negative). This shows that strong evaporation usually does not induce positive humidity anomalies (in this case, the correlation would be negative) but that the surface moisture flux is rather responding to atmospheric RH anomalies. This is consistent with the commonly used bulk formulation of air-sea fluxes, where evaporation is determined by the near-surface humidity gradient (see again Lorenz et al. ). Only in some tropical regions, slightly negative correlations between RH and latent heat flux occur (see again Figure 9). There, a possible mechanism is that evaporation might be enhanced by strong winds induced by convective updrafts and downdrafts [cf. Redelsperger et al. 2000] and might thus contribute to the positive RH anomaly on days with convective activity (see section 3.2).
 In this study, statistical correlation analysis has been combined with investigations of physical mechanisms and causality for exploring the daily covariability of temperature and atmospheric humidity close to the ocean surface. Two types of data sets have been analyzed, in situ observations and ERA-Interim reanalyses, and the results from both have appeared to be greatly consistent.
 In the inner tropics, the relationship between daily variations of temperature and specific humidity is weak, and T and RH are strongly anticorrelated. The minor influence of the Clausius-Clapeyron constraint in this region is thought to be partly due to the small magnitude of daily temperature changes (see again Lu ). Other processes superimpose the first-order thermodynamical forcing, in particular the influence of daily precipitation intensity on both T (through vertical mixing and radiative effects of clouds) and RH. For the latter, it is however not clear if RH anomalies primarily support the occurrence of convective precipitation or vice versa. Hence our identification of physical mechanisms relating T and RH does not lead to an ultimate process-based explanation of daily RH variability alone.
 Over the midlatitude oceans, there is a positive correlation between T and RH and thus a “super-Clausius-Clapeyron” relationship of T and q in large areas (i.e., q increases stronger with T than given by Clausius-Clapeyron). Dynamical processes, in particular the advection of air masses from different latitudes, have been identified as the main driver of this correlation. In addition to creating temperature anomalies, meridional transport also leads to corresponding RH anomalies owing to the associated (large-scale or turbulent) vertical moisture transport. As in the free subtropical troposphere (the advection-condensation paradigm [see Sherwood et al. 2010]), the air mass history also seems to play an important role for RH in the midlatitude boundary layer over the ocean. In future research, it may be interesting to investigate if the transport patterns inducing positive T-RH correlations are related to synoptic-scale atmospheric flow features like, for instance, warm conveyor belts [cf. Carlson, 1980].
 Evaporation from the sea has been of minor relevance for explaining T-RH correlations in this study. Over large parts of the global oceans, other atmospheric processes seem to be more crucial for inducing daily RH variations and evaporation should be seen as a consequence of the RH changes rather than as their cause (see also Lorenz et al. ). Variations of RH may thus trigger evaporation anomalies and in this way affect atmospheric as well as ocean dynamics.
 The results from this study, in addition to enhancing our understanding of the atmospheric water cycle in general, may be helpful for several other research fields, related to, for instance, climate feedbacks, the validation of climate models, and the interpretation of stable water isotope signals. Long-term changes in RH are very important for the water vapor feedback in a changing climate. The daily correlation pattern of RH and T observed here is still apparent on monthly timescales (see again Figure 5), although weaker. Also with respect to interannual variations, some general characteristics are preserved (albeit with much weaker amplitude), in particular the negative correlation coefficients over the tropical oceans and the more positive values in higher latitudes, e.g., over the northern Atlantic [see Dai, 2006, Figure 18b]. This may indicate that the processes investigated here might also influence RH variability on longer timescales. Furthermore, the correlation patterns can be used as a test bed for general circulation models and their ability to reproduce the most important processes determining humidity variations over the ocean. For example, the slightly less good agreement of results from observations and reanalyses in the tropics (see section 3.1) might relate to problems of the ECMWF model in properly representing feedbacks within tropical convective systems, which have to be parameterized in the model. Finally, the correlation of T and RH is of potential relevance for understanding processes related to water isotope physics, particularly the role of the deuterium excess as an indicator of moisture source conditions [Pfahl and Wernli, 2008].
 In future research, regional aspects of the present study may be investigated in more detail, e.g., the seasonal cycle of T-RH correlations north and south of Japan, the role of sea ice close to the Antarctic continent, or the slightly unusual correlation patterns in some coastal regions. Moreover, the investigation may be extended to land areas, where additional complexities are expected owing to the limited moisture supply as well as interactions with soil and biosphere.
 We are grateful to P. Knippertz (University of Leeds) and H. Wernli (ETH Zurich) for helpful discussions. Comments by H. Wernli and two anonymous reviewers have helped to improve the manuscript. NOAA is acknowledged for giving access to ICOADS data, NASA for providing TRMM precipitation estimates, and MeteoSwiss for providing access to ECMWF analyses. The analyses and graphics for this study were produced using the software package R.