The surface energy balance is a fundamental property of the climate system. How it is partitioned among its different components, and how it varies in space and time tempers the behavior of the atmosphere above, and the land or water below e.g.,. Among its varied components, the main balance is between moisture fluxes, extracting energy from the surface through evaporation, and the absorption of energy from the sun. Sensible energy transfers, and net radiant energy fluxes in the thermal infrared also combine to cool the surface, but on average only half as strongly as the evaporation of water which maintains the flux of moisture to the atmosphere e.g.,. In addition to providing an energetic link between the surface and the atmosphere, the moisture flux links the water and the energy cycles e.g.,. Despite their importance, the evaporative (or moisture) fluxes are difficult to measure, and they are both one of the largest, and most uncertain terms in the surface energy balance e.g.,. An improved ability to quantify evaporative fluxes is therefore essential for observation-based studies of the water and energy cycles, and the dynamics of weather systems and circulations that they fuel.

These fluxes can be reasonably well estimated from the covariance of anomalies in moisture, q′, and vertical air motions, w′, i.e., as ρℓvw′q′‾, with ρ the density and ℓv the vaporization enthalpy. Surface layer similarity provides a mean field theory for the evaporative flux, which is encapsulated by the bulk aerodynamic formula e.g.,, taking the form, 1w′q′‾=C|U|Δq,whereΔq≡qs-qa so that the evaporative flux can be directly related to the difference, Δq, in the specific humidity deficit of the air, qa, as compared to the surface, qs, and the near-surface wind speed, |U|, with C being an exchange coefficient. The value of C depends on surface properties and atmospheric stability (often expressed using Monin–Obukhov similarity and the stability parameter z/L), and has been characterized by decades of observations and theory . We refer to COARE as a representative bulk algorithm but note that different bulk formulations and transfer-coefficient parameterizations can yield differing latent heat flux estimates for identical bulk inputs, particularly under very low- and very high-wind conditions. Thus, uncertainties in qa influence flux estimates directly through Δq and indirectly through stability-dependent transfer coefficients. The surface moisture fluxes can therefore be reasonably well determined given knowledge of the specific humidity of the near-surface air, qa, the saturation specific humidity at the surface temperature and pressure, qs, as well as the near-surface winds, |U|.

Following the bulk aerodynamic formulation of surface fluxes, we assume that the water vapor pressure at the ocean surface is at saturation, so that the surface specific humidity qs equals the saturation specific humidity q*(Ts,Ps). This approximation in bulk theory reflects the near-equilibrium condition at the air–sea interface and is a standard assumption in flux parameterizations, sometimes with a 0.98 correction for typical salinity e.g.,. Satellite remote sensing can provide reasonable estimates of Ts, which given Ps determines q* and hence qs. Likewise a variety of measurements provide increasingly accurate estimates of surface wind speeds e.g.,. The main limitation in estimating evaporative fluxes over the ocean is therefore the measurement of the near-surface specific humidity of the air, qa, a quantity for which there is no real proxy. As a result, satellite-based climatologies of evaporative fluxes over the ocean depend on qa correlating with other quantities that can be remotely sensed, so that it (or the evaporative flux as a whole) can be inferred statistically. Various approaches to this problem are described in . These include retrievals from passive microwave measurements, such as the Hamburg Ocean Atmosphere Parameters and Fluxes from Satellite (HOAPS4) and SeaFlux CDR , as well as approaches that combine reanalysis and passive microwave data, such as IFREMER4 and J-OFURO3 . , for instance, compared HOAPS climatology with in situ buoy and ship measurements and found retrieval uncertainties in latent heat flux of 15 Wm-2, with a global-mean error of 25 Wm-2. Errors were found to be particularly large over the subtropical oceans, where evaporative fluxes are large in magnitude, with an average of 37 Wm-2 in random instantaneous retrieval errors .

A number of studies have confirmed that the most uncertain term in Eq. () is qa e.g.,. estimated that contributions from qa contribute approximately 60 % to overall uncertainty in the evaporative flux, whereas uncertainties from the wind speed contribute about 25 %.

Given this uncertainty, our goal is to develop a method to estimate q_a over convective oceanic regions. To this end, we exploit the physical connection between cloud base height h and near-surface relative humidity Wa: in a convective, well-mixed subcloud layer the cloud base forms near the lifting condensation level (LCL) and thus the height at which it forms depends primarily on near-surface T and q.

Our method takes advantage of the fact that a convective cloud-topped boundary layer is ubiquitous over the world oceans (Fig. ). We demonstrate this ubiquity by analyzing daily ERA5 surface fluxes from the year 2020 to compute the climatological frequency of positive surface buoyancy flux, B0, representing the annual frequency of convectively unstable surface conditions. The resulting “buoyancy-favorability” map (Fig. ) shows that near-surface convective instability prevails over most tropical and subtropical oceans, with ocean-only mean frequencies of 85 % globally and 99 % between 30° S and 30° N.

Building on this link, we test the idea that Wa (and hence qa) can be inferred from h and a small set of parameters, as a basis for a possible retrieval. To this end, we summarize notation and data (Sect. ); we then derive the relationship between h, Wa, and Δq≡qs-qa and quantify sources of uncertainty (Sect. ). Using coincident ceilometer–radiosonde and lidar–dropsonde measurements from EUREC⁴A, we validate the h–Wa linkage from surface and airborne platforms (Sect. , ). We estimate the two near-surface control parameters, dW/dz and ΔaT, from observations (Sect. ) and evaluate retrieval skill in qa (Sect. ). Finally, we discuss scope, caveats, and practical use, and conclude (Sects. , ).

Throughout, for notation, the subscript s denotes surface quantities and the subscript a denotes near-surface atmospheric quantities evaluated at the reference height za=40m. This height corresponds to the lowest reliable sonde level and is close to the R/V Meteor air-temperature measurements at 28.3 m used in this study. The ocean surface temperature Ts is the skin temperature. Near-surface atmospheric variables carry the a subscript; for example, qa, Ta, and Wa refer to conditions at za. Air pressure is denoted by P and vapor pressure by e, with e* denoting the saturation value for a plane of pure water. Hence, because the surface is water (albeit wavy and not pure), es≈e*(Ts). To make it easier to manipulate in equations, for which abbreviations make poor symbols, we use the symbol W to denote relative humidity.

Regarding data, we employ coincident sounding and lidar data from a variety of ground-based and airborne observing platforms deployed as part of the EUREC⁴A field campaign (ElUcidating the RolE of Cloud-Circulation Coupling in Climate), which took place in January and February 2020 in the trade-wind zone east of Barbados . During EUREC⁴A the German High Altitude and Long Range Research Aircraft (HALO) launched 810 dropsondes between 22 January and 15 February 2020 (see the EUREC⁴A data paper for HALO by ). These dropsondes yield vertical profiles of pressure, temperature, and relative humidity with a manufacturer-stated accuracy of 0.4 hPa, 0.1 °C, and 2 %, respectively . One unique aspect of EUREC⁴A is the sampling strategy that provides aggregated, statistical estimates of a larger-scale signal, compared to individual point-wise measurements. During EUREC⁴A, dropsonde measurements were distributed along a fixed flight pattern, the “EUREC⁴A circle” – a circular flight pattern with an approximately 220 km diameter, centered at 13.3° N, 57.7° W, at 9.5 km altitude. Following , one circle-mean refers to the mean of typically 12 dropsondes launched over one hour along the EUREC⁴A circle (due to operator and instrument errors, on some circles fewer sondes were launched, but never fewer than seven). A circling-mean is defined as the mean of three consecutive circle-means (or in two cases, two circle-means), corresponding to 30–36 consecutive soundings aggregated over 210 min.

Also from HALO, atmospheric backscatter and water vapor DIfferential Absorption Lidar (DIAL) profiles were recorded using the airborne demonstrator for the WAter vapor Lidar Experiment in Space (WALES) onboard HALO. Due to its high horizontal and vertical resolution, airborne lidar data is amenable to studying small-scale clouds, such as in trade cumulus regions. Here we evaluate the lidar data at the highest possible resolution, e.g., the backscatter ratio and aerosol depolarization data are analyzed at 0.2 s time resolution and 7.5 m vertical resolution. For the analyzed flights, the altitude was nearly constant (∼ 10.4 km) and the aircraft speed was about 210 m s⁻¹, resulting in consistent horizontal spatial resolution of ∼ 42 m. Only data at a wavelength of 532 nm are used. The backscatter profiles are extinction corrected using the High Spectral Resolution Lidar (HSRL) method . All data are regridded to a constant altitude scale over the EGM96 geoid.

During the same period, radiosondes were launched as part of the campaign from the Barbados Cloud Observatory BCO, and the research vessel, R/V Meteor , from 16 January to 1 March 2020. Ceilometer measurements of cloud base height were made from 18 January to 14 February 2020 from the same platforms. At the BCO the ceilometer is an OTT CHM 15k pulsed laser cloud height detector at 1064 nm used to detect cloud base height and lifting condensation level; at the R/V Meteor, the ceilometer is a Jenoptik system measuring vertical profiles of attenuated backscatter at 1064 nm to infer cloud base as a function of altitude and aerosol .

Before quantifying empirical relationships between cloud base height, h, and near-surface relative humidity (Wa), we outline the theoretical basis linking both quantities. In a well-mixed and unsaturated subcloud layer, the specific humidity is nearly constant while temperature follows a dry-adiabatic profile. Relative humidity is defined as 2W=ee*(T)=qRvRPe*(T), where R=(1-q)Rd+qRv is the gas constant of an ideal mixture of “dry-air” and water vapor, e*(T) is the saturation vapor pressure, and q the specific humidity.

For an adiabatic process for which pressure varies hydrostatically, dT/dz=-g/cp, and negligible vertical humidity gradients (dq/dz≈0), the vertical gradient of W simplifies to 3dWdz=gTℓvcpRvT-1RW, which gives the adiabatic rate of increase of relative humidity with height. Averaging across a well-mixed boundary layer with a depth of 600 m, q=15gkg-1 and T varying dry-adiabatically about a mid-layer (300 m) mean value of 296.41 K – values derived from the Meteor and BCO radiosondes – yields a boundary layer mean value of dWdz=4.0%hm-1 (referring to percent per hectometer, or 100 m).

Our analytical framework is closely related to earlier work connecting near-surface thermodynamic properties to the lifting condensation level. provided a simple linear approximation relating the dewpoint depression to relative humidity, showing that W≈1-(T-Td)/A with A≈4.3K near typical surface conditions; inverting this for a well-mixed subcloud layer yields an LCL height proportional to the dewpoint depression, consistent with the classical 125 mK-1 rule. derived an exact, implicit expression for the LCL temperature and pressure by conserving entropy and total water along a dry adiabat, obtaining an analytical result valid over a wide range of conditions. Our approach differs in emphasis, in that rather than computing the LCL from surface (T,q), we invert the relationship – given a remotely sensed cloud base height h, we recover Wa and hence qa.

In reality, the subcloud layer departs slightly from adiabaticity due to entrainment of drier air from above and the partial compensation of temperature and moisture tendencies by turbulent mixing , or due to rainfall and cold pools. Allowing weak vertical gradients in both T and q, the more general form of the relative-humidity lapse rate is 4dWdz=1q-Rv-RdRdqdz-gRT-ℓvRvT2dTdzW, which reduces to Eq. () when dq/dz=0 and dT/dz=-g/cp.

Using representative trade-wind conditions from , dq/dz≈-1gkg-1km-1 and dT/dz≈-9.4Kkm-1, together with T=296.4K and q=15gkg-1, Eq. () gives (1W)dWdz≈4.0×10-4m-1, corresponding to dWdz≈3.6%hm-1 for W≃0.9. This non–well-mixed estimate is about 10 % smaller than the adiabatic value, with most of the reduction arising from the moisture-dilution term (1q-Rv-RdR)dqdz.

The method proposed in this study is designed for convective marine boundary layers in which the subcloud layer is well mixed and shallow cumulus clouds are coupled to the surface. These conditions are ubiquitous over the world ocean (Fig. ). Under such conditions, the cloud base height corresponds closely to the lifting condensation level, which depends primarily on the near-surface temperature and humidity.

Despite the ubiquity of favorable conditions, several processes can violate the proxy's assumptions or introduce measurement bias. Cold pools from downdrafts and rain-driven outflows can produce shallow, moist layers decoupled from the overlying cloud, lowering the observed cloud base relative to the environmental LCL and thus overestimating qa. Optically thick or multilayer clouds pose observational limits: a lidar or ceilometer may detect an upper cloud base rather than the lowest, inflating the apparent cloud base height and biasing the inferred near-surface humidity low; optical-depth and multilayer screening are therefore required. Shallow or weakly mixed layers, in addition to those induced by cold pools, depart from the well-mixed assumption, weakening the cloud base and surface-humidity link and typically yielding low-biased estimates of qa unless filtered.

Accordingly, the proxy should be applied only where boundary-layer conditions are convective and the detected cloud base is the lowest layer coupled to the surface. These conditions can be diagnosed using coincident lidar backscatter, optical-depth screening, or reanalysis-based buoyancy metrics as in Fig. . Within such convective marine regimes, the method's assumptions hold and the resulting estimates of near-surface specific humidity are expected to be reliable.

We show that downward-looking lidar retrievals of cloud base height can be used to infer near-surface relative humidity, a key missing ingredient for remote-sensing estimates of the surface water vapor flux. Combined with wind speed, sea surface temperature, and the near-surface air–sea temperature difference, this information enables physically-based estimates of the surface water vapor flux. Over the ocean, where such measurements are both scarce and critical for the surface energy balance, scatterometers provide wind speed, and long-running satellite records provide sea-surface temperature. The air–sea temperature difference varies only modestly over much of the open ocean on monthly and basin scales, and it can therefore often be estimated statistically; however, this assumption breaks down in regions of strong gradients such as western boundary currents, upwelling zones, and frontal regions, where variability is large and direct observations or physically based corrections remain important.

The method we propose for estimating near-surface humidity requires unbiased estimates of cloud base height, and the satisfaction of two further assumptions: (i) that the relative humidity lapse rate is near the value it would obtain in a well-mixed layer, and thus relatively constant; and (ii) that the near-surface air temperature is cooler than the surface, so that the layer above is convectively driven. Convective boundary layer clouds – which form in the radiatively cooled, cold advection-dominated boundary layers that prevail over tropical oceans – both underpin our near-surface humidity estimates and confirm that the very conditions required for those estimates are in place. While this physical situation limits the application of the method to conditions where shallow convective clouds are present, they are ubiquitous, even in regions of deep convection. Our analysis shows that the method will benefit from some calibration for estimating cloud base from a distribution of lidar echoes, for estimating the relative humidity lapse rate, and for estimating the air-sea temperature difference. Their unbiased estimation will be required for using the proposed method to establish large-scale climatologies of near-surface relative humidity and associated moisture fluxes.

Finally, we note that improving qa addresses only one, albeit dominant, term in Eq. (). For latent heat flux applications, residual uncertainties will remain associated with wind speed retrievals and with the wind- and stability-dependence of the exchange coefficient, C. In particular, low-wind conditions require special treatment in many bulk algorithms (e.g., convective gustiness terms), and high-wind conditions can involve additional processes (e.g., sea state and spray) that affect transfer coefficients. Thus, the value added by a cloud base–constrained humidity estimate should be assessed jointly with wind-speed regime and the chosen bulk parameterization when developing and evaluating flux climatologies.

As an outlook we note that the method we propose could facilitate the development of a long-term, day and night, and physically-based near-surface humidity climatology if applied to global data of cloud base height. Techniques using multi‐angle satellite imagery have been shown to retrieve cloud base height, albeit over longer timescales . The most promising candidate for obtaining such data is measurements using a spaceborne lidar. Currently the newly-launched EarthCARE satellite provides HSR-Lidar data. It provides backscatter data with a horizontal resolution of about 280 m and a vertical resolution of 100 m. While the horizontal resolution appears to be sufficient to apply our method, the limited vertical resolution would imply an error of the near-surface humidity of about 0.5 gkg-1 attributed to the vertical sampling error alone (based on Eq. () assuming typical values for Wa,h, etc.). With sufficient sampling, and given the variability of cloud base height, it might be possible to obtain greater precision in estimates of the mean cloud base height than what is implied by the single-snapshot vertical resolution. Laser ranging using more sophisticated methods, such as employed by the Global Ecosystem Dynamics Investigation lidar aboard the International Space Station, could provide better estimates of cloud base height. But presently GEDI does not provide data products that allow this capability to be explored. Future satellites refining these technologies could be adapted to the requirements of our proposed method, and potentially could provide coincident estimates of near-surface wind speed and air-sea temperature difference. In this context, measurements of ocean surface texture using synthetic aperture radar could also be explored as a way to estimate the difference between the surface temperature and that of the air just above it, which would better constrain the proposed estimates both directly, and indirectly due to the expected covariability of the relative humidity lapse rate and the air-sea temperature difference. At the least, our work suggests that cloud base height information from lidar measurements could be usefully incorporated into reanalyses and into existing statistical flux retrieval frameworks – such as those used in HOAPS, SeaFlux, IFREMER, or J-OFURO climatologies e.g., – to better constrain near-surface humidity and surface moisture fluxes.