The input satellite data to our analysis are from the Cloud–Aerosol Lidar with Orthogonal Polarization CALIOP; onboard the Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite that is part of the A-Train satellite constellation on a sun-synchronous low-Earth orbit with Equator crossings at approximately 13:30 local time. The cloud base product relies on the retrieved vertical feature mask VFM;. For each CALIOP lidar backscatter profile, the VFM identifies features such as clear air, cloud, aerosol, or planetary surface; this is termed the “feature type”. (When the lidar beam is completely attenuated, this is reported as a feature type.) In addition to the feature type, the VFM records the degree of confidence in the identification (“none” to “high”, termed the “feature type QA flag”), the thermodynamic phase of a layer identified as cloud as well as the degree of confidence therein (termed “ice water phase” and “ice water phase QA flag”), and the horizontal distance over which the algorithm had to average to identify a feature above noise and molecular atmospheric scattering (“horizontal averaging distance”).

In the present analysis, we use VFM version 4.10 , the current standard release, for the years 2007 and 2008. The VFM files are obtained from ICARE (http://www.icare.univ-lille1.fr/, last access: 4 December 2018).

For optimizing several parameters of the algorithm, for determining the expected cloud base uncertainty, and for evaluating the trained algorithm, reference measurements of z are required. The source of these “true” z values in this work is ground-based cloud observations at airports. Weather observations at airports are disseminated worldwide in aviation routine and special weather reports METARs and SPECIs, collectively referred to as METARs henceforth;. Apart from providing airport weather information for aviation, METAR data are used for assimilation into numerical weather prediction (NWP) models e.g.,. In many locations, z reported in METARs is measured by a ceilometer over a period of time (tens of minutes) and then objectively grouped into cloud layers and their respective fractional coverages, using the temporal variation at a fixed point under an advected cloud field as a proxy for spatial variability in the cloud field e.g.,. METAR data are widely distributed and archived; the data for the present analysis were downloaded from the Weather Underground archive (https://www.wunderground.com/history/airport/, last access: 4 December 2018).

In the US, z is mostly derived automatically by laser ceilometers that form part of the Automated Surface Observing Stations ASOS, system; see, e.g., and for recent examples of ASOS application to deriving cloud climatologies or NWP model evaluation. In other parts of the world, the cloud bases may be estimated by human observers or may be omitted under certain conditions when the lowest cloud base is higher than 1524 m, complicating objective comparison to satellite z. To ensure that the ceilometer z values are of high and spatially uniform quality, we restrict ourselves to METARs from the contiguous continental US.

There are 1645 stations throughout the continental US that lie within 100 km of a CALIOP footprint. In normal operation, the time resolution of z reports is 1 h, but during rapidly changing conditions, more frequent updates may be provided; for comparison to satellite z, the ceilometer observation closest in time to the satellite overpass is used, provided that the time difference is less than 1 h. For training the algorithm, we use ceilometer observations from the year 2008. For unbiased evaluation of the algorithm performance, a statistically independent dataset is required; we use ceilometer observations from the same stations from the year 2007. Figure  shows the locations of these stations along with the number of satellite–ceilometer z coincidences and the closest co-location distance during the year 2007.

Profile zc is determined from the CALIOP VFM for each profile with a surface return. The rationale is that a surface return indicates that the lidar did not attenuate within the cloud and that the lower limit of the layer identified as cloud therefore corresponds to the cloud base; Fig.  illustrates the idea. For these profiles, the location, zc, cloud top height, feature type between the cloud base and the surface, cloud thermodynamic phase, and associated quality assurance flags from the VFM algorithm are recorded.

We assess the quality of the CALIOP zc using the RMSE with respect to the ceilometer-observed z^. The RMSE is defined as RMSE=1N∑i=1Nzci-z^2. The sum runs over all CALIOP profiles containing at least one cloud layer and a surface return that are within 100 km in horizontal distance of the ceilometer, occurring within 3600 s of a ceilometer observation, and having their lowest CALIOP cloud feature within 3 km of the surface. Ceilometer observations are only used if the observation closest in time to the CALIPSO overpass contains a cloud within 3 km of the surface. This height limit is imposed because a subset of the ceilometers has a range limit of 3810 m, and all ceilometers report ceilings above 3048 m with reduced granularity (152.4 m); the 3 km threshold is safely below these ceilometer limitations and mimics the International Satellite Cloud Climatology Project ISCCP; definition of low cloud (p>680 hPa).

The following metrics, which are useful for a qualitative assessment of the quality of the satellite cloud base, are also calculated but play no quantitative role in the algorithm: correlation coefficient

between the CALIOP cloud base and ground-based observation of the cloud base (we use the Pearson correlation coefficient, ideally unity);

CALIOP's ability to detect cloud base depends on the properties of the cloud. Therefore, we expect that the zc quality will vary among different cloud profiles. We expect that measuring the quality as a function of various properties of the CALIOP column will allow us to predict the quality of other columns with the same combination of properties. The properties that are easily accessible in a single column and have substantial effects on quality are

horizontal distance D from the ceilometer,

CALIOP z only exists sporadically, when CALIOP happens to hit a sufficiently thin cloud. To infer the z at a point of interest that does not necessarily coincide with the location of a thin-cloud CALIOP column, we proceed as follows. We first select all CALIOP column zc measurements within a horizontal distance Dmax=100 km of the point that satisfy the additional quality cuts described in Sect. .

For each remaining column zc,i, we determine the predicted uncertainty σc,i based on the categories established in the previous section. We determine a combined z z=∑inwizci∑inwi with weights wi=1σc,i2 (optimal weights for uncorrelated least squares). The sum is calculated over the n zc estimates within Dmax that satisfy all criteria listed in the previous subsection. In practice, the individual measurements of cloud base are highly correlated with fairly similar σi. The cloud base estimate by Eq. () with weights given by Eq. () remains unbiased even in the presence of correlations. However, for the combined cloud base uncertainty, the uncorrelated weights would yield a biased estimate in the presence of correlations. The expression σ2=1n∑inσc,i2 yields acceptable results, as would be expected for highly correlated and fairly similar σc,i.

Having trained the algorithm on data from the year 2008, we evaluate it using a statistically independent dataset from the year 2007. In the evaluation dataset, the true (i.e., ceilometer-measured) z^ is known in addition to the estimated z and the estimated cloud base uncertainty σ, determined according to the procedure described in the previous section. Figure  shows the joint distribution of CBASE z and ceilometer-observed z^.

For satellite-derived measurements of z that are unbiased with respect to the ceilometer-observed z^ and have correctly estimated uncertainties σ, the probability density function of the quantity (z-z^)/σ has zero mean and unit standard deviation. In our evaluation dataset, we find a mean of 0.04 and a standard deviation of 1.06, shown in Fig. ; this corresponds to a z bias of 4 % and uncertainty bias of 6 %, both relative to the predicted uncertainty. Thus, we find that both the cloud base estimate and the uncertainty estimate are unbiased at better than the 10 % level.

As a further test of the reliability of the expected uncertainty, we divide the validation dataset into deciles of the expected uncertainty. Table  shows that the actual RMSE within each decile is within 10 % of the expected uncertainty (with the exception of the highest-uncertainty decile) and that linear regressions within each decile are close to the one-to-one line.

To check that the algorithm satisfies its design constraints (i.e., to ensure that we made no methodological error when implementing the algorithm), we have also verified that linear regression between z and z^ has zero intercept and unit slope and that the quantity (z-z^)/σ has zero mean and unit standard deviation when this validation is performed on the training dataset.

It is possible that z estimates outside North America could have greater biases or greater uncertainty than this evaluation leads us to believe. This would be the case if continental clouds over North America are not representative of clouds elsewhere in a way that is not accounted for by the cloud properties considered by the uncertainty estimate. Since the validation sample spans an entire year on a continental scale, we expect that most cloud morphologies are included. However, cloud types that occur predominantly over ocean, namely marine stratocumulus with horizontally extensive but vertically thin liquid-phase anvils, present a particular challenge to the method. Due to the typical z uncertainty of several hundred meters, the method is unlikely to be applied to stratocumulus cloud; nevertheless, a marine-cloud validation dataset would be desirable. For the present work, no suitable marine-cloud evaluation dataset was available; ship-based z observations were either based on human observers with coarse vertical resolution and a precision that is difficult to characterize or available only over a limited duration at limited locations, resulting in a severely statistics-limited set of coincidences with the CALIOP track.

Comparison with 2B-GEOPROF-LIDAR cloud bases (version P2_R04_E02, based on the 2B-GEOPROF and CALIOP VFM products) is shown in Fig. . 2B-GEOPROF-LIDAR distinguishes among radar-only, lidar-only, and radar–lidar combined cloud bases; the last category is rare for warm clouds and is not shown. For radar-only clouds, the mean error is large because the radar z predominantly clusters around the top of the ground clutter region with little dependence on the actual z.

Lidar-only 2B-GEOPROF-LIDAR cloud base performs comparably to the CBASE cloud base on average; this is to be expected, as the underlying physical measurement (the CALIOP attenuated backscatter) is the same for all three products considered (2B-GEOPROF-LIDAR, CALIOP VFM, and CBASE). Figure  shows the relationship between CBASE z and the 2B-GEOPROF-LIDAR cloud base closest to the ceilometer for each overpass. The CBASE z for low clouds tends to be higher than the 2B-GEOPROF-LIDAR estimate because the CBASE algorithm has been designed to agree with ceilometer heights, which also tend to be higher than the 2B-GEOPROF-LIDAR estimate (see Fig. ). Otherwise, the relationship is fairly close (linear correlation coefficient of 0.79), again as expected due to the similarity in the underlying measurement.

Unlike 2B-GEOPROF-LIDAR and the CALIOP VFM, CBASE provides a validated point-by-point uncertainty estimate, which allows an analysis to select only low-uncertainty cases or to statistically weight z according to uncertainty, as appropriate for the application.