Comparison of Backscatter Coefficient at 1064 nm from CALIPSO and Ground–Based Ceilometers over Coastal and Non–Coastal Regions

: This study investigates the direct comparison of backscatter coefficient profiles at 1064 nm which were measured by CALIOP (Cloud–Aerosol Lidar with Orthogonal Polarization) and by ground–based ceilometers located in coastal and non–coastal regions. The study uses data recorded between 2013 and 2016 to investigate the challenges involved in performing such a comparison in different environments. The standard Level 2 CALIOP Aerosol Profile version 4 product is evaluated against data from two ground–based Jenoptik CHM15K ceilometers: One at Mace Head (western Ireland) and the other at Harzgerode (central Germany). A statistical analysis from a series of CALIOP overpasses within 100 km distance from the ground–stations is presented considering different along–track averages in CALIOP data (5 km, 15 km, 25 km, 35 km, and 100 km) at the closest approach. The mean bias calculated from the correlative measurements between CALIOP and the ground–based ceilometers shows negative bias for 80% of the cases analyzed at Mace Head and positive bias for 68% of the cases investigated at Harzgerode, considering both daytime and nighttime measurements in cloud–free scenarios. The correlation of these results with HYSPLIT shows that different air samples play a role in the comparison. To our knowledge, this is the first study that addresses the limitations and capabilities in comparing CALIOP data with ground–based ceilometers at 1064 nm wavelength in different environments.


Introduction
Aerosol scattering and absorbing properties have a direct impact on the global radiative budget and an indirect impact on cloud formation and microphysics [1]. The tropospheric aerosols possess a substantial spatial and temporal variability, which leads to significant uncertainties in the estimation of radiative forcing in climate change studies [2]. The aerosol radiative forcing has a strong dependence on its vertical distribution. Since the increase in aerosol size with relative humidity happens in the lower troposphere, aerosols with scattering properties show bigger forcing when most of their mass is located in that region. Aerosols with absorbing properties, on the other hand, exhibit a more significant forcing when their mass is above cloud layers [3]. Accordingly, a better understanding of aerosol vertical (and also horizontal) distribution and lifetime in the atmosphere is essential to investigate climate change and to improve forecast and dispersion models [4]. Aerosol and cloud properties can be observed either by in-situ or remote sensing instruments. Remote sensing can be either ground-based, satellite-based, or aircraft-based. Ground-based remote sensing has the advantage of continuous monitoring of the atmosphere at one location at high temporal resolution, whereas satellite-based remote sensing provides global spatial coverage. Both passive and active remote sensing instruments on-board satellites have been used to investigate the global distribution of aerosols and its optical properties. Moreover, active remote sensing instruments have been able to provide the vertical structure of the atmosphere. Lidars, for instance, are active remote sensing instruments which use laser beams to measure vertical profiles of aerosol layers with high horizontal, vertical, and temporal resolution [5]. The lidar technique can also be used to distinguish clouds from aerosols, to investigate optically thin clouds and at the same time, to investigate cloud-aerosol interactions thereby improving the understanding of the indirect effects of aerosols in the radiative budget [6]. Several different ground-based lidar networks were established over the years in order to enhance the study of aerosol transport on large spatial scales. These include the European Aerosol Research Lidar Network (EARLINET) with twenty-seven stations all over Europe [7], the NASA Micro-Pulse Lidar Network (MPLNET) with twenty-one permanent stations distributed worldwide [8], the Latin American Lidar Network (LALINET) with nine stations in South America [9], and the Asian Dust and Aerosol Lidar Observation Network (AD-Net) with twenty stations distributed over East Asia [10]. However, better and more complete coverage of the measurements of the vertical distribution of aerosols can be achieved by combining measurements of ground-based lidars with the satellite-based ones [11]. As highlighted by [4], simultaneous measurements of space-borne and ground-based instruments complement each other and can be combined in order to improve the information about the vertical distribution of aerosols and clouds. The satellite-based lidar called CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) was launched in 2006. CALIOP is a two-wavelength lidar that provides profiles of backscatter at 532 nm and 1064 nm as well as the degree of the linear polarization of the 532 nm signal [12]. CALIOP, along with two other instruments, is on board a polar-orbit satellite called CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) [13]. Over the past years, several different comparison studies between CALIOP and ground-based lidars were performed by various research groups using different approaches [7,11,[14][15][16]. Some of them followed the criterion established in the CALIPSO validation plan and considered only measurements that were taken when the satellite was passing over the ground-stations within 100 km distance [7]. The majority of these studies investigated the findings related to the 532 nm wavelength because they used ground-based Raman lidars to perform the comparison. The efficiency in Raman scattering is proportional to inverse wavelength to the fourth power so the 1064 nm wavelength was rarely used for validation studies. Comparison with the 532 nm CALIOP channel is also more common because of its greater sensitivity to molecular scattering [17]. Consequently, only a few studies [7,18,19] investigated the results of a comparison using the 1064 nm wavelength. [18], for example, used the measurements taken during the second Saharan Mineral Dust Experiment (SAMUM-2) in 2008 to validate the Level 2 (L2) CALIOP aerosol products for dust and smoke in the vicinity of Cape Verde region. The proposed validation approach considered 33 overpasses of CALIOP over the ground-based instrument and compared, among other parameters, the backscatter coefficient at 1064 nm. The findings for that variable showed good agreement between the instruments in the case of mixed dust/smoke layers and an overestimation of the backscatter coefficient in CALIOP data within pure dust layers. Wu et al. [19], evaluated CALIOP data (both at 532 nm and 1064 nm) with combined ground-based lidar and AERONET (Aerosol Robotic Network) sunphotometer measurements in the metropolitan area of New York City. The retrieval of lidar ratios and the Angstrom exponent from the combined ground-based data was later compared to the ones derived from CALIOP, resulting in good agreement at 532 nm and some bias at 1064 nm. Further, this research also compared aerosol extinction and backscatter profiles at both wavelengths for day and night cases, finding consistent agreement between them in terms of profile shape for night-time and some fluctuations in the signal during daytime due to noise. The studies that investigated the 1064 nm channel commonly used multi-wavelength ground-based lidars. However, the operational cost to run such instruments is high, and consequently, the spatial resolution is limited (as it is not viable to have them at many different locations) [20]. EARLINET stations, for example, besides only performing measurements three times a week or on special occasions (Sahara dust outbreak, volcanic eruptions), are within a typical distance on the order of several hundreds of kilometers from each other [21]. Alternatively, ceilometer networks built by different national weather services can be used to overcome this problem. Ceilometers are single-wavelength lidars which provide data in near real time with a low operational and maintenance cost [22]. Initially, they were designed to determine cloud base height (CBH) from 300 m to 15 km but after some enhancements were also able to provide information about vertical profiles of aerosols at 1064 nm [23]. Over the last years, ceilometers were vastly used in studies related to the characterization of the atmospheric boundary-layer [24][25][26][27], the detection of volcanic ash, smoke, and Saharan dust [28][29][30][31][32][33], air quality monitoring [34,35], and light pollution modeling [36,37]. Thus, this study aims to compare the backscatter coefficient at 1064 nm from two ground-based Jenoptik CHM15K lidar ceilometers with CALIOP. However, such a comparison can be challenging because the ground-based ceilometers are low-power lidars, and for that reason, they have a small sensitivity to detect aerosol/cloud layers at high altitudes (above 15 km). Contrarily, space-borne lidars like CALIOP have less sensitivity to detect thin aerosol/cloud layers at lower altitudes. These differences of top-down versus bottom-up view between ground-based and space-borne lidars were addressed over the years by different studies [38,39]. Furthermore, the sensitivity of the instruments is also affected by the age of the lasers, which tends to deteriorate over time. An example of the difference in sensitivity between a ceilometer located in Mace Head (Western Ireland) and CALIOP can be seen in Figure 1.  Figure 1, although the backscatter values present the same range (10 −7 sr −1 km −1 to 10 −4 sr −1 km −1 ). This difference is associated with the level of noise in the data, which represent by white for the Mace Head image (top) and by blue in CALIOP image(bottom). The ceilometer plot (top) was obtained from Cloudnet. Figure 1 shows that the ceilometer (top) is able to detect aerosol layers close to the ground while in CALIOP measurements, the aerosol layers are barely distinguishable from noise. Likewise, another limiting factor for comparing CALIOP with ground-based ceilometer measurements is the difference in the vertical resolution of the instruments, which leads to different numbers of available data points for comparison. As demonstrated in Figure 1, representativity of CALIOP observations along the ground-track additionally depends strongly on the horizontal distribution of observed layers. Furthermore, the level of noise associated with the 1064 nm wavelength in CALIOP data is higher than at 532 nm [40]. Thus, all these factors resulted in a relatively smaller number of studies of CALIOP versus ground-based ceilometer comparisons using the 1064 nm wavelength over the years. Even so, taking the above discussion and challenges into account, the present work is focused on performing a comparison of backscatter coefficient profiles at 1064 nm between CALIOP and two ground-based ceilometers in two different environments: (i) A coastal site in Ireland (Mace Head) where marine aerosols predominate; and (ii) a non-coastal site in central Germany (Harzgerode-Deutscher Wetterdienst) where continental aerosols predominate. The availability of instruments and the measurements associated with them at such distinctly different areas gives the possibility for an improved understanding of atmospheric properties through increased earth observation capabilities in the vertical. Because both areas are influenced by different meteorological systems and consequently have different aerosols types, the comparison described here may help verify and quantify the differences and/or similarities between spaceborne and ground-based lidar ceilometer measurements in a wider range of conditions. Data from the two ground-based instruments used here were not previously employed for such a purpose. The findings of a four-year comparison of two ground-based ceilometer measurements with CALIOP overpasses within 100 km distance is presented in this paper. Section 2 describes the characterization of the instruments used in this study. It is followed by a description of the study sites in Section 3. Section 4 describes the employed methodology, and Sections 5 and 6 present the results and conclusion, respectively.

CALIOP
CALIOP is a two-wavelength polarization-sensitive satellite-based lidar launched in 2006 by the National Aeronautics and Space Administration (NASA) in collaboration with the Centre National d'Etudes Spatiales (CNES) to study the vertical structure of aerosols and clouds, their interactions in the atmosphere and their role in the climate system [5]. The instrument is composed of a solid-state neodymium-doped yttrium aluminum garnet (Nd: YAG) laser with a pulse length of about 20ns and a frequency of 20.16 Hz [13]. CALIOP is on board the CALIPSO satellite platform along with a three-channel (8.65 μm, 10.60 μm, and 12.05 μm) imaging infrared radiometer (IIR) and a wide field of view camera (WFC) [13]. CALIPSO is a part of the A-train (afternoon train) constellation and follows a sun-synchronous polar orbit at 705 km altitude with a 16-day repetition cycle and an equator-crossing time around 1330 [13]. Linearly polarized laser light at 532 nm and 1064 nm is transmitted by CALIOP, which measures vertical profiles of elastic backscatter at both wavelengths as well as profiles of linear depolarization at 532 nm during both day and night [41]. The instrument directly measures the vertical profile of the total attenuated backscatter with a 30 m vertical and a 333 m horizontal spatial resolution (Level 0). Vertical and horizontal averages are performed in this Level 0 (raw) data, and the information is sent to the NASA Langley Research Centre (LaRC) where different algorithms are used to produce various levels of data products (Level 1, Level 1.5, Level 2, and Level 3) which are given in different spatial resolution [13]. The signal-to-noise ratio (SNR), which defines the accuracy in measuring backscatter signals, is much lower in CALIOP compared to a ground-based, airborne or shuttle-based lidars. The reason for that is the distance between the lidar and the targets. Consequently, more vertical and horizontal averaging can improve CALIOP's SNR [42]. Because the backscatter coefficient at 1064 nm is a product from the CALIOP Level 2 (L2) data retrieved with fewer a priori assumptions [7] and because the ground-based lidars are also measuring this parameter (enabling a direct comparison), the backscatter coefficient at 1064 nm along with, latitude, longitude and profile UTC-time from the standard L2 Aerosol Profile version 4 products (CAL-LID-L2-05kmAPro-Standard-V4-10) are used in this work. This version is the first major review since May 2010 and the improvements have reduced the uncertainties in the calibration coefficients [40]. CALIOP L2-APro presents a vertical resolution that varies as a function of altitude (60 m between −0.5 km and 20 km) and a spatial resolution of 5 km [43,44]. The calibration of the 1064 nm channel of CALIOP is made relative to the 532 nm channel, which is precisely calibrated through the normalization of the molecular backscatter from an aerosol-free altitude to molecular model data obtained from NASA. The reason for this relative calibration is because the SNR of CALIOP's molecular backscatter measurements is excessively lower at 1064 nm compared to 532 nm, which makes the molecular normalization with altitude not viable at 1064 nm [13]. So, the 1064 nm relative calibration to the 532 nm uses backscatter measured from a subset of cirrus clouds measurements that were carefully selected. Moreover, the extinction coefficients at 532 nm and 1064 nm are assumed to be identical, so the ratio of the LR is consistent with the ratio of particulate backscatter coefficients calculated from previous Mie calculations [40].

Jenoptik CHM15K Lidar Ceilometer
The ground-based instruments used here are Jenoptik CHM15K lidar ceilometers that employ a solid-state Nd: YAG laser source with a typical pulse energy of 7 μJ and a pulse repetition rate of about 5-7 kHz. The receiver field of view is 0.45 mrad (half angle), and the height of the complete overlap is around 1500 m [24]. Due to the stability of the optical system, the overlap of the laser beam and telescope field of view of the ceilometer can be corrected down to 600 m [22,45]. The instrument uses a photon-counting recording system to measure backscatter profiles at 1064 nm over a nominal range of 0.03 km-15 km and a time resolution that varies from 2 to 600 s. The instrument can detect profiles of aerosol backscatter, cloud height, boundary layer height and visibility and it has a vertical resolution of 15 m. Its full operational range is 15 km, so lower cloud layers and cirrus clouds can also be detected [15]. The signal received by the ceilometer must be calibrated to retrieve the backscatter coefficient at 1064 nm. Overall, most ceilometers use the socalled Rayleigh calibration to determine a calibration factor. In Rayleigh calibrations the backscatter signal in a clear atmosphere (no clouds or aerosol) is fitted to the theoretical curve for Rayleigh scattering by molecules using only atmospheric pressure and temperature profiles [23]. Rayleigh calibrations require a few hours of averaging of the ceilometer backscatter signal and are done periodically, whenever clear night observations provided good conditions to obtain the calibration factor. This calibration factor can only be calculated from nighttime measurements to avoid solar background radiation causing low signal-to-noise ratios (SNR). However, the factor is also applicable during the day because of the stable optical setup of the ceilometer. Nevertheless, Rayleigh calibrations depend on assumptions that need to be made (clean atmosphere in calibration range, fixed LR, amount of averaging of the signal in clear nights). The individual calibration process of the ceilometers is explained in more detail in the next section. The main difference from the calibration of the ceilometers used in this study to those of [23] is the missing sun-photometer information.

Study Sites
The study was conducted using data from 2013 to 2016 over two measurement stations. They are chosen as representative of two different geographical domains with varying climatology and topography.

Coastal Area: Mace Head (MH)
Mace Head is an atmospheric monitoring and research station located on the west coast of Ireland (Connemara, County Galway) at 53°19′33" N, 9°53′58" W. The station is based 21 m above sea level, around 300 m from the sea and it has been a Cloudnet (cloud network environment technology) station since 2009 [46]. Its relatively high latitude at a coastal area is an ideal location to measure marine aerosols [47] as well as westerly-south-westerly air masses from the North Atlantic Ocean [48]. The geographical location of Mace Head provides a unique scientific niche for studies related to marine aerosol, volcanic ash from Iceland, Saharan dust, anthropogenic pollution and biomass burning [46,[49][50][51][52]. The research facility is equipped with a CHM15K ceilometer from Lufft (formerly Jenoptik) that is used in this study, among several other instruments. The profiles of aerosol backscatter coefficient at 1064 nm are calculated as explained in Section 2.2, through Rayleigh calibrations. Assuming a fixed LR of 60 sr, the calibration process is done regularly by averaging the backscatter signal over one to five hours in clear nights, over a height range of about 1-2 km. The variability in the calibration constant was less than 2% between 2013 and 2016. After the calibration, the profiles of backscatter coefficient are produced every 5 min.
The stability of the optical system along with the correction function provided by the manufacturer allows an estimate of the backscatter coefficient above 300 m. According to Hervo et al. [45], the uncertainty introduced by the manufacturer-provided overlap correction function can be up to 45% at 300 m, and less above. However, they also showed a clear temperature dependence of the overlap correction, with a much smaller or even negligible effect at low internal temperatures. Mace Head is affected by cool coastal climate. Therefore, we reduced the minimum profile height for Mace Head from 600 m to 300 m in favor of data availability.

Non-Coastal Area: Harzgerode (DWD)
The second measurement station used in this study is representative of inland central Europe, and it is based 404 m above sea level. It is located in Harzgerode, in a remote and relatively clean site at the eastern edge of the Harz mountain range (which can reach up to 1.1 km m.s.l) in central Germany 51°38′60" N, 11°8′24" E. The station is part of the German weather service (Deutscher Wetterdienst-DWD). The Jenoptik CHM15K lidar ceilometer from this station has measured profiles of aerosol backscatter coefficient at 1064 nm since November 2008. The ceilometer is delivering data to E-Profile [53], a program for automatic surface-based profile observations by EUMETNET, a group of European national meteorological services. The backscatter coefficient at 1064 nm is obtained, as explained in Section 2.2, through Rayleigh calibrations. Assuming a fixed LR of 50 sr, the Rayleigh calibration method of E-PROFILE is applied by screening the calibration values for outliers. Following, these calibrations values are smoothed and then interpolated to produce hourly profiles of the backscatter coefficient. Profiles of backscatter coefficients were available from 600 m above ground level, following recommendations by Wiegner et al. [22] and Hervo et al. [45].

Comparison Methodology
A direct four-year comparison of backscatter coefficient at 1064 nm between CALIOP and the two ground-based ceilometers in different environments (coastal and non-coastal) is made. During this period, CALIOP overpasses within 100 km from the ground-based stations are considered. In the presence of clouds, aerosol backscatter and extinction are difficult to retrieve due to the strong attenuation of the signal; thus, cloud-free scenarios must be considered [54]. However, due to its geographical location, low clouds are present over Mace Head most of the time, although they are sometimes scattered and/or optically thin. So, cases with the presence of low/thin clouds (in both sites) are also investigated. The distinction between cloud-free scenarios and cases with thin clouds was based on a 35.5 GHz Ka-band Doppler cloud radar for Mace Head and on a cloud base height (CBH) flag in Harzgerode-DWD data. Daytime measurements and clouds in general, especially low and bright clouds, are responsible for an increase in the background radiation. Nighttime measurements and cloud-free scenarios, on the other hand, contribute to a decrease in the background radiation. To account for these changes, the sensitivity of the Jenoptik CHM15K ceilometer changes automatically. During daytime measurements and when bright clouds are in the line of sight, the sensitivity is reduced through the reduction of the high voltage supply of the APD, which leads to an adaptation to the new background radiation. For nighttime measurements, an analogue process is made, and the sensitivity increases [23]. As described by Wiegner et al. [23], we correct for changes in the detector voltage before calculating profiles of the backscatter coefficient.
After cloud screening, the closest passage time related to the minimum distance between the instruments is found. At Mace Head, the satellite overpass time is around 0300 UTC and 1330 UTC whereas for Harzgerode it is around 0100 UTC and 1200 UTC. Then, the profiles related to the minimum distance and time are directly compared. Following that step, averages centered in those profiles are performed. Along-track averages (5 km, 15 km, 25 km, 35 km, and 100 km) centered in the profile related to the minimum distance are made for CALIOP while, for the ground-based instruments, temporal averages centered in the profile related to the closest passage time are performed. The spatial resolution of CALIOP L2-Apro data is 5 km, which corresponds to one vertical profile. Consequently, along-track averages over 15 km, 25 km, 35 km, and 100 km correspond to 3, 5, 7, and 20 vertical profiles, respectively. Since the ground-based instruments present a different temporal resolution, being 5 min for Mace Head and 1 h for Harzgerode, only the profiles of the first one are averaged. The average in the Mace Head temporal series is centered in the closest passage time considering different intervals (5 min, 30 min, and 60 min). At Harzgerode, two profiles are directly compared to CALIOP: One profile considering the closest passage time at daytime 1200 UTC and one considering the closest passage time at nighttime 0100 UTC. An illustration of the comparison methodology can be seen in Figure 2. The interval between the white lines in Figure 1 (bottom) shows an example of the along-track averages within 100 km from CALIOP that are used for the comparison. At the same time, the interval between the black lines in Figure 1 (top) represents the one-hour interval from the groundbased data used for the comparison with CALIOP. Finally, the difference in the vertical resolution of the instruments is considered. The altitude scale of the ground-based ceilometer profiles is adjusted to be the same as of CALIOP (above mean sea level, m.s.l.) by vertically averaging the data every 60 m. Besides, the evaluation of CALIOP backscatter coefficient at 1064 nm is carried out in the region above 0.3 km m.s.l for Mace Head and 0.6 km m.s.l for Harzgerode to account for overlap effects, and ground returns. Furthermore, only altitude ranges where both instruments reported backscatter are used. A statistical analysis is made to evaluate the agreement between CALIOP and the ground-based measurements of backscatter coefficient at 1064 nm, and to assess possible bias between the measurements. The correlation coefficient (R), p value, the mean percentage difference (MPD), the mean bias (MB) and the factor of exceedance (FoE) are used for such a purpose. The correlation coefficient, shows the strength of a linear relationship between the measurements and can vary from −1 (total negative correlation) to +1 (total positive correlation) with a value of 0 indicating no correlation. The p value shows the level of statistical significance between the measurements. The smaller the p value, the lower is the probability of the results being random. In this study, we consider as statistic significant, cases with p value ≤0.05. The MPD is the mean of the differences between two measurements given in percentage. The mean bias (MB), reports the over (MB > 0) or underestimation (MB < 0) of one variable with respect to the other. The factor of exceedance (FoE) can also be used as tool to quantify the over (0 < FoE < 0.5), or underestimation (−0.5 < FoE < 0) of one variable with respect to the other. An FoE = 0 indicates that the measurements are half under, and half overestimated [56]. All the mathematical definitions can be seen in Appendix A. Afterwards, a comparison with a back-trajectory model is performed to verify the origin of the air samples and to investigate if they present any relation with the statistical results. The Hybrid Single-Particle Lagrangian Integrated Trajectory Model (HYSPLIT) [57] is run for each case individually, and visual screening of the model's output is made, separating the air samples according to different types. Standard air mass classification is not applied for this study. Instead, the term "air samples" is used because the idea is to evaluate if the ambient air sample has either a marine or a continental contribution (or both). So, the ambient air samples are generically classified as pure Marine (M), Marine Polluted (MP), pure Continental (C), and Continental Polluted (CP). The ambient air sample is considered MP when it is originated and travels most of the time over the ocean but reaches the station through the continent. We classify as CP, an air sample that is marine originated but travels most of the time and reaches the station through the continent. So, the term "polluted" used here is more related to a continental contribution than to pollution itself.

Results and Discussion
During four years, from 2013 to 2016, CALIPSO overpasses within 100 km from Mace Head and Harzgerode were analyzed. Considering the data availability, (both satellite and groundbased), and cloud-free and thin-cloud scenarios, 30 cases were investigated for Mace Head and 40 for Harzgerode. Within these period, four case studies are selected to be discussed separately here. Following, a long-term comparison is performed considering all CALIOP overpasses at Mace Head and Harzgerode between 2013 and 2016.

Case Studies
In order to demonstrate the methodology described in the previous section, two particular cases are discussed for Mace Head, Ireland and two for Harzgerode, Germany. The cases represent the comparison between the satellite and the ground-based instruments for cloud-free scenarios and cases with the presence of thin clouds. The ceilometers in Mace Head and Harzgerode have different temporal resolutions (as explained in Section 4). While Mace Head provide backscatter coefficient values every 5 min, Harzgerode provides it every hour. Therefore, due to the aerosol inhomogeneity, the strongest probability of obtaining a good correlation between CALIOP and the ground-based measurements is to use the shortest averaging in both time and space, at the closest approach [55]. So, the case studies presented here consider the maximum temporal resolution of both ceilometers. The results of the comparison considering different temporal averages in Mace Head data (30 min and 60 min) are presented in the Appendix C. Figure 3 shows the satellite overpass on the west coast of Ireland on the cloud-free case (18/11/14-orange line) and the case of a thin cloud (19/07/16-blue line). The overpass for the cloud-free case occurred during the day at 29.56 km from Mace Head. The overpass for the case with a thin cloud, occurred at night at 60.11 km distance from Mace Head. The white dot represents Mace Head station, and the green dots show all the along-track profiles from CALIOP that are spatially averaged. The direct comparison of backscatter coefficient at 1064 nm profiles measured by CALIOP (green lines) and Mace Head (blue line) with their respective standard deviations (shaded area) and the corresponding mean percentage difference between the measurements is given in Figure 4 for (a, b) cloud-free case and (c, d) the case with a thin cloud. The different along-track averages performed in CALIOP data are represented by different line styles. According to [43], the blank spaces in CALIOP profile (green lines) are related to range bins were no particulates were detected. Overall, the agreement between CALIOP and Mace Head is good in terms of profile shape for both cases. Considering the cloud-free case (Figure 4a), the vertical profiles are characterized by a reasonable agreement, especially when less along-track averaging is performed in CALIOP data. Only when CALIOP data is averaged over 100 km, the most significant discrepancy occur, and a peak in the backscatter values (~2 × 10 −2 sr −1 km −1 ) is observed. It is also evident that the best agreement is found at the lowermost part of the profile (below 0.75 km). The mean backscatter coefficient values for all CALIOP along-track averages with the respective standard deviation can be seen in Appendix B, Table A1. The mean percentage difference between CALIOP and Mace Head for the cloud-free case is presented in Figure 4b. It is evident that most of CALIOP backscatter coefficient measurements are underestimated with respect to Mace Head measurements. Besides, the negative MPD observed for all the along-track averages could also be attributed to the high aerosol inhomogeneity within the diurnal boundary layer. Considering the entire profile and all CALIOP's along-track averages, the MPD, R, the p value and MB are presented in Table 1. A stronger correlation between the measurements is found when CALIOP data is averaged over 35 km. However, in general, the correlation coefficient presents a small variability within all the along-tracks performed up to 35 km. The same is true for the p value, which remains ≤0.05 between 5 km and 35 km. When the along-track averaging is performed over 100 km the agreement between the measurements gets worse, with the R reaching 0.06 and the p value drastically increasing to 0.82. The MB is also negative for all the along-track averages which indicates an underestimation of CALIOP measurements with respect to Mace Head measurements. Besides, the MB is almost constant for all along-track averages which might also indicate a systematic difference between the measurements.

Coastal Region-Mace Head
Considering the case with a thin cloud (Figure 4c) only the ceilometer can detect some atmospheric features of low backscatter value (~0.75 km). However, R between all the vertical profiles is larger compared to the cloud-free case. A peak in the backscatter coefficient values between 1.25 km and 1.5 km demonstrates that both CALIOP and the ceilometer were able to identify the same thin cloud. The mean backscatter coefficient value for all the along-track averages with the respective standard deviation can also be seen in Appendix B, Table A1. The mean percentage difference between CALIOP and Mace Head backscatter coefficient values for the case with a thin cloud is given in Figure 4d. A negative MPD is observed between the measurements. These negative differences could be attributed to the presence of a thin cloud, which contributes to multiple scattering effects in CALIOP measurements resulting in less attenuation of the signal compared to the ground-based measurements. Below the cloud, attenuation of CALIOP's signal might contribute to the negative MPD. Considering the entire profile and all CALIOP's along-track averages, the MPD, R, p value and MB are summarized in Table 1. High dependence of R on horizontal averaging is observed, with the value decreasing from 0.87 for 5 km to 0.58 for 100 km. MB remained negative and almost constant for all the along-track averages which shows an underestimation of CALIOP measurements with respect to Mace Head and might also indicate a systematic difference between the measurements.
We also investigated the influence of presence of different air samples on the obtained statistical comparison using HYSPLIT back trajectory model. The HYSPLIT back trajectory model ( Figure 5) is run over 72 h for (a) the cloud-free case (18/11/14) and (b) the case with the presence of a thin cloud (19/07/16). The criteria used for the classification of the air samples is explained in Section 4. The result of the cloud-free case (Figure 5a) shows that the ambient air sample passing through Mace Head at the time of the analysis is pure continental (C). For the case with a thin cloud (Figure 5b), the ambient air sample passing through Mace Head at the time of the analysis is marine polluted (MP). Overall, a stronger correlation between CALIOP and Mace Head measurements (higher R values) is found for the case with a thin cloud, when a polluted ambient air sample (MP) is passing over Mace Head. A similar result was shown by [18] when using CALIOP and a groundbased instrument to investigate different types of aerosol transport over the tropical Atlantic. The study analyzed both 532 nm and 1064 nm and found that at 1064 nm, polluted air samples provided a better agreement between CALIOP and the ground-based instrument compared to pure ones. Figure 6 shows CALIPSO orbit over Harzgerode-DWD on the cloud-free case (06/08/14-blue line) and the case with a thin cloud (04/05/16-orange line). The overpass for the cloud-free case occurred at nighttime at 33.65 km from the DWD station in Harzgerode. The overpass for the case with a thin cloud occurred at daytime at 43.65 km distance from the Harzgerode. The white dot represents the Harzgerode-DWD station, and the green dots show all the along-track profiles from CALIOP that were spatially averaged and used in the comparison. The direct comparison of backscatter coefficient at 1064 nm profiles measured by CALIOP (green lines) and Harzgerode-DWD (blue line) with their respective standard deviations (shaded area) and the corresponding MPD between the measurements is given in Figure 7 for (a, b) cloudfree case and (c, d) the case with a thin cloud. According to [43], the blank spaces in CALIOP profile (green line) are related to range bins were no particulates were detected. Overall, the agreement between CALIOP and the ground-based ceilometer is good in terms of profile shape for both the cloud-free and the thin-cloud cases. For the cloud-free case, Figure 7a shows that the DWD ceilometer in Harzgerode was able to detect a full profile of backscatter coefficient up to approximately 3 km. In contrast, CALIOP was not able to record any measurements between 1.5 km to 2.0 km. However, the measurements still present a strong agreement in terms of profile shape, especially at the lowest part of the profile (0.5 km to 1.5 km). At the uppermost section of the profile, above 2 km, even with a lower SNR, CALIOP is able to detect some thin atmospheric features that the Harzgerode-DWD ceilometer cannot detect (around 2.5 km). The reason for that can be attributed to the relatively low temporal resolution of Harzgerode data (1 h). This hypothesis can be supported through the analysis of the comparison between CALIOP and the different temporal resolutions performed in Mace Head data (Appendix C). Although the Mace Head ceilometer is still capable of detecting some low signal in the atmosphere (Figures A1 and A2) even with a lower temporal resolution (30 min and 60 min), the agreement with the CALIOP data worsens. Tables A3-A5 shows that the strength of the correlation between CALIOP and Mace Head measurements decreases for both the cloud-free and thin cloud case when Mace Head data is averaged over 30 min, but especially over 60 min. The mean backscatter coefficient values for all CALIOP along-track averages and for the Harzgerode-DWD profile with the respective standard deviation can be seen in Appendix B, Table A2. Figure 7b shows the MPD between CALIOP and Harzgerode-DWD measurements for a cloud free case. Excellent agreement was found in the lower part of the profile between 0.5 and 1.5 km. In the top part, between 2 and 3 km, strong positive bias was observed between the measurements, showing an overestimation of CALIOP backscatter values with respect to Harzgerode-DWD backscatter values. Considering the entire profile and all CALIOP's along-track averages, the MPD, R, p value and MB are presented in Table 2. The mean percentage difference (MPD) between CALIOP and Mace Head, shows significant discrepancies, with mean values above 270% for all the along-track averages. However, these discrepancies are due mostly to the uppermost part of the profile (above 2 km), where the differences are greater than 250%. If we calculate the MPD considering only the lower part of the profile (below 1.5 km), the values decrease, being 52 ± 74%, 52 ± 74%, 47 ± 71%, 38 ± 67%, and 15 ± 70% for 5 km, 15 km, 25 km, 35 km, and 100 km, respectively. Similarly to Mace Head, the results show small variation of R within all CALIOP along-track averages up to 35 km. After that, the correlation weakens, but still can be considered significant (p value ≤ 0.05). The MB remains equal to zero for all along-track averages, showing no significant bias between the two datasets.

Non-Coastal Region-Harzgerode-DWD
Considering the case with a thin cloud (Figure 7c), the vertical profiles are characterized by a strong agreement in terms of profile shape even with the measurements concentrated at low altitudes. Around 1 km, both instruments registered a peak in backscatter coefficient values. The most visible difference between CALIOP and the ceilometer profile is the scattering along height, which is stronger in CALIOP data. The mean backscatter coefficient values for all CALIOP alongtrack averages and the Harzgerode-DWD profile with the respective standard deviation can be seen in Appendix B, Table A2. The MPD between CALIOP and Harzgerode-DWD measurements for a thin cloud case is given in Figure 7d. Overall, the agreement between CALIOP and Harzgerode-DWD is high, with MPD values close to zero and within 23%, which is the expected error for CALIOP L2 daytime measurements within the PBL [40]. Considering the entire profile and all CALIOP's along-track averages, the MPD, MB, p value, and R are presented in Table 2. Equivalently to the cloud-free case, R and the p value show small variation when the comparison between CALIOP and the ceilometer is performed averaging CALIOP data up to 35 km. After that, the correlation weakens, with the correlation coefficient decreasing to 0.44 and the p value increasing to 0.09. MB remains equal to zero for all the along-track averages, showing no significant bias between the two datasets.
Also, for Harzgerode, we investigated the influence of presence of different air samples on the obtained statistical comparison using HYSPLIT back trajectory model. HYSPLIT (Figure 8) is run over 72 h for (a) the cloud-free (06/08/14) and (b) the thin cloud case (04/05/16). The criteria used for the classification of the air samples is explained in Section 4.

Long-Term Comparison
A statistical analysis of all 30 CALIOP overpasses at Mace Head and all 40 overpasses at Harzgerode-DWD is made. Because multiple scattering is not negligible in the presence of thin clouds, only cloud-free cases are considered, reducing the number of cases to 15 for Mace Head and 28 for Harzgerode. To compare Mace Head and Harzgerode-DWD results in the long-term, the temporal resolution of both ground-based measurements needs to be the same. In order to obtain that, Mace Head data is first averaged over one hour centered in the closest passage time as explained in Section 4. Thereafter, the cases are divided in day and night overpasses and made comparable to the averages of Harzgerode's 1200 UTC (day) and 0100 UTC (night) profiles. Mace Head has 9 night and 6 day overpasses while Harzgerode has 24 night and 4 day overpasses. To account for noise level, all data points with values lower than three times the standard deviation of the mean are discarded. To assess possible bias between CALIOP and the ceilometers measurements of daytime and nighttime overpasses, MPD and MB are calculated. The strength of the correlation between CALIOP and the ground-based measurements is evaluated with the correlation coefficient (R) and the Pvalue, which are also calculated for both daytime and nighttime cases considering all the different along-track averages in CALIOP data. In total, positive values of correlation coefficient (R) are found in 60% of Mace Head and 50% of Harzgerode cases. However, due to the low number of cases and available points for comparison, the p value is greater than 0.05 for all along-track averages. Consequently, the R cannot be considered as statistically significant for any of the overpasses. Figure 9a,c show the direct comparison of the mean backscatter coefficient at 1064 nm profiles measured by CALIOP (green lines) and Mace Head (blue lines) for daytime and nighttime cases with their respective standard deviations (shaded area). The corresponding MPD between CALIOP and ceilometer measurements at Mace Head is shown in Figure 9b,d.  Figure 9a shows that overall, CALIOP and Mace Head vertical profiles are characterized by a relatively good agreement in terms of shape, although discrepancies are evident. Considering CALIOP daytime overpass at Mace Head (Figure 9a), CALIOP and Mace Head vertical profiles appear to be slightly offset. The MPD between CALIOP and Mace Head for the daytime overpasses is given in Figure 9b. Strong negative mean percentage difference is observed between the measurements. These strong negative differences could be attributed to the high aerosol inhomogeneity within the diurnal boundary layer. The comparison between CALIOP nighttime profiles and Mace Head is given in Figure 9c. Due to its higher SNR, the ceilometer at Mace Head is able to detect more optically thin atmospheric features compared to CALIOP. The mean percentage difference between CALIOP and Mace Head measurements for the nighttime cases is shown in Figure 9d. Overall, the discrepancies between CALIOP and Mace Head measurements are higher for the nighttime measurements compared to the daytime measurements even without the interference of solar background radiation. The MPD yields strong negative values, especially below 1.5 km. The mean backscatter coefficient values with the respective standard deviation for both daytime and nighttime profiles is given in Appendix D, Table A6. Considering the entire profile for both daytime and nighttime overpasses and all CALIOP's along-track averages over Mace Head, MPD, and MB are presented in Table 3. Table 3. Statistical results (MPD, MB) derived from simultaneous measurements between CALIOP and Mace Head data for the 6 daytime and 9 nighttime cases considering different along-track averages in CALIOP data (5 km, 15 km, 25 km, 35 km, and 100 km). According to Table 3, MPD and MB remained negative for both daytime and nighttime overpasses, showing that the Mace Head ceilometer tends to measure higher backscatter coefficient values compared to CALIOP. Besides, the MB also remained constant for all the along-track averages which might indicate a systematic difference between the measurements.

Temporal Resolution 60 min DAYTIME 6 Cases NIGHTTIME 9 Cases MPD (%) MB (sr −1 km −1 ) MPD (%) MB (sr
CALIOP's daytime and nighttime overpasses at Harzgerode are given in Figure 9e-h and the statistical results are presented in Table 4. In general, CALIOP and Harzgerode-DWD vertical profiles show a reasonable agreement in terms of profile shape for CALIOP's daytime overpass (Figure 9e,f) and a strong disagreement for CALIOP's night overpass (Figure 9g,h). Considering the daytime overpass (Figure 9e), most of the discrepancies observed between CALIOP and Harzgerode-DWD happen at the lowermost (below 1 km) part of the profile. Above 1 km, the agreement between CALIOP and Harzgerode is more substantial with both instruments detecting the same atmospheric features. These discrepancies are also evident when analyzing Figure 9f, which gives the mean percentage difference between the measurements. Strong positive bias is observed between the measurements, especially below 1km. This is roughly the peak height of the Harz mountain range at 1.1 km. Therefore, CALIOP profiles might be affected by ground returns (personal communication with Dr. Ina Mattis). Table 4 shows, for all the along-track averages, high positive MPD values between the measurements which indicates an overestimation of CALIOP backscatter values with respect to Harzgerode-DWD backscatter values. However, if we consider only the interval between 1 km and 2 km, the discrepancies are smaller with MPD values close to zero and within 23%, which is the expected error for CALIOP L2 daytime measurements in the PBL [40]. For 5 km, 15 km, and 25 km, the MPD values between 1 km and 2 km are 4 ± 51%. For 35 km and 100 km, the values are 4 ± 50% and 2 ± 46%, respectively. MB remained positive for all daytime cases, also showing an overestimation of CALIOP measurements with respect to the Harzgerode-DWD measurements.
Considering CALIOP's nighttime overpass at Harzgerode-DWD (Figure 9g), it is evident that the vertical profiles have a strong disagreement in terms of profile shape. CALIOP's profiles are noisier than the Harzgerode-DWD profile even during the nighttime when the solar background radiation is not interfering with the measurements. The differences in the measurements are even more evident when CALIOP data is averaged over 100 km, with a prominent peak in CALIOP backscatter values visible between 1.5 km and 2 km. The MPD between CALIOP and Harzgerode-DWD for the nighttime overpass is given in Figure 9h and clearly shows that most of the higher differences on the whole profile are mainly below 3 km. Table 4 shows strong positive mean percentage difference for all the along track averages, with values greater than 440% for 100 km. However, if we consider only the measurements taken above 3 km, the discrepancies decrease significantly. For 5 km and 15 km, the mean percentage difference above 3 km is 68 ± 240%. For 25 km, 35 km and 100 km, the mean percentage difference above 3 km is 65 ± 239%, 69 ± 237% and 70 ± 236%, respectively. The mean backscatter coefficient values with the respective standard deviation for both daytime and nighttime CALIOP profiles over Harzgerode is given in Appendix D, Table  A7.
Moreover, considering all 15 CALIOP overpasses at Mace Head and all 28 CALIOP overpasses at Harzgerode on cloud-free scenarios, Table 5 shows the percentage of occurrence of different FoE and MB values.  Table 5 shows that 80% of Mace Head cases presented negative values of MB, with a mean value of −3 × 10 −3 sr −1 km −1 . Correspondingly, the factor of exceedance (FoE) was also negative (−0.5 < FoE < 0) for the majority of the cases, with a mean value of −0.28. At Harzgerode-DWD, all the cases yielded a mean bias greater or equal to zero with a mean value of 3 × 10 −3 sr −1 km −1 . Correspondingly, the FoE was positive (0 < FoE < 0.5) for all the cases, with a mean FoE value of 0.34. We also investigated the influence of presence of different air samples on the obtained statistical comparison using HYSPLIT back trajectory model. HYSPLIT is run for the 15 Mace Head and the 28 Harzgerode cases, and the results are then compared to the percentage of occurrence of different MB values ( Figure 10). Firstly, Figure 10a shows that for Mace Head, pure continental (C) air samples are related only to negative MB. So, when the contribution in the air sample is entirely due to continental aerosols, CALIOP measurements of backscatter coefficient values tend to be lower compared to the backscatter coefficient values measured by ceilometer at Mace Head. Secondly, pure marine (M) air samples, tend to exhibit a mix of negative, positive and null MB. Thus, when the contribution in the air sample is entirely due to marine aerosols (sea salt), CALIOP measurements of backscatter coefficient are not necessarily lower than Mace Head measurements. Lastly, marine polluted (MP) air samples, which have a mix of marine and continental aerosols, are related most of the time to negative mean bias (MB < 0). Figure 10b shows the percentage of occurrence of different mean bias (MB) per different air samples at Harzgerode-DWD. Different from Mace Head (Figure 10a), the results for Harzgerode-DWD shows that at the non-coastal station, the MB calculated between CALIOP and Harzgerode-DWD backscatter coefficient values yielded only MB > 0 or MB = 0 results regardless of the type of air sample. This finding shows that overall, the backscatter coefficient values measured by CALIOP were higher than the backscatter coefficient values measured by the DWD ceilometer at Harzgerode.
In this long-term analysis, the comparison between CALIOP and the ground-based ceilometers yielded different results between the coastal and non-coastal regions. At Mace Head, the comparison between CALIOP and the ceilometer yielded only negative MPD. At Harzgerode, the comparison between CALIOP and the ground-based ceilometer only produced MB ≥ 0. Besides, the discrepancies found in the comparison between CALIOP and the ceilometer were much higher at Harzgerode.
These differences between Mace Head and Harzgerode can be attributed to different factors. First, the geographical location of the ground-based instruments and CALIOP ground-track near them. At Mace Head, most of the closest CALIOP's overpasses occur over the ocean while for Harzgerode, CALIOP's ground-track are over land. Besides, at Harzgerode, CALIOP ground-track might also be affected by the mountains surrounding the ground-based ceilometer. Second, the differences observed between Mace Head and Harzgerode in the long-term analysis can also be related to calibration process of both ceilometers. Although both apply Rayleigh calibrations to retrieve the backscatter coefficient at 1064 nm, they use different assumptions (Sections 3.1 and 3.2). The influence of the lidar ratio (LR) assumption on the shape of backscatter profiles at 1064 nm is minimal. However, the influence of calibration on the absolute values can be much more considerable, introducing systematic errors in the backscatter coefficient measurements. These systematic errors are always the same and hence does not present a significant impact on the variability. However, systematic errors can introduce an offset in the data. This could explain, at least partially, systematically higher backscatter coefficients from the Mace Head ceilometer compared to CALIOP, and/or systematically lower backscatter coefficients from the Harzgerode-DWD ceilometer compared to CALIOP. Lastly, the different ways of correcting for incomplete overlap in both ceilometers could also have influenced the results. At Harzgerode, the correction function provided by the manufacturer allows an estimate of the backscatter coefficient above 600 m. At Mace Head, in favor of data availability, the overlap function provided by the manufacturer was applied down to 300 m, introducing additional uncertainty in the backscatter coefficient estimate at low altitudes.

Summary and Conclusions
Over four years, 53 CALIPSO overpasses occurred within a 100 km ground track offset distance from an operating ceilometer in the coastal site of Mace Head, Ireland, and 50 occurred from the non-coastal site of Harzgerode, Germany. This study presents data from 30 and 40 overpasses from Mace Head and Harzgerode, respectively, considering only cloud-free scenarios and cases with the presence of thin clouds. The challenges in finding these cases were related to the data availability of the ceilometers and also to the high incidence of clouds, especially at Mace Head. First, two case studies were analyzed separately for each site, considering cloud-free cases and cases with the presence of thin-clouds. The maximum temporal resolution of the ground-based instruments was used (5 min for Mace Head and 60 min for Harzgerode-DWD) and compared against different along-track averages performed in CALIOP data (5 km, 15 km, 25 km, 35 km, and 100 km). The case studies showed an overall high agreement of backscatter coefficient at 1064 nm measured by CALIOP and by the ground-based ceilometers, even when thin clouds were involved in the analysis. At Mace Head, the mean percentage difference (MPD) between CALIOP and the ceilometer for both the cloud-free and the thin cloud cases was negative showing an underestimation of CALIOP measurements with respect to Mace Head measurements. At Harzgerode, the MPD yielded positive results. The Mace Head case studies also demonstrated a high dependence of the correlation coefficient (R) on horizontal averaging. Overall, a stronger correlation was found when along-track averaging up to 35 km was performed in CALIOP data. At Harzgerode, the dependence of R on horizontal averaging was less evident. Lastly, the correlation coefficient between CALIOP and the ceilometer measurements showed a dependence on the type of air sample. Polluted air samples produced a stronger correlation between CALIOP and the ceilometers compared to pure air samples.
Following, a long-term comparison accounting for all the 30 CALIOP overpasses at Mace Head and all the 40 CALIOP overpasses at Harzgerode between 2013 and 2016 was investigated. Due to the multiple scattering caused by thin clouds, which attenuates CALIOP's signal, only cloud-free cases were analyzed in this part of the study, reducing the number of cases to 15 for Mace Head and 28 for Harzgerode. Mace Head data was averaged over 1 h and then divided in daytime and nighttime overpasses. At Harzgerode, the profiles related to CALIOP's closest passage time were used for day (1200 UTC) and night (0100 UTC) overpasses. Different along-track averages in CALIOP (5 km, 15 km, 25 km, 35 km, and 100 km) data were used and compared against Mace Head and Harzgerode-DWD for both daytime and nighttime overpasses. Due to the low number of cases and available points for comparison at both sites, the p value was greater than 0.05 for all along-track averages and the R could not be considered as statistically significant for any of the overpasses. At Mace Head, both daytime and nighttime overpasses yielded an overall good agreement between CALIOP and the ceilometer measurements in terms of profile shape. The MPD between the measurements yielded strong negative values for both the daytime and nighttime cases, showing an underestimation of CALIOP measurements with respect to Mace Head measurements.
At Harzgerode, the daytime overpasses yielded better agreement in terms of profile shape between CALIOP and the ceilometer measurements compared to the nighttime measurements. Although the influence of background radiation is lower during the night, CALIOP's measurements may have been influenced by ground returns caused by the Harz mountain range (that can reach altitudes up to 1.1 km) nearby the ceilometer site.
The results of the long-term analysis that investigated the influence of different air samples in the comparison showed that negative mean bias was found in 80% of the Mace Head cases while positive (and/or null) mean bias was found for all of Harzgerode cases. The different geographical locations, different ground-tracks (ocean versus land), proximity to mountains and also the assumptions made in the calibration of the ceilometers can be attributed to being the cause of these differences. Moreover, the air samples with higher or lesser content of marine aerosols can also be related to the different biases observed within the datasets. However, a more in-depth analysis is needed to investigate if different aerosol types genuinely play a significant role in the comparison.
With this study, we attempted the first ever, to the best of our knowledge, comparison of backscatter values at 1064 nm wavelength from ceilometers and CALIOP over Mace Head, Ireland, and Harzgerode, Germany. It was found that frequent presence of clouds at Mace Head limited the number of available cases for this comparative study. Whereas, the presence of mountains around the Harzgerode site could have influenced the ground returns of CALIOP and hence the comparison. Furthermore, the ceilometers using different assumptions in the calibration process could have also played a role in the comparison involving coastal and non-coastal regions. To conclude, even with some limitations, this study demonstrates a possible way to compare CALIOP and ceilometer data at 1064 nm over two different environments. Comparing CALIOP and ceilometer measurements can be useful not only for validation purposes, but also for the possible use of combining space-borne and ground-based measurements to study aerosols and clouds variability over the globe with higher spatial resolution.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A. Statistical Terms
This Appendix provides mathematical definitions of the statistical terms used in this study The correlation coefficient (R), shows the strength of a linear relationship between the measurements and can vary from −1 (total negative correlation) to +1 (total positive correlation) with a value of 0 indicating no correlation.  [46].

Appendix B. Mean Backscatter Coefficient Values for the Case Studies
Appendix B.1. Mace Head