1. Introduction

Water attenuation coefficients, such as diffuse attenuation coefficient (Kd, m⁻¹) [1], lidar attenuation coefficient (k_lidar, m⁻¹) [2] and beam attenuation coefficient (c, m⁻¹) [3], are measures of how much light is absorbed or scattered by water. They are important parameters for understanding the properties of water bodies and have important implications for a wide range of applications as well. For example, the attenuation of light in water affects the quality and quantity of light available for photosynthesis in marine ecosystems and can limit the distribution of aquatic organisms that require light for growth and survival [4]. Water attenuation coefficients are also important parameters in the development of models to simulate the behavior of light radiation in water, such as those used in ocean remote sensing applications [5].

The diffuse attenuation coefficient of downwelling irradiance (Kd, m⁻¹) is an important water property related to light penetration and availability in aquatic systems that is now generated routinely from satellite ocean color observations. These include Kd at 490 nm from the moderate resolution imaging spectroradiometer (MODIS) on-board the NASA Earth observing aystem (EOS) Aqua and Terra satellites [6,7], from the visible infrared imaging radiometer suite (VIIRS) on-board the polar orbiting Suomi-NPP and NOAA-20 satellites [8,9], from the ocean and land color instrument (OLCI) on-board the European Space Agency’s (ESA) Sentinel-3 mission [10], from medium resolution imaging spectrometer (MERIS) on-board the ESA’s ENVISAT satellite [11], and from the geostationary ocean color imager (GOCI) on-board South Korean communication, ocean, and meteorological satellite (COMS) [12]. The ocean color instrument (OCI) on-board the upcoming plankton, aerosol, cloud, ocean ecosystem (PACE) mission [13] scheduled for launch in early 2024, will provide standard retrievals of Kd at multiple wavelengths between 350 and 700 nm. Satellite ocean color remote sensing is an effective method to provide large-scale maps of Kd over basin and global scales for ocean waters at high spatial and temporal resolutions [8–12]. Despite the tremendous success of satellite ocean color measurements, this passive remote sensing technique has fundamental limitations [14–16], such as necessary atmospheric corrections [16–18] that could result in seasonal biases in remote sensing reflectance (Rrs, sr⁻¹) that can be propagated into derived chlorophyll, absorption, and other Kd products [19]. Because passive remote sensing techniques rely on sunlight as their radiation source, they yield little, if any, information on global oceans during nighttime and cannot provide observations during polar winters or in sea ice covered waters [20].

Space lidar has the potential to provide a wealth of new insights into the upper ocean to complement the satellite passive ocean color observations [14,15]. For example, the cloud-aerosol lidar with orthogonal polarization (CALIOP) onboard the cloud-aerosol lidar and infrared pathfinder satellite observations (CALIPSO) satellite [21–23] has provided a first glimpse into a ‘new lidar era in satellite oceanography’ on global scale plankton studies during both daytime and nighttime [20,24,25]. The advanced topographic laser altimeter system (ATLAS) onboard the NASA the ice, cloud, and land elevation satellite-2 (ICESat-2), NASA’s newest Earth observing satellite designed for global elevation studies [26,27], provides unique new information that augments existing satellite ocean color measurements and CALIOP lidar measurements by adding the depth dimension with high horizontal (∼0.7 m) and vertical resolution measurements [28]. During the past decade, innovative retrieval methods have been developed to translate space-borne lidar signals into ocean optical properties such as particulate backscattering coefficient (b_bp, m⁻¹) [29,30] and subsurface depolarization ratio [28]. Lidar can be used to measure the lidar attenuation coefficient (k_lidar, m⁻¹) of water, which describes how quickly laser light is absorbed or scattered as it travels through the water column [31,32]. However, literature regarding the k_lidar over basin and global scales for ocean waters including Arctic and Southern oceans is currently very limited.

This study demonstrates the utility of space lidar (ATLAS/ICESat-2) for measurements of the lidar attenuation coefficient in the global oceans at night. In section 2, we propose an easily implemented method to calculate values of k_lidar from ATLAS lidar measurements. The seasonal distributions of ATLAS observed k_lidar over open oceans and polar oceans are presented in section 3. Some brief conclusions are given in section 4.

2. Data and method

2.1 Dataset

The only instrument onboard ICESat-2 is ATLAS, a 532 nm photon-counting lidar with a 10 kHz pulse repetition rate and a laser spot footprint diameter of ∼11 m at the Earth’s surface [33,34]. ATLAS combines a multi-beam transmitter (6 beams) that delivers nearly contiguous along-track measurements (0.7 m resolution) with a high vertical resolution photon counting receiver and extended orbital coverage (88° N to 88° S) to provide high-resolution, accurate measurements of Earth’s surfaces [33,34]. The more detailed information on the ICESat-2 mission is summarized in [26].

Version 5 of the ICESat-2 ATL03 geolocated photon data [35] from October 2018 to November 2020 was used in this work. The ATL03 product, which is publicly available through the National Snow and Ice Data Center (NSIDC) [36], was designed to be a single source for all photon data and ancillary information (e.g., the ATLAS impulse response function) required by one or more higher-level data products [37]. The data used in this work are restricted to ATLAS nighttime ocean measurements having surface backscatter photon counts between 1 and 12 per laser pulse and for which the atmospheric column optical depths are less than 0.2. Cases for which the ocean surface return is greater than 12 counts/pulse or less than 1 count/pulse are removed in the retrieval process due to, respectively, possible saturation from specular reflection and low signal-to-noise ratio (SNR) [38]. The cases with atmospheric column optical depths > 0.2 are eliminated to avoid atmospheric forward scattering effects on the ocean returned lidar profiles [39]. During daytime, the solar background noise could be higher than the subsurface returned signals [40], which presents challenges for the k_lidar retrieval. As a result, in this study we only use the ATLAS nighttime measurements to investigate the values of k_lidar in global oceans. These nighttime data will complement the daytime-only results of diffuse attenuation coefficient Kd obtained from satellite-based passive sensor ocean color observations.

MODIS monthly products of absorption (a, m⁻¹) and backscattering (b_b, m⁻¹) coefficients at 531 nm from 2018 to 2020 were used in this study to estimate the Kd at 531 nm by a semi-analytical model described in [6] (named as method 1 hereafter). In addition, MODIS monthly products of diffuse attenuation coefficient Kd at 490 nm were used to estimate the Kd at 532 nm as Kd(532) = 0.68(Kd(490)-0.022) + 0.054 [30] (named as method 2 hereafter). The scattering coefficient (b, m⁻¹) at 531 nm can be estimated from the MODIS monthly chlorophyll-a concentration product (chl, mg/m³) as: $b = 0.00226 + 0.31 \times ch{l^{0.62}}$ [41]. Finally, the MODIS beam attenuation coefficient (c, m⁻¹) is a sum of the absorption (a) and scattering (b) coefficients, i.e., $c = a + b$. MODIS Kd at 531 nm and 532 nm, along with a and c at 531 nm, are used to investigate the relationships between ATLAS observed k_lidar and MODIS retrievals in global oceans.

To investigate the values of k_lidar over the sea ice covered oceans, we used the daily sea ice concentrations generated from brightness temperature from the following passive microwave sensors: the Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR), the Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imagers (SSM/Is) and Special Sensor Microwave Imagers/Sounder (SSMIS) [42,43].

2.2 Method

CALIOP’s coarse vertical (30 m in the atmosphere, 22.5 m in the water) and horizontal (333 m) resolutions [21] and the nonideal transient response of the 532 nm detectors (e.g., noise tails after ocean surface) [44,45] present substantial challenges in retrieving ocean subsurface profiles [28,32]. The ATLAS instrument architecture differs significantly from CALIOP, allowing it to overcome many of CALIOP’s subsurface measurement deficiencies. For example, Fig. 1 shows lidar penetration depth profiles measured by ATLAS over the open ocean (blue) and a sea ice covered ocean (red). The profile data are the photon counts detected at each 15 cm vertical bin (∼11 cm in water) normalized by the photon count detected at the water surface (i.e., altitude = 0) [46]. To increase the SNR, 10 consecutive laser shots were averaged to generate the lidar depth profiles. Note too that the lidar depth profiles have been corrected for artifacts introduced by the ATLAS impulse response. A comprehensive derivation of this impulse response correction is given in [40,46]. The negative x-axis values in Fig. 1 represent nominal “in air” penetration distances below the Earth’s surface. These values are calculated without corrections for the refractive index of water [47], and hence do not indicate the penetration depth within sea ice. We use this quantity because the photons that penetrate through the pack ice or snow-covered sea ice surfaces can undergo multiple scattering, which can cause a time delay and result in a longer path length for the photons to travel through before arriving the detector [39,48]. The sharp drop of the signals after 16 m in Fig. 1 is because the ATL03 data product dose not include photons backscattered from >16 m below water surface for open oceans. This restriction is imposed by the ICESat-2 telemetry window, which limits the amount of data downlinked to ground stations [37].

 

Fig. 1. Examples of normalized Lidar depth profiles observed by ATLAS over open ocean (blue) and a sea ice covered region (red). The green and black lines show the exponential fits to the subsurface portions from 4 to 14 m below ocean surface and sea ice surface, respectively.

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The effective lidar attenuation coefficient (k_lidar, m⁻¹) can be calculated from the exponential decay of the lidar signal as,

In this study, the region from 4 to 14 m below the signal peak (approximately 3 to 10.5 m in water) was used for k_lidar retrieval. As shown in Fig. 1, the green and black lines are the exponential fits to the subsurface portions from 4 to 14 m below the surface peaks. The lidar signals from the surface to the depth of ∼3 m are not selected for the k_lidar retrieval to avoid complications introduced by measurements closer to the surface, which could potentially include effects from the laser pulse width, sea surface roughness, and waves within the ATLAS field of view. The signals at larger depths (>10.5 m) are not used due to the distortions in these lidar signals caused by the ICESat-2 telemetry window limitation (e.g., Fig. 1). Here it is assumed that the backscattering coefficient and k_lidar are both constants within the retrieval depth region (3-10.5 m), which is usually true within a well-mixed layer as shown in Fig. 1.

For the two cases shown in Fig. 1, the values of k_lidar are about 0.05 m⁻¹ and 0.16 m⁻¹ for the open water and sea ice covered water, respectively. To investigate the k_lidar variations from open water to pack ice, Fig. 2 presents the ATLAS retrieved k_lidar (blue, left y-axis) along the ICESat-2 ground track (x-axis, black line in the insert image) on January 17, 2020, with the corresponding microwave observed sea ice concentration [42,43] shown in red (right y-axis). It is clear from Fig. 2 that the k_lidar in open waters (0% of sea ice concentration) is ∼0.063 ± 0.008 m⁻¹, and that k_lidar is positively correlated with the sea ice concentration (correlation coefficient: R = 0.93), varying from ∼0.08 m⁻¹ to ∼0.38 m⁻¹ for sea ice concentrations ranging from ∼20% to ∼88%.

 

Fig. 2. The values of ATLAS retrieved k_lidar (blue, left y-axis) on January 17, 2020, along ICESat-2 ground track (x-axis) vs. sea ice concentration (red, right y-axis). The black line in the insert image shows the ICESat-2 ground track with the background color representing the sea ice concentration.

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The higher values of k_lidar over sea ice covered areas are open to multiple interpretations. If the ice is especially clear and wholly transparent to the incident laser beam, e.g., the sea ice is relatively thin and not heavily snow-covered, the lidar pulses can penetrate the ice surface and reach the ice-water interface, the higher values of k_lidar below would suggest that the water there is considerably more turbid than is typically found in open oceans, and perhaps indicate the presence of phytoplankton blooms [49]. On the other hand, if the ice is multi-layered or snow-covered or contains air bubbles or other occlusions, multiple scattering can introduce time delays (i.e., pulse stretching) into the photons backscattered from within the ice. In this case, the apparent subsurface signal used to calculate k_lidar is most likely some combination, in unknown proportions, of single scattered photons from the water below the ice pack and multiply scattered photons from within the ice. The lidar signals may be partially or completely attenuated before they reach the ice-water interface. At present, we know of no generally applicable remote sensing method for reliably distinguishing between single scattered returns and multiply scattered returns. ATLAS retrieved k_lidar over global oceans and the entire Arctic and Southern oceans, including sea ice covered oceans, are given in next section.

3. Results and discussion

3.1 Seasonal distribution of global k_lidar

In this section, we provide the global distributions of effective lidar attenuation coefficient observed from ATLAS nighttime measurements, which are seasonally averaged for the 2018-2020 period and binned on a 0.5° latitude by 0.5° longitude grid over global open oceans (Fig. 3). Figures 4 and 5 show ATLAS observed k_lidar over Arctic and Southern oceans binned into 25 km² grid cells, including sea ice covered regions. The white areas in high latitudes in Figs. 3–5 indicate either no ICESat-2 nighttime measurements or measurements that are excluded from our analyses, as described in section 2.1. Histogram of ATLAS observed k_lidar over open ocean (blue), Arctic (red) and Southern Oceans (black), as well as MODIS Kd at 531 nm (green) and 532 nm (pink), are given in Fig. 6.

 

Fig. 3. Seasonal distributions of ATLAS observed effective lidar attenuation coefficient (k_lidar) during nighttime (a) March-May; (b) June – August; (c) September – November; and (d) December – February. Data are seasonally averaged climatologies for the 2018 -2020 period binned to 0.5 latitude by 0.5 longitude pixels.

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Fig. 4. Seasonal distributions of effective lidar attenuation coefficient (k_lidar) during nighttime (a) March-May; (b) June – August; (c) September – November; and (d) December – February. Data are seasonally averaged and binned to a grid cell size of 25 km by 25 km.

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Fig. 5. Seasonal distributions of effective lidar attenuation coefficient (k_lidar) during nighttime (a) March-May; (b) June – August; (c) September – November; and (d) December – February. Data are seasonally averaged and binned to a grid cell size of 25 km by 25 km.

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Fig. 6. (a) Histograms of ATLAS observed effective lidar attenuation coefficient k_lidar in global open ocean (blue) vs MODIS observed diffuse attenuation coefficient Kd (green at 531 nm and pink at 532 nm by two methods). (b) Histograms of ATLAS observed effective lidar attenuation coefficient k_lidar over Arctic (red) and Southern (black) oceans.

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The values of k_lidar at 532 nm are from 0.045 to 0.39 m⁻¹ over the global open oceans (blue in Fig. 6(a)), while MODIS Kd are from 0.055 to 1.52 m⁻¹ at 531 nm by method 1 (green in Fig. 6(a)) and from 0.051 to 4.39 m⁻¹ at 532 nm by method 2 (pink in Fig. 6(a)). In clear oceanic waters (e.g., oligotrophic ocean gyres), ATLAS observed k_lidar is typically low, with values ranging from 0.045 to 0.07 m⁻¹ with a mean of ∼0.058 m⁻¹ (Figs. 4 and 6(a)), which are consistent with MODIS results with mean values of clear water Kd ∼0.060 ± 0.010 and ∼0.055 ± 0.011 m⁻¹ by the two methods. As shown in Fig. 3, the higher values of k_lidar (e.g., > 0.1 m⁻¹) are often found in coastal regions and at sea ice edges, where high levels of suspended particles and phytoplankton biomass limit light penetrations into the water column [50–53]. Figure 3 indicates that k_lidar also varies seasonally, especially in high latitude oceans such as the North Atlantic Ocean (> 50°N), where mean values of ∼0.063 ± 0.010, 0.071 ± 0.011, 0.068 ± 0.008, 0.063 ± 0.005 m⁻¹ are measured in, respectively, spring (Fig. 3(a)), summer (Fig. 3(b)), fall (Fig. 3(b)), and winter (Fig. 3(d)), reflecting relatively higher values in the summer and fall months, and smaller values in winter and spring months.

The observed k_lidar are ∼0.073 ± 0.013 m⁻¹ and 0.057 ± 0.01 m⁻¹ for the waters without sea ice cover in Arctic and Southern oceans, respectively (Fig. 6(b)). Compared with the open water, the values of k_lidar over sea ice covered regions are much higher. The k_lidar of sea ice covered areas in Arctic is from 0.16 to 0.39 m⁻¹ with a mean of ∼0.202 m⁻¹ (red in Fig. 6(b)), and it is from 0.14 to 0.29 m⁻¹ with a mean of ∼0.192 m⁻¹ for sea ice covered regions in Southern Ocean (black Fig. 6(b)). It is clear from Figs. 4 and 5 that the seasonal changes of k_lidar in polar regions are closely related to the extent and distribution of sea ice, which can limit the amount of light penetrating the ocean surface and which in turn affects the amount of light available for photosynthesis by phytoplankton and other marine organisms living underneath sea ice [54–56].

3.2 Discussion

The relations among effective lidar attenuation coefficient, k_lidar, diffuse attenuation coefficient, Kd, and water inherent optical properties (IOP), namely beam attenuation coefficient (c, m⁻¹) and absorption coefficient (a, m⁻¹), are complex. The effective lidar attenuation coefficient is found to be strongly dependent on the water optical properties and as well as the lidar system, e.g., receiver field of view. Many researchers have suggested that k_lidar is fully or partially linked to both Kd and beam c [31,57]. For example, Lee et. al. reported that k_lidar from airborne lidar measurements agrees well with in-situ Kd in East Sound, Washington [58]. From a ship in the Southern California Bight, Churnside et. al. measured k_lidar values between 0.08 m⁻¹ and 0.12 m⁻¹ that were highly correlated with in situ measured beam c [2]. In addition, some investigators have suggested that k_lidar is between absorption a and beam c [59–61]. For example, Collister et. al., showed that the k_lidar from shipborne lidar is close to absorption coefficient of particulate and dissolved matter under wide field of view for shallow optical depth waters [62].

The relationship between ATLAS measured k_lidar and MODIS beam c is tested in Fig. 7, which provides k_lidar/c (y-axis) as a function of c × r (x-axis) where the radius of spot (r) is ∼ 21.25 m on the surface given that the ATLAS has a field of view of 85 $\mu $rad and an altitude of ∼500 km. It is evident from Fig. 7 that the ATLAS measured k_lidar is close to beam c when the c × r is close to zero, which is consistent with the Monte Carlo simulations shown by Gordon [31]. The value of k_lidar/c decreases as the value of c × r increases. This could be due to the multiply scattered photons that contributed to the received lidar signal and thereby reduces k_lidar below the value ofc.

 

Fig. 7. k_lidar/c as a function of c × r, where the radius of spot (r) is ∼ 21.25 m on the surface. The color represents the number of occurrences for a $\Delta ($c × r) - $\Delta ($k_lidar/c) box of 0.1 by 0.005.

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The relations between ATLAS measured k_lidar and MODIS Kd are given in Fig. 8(a) with the values of c × r greater than 2, which indicates k_lidar are related with Kd with a correlation coefficient of ∼0.56. Also, ATLAS k_lidar are larger than MODIS absorption coefficient as shown in Fig. 8(b) and smaller than MODIS beam c in Fig. 8(c). The cases with MODIS absorption coefficient larger than ATLAS observed k_lidar are almost all from nearshore shallow waters where the bottom reflectance could be significant and contribute to the MODIS remote sensing reflectance, Rrs, which in turn could introduce errors into the subsequent Kd and a retrievals. However, variations in the water attenuation coefficient over shorter time scales, such as diurnal changes, could also be responsible for the differences between ATLAS measured k_lidar and MODIS Kd shown in Fig. 8(a), because k_lidar presented in this study are from ATLAS nighttime measurements, while MODIS ocean results are from daytime observations. One factor that can affect the diurnal changes in the water attenuation coefficient is the presence of phytoplankton that live in the upper layers of the ocean and can undergo daily cycles of photosynthesis and respiration [63–65].

 

Fig. 8. (a) ATLAS observed k_lidar at 532 nm vs MODIS Kd at 531 nm. (b) ATLAS observed k_lidar vs MODIS absorption coefficient (a, m⁻¹). (c) ATLAS observed k_lidar vs MODIS beam c (m⁻¹). The red line is the 1:1 line. The color represents the number of occurrences.

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4. Summary

In this study, we present the first global and seasonal distribution of lidar effective attenuation coefficient, k_lidar obtained from ATLAS/ICESat-2 nighttime measurements. In clear oceanic waters, the value of k_lidar obtained from ATLAS is typically low and consistent with MODIS diffuse attenuation coefficient. In polar oceans, ATLAS observed k_lidar varies seasonally depending on the sea ice area and extent. The changes of k_lidar can have significant implications for the availability of light and phytoplankton in the ocean. For example, higher k_lidar over sea ice covered waters means that light is being more rapidly attenuated or absorbed, resulting in less light reaching greater depths, which in turn could limit the growth and distribution of phytoplankton and other photosynthetic organisms. Conversely, lower values of k_lidar suggest that light can penetrate deeper into the water, indicating higher clarity and better light availability at greater depths. Future work will analyze ATLAS daytime data (e.g., accurately remove solar background noise effects on ocean subsurface vertical profiles) for k_lidar retrieval and as well as the day-night k_lidar analysis to investigate the phytoplankton diurnal variations.

Our results demonstrate that ATLAS/ICESat-2 can provide important information about water attenuation coefficient which can be used to complement and/or validate the passive ocean color records such as MODIS and NASA’s upcoming Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission. Moreover, the atmospheric and ocean results from ATLAS/ICESat-2 measurements, as well as the retrieval algorithms, will benefit future space lidars such as ESA’s upcoming Earth clouds,aerosols and radiation explorer (EarthCARE), NASA’s atmosphere observing system (AOS), and Italy’s cloud aerosol lidar for global scale observations of the ocean-land-atmosphere system (CALIGOLA) missions.