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Abstract
Chlorophyll-a concentration (chl-a) is a great indicator for estimating phytoplankton biomass and productivity levels and is also particularly useful for monitoring the water quality, biodiversity and species distribution, and harmful algal blooms. A great deal of studies investigated to estimate chl-a concentrations using ocean color remotely sensed data. With the development of photon-counting sensors, spaceborne photon-counting lidar can compensate for the shortcomings of passive optical remote sensing by enabling ocean vertical profiling in low-light conditions (e.g., at night). Using geolocated photons captured by the first spaceborne photon-counting lidar borne on ICESat-2 (Ice, Cloud, and Land Elevation Satellite-2), this research reported methods for deriving vertical profiles of chl-a concentration in the upper layer of ocean waters. This study first calculates the average numbers of backscattered subaqueous photons of ICESat-2 at different water depths, and then estimates the optical parameters in water column based on a discrete theoretical model of the expected number of received signal photons. With the estimated optical parameters, vertical profiles of chl-a concentration are calculated by two different empirical algorithms. In two study areas (mostly with Type I open ocean waters and small part of Type II coastal ocean waters), the derived chl-a concentrations are generally consistent when validated by BGC-Argo (Biogeochemical Argo) data in the vertical direction (MAPEs<15%) and compared with MODIS (Moderate Resolution Imaging Spectroradiometer) data in the along-track direction (average R2>0.86). Using globally covered ICESat-2 data, this approach can be used to obtain vertical profiles of chl-a concentration and optical parameters at a larger scale, which will be helpful to analyze impact factors of climate change and human activities on subsurface phytoplankton species and their growth state.
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1. Introduction
Phytoplankton is the main source of primary productivity in marine ecosystems [1]. The productivity of phytoplankton determines the state of material cycling and energy flow in the ocean [2] and plays a crucial role in the marine biogeocycle [3]. Chlorophyll concentration is a great indicator for estimating phytoplankton biomass and productivity levels [4], and is also particularly useful for monitoring the marine environment, such as water quality, biodiversity and species distribution, and harmful algal blooms [5–6]. Conventional techniques of acquiring chlorophyll concentration in seawater are mainly in-situ ship-based/buoy-based measurements, which can provide vertical profiles with high accuracy, but generally has a limited spatial coverage [7]. With the development of space-based Earth observation sensors, satellite ocean color remote sensing has been widely used in marine environment monitoring and achieved large-scale and long-term observations for chlorophyll-a (chl-a) concentration [8–13]. However, this approach is limited by the solar radiation and satellite orbit, making it more arduous to work at high latitudes or at night and unable to provide vertical profile distributions.
Marine lidar techniques can compensate for the shortcomings of passive remote sensing. Both ship-based lidars [14–17] and airborne lidars [18–23] are able to obtain optical vertical profiles of the upper ocean, which include vertical profiles of chl-a concentration. For areas that are inaccessible to airborne or shipborne platforms, satellite-based lidar can provide a new solution of implementation. CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) borne on CALIPSO (Cloud-Aerosols Lidar and Infrared Pathfinder Satellite Observations) and launched in 2006 can monitor aerosols and clouds 24 hours a day [24–25]. Hu et al. extended the application of CALIOP data to the marine for the first time [26]. Then, many studies investigated to calculate seawater optical parameters from CALIOP data and confirmed the reliability of the proposed inversion methods [27–30]. Behrenfeld et al. made a great progress on the use of CALIOP data to obtain phytoplankton biomass, breaking through the limitations of passive ocean color remote sensing that cannot work at polar night [31]. The tremendous advances directly demonstrated the great potential of satellite-based lidars to obtain many key parameters at the upper layer of seawater. However, the low vertical resolution of CALIOP, only 22.5 m in seawater [25,31], limited the acquisition capacity of vertical distribution information.
In 2018, NASA successfully launched ICESat-2 (Ice, Cloud, and Land Elevation Satellite-2), the world's first satellite carrying a photon-counting lidar, i.e., ATLAS (Advanced Topographic Laser Altimeter System). Benefitting from the extremely sensitive photon-counting sensors, ATLAS can respond to the weak signal at a single photon level, making it possible to acquire weak subaqueous signals via the satellite platform [32–33]. ATLAS has three strong and three weak beams in the cross-track direction. The interval of adjacent laser spots is only ∼0.7 m on ground (with a high repetition frequency of 10kHz) and the vertical resolution is only 0.0225 m in water (the time to digital converter achieves the time bin of 200ps) [34–35], allowing the construction of six topographic profiles with a vertical accuracy of several tens of centimeters [36]. Lu et al. used ICESat-2 data for the first time to obtain and validate the vertical distribution of optical parameters in seawater [37–38] and also to quantitatively analyze polar phytoplankton carbon biomass [39]. Their studies demonstrated the great potential of ICESat-2 to obtain vertical profiles of ocean optical properties.
The main objective of this study is to estimate the vertical profiles of chl-a concentration within the upper layer of seawater on the use of ICESat-2 photon-counting lidar data. Monitoring vertical profiles of chl-a concentration provides an additional basis for seawater environment monitoring and phytoplankton biomass assessment. Considering the extremely weak subaqueous signal and the interference from the device and environment, the preprocessing was conducted to extract and recover water column signals. Then, the inversion of seawater optical parameters was achieved by constructing discrete analytical models using ICESat-2 data. On this basis, the vertical profiles of chl-a concentration in the upper layer of ocean waters were estimated separately using two different empirical algorithms or ways, i.e., using the volume scattering coefficient β(π, z) at different depths and the attenuation coefficient α(z). In two study areas in the Pacific and Indian Oceans with different water qualities, the derived vertical chl-a concentration from two methods were quantitatively validated with in-situ BGC-Argo data and compared with the MODIS derived chl-a concentration.
2. Data and study areas
The laser pulse on ICESat-2 generated by a 532 nm laser transmitter is split into six beams, i.e., three strong beams and three weak beams in the cross-track direction. The energy of the weak beams is approximately to a quarter to that of the strong beam. With the repetition frequency of 10 kHz and flight altitude of 500 km, the interval of adjacent laser footprints is approximately 0.7 m in the along-track direction. The green laser can penetrate the air water interface and propagate in the water column. The photon-counting lidar on ICESat-2 substantially differs from full-waveform lidars in that it can detect signals at a single photon level, i.e., the extremely weak backscattered photons in the water column can be detected and responded as photon events with specific time tags [33]. In this study, the ICESat-2 ATL03 product is used, which records and transforms each photon event into the geolocated photon with a unique time tag, latitude, longitude, and elevation based on the WGS84 ellipsoid [40]. For each geolocated photon, the ATL03 product also has a confidence level of 0-4 to preliminary identify signal photon from noise (a higher value means more likely being a signal photon). As ICESat-2 flies, six laser beams generate six ground tracks (GT), which correspond to GT1L, GT1R, GT2L, GT2R, GT3L, and GT3R from left to right in the ATL03 product [41].
As shown in Fig. 1, two ground tracks of ATL03 datasets which were obtained in the Indian Ocean (2019/03/27, RGT #1362, GT1L) and Pacific Ocean (2019/03/31, RGT #0027, GT1L) are used as the test data. The water quality around the laser track in the Indian Ocean is worse than that in the Pacific Ocean, especially around the north segment where is close to the shore, i.e., the purple box in Fig. 1(a). ICESat-2 ATLAS can detect signals at a single photon level with extremely high sensitivity. The solar-induced background noise rate (scattered from atmosphere, water surface, and water column) is approximately several MHz in daytime, which introduces interference on weak subaqueous backscattered signal. As a result, this study directly selected the ICESat-2 data measured at night to exclude possible influence arising from the solar background radiation. NCEP FNL (National Centers for Environmental Prediction – Final) Global Analysis provides wind speed data above sea surface with 1-degree by 1-degree grids every six hours [42]. These wind speed observations are linearly interpolated in time and bilinearly interpolated in space to ICESat-2 laser tracks, and are further used as auxiliary data to calculate the coefficient including lidar system and environmental parameters A.
Fig. 1. Main panel (left) illustrates two ICESat-2 ground tracks (white lines) and BGC-Argo positions (red and green crosses). The base map shows the bathymetry of the global ocean, derived from the ETOPO dataset [46]. BGC-Argo locations are enlarged in the right panels (the enlarged maps corresponding to two yellow boxes in the left panel). Two vertical profile data of chlorophyll-a (chl-a) were obtained by the station 2902120 in the Indian Ocean (a), and other two vertical profile data were obtained by the station 6902827 in the Pacific Ocean (b).
In each study area, the BGC-Argos (Biogeochemical Argo) that were around the laser track of ICESat-2 are used to verify the performance of the ICESat-2 derived chl-a vertical profiles. BGC-Argos from the Global Data Assembly Centre (GDAC) (ftp://ftp.ifremer.fr/ifremer/argo/dac/) provide multiple bio-optical parameter profiles, such as chl-a concentration, particle backscattering coefficient, and CDOM (Colored Dissolved Organic Matter) [43–45]. Figs. 1(a) and 1(b) show the locations of two buoys including station 2902120 and 6902827, respectively. These two BGC-Argos correspond to the ICESat-2 datasets in the Indian and Pacific Oceans, respectively. Each BGC-Argo has two independent observations, and the acquisition times are close to that when ICESat-2 flew over the study area. In addition, MODIS (Moderate Resolution Imaging Spectroradiometer) global chl-a products with 4-km spatial resolution are used as complementary datasets in large-scale verification, as the BGC-Argo data that has well spatiotemporal synchronization with ICESat-2 is relatively sparse. Considering that the possible vacancies at 4-km grid in MODIS daily data, the MODIS monthly average data product was chosen in this study. The MODIS products are provided by the NASA Ocean Color Website (https:// oceancolor.gsfc.nasa.gov).
3. Methods
In this study, the flow chart for deriving the vertical profile of chl-a concentration using ICESat-2 data has two main steps as shown in Fig. 2. Step (1): The ATL03 geolocated photons are pre-processed to 1) obtain the along-track averaged numbers of backscattered photons at different water depths, which includes distinguishing photons in the water column from signal photons on the sea surface, 2) calculate the averaged numbers of backscattered photons at different water depths, 3) calculate the impulse response function of ICESat-2 and correct the after-pulse effect coupled in subaqueous signals.
Step (2): The vertical profiles of chl-a concentration (Cchl, mg/m−3) are calculated by two different empirical methods. Method 1: the basic assumption is that the lidar attenuation coefficient α is a constant, and then the volume scattering coefficients β(π, z) at different depths can be calculated from the ICESat-2 measured data, where λ is the laser wavelength and z is the depth. Finally, the chl-a concentrations are obtained from the particulate backscattering bbp(λ, z), which are calculated from the volume scattering coefficients β(π, z) [47–48]. Method 2: the basic assumption is that the relationship of the attenuation coefficients α(z) and volume scattering coefficients β(π, z) can be linked as β(π, z)=Cα(z)k, and then α(z) and β(π, z) can be calculated from the ICESat-2 measured data. Finally, the chl-a concentrations are obtained from the diffuse attenuation coefficients Kd(z), which can be calculated from the β(π, z) and α(z) [49–52]. These two methods include 1) deriving the discrete theoretical model of the expected number of received signal photons on the water surface and in the water column, 2) calculating the coefficient including lidar system and environmental parameters A, and 3) calculating the chl-a vertical profiles using the spectrally resolved empirical models. The vertical profile is validated by the BGC-Argo data and the chl-a concentration is compared with the MODIS data in the along-track direction.
3.1 Preprocessing backscattered photons in water column
In open ocean areas (with deep water), the photons received by ICESat-2 mainly consist of laser photons (scattered by atmosphere, reflected by the water surface, and scattered from the water column) and noise counts (including dark noise and after-pulsing counts) [39,53]. Since the reflection coefficient of the water surface is much larger than the backscattering coefficient of the atmosphere and water, the photons with high spatial density (i.e., high confidence level in ATL03 products) are more likely to be the water surface reflected photons. The confidence level value ranges from 0 to 4 for each geolocated photon and a higher value means more likely being a signal photon. In this study, the photons with the confidence level of 4 are regarded as preliminary sea surface photons [41]. For ICESat-2, the expected number of water surface reflected photons are generally around one per laser shot, whereas the expected number of the subaqueous photons are much less than one [33]. The water surface reflected photons should be carefully removed from subaqueous photons; otherwise, the number of subaqueous photons will be overestimated.
ICESat-2 has a laser pulse width of 1.5 ns (full width at half maximum, FWHM) [33], and in the air-water interface, the vertical range within the pulse width may simultaneously contain the water surface and subaqueous photons. The laser pulse width of 1.5 ns corresponds to approximately 0.17 m in depth. Moreover, due to the wave effects, the elevation of the water surface fluctuates in the along-track direction, and here, an elevation thresholding method is proposed to determine the upper elevation boundary of the subaqueous photons. To be specific, in each along-track segment with a length of Δl, the mean sea level hmean are calculated using the preliminary sea surface photons within current segment and the standard deviation σ are calculated in ten neighboring along-track segments. Then, the photons whose elevations are within the lower and upper boundaries [Hmin, Hmax] construct the set of sea surface photons ns, where Hmin=hmean-4σ and Hmax=hmean+4σ. The upper elevation boundary of subaqueous photons was set as Hmin, i.e., the black curve illustrates this boundary in Fig. 3 in many along-track segments. Eq. (1) shows the criteria of this classification for the i-th along-track segment. Within the i-th along-track segment, L(i) is the start position of the along-track distance and [lj, hj] are the coordinates of the j-th ATL03 geolocated photons, where lj represents the along-track distance (transformed from the latitude and longitude) and hj represents the height. ns and nu correspond to the sets of sea surface photons and subaqueous photons, respectively. nl is the total segment number of the used laser track.
Fig. 3. ICESat-2 photons captured in the Pacific Ocean on March 31, 2019 (the latitudes range from 4.9°S to 4.9335°S), in which the black curve is the boundary between the sea surface and water column, i.e., hmean-4σ. The horizontal axis corresponds to relative along-track distances, and the vertical axis corresponds to photon heights based on the EGM2008 orthometric height, which are converted from the WGS84 ellipsoidal heights via VDatum Tool (https://vdatum.noaa.gov/vdatumweb/). In this study, the segment length Δl is set to 7 m. It should be noted that in the ATL03 product, the elevation of subaqueous photons does not consider the refraction effect in the water column, i.e., the actual depth is smaller than that shown in this figure.
Fig. 4. Definition of variables that are used to calculate the average number series of subaqueous photons Nu(z).
Here, we clarify why the bin size is set as 4 km×1 m as shown in Fig. 4. The basic criterion of the bin size is to balance the spatial resolution and precision when deriving the vertical profiles of chl-a concentration. For ICESat-2, the signal level of backscattered photons in the water column in Type I open ocean waters is generally from 10−3 to 10−2 counts per meter per laser shot (within 10 m in depth), which is roughly estimated using the cumulative histogram of subaqueous photons. This signal level of 10−3 to 10−2 counts per meter is extremely weak, and approximately only one photon event is generated by a photon-counting detector in 100 to 1000 successive laser pulses. In such signal level, the randomness or shot noise effect is the dominant error source, which directly influences the final derived chl-a concentration. As a result, thousands of successive measurements in the along-track direction should be accumulated to generate a cumulative histogram of subaqueous photons in the vertical direction. This accumulation of thousands of successive measurements is equivalent to averaging the small number of subaqueous photons and decreasing the randomness effect (or shot noise effect), which can obtain more a reliable result of chl-a concentration.
To quantify a reliable bin size, the basic theory and calculation are as follows. The probability that a photon-counting detector receives a specific number of photons in each time bin (200 ps for ICESat-2) satisfies the Poisson distribution [55]. According to the additivity of the Poisson distribution, with the accumulation of photons in successive laser pulse measurements, the number of photons in each time bin still obeys the Poisson distribution. The statistical fluctuations between the actual received photon number ε and the expected received photon number nM (nM=n(t, t+τ)⋅M considering accumulations) are the shot noise effect (or Poisson noise). n(t, t+τ) is the expected received photon number within the time bin (t, t+τ) in a single shot (without accumulations), and M is the accumulation number. Then, the absolute expected error of the shot noise within the time bin (t, t+τ) can be expressed as
The normalized shot noise is Error/nM. The normalized error Error/nM decreases gradually with increase of nM, and the normalized error should be generally less than 10% because it directly introduces nearly same level error to the deriving chl-a concentration. With a signal level of 10−3 to 10−2 count per meter, a bin size of 4 km×1 m contains approximately 5714 laser shots for ICESat-2 and ensures to accumulate more than 35 counts of photons, which corresponds to the threshold of 10% normalized error. However, accumulating a larger number of successive measurements, the spatial resolution of the derived chl-a concentration decreases accordingly. Within a bin size of 4 km×1 m, only one result of the chl-a concentration can be calculated. In addition, an excessively large number of accumulating successive measurements has an impact on the deriving results because the chl-a concentration itself may be changeable within a large bin size. In summary, the bin size of 4 km×1 m is generally a reasonable selection that balances the spatial resolution and precision when deriving the vertical profiles of chl-a concentration. In addition, to further suppress the fluctuations of derived chl-a concentrations, an overlapping strategy is also used as illustrated in Fig. 4. Using the segmental overlap in the vertical direction, more sampled values can be obtained at different depths, which improves the stability of derived results especially in the next process of Richardson-Lucy Deconvolution (RLD).
To obtain more reliable backscattered signals in the water column, the nonlinearity of the radiative transmission due to the after-pulse effect must be considered and corrected. This effect is mainly arising from the photon-counting detector and fiber for ICESat-2 [56] and make the measured signal always larger than the actual signal [57]. In this study, the RLD algorithm is used to recover the actual number series of subaqueous photons at different depths $\bar{N}_{u}(z)$ through iterations [58], and the k-th iteration process can be expressed as
According to the pioneering investigation [56], the impulse response function fs_mean(z) can be calculated from the ICESat-2 signal photons captured in the Sahara Desert at night because (1) nighttime data excludes all effects related to solar background radiation; (2) 532 nm laser pulses from ICESat-2 cannot penetrate desert surfaces; and (3) the desert has very little surface covering (e.g., vegetation) and the surface is relatively flat at the size of the 12 m laser spot.
3.2 Calculating vertical profiles of chl-a concentration
Given that the number series of subaqueous photons at different depths $\bar{N}$u(z) is discrete, in the process of propagating a unit optical length, the expected subaqueous photon number at a given depth can be expressed as
Alternatively, the signal photons reflected by the sea surface can be used to obtain A that is expressed as Eq. (5) [37]. The expected number of reflected signal photons on water surface $\bar{N}$s can be expressed as [53]
A is the coefficient including lidar system and environmental parameters, which can be approximated by A≈4π${s^{2}}{T^{2}_{w}}{{\bar{N}}_{s}}$/${n^{2}_{w}}{{\rho}_{s}}$. A is determined by the combination of the hardware parameters and the corresponding environmental parameters at the acquisition time.
Before calculating vertical profiles of chl-a concentration, the lidar attenuation coefficient α(z) and the volume scattering coefficient β(π, z) should be obtained in Eq. (6). The attenuation coefficient α can be obtained with an assumption of a fixed exponential decay of lidar subaqueous signal, i.e., using a constant lidar attenuation coefficient in the water column [39]. In this case, Eq. (6) can be simplified as
Based on Eq. (7), the volume scattering coefficient β(π, z) can be calculated at different depths. The backscattering coefficient of water bb can be expressed as bb(z)=2πβ(π, z) for nearly isotropic backscattering [65–67]. Considering the laser wavelength λ, bb(λ, z) can also be expressed as the sum of the seawater backscattering bbw(λ, z) (that is generally constant at different depths) and the particulate backscattering bbp(λ, z) [68]. Here, the wavelength λ is 532 nm using in ICESat-2. Regardless of the wavelength, in open ocean areas, the particulate backscattering bbp(λ, z) increase regularly with rising chl-a concentration Cchl, and a spectrally resolved empirical model between bbp(λ, z) and Cchl (that is valid from 420 nm to 650 nm) can be expressed as [48]
where ϕ(λ) and φ(λ) are wavelength-related coefficients [48]. Using Eq. (8), the vertical profiles of chl-a concentration Cchl(z) can be calculated, and here, we label this result as Method 1 to distinguish from the result obtained by the following method.However, in reality, most water column is non-uniform. The Klett algorithm is improved on the basis of the slope method [61], where α(z) and β(π, z) can be approximately related according to the form of β(π, z)=Cα(z)k and C is a constant. As a result, the lidar attenuation coefficient α(z) can be calculated as
Using Eq. (9) and Eq. (10), the vertical distribution of the lidar attenuation coefficient α(z) can be obtained. The relationship between the diffuse attenuation coefficient Kd and the lidar attenuation coefficient α mainly depends on the size of the field of view (FOV) [59,73,74] and these two parameters are nearly identical for ICESat-2, i.e., α(z)≈Kd(z) [54]. Then, the empirical relationship between the diffuse attenuation coefficient Kd and chl-a concentration Cchl can be used to calculate the vertical profiles of chl-a concentration as [49]
4. Results and discussion
Figures 5(a) and 5(b) illustrate the derived along-track vertical profiles of chl-a concentration in two study areas, which correspond to two laser tracks in Fig. 1(a) and Fig. 1(b). In the Indian Ocean, Fig. 5(a-1) represents the results calculated by Method 1 and Fig. 5(a-2) represents the results calculated by Method 2. Figure 5(a-3) shows the comparison between ICESat-2 depth-averaged chl-a concentrations by two methods and MODIS monthly average results. The right panels in Figs. 5(a-4) and (a-5) validate the derived vertical profiles of chl-a concentration with BGC-Argo measurements along the depth direction. Specifically, Fig. 5(a-4) corresponds to the red cross location in Fig. 1(a) and Fig. 5(a-5) corresponds to the green cross location. Similar results and comparisons in Figs. 5(b-1) to 5(b-5) are illustrated in the Pacific Ocean. As shown in Figs. 5(b-1) to 5(b-3), there are along-track gaps in the Pacific Ocean near 13°S and 7°S, and the co-located ICESat-2 ATL09 data indicate that, clouds exist at those areas and the sea surface was not detected in ICESat-2 ATL03 products. In two study areas, 4σ mainly range from 1 m to 2.5 m, where σ is the root mean square wave height of the sea surface. The vertical boundaries between the sea surface and subaqueous photons (i.e., hmean-4σ) generally locate at the depth from 1 m to 2.5 m. Considering the bin size of 4 km×1 m (as shown in above Fig. 4), if the more conservative value of 2.5 m is used, the layer of 3 m in depth should consider the subaqueous photons ranging from 2.5 m to 3.5 m. As a result, the derived vertical profiles of chl-a concentration (in Fig. 5) start from a depth of 3 m.
Fig. 5. Vertical profiles of chl-a concentrations corresponding to two ground tracks in the Indian Ocean on 2019/03/27 (a) and Pacific Ocean track on 2019/03/31 (b). In both (a) and (b), (1) represents the results calculated by Method 1 and (2) represents the results calculated by Method 2. Sub-figures (3) show the ICESat-2 chl-a concentration results versus MODIS results, including ICESat-2 Method 1 results (M1 yellow curves), ICESat-2 Method 2 results (M2 red curves), and MODIS products (green curves). The right panels (4) and (5) show the comparison between ICESat-2 chl-a concentrations and BGC-Argo measurements along the depth direction, i.e., (4) corresponds to the red cross location in Fig. 1 and (5) corresponds to the green cross location. The along-track gaps in (b-1) and (b-2) indicate that the sea surface at those areas was not detected in ICESat-2 ATL03 products, which is influenced by clouds. In (a-1) to (a-3), the purple box corresponds to the area close to the coast of India, which corresponds to the purple box in Fig. 1(a).
From Fig. 5, the chl-a concentration varies in the along-track direction, from blue (0.0 mg/m3) to red (∼5 mg/m3) that corresponds to the purple box in Fig. 5(a). The chl-a concentration also has intermittent and relatively sharp fluctuations in vertical profiles. In the validation with BGC-Argo in-situ measurements (four vertical profiles in the right panels in Fig. 5), the average MAPEs (Mean Absolute Percentage Error) of chl-a concentrations (Cchl mg/m3) in two study areas were 13.18% (Method 1) and 13.73% (Method 2), respectively. Table 1 lists the detailed MAPEs and RMSEs (Root Mean Square Error) for each vertical profile. In general, the MAPEs are less than 15% for two methods, which indicates that ICESat-2 derived vertical profiles of chl-a concentration have a good consistency with BGC-Argo in-situ measurements. Note that although we effectively suppress the shot noise effect using the accumulation strategy in both along-track and vertical directions, small remaining shot noise still has impact on the precision of derived vertical profiles of chl-a concentrations.
Table 1. Validation and comparison of chl-a concentration results from ICESat-2, MODIS, and BGC-Argo.
As a complementary in large-scale verification, depth-averaged chl-a concentrations derived from ICESat-2 were compared with co-located MODIS measurements. In this comparison, R2 (coefficient of determination) and RMSEs were used and the detailed R2 and RMSEs for two laser tracks are listed in Table 1. Generally, the average R2 in two study areas for Method 1 and Method 2 are 0.861 and 0.881, respectively. The comparison (R2>0.86) between MODIS and ICESat-2 derived depth-averaged chl-a concentrations verifies the effectiveness of using ICESat-2 to generate chl-a concentrations (ranging from 0 to exceeding 5 mg/m3) in different water quality environments. Inevitably, there are differences of measuring time and locations during the validation process, e.g., MODIS chl-a concentration is monthly averaged and observed in local daytime, whereas the used ICESat-2 data are captured at night. Such factors of temporal and spatial differences between ICESat-2 data and BGC-Argo/MODIS data introduce errors in the validation/comparison.
As shown in Fig. 5, in each study area, the ICESat-2 derived chl-a concentrations using two different methods (M1 and M2) are consistent or similar in magnitude, but the chl-a concentrations from Method 2 show a larger jitter than that from Method 1. Also, in Table 1, the chl-a concentrations obtained by the two methods have approximately the same accuracy in the validation/comparison. In the elastic lidar measurements as shown in Eq. (6), two unknowns (i.e., the volume scattering coefficient β(π, z) and lidar attenuation coefficient α(z)) need to be solved. To simultaneously solve the two parameters, different assumptions were pulled in different methods. Specifically, Method 1 based on Eq. (7) and Eq. (8) assumes that the water column is homogeneous and the attenuation coefficient α(z) does not vary with depths (α is constant). This assumption implies that the volume scattering coefficient β(π, z) should also be relatively stable at different depths. However, after obtaining constant α using a fixed exponential decay, β(π, z) (that is calculated using Eq. (7) and further used to obtain chl-a vertical profile) is actually depth dependent.
Method 2 based on Eq. (6) and Eqs. (9)–(11) overcomes the limitation of homogeneous water column assumption, and the attenuation coefficient α(z) was actually used to obtain chl-a vertical profile using Eq. (11). However, the calculated chl-a vertical profiles from Method 2 are generally more fluctuating than that from Method 1 in the vertical direction. This phenomenon may be influenced by the lower boundary Sm in Eq. (9), i.e., the maximum depth that can be detected. As the cumulative value in the denominator of Eq. (9) increases, the calculated α(z) will be more stable. However, although ICESat-2 can obtain exceeding 40 m in depth, the range window of the downloaded data in open ocean areas is only ∼60 m in vertical and only less than half corresponds to subaqueous photons. In other words, considering the refractive index in water column (the depth in water column will be shortened than the height in atmosphere due to the refraction effect in water column), the maximum depth that is recorded in an ATL03 product is approximately 15 m in open ocean areas. This is also the reason that the depth range in Fig. 5 is 10 m.
It should be noted that subaqueous backscattered signals from the ICESat-2 photon-counting lidar can reflect the magnitude of chl-a concentration profiles in seawater, but the used two bio-optical empirical relationships between bbp and chl-a [47,48], kd and chl-a [49–52] in the water column are generally reliable in Type I open ocean waters (chl-a ranging from 0.02 to 2 mg/m-3). The water quality in the two study sites in this study satisfies this standard except for the area close to the coast of India, which corresponds to the purple boxes in Fig. 1(a) and Fig. 5(a). This area has Type II coastal ocean waters, where the light scattering is more complicated by the addition of other substances that are independent of phytoplankton changes (such as dissolved yellow substances and suspended particulate matter), i.e., the nonselective light scattering will provide limited information. As shown in Fig. 5(a), these Type II coastal ocean waters have higher chl-a concentrations and have lower coefficients of determination for two methods (R2=0.78 and R2=0.75) than that of the entire laser track (R2>0.91 and R2>0.93), which indicates that the current bio-optical empirical relationships may not be suitable for other quality waters or at least introduces more errors.
For the issue that whether ICESat-2 can derive chl-a concentrations in the daytime, we roughly calculate the ICESat-2 measured noise rates under different solar elevation angles when ICESat-2 flies over open oceans. The solar elevation angles and measured noise rates can be directly obtained in the ATL03 product, i.e., solar_elevation and bckgrd_rate. Generally, in the daytime with the solar elevation angle smaller than 60°, the noise rates normally range from 0.5 to 1.5 MHz on ocean surfaces for ICESat-2, which correspond to noise photon number per meter in depth per laser shot from 4.4×10−3 to 10−3 counts. The magnitude of the backscattered signal per meter per laser shot in the water column ranges from 10−3 to 10−2 counts in Type I open ocean waters (within 10 m in depth for ICESat-2). To remove the noise counts, at least the signal-to-noise rate should be larger than 1 [75]. As a result, only when the solar elevation angle is smaller than 30° (i.e., the noise rate is generally less than 0.5 MHz), it is possible to derive the chl-a concentrations. For ICESat-2 photon clouds over oceans at noon at low latitude regions, it is generally impossible to derive the optical parameters and also the chl-a concentrations in the water column.
5. Conclusions
We reported a method for deriving a vertical profile of chl-a concentration in the upper layer of ocean waters using ICESat-2 photon-counting lidar data. The experiments in two study areas indicate that the derived chl-a concentration results generally have a good performance when validating with BGC-Argo data in the vertical direction (MAPEs<15%) and comparing with MODIS data in the along-track direction (average R2>0.86). Using ICESat-2 data, the developed method can derive vertical profiles of chl-a concentration and optical parameters, which can be further used to investigate the vertical distribution of other key parameters in marine ecosystems, e.g., the growth and distribution of algae in water. Note that the method is generally more reliable in Type I open ocean waters. Also, in contrast to passive remote sensing using solar radiation, ICESat-2 is able to obtain the vertical profiles of chl-a concentrations in ocean waters during nighttime.
Currently, the existing satellite ocean remote sensing techniques are generally two-dimensional plane, which differs significantly from the water profile or three-dimensional measurements required by industrial and scientific applications. On one hand, ICESat-2/ATLAS has made a breakthrough in the field of satellite ocean vertical profiling, and is a good reference for three-dimensional field inversion, especially for nighttime or polar areas where passive optical remote sensing is generally difficult to work. On the other hand, the research will no longer be limited to obtain vertical distributions of chl-a concentrations and optical parameters, but expand to analyze impact factors of climate change and human activities on subsurface phytoplankton species and their population growth. Based on this consideration, future work may be conducted to combine ocean color remote sensing with ICESat-2 photon-counting lidar. The fusion of active and passive remote sensing may be helpful to quantitatively investigate the spatial distribution and seasonal changes of ocean subsurface variables.
Funding
National Natural Science Foundation of China (42076185); China Postdoctoral Science Foundation (2020T130481); Natural Science Foundation of Shandong Province (ZR2020MD022).
Acknowledgments
We sincerely thank the NASA National Snow and Ice Data Center (NSIDC) for distributing the ICESat-2 data, the NASA Ocean Biology Processing Group (OBPG) for distributing the MODIS chl-a concentration data, the National Centers for Environmental Prediction (NCEP) for distributing the wind speed data, the International Argo Program for distributing the BGC-Argo floats data, and the National Geophysical Data Center for distributing the ETOPO topographic data.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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