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Supplementary Information for manuscript “Antarctic Spring Ice-Edge

Blooms observed from Space by ICESat-2”

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Materials and Methods

ICESat-2/ATLAS Detector’s impulse response

ICESat-2/ATLAS uses photomultiplier tubes (PMTs) as detectors in photon counting mode

where single photons reflected from the Earth’s surface will trigger a detection within the ICESat-

2 receiver. Each individual photon is time tagged and geolocated. This scenario is much different

than the full-waveform data collected by avalanche photodiodes (APDs) used by the first ICESat

mission (Abshire et al., 2005; Zwally et al., 2002). However, one possible artifact of PMT

measurements is after-pulses, which are small amplitude pulses appearing after the primary signal

output pulse (Hamamatsu photonics K.K., 2006). These PMT after-pulses can contaminate

otherwise accurate measurements of low level signals following a large amplitude of signal, for

example, the measurement of ocean subsurface signals where the ocean surface signal can be ~30

times greater than subsurface signal (Hu et al., 2007, 2016; Lu et al., 2016). There are two types

of PMT after-pulses: one is output with a very short delay (several nanoseconds to several tens of

nanoseconds) after the signal pulse and the other appears with a longer delay ranging up to several

microseconds. After-pulses with a longer delay are caused by the positive ions which are generated

by the ionization of residual gases in the photomultiplier tube. These positive ions return to the

photocathode (ion feedback) and produce many photoelectrons which result in after-pulses. The

time delay with respect to the signal output pulse ranges from several hundred nanoseconds to over

a few microseconds (Hamamatsu photonics K.K., 2006). More details about the PMT after-pulses

can be found in the PMT handbook (Hamamatsu photonics K.K., 2006).

The ICESat-2/ATLAS measured photons from land surfaces show these after-pulsing effects.

ICESat-2 ATL03 data provides time, latitude, longitude, and ellipsoidal height for each photon

event downlinked from ATLAS. Heights are corrected for several geophysical phenomena, such

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as effects of the atmosphere, tides, and solid earth deformation (Neumann et al., 2018). Figure

S1(A) shows the ICESat-2/ATLAS photon height distribution from the ground surface in the

along-track direction for the time period from 210 s to 250 s since start of the granule acquired on

October 16, 2018. The photon counts are averaged in 15 cm vertical and 0.001 s (~7 m) along-

track bins. The peak normalized photon counts averaged from 220 s to 240 s are shown in Fig.

S1(B), where the x-axis is normalized photon counts per bin and the y-axis is altitude in meters.

Note the altitude of the land surface return (peak photon counts) is set to 0 meters in Fig. S1 (B).

Because the 532 nm laser pulse cannot penetrate the land surface, the lidar backscatter signal from

a land surface goes quickly from a small value (in the atmosphere immediately above the land) to

a very large value and then, under ideal conditions, quickly back to zero (Hunt et al., 2009).

However, Fig. S1 clearly shows after-pulsing. A secondary signal excursion from ~10 m to ~45 m

below the primary surface return is due to PMT after-pulses with longer delay time. The amplitude

of this secondary return is more than 1000 times smaller than the value of primary return. The

narrow echoes at ~2.3 m and ~4.2 m below the primary return are due to PMT after-pulses with

short delay time.

Another example of ICESat-2/ATLAS PMT after-pulse effects is shown in Fig. S2. Figure S2

is same as Fig. S1 but the photons are from the ocean surface in the along-track direction during

the time period from 150 s to 200 s since start of granule on October 16, 2018. Similar to Fig.

S1(B), Fig. S2(B) also shows two small narrow echoes spaced at ~2.3 m and ~4.2 m below the

primary ocean surface return. Since these two small narrow echoes appear after any surface return,

irrespective of the surface reflectance, we conclude that they are persistent artifacts due to short

time delay PMT after-pulses.

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Compared with the land surface return of Fig. S1(B), the signal decay after the ocean surface

(Fig. S2(B)) is much slower and less deformed than the signal decay from land surface. This is

because this part of the profile contains legitimate signal arising from photons backscattered from

beneath the ocean surface. Nevertheless, Figures S1 and S2 both indicate that the ICESat-

2/ATLAS PMT detectors exhibits a non-ideal (slow decay) recovery of the lidar signal after the

surface return.

Comparison with MODIS ocean color results

In order to validate the retrieved ICESat-2 ocean subsurface results near Antarctic ice-

edges, the retrieved diffuse attenuated coefficient, Kd, particulate backscattering coefficients, bbp

and integrated ocean subsurface attenuated backscatter, Rrs, are compared with the available

results obtained from MODIS-Aqua monthly ocean color measurements. Figure S6 and S7 show

the comparisons between ICESat-2 retrieved ocean subsurface optical properties and

corresponding MODIS results on October 19th and November 17th, 2018.

Lidar integrated attenuated backscatter Vs. MODIS remote sensing reflectance.

The space-borne lidar equation is given by (Hostetler et al., 2006):

𝑃(𝑧) = !"!𝐸#𝜉𝐶$𝛽(𝑧)exp(−2∫ 𝜎𝑑𝑟′)"

$ (1)

where 𝑟 = (𝑧%&' − 𝑧)/cos(𝜃), is the distance from satellite lidar (𝑧%&') to the scattering volume

at altitude z. 𝜃 is off-nadir angle, 𝐸# is average laser energy, 𝜉 is lidar system parameter (e.g.

amplifier gain), and 𝐶$ is the lidar calibration constant. The 𝛽 and 𝜎 are volume backscatter

coefficient and volume extinction coefficient at altitude z, respectively. The range-scaled, energy

normalized, and gain-normalized signal is:

𝑆(𝑧) = "!((*),"-

= 𝐶$𝛽(𝑧)T.(𝑧) (2)

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where the two-way transmittance from the space lidar to the scattering volume at altitude z is:

𝑇.(𝑧) = exp(−2∫ 𝜎𝑑𝑟′)"$ . For the atmospheric lidar, the signal /(*)

0"= 𝛽(𝑧)T.(𝑧) is attenuated

backscatter coefficient (Hostetler et al., 2006).

For the ocean lidar signal, the range-scaled, energy normalized, and gain-normalized signal

can be written as:

𝑆(𝑧) = 𝐶$𝑇&'1. (0)𝛽′(𝜋, 𝑧)T.(𝑧) = 𝐶𝛽′(𝜋, 𝑧)exp(−2𝛼𝑧) (3)

where 𝐶 = 𝐶$𝑇&'1. (0) is the calibration constant (Section 3.2 in the paper), 𝑇&'1. (0) =

exp(−2 ∫ 𝜎𝑑𝑟′)"2(*#$%3$)/567(9)$ is atmospheric two-way transmittance between the lidar and the

Earth’s sea surface, which is at 0 meters. The 𝛽′(π, z) and 𝛼 are volume backscatter coefficient

and effective attenuation coefficient of water at depth z below sea surface. Equation (3) is the same

as Eq. (1) in the paper. At ocean surface with z=0, Eq. 3 can be written as:

𝑆(0) = 𝐶$𝑇&'1. (0)𝛽′(π, 0) = 𝐶𝛽′(π, 0) = 𝐶𝛽% (4)

Here 𝛽% is the theoretical ocean surface backscatter estimated from wind speed (Hu et al., 2008).

Eq. (4) indicates that the measured sea surface signal, S(0), is attenuated by the atmospheric

absorption and scattering between the lidar and the Earth’s sea surface (two-way atmospheric

transmittance, 𝑇&'1. (0)). Section 3.2 in the paper describes the way to estimate the value of

calibration constant using 𝐶 = /($):#

. The proposed calibration procedure in Section 3.2 corrects the

effects of laser energy (𝐸#), lidar system parameter (𝜉), off-nadir angle (𝜃), lidar-sea surface

distance (r), and atmospheric two-way transmittance (𝑇&'1. (0) ) for each single laser shot

measurements.

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The lidar depth-integrated attenuated backscatter within the ocean’s surface layer at 532

nm, 𝑅𝑟𝑠;<=&" (sr-1), is obtained from the calibrated attenuated backscatter coefficients (/(*)0

),

through (Behrenfeld et al., 2013, Lu et al., 2016):

𝑅𝑟𝑠;<=&" = ∫ /(*)0𝑑𝑧 = ∫𝛽>(𝜋, 𝑧) exp(−2𝛼𝑧) dz = :&(?)

.@(5)

where β′(𝜋) (sr-1 m-1) is the volume scattering function (VSF) at the 180º scattering angle (Chami

et al., 2006), and 𝛼 (m-1) is the lidar effective attenuation coefficient.

The spectral radiance upwelling from beneath the ocean surface normalized by the

downwelling solar irradiance is expressed as MODIS spectral “remote sensing” reflectance, Rrs(𝜆)

at each wavelength 𝜆 in the visible domain with units of sr-1 (Lee et al., 1994). The MODIS Rrs

(sr-1) within the ocean’s surface layer at 531 nm can be written as:

𝑅𝑟𝑠 = ∫𝛽>(𝜗, 𝑧) exp(−2𝐾𝑑𝑧) dz = :&(A).B=

(6)

where β′(𝜗) (sr-1 m-1) is the volume scattering function at a scattering angle from 90º to 180º

(Mobley, 2001), and Kd (m-1) is the diffuse attenuation coefficient.

We now take into account the lidar 𝑅𝑟𝑠;<=&" of Eq. 5 and MODIS Rrs of Eq. (6), with two

assumptions. Assumption (A): we first assume that the water medium is isotropic, i.e., its influence

on light is the same in all directions at a given point, that is β>(𝜋) = β′(𝜗). Assumption (B): we

also assume that the lidar effective attenuation coefficient is equal to the diffuse attenuation

coefficient, that is 𝛼 = 𝐾𝑑. If these two assumptions are true, then the lidar 𝑅𝑟𝑠;<=&" (Eq.(5)) and

MODIS Rrs (Eq.(6)) are equivalent.

Assumption (A) is a reasonable assumption for natural waters in which the particles are

randomly oriented by turbulence. The theory and in situ measurements of volume scattering

function (VSF) (Berthon et al., 2007; Chami et al., 2006; Sullivan and Twardowski, 2009) also

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suggest that assumption (A) is valid. The lidar effective attenuation coefficient, 𝛼, lies between

the beam attenuation coefficient (unit: m-1) and the diffuse attenuation coefficient, Kd, depending

on the lidar spot size at the ocean surface (Montes et al., 2011; Vasilkov et al., 2001). For the spot

size of the ICESat-2 (~ 42.5 m), the lidar effective attenuation coefficient, 𝛼, is equal to the diffuse

attenuation coefficient Kd (Montes-Hugo et al., 2010; Churnside and Marchbanks, 2019).

Assumption (B) is valid.

As a result, the retrieved ICESat-2 integrated attenuated backscatter results at 532 nm are

compared with collocated MODIS Rrs at 531 nm in the main paper.

Data and materials availability: ICESat-2 ATL03 data available from National Snow and Ice

Data Center (NSIDC) are used in this study. GMAO MERRA-2 wind speed data are used for water

surface backscatter calibration and are available from MDISC managed by the NASA Goddard

Earth Sciences (GES) Data and Information Services Center (DISC). The sea ice concentration

data are from Nimbus-7 SMMR and DMSP SSM/I-SSMIS passive microwave data, version 1,

which can be freely downloaded from NSIDC. MODIS Aqua downwelling diffuse attenuation

coefficient, remote sensing reflectance and total backscattering coefficient data are provided by

the NASA Ocean Color Data Web (http://oceandata.sci.gsfc.nasa.gov accessed on 11/12/2019).

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Fig. S1.

(A) Photon distributions from land surfaces in the ICESat-2 along-track direction during from 210

s to 250 s since the start of the granule acquired on October 16, 2018. (B) The photons vertical

distribution profile; i.e., the normalized photon counts averaged from 220 s to 240 s. The x-axis is

normalized photon counts accumulated over 15 cm vertical bins and 0.001 s horizontal bins. The

altitude of the peak surface return is set to 0 meters in (B), while the altitudes below the land

surface are set to negative values.

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Fig. S2.

(A) Photon distributions from the ocean surface in the ICESat-2 along-track direction from 150 s

to 200 s since the start of the granule acquired on October 16, 2018. (B) The averaged normalized

signal return from 150 s to 200 s. The x-axis is normalized photon counts per accumulated over

15 cm vertical bins and 0.001 s horizontal bins. The altitude of the peak surface return is set to 0

meters in (B), while the altitudes below the sea surface are set to negative values in (B).

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Fig. S3.

Vertical distributions of ocean subsurface attenuated backscatter signal, (S(z)/C, sr-1m-1), observed

by ICESat-2/ATLAS at 532 nm on October 16th (A), 19th (B) and November 17th (C), 2018. The

colors show a logarithmic scale of calibrated attenuated backscatter: log10(S (z)/C).

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87

Fig. S3.88

Vertical distribution of ocean subsurface attenuated backscatter signal (S(z)/C, sr-1m-1) observed 89

by ICESat-2/ATLAS at 532 nm on October 16th (A), 19th (B) and November 17th (C), 2018. The90

color is logarithmic scale of calibrated attenuated backscatter: log10(S(z)/C).91

92

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Fig. S4.

ICESat-2/ATLAS retrieved ocean subsurface diffuse attenuation coefficient, Kd (m-1), at

532 nm on October 16th (A), October 19th (B) and November 17 (C), 2018. The ICESat-2

ATL03 data used in ocean subsurface study are shown on each panel.

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93

Fig. S4.94

ICESat-2/ATLAS retrieved ocean subsurface diffuse attenuation coefficient, Kd (m-1) at95

532 nm on October 16th (A), October 19th (B) and November 17 (C), 2018. The titles on 96

each panel are the ICESat-2 ATL03 data that were used in ocean subsurface study. 97

98

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Fig. S5

ICESat-2 orbit track (red) on October 16th, 2018. The red line shows the region used for the ocean

subsurface study. The background color is the MODIS diffuse attenuation coefficient at 490 nm

scaled to 532 nm.

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99

Fig. S5100

ICESat-2 orbit track (red) on October 16th, 2018. The red line is the area for ocean subsurface101

study. The background color is the MODIS diffuse attenuation coefficient at 532 nm.102

103104

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Fig. S6.

(A): ICESat-2/ATLAS retrieved ocean subsurface diffuse attenuation coefficients, Kd (m-1) (blue),

on October 19th, 2018 compared with co-located MODIS diffuse attenuation coefficients at 532

nm (red monthly; black daily). (B): ICESat-2/ATLAS retrieved layer-integrated particulate

backscattering coefficient, bbp (m-1) (blue), with co-located MODIS bbp (=bb-bbw) at 531 nm (red

monthly; black daily). (C): ICESat-2/ATLAS retrieved layer-integrated ocean subsurface

attenuated backscatter (sr-1) (blue) and co-located MODIS remote sensing reflectance, Rrs, at 531

nm (red monthly; black daily).

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105

106Fig. S6.107

(A): ICESat-2/ATLAS retrieved ocean subsurface diffuse attenuation coefficient, Kd (m-1) (blue) 108

on October 19th, 2018 was compared with co-located MODIS diffuse attenuation coefficient at109

532 nm (red monthly; black daily). (B): ICESat-2/ATLAS retrieved layer-integrated particulate110

backscattering coefficient, bbp (m-1) (blue) with co-located MODIS bbp (=bb-bbw) at 531 nm. (C):111

ICESat-2/ATLAS retrieved layer-integrated ocean subsurface backscatter (sr-1) (blue) with co-112

located MODIS remote sensing reflectance, Rrs at 531 nm.113

114115

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Fig. S7.

(A): ICESat-2/ATLAS retrieved ocean subsurface diffuse attenuation coefficients, Kd (m-1) (blue),

on November 17th, 2018 compared with co-located MODIS diffuse attenuation coefficients at 532

nm (red monthly; black daily). (B): ICESat-2/ATLAS retrieved layer-integrated particulate

backscattering coefficient, bbp (m-1) (blue) with co-located MODIS bbp (=bb-bbw) at 531 nm (red

monthly; black daily). (C): ICESat-2/ATLAS retrieved layer-integrated ocean subsurface

attenuated backscatter (sr-1) (blue) with co-located MODIS remote sensing reflectance, Rrs, at 531

nm (red monthly; black daily).

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116117

Fig. S7.118

(A): ICESat-2/ATLAS retrieved ocean subsurface diffuse attenuation coefficient, Kd (m-1) (blue) 119

on November 17th, 2018 was compared with co-located MODIS diffuse attenuation coefficient at120

532 nm (red). (B): ICESat-2/ATLAS retrieved layer-integrated particulate backscattering 121

coefficient, bbp (m-1) (blue) with co-located MODIS bbp (=bb-bbw) at 531 nm. (C): ICESat-122

2/ATLAS retrieved layer-integrated ocean subsurface backscatter (sr-1) (blue) with co-located 123

MODIS remote sensing reflectance, Rrs at 531 nm.124

125

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