Remote Sensing of Environment 184 (2016) 199–211

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Remote Sensing of Environment

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Evaluation of satellite-based algorithms to estimate photosyntheticallyavailable radiation (PAR) reaching the ocean surface at highnorthern latitudes

Julien Laliberté a, Simon Bélanger a,⁎, Robert Frouin b

a Université du Québec à Rimouski (UQAR), 300 Allée des Ursulines, Rimouski, Qc, Canadab Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, USA

⁎ Corresponding author.E-mail address: simon_belanger@uqar.ca (S. Bélanger)

http://dx.doi.org/10.1016/j.rse.2016.06.0140034-4257/© 2016 Elsevier Inc. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 12 October 2015Received in revised form 6 June 2016Accepted 10 June 2016Available online 10 July 2016

Two satellite-basedmethods to estimate daily averagedphotosynthetically available radiation (PAR) at the oceansurface are evaluated at high northern latitudes. The first method employs a precomputed Look-Up-Table (LUT)generated from radiative transfer simulations. The LUT associates spectral irradiance reaching the surface to agiven set of input parameters, namely solar zenith angle, cloud optical thickness, cloud fraction, ozone concentra-tion, and surface albedo. The secondmethod, as implemented byNASA's Ocean Biology ProcessingGroup (OBPG)in the standard Ocean Color data processing chain, expresses the energy budget of the atmosphere-surface-oceansystem via a simple radiative transfer model. The performance of these methods is evaluated using an extensivein situ PAR dataset collected in the Arctic Ocean between 1998 and 2014, with daily values ranging from 0.08 to61.07 Em−2 d−1. Amethodology is developed to compare in situmeasurements and satellite products of differentspatial and temporal resolution. Agreement is generally good between satellite-derived estimates and ship-baseddata and betweenmethods. Specifically, both methods yield a small positive bias of 6% and 2% and a relative un-certainty larger than that observed at low latitude, with a rootmean squared error (RMSE) of 33% and 20% for theLUT and OPBGmethods, respectively. This is attributed to the peculiar environmental conditions encountered inthe Arctic, namely low solar elevation, changing surface albedo due to sea ice, and persistent cloudiness. TheRMSE difference among methods is due to the high temporal resolution (3 h) of the International SatelliteCloud Climatology Project (ISCCP) LUT input not fully compensating for its low spatial resolution (280 km gridcells). The LUT method has the major advantage of providing PAR estimates in all conditions, including ice-cov-ered regions, while the OBPGmethod is currently limited to openwaters and a solar zenith angle lower than 83°.Consequently, the OBPG method may not account for as much as 38% of PAR reaching the Arctic ocean surfaceannually. Bothmethods have the potential to provide useful PAR estimates just below the ice, by including infor-mation about ice transmittance.

© 2016 Elsevier Inc. All rights reserved.

Keywords:Photosynthetically available radiationArctic OceanPrimary productionOcean colorPhotochemical processesClouds and sea ice

1. Introduction

Incident Shortwave Radiation (SW) at the Earth surface influencesthe atmospheric and oceanic circulation as well as the climate. At highnorthern latitudes, the most important parameters impacting SW aresolar elevation, fog, cloud cover, and sea ice cover (Gorodetskaya &Tremblay, 2008; Zhao & Garrett, 2015; Zygmuntowska, Mauritsen,Quaas, & Kaleschke, 2012).With globalwarming, there is clear evidencethat Arctic cloud cover is increasing during spring and summer months(Schweiger, 2004; Vavrus, Holland, & Bailey, 2010), while sea ice extentand thickness are decreasing (Stroeve et al., 2012). On the one hand, in-creasing clouds have resulted in dimming the SW flux reaching the sea

.

surface (Wang & Key, 2005; Dutton et al., 2006). On the other hand, lesssea ice allows more SW to penetrate the water column, creating a pos-itive feedback that further accelerates sea ice melting (Perovich,Nghiem, Markus, & Schweiger, 2007).

Changes in SWalso have implications on various key photobiologicaland photochemical processes that drive biogeochemical cycles. Throughphotosynthesis, phytoplankton harvest light to fix carbon dioxide(CO2), synthesizing organic matter (OM) that fuels the marine food-web (Platt & Jassby, 1976). Various photochemical reactions driven byenergetic ultraviolet radiation (UVR) also have profound impact onOM cycling, as well as cell damage-repair processes in marine systems(Gao & Zepp, 1998; Mopper & Keiber, 2002; Morrow & Booth, 1997;Smith & Cullen, 1995; Zepp, Erickson, Paul, & Sulzberger, 2011). Basedon satellite observations, several recent studies of the Arctic Oceanand its surrounding seas have attempted to quantify the impacts of

Fig. 1. Diagram of the study objectives.

200 J. Laliberté et al. / Remote Sensing of Environment 184 (2016) 199–211

environmental changes on phytoplankton photosynthesis (Arrigo, vanDijken, & Pabi, 2008; Bélanger, Babin, & Tremblay, 2013; Pabi, VanDijken, & Arrigo, 2008) and photochemical processes (Bélanger et al.,2006; Tank, Manizza, Holmes, McClelland, & Peterson, 2012; Xie,Bélange, Song, Benner, Taalba, Blais & Lefouest, 2012).

To quantify photochemical and photobiological processes, accurateestimations of UVR and visible solar radiation are imperative. Currentapproaches to estimate solar radiation reaching the sea surface arebased on satellite-derived observations and numerical modeling. How-ever, the uncertainties in these satellite-based assessments remain to bequantified. Thework presented here is motivated primarily by the needfor an adequate Arctic representation of the day-to-day variations ofUVR and photosynthetically active radiation (PAR), herein defined asthe photosynthetic photon flux density in Einstein (E) (mole of pho-tons) per unit area and unit time integrated over the 400 to 700 nmspectral range (Em−2 s−1 or Em−2 d−1). A remote access to synopticand reliable PAR information is necessary, among other things, formost marine primary production (PP) assessment (Campbell et al.,2002; Lee et al., 2015; Morel, 1991; Platt & Sathyendranath, 1993),and therefore crucial towards precise and unbiased satellite-based PPestimation methods. A method that provides information on the spec-tral distribution of incident light is needed for applying spectrally-re-solved PP models (Bélanger et al., 2013; Smyth, Tilstone, & Groom,2005) and describing photochemical processes involving chromophoricdissolved OM (Bélanger et al., 2006; Xie, Bélanger, Demers, Vincent, &Papakyriakou, 2009; Xie et al., 2012; Song, Xie, Bélanger, Leymarie, &Babin, 2013).

Satellite-based surface irradiance estimations are available from var-ious Earth observingprograms, but are often unreliable at high latitudes.For example, Zhang et al. (2013) pointed out that the shortwave flux ofthe Global Energy and Water Cycle Experiment Surface Radiation Bud-get (GEWEX-SRB) dataset has large uncertainties in polar areas. Dueto confusion between sea ice and clouds, the Ozone Monitoring Instru-ment (OMI) Surface Solar Irradiance (SSI) product excludes data at highlatitudes (Wang, Liu, Chance, González, & Chan, 2014). The Earth Sys-tem Science Workbench (ESSW) only estimated PAR below 60° N. TheTotal Ozone Mapping Spectrometer (TOMS) PAR product is limited tolatitudes lower than 66° N (Eck & Dye, 1991). Many of those productsare no longer operational and not suitable for Arctic applications pri-marily because of limited spatial coverage. Alternatives such as usingroutinely derived global total SW irradiance to estimate visible fluxexist, but the conversion from SW to PAR is contingent on uncertaintiesdue to atmospheric composition (e.g., water vapor, clouds, aerosols,etc.) (Baker & Frouin, 1987; Frouin & Murakami, 2007; Pinker &Laszlo, 1992). The Surface and Atmospheric Radiation Budget (SARB)product from the Clouds and the Earth's Radiant Energy System(CERES) (Wielicki et al., 1996) data can be converted to PAR (Su,Charlock, Rose, & Rutan, 2007) and performs relatively well over land-based mid-latitude stations with relative bias from in situ measure-ments ranging from 1.4% to 9.3%, but to our knowledge no one has eval-uated it over the Arctic.

NASA's Ocean Biology Processing Group (OBPG) produces instanta-neous and daily averaged PAR quantities on an operational basis usinglow Earth orbit (LEO) satellites designed to quantify ocean color (e.g.,Sea-Wide Field-of-ViewSensor (SeaWIFS) and theModerate ResolutionImaging SpectroradiometersMODIS-AQUA andMODIS-TERRA) (Frouin,Franz, & Werdell, 2003). Processing such multispectral radiometricmeasurements at high latitudes implies strict conditions. First, the avail-ability of the data is restricted by solar elevation. In fact, NASAOBPG PARproduct is limited to solar zenith angles b83° (has of Oct. 2015). Thislimitation means NASA OBPG PAR quantities are not available forN61% of the annual time at latitudes above the circumpolar Arctic Circle.Second, no PAR estimate is availablewhen N10% of a pixel is occupied bysea ice (as derived from passive microwave data). Third, the temporalbinning used to produce Level 3 (L3) time-composite PAR productscompromises accuracy yet does not systematically solve the gaps in

the Arctic area, resulting in many binned pixels with no informationor severe bias. As a result, PAR estimates at high latitudes can be unrep-resentative of the true central tendancy.

Due to limitations outlined above, Bélanger and co-workers pro-posed an alternative method to estimate spectrally-resolveddownwelling solar irradiance at the ocean surface (hereafter denotedas Ed(λ) where λ stands for wavelength) for all atmosphere and seaice conditions. The methods was developed to feed spectrally-resolvedphotochemical models going down to 290 nm in the UV-B domain(Song et al., 2013; Xie et al., 2009, 2012), as well as spectrally-resolvedphytoplankton photosynthesis models (Bélanger et al., 2013; Le Fouestet al., 2011; Tremblay et al., 2011).

Themain objective of the present study is to quantify the uncertain-ty and potential biases of Bélanger's method, as well as the OBPGmeth-od, using an extensive in situ data set of surface irradiance gatheredfrom various research cruises conducted in Arctic waters (Fig. 1-1,2).Becausemost in situmeasurements weremadewith quantum PAR sen-sors, we limit our evaluation to this spectrally-integrated quantity. Inaddition, the evaluation is particularly challenging since in situmeasure-ments are instantaneous and punctual in space,while satellite-based es-timation are spatially-integrated and sometime time-integrated.Consequently, we further examine the temporal and spatial variabilityof incident radiation. To complete the evaluation, satellite products gen-erated using the two methods are compared (Fig. 1-3).

2. Satellite-based methods to estimate surface solar irradiance

2.1. Look-up-table (LUT) approach

Bélanger and co-workers developed amethod for estimating inci-dent spectral irradiance in all atmosphere and sea surface conditionsusing a look-up-table (LUT) approach. The method yields adownwelling irradiance spectrum, Ed(λ), at the sea surface for agiven set of input parameters, namely the solar zenith angle (SZA),cloud optical thickness (τcl), cloud fraction (CF), ozone concentra-tion (O3) and sea ice concentration (SIC). The method employsprecomputed LUT of Ed(λ) that is interpolated for the current set ofinput parameters (hereinafter referred as the LUT method). This sec-tion describes the LUT generation and its interpolation to obtain thefinal Ed(λ, SZA, τcl, CF, O3, SIC), just above (0+) or below (0−) the air-sea interface.

2.1.1. LUT generationEd(λ) LUTwas generated using the radiative transfer model SBDART

(Santa Barbara DISORT Atmospheric Radiative Transfer; Ricchiazzi,Yang, Gautier, & Sowle, 1998). SBDART model was used since it hasbeen tested extensively over the years (Su, Charlock, & Rose, 2005;Su et al., 2007). Simulations were made for 19 values of SZA (0 to 90°),8 τcl (0 to 64), 10 O3 (100 to 500 Dobson Units (DU)) and 7 surface albe-do (As) (0.05 to 0.85), yielding a total number of 10,640 downwellingirradiance spectra covering the spectral range from 290 nm to 700 nmat 1 or 5 nm resolutions (N λ= 83 or 401). Note that the previous ver-sion of the LUT (Bélanger et al., 2013) did not account for the variability

Table 1Summary of field campaigns for which continuous surface irradiance were measured.

Cruise orprogram Year Instrument Measurements Months

Numberof days

The NOrth Water(NOW)

1998 LI-COR 192SAa PAR 4,6 321999 LI-COR 192SAa PAR 8–10 29

Canadian ArcticShelf ExchangeStudy (CASES)

2003 GUV-510b PAR 10 72004 GUV-510b PAR 6 20

MALINA 2009 PARlitec/SUB-OPSd

PARSpectral

8 23

TARA OCEAN 2013 C-OPSe Spectral 5–12 105VITALS 2014 C-OPSf Spectral 5 11ArcticNet (AN) 2005 LI-190SAa PAR 8–10 56

2006 LI-190SAa PAR 9 152007 LI-190SAa/PARlitec PAR 8,10–11 282008 LI-190SAa/PARlitec PAR 8–9 192009 LI-190SAa/PARlitec PAR 7–11 952010 LI-190SAa/PARlitec PAR 7–10 1132011 LI-190SAa/PARlitec PAR 7–10 842013 C-OPSf/PARlitec Spectral/PAR 8–10 432014 C-OPSf Spectral 8–9 24

a Data provided by Dr. Michel Gosselin (UQAR).b Data provided by Dr. Serge Demers (UQAR).c Data provided by Dr. Tim Papakiriakou (U. of Manitoba).d Data provided by Dr. Stan Hooker (NASA).e Data provided by Dr. Marcel Babin (Laval University).f Data provided by Dr. Simon Bélanger (UQAR).

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in As, which was kept constant at 8% (see discussion below). Total solarirradiance at the top of the atmosphere was taken to be 1366.7 Wm−2

(Thuillier et al., 2003). Marine aerosols (Shettle & Fenn, 1979) with anoptical thickness of 0.05 at 550 was kept constant. This value of aerosoloptical thickness represents a climatology established from sun pho-tometer measurements made at Barrow (71.3° N; 156.8° W) (Tomasiet al., 2012). A subarctic summer standard atmosphere was selected todepict typical maritime pressure, temperature and water vapor profiles(McClatchey, Fenn, Selby, Volz, & Garing, 1971).

SBDART computes both direct and diffuse components of thedownwelling irradiance above the sea surface Ed(0+,λ), which areused to compute the downwelling irradiance just below the sea surfaceEd(0−,λ). The diffuse component of Ed(0+,λ)wasmultiplied by 0.934 toaccount for the specular reflexion at the sea surface (6.6%, (Morel,1991)). The direct component of Ed(0+,λ) was multiplied by 1 minusthe Fresnel reflexion coefficient calculated using Gregg and Carder(1990)’s formulation for a wind speed of 4 m s−1. For evaluation pur-poses, a second LUT was generated for the downwelling irradiancejust above the sea surface Ed(0+,λ) by summing the direct and diffusecomponents of Ed. The downwelling irradiance (Wm−2 μm−1) wasconverted into photon flux (E m−2 nm−1) before it was stored in theLUTs. The 5-dimensional Ed LUTs (λ, SZA, τcl, O3, As) at 5 nm and 1 nmspectral resolutions comprise 883,120 and 4,266,640 elements, respec-tively. The next section explains how the LUT is used to obtain Ed for agiven time and pixel location.

2.1.2. LUT interpolationThe LUT can be interpolated to get Ed(λ) for any combination of in-

puts, i.e. SZA, τcl, O3, and As, as long as their values fall within therange of input parameters defined above. In general, large ocean pixelsare partly cloudy, therefore the cloud fraction (CF) over the surfacemustbe accounted for. To calculate the downwelling irradiance for a givenocean pixel, the Edclear and Edcloud are summed with respect to CF. Edclear

is obtained from the LUT by assuming τcl equal to 0. Edclear and Edcloud

are then added together to form the downwelling irradiance above (orbelow) the sea surface.

Epixeld λð Þ ¼ Ecloudd λð Þ � CFþ Ecleard λð Þ � 1−CFð Þ ð1Þ

Both Edclear(λ) and Edcloud(λ) are obtained from the LUT for the givenset of SZA, τcl, O3, and As using a full quadratic-linear interpolationscheme. SZA is simply calculated for a given time and position onEarth, while other inputs are obtained from satellite observations. Forthe surface albedo, assumptions need to be made. In high northern lat-itudes, presence of sea ice and low sun elevation significantly increaseAs. Here we estimate As by accounting for SIC. Assuming an ocean albe-do of 0.06 (Frouin & Chertock, 1992), the surface albedo was calculatedas follow:

As ¼ 0:06� 1−SICð Þ þ Aice DOYð Þ � SIC ð2Þ

where Aice(DOY) is the sea ice albedo that varies as a function of the dayof year following the data reported by Perovich et al., 2007; their(Fig. 3), and SIC is the fractional sea ice concentrationwithin a pixel pro-vided by satellite passive microwave observations.

2.2. OBPG approach

OBPG estimates daily PAR from ocean color satellites followingFrouin et al., 2003. The method employs an energy budget approach.Briefly, the energy reaching the surface is the initial flux that was notreflected nor absorbed by the atmosphere-surface system. The PARmodel, based on Frouin and Chertock (1992), uses plane-parallel theoryand assumes that cloud and atmospheric component can be decoupledwith no absorption by clouds in the visible portion of the solar spec-trum. The planetary atmosphere is therefore modeled as a clear sky

atmosphere positioned above a cloud layer and the solar flux reachingthe surface is

Ed ¼ Ecleard1−Að Þ1−Asð Þ ð3Þ

where A is the albedo of the cloud-surface systemand As is the albedo ofthe ocean surface, Edclear being the energy thatwould reach the surface inthe absence of clouds if the surface were not reflecting. In order to ex-press A as a function of the radiance measured in the PAR spectralrange by the satellite sensor, radiometric measurements are convertedinto reflectance using the incoming solar irradiance. This reflectance iscorrected for the effect of atmospheric transmission through absorption(ozone and water gases) and scattering (molecules and aerosols) in theatmosphere. Albedo of the cloud-surface system is then obtained bytransforming the resulting spectral reflectance into albedo. This is ac-complished using a typical cloud bidirectional function for the cloudyfraction of the reflectance, noting that A≈CF×Ac+As, where Ac iscloud albedo. All values are weighted and normalized by the extrater-restrial solar irradiance and averaged over the PAR spectral range.They are then integrated over day length according to SZA to yield adaily averaged PAR value. The observation made at the moment of thesatellite overpass is assumed to be representative of cloud conditionsduring the day. When several observations are acquired over a giventarget (or pixel), the individual daily estimates from 0:00 to 24:00UTC are weight-averaged using the cosine of SZA. This algorithm wasoriginally conceived for SeaWIFS but has been generalized to operateon any ocean color sensor with enough visible bands that do not satu-rate over clouds (e.g., MODIS).

3. Data and methods

3.1. In situ measurements

3.1.1. Field campaignsSeveral field programs collected continuous PAR measurements

ranging from 50°N to 80°N in the Arctic from 1998 to 2014 (Table 1).The oceanographic programs include the North Water polynya(NOW), Canadian Arctic Shelf Exchange Study (CASES), MALINA,

202 J. Laliberté et al. / Remote Sensing of Environment 184 (2016) 199–211

ArcticNET, TARA Oceans Polar Circle and Ventilation, Interactions andTransports Across the Labrador Sea (VITALS). The field data were col-lectedwhile the schooner (TARAOceans Polar Circle) or the icebreakerswere sailing in both open waters and variable sea-ice cover conditions.Most observationswere from late summer to autumn (Fig. 2),which is aperiod of the year where persistent cloud cover is usually encounteredin the Arctic (Chernokulsky & Mokhov, 2012).

3.1.2. Data processingInstrumentswere calibrated by themanufacturer before each cruise.

All instrumentswere cleaned on a regular basis andwere recording PARcontinuously (at 1 to 15 min intervals) throughout the field campaigns,providing detailed diurnal and seasonal variability of incoming light inArctic. This extensive dataset (837 days of observation) is used as a ref-erence to evaluate the satellite-based irradiance estimation methodsand to study its natural variability in the Arctic. To control the qualityof the data, the daytime solar zenith angle (SZA) was plotted togetherwith PAR measurements (Fig. 3A) and a scatter plot of PAR vs SZA wasexamined (Fig. 3B) to detect possible errors. For any given day, if twodistinct curve shapes in SZA vs PAR were observed between sunriseand sunset, the daily PAR was flagged and further examined. Days con-taining gaps or obvious outliers were screened out.

Moreover, data collected at sea sometimes suffered from shadows orreflection resulting from ship structure (e.g., communication towers).On-board precautionswere taken to avoid contamination from externalinfluences on natural light. In order to assess such uncertainties sources,during 7 cruises out of 16 (ArcticNET 2007–2011, 2013 andMALINA), 2sensors were positioned at distant locations on the ship. The examina-tion of the difference in PAR recorded under different conditionsallowed rigorous quality control and efficient elimination of outliers. Atotal of 704 days of observations out of 837 (84%) passed the qualitycontrol tests.

3.2. Satellite data

3.2.1. Atmosphere and sea iceIn this study, aswell as in our previous studies (Bélanger et al., 2013;

Tremblay et al., 2011; Song et al., 2013; Xie et al., 2009, 2012), atmo-spheric parameters (i.e., τcl, O3, and CF) needed to interpolate the EdLUT were obtained from the International Satellite Cloud ClimatologyProject (ISCCP; Rossow & Schiffer, 1991 (Rossow & Schiffer, 1991)).ISCCP produced a 26 year long (1983 to 2009) time series at 3 h timesteps, on a global equidistant grid of 280 km resolution, distributed asa radiative flux profile data set (ISCCP-FD-SFR) that includes the atmo-spheric inputs of interest used to interpolate the LUT (Zhang, Rossow,Lacis, Oinas, & Mishchenko, 2004). The total column ozone abundancesare from the Total Ozone Mapping Spectrometer (TOMS, Version 7),while clouds properties (c.f., τcl and CF) were calculated using infraredobservations provided by geostationarymeteorological satellites for lat-itudes b60° (Meteosat, GOES, GMS and Insat, (Desormeaux, Rossow,Brest, & Campbell, 1993)) and Advanced Very High Resolution Radiom-eter poleward (AVHRR) (Schweiger, Lindsay, Key, & Francis, 1999) onboard of polar-orbiting meteorological NOAA satellites for latitudesN60°. Sea ice concentration, which is used to estimate As, was obtainedfrom the National Snow and Ice Data Center (NSIDC). SIC were derivedfrom the SMMR and DMSP SSM/I-SSMIS passive microwave observa-tions (1984 to 2007) (Cavalieri, Parkinson, Gloersen, & Zwally, 1996),and near-real-time DMSP SSMIS observations (Maslanik & Stroeve,1999).

3.2.2. Ocean colorDaily PAR data derived using the method described in Section 2.2

from ocean color sensors SeaWiFS, MODIS-Aqua, and MODIS-Terrawere obtained from the OPBG web browser at the level 3 (http://oceancolor.gsfc.nasa.gov/cgi/l3). The OBGP product used here repre-sents the average value of the PAR geophysical variable over the length

of 24 h. The algorithm in use generates daily PAR values from all avail-able satellite passes directly converted to daily PAR. As indicatedabove, L2 daily PAR for each satellite overpass are binnedwith aweight-ed mean based on the cosine of the solar zenithal angle to produce L3daily PAR product (Patt et al., 2003). In the present OBPG PAR process-ing scheme, three criteria may prevent PAR from being produced overthe ocean: 1) the presence of high sun glint at the air-sea interface, 2)a SZA larger than 83°, and 3) SIC larger than 10% at the pixel. A combi-nation of SeaWiFS, MODIS-Aqua and MODIS-Terra should account forthe diurnal variability of the clouds and considerably reduce the satellitebiases. MODIS-Aqua has an ascending equatorial crossing time of 13:30(local solar time), while MODIS-Terra and SeaWiFS have descendingequatorial crossing time of 10:30 and noon, respectively. Therefore,MODIS-Aqua, MODIS-Terra and SeaWIFS L3 daily products (9.28 km)were merged with a simple median function.

3.3. Comparison of satellite products and in situ data

Satellite-based estimates of PAR are matched in the temporal andspatial frame shared with the available in situ data. The evaluation ofthe LUT and OBPGmethods through separate matchup exercises is con-ducted to account for the environmental variability. Since the in situdata were acquired on moving ships, hourly estimates of Ed(λ) fromthe LUT are computed with respect to the ship position and time. Be-cause the ISCCP data are distributed on a 280 km resolution grid at a3 h time interval, the atmospheric inputs are interpolated both inspace (bi-linear) and time for any given ship position and time. Forthat given position and time, As is calculated using Eq. (2) with SIC ofthe nearest neighbor 25 km resolution pixel and assumed constant dur-ing the day (daily SIC are used). The instantaneous output Ed(λ) fromthe interpolated LUT was numerically integrated from 400 to 700 nmto obtain PAR. Finally, the daily PAR was generated with a trapezoid in-tegration of the 24 instant hourly estimates (UTC).

Since the OBPG method was designed to produce PAR on a dailyscale, and that we cannot distinguish the spatial from the temporalvariability with the in situ dataset, the matchup exercise was onlyrelevant if the environmental variability within a given day of sam-pling was weak (hereafter referred to as intraday variability). Toevaluate the intraday variability during a day of in situ measure-ments, we extracted daily PAR from OPBG for each hourly positionvisited by the ship during day time (i.e. SZA b 90°). In other words,for a given day of in situ PAR measurements on a moving ship, upto 24 daily PAR estimates were obtained from OBPG for that day.Then the intraday variability was assessed using the coefficient ofvariation (CVintraday), calculated as

CVintraday %ð Þ ¼ 100� σPAR � PAR−1 ð4Þ

where σPAR is the standard deviation of the N ≤ 24 daily PAR esti-mates andPAR is themean daily PAR for that day. If the ship remainedat the same position during the whole day (or within a given 4.64 or9.28 km pixel), for example, CVintraday would be equal to 0% (N = 1,σPAR = 0), because only one pixel would be concomitant in spacewith the all the ship's positions. In contrast, if the ship was transitingin open waters over several km during summer time, up to24 OBPG pixels were used to compute CVintraday. Therefore, CVintraday

is essentially a measure of the spatial variability of PAR during agiven day of data acquisition. For example, under discontinuouscloud cover, CVintraday could reach values as high as 50%. In suchcases, the PAR evaluation may be irrelevant (see Section 4.2 formore details). We considered this variability when daily in situ PARwas compared to the mean OBPG PAR values obtained from thepixels encountered during day time.

Fig. 2. Number of days for which Ed was measured in situ, for each year and month.

203J. Laliberté et al. / Remote Sensing of Environment 184 (2016) 199–211

3.4. Evaluation metrics

To evaluate the performance of the algorithms, the mean bias (sys-tematic error) and the rootmean squared error (RMSE)were calculated.These metrics are considered sufficient for comparison with other stud-ies. Mean absolute difference is similar to RMSE and in our case do notprovide supplementary information for our analysis. These errors aredefined as follows:

BIAS ¼ 1N

XPARestimated−PARin situ

� �ð5Þ

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

XPARestimated−PARin situ

� �2r

ð6Þ

The bias and RMSE were also normalized by the average PARin situ

and express in relative unit (%) to facilitate comparison. Finally, we ap-plied a major axis (MA) regression model of type II (R package lmodel2(Legendre, 2014)) to estimate the slope (S) and the intercept (I) of thelinear regression.We examined whether we can reject the null hypoth-esis that S and I are unity and zero, respectively, at a significance level of0.05.

4. Results

4.1. Evaluation of LUT method

Arctic in situ daily PAR observations exhibited a wide range of natu-ral variability (≈three orders of magnitude). The maximum in situ PARvalue (61.07 Em−2 d−1) was observed around the summer solstice andthe minimum value (0.08 Em−2 d−1) was in mid-autumn. A relativelygood agreement was seen between in situ daily PAR and LUT estimateswith a high coefficient of determination (R2 = 0.881) for all matchups(Table 2). In fact, 318 days of observations out of 490 passed the qualitycontrol test for the period, which was restricted to 1998–2009 corre-sponding to ISCCP data availability. Due to the temporal bias in our insitu data set towards late summer and autumn (Fig. 2), more matchupdays are available for relatively low in situ PAR values (median =10.99 E m −2 d −1). The slope (1.033) and the intercept (0.350) of thelinear regression (Type II, major axis) were not significantly differentfrom 1 and 0, respectively (p N 0.05). The method was, however, posi-tively biased (6%), suggesting an overall overestimation of the predictedvalues (Fig. 4). The RMSE reached 4.952 Em−2 d−1, which gave a in rel-ative uncertainty of 33%. Finally, 63% of the matchups are within 30% oferror and 81% are within 50% of error. When restricting the evaluationto open water (N = 136), i.e. when SIC is smaller than 10% during thewhole day, (Table 2) the bias increases from 6 to 7% and the RMSEfrom 33 to 38%, possibly because the ship travels faster in absence ofice and experiencesmore spatial variability. Accordingly, statisticalmet-rics improved when the evaluation is limited to days for which the shipsailed b30 km (e.g., bias reduced to 2%, RMSE reduced to 30%; Table 2).

Table 2Performance of the satellite-derived daily PAR estimates. Statistics are provided for thewhole matchups and various subsets (see text).

Method N Bias RMSE Slopea Intercepta R 2

LUT 318 0.853 (6%) 4.952 (33%) 1.033 0.350 0.881LUT (SIC b 10%) 136 0.793 (7%) 4.545 (38%) 1.012 0.645 0.813LUT (Dist. b 30 km) 116 0.256 (2%) 4.464 (30%) 1.001 0.244 0.913OPBG 208 0.456 (2%) 5.227 (20%) 0.927 2.360 0.886OBPG (C.V. b 20%) 168 0.669 (2%) 5.155 (19%) 0.932 2.522 0.900OBPG (C.V. b 10%) 110 0.799 (3%) 5.319 (18%) 0.916 3.355 0.906OBPG (Dist. b 30km)

53 −0.093 (0%) 4.466 (17%) 0.892 2.675 0.931

a The slope and interceptwere calculated using a type 2 regression and numbers in boldare significantly different from 1 and 0, respectively, at p b 0.05.

4.2. Evaluation of OBPG method

Out of the 704 daily in situ PAR, 208matchupswere found for the pe-riod from 1998 to 2014. As mentioned above, this is because OBPG doesnot calculate PAR in presence of sea ice or when the sun is low on thehorizon. In addition, only 110 days out of 208 were characterized by anegligible intraday variability, i.e., when the coefficient of variation(Eq. (4)) for daily PAR extracted from the ship location during a givenday was below 10%. To illustrate the intraday variability concept, Fig. 5presents twomatchup days showing low and high CVintraday respective-ly. The top panels show the hourly positions of the ship during the twoselected days in northern Baffin Bay (left; August 21, 2005) and HudsonBay (right; August 9, 2007). The total distances travelled during thesedays were 301 and 402 km, respectively. The day in Baffin Bay clearlyexhibited a small intraday variability for the three ocean colors satellites(CVintraday= 2%) (Fig. 5b; left). In contrast, inhomogeneous cloud coveralong the 400 km transect in Hudson Bay created large differences indaily PAR (up to a factor of three) derived from each sensor (Fig. 5b;right). Part of the difference is probably due to the different orbit char-acteristics, which results in the observation of the same location at dif-ferent times of the day. In addition, large differences in the mean dailyPAR (CVintraday = 27%) appear along the transect due to combined spa-tial and temporal variability in cloud cover. This variability is partly cap-tured by the 3 h resolution of the ISCCP inputs (Fig. 5c). Both daysshowed variable cloud fraction ranging from 0.20 to 0.75, but the vari-ability was clearly smaller in Baffin Bay. The cloud optical thicknesswas smaller in Baffin Bay (b20) compared to that observed in HudsonBay (N20). As expected the observed short-term variability in instantPAR was generally higher than that captured by the satellite-based esti-mates from the LUT (Fig. 5d). In Hudson Bay, the presence of thickclouds between 12:00 and 15:00 UTC dimmed PAR, followed by anabrupt increase in PAR around 15:00UTC. This diurnal patternwas part-ly captured by the LUT method using ISCCP inputs.

Measured daily PAR in the Baffin Bay reached 30.2 compared to26.0 Em−2 d−1 for the LUT method. For comparison, the OBPG PARalong the 301 km transect varies within a relatively narrow range of29.9 to 32.2 Em−2 d−1, with a mean of 31.1 Em−2 d−1. If the mean isrestricted to daytime (Fig. 5b, black curves), the PAR remained thesame. In Hudson Bay, the in situ PAR was 35.1 compared to 32.4 and55.1 Em−2 d−1 for the LUTmethod and the clear sky simulation, respec-tively. For this particular day, the PAR along the ship transect derivedfrom OBPG varies by nearly a factor of 2 (28.3 to 47.5 with a mean of39.7 Em−2 d−1; Fig. 5b right). However, if we averaged the PAR for day-time only (Fig. 5b, black curves), the OBPG estimate (37.4 Em−2 d−1)

Fig. 3. June 12th 2004 (DOY= 164) around 71° N,−127W: a) example of measured surface PAR and expected SZA calculated as a function of attributed position and timestamp; b) PARversus SZA scatter plot with Pearson's R.

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falls closer to the in situ observation. These results suggest the evalua-tion of the performance of the OBPG using a moving ship will dependupon the spatial variability of the cloud cover encountered along itscourse during a given day.

Fig. 6 displays the scatter plot of in situ versus OBPG PAR esti-mates for the matchups available for the 1998–2014 period. Whenconsidering all available matchups (N = 208), we obtained a weakpositive bias of 2% and a RMSE of 20%. The relative RMSE slightly im-proved when matchups showing high intraday variability are ex-cluded from the analysis (Table 2). On average the intraday

Fig. 4. Scatter plot of in situ daily PAR versus satellite-derived daily PAR using the LUTmethod. The dot color corresponds to the surface state derived from the NSIDC (Ice forSIC ≥ 10%). Dashed line marks the 30% error. Inset is the scatter plot in logarithmic scale.

variability (CVintraday) computed using OBPG daily PAR estimatebetween sunrise and sunset was 12%, and 91% of the matchups(N= 190) showed a CVintraday lower than 30%. When only matchupswith negligible intraday variability are considered (CVintraday b 10%;N = 110), the bias increases to 3% and RMSE was lowered to 18%,while the R2 increase to 0.906. Finally, we also computed thestatistics for days when ship displacement was minimal (i.e.,b20 km; N = 41), and found even better performance of the OBPGmethod in terms of bias (0%) and RMSE (17%) with high coefficientof determination (R2 = 0.931), but with a slope significantly lowerthan 1 (S = 0.892) and an intercept significantly higher than 0(I = 2.675).

4.3. LUT versus OBPG methods

In this section, we compare the two satellite-based methods to esti-mate daily PAR. First we examine the typical spatial variability given byeach method. On one hand, the LUT method uses as input ISCCP cloudproducts at 280 km. OBPG uses averaged ocean-color satellite observa-tions (L3) on a 4.6 km resolution grid. The PAR spatial variationwithin a280 km pixel of the ISCCP grid is assessed usingMODIS-A andMODIS-Tmerged products, which are considered to reflect the true spatial vari-ability at this spatial scale. For this exercise, we selected an ISCCP pixelin the Norwegian sea located Northeast of Iceland (Fig. 7, inset). The580 4.6 km MODIS pixels falling within an ISCCP pixel were extractedfor each day of the month of July 2004. PAR from LUT method was cal-culated using the ISCCP data interpolated both in space and time foreach MODIS pixel centroids (see Section 2.1).

Spatial PAR variability, as represented by the error bars in Fig. 7, ismuch greater for MODIS (CV = 26%) than the one obtained from theLUT method (CV= 7%). As expected, based on the ISCCP's pixel resolu-tion (280 km), the bilinear interpolation will always give a smooth dis-tribution of pixel values. It is thus not precisely describing the locallyvarying conditions (e.g., situation of heterogeneous cloud cover) asthe OBPG method or the in situ data do. On average, 19% of the CV isnot accounted for with the LUT method interpolation and the differ-ences can reach up to 35% in certain cases.

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We also compare the twomethods over the whole Arctic Ocean, de-fined as the geographic region above the Arctic circle at 66.6° N (Fig. 8).Only pixels where OBPG PARwas availablewere considered in the com-parison (SeaWIFS, MODIS-A andMODIS-T, 9.26 km grid). The daily PARfrom year 2004 was arbitrarily chosen for this comparison. Fig. 8a illus-trates the average daily PAR calculated on the basis of the number ofavailable OBPG observations (Fig. 8b). The highest PAR values arefound in the Bering and Barents seas, whereas lowest values are foundin regions where sea ice is more important. The maximum number ofdayswith PAR data (N=203) is found at latitude 66.6° N in permanent-ly open waters. The latitudinal decreasing gradient of gaps in the dailydata was caused by the variations in the SZA over the year, combinedwith the presence of sea ice. In an additional analysis (not shown), welook at the number of available pixels in the Arctic as function of time.From January 1 to March 12th, no information is available. The numberof available pixels then increases until April 20th when the progressionis stopped by ice cover. From mid-June on, the number of availablepixels starts to expand again, following sea ice export and melt withoutany constraint from the SZA. It reaches amaximumonAugust 22nd, andthen declines until the end of autumn, as the day length shortens andthe ice starts to form again. After September 30th above the Arctic Cir-cle, no OBPG data are available.

For each day, the daily PAR estimates from the LUT method weresubtracted from the OBPG PAR pixel by pixel (Fig. 8c). Interestingly,the LUT method tends to yield higher PAR values prior to the summersolstice (negative values on Fig. 8c), and then returns lower values forthe rest of the season. This may be due to the higher surface albedo,which is accounted for in the LUT. The relative frequency distributionof daily PAR values for both methods show some differences, but themean values (dashed lines) are very similar (Fig. 8d). The OBPG distri-bution is wider and shows a peak around 19 Em−2 d−1, while the LUTdistribution presents three peaks (15, 25 and 30 Em−2 d−1). The geo-graphical distribution of average daily PAR difference betweenmethods(Fig. 8e) shows large discrepancies in some specific regions such as thenorthern Barents Sea and northern Baffin Bay where the OBPG methodyields higher values than the LUT method. The opposite situation(OBPG b LUT) occurred near the ice edge (e.g. Beaufort Sea, LaptevSea) but also in permanently open waters (e.g. Norwegian Sea, Green-land Sea and southern Barents Sea). Overall, bothmethods are in agree-ment with a difference in PAR estimates of mean 0.29 Em− 2 d− 1 andstandard deviation of 6.78 Em−2 d−1 (Fig. 8f).

On a pixel to pixel basis, both methods showed small overestimateswith in situ data. On an annual basis, however, the OBPG methodis limited by SIC and SZA and is therefore clearly missing an importantamount of PAR reaching the Arctic ocean surface. This is illustratedby Fig. 9, which presents the time-integrated PAR reaching thesurfaceover the year. Even in the central Arctic ice pack, the solar energyis not negligible, with values ≈550 Em−2 y−1 above 80° N (Fig. 9right panel). Above 70° N, the cumulative estimates of PAR over theyear from the LUT method are higher than those from the OBPG meth-od. This is because the LUT method estimates PAR in all sea ice condi-tions and for SZA up to 90°. Quantitatively, when PAR is integratedover all ocean pixels above the Arctic Circle, we obtain an annual fluxof 17.2 Peta(10e15) E y–1 and 28 Peta E y–1 for OBPG and LUT methods,respectively. As a result of the known limitations, an amount as high as38% of PAR is not being accounted for by the OBPG over the ArcticOcean.

5. Discussion

5.1. Comparison of performance by various studies

Here we compare the performance of the two satellite-basedmethods evaluated in this study (Table 2) to the performance obtainedby satellite products at lower latitudes. Several PAR models based onsatellite observations have been published in the last decades (e.g.,

Bouvet, Hoepffner, & Dowell (2002); Carder, Chen, & Hawes (2003);Frouin & Chertock (1992); Frouin et al. (2003); Frouin & Murakami(2007); Frouin & McPherson (2012)), but few of them have been vali-dated using ship-based in situmeasurements. In general, evaluation ex-ercise relies on fixed platform or moored buoys (Bouvet et al., 2002;Frouin, Mcpherson, Ueyoshi, & Franz, 2013).

A preliminary assessment of the SeaWiFS PAR products was pub-lished in the NASA SeaWiFS Technical Report Series (Patt et al., 2003;Frouin et al., 2003). In situ data were obtained from two mooredbuoys sites: off the west coast of Canada (Halibut bank, 49.34° N); andthe central Pacific (0° N). On average the bias was 2.2 Em−2 d−1 (5.3%)and the RMSE was 6.2 Em−2 d−1 (15%). When the data were integratedover time (8-days, monthly), the bias remained the same but the RMSEdropped to 8%. More recently, Frouin et al. (2013) evaluated OBPG PARproducts using the in situmeasurements collected during 2005–2010 atthe CERES Ocean Validation Experiment (COVE) site located off Chesa-peake Bay in the North Atlantic (36.9° N). They found RSME rangingfrom 6.3(20%) to 6.8 Em−2 d−1(21%) with relatively high R2 (0.855 to0.883) for the sensor taken individually (i.e. SeaWiFS, MODIS-A andMODIS-T). Interestingly, the PAR estimates from all sensors exhibited apositive bias, ranging from 1.8(6%) (MODIS-A) to 2.8 Em−2 d−1 (9%)(SeaWiFS). An improved performance was obtained when PAR fromthe three sensorswere averaged,which augments the number of satelliteoverpasses during a given day (bias = 1.4 Em−2 d−1 (4%), RMSE =4.6Em−2 d−1 (14%); R2 = 0.925). When PAR was integrated over time(week or month), the performance of the satellite-based improved interms of RSME (b3.3Em−2 d−1 (10%)) and R2 (N0.968), but the positivebias remained unchanged (Frouin et al., 2013). In the OBPG method, theeffects of the clear atmosphere and of the cloud-surface layer aredecoupled, and the cloud-surface layer is assumed to be located belowthe clear atmosphere. Consequently, the correction of scattering bymolecules and aerosols in the presence of clouds may be too large, yield-ing a lower cloud-surface albedo, therefore a higher PAR. In clear sky andopen water situations, the SZA drives the PAR and the estimates errorshould be really small. Comparisons in these situations (not shown)suggests the possibility of calibration errors, which would contribute tothe bias.

Conjointly, our evaluation of the OBPG method reveals a small posi-tive bias of 0.5 Em−2 d−1 (2%). The LUT method also shows a positivebias 0.9 Em−2 d−1 (6%). However, most of the positive bias of bothmethods disappeared when the evaluation was performed usingmatchups forwhich the shipwasmore or less stationary (i.e., ship traveldistance b30 km). It is therefore not clear whether the positive bias isdue to the fact that we used a moving vessel rather than a fixed plat-form. While no definitive explaination is offered, it could be due to spa-tial and temporal variability of cloudiness and surface albedo, and/or tomodel uncertainties.

Bouvet et al. (2002) developed a method based on the Gregg andCarder (1990) model that uses as input several satellite-derived vari-ables (TOA reflectivity, water vapor content, aerosol optical thicknessand angstrom exponent, wind speed) and climate model parameters(pressure and relative humidity). Based on in situmeasurements fromtwo array systems of moored buoys in the equatorial and tropical re-gions, a RMSE of 5.2% were obtained for their monthly PAR estimates.Our results cannot be directly compared to these results as the time-in-tegration over amonth necessarily improved themodel performance, asshown by Frouin et al. (2013). However, it is unlikely that the RMSE ob-tained for both OBPG and LUTmethodswould drop to value as low as 5%with a monthly integration.

Higher uncertainty obtained in our study (i.e., 17–20% for the OBPGmethod and 30–38% for the LUT method) may be due to a number offactors. As a first consideration, we would expect that the evaluationmethod itself, based on ship-bornemeasurements, increases the uncer-tainty associated with the methods. A second consideration would bethat part of the higher uncertaintymay result from the specific environ-mental conditions encountered in the Arctic.

Fig. 5. Examples of diurnal variability of modeled and measured irradiance, and environmental conditions along the ship track for two contrasting situations. On the left hand side,observations were made on August 21st (day 233) 2005 in northern Baffin Bay. On the right hand side, observations were made on August 9th (day 221) 2007 in Hudson Bay. Panelsdepict: a) 24 hourly ship position along the transects; b) the retrieved daily PAR values from MODIS-Aqua (squares), MODIS-Terra (circles), SeaWiFS (triangles) and the mean of thethree (thick black line); c) interpolated ISCCP parameters (yellow: O3/1000, black: CF and thickness the τcl) for each time and position and surface albedo (blue) calculated usingnearest neighbor SIC; d) measured instant PAR (solid line) and its corresponding estimate using the LUT method (dashed line) with inputs presented in c), and the clear sky radiativetransfert simulation computed with local conditions (dotted line).

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Fig. 6. Scatter plot of in situ daily PAR versus satellite-derived daily PAR using the OBPGmethod. The dot color corresponds to the CV intraday and the inset is a cumulativefrequency distribution of the number of matchups as a function of CV intraday threshold.

Fig. 7. Scatter plot of daily PAR derived using LUT and OBPG methods inside a 280 kmISCCP pixel. Each point represents the PAR average for one day of the month of July2004. The error bars represent the standard deviation calculated using the 580 4.6 kmpixels within the 280 km ISCCP pixel. The 4 points outside the 30% dashed lines arecases where LUT method yields higher PAR values than the OPBG method.

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5.2. Arctic environment issues

As mentioned above, we expect to see the smallest differencesbetween in situ data and model estimates in the simplest situations,that is, in days of clear skies over open waters. When situationsget more complicated, more differences may emerge from differentways of modeling the environment. The accuracy of a satellite PARproduct, here obtained from the comparison with in situ values, can beevaluated by examining the specific environmental factors. The mostimportant ones for light propagation in the Arctic are persistent lowsolar elevation, changing surface albedo due to sea ice, and high cloud-iness. This section examines the residuals between satellite-derived andin situ daily PAR as a function of local solar noon (minimum daily SZA),the effects of the clouds and surface albedo (Fig. 10; Table 3).

5.2.1. Sun elevationWe found a weak significant negative relationship between the SZA

at noon time and the PAR error for the LUTmethod (Table 3).When SZAat noon was N80°, the LUT-based method almost systematicallyunderestimated daily PAR. First, this result may be explained by thefact that the lower the sun rises above the horizon, the more energycomes from diffuse relative to direct irradiance, increasing the impor-tance of accurate aerosol andwater vapor estimation,which are consid-ered constant. Second, high SZAs invalidate the plane-parallelassumption used in the SBDART radiative transfer model. As a result,PAR tends to be underestimated during days with dimmed light frombelow the horizon. A spherical geometry in radiative transfer model(Sobolev, 1975; Lenoble, 1985; Dahlback & Stamnes, 1991; Thomas &Stamnes, 1999; Spurr et al., 2007) may be used to properly estimatedaily PAR at the beginning of the polar spring and fall.

In contrast, the OBPG method shows a very weak but positive rela-tionship between the SZA at noon time and the PAR error (Table 3).This relationship is, however, restricted to SZA lower than 83° at thesatellite passing time. Unlike the LUTmethod, the energy budget meth-od is not dependent on Earth's sphericity, but may be more sensitive toreflectance bidirectionality properties. The algorithmwas originally de-veloped for SeaWIFS, which orbital parameters combined to instrumentphysical configuration did not allow to record scenes in the Earth's

twilight zone. Themore recent satellites image all theway to the Earth'sterminator, but the recorded scenes are excluded from the daily PARproduct, so recorded scenes for that geometry are not merged to bepart of the daily PAR. For the Arctic, this constraint in the algorithm re-sults in 1) less satellite passes contributing to the daily PAR productand 2) less spatial coverage for the time-integrated L3 products distrib-uted by the OBPG (e.g., Fig. 9).

5.2.2. Surface albedoAn earlier version of the Ed LUT used a constant surface albedo (0.06

for clear water), independent of the amount of ice cover. A fairly strongnegative relationship between the relative error of the estimates andthe increase in SIC was found, suggesting an increase in PAR underesti-mation (negative slope) when SIC was increasing (Laliberté & Belanger,2014). This was explained by the fact that the presence of SIC in a pixelincreases the surface albedo, which amplifies the surface irradiance bymultiple scattering between the surface and the overlying atmosphere(Gardiner, 1987). Following this, a sensitivity analysis of the surface al-bedo was performed through radiative transfer simulations. An exam-ple is shown for the 29th of April 1998 (Fig. 11) when the ship was inthe completely ice covered sector of the Baffin Bay (74.7° W, 76.3° N) .Assuming a typical surface albedo for an open ocean surface (0.06), adaily PAR underestimation of 30% was obtained. A very good PAR esti-mation (underestimation of 3%) was obtained when coupling openwa-ters As with the modeled surface albedo using SIC (Eq. (2)).

The inclusion of the As as an input parameter to our Ed LUT stronglyreduced the linear negative relationship previously found between SICand the PAR residual (for As, p b 0.1, R2 = 0.02), but increased theRMSE of PAR estimation under open water conditions (+5%) (Tables2 and 3; Fig. 10b). This may be attributed to a combination of factorslike the overestimation of sea albedo or inexact assumption on aerosolstype and load (or due to ship displacement, see Section 4.1). The OBPGalgorithm determines As with aerosols and solar zenithal angle, there-fore not varying wind, sea ice, white caps, or diffuse water reflectance.The algorithm discards icy areas (i.e., SIC N10%) because they wouldbe interpreted as cloudy in the PAR algorithm. Alternatively, if OBPGcould process their PAR product in spite of surface conditions, theOBPG PAR database would be much more complete, increasing the

Fig. 8. a) Averaged daily PAR computed using available daily PAR from OBPG for year 2004; b) number of days with OBPG daily PAR available; c) evolution of the differences in daily PARbetweenmethods (OBPG - LUT)with a loess (locallyweighted regression) smoothing function applied (blue linewith its standarddeviation in gray); d) frequency distribution of daily PARfor both methods; e) map depicting average difference in daily PAR between methods (OBPG - LUT), and f) histogram of all the differences.

Fig. 9. Sum of the daily PAR (Em−2 d−1) for the 2004 PAR from OBPG(left) and LUT(right).

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Fig. 10. Scatter plot of residuals between LUT estimates and in situ data as a function ofa) solar noon, b) surface albedo and c) the cloudiness, here defined as the product of CFand τcl.

Table 3Results from regressions between the relative error in PAR retrieval versus environmentalconditions.

Solar noon (LUT) Solar noon (OBPG) Cloud effect Surface albedo

y=−1.16x+84.73 y=0.3x+−9.61 y=0.01x+6.92 y=−26.55x+4.66R 2=0.11 R 2=0.02 R 2=0 R 2=0.02pb0.001 pb0.049 pb0.98 pb0.1

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reliability of the spatial and temporal bins. Ideally, this would incorpo-rate the ice bidirectional effect at a pixel-level spatial, temporal andspectral resolution.

5.2.3. CloudinessCloudy sky conditions dominate over the Arctic ocean (Eastman &

Warren, 2010). The effect of clouds is parameterized as the productsof fractional cloud cover and cloud optical thickness, that is CF ×τcl. Asillustrated in the Fig. 10c, the effect of clouds is not related to PAR resid-uals (p = 0.98 ; Table 3). This means estimates under an overcast skymay be subject to the same error as estimates under clear sky. Smallfluctuations decreasing or increasing the effect of clouds, like sunbreaksor isolated clouds, are equally under-represented at the coarse ISCCPpixel resolution. Transmission through broken clouds or multiplecloud layers affects the PAR amplitude, spectral shape, and diffuse-to-direct ratio and is highly position-dependent.While difficult to quantify,these cloud effects surely increase the inherent uncertainty associatedwith the LUT method.

By using coarse ISCCP input for clouds, the LUTmethod does not pre-cisely account for transitions in the cloud conditions. Part of a pixel areamay be coveredwith thick clouds and the other partmay be under clearsky conditions, but anywhere in the pixel is a gradient between the localconditions and the one found with the surrounding pixels, causing thePAR values to be averaged on relatively large scales. This alters PAR ac-curacy as soon as the estimate is spatially close to abruptly changingconditions, like passing from a clear sky to an overcast sky. Moreover,the method does not precisely distinguish between configurations ofthe ice-cloud andwater-cloud conditionswithin the pixel. The presenceof sea ice under cloudy conditions have a strong impact on the PAR.

Fig. 11. Sensitivity analysis of surface albedo performed using SBDART. Open black circlesare in situ instant PAR observations onboard the CCG Pierre Radisson during the NOWproject, gray and black lines are SBDART simulations using As = 0.06 and 0.95,respectively. SZA is shown as open gray circles. Simulations were made from 8 daily CF,τcl and O3 (ISCCP).

Ignoring the interaction aspect may lead to significant estimationerror on regional scales. Therefore, as soon as the environmental condi-tions are distributed heterogeneously within the pixel, there will be anerror on a local estimation. Nonetheless, this effect should fade whenlarge scales are considered.

Chernokulsky andMokhov (2012) showed that the ISCCP total cloudcover variability over the Arctic was lower than that observed in situ orby other satellites and reanalysis. In addition, they showed that theISCCP cloudiness was underestimated in summer. This may explainwhy the LUT method yields higher PAR values when compared to insitu measurements (Fig. 4) or to OBPG estimates in May (Fig. 8c).

The OBPG algorithm estimates daily PAR from a single satellite pass,but several passes are available at high latitudes providing multipledaily PAR estimates for a single pixel. The representation of diurnal var-iability in cloud cover is limited to the number of valid scenes imaged bythe sensor. Theoretically, the OBPG products could be more precise inthe Arctic since more satellite passes are available for a given region,contributing to the daily average. Binning of multiple satellites (usinga weighted mean with respect to SZA) helps to overcome the assump-tion of a stable cloud-surface system, thus addressing the largest accept-ed drawback of the OBPG method.

Note that the conversion to flux would be improved if a more accu-rate (ormore representative of Arctic conditions) cloud bidirectional ef-fect was considered (Macke, Dlhopolsky, Mueller, Stuhlmann, &Raschke, 1995). Overall, themethod accounts for important parameters(solar elevation and cloud-surface albedo) but lacks precision to esti-mate cloud-surface albedo, which may lead to increased errors in anArctic environment where in the summertime, cloud cover usually oc-cupies 80% to 90% of the sky (Vavrus & Waliser, 2008; Warren, Hahn,London, Chervin, & Jenne, 1988; Rossow & Schiffer, 1991).

6. Conclusion and perspectives

Our evaluation showed that the LUT method is characterized by anuncertainty of 33% compared to 20% for the OPBGmethod. This is main-ly due to difference in spatial and temporal resolution of inputs used tointerpolate the LUT. The former method will always represent bulk PARvalues for a large region, while the latter will be more appropriate forfine-scale features. Since the mean values of the PAR distributions arequite similar in both cases, the LUTmethod,when fedwith low resolutionISCCP inputs, ismore appropriate for large-scale studiesmostly because itcovers pixels with ice and periods of low sun elevation.

The very high temporal resolution of ISCCP input (3 h) did not fullycompensate for its low spatial resolution (280 km). In addition, cloudfraction alone over the ocean is only accurate to 15–25% in polar regionsduring summer (Rossow&Garder, 1993). Radiative transfer calculationshave an uncertainty of 3% evenwhen atmospheric properties are knowna priori (Ricchiazzi et al., 1998). Nevertheless, the performance of theLUTmethodmay be considerably improved if cloud and atmospheric in-formation with better spatial resolution is used as input. For example,cloud optical thickness and cloud fraction are already derived fromocean color sensors such asMODIS andMERIS (and soon fromEuropeanSpace Agency's Ocean and Land Colour Imager (OLCI) onboard Sentinel-3 satellites). Adding new dimensions to the LUT for aerosol and watervapor, also derived from ocean color sensors, could further improvethe method.

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The LUTmethodwas initially conceived to include spectral UV-B andUV-A for water column photochemical modeling purposes. A prelimi-nary validation using GUV-510 measurements at 313 nm (Xie et al.,2012) show similar model performance in the UVB. In addition, LUTsfor under water spectral irradiance (i.e., Ed(λ, 0−)) taking into accountdirect and diffuse irradiance specular reflectance are already imple-mented and could be made available to the community.

Open waters within the central Arctic ice pack are frequent in sum-mer. Given that light is available, primary productivity (PP) may be sig-nificant in these waters if phytoplankton have access to nutrients. Thus,for PP modeling, PAR estimation is relevant in all sea ice conditions. Astep forward for future applications and a significant improvement ofthe LUT method would be to assume a transmission function for icecover and subsequently be able to estimate PAR in the water columnunder sea ice. Light transmission model through sea ice and meltpondare now becoming available and used to assess under-ice primary pro-duction (Arndt & Nicolaus, 2014; Fernández-Méndez et al., 2015).Adding an ice component to the model would produce a complete andrelevant estimation of the irradiance reaching the water over thewhole Arctic ocean, especially useful to study phytoplankton springbloom and in-ice or under-ice photochemical processes.

Despite a relatively good precision, the NASA OBPG L3 PAR productshould be used with caution at high latitudes because it is limited toopen waters and do not provide estimates during the period of theyear when the sun is just above the horizon (e.g., Fig. 9). Extendingthe OBPG's energy budget approach over sea ice is feasible, but wouldrequire estimating surface albedo and light absorbed within the icepack, which is difficult in the presence of clouds, or when the pixel ispartially covered with ice. However, the method is more accurate, atleast in principle, to estimate PAR just below the ocean surface (the sur-face albedo term disappears in Eq. (3)), offering the possibility to obtainuseful estimates of PAR just below sea ice when information about PARabsorption within the snow/ice cover is available.

Acknowledgments

The authors are grateful to the three anonymous reviewers and EricRehm for their insightful comments and corrections of the manuscript.We are grateful to Bryan Franz (NASA-OBPG) for his support with thePAR algorithm.We are also thankful to the in situ and satellite data pro-viders: Marjolaine Blais, Michel Gosselin, Tim Papakariakou, HuixiangXie, Claudie Marec, Stanford B·Hooker, Maxime Benoît-Gagné, theOBPG and the CERES project (COVE data). The work was supported bythe Natural Sciences and Engineering Research Council of Canada(NSERC) discovery grant and the ArcticNet Marine Hotspot project toSB, the Québec-Océan Fonds de recherche du Québec en Nature et tech-nologies (FQRNT) and Boréas (UQAR) support to JL. RF was supportedby the National Aeronautics and Space Administration under grantsNos. NN14AL91G and NN14AQ46A.

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