Algorithm types

Semi-empirical baseline algorithms: The algorithm by Dekker (1993) takes the average of reflectance in two wavelengths (i.e., P600 and P648) to draw a reference baseline and then subtracts the average reflectance at 624 m (i.e., the absorption maximum of phycocyanin). The coefficient of 0.5 accounted for the inherent optical properties in 10 shallow eutrophic lakes in the Netherlands. Li et al. (2016) modified the algorithm by increasing the band widths around P600, P648 and P624.

PC (µg/L) = 0.5 * ((P600 + P648) – P624)Dekker (1993)N=21, R2 = 0.56.
PC (µg/L) = 0.5 * ((P591 – P609) +
(P647 – P628)) – (P619 – P638)
Modified by Li et al. (2016)
PC (µg/L) = 0.5 * ((P600 + P647) – P628)Modified by Li et al. (2016)

Single reflectance band ratio: Uses a phycocyanin fluorescene peak of around 650 nm and the phycocyanin absorption peak of ~ 625 nm. The formulations were obtained from spectra obtained using a high resolution spectroradiometer from a hypereutrophic lake (Carter Lake) in Nebraska, USA (Schalles and Yacobi, 2000) during September 1994 to July 1998 (every2 weeks at 1-3 locations). Mishra et al. (2009) used reflectance at P700 nm as reference and targeted phycocyanin absorption at 699 nm in order to minimise chlorophyll a interference. The index was developed through four experiments and using two different laboratory-cultured cyanobacterial species, Synechocystis sp (PCC 6803) and Anabaena sp. (or Nostoc; Pcc 7120) and one species of algae, Ankistrodesmus falcatus. Mishra (2012) took water samples from 15 aquaculture ponds (Missouri, USA; July 2010, April, 2011) and found relationships with two reflectance band ratios.

PC (µg/L) ~ P650/P625Schalles and Yacobi (2000)R2 = 0.612
PC(µg/L) ~ P648/P624
PC(µg/L) ~ P647/P628
Chl-a (µg/L) and PC (Cells/ml) ~ P700/P600Mishra et al. (2009)N = 11, 20, 12, and 11.
N= 30 for calibration and 24 for validation
R2 = 0.95.
Chl-a (µg/L) and PC (Cells/ml) ~ P724/P600Mishra et al. (2009) modified by Ogashawara et al. (2013)
PC(mg*m-3) ~ P708/P600Mishra (2012)N = 16 (calibration), 9 (validation)
R2 = 0.77
PC(mg*m-3) ~ P708/P620Mishra (2012)N = 16 (calibration), 9 (validation)
R2 = 0.82

Semi empirical: Worzniak (2016). Gitelson et al. (1995) developed an algorithm based on 5 spirulina cultures, although these were based on the vertical attenuation coefficient Kd instead of surface reflectance. Dash et al. (2011) developed a semi-empirical algorithm using data from the Ocean Colour Monitor (OCM) on board the OCEANSAT-2 satellite and measurements from Lac des Allemands in south-eastern Louisiana. More complicated algorithms for retrieving phycocyanin were developed were Chlorophyll-a, NAP and the concentration of dissolved organism matter (CDOM) were subtracted, with these considered more robust.

PC(mg*m-3)~ (P625/P650) combined with P620/P710Wozniak (2016)N=71, R2=0.73 Adjusted R2=0.72
PC(ug/L) & Kd (m-1) ~ P624
*PC (µg/L) = Slope ((P556.4) : (P510.6)) = ((P556.4)−(P510.6))/((P556.4)−(P510.6) Dash et al (2011)N=72
*The 20 nm bandwidth of the OSM is broader than the wavelengths indicated so P556.4 is technically P547-567 and P510.6 is P502-P522.

Nested semi-empirical (analytical) band ratios: The algorithm was developed for use with the European Space Agency’s (ESA) Medium Resolution Imaging Spectrometer (MERIS) and was original developed through reference to two lakes in the Netherlands, Loosdrecht and Ijsselmeer (Sims et al., 2005). Phycocyanin pigment abundance was determined based on the optical properties of phycocyanin and knowledge of the attenuation and backscattering of other optically active constituents present in turbid inland water. The equations used the coefficients a, which is the absorption coefficient of phycocyanin (m-2) and b, the phycocyanin specific absorption at P620. Randolph et al. (2008) also applied the algorithm of Simis (2005) to the Geist (N = 25, R2 = 0.75) and Morse reservoirs (N = 23, R2 = 0.91)in Spain.

PC(ug/L) = P709/P620 +> a * P620Simis et al. (2005)N=34, R2=0.94*
PC(ug/L) = (P620/a) b * P620Simis et al. (2005)
PC(ug/L) = P704/P628Simis et al. (2005) modified
by Li et al., (2016)
*20 % error up to 80 ppb.

Three-band algorithms: This semi-analytical nested band ratio was developed by Hunter et al. (2010) based on measurements from two shallow eutrophic lakes in the UK (Loch Leven and Esthwaite Water), and uses P725 as the reference and targets the phytocyanin absorption by using the difference in P600 and P620. The algorithm is a modification of Hunter et al. (2008). Mishra and Mishra (2014) developed a three-band algorithm that removed the influence of chlorophyll-a by including wavelengths specific for absorption by this pigment, with samples taken from 15 aquaculture ponds in Missouri, US (July 2010 and April 2011).

PC (mg*m-3) ~ ((P630)-1 – P660-1) * P750)Hunter et al. (2008)
PC (mg*m-3) ~ ((P615)-1 – P600-1) * P725)Hunter et al. (2010)N= 18

PC (µg/L) ~ (P629-1 – P659)-1 * P724) 
Mishra and Mishra (2014)N=24
R2=0.89 (0.95*)
PC (µg/L) ~ (P620-1 – P665)-1 * P778) Mishra and Mishra (2014)N=24
R2=0.88 (0.98*)
PC (µg/L) = ((Pλ1-1 – Pλ2-1) * Pλ3))Song et al. (2013)N and R
2006: 34; 0.83
2007: 30; 0.87
2008: 18; 0.93
2010: 30; 0.79
Combined: 111; 0.78
Post correction (ψ) for chlorophyll absorption at P620 and P665 (ψ=aChl-a (P665)/aChl-a (P620)).


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