Estimating phycocyanin pigment concentration in productive inland waters using Landsat measurements : A case study in Lake Dianchi

Using remote sensing reflectance (Rrs(λ), sr) and phycocyanin (PC, mg m) pigment data as well as other bio-optical data collected from two cruises in September and December 2009 in Lake Dianchi (a typical plateau lake of China), we developed a practical approach to estimate PC concentrations that could be applied directly to Landsat measurements. The visible and near-IR bands as well as their band ratios of simulated Landsat data were used as inputs to the algorithms, where the algorithm coefficients for each Landsat sensor were determined through multivariate regressions. The coefficients of determination (R) between the Rrs-modeled and measured PC were all > 0.97 for the spectral bands corresponding to Landsat 8 OLI, Landsat 7 ETM + , Landsat 5 TM, and Landsat 4 TM, with mean absolute percentage errors (MAPE) < 10% for PC ranging between ~80 and 700 mg m (n = 14). The algorithms were further evaluated using an independent data set (n = 14), yielding larger but still acceptable MAPE (~30%) for PC ranging between ~80 and 500 mg m. Application of the approach to Landsat 8 measurements over Lake Dianchi suggests potential use of the approach for periodical assessment of the lake’s bloom conditions, yet its empirical nature together with the lack of specific narrow bands on Landsat sensors to explicitly account for the PC absorption around 625 nm calls for extra caution when applied to other eutrophic lakes. ©2015 Optical Society of America OCIS codes: (010.0280) Remote sensing and sensors; (010.7340) Water. References and links 1. C. Hu, Z. Lee, R. Ma, K. Yu, D. Li, and S. Shang, “Moderate Resolution Imaging Spectroradiometer (MODIS) observations of cyanobacteria blooms in Taihu Lake, China,” J. Geophys. Res. 115(C4), C04002 (2010), doi:10.1029/2009JC005511. 2. N. Johnson, C. Revenga, and J. Echeverria, “Ecology. 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Introduction
Eutrophication of freshwater lakes has received increasing attention due to its adverse effect on the aquatic environment and on human and animal health [1][2][3][4].Frequent cyanobacterial blooms, as one distinct manifestation of eutrophication, have posed a serious threat to both the environment and humans, as lakes often serve as important resources for drinking and irrigation water supplies, fishing, and recreational use of surface waters [5].Thus, it is necessary and essential to detect and quantify cyanobacteria blooms in freshwater lakes, particularly through remote sensing techniques, as remote sensing provides synoptic and frequent measurements.
Chlorophyll a (Chla) has been used as a general proxy of phytoplankton biomass [6], whose concentration in surface waters can be quantified through remote sensing using customized and locally tuned algorithms [7][8][9][10][11][12].Chla exists in all phytoplankton.Phycocyanin (PC), on the other hand, is a cyanobacteria-specific pigment, thus providing a good index to assess cyanobacterial blooms [13][14][15]; the use of PC is also as an indicator of cyanobacteria abundance although its concentration may be a variable in the same phytoplankton population depending on the environmental conditions.
As the Medium Resolution Imaging Spectrometer (MERIS, 2002 -2012) is equipped with the spectral bands required by these models (e.g., 620 and 709 nm [20], 510 and 560 nm [21], 620, 665, 709, and 779 nm [15], some of these models can be used with MERIS data.However, all the models depend on accurate atmospheric correction of MERIS data, which is still a challenge for eutrophic lakes.The band-subtraction model of Qi et al. (2014) [23] is relatively insensitive to aerosol perturbations but it is a special case.Furthermore, because MERIS ceased functioning in April 2012, it is now impossible to detect the bloom state with the MERIS-based approaches until the launch of a new MERIS-like sensor (e.g., the Ocean and Land Color Instrument on Sentinel-III by the European Space Agency).
Most of these approaches rely on a specific narrow band centered around 620 nm to account for PC absorption.In the absence of such bands, empirical approaches such as the one used for Landsat TM may be developed and used to estimate PC for small water bodies [18].The approach used a multivariate regression between Landsat TM data in bands 1, 3, 4, 5, 7 and concurrent field-measured PC concentrations.This is because that even though Landsat does not have a narrow band around 620 nm to target optical features associated with PC, Landsat bands may be correlated with PC through the total absorption and scattering properties, which can be implicitly correlated with PC [24].Although the applicability of multivariate regression models across time and space has not been conclusively demonstrated [25], the approach suggested by Vincent (2004) [18] may be a practical solution for inland waters as long as the optical variability and its dependence on the water constituents are well defined and understood.However, Landsat TM data was discontinued since December 2011.Thus, it is necessary to develop and validate PC-retrieval algorithms that can be applied to existing medium-and high-resolution satellite sensors such as Landsat 8 OLI and Landsat 7 ETM + .This algorithm development is particularly urgent for China, because in recent years, cyanobacterial blooms in the inland lakes of China have been occurring with increasing frequency [1,[26][27][28].Of these lakes, Lake Dianchi (a typical plateau lake which has been classified continuously during the past 10 years) shows serious water quality deterioration and ranks among the worst of nearly all typical inland lakes of China (Fig. 1; China's Environmental Bulletin (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013), Environmental Protection Department of the People's Republic of China, http://jcs.mep.gov.cn/hjzl/zkgb/).As it is unclear how existing algorithms perform for this eutrophic lake, not only are the means to assess the eutrophic state through systematic mapping of PC concentrations lacking, but the establishment of a time-series and its long-term application is impossible.
Thus, the two main objectives of the present study are to develop a practical PC-retrieval approach for Lake Dianchi applicable to Landsat satellite series (including the TM, ETM + , and OLI sensors), and secondly, to compare the performance of the new algorithms with existing algorithms.

Study region
Located between 25°01′ N -24°40′ N and 102°36′ E -102°47′ E in Province Yunnan and known as the "Pearl of the Highland", Lake Dianchi is a typical plateau lake with an altitude of 1886.5 m (Fig. 2).The lake covers a water surface area of ~300 km 2 with a mean water depth of ~5.5m [29].Since the 1970s the lake has been suffering from serious contamination caused by various pollutants from urban industrial development, farmland reclamation, and resident wastewater discharge.At the present, water eutrophication has become extremely serious, and cyanobacteria blooms occur frequently from April to November each year [28,30,31].

Filed data collection
Water samples and optical data were collected at 28 stations during two surveys in September and December 2009.The first survey covered 24 stations as shown in Fig. 2; the second survey covered 4 of the 24 stations.At each station, water collection and radiometric measurements were conducted simultaneously between about 10:00 and 14:00 h local time.Water samples were collected at the surface (to about 30 cm water depth) using a standard polyethylene water-fetching Niskin bottle (2.5L), and then preserved in a storage bin at low temperature (2-4°C) before being brought back to the lab for analysis on the same day.

Radiometric measurement
Radiometric measurement was conducted via an ASD FieldSpec spectroradiometer.The 512channel instrument has a spectral range of 350-1050nm at an increment of 1.5nm.Following the above-water measurement method described in the Ocean Optical Protocols [32], the radiance spectra of a reference panel, water, and sky were collected at each station.To avoid the interference of the ship and sun glint, the instrument was positioned at an angle φ v of 135° away from the sun and a nadir angle θ v of 40° from the water surface and the nadir sky [32].
Ten spectra were acquired for each target, and then analyzed to eliminate abnormal spectra (i.e., outliers from the majority) due to occasional factors such as floating chippings on water surface, different viewing angle when pointing to the sky, etc. Valid spectra were averaged to derive the remote sensing reflectance (R rs (λ)) as: where L t is the total radiance received from the water surface; L sky is the radiance from the sky; L p is the radiance measured from the reference panel.In this process, skylight reflectance at the air-water surface (r) was taken as 2.2% for calm weather, 2.5% for wind speed of up to 5 m s −1 , and 2.6-2.8% for wind speed of about 10 m s −1 [33,34].The reflectance of the reference panel panel (ρ p ) was 30%.
The concentrations of total suspended matter (TSM), organic suspended matter (OSM), and inorganic suspended matter (ISM) were determined gravimetrically.Water samples were filtered through Whatman GF/F fiberglass filters (pre-combusted at 550 ο C for 4 hours and dried at 105 ο C for 4 hours to remove organic traces), and weighed according to Huang (1999) [37].The filters were then re-combusted at 550 ο C for 4 hours in order to remove the organic fraction, and weighed again to obtain ISM.By subtracting ISM from TSM, the OSM concentration was obtained.Phycocyanin (PC) was determined using the techniques of freezing and thawing and homogenization described by Sarada et al. (1999) [38].Water samples were filtered through Whatman GF/F fiberglass filters which were frozen until analysis.Prior to analysis, filters were transferred to a 50 ml centrifuge tube with a phosphate buffer (pH 6.7, Simis et al., 2007 [39]).Phycocyanin was extracted by repeated freezing and thawing of cells about 5 times in the phosphate buffer.The filters were then broken up manually using a pestle and homogenized with the 20 ml buffer.The extracts were clarified by centrifugation (10 min, 5000 × g), and then the supernatant fluids were collected and diluted according to Sarada et al. (1999) [38].The supernatant fluids were fluorometrically analyzed for phycocyanin concentrations using a Shimadzu RF-5301 Fluorometer, which had a Phycocyanin Optical Kit with 630nm excitation and 660nm emission filters.The Fluorometer was calibrated using a highly purified powder phycocyanin (P6161) purchased from Inc. Sigma-Aldrich, which determined the used standard in our fluorometric quantification.
Absorption coefficients of particulates, including phytoplankton, non-algal particle, and total particulate matter, were measured using the quantitative filter technique (QFT) described by Mitchell (1990) [40] and Mueller et al. (2003) [32].Water samples were filtered onto 47mm diameter Whatman GF/F fiberglass filters.Absorption spectra were recorded using a Shimadzu UV-2401PC spectrophotometer.The path length amplification was corrected by using the equation of Cleveland and Weidemann (1993) [41].After measurement of the total particulate matter absorption (a p (λ)), the filter was soaked in methanol for 4 hours to dissolve phytoplankton [42,43], and rinsed with filtered water.The absorption spectra of the soaked filter were then measured again to obtain the non-algal particle absorption (a nap (λ)).The difference between a p (λ) and a nap (λ) was the phytoplankton pigment absorption (a ph (λ)).The CDOM absorption (a cdom ) was obtained from the water samples filtered through Millipore filters with 0.22-μm pore size using a spectrophotometer with Milli-Q water as the reference [44,45].

Landsat data
The PC models developed in this study are to be used for Landsat data, including Landsat 8 OLI (Operational Land Imager), Landsat 7 ETM + (Enhanced Thematic Mapper Plus), Landsat 5 TM (Thematic Mapper), and Landsat 4 TM.These data were obtained from the U.S. Geological Survey (USGS) (http://earthexplorer.usgs.gov/).An example of Landsat 8 OLI data collected on 23 April 2014 was used to show the application of the new PC-retrieval models.The digital data were first converted to top-of-atmosphere (TOA) reflectance (ρ t ), and then used to derive R rs through a customized atmospheric correction, as described below.

Atmospheric correction
The TOA reflectance (ρ t ), after correction to account for the two-way ozone absorption [46], was used to derive R rs through the following equation using the approach of Barnes et al. (2014) [47]: where ρ r (λ) is the contribution from Rayleigh scattering, ρ a (λ) is the contribution from aerosol scattering and aerosol-Rayleigh interactions, t(λ) and T(λ) are the diffuse transmittance from the target to the sensor and from the sun to the target, respectively.For simplicity, the contributions from sun glint and whitecaps are omitted here, as they can be avoided by careful selection of the satellite data.ρ r (λ) for each Landsat band was calculated using the relative spectral response of each band [46] and the MODIS Rayleigh scattering look-up tables provided in SeaDAS (http://seadas.gsfc.nasa.gov/download.html).Because ρ r (λ) depends on atmosphere pressure (P) which is also a function of altitude, ρ r (λ) is adjusted by surface pressure obtained from NCEP data on the same day of the Landsat measurements.Then, assuming R rs (λ) for the shortwave-IR wavelengths is negligible due to the large absorption of water molecules, and following the approach of Wang and Gordon (1994) [48] and Wang and Shi (2005) [49], aerosol scattering spectral slope in the shortwave-IR was derived as where λ 0 and λ 1 are the reference wavelengths in the shortwave-IR.ε(λ, λ 0 ) can also be approximated as [48] 0 0 where c is a wavelength-independent constant.Then, for a given wavelength λ, ρ a (λ) can be derived from ρ r (λ 1 ) and ρ r (λ 0 ) using Eqs.( 3) and (4).Because aerosol scattering is strongly forward (i.e., negligible diffuse attenuation), t(λ) and T(λ) could be approximated as where θ is the sensor zenith angle, θ 0 is the solar zenith angle, and τ r (λ) is the known Rayleigh optical thickness.Such derived t(λ), T(λ), ρ a (λ), together with the pre-computed ρ r (λ) were used to estimate R rs (λ) from ρ t (λ) for each pixel.The SWIR method has been proposed and validated for another typical inland lake (Lake Taihu) by Wang et al. (2011Wang et al. ( & 2013) ) [50,51] though using MODIS data, and a similar approach has also been used for Landsat measurements over coastal shallow waters in the Florida Keys [47].For clarity the above steps are summarized schematically in Fig. 3.

Multivariate regression and accuracy assessment
MathWorks' MATLAB software was used to perform the multivariate regression analysis with R rs (λ) as the independent variables and corresponding PC concentration as the dependent variable.Three indicators (coefficient of determination or R 2 ; mean absolute percentage error or MAPE; and relative error or RE) were used to measure the performance of regression models: ) Here PC i meas and PC i pred represent the measured and predicted PC concentrations for the i-th sample, respectively.

Data distribution
The water quality parameters determined from field samples showed high dynamic range and substantial variability (Table 1 and Fig. 4).Chla ranged between 39.0 and 156.2 mg m −3 with a mean value of 91.5 mg m −3 (standard deviation = 32.9mg m −3 ).PC varied from 77.6 to 754.9 mg m −3 (mean = 247.4mg m −3 , standard deviation = 162.3mg m −3 ).TSM ranged between 24.7 and 66.6 mg L −1 .In general, higher concentrations were found in September 2009 than in December 2009.For instance, mean Chla decreased from 94.8 to 71.6 mg m −3 and mean PC dropped from 262.2 to 158.5 mg m −3 .The field measured R rs (λ) showed typical spectral characteristics of productive turbid inland waters (Figs.5(a) and (b)), with a dominant phytoplankton component and clear presence of phycobilipigments.For instance, the local reflectance trough near 675 nm was caused by phytoplankton absorption; The peak around 705nm is mainly due to low absorption and high scattering.Note that this peak is of similar magnitude as the green peak where pigment absorption is also minimal.Such a similar magnitude suggests a weak spectral slope of backscattering, which indicates relative abundance of weak scatters (i.e.large phytoplankton cells).Although their over spectral shapes appear similar, there is indeed some variability in both the magnitudes and the shapes.For example, the variance (ratio of standard deviation divided by mean) is 23.3% at 555 nm and 24.7% at 705 nm, and ratios of 555/675 and 705/675 have variances of 25.5% and 27.7%, respectively.These spectral characteristics are also similar to those reported in other turbid waters [52][53][54].

PC-retrieval model development and validation
Because the ultimate objective is to use Landsat data to estimate PC concentrations, the fieldmeasured R rs (λ) were first aggregated to simulate Landsat R rs (λ) using the relative spectral   10), with coefficients listed in Table 3).
The remaining half of the field data set (which was not used in the model development), was used to further evaluate the model performance using the established model coefficients.The scatter plots between measured and predicted PC are shown in Fig. 7.Although RE for individual data points varied between −100% and 100%, MAPE of the entire validation data set (n = 14) was generally low, ranging between 26.8% for Landsat 8 OLI and 38.3% for Landsat 4 TM for a large dynamic range (PC from 80 to 50 mg m −3 ).Considering that the typical uncertainty requirement for Chla retrievals from satellite ocean color measurements is 35% [55], these MAPE measures suggest that the field-based PC-retrieval models have great potentials in their application to Landsat data over Lake Dianchi.

Model application to Landsat data
The above results were all based on simulated Landsat R rs data using field measurements.The ultimate measure of model performance should be through evaluation of Landsat-derived PC distributions, gauged by concurrent and collocated field measurements.Unfortunately, from the entire Landsat archive, the nearest Landsat data were collected at least 11 days away from the field measurements, thus presenting an obstacle for direct validation.However, even without concurrent field measurements, inspection of the Landsat-derived properties might still provide a qualitative measure of the developed approach.An example is given in Fig. 8 to show the distributions of the various Landsat-derived properties.For the Landsat 8 OLI data collected on 23 April 2014, Fig. 8 shows the derived ρ rc (λ), ε(λ), c, and PC.Four sites from different lake segments were used to visualize these properties in Figs.8(a), 8(c), and 8(d).ρ rc (λ) showed a distribution of 0.04-0.08(dimensionless) for the Blue, Green, Red, and NIR bands, where R rs (λ) ranged between 0.005 and 0.04 sr −1 .Compared with the field-measured R rs (λ) (Fig. 5(a)), the Landsat-derived R rs (λ) showed similarity in both their magnitudes and spectral shapes, suggesting that the atmospheric correction approach was reasonable.ε(λ) had a spectral dependence while c was spectrally independent but varied spatially in the range of 0.0007-0.0014nm −1 over the whole lake.The final outcome in Fig. 8E shows spatially varying PC distributions, with much higher PC concentration in the north than in the rest of the lake.Although water samples were not available to perform a direct validation, the general patterns agree qualitatively with those determined from the field survey during another time of the year (September, Figs. 2 and 4).

Interpretation of the PC model performance
Empirical algorithms, without explaining the mechanisms, require extra caution when used for satellite applications.In this study, the PC model used all visible-NIR Landsat bands.The question then became whether the 4 spectral bands carried sufficient information for the PC pigment (either directly or indirectly), or the model performance was simply a coincidence.By examining the bio-optical properties of Lake Dianchi (Fig. 5), the former appeared to be the reason behind the acceptable model performance.Specifically, optical properties (absorption and scattering, hence reflectance) were generally controlled by particulate matters (including phytoplankton and non-algal particles) of turbid inland lakes where CDOM played a relatively minor role [56][57][58].This is particularly true for Lake Dianchi, where the contribution of CDOM to total non-water absorption was relatively small (mean < 30% even for the blue-green wavelengths, Fig. 5(e)).Of all particulate matters, OSM showed a dominant role, with the mean OSM/TSM ratio being 81.1% ( ± 3.6%), suggesting the dominant contribution of phytoplankton (and their associated organic detrital particles) to TSM (Fig. 5(e)).This is particularly true for the red wavelengths.Figure 5(c) further shows that OSM had a much tighter relationship with TSM (R 2 = 0.967) than ISM, confirming those observed from the absorption budget in Fig. 5(e).Thus, the optical properties of Lake Dianchi are driven by phytoplankton, providing a theoretical basis why a 4-band empirical regression model could work for the turbid lake.
The PC:Chla ratio is an indicator of the relative abundance of cyanobacteria in the total phytoplankton biomass [59].The ratio ranged from 1.5 to 6.4 with a mean value of 2.6 (standard deviation = 1.1) from the 28 samples collected from Lake Dianchi (Table 1 and Fig. 5(d)).These are close to those of the Spanish lakes and reservoirs [14] but much higher than those of the Morse and Geist Reservoirs (mean PC:Chla = 1.0) [59].The high PC:Chla ratios found in this study indicate that phytoplankton in Lake Dianchi are dominated by cyanobacteria, consistent with the findings in Wan et al. (2008) [28], Wu (2000) [60], and Zhang et al. (2006) [31].Such high ratios, together with the tight relationship between PC and Chla, provide another reason for the acceptable performance of the 4-band empirical PCretrieval model.Indeed, cyanobacteria do appear different from most other phytoplankton, particularly when considering the species that proliferate in eutrophic lakes.The PC pigment is not the only optical difference between cyanobacteria and other phytoplankton, thus making it possible to develop an empirical multivariate regression model that correlates Landsat reflectance to cyanobacteria abundance.The possible mechanisms behind such correlations may include: cyanobacteria have generally lower blue/red absorption ratios, potential correlation between phytoplankton scattering and reflectance that is indirectly related to PC, different fluorescence characteristics, and species that produce gas vacuoles can greatly enhance scattering.Additionally, the use of the NIR band could take into account of blooms when cyanobacteria form surface scums, as these scums showed elevated reflectance in the NIR [1,27,61].These collectively supported a multivariate regression approach in estimating PC concentrations in the eutrophic Lake Dianchi.Note that the PC concentrations in this study are relatively high (80 -700 mg m −3 ).For PC concentrations much lower than this range the validity of the model still needs to be tested.
To further test the applicability of the multivariate regression to different water types, the data were divided into two groups, i.e., one group with PC:Chla<2.6(mean ratio of all data) and the other group with PC:Chla≥2.6.The same regression using Eq. ( 10) was applied to each group, with resulting coefficients listed in Table 4.For reference, results from the calibration data for our multi-variate regression model are also listed.Clearly, all models are still sensitive to bands 2 and 3.This is similar to another moderately turbid estuary in the eastern Gulf of Mexico where Chla was found to be highly corrected with the red and green bands of MODIS [62].What is noteworthy is the negative correlation with band 2 but positive correlation with band 3.This is particularly important because such opposite signs should compensate for some atmospheric corrections errors as these errors tend to have the same sign in different visible bands due to extrapolation in the atmospheric correction [63].Nevertheless, there are considerable differences between the K 0 , K 1 , and K 4 terms after the data were partitioned into two groups, suggesting that even though the general form of the model may work for a particular lake body, the model coefficients often need to be tuned.

Comparison with existing algorithms
As introduced earlier, various PC retrieval models have already been established.It is thus necessary to know how the current model compares with those.Vincent et al. (2004) first demonstrated such an approach using all Landsat TM VIS-NIR-SWIR bands (except band 2) for Lake Erie [18].However, a direct comparison with the Vincent approach was not possible because the ASD instrument used in this study was restricted to 350 -1050 nm without the SWIR bands.A direct application of the Vincent et al. ( 2004) [18] model together with its original model coefficients to the Landsat-8 scene in Fig. 8 did not lead to satisfactory results as the modeled PC was much lower in the north than in the south, a result counter-intuitive to our a priori knowledge of the general PC distributions.This certainly does not imply that the Vincent et al. ( 2004) model [18] is inferior as its model coefficients were developed from Lake Erie without tuning for Lake Dianchi.However, because the current model uses atmospherically corrected R rs as the model input (in comparison, the Vincent et al. ( 2004) model [18] used total radiance after normalization to dark water as the model input), crossimage inconsistencies due to variable aerosols and solar/viewing geometry might be reduced at the price of additional computations (for atmospheric correction).Whether this is the case requires future coordinated field sampling to compare with concurrent Landsat measurements.In any case, the performance of all these empirical models should not be over interpreted, because whether or not they may work strictly depend on the optical variability of the various water constituents, which may be different across different water bodies.
Although other models were not designed for Landsat, a performance comparison can be achieved when the in situ Rrs data were used to simulate the specific bands used by the models.Here, the performance of three other models, namely the band ratio quadratic model [20], the spectral slope exponential model [21], and the semi-analytical model [15], were tested and compared with the performance of the new PC-retrieval model developed here using the Lake Dianchi data set.
Figure 9 showed the performance of the three models using the field-measured R rs as the model inputs.The model coefficients were tuned using the calibration data set of this study (n = 14), and then evaluated by the independent validation data set (n = 14).These two data sets were the same as those used in the new model development and validation.Two measures, namely model calibration accuracy and validation error, were used to assess the performance of these models.For the calibration accuracy, the existing models showed lower performance than the new PC models (Fig. 6).For the validation error, the band ratio quadratic model showed lower error (MAPE = 20.8%)than the new PC models; the spectral slope exponential model and the semi-analytical model showed similar errors to the new PC models.
Although the three existing models may sometimes outperform the new PC-retrieval model (e.g., Fig. 9B), these models were not applicable to Landsat because of lack of spectral bands required for the models.The new PC-retrieval model, specifically designed to use the Landsat data, represents an alternative to the established models to estimate PC concentration in eutrophic lakes.This is particularly useful for small water bodies where water can be very patchy and thus demands higher resolution than MERIS (300 m) can provide.The long-term data availability from the Landsat series (> 40 yrs, 1972 -present) also makes it possible to establish a Landsat-based bloom record for Lake Dianchi and possibly, in a more broad sense, for other similar eutrophic lakes.
Note that the PC model developed here is based on simulated Landsat reflectance.This is because that it was very difficult to achieve concurrent matchups with Landsat measurements for algorithm development and validation due to the 16-day repeat cycle and frequent cloudcover.This also points to the need a constellation of Landsat-like sensors for operational monitoring.Fig. 9. Performance of three existing PC-retrieval models over the field-collected data from Lake Dianchi.Two results were obtained for each model: the model calibration result (left column) using 14 samples, and the model validation result using 14 other independent samples.These samples were the same as those used for the development and validation of the new PCretrieval model in this study.A and B: Band ratio quadratic model [20]; C and D: Spectral slope exponential model [21]; E and F: Semi-analytical model [15].

Conclusion
PC is an index for cyanobacteria abundance, yet it has been difficult to remotely estimate PC concentrations in small eutrophic lakes.Using Lake Dianchi as an example, we developed and validated a PC-retrieval approach targeted for the Landsat sensors including Landsat 8 OLI, Landsat 7 ETM + , Landsat 5 TM, and Landsat 4 TM.Based on atmospherically corrected R rs data for the 4 VIS-NIR Landsat bands, a multivariate regression was used to determine the model coefficients for each Landsat sensor.Evaluation of these models using other independent data and comparison with other established models (targeted for sensors other than Landsat) showed acceptable model performance for a large PC concentration range (70 -500 mg m −3 ).This suggests high potential of the new approach for small eutrophic water bodies with repeated cyanobacterial blooms.However, routine application of the models to historical and current Landsat data for Lake Dianchi and other similar eutrophic lakes still requires further validation as the exact mechanisms behind the models are only implicitly included in the model coefficients.

Fig. 1 .
Fig. 1.Eutrophication levels of typical inland lakes of China in 2013 (China's Environmental Bulletin, 2013).The dotted lines on the x-axis denote lakes that are not shown due to the limited space.

Fig. 2 .
Fig. 2. Location of Lake Dianchi in China, with sampling stations overlaid on a background Red-Green-Blue image of Landsat 8 OLI collected on 23 April 2014.

Fig. 4 .
Fig. 4. PC and Chla measured from discrete sampling stations of Lake Dianchi during two cruise surveys in September and December 2009.Note that the first 3 stations are in the north of the lake (see Fig.2).

Fig. 7 .
Fig. 7. Scatter-plots of PC model validation between measured and model-predicted PC.An independent data set (n = 14) was used in the validation.