3. Results
Single-band output from the Band Math function in ENVI for each BGA algorithm (ENVI Band Math Field in
Table 2 and
Table S1) was point sampled using the coincident surface observation locations (
Figure 2) to extract BGA index (image) values for comparison with measured YSI sonde BGA/PC relative fluorescence unit values (BGA_PC_RFU) collected within 1 h of the CASI overflight. Strong correlations (Pearson’s r
2 > 0.6;
p < 0.001) between image derived indices and dense coincident surface observations of BGA during this experiment indicate that Be162BsubPhy, SI052BDA, Be162B700sub601, Be16NDPhyI, Gi033BDA, Da052BDA, SM122BDA, Ku15PhyCI, MM092BDA, MI092BDA, Wy08CI, Zh10FLH, and MM12NDCI BGA algorithms worked well with CASI imagery. The Be162BsubPhy, SI052BDA, Am092Bsub, Be16NDPhyI, Mi092BDA, and MM12NDCI BGA algorithms worked well (Pearson’s r
2 > 0.6;
p < 0.001) with simulated WorldView-2 and -3, imagery; the Be162Bsub algorithm with simulated Sentinel-2 imagery; the Be16FLHviolet with simulated Landsat-8 imagery; and the MM092BDA, Be16NDPhyI, MM12NDCI, Go04MCI, Ku15PhyCI, Wy08CI, SI052BDA, Be162BsubPhy, and Hu103BDA BGA algorithms with simulated Sentinel-3/MERIS/OLCI imagery. The Be162BsubPhy algorithm was the most widely applicable BGA algorithm with good performance for CASI, WorldView-2 and -3, Sentinel-2 and MERIS-like imagery and limited performance with MODIS imagery. The Be16FLHviolet “greenness” algorithm yielded the best (although poor) BGA/PC estimates with simulated Landsat-8 imagery.
We also conducted an extensive survey of other water quality parameters in the lake at the time of acquisition in order to determine why some proxy indices such as Chl-a may also work with regard to BGA estimation. Details of our statistical treatment of the data are available in Beck et al. [
6]. Type 1 (Pearson’s) r
2 values were used to evaluate algorithm performance with raw index values vs. BGA/PC relative fluorescence units (BGA_PC_RFU) values measured with YSI BGA optical sondes in the water (
Table S2) and as index values normalized to BGA values vs. BGA_PC_RFU values (
Table S3) to facilitate comparison.
We used a critical
p-value of 0.001 for all Pearson’s r Type 1 regression tests. Some researchers prefer Standard Error of Regression (Standard Error of Estimate or S) values to Type 1 (Pearson’s) r
2 values so we have also included them for the top performing algorithms from
Table S3 for comparison (
Table 3). Other researchers prefer Type 2 regressions [
48] to test correlations of observed vs. measured values [
49] in natural systems. Therefore, we also applied the Type 2 geometric mean method of Peltzer [
48] to BGA estimation at Harsha (East Fork) Lake with all results again normalized to calculated BGA values for top performing algorithms for each imager by Type 1 regression tests [
17] (
Table 4). A combined error budget for radiometry and multispectral image synthesis is presented in the chlorophyll-a companion paper [
6].
Examples of promising algorithms as applied to real CASI aircraft hyperspectral imagery and synthetic multispectral satellite imagery are discussed below.
3.1. CASI Imagery
We applied 27 algorithms in the form of 70 variants to the 1-m, 48-band CASI VNIR hyperspectral reflectance image mosaic (
Tables S1, S2 and S4 and
Figure 7). CASI has a narrow band capable of measuring the 620 nm phycocyanin absorption feature. The performance of each algorithm in
Table 2 and
Table 3 applied to the CASI reflectance imagery was then evaluated using 29 coincident surface observations for the sake of consistency with synthetic WorldView-2 and -3, Sentinel-2 and Landsat-8 imagery (other sub-30 m imagery). Simple subtraction, ratio-based and shape metric (second derivative) algorithms that include the 620 nm phycocyanin absorption feature and/or reflectance in the near-infrared suppress illumination variation well and had the best performance with regard to BGA estimation. In decreasing order of performance (Pearson’s r
2), the CASIBe152BsubPhy, CASISI052BDA, CASIBe162B700sub601, CASIBe16NDPhyI, CASIGi033BDA, CASIDa052BDA, CASISM122BDA, CASIKu15PhyCI, CASIMM092BDA, CASIMi092BDA, CASIWy08CI, CASIZh10FLH, and CASIMM12NDCI algorithms worked well (Pearson’s r
2 > 0.600) for BGA estimation with CASI imagery. Index imagery with raw and normalized index Type 1 (Pearson’s r) linear regressions are shown for the best performing algorithm (CASIBe152BsubPhy) in
Figure 7.
Excellent results for several algorithms with CASI high resolution aircraft imagery for BGA_PC_RFU value estimation and their resulting index maps (
Figure 7a) reveal considerable spatial heterogeneity at the 1 m scale in Harsha Lake at the time of aircraft image acquisition. This spatial heterogeneity of BGA/PC values in the imagery is supported by strong correlations with dense coincident surface observations (
Figure 7b,c).
Figure 5a also shows a strong correlation between the locations of the inflow from the East Fork of the Little Miami River in the NE corner of the image and the largest region of high BGA_PC_RFU values. In general the east basin of Harsha Lake has higher BGA/PC values than the west basin (
Figure 7a). One can also see gyre-like structures associated with the dissipation of the BGA/PC-rich waters from east to west across the lake. The spatial heterogeneity displayed by the processed CASI images is masked to varying degrees in the coarser spatial resolution synthetic satellite data derived from this real CASI relative reflectance data as shown below. This masking of spatial heterogeneity in the east and west basins in coarse resolution satellite imagery also appears to exaggerate the contrast in BGA/PC values between the east and west basins of Harsha Lake. We view the high correlations of coincident surface observations with predicted BGA/PC values with coarse resolution synthetic MERIS/OLCI data presented below with some caution accordingly.
3.2. WorldView-2 (Synthetic)
We applied 11 existing and two new algorithms in the form of 25 variants to synthetic 1.8-m, WorldView-2 imagery to examine the degree of portability of some of the simpler algorithms between (synthetic) satellite imaging systems (
Tables S1, S2 and S4 and
Figure 8). WorldView-2 has a narrow band capable of measuring the 620 nm phycocyanin absorption feature. We also applied a new subtraction algorithm (Be162Bsub) and a new modified NDCI algorithm [
32] (Be16NDPhyI) tuned to the 620 nm phycocyanin absorption feature. In decreasing order of performance, seven algorithms, WV2Be162Bsub, WV2SiO52BDA, WV2Am092Bsub, WV2Be16NDPhyI WV2Mi092BDA, and WV2MM12NDCI, had acceptable performance (Pearson’s r
2 > 0.6;
p < 0.001) with this sensor in this exercise (
Figure 8). The performance of each algorithm in
Table 2 and
Table S1 applied to the synthetic WorldView-2 imagery was evaluated using 29 coincident surface observations (
Table S2 and S4). As with CASI, simple subtraction and ratio-based algorithms that include the 620 nm phycocyanin absorption feature and/or reflectance in the near-infrared suppress illumination variation well and had the best performance with regard to BGA/PC value estimation. Index imagery with raw and normalized index Type 1 (Pearson’s r) linear regressions are shown for the best performing algorithm (WV2Be162Bsub) in
Figure 8.
3.3. Sentinel-2 (Synthetic)
We applied eight existing and five new algorithms in the form of 23 variants to the 20-m, synthetic Sentinel-2 imagery. Sentinel-2 lacks a narrow band capable of measuring the 620 nm phycocyanin absorption feature. The performance of each algorithm in
Table 2 and
Table 3 applied to the synthetic Sentinel-2 imagery was evaluated using 29 coincident surface observations coincident surface observations chosen to avoid pixels that mixed land and water at 20 and 30 m spatial resolutions (
Table S2 and S4). Six algorithms, S2Be162Bsub, S2SiO52BDA, S2Am092Bsub, S2MM12NDCI, S2Mi092BDA, and S2Be16NDPhyI, had acceptable performance (Pearson’s r
2 > 0.6;
p < 0.001) with this sensor in this experiment. The S2Be162Bsub, S2SiO52BDA, S2MM12NDCI, S2Mi092BDA, and S2Be16NDPhyI algorithms also appear to have good portability between CASI, WorldView-2/-3 and Sentinel-2 imagery (
Table S2 and S4 and
Figure 9). The strong performance of these algorithms with synthetic Sentinel-2 imagery and their wide swaths and dual constellation suggest that Sentinel-2 satellites will play a key role in future BGA monitoring systems for inland water quality. Index imagery with raw and normalized index Type 1 (Pearson’s r) linear regressions are shown for the best performing algorithm (S2Be162Bsub) in
Figure 9.
3.4. Landsat-8 (Synthetic)
We applied nine existing algorithms in the form of 17 variants to the 30-m, synthetic Landsat-8 imagery. Landsat-8 lacks a narrow band capable of measuring the 620 nm phycocyanin absorption feature. All of the algorithms applied here were indirect Chl-a proxy algorithms [
6] accordingly. Moreover, the widths and positions of Landsat-8 bands also make the application of shape metrics for the Chl-a NIR reflectance peak feature infeasible and the application of some of the simple band ratio algorithms challenging (
Table 2 and
Table S1,
Figure 10). The best performing algorithm was the green peak FLH Violet algorithm that incorporated the new ultra blue (“violet”) coastal band for this sensor in this experiment [
6].
None of the simple spectrally-oriented semi-analytical algorithms (based at least in part on known spectral features associated with known water quality parameters) considered here had acceptable performance (Pearson’s r
2 > 0.6;
p < 0.001) with regard to BGA estimation with Landsat-8 in this exercise due to its design for land vegetation (Chl-a) rather than BGA/PC in water. Index imagery with raw and normalized index Type 1 (Pearson’s r) linear regressions are shown for the best performing algorithm (L8Be15Flhviolet) in
Figure 10. Local empirical algorithms based on other water quality parameters such as Chl-a and turbidity with local calibration and validation are required for use with Landsat-8 for reliable BGA estimation because Landsat-8 cannot sense the 620 nm phycocyanin absorption feature [
22].
3.5. MODIS (Synthetic)
We applied three existing algorithms (NDCI, 2BDA and Am092Bsub) in the form of six variants to synthetic MODIS bands 1 and 2 [
43] for BGA estimation with limited success (
Tables S1, S2 and S4,
Figure 11). None of the spectrally-oriented semi-analytical algorithms considered here had acceptable performance (Pearson’s r
2 > 0.6;
p < 0.001) with regard to BGA estimation with this sensor in this experiment due to the wide MODIS bands. While MODIS could be a part of operational monitoring systems, its wide bands and coarse spatial resolution suggest that it will have limited value in operational monitoring systems for inland water quality, especially for smaller water bodies less than a few kilometers across. MODIS also lacks a narrow band capable of measuring the 620 nm phycocyanin absorption feature [
50].
The performance of each algorithm in
Table 2 and
Table S1 applied to the synthetic MODIS imagery was evaluated using nine coincident surface observations. These nine points were chosen to avoid pixels that mixed land and water at 250 and 300 m spatial resolutions. MODIS bands 1 and 2 were simulated with the CASI data at 250 m spatial resolution to facilitate comparison of algorithm performance. MODIS bands 1 and 2 are commonly available at the 250 m spatial resolution and are part of the better performing algorithm (NDCI). This suggests that MODIS NDCI may have some modest utility with regard to BGA estimation and algal bloom monitoring in some larger inland water bodies. The large pixel sizes associated with MODIS make it more appropriate for relatively large water bodies using other water quality parameters such as Chl-a or turbidity as proxies for BGA/PC. MODIS imagery will also require severe masking to avoid shorelines (mixed land and water pixels) (
Figure 9a). Index imagery with raw and normalized index Type 1 (Pearson’s r) linear regressions are shown for the best performing algorithm (MODISMM12NDCI4) in
Figure 11.
3.6. MERIS (Synthetic)
We applied the 13 existing and four new algorithms in the form of 35 variants for BGA estimation to synthetic Sentinel-3/MERIS/OLCI data for Harsha Lake with limited success (
Tables S1, S2 and S4,
Figure 12) before severe masking (
Figure 12a). MERIS has a narrow band capable of measuring the 620 nm phycocyanin absorption feature. Ten of the BGA (direct) and Chl-a (indirect or proxy) spectrally-oriented semi-analytical algorithms considered here had acceptable performance (Pearson’s r
2 > 0.6;
p < 0.001) when tested against in situ YSI BGA probe data (BGA_PC_RFU) with this sensor in this experiment after severe masking. In order of decreasing performance, the MERISMM092BDA, MERISBe16NDPhyI, MERISMM12NDCI, MERISGo04MCI, MERISWy08CI and MERISKu15PhyCI, MERISSi052BDA, MERISBe162Bsub, MERISHu103BDA, and MERISMM143BDAopt algorithms all estimated BGA well in this exercise. We agree that MERIS/OLCI can be a part of operational water quality monitoring systems [
20]. However, high-spatial resolution CASI data show that there was significant spatial heterogeneity in the values of BGA on a scale much finer than either Sentinel-3/MERIS/OLCI (300 m) or MODIS (250 m) pixels. Index imagery with raw and normalized index Type 1 (Pearson’s r) linear regressions are shown for the best performing algorithm (MERISMMO92BDA) in
Figure 12.
Type 1 Standard Error of Regression (Standard Error of Estimate or S) values track our Pearson’s r
2 values (
Table 3). The Type 2 geometric mean regressions [
41] show an ordering of correlation similar to those of Type 1 regressions [
17,
49] with somewhat poorer results for Landsat-8 (
Table 4).
4. Discussion
The focus of this study is on simple, portable, semi-analytical algorithms based on the phycocyanin and Chl-a spectral signatures. CASI, WorldView and MERIS are capable of sensing the narrow 620 nm phycocyanin absorption feature (
Figure 1,
Table 1). Algorithms specifically tuned to this phycocyanin feature had the best performance for 1 m CASI imagery (CASIBe152BsubPhy, r
2 = 0.776) and 1.8 m WorldView imagery (WV2Be162Bsub, r
2 = 0.790) and the second best for 300 m MERIS imagery (MERISBe16NDPhyI, r
2 = 0.852) (
Table S4). An indirect BGA index algorithm, MERISMM092BDA (r
2 = 0.863), designed to measure Chl-a had the best performance with regard to BGA estimation with simulated MERIS/OLCI imagery.
Wheeler et al. [
30] observed similar results for MERIS in Lake Champlain, New York, USA, with a stronger correlation of BGA to NIR reflectance than 620 nm absorption. They ascribed this result to non-linear absorption at 620 nm, spectral interference of Chl and other pigments with the 620 nm feature, due in part to surface scums, and temporal/environmental differences in phycocyanin absorption efficiency. Our results suggest that the large pixel sizes of MERIS may contribute to the masking of the 620 nm phycocyanin absorption feature, although the phycocyanin-tuned MERISBe16NDPhyI algorithm still had excellent performance (r
2 = 0.852) probably due to the strong algal and turbidity contrasts between the eastern and western basins of Harsha Lake at the time of aircraft image acquisition. In addition, MERIS does not capture the spatial variation observed in higher resolution imagery discussed above accordingly [
6]. We conclude that phycocyanin specific algorithms with strong performance are available for CASI, WorldView and MERIS-like imagers.
In contrast, Sentinel-2, Landsat-8 and MODIS are not capable of sensing the narrow 620 nm phycocyanin absorption feature (
Figure 1,
Table 1). We relied on Chl-a proxy algorithms summarized in [
6] for BGA estimation with these imagers accordingly. The best performing Chl-a proxy algorithms for BGA were S2Be16Bsub for Sentinel-2 (r
2 = 0.704), L8Be15Flhviolet for Landsat-8 (r
2 = 0.339) and MODISMMNDCI12 for MODIS (r
2 = 0.183). The strong performance of Sentinel-2 for BGA estimation via the S2Be16Bsub Chl-a algorithm makes it a valuable component for cyanobacterial monitoring in at least some inland water bodies similar to Harsha Lake. The poor performance of these semi-analytical Chl-a proxy algorithms for BGA estimation with Landsat-8 and MODIS mirrors their poor performance for Chl-a estimation due to their wide bands relative to distinctive parts of the Chl-a spectral signature in water [
6]. Indirect empirical local algorithms based on one or several other co-varying water quality parameters may be necessary for Landsat-8 and MODIS algorithms accordingly and will require local tuning.
Ogashawara et al. [
14] completed a performance review of reflectance based algorithms for predicting phycocyanin values in waters with both field and laboratory fluorometry. For this study we used field-based fluorometery using a calibrated YSI BGA probe. Despite our differences in approaches (surface remote sensing reflectance (Rrs) vs. aircraft relative reflectance) our results are remarkably similar. Ogashawara et al. [
14] simulated Hyperion, CHRIS and HyspIRI narrow band imager data from their surface spectroradiometer data. They found the SI05, MM09, and MI09 algorithms all performed well (strong r
2 values with modest RMSE values) with more modest results for the SC00 (SY00 in our study) [
47] algorithm in their study. Our real calibrated aircraft relative reflectance based imagery showed the same pattern (
Table S4). In fact, we found only one simple subtraction (Be162BsubPhy715sub615) algorithm that exceeds the performance of the simplified Simis algorithm [
7] in our study. This simple subtraction algorithm leverages the band choices of Mishra et al. [
11] for minimizing the Chl-a spectral overlap with that of the 620 nm phycocyanin absorption feature in their MI09 band ratio algorithm.
The strong performance of our simple subtraction algorithm in this particular “snap-shot” study with real narrow band CASI data may not hold for time-series imagery with illumination variation between dates of acquisition. Like Mishra et al. [
11] we expect their MI09 ratio-based algorithm (and other band ratio and shape metric algorithms) to be more robust across time-series imagery because they inherently damp variations in illumination. In addition, similar to Mishra et al. [
11], we used the simplified version of the Simis et al. [
7] algorithm because we are trying to evaluate the portability of relatively simple algorithms between narrow, moderate and broad band satellite imagers [
6], some of which have relatively limited band choices in order to create meta-constellations of current and near-term imagers for operational algal bloom monitoring. The performance of these algorithms with real imagers will vary due to differences in their on-orbit radiometry and for other water bodies due to variable values of BGA/PC and co-occurring water quality parameters including those described below.
This study measured 41 water quality parameters (
Table 5) at each of the 44 coincident surface observation sites during the hyperspectral overpass used to construct the coincident synthetic imagery for the satellite imaging systems considered above. These data helped to determine when and why some proxy algorithms such as those for Chl-a also work for BGA estimation. Of primary importance was quantifying the output of our YSI BGA fluorescence probes which recorded in BGA phycocyanin (PC) relative fluorescence units (BGA_PC_RFU) vs. total laboratory BGA cell counts (
Figure 13). A comparison of these optical sonde BGA values (BGA-PC-RFU) vs. laboratory determined Cyanobacterial Sum of Total Biovolume (CSTB) values measured on the same day resulted in Pearson’s r
2 = 0.757 with
p < 0.001 and
n = 39 (
Figure 13). We are confident in the validity of using optical sonde BGA_PC_RFU values as the basis for our coincident BGA surface observations accordingly.
Our normalized phycocyanin index values for the best performing algorithms for all imagers except MODIS allow us to predict phycocyanin values (BGA_PC_RFU) and in turn cyanobacterial sum of total biovolume (CSTB). For example if we were to determine that a CASI pixel has an estimated normalized index value of 12 (
Figure 7c) this would correspond to a BGA_PC_RFU value of 12 as well. This BGA_PC_RFU value of 12 would in turn correspond with a CSTB value of approximately 1.2 µm
3/L. One can make similar phycocyanin value estimates with WorldView-2 (
Figure 8c), Sentinel-2 (
Figure 9c), Landsat-8 (
Figure 10c), and perhaps Sentinel-3/MERIS/OLCI (
Figure 11c) and then CSTB estimates from
Figure 13, respectively. We expect slopes and intercepts for normalized phycocyanin index values for the best performing algorithms derived from real WorldView-2, Sentinel-2, Landsat-8 (
Figure 10c), and perhaps Sentinel-3/MERIS/OLCI reflectance imagery to differ somewhat from the synthetic results here. Once we have calibrated the time-series imagery from these imagers for the most promising algorithms identified here we will be able to make similar phycocyanin values and CSTB estimates for real satellite imagery.
Operational use of this method for estimating phycocyanin values (BGA_PC_RFU) and CSTB will be facilitated by the use of multiple satellite imaging platforms that will improve revisit times and help to alleviate summer cloud cover which limits the utility of single satellite HAB monitoring systems. For example cloud free images of Harsha Lake from Landsat-8 are available for perhaps 1 out of 4 overpasses. We hope to improve our temporal resolution by using the technique described above to approximately every two weeks by using Landsat-8 in combination with Sentinel-2a and -2b at a minimum. We will augment this coverage with WorldView-2 and -3 imagery when it is available to us. Larger water bodies should be able to use Sentinel-3/MERIS/OLCI imagery as well.
Our results show that several other water quality parameters were also correlated with BGA_PC_RFU values in Harsha reservoir at the time of hyperspectral image acquisition (
Table 6). Thirteen water quality parameters had Pearson’s r
2 values greater than 0.500. They were, in order of decreasing correlation, Turbidity (NTU) (r
2 = 0.852), total suspended solids (TSS) (r
2 = 0.789), total phosphorous (TP) (r
2 = 0.724), particulate phosphorous (PP) (r
2 = 0.697), volatile suspended solids (VSS) (r
2 = 0.666), dissolved reactive phosphorous (DRP) (r
2 = 0.661), total nitrogen (TN) (r
2 = 0.656), Chlorophyll as concentration and as RFU (r
2 = 0.651 and 0.640, respectively), total dissolved phosphorous (TDP) (r
2 = 0.610), particulate nitrogen (PN) (r
2 = 0.591), bicarbonate (HCO3-) (r
2 = 0.551) and alkalinity as mg of CaCO3 (r
2 = 0.542) (
Table 5 and
Table 6). Of these parameters, only Turbidity (NTU), TSS, VSS, and CHL, are spectrally active. Nonetheless, their strong co-variance with spectrally inactive water constituents explains why local empirical regressions against band reflectance values may be used to locally estimate a number of water quality parameters after local calibration [
14,
23,
30] although their portability may be limited.
In summary, there are several excellent semi-analytical spectrally based algorithm/imager combinations capable of estimating BGA values and cyanobacterial total volumes in smaller inland water bodies either directly via the phycocyanin signature with CASI, WorldView-2/-3, and Sentinel-3/MERIS/OLCI (
Table S4) or indirectly via the Chl-a signature with Sentinel-2 and to a lesser extent Landsat-8 [
6].