# A Statistical Algorithm for Estimating Chlorophyll Concentration in the New Caledonian Lagoon

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## Abstract

**:**

_{rs}). The algorithm is developed via supervised learning on match-ups gathered from 2002 to 2010. The best performance is obtained by combining two models, selected according to the ratio of R

_{rs}in spectral bands centered on 488 and 555 nm: a log-linear model for low [chl-a] (AFLC) and a support vector machine (SVM) model or a classic model (OC3) for high [chl-a]. The log-linear model is developed based on SVM regression analysis. This approach outperforms the classical OC3 approach, especially in shallow waters, with a root mean squared error 30% lower. The proposed algorithm enables more accurate assessments of [chl-a] and its variability in this typical oligo- to meso-trophic tropical lagoon, from shallow coastal waters and nearby reefs to deeper waters and in the open ocean.

## 1. Introduction

^{2}, contains one of the most extensive reef systems in the world. These systems exhibit exceptional diversity of coral and fish species and a continuum of habitats from mangroves to sea grasses [1]. UNESCO added the New Caledonia Barrier Reef to the World Heritage List on 7 July 2008 [2], emphasizing the importance of preserving such biodiversity sites.

^{−1}except in bays subject to anthropogenic influences where [chl-a] may increase to 3.6 µg·L

^{−1}[7]. Acanthaster planci (a coral-eating starfish) proliferation is probably due to algae proliferation, which is itself due to increased anthropogenic inputs, and a recent study highlighted a link between Acanthaster outbreaks and ocean productivity, favored by upwelling increased due to wind forcing [8].

^{−1}observed in the South Western lagoon) are either linked to rain [9,10] or to other processes such as upwelling or tides [11,12], which were recently modelled [13,14]. Climate change is also a factor of stress for reefs and lagoon ecosystems. Increase of ocean temperature, acidity, overexposure to sunlight and decrease in salinity affect the rate at which lagoons lose or gain water from evaporation, precipitation, surface runoff, and exchange with the ocean, and therefore water quantity and quality. Disturbances and other stressors may act concomitantly, or even interact, at multiple spatial and temporal scales, with consequences already documented or expected for the physical structure, ecological properties, and social values associated with lagoons. Many coral reefs in the world already suffer from climate and anthropogenic changes. Since 1985, Great Barrier Reef in Australia has lost more than half of its coral meadows [5]. Coral bleaching events happened in 1998 and 2002: more than 60% of the coral populations were hit, and even though the situation improved after several weeks, about 10% of the population perished [5,15,16]. To avoid or to monitor such events, it is necessary to accurately assess water properties in terms of chemical, biogeochemical and thermal characteristics, among which is chlorophyll concentration, an indicator of phytoplankton biomass.

_{rs}ratios. The relation used for MODIS imagery is a polynomial function of the maximum R

_{rs}ratio in spectral bands centered on 443 and 555 nm and 488 and 555 nm. This algorithm is valid in oceanic waters where a change in [chl-a] mainly causes a shift in the blue to green water reflectance ratio [19]. By using a color index defined as the difference between R

_{rs}in the green and a reference formed linearly between R

_{rs}in the blue and in the red, [20] improved OC3 assessments in global ocean where [chl-a] is less or equal to 0.25 µg·L

^{−1}. In coastal waters, the ratios used in these algorithms can vary due to the influence of other optical components (colored dissolved organic matter—CDOM—and suspended sediments) besides [chl-a], which may introduce large errors in [chl-a] retrievals from satellite data [21,22]. Recently, a round-robin exercise for MERIS was conducted for some coastal areas of the world including the Great Barrier Reef, giving clues for discrepancies noticed in optically complex waters [23]. In coastal waters with high [chl-a] (10 µg·L

^{−1}), algorithms based on regressions between MODIS reflectance ratios and [chl-a] improved the [chl-a] estimates [24]. Supervised learning was also used to develop an algorithm adapted to a coastal eutrophic region (between 5 and up to 50 µg·L

^{−1}chl-a) [25,26]. Camps-Valls et al. [27] showed how to improve the use of Support Vector Regression (SVR) or Relevance Vector Machine (RVM) [28] to estimate oceanic [chl-a] from remote sensing.

_{rs}not only depends on the absorption and scattering properties of dissolved and suspending materials in the water column but also on the depth and reflectivity of the bottom [32]. Recently, an inversion method was developed for the lagoon waters of New Caledonia [33]. A recent study has shown that depth strongly influences [chl-a] assessments [34]. Moreover, the influence of attenuation on seabed reflectance and exact bathymetry retrievals has been defined for the New Caledonia lagoon [35]. Thus, NASA products based on OC3 are not adapted to New Caledonia coastal waters.

^{−1}, but lower values are sometimes encountered in the New Caledonia lagoon [38] (see also below).

## 2. Material and Methods

#### 2.1. Data

_{rs}values in several spectral bands centered on 412 nm, 443 nm, 488 nm, 531 nm, 555 nm, and 667 nm for NCDataBase [29,31,38] and 547 instead of 555 nm for SeaBASS [40,41]. All MODIS R

_{rs}over New Caledonia in the NCDataBase were extracted from 2002 to 2010 [42]. When the two databases are merged, which we call Full DataBase (FDB), it is assumed that the 547 and 555 nm spectral bands give an equivalent signal, i.e., they are considered one category [20]. The NCDataBase contains bathymetry (in meters) and in situ [chl-a] (µg·L

^{−1}) measured by fluorometry and spectrofluorometry [29,43]. Water samples were collected from a Niskin bottle at 2 m depth. SeaBASS contains in situ [chl-a] obtained by fluorometry and HPLC, but for consistency only fluorometric measurements were used, and bathymetry was extracted from each latitude-longitude of the measurements.

^{−1}. The two methods for satellite assessments (closest and weighted mean) are introduced in Section 2.2. When constructing the NCDataBase [43], all field measurements of [chl-a] by fluorometry collected from 1997 to 2010 during more than ten campaigns, mainly in the Southern lagoon [26], were selected with coincident MODIS R

_{rs}. The full area extends from 165.95° to 168.65°E and from 24° to 19.99°S [38]. Figure 2 and Figure 3 display measurement stations and Table 1 gives information about dates and campaigns used for the NCDataBase. Data were collected during each seasonal period for 13 years, which ensures a large range of situations. As several years and all seasons are sampled, we expect no bias due to El-Niño or La Niña event and seasonal variations.

**Figure 1.**(

**a**) SeaBASS [chl-a] histogram (from the SeaBASS website): green line for in situ measurements and blue line for MODIS Aqua assessments; (

**b**) NCDataBase [chl-a] histogram: green line for in situ measurements, cyan line for “OC3-Closest pixel” assessment and blue line for “OC3-Weight Mean” assessment.

**Table 1.**Sea campaigns from 1997 to 2010 in New Caledonia in [43].

Sea Campaign | Dates | Study Area |
---|---|---|

Camelia and Camecal (1–9) | 21 Oct. 1997 to 27 Jun. 2003 | South-West lagoon |

Diapalis (1–9) | 13 Oct. 2001 to 15 Oct. 2003 | Loyalty Channel/Ouinné lagoon |

Topaze 1–29 | 26 Apr.2001 to 26 Jan. 2004 | South-West lagoon |

Transects 1 | 1 Apr. 2003 to 10 Apr. 2003 | South-West lagoon |

Timeseries | 12 Dec. 2001 to 22 Apr. 2003 | South-West lagoon |

Transects 2 | 4 May 2002 to 29 Feb. 2004 | South-West lagoon |

Southern and Northern 1 transect | 21 Jun. 2003 to 7 Aug. 2003 | South-West lagoon |

Southern and Northern 2 transect | 9 Nov. 2004 to 9 Dec. 2004 | South-West lagoon |

Bissecote | 1 Feb. 2006 to 14 Feb. 2006 | South-West lagoon |

Echolag | 14 Feb. 2007 to 5 Mar. 2007 | Great South Lagoon |

Zonalis | 2 Mar. 2008 to 14 Mar. 2008 | South of New Caledonia |

Valhybio | 22 Mar. 2008 to 8 Apr. 2008 | LSO and GLS, offshore stations |

ValhybioSM | 27 Apr. 2008 to 21 Jul. 2010 | Lagoon and offshore OC1 station |

^{−1}) and low values (≤3 µg·L

^{−1}) separately; see Section 2.3.

[chl-a] (µg·L^{−1}) | |||||
---|---|---|---|---|---|

Data base | N | Min | Max | ≤3 (%) | >3 (%) |

FDB (NCDataBase + SeaBASS) | 1378 | 0.03 | 38.07 | 81.28 | 18.72 |

NCDataBase (<20 m) | 300 | 0.08 | 2.71 | 100 | 0 |

NCDataBase (20 m ≤ bathy ≤ 70 m) | 352 | 0.11 | 3.70 | 99.53 | 0.47 |

NCDataBase (>70 m) | 159 | 0.08 | 1.05 | 100 | 0 |

NCDataBase (total) | 811 | 0.08 | 3.70 | 99.75 | 0.25 |

SeaBASS (<20 m) | 262 | 0.37 | 38.07 | 13.36 | 86.54 |

SeaBASS (20 m ≤ bathy ≤ 70 m) | 20 | 0.22 | 6.26 | 75.00 | 25.00 |

SeaBASS (>70 m) | 285 | 0.03 | 13.18 | 91.58 | 8.42 |

SeaBASS (total) | 567 | 0.03 | 38.07 | 54.85 | 45.15 |

#### 2.2. Match-Up

_{rs}data were matched with MODIS Aqua standard retrievals for NCDataBase at original resolution (1-km, non-gridded data) [41], as provided by the NASA Ocean Color Biology Processing Group (OBPG). The atmospheric correction scheme took into account non-black pixels in the near infrared, but no adjacency effects. SeaDAS flags were applied to the satellite data to eliminate situations with sun glint, large viewing zenith angle, high water turbidity, clouds, land, high top-of-atmosphere radiance, and stray light [42]. To assign a value to a station on a day, two methods were used. The first method consists in assigning the value of the closest pixel: the closest neighbor method (CL) [38,41]. The second method consists in averaging the values from neighboring pixels, using weights depending on the distance to the station: the weighted mean method (WMM) [38,41]. This was done for the spectral bands centered on 412, 443, 488, 531, 555 and 667 nm.

_{rs}matched data. It highlights that RMSE is not affected by the temporal window with a difference lower than 0.001 both between 0-day CL and 5-day CL, and between 0-day WMM and 5-day WMM. The VC values are very close too (0.358 for 0-day WMM and 0.355 for 5-day WMM). Moreover, NMB and MNB are better with a 5-day window (from −0.266 for 0-day WMM to −0.204 for 5-day WMM for NMB, and from −0.171 for 0-day WMM to −0.101 for 5-day WMM for MNB). Thus using a 5-day temporal window does not affect much the accuracy of results to assess R

_{rs}(443) retrievals and the WMM [29,38,41,43] provides the best performance. Figure 4 and Figure 5 display error densities computed with the different in situ measurements and remote sensing assessments of R

_{rs}(443) for the two methods. “Error densities” enable detection of whether an algorithm tends to overestimate, and whether errors are balanced or distributed around 0. They highlight that errors done with a 5-day temporal window are not much larger than errors made with a narrower window. This is explained by the fact that algorithm errors are similar to those introduces by temporal variability over a few days (see also Section 4.4). Moreover, our full dataset contains more than 86% of match-ups for which the temporal window is lower than or equal to 2 days. In order to keep a maximum of coincidences, we used the 5-day temporal window with the WMM. Since the weighted means method is more efficient, R

_{rs}values were determined using this second method in our NCDataBase to investigate appropriate [chl-a] algorithms for the region.

**Table 3.**Different methods for generating R

_{rs}(443) (sr

^{−1}) match-ups in New Caledonian waters. Min, Max, Mean Median and RMSE are given in sr

^{−1}.

Methods | n | Min | Max | Mean | Median | VC | NMB | MNB | RMSE |
---|---|---|---|---|---|---|---|---|---|

0-day CL | 397 | 0.0000 | 0.0281 | 0.0062 | 0.0057 | 0.4298 | −0.2700 | −0.1633 | 0.0047 |

0-day WMM | 397 | 0.0003 | 0.0213 | 0.0062 | 0.0058 | 0.3584 | −0.2660 | −0.1705 | 0.0044 |

1-day CL | 752 | 0.0000 | 0.0281 | 0.0063 | 0.0059 | 0.3990 | −0.2495 | −0.1592 | 0.0047 |

1-day WMM | 752 | 0.0003 | 0.0213 | 0.0065 | 0.0062 | 0.3452 | −0.2311 | −0.1454 | 0.0044 |

5-day CL | 986 | 0.0000 | 0.0281 | 0.0062 | 0.0058 | 0.4096 | −0.2289 | −0.1274 | 0.0045 |

5-day WMM | 986 | 0.0003 | 0.0213 | 0.0064 | 0.0061 | 0.3550 | −0.2044 | −0.1036 | 0.0042 |

**Figure 4.**Error densities between in situ measurements and satellite assessments for R

_{rs}(443) at the same day (D0), and from a 1-day temporal (D1) window to a 5-day temporal window (D5). Closest neighbor method.

**Figure 5.**Error densities between in situ measurements and satellite assessments for R

_{rs}(443) at the same day (D0), and from a 1-day temporal window (D1) to a 5-day temporal window (D5). Weighted mean method.

#### 2.3. Algorithm Steps

_{rs}. This is a different approach from the OC* algorithms from NASA, which use in situ R

_{rs}as explanatory variables. The statistical study was conducted without a priori knowledge, i.e., all potentially explanatory variables (R

_{rs}in the various spectral bands) were taken in account.

^{−1}) in the NCDataBase. As a result, the algorithm built from the NCDataBase will not be adapted to cases where the [chl-a] is high. The steps to get an algorithm adapted to New Caledonia are the following: (1) using the NCDataBase, determine a model for low [chl-a] (AFLC), i.e. a well-suited model for waters having low [chl-a]; (2) using the SeaBASS database, determine a model for waters with high [chl-a] (AFHC); (3) using the two merged databases, determine a criterion to distinguish low and high [chl-a]; and (4) implement a continuous connection between the models for low and high [chl-a].

_{rs}(412), R

_{rs}(443), R

_{rs}(488), R

_{rs}(531), R

_{rs}(555) and R

_{rs}(667)) is 63 (${{\displaystyle \sum}}_{i=1}^{6}\left(\begin{array}{c}6\\ i\end{array}\right)=63$). When a model formed with many variables gave results equivalent to a model formed with fewer explanatory variables, the model with fewer variables was chosen. For each of these 63 models, 50 RMSE values, one per sample, were computed. Results were compared by calculating averages, confidence intervals of RMSE averages, and by testing the equality of means. As computed averages did not follow a Normal Law, the Kruskal-Wallis test of means comparison was applied. For both the SeaBASS and NCDataBase combined, the best results were obtained with R

_{rs}(443), R

_{rs}(488) and R

_{rs}(531). Once the best predictors were known, relations, such as a linear or a log regression, between [chl-a] and predictors and ratios of predictors were sought, with a method similar to the previous one: using bootstrap with 50 draws. With results statistically equivalent on test samples between the best SVM and a simpler relation, the simpler relation was selected.

^{−1}. A SVM model was built with a similar method as in Step 1. The predictive variables are the R

_{rs}in the five spectral bands centered on 412, 443, 488, 531, and 555 nm. This SVM model was compared to OC3. The best model between this SVM and OC3 was chosen to complete the algorithm for high [chl-a].

_{rs}if the [chl-a] is high or low. In this step, two methods were tested to determine what MODIS color ranges are linked to a high or a low [chl-a]: SVM (as a classifier) and decision tree. As explained in more detail later (Section 4.1), the decision tree was preferred to the SVM because of its practicality. Indeed, only the ratio ${R}_{rs}\left(488\right)/{R}_{rs}\left(555\right)$ is used to determine which group of [chl-a] should be linked to a MODIS color.

_{rs}channels 443, 531 and 555 nm. The SVMg and the “AFLC + AFHC” algorithms were also compared with OC3.

#### 2.4. Statistical Tests

## 3. Results

#### 3.1. Algorithm Specifics

^{−1}and an SVM model or OC3 for [chl-a] above 3 µg·L

^{−1}. The log-log linear model, built in Step 1, uses the R

_{rs}ratio of spectral bands centered on 488 and 531 nm and 443 and 531 nm, that is:

_{rs}(443)/R

_{rs}(555); R

_{rs}(488)/R

_{rs}(555))], and the polynomial used in our relation is a 1st degree polynomial with two variables. The SVM model for high [chl-a], built in Step 2, uses a radial basis kernel and R

_{rs}in five spectral bands (412, 443, 488, 531 and 555 nm) as predictors.

^{−1}. The decision tree gave a 95.7% success rate with only two branches:

- $\frac{{R}_{rs}\left(488\right)}{{R}_{rs}\left(555\right)}\ge 0.76$: 97% of the pixels have a low [chl-a] and 3% have a high [chl-a];
- $\frac{{R}_{rs}\left(488\right)}{{R}_{rs}\left(555\right)}<0.76$: 12% of the pixels have a low [chl-a] and 88% have a high [chl-a].

#### 3.2. Algorithm Performance

Product Name | Database | Mean of RMSE (µg·L^{−1}) | Variance of RMSE (µg·L^{−1})^{2} | RMSE Range (µg·L^{−1}) |
---|---|---|---|---|

OC3 | FDB | 2.832 | 0.179 | 2.013–3.706 |

SVMg | FDB | 2.766 | 0.245 | 1.868–3.774 |

AFLC + SVM | FDB | 2.811 | 0.217 | 1.859–3.799 |

AFLC + OC3 | FDB | 2.871 | 0.202 | 1.993–3.798 |

OC3 | NCDataBase (shallow) | 1.130 | 0.063 | 0.700–1.709 |

SVMg | NCDataBase (shallow) | 0.940 | 0.061 | 0.584–1.560 |

AFLC + SVM | NCDataBase (shallow) | 0.923 | 0.222 | 0.234–1.829 |

AFLC + OC3 | NCDataBase (shallow) | 0.713 | 0.113 | 0.234–1.463 |

OC3 | NCDataBase (deep) | 0.363 | 0.011 | 0.228–0.558 |

SVMg | NCDataBase (deep) | 0.412 | 0.011 | 0.294–0.816 |

AFLC + SVM | NCDataBase (deep) | 0.364 | 0.052 | 0.149–0.802 |

AFLC + OC3 | NCDataBase (deep) | 0.280 | 0.012 | 0.149–0.481 |

OC3 | NCDataBase (ocean) | 0.208 | 0.001 | 0.164–0.256 |

SVMg | NCDataBase (ocean) | 0.406 | 0.125 | 0.215–2.767 |

AFLC + SVM | NCDataBase (ocean) | 0.163 | 0.001 | 0.108–0.217 |

AFLC + OC3 | NCDataBase (ocean) | 0.163 | 0.001 | 0.108–0.217 |

OC3 | NCDataBase (total) | 0.669 | 0.017 | 0.426–0.969 |

SVMg | NCDataBase (total) | 0.667 | 0.023 | 0.442–1.075 |

AFLC + SVM | NCDataBase (total) | 0.589 | 0.060 | 0.205–1.108 |

AFLC + OC3 | NCDataBase (total) | 0.449 | 0.027 | 0.205–0.829 |

^{−1}) than with OC3 (Mean of RMSE = 0.669 µg·L

^{−1}). Using OC3 with AFLC rather than SVM enables better results on New Caledonia data. The mean of RMSE is about 33% lower with “AFLC + OC3” (Mean of RMSE = 0.449 µg·L

^{−1}) than with OC3 (Mean of RMSE = 0.669 µg·L

^{−1}). Results are also improved with “AFLC + OC3” both in shallow lagoon waters and in deep lagoon waters.

^{−1}(AFLC + OC3) and 0.589 µg·L

^{−1}(AFLC + SVM) instead of 0.667 µg·L

^{−1}. Consequently, choosing the simple model (i.e., AFLC, Equation (6)) is obvious.

^{−1}, is less obvious with OC3 (Figure 6e). It is linked, however, to the fact that two different algorithms are applied below and above 3 µg⋅L

^{−1}, hence the need to introduce a continuous connection between the two models forming the complete algorithm. According to the bathymetry in oligotrophic waters (Figure 6b,d,f), overestimation in shallow waters and underestimation in the open ocean in New Caledonian waters with OC3 both disappear. Figure 6e shows that both the overestimation in shallow waters and underestimation in deep waters by OC3 is not observed with the SeaBASS data. This means the real improvement is made in the New Caledonia area (Figure 6b,d,f), for which points of oceanic stations as well as points of shallow stations are distributed around the first bisector. The AFLC points are generally closer to the line y = x than the OC3 points. In some instances, overestimation is large, especially in shallow waters, but reduced when using AFLC instead of OC3 in oligotrophic waters.

_{rs}in spectral bands in the blue that may be noisy and not sensitive to [chl-a] in the presence of CDOM. Moreover, the use of OC3 to complete the algorithm for waters with high [chl-a] provides good results and is more generic than a SVM model. The use of SVM is suitable for the New Caledonia area, but not necessarily for other parts of the world.

**Figure 6.**Comparisons of different algorithms on a test sample including data from SeaBASS and data from NCDataBase (left column) and on NCDataBase (right column) (

**a**) “AFLC + OC3”; (

**b**) idem on full NCDataBase; with 3 bathymetry groups (

**c**) “AFLC + SVM”; (

**d**) idem on full NCDataBase; (

**e**) Result of OC3; (

**f**) Idem on full NCDataBase; RMSE, R

^{2}

_{ajusted}and the linear regression line between $\mathrm{log}\left(chl-{a}_{insitu}\right)$ and $\mathrm{log}\left(chl-{a}_{algorithm}\right)$. The line y = x is red and the regression line is green.

**Figure 7.**Log[chl-a] error densities for two test samples. (

**a**) Test sample from Full DataBase; (

**b**) Test sample uniquely from NCDataBase.

#### 3.3. Continuous Connection between Low and High [chl-a]

Algorithms without and with Connections | RMSE on NCDataBase | RMSE on SeaBASS | RMSE on a Test Sample |
---|---|---|---|

OC3 | 0.640 | 2.850 | 2.018 |

AFLC | 0.267 | 3.016 | 3.105 |

No continuous connection (AFLC + OC3) | 0.496 | 2.976 | 2.000 |

Linear weight function | 0.448 | 2.799 | 2.050 |

Square root weight function | 0.366 | 2.874 | 2.161 |

Quadratic weight function | 0.515 | 2.766 | 2.011 |

Logarithmic weight function | 0.415 | 2.845 | 2.087 |

Exponential weight function | 0.469 | 2.773 | 2.033 |

Arc-tangential weight function | 0.476 | 2.910 | 2.021 |

^{−1}in Figure 6a,c has disappeared in Figure 8. RMSE computed on NCDataBase is lower using “AFLC + OC3” continuously connected with weighting functions (0.515 µg·L

^{−1}maximum) than using OC3 (0.640 µg·L

^{−1}). Results provided by the different kinds of connection are very close. For the test sample (last column of Table 5), RMSE values are between 2.011 µg·L

^{−1}and 2.161 µg·L

^{−1}. Moreover, accuracy is not greatly affected according to Table 5, i.e., results in terms of performance are very close with and without the connection scheme. The worst result obtained with a quadratic weight function provides a RMSE 8% higher than does “AFLC + OC3” without continuous connection.

**Figure 8.**Complete algorithm with a continuous connection applied on a test sample (

**a**) with a linear; (

**b**) a quadratic; (

**c**) a square root and (

**d**) an arc-tangential connection. Comments are similar to comments on Figure 6.

#### 3.4. Application to MODIS Imagery

^{−1}with OC3 and 1.5 µg·L

^{−1}with the proposed algorithm. In Figure 9b and Figure 10b (South lagoon), [chl-a] values in the red circle are about 0.2 µg·L

^{−1}with our algorithm, but OC3 gives 0.3 µg·L

^{−1}.

**Figure 9.**(

**a**) Coral reefs and [chl-a] assessment (µg·L

^{−1}) with OC3 in the North-East lagoon of New Caledonia on 20 July 2008; (

**b**) Coral reefs and [chl-a] assessment (µg·L

^{−1}) with OC3 in the South lagoon of New Caledonia on 20 July 2008.

**Figure 10.**(

**a**) Coral reefs and [chl-a] assessment (µg·L

^{−1}) with “AFLC + OC3 linearly connected” in the North-East lagoon of New Caledonia on 20 July 2008; (

**b**) Coral reefs and [chl-a] assessment (µg·L

^{−1}) with “AFLC + OC3 linearly connected” in the South lagoon of New Caledonia on 20th July 2008.

^{−1}whereas with OC3 it extends from 0 to 1913 µg·L

^{−1}(Table 6). The interquartile range is about two times lower with “AFLC + OC3 linearly connected” showing a much lower spread.

**Figure 11.**Densities of [chl-a] assessments in the lagoon of New Caledonia on 20 July, 2008. The red line is the OC3 assessment density and the blue line is the “AFLC + OC3 linearly connected” assessment.

**Table 6.**Quantiles of [chl-a] assessments (µg·L

^{−1}) in the lagoon of New Caledonia on 20 July 2008.

Quantile | OC3 | AFLC + OC3 Linearly Connected |
---|---|---|

0 | 0 | 0.04 |

0.25 | 0.26 | 0.28 |

0.5 | 0.49 | 0.41 |

0.75 | 0.94 | 0.64 |

1 | 1913 | 58.26 |

## 4. Discussion

#### 4.1. Comparison with Other Algorithms

^{−1}), but with AFLC + OC3 values are generally lower than 1 µg·L

^{−1}. Figure 9 and Figure 10 indicate that the effect of coral reefs on [chl-a] retrieval is smaller with this new algorithm compared to OC3: [chl-a] values are smoother around the coral reef barrier. Since [chl-a] estimated with the complete algorithm (AFLC + OC3 continuously connected) are higher in the open ocean and lower in the lagoon than with OC3, and as the bottom effect of shallow waters is reduced, results are globally satisfying.

^{−1}with OC3. Bathymetry obviously decreases the algorithm performance in shallow waters and the best results are obtained in the deepest waters where the water column is sufficiently deep to avoid a bottom effect on assessments. For instance, RMSE values computed with OC3 are equal to 4.59 µg·L

^{−1}for the group “bathy < 20 m” and equal to 1.26 µg·L

^{−1}for the group “bathy > 70 m” and results are similar with AFLC + OC3 with 4.66 µg·L

^{−1}and 1.33 µg·L

^{−1}, respectively. MNB values highlight the efficiency of AFLC in each bathymetry group, since they are always lower than those computed with OC3. This observation clearly shows that AFLC provides better results, especially for low [chl-a] in both SeaBASS and NCDataBase.

RMSE (µg·L^{−1}) | MNB | |||
---|---|---|---|---|

OC3 | AFLC + OC3 | OC3 | AFLC + OC3 | |

FDB (bathy < 20 m) | 4.59 | 4.66 | 0.69 | 0.42 |

FDB (20 m ≤ bathy ≤ 70 m) | 0.42 | 0.39 | 0.24 | 0.14 |

FDB (bathy > 70 m) | 1.26 | 1.33 | 0.10 | 0.03 |

SeaBASS (bathy < 20 m) | 6.23 | 6.37 | 0.41 | 0.35 |

SeaBASS (20 m ≤ bathy ≤ 70 m) | 1.12 | 1.14 | 1.29 | 0.32 |

SeaBASS ocean | 1.56 | 1.65 | 0.38 | 0.05 |

NCDataBase (bathy < 20 m) | 1.08 | 0.82 | 1.01 | 0.49 |

NCDataBase (20 m ≤ bathy ≤ 70 m) | 0.34 | 0.30 | 0.18 | 0.13 |

NCDataBase (bathy > 70 m) | 0.21 | 0.16 | −0.40 | −0.01 |

_{rs}ratios. Then, users count on a suitable atmospheric correction to retrieve R

_{rs}and to apply the relation obtained using in situ R

_{rs}. For AFLC, in contrast, match-ups link directly in situ [chl-a] to satellite R

_{rs}, already atmospherically corrected. Consequently, the relation found with the AFLC algorithm is dependent of the MODIS sensor and of the atmospheric correction applied to retrieve R

_{rs}. It will be interesting to check whether the change in the coefficients α,β,γ will provide good results or whether a different relation than Equation (6) should be used for another sensor and/or another atmospheric correction scheme.

_{rs}. This relation is not necessarily suitable for the New Caledonian lagoon. Even if it is not perfect, statistical learning from the large dataset NCDataBase enables this uncertainty to be overcome or reduced. Improved [chl-a] are expected, but only when atmospheric corrections will provide more accurate R

_{rs}values.

#### 4.2. Functional Form of the Algorithm

_{rs}in the blue and green.

_{rs}at 488 and 555 nm, i.e., blue and green, which is consistent with expectations e.g., [11]. Note that Kahru et al. [45] found a similar relation in the California Current. They used the ratio of 488 and 547 nm to determine if [chl-a] is either high or low and they found that when R

_{rs}(488)/R

_{rs}(547) < 0.8, [chl-a] is greater than or equal to 3.3 µg·L

^{−1}.

#### 4.3. Adding Other Variables Than Reflectance in the Area of New Caledonia

_{rs}.

_{rs}is probably sufficient. Nevertheless, in recent studies, bottom types were mapped in the south part of the lagoon in New Caledonia [35]. This information could be used to get more efficient estimates. According to bottom types, we could predict whether an algorithm tends to overestimate or underestimate [chl-a]. Potentially, bathymetry would complete this new information with coefficients relative to depth, and the bottom effect on [chl-a] assessments could be reduced. With such an approach, it would be possible to generalize the algorithm to other areas in the world, provided that we can retrieve both bottom color and bathymetry maps in these other areas with dedicated algorithms [33,34,35].

#### 4.4. Temporal Window for Match-Ups

_{rs}(better than the CL—see Section 2.2).

^{−1}, obtained for AFLC + OC3 without continuous connection. There are more differences in choosing the algorithm (OC3, AFLC or mixing AFLC and OC3) than in choosing a temporal window of 0 or 5 days, suggesting that algorithm errors could be more important than the variability for two or five days.

_{rs}and therefore [chl-a] estimates are also affected by atmospheric correction. We must therefore admit that spatial errors can be greater than temporal errors, but this does not mean that lagoon waters in New Caledonia have a high residence time. On the contrary, coastal variability from rivers, upwelling processes and tides have major impacts [13,14]. A larger temporal window provides more match-ups, indeed, but improving atmospheric correction and getting coincidences as close as possible both spatially and temporally will certainly improve [chl-a] assessments.

**Table 8.**Indices to compare the accuracy of assessment when using different temporal windows for six algorithms: OC3, AFLC, AFLC + OC3 without continuous connection, AFLC + OC3 with a linear connection, AFLC + OC3 with a quadratic connection and AFLC + OC3 with an arc-tangential connection. Min, Max, Mean, Median, and RMSE are given in µg·L

^{−1}.

Methods | n | Min | Max | Mean | Median | VC | NMB | MNB | RMSE |
---|---|---|---|---|---|---|---|---|---|

0-day OC3 | 330 | 0.019 | 7.912 | 0.598 | 0.382 | 1.847 | 0.280 | 0.270 | 0.682 |

0-day AFLC | 330 | 0.098 | 1.488 | 0.444 | 0.387 | 0.508 | −0.051 | 0.177 | 0.296 |

0-day no continuous connection | 330 | 0.098 | 7.912 | 0.514 | 0.387 | 1.573 | 0.099 | 0.223 | 0.588 |

0-day linear connection | 330 | 0.098 | 7.023 | 0.508 | 0.387 | 1.358 | 0.088 | 0.226 | 0.493 |

0-day quadratic connection | 330 | 0.098 | 7.789 | 0.529 | 0.387 | 1.574 | 0.132 | 0.246 | 0.580 |

0-day arc-tangential connection | 330 | 0.098 | 7.657 | 0.512 | 0.387 | 1.476 | 0.094 | 0.225 | 0.542 |

1-day OC3 | 614 | 0.019 | 8.053 | 0.577 | 0.386 | 1.812 | 0.315 | 0.314 | 0.667 |

1-day AFLC | 614 | 0.098 | 1.893 | 0.437 | 0.389 | 0.528 | −0.003 | 0.192 | 0.263 |

1-day no continuous connection | 614 | 0.098 | 8.053 | 0.485 | 0.389 | 1.452 | 0.105 | 0.242 | 0.547 |

1-day linear connection | 614 | 0.098 | 7.249 | 0.489 | 0.389 | 1.307 | 0.114 | 0.250 | 0.483 |

1-day quadratic connection | 614 | 0.098 | 7.948 | 0.506 | 0.389 | 1.505 | 0.153 | 0.269 | 0.558 |

1-day arc-tangential connection | 614 | 0.098 | 7.825 | 0.488 | 0.389 | 1.395 | 0.113 | 0.246 | 0.519 |

5-day OC3 | 811 | 0.019 | 8.053 | 0.565 | 0.385 | 1.688 | 0.287 | 0.307 | 0.640 |

5-day AFLC | 811 | 0.098 | 1.893 | 1.436 | 0.391 | 0.518 | −0.007 | 0.172 | 0.267 |

5-day no continuous connection | 811 | 0.098 | 8.053 | 0.472 | 0.391 | 1.286 | 0.075 | 0.209 | 0.496 |

5-day linear connection | 811 | 0.098 | 7.249 | 0.478 | 0.391 | 1.178 | 0.089 | 0.222 | 0.448 |

5-day quadratic connection | 811 | 0.098 | 7.948 | 0.493 | 0.391 | 1.357 | 0.124 | 0.241 | 0.515 |

5-day arc-tangential connection | 811 | 0.098 | 7.825 | 0.476 | 0.391 | 1.246 | 0.085 | 0.217 | 0.476 |

#### 4.5. Behavior of the Algorithm in New Caledonian Waters

^{−1}off the barrier reef to 0.38 mg·L

^{−1}in the middle part of the lagoon (deep lagoon) to up to 2 mgL

^{−1}in bays [46] (there are exceptional values of 6 mg·L

^{−1}in some laterite impacted bays during special events, such as cyclones or strong rains [29,31]). In this study, few match-ups are in bays, and it is difficult to get match-ups during rainy events because of clouds. Thus most of our coincidences in NCDataBase are in fact obtained over clear waters, i.e., the impact of NAP on algorithm performance is not significant.

## 5. Conclusions

_{rs}without a priori information, based solely on statistical considerations. Through this approach, we have obtained a suitable algorithm for optically complex waters of New Caledonia. The bottom influence in the lagoon is smaller than with OC3. The main improvement is obtained for waters with [chl-a] less than 3 µg·L

^{−1}, with a RMSE 30% lower in average than with OC3 in New Caledonian lagoon waters. We have also shown satisfactory results for both world data and New Caledonia data.

_{rs}corresponding to wavelengths of blue and green light. For the data sets considered, the best wavelengths are 443, 488, and 531 nm. To classify a pixel in the group of high or low [chl-a], it is sufficient to simply use a threshold in the ratio of R

_{rs}in the blue (488 nm) and green (555 nm), here 0.76 to separate waters with [chl-a] below and above 3 µg·L

^{−1}. This algorithm is sensor-dependent but it had been constructed and checked with around 1400 match-ups from two different data sources. The risks of overtraining are very low and it is therefore possible to apply this algorithm at least to MODIS data. Tests should be performed to extend this algorithm to other sensors and coefficients should be adjusted accordingly.

_{rs}measurements. The [chl-a] algorithms will then provide more accurate results, allowing more efficient evaluation of the impact of environmental stress factors on lagoon ecosystems, especially coral reefs. Stress factors affect coral health both with intensity and time, hence the interest in having a continuous monitoring of water properties over large areas, which is only possible thanks to satellite data.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Wattelez, G.; Dupouy, C.; Mangeas, M.; Lefèvre, J.; Touraivane; Frouin, R. A Statistical Algorithm for Estimating Chlorophyll Concentration in the New Caledonian Lagoon. *Remote Sens.* **2016**, *8*, 45.
https://doi.org/10.3390/rs8010045

**AMA Style**

Wattelez G, Dupouy C, Mangeas M, Lefèvre J, Touraivane, Frouin R. A Statistical Algorithm for Estimating Chlorophyll Concentration in the New Caledonian Lagoon. *Remote Sensing*. 2016; 8(1):45.
https://doi.org/10.3390/rs8010045

**Chicago/Turabian Style**

Wattelez, Guillaume, Cécile Dupouy, Morgan Mangeas, Jérôme Lefèvre, Touraivane, and Robert Frouin. 2016. "A Statistical Algorithm for Estimating Chlorophyll Concentration in the New Caledonian Lagoon" *Remote Sensing* 8, no. 1: 45.
https://doi.org/10.3390/rs8010045