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Potential zone for photosynthesis in natural waters is restricted to a relatively thin illuminated surface water layer. The thickness of this layer is often indirectly estimated by measuring the depth in which 1% of the photosynthetically active radiation entering the water remains. This depth is referred to as the euphotic depth. A coarser way to evaluate the underwater light penetration is to measure the Secchi depth, which is a visual measure of water transparency. The numerical relationship between these two optical parameters,

Underwater light is an important environmental variable because its low availability limits the photosynthetic activity, and thereby the primary production of the aquatic ecosystem [

Due to the efficient attenuation in natural waters, the illuminated surface layer, and consequently the potential zone for photosynthesis, is relatively thin. The thickness of the photosynthetically active water layer can be assessed by comparing the amounts of photoautotrophic production and heterotrophic consumption, but it can also be roughly estimated by measuring the amount of light in the water column, e.g., [_{eu}

Another way to evaluate the underwater light penetration is to measure the Secchi depth (_{SD}_{SD}

The Secchi disc readings and underwater light sensors react differently to changes in the absorption/scattering balance, _{eu}_{SD}_{eu}_{SD}

The reported values of the conversion coefficient,

Preisendorfer [_{SD}_{eu}_{SD}_{SD}

All in all, _{SD}_{SD}_{SD}_{SD}

Due to the reasons mentioned above, researchers will undoubtedly continue to convert _{SD}_{eu}_{SD}_{eu}_{SD}

Geographical information systems (GIS) are widely utilized in marine research, especially in coastal areas. Spatial data and modeling methods add to the understanding of the marine ecosystems from the littoral to the benthic environments. Characteristic to the shallow coastal seas, the euphotic zone regulates the occurrence and depth distribution of seafloor habitats. For instance, in our study area, the euphotic seafloor area fluctuates approximately 100% from yearly minimum to maximum [_{eu}

In this paper, we compare alternative methods for determining the coefficients between _{SD}_{eu}

Both Secchi depth and euphotic depth data were collected by ^{−1}·m^{−2}) in the 400–700 nm wavelength area,

The underwater measurements were started by recording PAR readings just below the sea surface, proceeding downwards with an interval of one meter. The maximum measurement depth was determined by the depth of the respective sampling station, however, never exceeding 20 m. At the shallowest sampling station the measurement range was 0–5 m. At least three separate measurements were logged from every depth with LI-1400 data logger (LI-COR Biosciences, Lincoln, NE, USA). Outliers, which deviated more than 20% from the median of the particular depth, were removed and averages of the remaining measurements were used as the final values for every measurement depth. These light profiles were then used to calculate the lower limit of the euphotic zone according to the rule of 1% PAR penetration (for a detailed method description, please see also [

In order to include variable underwater light conditions into the data, we conducted a field campaign that covers both the spatial and temporal changes in the optical properties of the coastal archipelago waters of the Baltic Sea. The campaign was conducted in the NE part of the SW-Finnish archipelago, which provides highly variable water quality conditions within relatively small distances. Optically, the Baltic Sea represents Case-2 waters with relatively high CDOM concentrations [

The campaign of the original training data included 11 sampling stations that were located within an area 45 km by 40 km, with distances of 7–16 km separating adjacent stations (_{SD}

To assess the applicability of the calibrated conversion methods, we also used independent testing data from year 2011. It included three networks of stations, located in the same sea area as the training data (_{SD}_{eu}

The study area and the sampling stations.

An empirical _{SD}_{eu}_{SD}

These seven locally calibrated methods were compared with 2 methods derived from literature. The first one is a general coefficient 3, which, as an integer, is convenient to use, and therefore often suggested in literature and used in practice. Secondly, we tested a 2-level water transparency classification introduced by Holmes [_{SD}

First, the performances of the conversion types were assessed for the original data. The modeled _{eu}^{2}) were added to the plots.

The second step was to assess the modeling accuracy of the same methods, except the one based on stations, with an independent dataset. Instead of calibrating the methods again, _{eu}_{SD}

The original training data included a total of 88 Secchi depths and light profiles. Within this dataset, _{SD}_{eu}_{SD}_{SD}_{SD}_{eu}

In general, the _{eu}_{eu}

The linear correlation between _{SD}_{eu}^{2} = 0.8864). The correlation between the measured _{SD}_{eu}_{SD}_{SD}_{eu}

Correlation (Pearson) between (_{SD}_{eu}

First we modeled _{eu}_{eu}_{eu}

The error indicators for the tested models.

Method | MAE | MRE | RRMSE |
---|---|---|---|

m | % | % | |

Constant 3 | 1.7 | 15.5 | 20.9 |

Constant 2.85 | 1.4 | 14.2 | 18.4 |

Week | 1.3 | 13.3 | 17.0 |

Station | 1.0 | 10.3 | 12.9 |

Zone | 1.1 | 11.2 | 14.1 |

2-Level | 2.0 | 19.5 | 24.0 |

Quartile | 0.9 | 8.7 | 11.1 |

Linear function | 0.9 | 10.8 | 14.3 |

Power function | 0.8 | 8.5 | 10.7 |

The observed _{eu}

We divided the _{SD}_{eu}_{eu}

Further comparisons can be made with scatter plots, which reveal rather similar problems for _{eu}_{eu}^{2} value is the highest of all of them, the error values also remain high as the trend is clearly biased. Some improvements in the prediction accuracy in clear waters were gained with the zone method (

Next, we tested the 2-level method suggested by Holmes [_{SD}_{SD}^{2} remains much lower compared to those of the other methods (

The water transparency classification based on _{SD}_{eu}

The 88 Secchi depths were divided into quartiles and an empirical coefficient _{eu}_{SD}

Category | Secchi Depth | |
---|---|---|

Q_{1} |
<2.1 m | 3.32 |

Q_{2} |
2.1–3.6 m | 3.08 |

Q_{3} |
3.7–4.5 m | 2.69 |

Q_{4} |
>4.5 m | 2.35 |

The _{SD}_{SD}_{SD}

Finally, a linear and a power function were derived to connect the two parameters. The previous resulted as
_{eu}_{SD}_{eu}_{SD}^{0.7506}

In general, the functions performed better than the fixed or scalable coefficients used in the conversion. The MAE remained under 1 m, as it did with the quartile method. The power function performed slightly better than the linear one, and actually resulted as the best option compared to all the tested methods (_{eu}_{eu}

Besides assessing the performance of the conversion methods with the training data, we wanted to test their modeling accuracy with an independent dataset. The results were varying. Within our testing data, the functions performed the best as they predicted more than 70% of the euphotic depths within the set limit of 1 m. As both the constants, also the zone, week, and 2-level method reached a success rate less than 40%, whereas the quartile method succeeded in more than half of the cases. By increasing the confidence limit to 2 m, all the success rates grew to be greater than 50%, except for the 2-level method, which performed the poorest. For the quartile method and the functions, almost all the modeled _{eu}

The results of the applicability testing with the independent dataset of 2011. The relative shares (%) of the modeled _{eu}_{eu}

1 m | 2 m | |
---|---|---|

27.7 | 53.2 | |

39.4 | 62.8 | |

28.7 | 51.1 | |

35.1 | 59.6 | |

18.1 | 43.6 | |

57.4 | 91.5 | |

72.3 | 94.7 | |

70.2 | 95.7 |

There was, however, great temporal and spatial variation in the success rates. Some conversion types performed better in early summer (e.g., quartile method), and some in late summer (e.g., constants and functions) (

The applicability of two conversion methods locally calibrated in this study were tested with independent data, and the performance was compared with that of a common fixed coefficient 3. The differences between the modeled and observed _{eu}

The aim of the study was to compare methods for determining the coefficients between _{SD}_{eu}

As suggested in literature, and supported by our data, the conversion coefficient changes as a function of water transparency change. The conversion functions process this transition as a continuum, and they do not require the sometimes problematic procedure of pre-classifying the data. According to the error indicators, the power function is the best performing conversion method in our study—even though there were only minor differences in the performance among the most accurate methods. Furthermore, the scatter plot illustrating the modeling accuracy of the power function revealed a relatively good fit of model throughout the entire data range. The same applies for the linear function in high _{eu}

The other option, besides using functions, is to use fixed or scalable coefficients. They, however, may be problematic, as always when compressing data into averages, some information is lost. Therefore, the values closer to the mean of the respective group are more accurate than the values approaching the limits of the class. Conversions based on averaged coefficients tend to overestimate the modeled _{eu}

Xu

These extremes in water quality can be separated by dividing the area geographically into fixed zones. A more flexible and efficient baseline is to divide the data according to water quality itself. A pre-classification of the original _{SD}_{SD}_{eu}_{SD}_{SD}

The functions do not require any decision-making in the execution phase of the conversion procedure, and thus their usage is rather unambiguous. Likewise, when using the quartile method, it is straightforward to select the appropriate coefficient according to the quartile in which the _{SD}

Furthermore, the conversion procedure ought to be flexible when the water quality does not remain stable. High spatio-temporal variability might be left unrecognized by using coefficients that are fixed for timings or locations, such as measurement weeks, stations, or the archipelago zones. They on the other hand require either locally or temporally restricted calibration procedures, but at the same time, they face the bulk problem on the other dimension. In contrast, the quartile method avoids the bulk problem in both of the dimensions. By choosing an appropriate conversion coefficient according to the water transparency, more flexibility is allowed for the procedure as certain areas or timings are not permanently fixed with certain coefficients. Actually, our results show that this flexibility is valuable, as for all the original stations—with only one exception—several of the four coefficients based on _{SD}

The accuracy of all the models depends on the success of their calibration. The coverage of the calibration data needs to be sufficient and suitable for the purpose. Preisendorfer [

Consequently, we urge the use of spatio-temporally comprehensive data when calibrating the coefficients. Including as wide and as variable data as possible in the calibration phase, the coefficients are more likely to perform well also in situations outside the calibration procedure. The link may well be untrustworthy if the coefficients are created based on data collected within a narrow time window, for example during cyanobacteria blooms, and if these coefficients are then used during the water transparency maximum. Instead, our data cover variation in both time and space, and thus the spatio-temporal differences are already included in the coefficients.

Nonetheless, there were spatio-temporal differences in the quality assessment made with the independent testing data (from year 2011). During the first test week, the accuracy improved towards the mainland, while in the second week, it improved towards the open sea. One possible explanation for the poorer performance in the outer archipelago during the first week is the high transparency of waters. Some of the _{SD}_{SD}_{SD}_{eu}

In our study, the method based on water transparency quartiles modeled the _{eu}

As geographical information is increasingly demanded in coastal research and administration, also euphotic depth data are needed. The applications for spatial _{eu}_{SD}_{SD}_{eu}

We suggest sufficient attention to be paid towards the methodology when converting Secchi observations to estimates of the euphotic depth—especially in waters, where the optical properties are poorly known. When _{SD}_{SD}_{SD}

The study was financially supported by Kone Foundation, EU Life+ (FINMARINET project), and the Academy of Finland (project 251806). We are grateful to Risto Kalliola for fruitful discussions and valuable comments on the manuscript, and for assistance with the

The authors declare no conflict of interest.