Conor A Nixon
email: conor.a.nixon@nasa.gov

James Abshire

Andrew Ashton

Jason W Barnes

Nathalie Carrasco

Niklas Edberg

Alexander Gagnon

Jason D Hofgartner

Juan Lora

Ralph D Lorenz

Michael Malaska

Kathleen Mandt

Marco Mastrogiuseppe

Erwan Mazarico

Marc Neveu

Taylor Perron

Jani Radebaugh

Sébastien Rodriguez

Farid Salama

Ashley Schoenfeld

Jason M Soderblom

Nicholas Teanby

Gabriel Tobie

Melissa G Trainer

Orenthal J Tucker

Elizabeth P Turtle

Sandrine Vinatier

Veronica Allen

Carrie Anderson

J Michael Battalio

Patricia Beauchamp

Ross A Beyer

Julie Brisset

John Cooper

Daniel Cordier

Thomas Cornet

Ellen C Czaplinski

Ravindra T Desai

Sarah Fagents

Tom G Farr

William Farrell

Lori K Fenton

Matthew Fillingim

Timothy A Goudge

Mark A Gurwell

Jennifer Hanley

Amy E Hofmann

Sarah Hörst

Mathieu Lapôtre

Sébastien Lebonnois

Alice Le Gall

Nicholas A Lombardo

Chris Mckay

Delphine Nna-Mvondo

Alena Probst

Kerry Ramirez

Miriam Rengel

Edward Sittler

Jennifer Stern

Cyril Szopa

Alexander Thelen

Tuan H Vu

The Science Case for a Titan Flagship-class Orbiter with Probes

Introduction -The Need for a Titan Orbiter with Probes

The joint NASA-ESA-ASI Cassini-Huygens mission [2,3], which investigated the Saturnian system from 2004 to 2017, provided the first detailed look at its largest moon, Titan. Through 127 targeted flybys of the Cassini orbiter and in situ investigations of the lower atmosphere and surface by the Huygens probe, Titan was revealed for the first time. The mission uncovered surface features such as seas, lakes, dunes, mountains, filled and desiccated river valleys and plains [4][5][6][7] that were reminiscent of Earth in some respects but utterly different in others, as well as a dynamic atmosphere laden with organic molecules and replete with multiple layers of haze, clouds and rain [8][9][10][11] (Fig. 1). Titan provides a unique opportunity to study terrestrial processes in a completely different regime, and to learn about our home planet even as we learn about the solar system.

In addition to its astounding successes, Cassini-Huygens left many questions about Titan unanswered (see Section 2). Insights into some of these questions will be provided by NASA's forthcoming Dragonfly mission, which will land on Titan's equatorial dune fields and sample the troposphere, surface and low latitude regions. However, Dragonfly will not address many other questions raised by Cassini-Huygens [12], including those related to global-scale geological history, atmospheric seasonal cycle and chemical processes, and origin and evolution of the polar seas, among other things. Furthermore, after Dragonfly only equatorial in situ measurements will have been obtained. Therefore, a complementary mission to investigate Titan's global-scale processes and make the first polar in situ measurements is highly desirable. These measurements could be accomplished by an instrumented orbiter, plus 1-2 entry probes that would investigate Titan's polar seas, giving the first ground-truth data from the only seas aside from Earth's found in the solar system, and a truly detailed global picture of Titan's dynamic atmosphere and surface.

Such a mission would advance NASA's most current goals in planetary science and should be pursued in the coming decade. For example, it would "advance scientific knowledge of the origin and history of the solar system, the potential for life elsewhere" (NASA Science Plan, 2020), and improve our understanding of "how geologic processes on Mars and on ocean-bearing worlds in our solar system might give rise to habitable environments". Similarly, it would address Strategic Objective 1.2: "scientific research of and from the Moon, lunar orbit, Mars, and beyond."

Titan from Cassini-Huygens

Through the Cassini-Huygens mission, Titan was discovered to have a subsurface water ocean, its surface was imaged in detail for the first time, and its atmospheric composition, thermal structure, and dynamics were examined from the surface to the exobase over two seasons.

At low latitudes, Titan was found to be mostly dry, except for large episodic methane rain storms [9] (Fig. 2(a)). The Huygens landing site was found to potentially be a dried river bed, with evidence of past streamflow. However, no liquids were observed filling the channels that were seen incising nearby hills [8] (Fig. 2(b)). Indeed Titan's methane hydrologic cycle is now the only other known example of such a cycle outside of Earth, composed of surface liquids, surfaceatmosphere fluxes, atmospheric transport, and precipitation [13]. In addition, vast dune fields of apparently organic material girdle Titan's equator, reaching hundreds of meters in height and hundreds of kilometers in length [5] (Fig. 2(c)). At mid-latitudes, Titan exhibits a mostly bland, undifferentiated appearance of as-of-yet undetermined organic material [14], perhaps overlaying and masking any historical record of impacts or geologic activity in the buried regolith. Impact craters (Fig. 2(d)) were found to be less abundant than anticipated, indicating a youthful surface age of 200-1000 Myr [15]. The large craters that were seen provided evidence of erosional and possible tectonic activity [16][17][18][19][20][21][22]. Hence, Titan's surface seems to be dominated by sedimentary and/or depositional processes with dunes at the equator, plains at mid-latitudes, and dissected organic plateaux and lakes at the poles [7]. However, a full interpretation of the complex history, interaction, and ages of formation of the fluvial, aeolian, and impact features and processes requires much greater compositional and morphological detail from future missions. Titan's polar regions provided the biggest surprises of the mission. Large, partially interconnected seas and myriad small lakes of liquid hydrocarbons were discovered at the north pole [4]. Cassini's radar was able to determine bathymetric and crude compositional information for the largest seas [23] (Fig. 3(I)) such as Ligeia, showing depths reaching 160 m and a methanerich composition. Titan's south pole appeared completely different, with only a single large lake (Ontario Lacus, Fig. 3(II)) with a composition including the less volatile hydrocarbon, ethane [24]. The great contrast between Titan's polar regions at the surface is only partially understood, but may in part be due to long-term cycles in Titan's seasons [25]. The recently-discovered presence of ramparts surrounding a few lakes imply that these lakes might be the youngest on Titan and require further investigation [26]. While there is no direct evidence currently available about possible subsurface reservoirs, they may have a large impact on climate stability [13,[27][28][29].

(a) (b) (c) (d)
(I) (II)
In the neutral atmosphere, Cassini's instruments unveiled the distribution of organic compounds like never before, showing how molecules are transported from equator to pole in a global circulation that reverses direction annually [30,31]. This reversal causes trace gases to seasonally accumulate over the winter pole and form ice clouds with complex compositions that need further investigation. The high-altitude 'detached' haze layer, first discovered by Voyager 1 in 1980, was seen to migrate between hemispheres, rising and sinking in a complex interplay between chemistry and dynamics [10]. However, the episodic nature of flyby observations have left a spatially and temporally incomplete picture of the seasonal changes occurring in Titan's atmosphere, greatly limiting our ability to constrain climate models.

Above the neutral atmosphere, Cassini's suite of six particle and field instruments also made unanticipated discoveries. The Ion and Neutral Mass Spectrometer (INMS) saw a rich cornucopia of organic molecular ions filling the mass range up to 100 Da [32]; the Cassini Plasma Spectrometer (CAPS) extended that range to hundreds of Da for positive ions and thousands of Da for negative ions, showing a continuum of masses from molecules to small aerosols [33]. The formation mechanisms, chemical composition, and evolution of these aerosols as they precipitate and travel through the atmosphere remains uncertain, as there are many gaps in our understanding of their transition from molecules to particles.

Cassini did not detect an internal magnetic field at Titan, suggesting a maximum permanent dipole moment of 0.78 nT ×RT 3 [34]. The magnetic interaction between Titan's atmosphere and Saturn's outer magnetosphere is variable due to periodic flapping of Saturn's plasma sheet [35]. Cold, dense nitrile and hydrocarbon ions were observed above the exobase (~2000 to 3000 km altitude) and several Titan radii down the magnetospheric wake with estimates of mass loss rates due to ion outflow of 10 27 amu/s [36][37][38][39]. This rate is significantly smaller than predictions of neutral loss rates near the exobase (~10 28 amu/s), leaving uncertainties about the atmospheric loss rates of CH4 in particular [40] -another major missing puzzle piece in our understanding of Titan's long-term atmospheric evolution and stability.

Cassini's Radio Science Sub-system (RSS) also probed Titan's interior, giving the first definitive confirmation that a deep water ocean exists [41,42], inspiring interest and speculation in Titan's astrobiological potential. However, the depth and boundaries of the internal water ocean have substantial uncertainties, requiring the collection of further data.

Although a resounding success, the Cassini-Huygens mission raised as many questions about Titan as it answered [12,43], including:

• What are the dominant escape processes at Titan's exobase, how do they vary with Titan's magnetospheric environment, and what is the fate of escaping molecules? • What is the nature of the Saturn magnetosphere-Titan ionosphere interaction and which plasma processes contribute to atmospheric escape? • Is the atmosphere in a steady-state, with on-going methane replenishment, or will it suffer long-term changes or collapse after methane depletion? • What chemical pathways synthesize complex organic molecules in Titan's atmosphere?

• What chemistry and microphysics produce organic aerosols and clouds in the atmosphere?

• How fast do erosive processes act to obliterate surfaces features, including impact craters?

• How symmetric are the physical and chemical responses to Titan's seasons, and do liquids eventually migrate between hemispheres on long timescales leaving a climate record? • What is the variability of composition between the lakes and seas, as well as surface terrains?

• Is there a vast, subsurface network of 'alkanofers' connecting the seas, acting as a reservoir for atmospheric methane? • Does Titan have any internal geophysical activity (tectonic, seismic, cryovolcanic)?

• Do organic compounds from the atmosphere enter the subsurface ocean, producing a potentially habitable environment?

Titan Flagship Mission Concept

To fully understand Titan as a global system, a mission that addresses polar and global science questions is required. Key goals for such a mission include:

Summary and Conclusions

While our knowledge of Titan expanded dramatically during the Cassini-Huygens era, it has also greatly increased the scope of scientific questions to be addressed by future missions. Cassini-Huygens revealed that Titan is the only body with topography, meteorology, surface evolution, and atmospheric chemistry as rich and complex as Earth; however, we are limited in further inquiry by the restrictions of the current global dataset. In addition, even after Huygens and Dragonfly, we will only have in situ data for low latitudes, whose nature strongly differs from the polar regions. To address the large questions remaining after Cassini-Huygens, a new dedicated Titan mission that addresses both global and local (polar) science and provides long-term temporal coverage of the atmosphere is required. This points to the need for a flagship-class orbiter along with one or more probes targeting the northern seas. A mission study could be performed in the near future, including during the current decadal survey, to make a full costing and risk analysis of the strawman payload. Downsizing or changing instrument complement, as well as investigating opportunities for international partnerships, could be investigated. Such a study would provide a robust baseline for future decision-making and mission prioritization.

Figure 1 :

 1 Figure 1: Titan's atmosphere and seas are in constant interaction, through aerosol sedimentation, precipitation, evaporation and other processes. A flagship mission accomplishing remote sensing (orbiter) and in situ (probe) measurements, would build on Cassini's legacy, and provide insights to key questions both for Titan, and our solar system as a whole. (Figure credit: [1])

Figure 2 :

 2 Figure 2: Views of Titan at low latitudes. (a) a vast arrow-shaped storm sweeps around Titan, wetting the surface with methane rain (NASA/JPL/SSI); (b) branching river networks seen during the Huygens descent (NASA/ESA/University of Arizona); (c) equatorial dunes showing east-west zonal morphology (NASA/JPL); (d) dunes flowing around a crater (NASA/JPL).

Figure 3 :

 3 Figure 3: Titan at high latitudes. (I) Northern seas (NASA/JPL/ASI); (II) Ontario Lacus near the south pole, showing changing shoreline from 2005 (A, from Cassini ISS) to 2009 (B, from ISS, and C, from Cassini radar). A polar orbiter could both map the polar regions at a consistent resolution and probe the sub-surface with radar, while probes could make measurements of the composition of the seas, giving insights into Titan's methane cycle and history.

  (a) global, multi-spectral surface and subsurface mapping at a uniform resolution sufficient to identify geologic processes; (b) temporal measurements of the atmosphere and exosphere to enable investigations of ongoing processes and seasonal change in the atmosphere and on the surface; (c) in situ measurements of the polar regions, including the polar atmosphere and surface.

Figure 4 :

 4 Figure 4: (a) Titan orbiter, with lander and balloon components in cruise configuration, from the 2007 Titan flagship study. An orbiter with two sea-landing probes could be stowed in a similar configuration, but without the depicted aerocapture heatshield. (b) Artists concept of Titan Mare Explorer (TiME) Discovery-class mission (2011 proposal) (G. Murdoch, Pop. Sci.).

kg) CBE (kg) CBE + Contin (kg)

	elease Version
	Vehicle Assembly
	Orbiter
			Orbiter Dry Mass		1160	1349
			Lander Mass		640	755
			Aerial Vehicle Mass		418	499
			Cruise Stage Dry		593	698
	Lander	Radiators	Mass
			Adapter		100	120
			Launch Dry Mass		2911	(17.5%) 3421
			Propellant		767
			Launch Wet Mass		4188
			System Margin	19.9%	682
	Radiators	Aerial Vehicle	S/C Dry Mass Alloc Launch Allocation		4103 4870
			Launch Capability*	Atlas V 551	4970
	Cruise Stage
			Dry Mass Allocation	Propellant Allocation
			Orbiter	1613	197	1810
			Lander	897	0	897
			Aerial Vehicle	588	0	588
			Cruise Stage	849	570	1419
			Launch Adapter	143	0	143
			Unallocated	13	0	13
			Total	4103	767	4870

2 lb Thruster (12) 25 lb Thruster (4) Star Tracker (2) X-band MGA Ox Tank (2) Fuel Tank (2) UHF Antenna *Adjusted from 5030kg, allocated 60kg to DLA; provides

Mass (kg)

Pressurant Tank additional 100kg capability above system margin X-band LGA

Mass (

The requirements for simultaneous global measurements and local polar information point to the need for dual investigation by a spacecraft in Titan polar orbit, surviving at least one full season (7.5 Earth years), and 1-2 probes targeting large polar seas and the near-surface environment. An orbiter with a suite of instruments would tackle the most important, high-level science questions raised by Cassini-Huygens at the global scale, while a probe would land in Kraken Mare, Titan's largest sea, and a possible second probe would target Ligeia Mare, Titan's second largest sea, to measure any compositional differences (see Fig. 4).

We envisage a flagship mission launching in the late 2020s. The final trajectory, including the gravity assist maneuvers, would be a factor determining launch vehicle size. It would be desirable for the mission to arrive at Saturn in the late 2030s, as the north pole emerges from winter and the probes are able to descend to the seas in daylight, with the possibility of direct radio monitoring from Earth. This would also allow direct comparison to Voyager and Cassini measurements made of the same season in 1980 and ~2010, two and one Titan years earlier, respectively.

Following cruise, the spacecraft would insert into Saturn's orbit, with apoapse near Titan. Probe release would occur during one of the subsequent Titan flybys, and the data relayed back to Earth. The probes for Titan's seas would be scaled down from Huygens or TiME [44] (Fig 4(b)). The probes would parachute to Titan's surface and use batteries for power, including thermal management, instrument operations and communications. Total operational lifetime would be several hours, sufficient to record data from the seas and relay back to the orbiter.

After probe data relay via the orbiter, the spacecraft would enter an elliptical polar orbit of Titan at high inclination (>80°), and later circularize using either atmospheric drag or a propulsive burn. The length of the circular mapping phase is expected to last at least 3 Earth years and would be determined during a mission design study. The orbiter vehicle would use next-generation RTGs for power and downlink the data to Earth via the Deep Space Network (DSN). The final instrument payload and number of probes would be determined by the available cost cap. An example payload for the orbiter and probes that meets the science requirements is given in Table 1.


Jonathan Derot
email: j.derot@soc.shimane-u.ac.jp

Hiroshi Yajima

François G Schmitt

Keywords: Algal bloom, autonomous monitoring, English Channel, Random Forest model, individual conditional expectation plots, water quality management

In aquatic ecosystems, anthropogenic activities disrupt nutrient fluxes, thereby promoting harmful algal blooms that could directly impact economies and human health. Within this framework, the forecasting of the proxy of chlorophyll a in coastal areas is the first step to managing these algal blooms. The primary goal was to analyze how phytoplankton bloom forecasts are impacted by different sampling frequencies, by using a machine learning model. The database used in this study was sourced from an automated system located in the English Channel. This device has a sampling frequency of 20 minutes. We considered 12 physicochemical parameters over a six-year period. Our forecast methodology is based on the random forest (RF) model and a sliding window strategy. The lag times for these sliding windows ranged from 12 hours to 3 months with four different sampling times until 1 day.

The results indicate that the optimal forecast was obtained for a 20 minutes time step, with an average R² of 0.62. Moreover, the highest values of fluorescence were predicted when the water temperature was approximately 11.8°C. Consequently, we demonstrated that the sampling frequency directly impacts the forecast performance of an RF model. Furthermore, this kind of model can recreate interactions that closely resemble biological processes. Our study suggests that the RF model can utilize the additional information contained in high-frequency datasets. The methodology presented here lays the foundation for the development of a numerical decision-making tool that could help mitigate the impact of these algal blooms.

Introduction

The technological developments in recent decades, both numerical and material, help us to understand the complex processes present in aquatic ecosystems at a biological compartment level. In lacustrine environments, it has been noted that pairing of machine learning and high-frequency database inputs from automatic devices (or long-term sampling), engendered encouraging results in phytoplankton community forecasting (Yajima and Derot 2018;[START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF]. For example, anthropogenic agricultural activities and the treatment of water and sewage, enrich nutrient levels in freshwater and coastal areas [START_REF] Anderson | Harmful algal blooms and eutrophication: nutrient sources, composition, and consequences[END_REF][START_REF] Smith | Eutrophication of freshwater and marine ecosystems[END_REF][START_REF] Roelke | A decade of fish-killing Prymnesium parvum blooms in Texas: roles of inflow and salinity[END_REF]). These disruptive nutrient fluxes lead to eutrophication by promoting the development of toxic algae, causing harmful algal blooms (HAB) [START_REF] Camargo | Ecological and toxicological effects of inorganic nitrogen pollution in aquatic ecosystems: a global assessment[END_REF]Schindler 2006). The size and intensity of these blooms has been increasing for over 20 years [START_REF] Burkholder | Cyanobacteria[END_REF][START_REF] Glibert | The global, complex phenomena of harmful algal blooms[END_REF].

The occurrence of HABs has a negative socio-economic impact on drinking water, fisheries, agriculture, and tourism [START_REF] Carmichael | Health impacts from cyanobacteria harmful algae blooms: Implications for the North American Great Lakes[END_REF][START_REF] Reynaud | A global meta-analysis of the value of ecosystem services provided by lakes[END_REF]. Moreover, they are often associated with cyanobacteria proliferation [START_REF] Backer | Cyanobacteria and algae blooms: review of health and environmental data from the harmful algal bloom-related illness surveillance system (HABISS) 2007-2011[END_REF]. In the marine environment, the Prymnesiophyceae Phaeocystis is an organism that blooms in response to increased nutrient levels. This species generally impacts tourism because of the large quantities of foam that appears on beaches during these blooms [START_REF] Veldhuis | Bloom dynamics and biological control of a high biomass HAB species in European coastal waters: a Phaeocystis case study[END_REF]. In some parts of the world, these algae generate losses in the aquaculture industry, which could potentially impact the economies of these countries [START_REF] Chen | Molecular evidence identifies bloom-forming Phaeocystis (Prymnesiophyta) from coastal waters of southeast China as Phaeocystis globosa[END_REF]. For many years, the problems relating to Phaeocystis were mostly confined to the English Channel [START_REF] Lancelot | Phaeocystis blooms and nutrient enrichment in the continental coastal zones of the North Sea[END_REF][START_REF] Lubac | Hyperspectral and multispectral ocean color inversions to detect Phaeocystis globosa blooms in coastal waters[END_REF][START_REF] Monchy | Microplanktonic community structure in a coastal system relative to a Phaeocystis bloom inferred from morphological and tag pyrosequencing methods[END_REF][START_REF] Danhiez | Optical properties of chromophoric dissolved organic matter during a phytoplankton bloom. Implication for DOC estimates from CDOM absorption[END_REF].

However, in recent years, this type of bloom has also been observed in other parts of the world, such as China and the Arabian Gulf [START_REF] Lancelot | On the ecological role of the different life forms of Phaeocystis. LIFEHAB: Life history of microalgal species causing harmful blooms[END_REF][START_REF] Schoemann | Phaeocystis blooms in the global ocean and their controlling mechanisms: a review[END_REF].

In this context, the ability to forecast algal blooms is currently a major issue in ecology [START_REF] Pennekamp | The intrinsic predictability of ecological time series and its potential to guide forecasting[END_REF]. The development of HABs is often directly linked to nutrient pollution, also termed eutrophication [START_REF] Heisler | Eutrophication and harmful algal blooms: a scientific consensus[END_REF][START_REF] Howarth | Nutrient pollution of coastal rivers, bays, and seas[END_REF][START_REF] Lapointe | Septic systems contribute to nutrient pollution and harmful algal blooms in the St. Lucie Estuary, Southeast Florida, USA[END_REF]. A numerical tool capable of understanding and forecasting HABs could help manage water quality, thereby enabling stakeholders to mitigate the impact of this toxic bloom. However, before creating this type of decision-making tool, it is imperative to focus on the prediction of more global biological processes, such as phytoplankton biomass. Classic hydro-ecological models work optimally for physical processes, but perform poorly when forecasts of the first echelon of the food web are involved [START_REF] Shimoda | Phytoplankton functional type modelling: running before we can walk? A critical evaluation of the current state of knowledge[END_REF]. This decrease in predictive performance can be explained by numerous complex interactions and nonlinear mechanisms between phytoplankton and environmental variables [START_REF] Edwards | Phytoplankton growth and the interaction of light and temperature: A synthesis at the species and community level[END_REF]). In addition, in open-ocean and coastal areas, there are strong currents and important phytoplankton migrations; therefore, it is increasingly complicated to forecast these biological processes using a machine learning model [START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF].

Scientific literature contains a wide variety of numerical models concerning the prediction of phytoplankton biomass or phylum, including models such as the hydro-ecological [START_REF] Bae | Analysis and modeling of algal blooms in the Nakdong River, Korea[END_REF][START_REF] Yajima | Changes in phytoplankton biomass due to diversion of an inflow into the Urayama Reservoir[END_REF], autoregressive moving integrated moving average (ARIMA) [START_REF] Chen | Online forecasting chlorophyll a concentrations by an auto-regressive integrated moving average model: Feasibilities and potentials[END_REF], and random forest (RF) [START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF]Yajima and Derot 2018;[START_REF] Shin | Prediction of cyanobacteria blooms in the lower Han River (South Korea) using ensemble learning algorithms[END_REF][START_REF] Kehoe | Who smells? Forecasting taste and odor in a drinking water reservoir[END_REF][START_REF] Rivero-Calle | Multidecadal increase in North Atlantic coccolithophores and the potential role of rising CO2[END_REF]. There is also a wide variety of models based on neuronal networks: artificial neural networks (ANNs) [START_REF] Shamshirband | Ensemble models with uncertainty analysis for multi-day ahead forecasting of chlorophyll a concentration in coastal waters[END_REF][START_REF] Lee | Monthly chlorophyll-a prediction using neurogenetic algorithm for water quality management in Lakes[END_REF][START_REF] Lee | Improved prediction of harmful algal blooms in four Major South Korea's Rivers using deep learning models[END_REF]; long short-term memory (LSTM) [START_REF] Cho | Merged-LSTM and multistep prediction of daily chlorophyll-a concentration for algal bloom forecast[END_REF][START_REF] Lee | Improved prediction of harmful algal blooms in four Major South Korea's Rivers using deep learning models[END_REF][START_REF] Cho | Deep learning application to time-series prediction of daily chlorophyll-a concentration[END_REF]; nonlinear autoregressive neural network (NAR) [START_REF] Du | Multistep-ahead forecasting of chlorophyll a using a wavelet nonlinear autoregressive network[END_REF], and deep belief network (DBN) [START_REF] Zhang | Deep-learning-based approach for prediction of algal blooms[END_REF]. Moreover, some of these models are coupled with a genetic algorithm [START_REF] Lee | Monthly chlorophyll-a prediction using neurogenetic algorithm for water quality management in Lakes[END_REF] or wavelet-transform [START_REF] Du | Multistep-ahead forecasting of chlorophyll a using a wavelet nonlinear autoregressive network[END_REF][START_REF] Shamshirband | Ensemble models with uncertainty analysis for multi-day ahead forecasting of chlorophyll a concentration in coastal waters[END_REF], or both [START_REF] Recknagel | Ecological relationships, thresholds and time-lags determining phytoplankton community dynamics of Lake Kinneret, Israel elucidated by evolutionary computation and wavelets[END_REF]. We can also find great diversity in the methods used to validate these models: coefficient of determination (R²) [START_REF] Du | Multistep-ahead forecasting of chlorophyll a using a wavelet nonlinear autoregressive network[END_REF][START_REF] Shamshirband | Ensemble models with uncertainty analysis for multi-day ahead forecasting of chlorophyll a concentration in coastal waters[END_REF][START_REF] Lee | Monthly chlorophyll-a prediction using neurogenetic algorithm for water quality management in Lakes[END_REF][START_REF] Lee | Improved prediction of harmful algal blooms in four Major South Korea's Rivers using deep learning models[END_REF][START_REF] Recknagel | Ecological relationships, thresholds and time-lags determining phytoplankton community dynamics of Lake Kinneret, Israel elucidated by evolutionary computation and wavelets[END_REF][START_REF] Kehoe | Who smells? Forecasting taste and odor in a drinking water reservoir[END_REF]; root mean squared error (RMSE) [START_REF] Du | Multistep-ahead forecasting of chlorophyll a using a wavelet nonlinear autoregressive network[END_REF][START_REF] Cho | Merged-LSTM and multistep prediction of daily chlorophyll-a concentration for algal bloom forecast[END_REF][START_REF] Zhang | Deep-learning-based approach for prediction of algal blooms[END_REF][START_REF] Lee | Improved prediction of harmful algal blooms in four Major South Korea's Rivers using deep learning models[END_REF][START_REF] Cho | Deep learning application to time-series prediction of daily chlorophyll-a concentration[END_REF][START_REF] Chen | Online forecasting chlorophyll a concentrations by an auto-regressive integrated moving average model: Feasibilities and potentials[END_REF][START_REF] Recknagel | Ecological relationships, thresholds and time-lags determining phytoplankton community dynamics of Lake Kinneret, Israel elucidated by evolutionary computation and wavelets[END_REF]; mean absolute error (MAE) [START_REF] Du | Multistep-ahead forecasting of chlorophyll a using a wavelet nonlinear autoregressive network[END_REF][START_REF] Shamshirband | Ensemble models with uncertainty analysis for multi-day ahead forecasting of chlorophyll a concentration in coastal waters[END_REF]; mean squared error (MSE) [START_REF] Lee | Monthly chlorophyll-a prediction using neurogenetic algorithm for water quality management in Lakes[END_REF][START_REF] Rivero-Calle | Multidecadal increase in North Atlantic coccolithophores and the potential role of rising CO2[END_REF]; mean relative error (MRE) [START_REF] Zhang | Deep-learning-based approach for prediction of algal blooms[END_REF]; absolute error peak (AEP) [START_REF] Chen | Online forecasting chlorophyll a concentrations by an auto-regressive integrated moving average model: Feasibilities and potentials[END_REF]; and pseudo-R² [START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF]; area under curve (AUC) [START_REF] Shin | Prediction of cyanobacteria blooms in the lower Han River (South Korea) using ensemble learning algorithms[END_REF].

This highlights the lack of standardized protocol to forecast the parameters linked to phytoplankton biomass in aquatic environments. Thus, it can be inferred that the use of this kind of artificial intelligence based model in this branch of science is still in its infancy. However, the pairing of high-frequency data with RF models seems to be an interesting alternative to forecast primary production. One way to measure RF usefulness is the usage of the pseudo-R² coefficient that comes from the cross-validation process, at an "out-of-bag" error level, and measures only the performance of the learning phase [START_REF] Breiman | Random forests[END_REF]. Although this coefficient has been used in several environmental studies, some researchers are aware that pseudo-R² cannot be assessed as a true forecast (Large et al. 2015;[START_REF] Teichert | Restoring fish ecological quality in estuaries: implication of interactive and cumulative effects among anthropogenic stressors[END_REF][START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF]. Therefore, in this study, we have chosen to compare the raw data from an automated system to the output of the machine learning model, using the coefficient of determination (R²).

Automatic devices may have different sampling frequencies; for example, time steps of 10 minutes, 20 minutes or 4 hours can be found [START_REF] Dur | Analysis of high frequency temperature time series in the Seine estuary from the Marel autonomous monitoring buoy[END_REF][START_REF] Derot | Correlation between long-term marine temperature time series from the eastern and western English Channel: Scaling analysis using empirical mode decomposition[END_REF][START_REF] Schmitt | Mesures à haute résolution dans l'environnement marin côtie[END_REF][START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF]. Currently, the impact of sampling frequency on the learning process is poorly understood. Therefore, in this study, we have explored the capacity of the RF model to leverage the supplementary information that is contained in the high sample frequency and water quality data.

Moreover, the predictive performance of this model was studied by varying the time steps used in our database. Before creating a decision-making tool to help stakeholders with water quality management, certain intermediate research stages are necessary. Furthermore, the coupling between machine learning and hydrodynamic models exhibits encouraging results for the prediction of ecological parameters directly linked to water quality [START_REF] Cuttitta | Linking surface hydrodynamics to planktonic ecosystem: the case study of the ichthyoplanktonic assemblages in the Central Mediterranean Sea[END_REF][START_REF] Jia | Physics guided recurrent neural networks for modeling dynamical systems: Application to monitoring water temperature and quality in lakes[END_REF][START_REF] Hanson | Predicting lake surface water phosphorus dynamics using process-guided machine learning[END_REF].

Within this framework, the purpose of our study is to better understand the impact of sampling frequency on algal bloom forecast capacity. Therefore, the results presented here could potentially improve this type of coupled numerical model.

Material and methods

Automatic device and study area

The high-frequency dataset used in this study was producedby an automatic device called MAREL Carnot. MAREL is a French acronym for Mesures Automatisées en Réseaux pour l'Environnement Littoral (automated sampling network for coastal area). It belongs to a network of fixed platform networks along French coasts called COAST-HF (http://coast-hf.fr). The MAREL Carnot device used here is located in the eastern English Channel on the French coastal area. More specifically, this automatic system is situated at the exit of the Boulogne-sur-Mer harbor on the Carnot sea wall (50.7404 N; 1.5676 W) (Fig. 1). The Boulogne-sur-Mer harbor is the first fishing port in France. Consequently, it is subjected to significant anthropogenic pollution. Moreover, the English Channel has been affected by HAB generated by Phaeocystis for several decades [START_REF] Lancelot | Phaeocystis blooms and nutrient enrichment in the continental coastal zones of the North Sea[END_REF][START_REF] Lubac | Hyperspectral and multispectral ocean color inversions to detect Phaeocystis globosa blooms in coastal waters[END_REF][START_REF] Monchy | Microplanktonic community structure in a coastal system relative to a Phaeocystis bloom inferred from morphological and tag pyrosequencing methods[END_REF][START_REF] Danhiez | Optical properties of chromophoric dissolved organic matter during a phytoplankton bloom. Implication for DOC estimates from CDOM absorption[END_REF]). In the eastern part, this kind of bloom has been a recurrent event since the 1990s [START_REF] Spilmont | Impact of the Phaeocystis globosa spring bloom on the intertidal benthic compartment in the eastern English Channel: A synthesis[END_REF][START_REF] Schmitt | Blooms de Phaeocystis sur la Côte d'Opale: investigations historiques[END_REF][START_REF] Houliez | Spectral fluorometric characterization of Haptophyte dynamics using the FluoroProbe: an application in the eastern English Channel for monitoring Phaeocystis globosa[END_REF][START_REF] Grattepanche | Succession of primary producers and micrograzers in a coastal ecosystem dominated by Phaeocystis globosaGrattepanche[END_REF]). This is one of the reasons for basing this kind of automated device in this area. It is pivotal to consider that the English Channel has very turbid waters and is subject to large tidal ranges. This has been tied to the fact that the bed of this sea is a continental shelf, with a maximal depth of 180 meters.

MAREL Carnot data

The MAREL Carnot sensors are attached to a floating system that nestles in a tube fixed to the sea wall. The data are constantly recorded at a depth of 1.5 meters below sea level. However, the measurement of the photosynthetically active radiation (P.A.R) parameter is an exception and for obvious reasons, the sensor is not installed in the tube, but on the top of the sea wall. Each parameter is recorded at a frequency of 20 minutes, except for the three nutrient parameters (nitrates, silicates, and phosphates) which are recorded with a periodicity of 12 hours [START_REF] Dur | Analysis of high frequency temperature time series in the Seine estuary from the Marel autonomous monitoring buoy[END_REF][START_REF] Derot | Long-term high frequency phytoplankton dynamics, recorded from a coastal water autonomous measurement system in the eastern English Channel[END_REF][START_REF] Zongo | Scaling properties of pH fluctuations in coastal waters of the English Channel: pH as a turbulent active scalar[END_REF][START_REF] Huang | Time dependent intrinsic correlation analysis of temperature and dissolved oxygen time series using empirical mode decomposition[END_REF]. Table 1 lists all the parameters that were used in our study. The data presented here can be obtained from the following sites: https://data.corioliscotier.org and the Seanoe site provided by [START_REF] Lefebvre | MAREL Carnot data and metadata from Coriolis Data Centre[END_REF].

Not all the available parameters, recorded by the MAREL device, have been used to avoid the problems linked with collinearity. The term collinearity is used when the two predictors that are input into a machine learning model, display a strong correlation. In order to decrease the computation time and avoid creating an unstable model with a degraded predictive performance, it is better to avoid selecting predictors showing correlations (Kuhn and Johnson 2013). To this end, we discarded the readings for percentage of dissolved oxygen and salinity: they were too close to the concentration of dissolved oxygen and the conductivity readings, respectively. In each case, we selected the parameter with the most complete data set. Time periods with missing data are an inherent problem for automatically generated datasets; many factors can create these missing values: maintenance periods, internal system failures, and vandalism [START_REF] Dur | Analysis of high frequency temperature time series in the Seine estuary from the Marel autonomous monitoring buoy[END_REF][START_REF] Derot | Long-term high frequency phytoplankton dynamics, recorded from a coastal water autonomous measurement system in the eastern English Channel[END_REF]. The percentage of missing data for each parameter is listed in Table 1. The MAREL Carnot platform did not work for most of 2014. During the last four years, the system experienced many problems; therefore, there is a high number of missing values for many parameters. In order to avoid bias, our analysis only uses data between 2005 and 2010. In other words, considering this 6-year period allows us to maintain consistency of the monitoring data used as input to the RF model. In Fig. 2, we can see the averaged raw data for fluorescence and water temperature for this time period of 6 years. Moreover, the type of machine learning used in this study is able to manage the missing values (see Section 2.2.1 for further details). These missing values are different for all the parameters. In some rare cases, some of these parameters could have more than one month in raw missing values. In this context, we preferred to keep these missing values in the inputs of the RF model, rather than using a numerical method to fill these gaps, which could create greater bias.

Numerical analysis

Machine learning

There are many different types of machine learning models. The RF model is an evolution of the classification and regression tree (CART) model, which was created by the same scientist in 1984 [START_REF] Breiman | Classification and regression trees[END_REF]. Contrary to the CART model that only uses one tree structure; the RF mode is composed of a predetermined number of trees, hence the term "forest". The input data of each tree comes from a random sub-sampling performed with a bootstrap technique, hence the term "random".

The first node of the tree is called the root node and split into two child nodes, and so forth until the terminal nodes, which contain the prediction of the model. By following this step, the RF model in regression mode will obtain an average between all the created trees. This stage is more generally referred to as "ensemble learning". For the RF model, this ensemble method is based on a cross validation process via the out-of-bag (OOB) error. These OOB are mainly calculated from the mean squared error (MSE) in the form of a ratio, in order to give a weight to each predictor. It is important to note that these scores are ratio; therefore, they do not have units. The extraction of the OOB after the learning phase allows us to examine the relative importance of each predictor.

Recent studies have shown that the RF model is well adapted to forecasting changes in the phytoplankton community (Yajima and Derot 2018;[START_REF] Derot | Response of phytoplankton traits to environmental variables in French lakes: New perspectives for bioindication[END_REF][START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF]. The tree structure combined with the bootstrap allows the RF model to effectively manage missing values in datasets, adapt to the study of nonlinear processes, and make no prior assumptions [START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF][START_REF] Breiman | Random forests[END_REF]). These properties coincide with the issues related to our long-term highfrequency sample database; the fluctuations in the phytoplankton abundance can be considered as a stochastic process [START_REF] Derot | Long-term high frequency phytoplankton dynamics, recorded from a coastal water autonomous measurement system in the eastern English Channel[END_REF], leading to the many gaps associated with sampling automation (see paragraph below). Within the framework of our study, the target signal is the phytoplankton biomass, measured by a proxy via fluorescence. The predictors are the remaining physicochemical parameters, as presented in Table 1. All our data are continuous; therefore, we used the RF model in regression mode.

Moreover, we used an individual conditional expectation (ICE) plot [START_REF] Goldstein | Peeking inside the black box: Visualizing statistical learning with plots of individual conditional expectation[END_REF], to identify if the interactions created during the learning phase are comparable with the real biological mechanisms. These ICE plots are an improvement on the partial dependence plot (PDP) used several times in previous scientific studies on phytoplankton and water environments [START_REF] Friedman | The elements of statistical learning[END_REF][START_REF] Cutler | Random forests for classification in ecology[END_REF][START_REF] Roubeix | Identification of ecological thresholds from variations in phytoplankton communities among lakes: contribution to the definition of environmental standards[END_REF][START_REF] Teichert | Restoring fish ecological quality in estuaries: implication of interactive and cumulative effects among anthropogenic stressors[END_REF][START_REF] Derot | Response of phytoplankton traits to environmental variables in French lakes: New perspectives for bioindication[END_REF]. The PDP highlights the marginal effect between a selected predictor and the target signal [START_REF] Friedman | Greedy function approximation: a gradient boosting machine[END_REF]. In this way, it is possible to observe the global relationship between these two variables. The ICE plots allow a much more refined vision, accounting for the individual effect of the observations on the target. To summarize, the PDP corresponds to the average of the ICE; however this average curve may overshadow the complexity of the relationship created by the model during the learning phase [START_REF] Goldstein | Peeking inside the black box: Visualizing statistical learning with plots of individual conditional expectation[END_REF].

All our numerical analyses were conducted using the MATLAB software and its "statistics and machine learning" toolbox. We used the "TreeBagger" function for the RF models and "plotPartialDependence" for the ICE plots. Once the learning is completed, the function "TreeBagger" creates a "fitted model object", which contains the model and all the related information. By directly inserting this "object" in the function "oobError", it is possible to observe the evolution of the out-of-bag error (Figs A1 -A4). The figures showing the ranking of predictor importance (Figs 5, A6 and A9-A11) are also from the same "object". We can extract these permutation out-of-bag observations across each input, using the array "OOBPermutedVarDeltaError". We used the function "barh" to visualize these ranking. In addition, the "rng" function was set to 1, in order to ensure that the results of the random draw could be used for reproducibility purposes. In our preliminary studies, we observed that 300 trees were sufficient to ensure the stability of the learning phases (Figs. A1 to A4). Given this, we performed all the RF runs in this study using this number of trees. The minimal number of observations per node was set to 5 [START_REF] Derot | Response of phytoplankton traits to environmental variables in French lakes: New perspectives for bioindication[END_REF]).

Forecast methodology

In order to understand the impact of the sampling frequency on the forecasts, we artificially created three databases with the following time steps: 1 hour, 12 hours, and 1 day from the original MAREL Carnot 20-minutes sample frequency database by performing a classical linear interpolation.

These interpolations were conducted using the MATLAB function "interp1" on all parameters; the results are presented in Table 1. Subsequently, each of these datasets was split according to the year, from 2005 to 2010, inclusively. As mentioned above, the coupling between machine learning and hydrodynamic models could be a way to achieve decision-making tools [START_REF] Jia | Physics guided recurrent neural networks for modeling dynamical systems: Application to monitoring water temperature and quality in lakes[END_REF][START_REF] Hanson | Predicting lake surface water phosphorus dynamics using process-guided machine learning[END_REF][START_REF] Cuttitta | Linking surface hydrodynamics to planktonic ecosystem: the case study of the ichthyoplanktonic assemblages in the Central Mediterranean Sea[END_REF]). However, the calibration of the biogeochemistry solver linked to hydrodynamic models is fairly sensitive and directly impacts on the capacity to reproduce the dynamics of the phytoplankton [START_REF] Shimoda | Phytoplankton functional type modelling: running before we can walk? A critical evaluation of the current state of knowledge[END_REF][START_REF] Anderson | Plankton functional type modelling: running before we can walk[END_REF][START_REF] Zhao | Competition patterns among phytoplankton functional groups: How useful are the complex mathematical models?[END_REF].

This is why the parameterization of this kind of solver is generally performed year by year [START_REF] Yajima | Changes in phytoplankton biomass due to diversion of an inflow into the Urayama Reservoir[END_REF]. The division into annual subsets of our database was performed to meet this temporal limitation. In all cases fluorescence is always the target signal (green boxes in Fig. 3) and the other physicochemical parameters (Table 1) are the predictors (blue boxes in Fig. 3).

As in our previous phytoplankton forecast study (Yajima and Derot 2018), we used the sliding window strategy to perform these forecasts [START_REF] Herrera | Predictive models for forecasting hourly urban water demand[END_REF]). To summarize, the sliding window is a classical methodology for re-farming time series data when we a forecast analysis is to be performed with machine learning models. A lag time is introduced between the target signal and the predictors.

For example, when the fluorescence is forecast with a lag time of one week, we removed the first week of this target signal and the last week for all other physicochemical parameters (predictors). In this way, a new input matrix is obtained, where the first value of the fluorescence corresponds to the first value of day 8. The first values of all predictors are still the same. Therefore, there is always a one-week lag between the target signal and the predictors. We used the following lag times for each of our four databases and each year: no lag, 1 day, 3 days, 1 week, 2 weeks, 1 month, 2 months, 2 and a half months and 3 months. Consequently, we performed nine RF runs for the1-year dataset. Therefore, we made 45 RF runs for all the years in one database. In total, we performed 180 RF runs in this study with our four datasets. It should be noted that by applying a sliding window of 2 weeks, we are forced to remove some data at the beginning of the target signal vector and some data at the end of the predictors' matrix (Yajima and Derot 2018). In order to perform our analyses using the same amounts of data, we cut the same time period for each case, depending on the largest lag time, that is. 3 months (yellow boxes in Fig. 3). We applied the same procedure for these 180 cases (Fig. 3).

First, the fluorescence vector was identified as the target signal (green boxes and arrows in Fig. 3), and the predictor matrix contained the other physicochemical parameters (blue boxes and arrows in Fig. 3). Second, we applied the sliding window with one definite lag time, and cut periods depending on the 3 months lag (yellow boxes in Fig. 3). Third, we split our data into two parts, the training part comprised 70% of the cut and lagged data and the remaining percentage was used for the test part (yellow boxes in Fig. 3). This split was realized with a semi-random draw via the MATLAB function "cvpartition". This function allowed the creation of two groups with similar intensity values.

Therefore, situations where in the training part contained all the high fluorescence values (bloom periods), leaving the test part with no bloom values, or vice versa were accounted for and skews in data were avoided. Fourth, we used the training part (both target and predictors) for the learning phase of the RF model (orange boxes in Fig. 3). Fifth, we used only the predictors from the test part to form a prediction or forecast of our target signal via the MATLAB function "predict".

Finally, to control the quality of the predictions and forecasts; we performed a correlation between the predicted target signal and the real data from the test part (red box in Fig. 3). These R² coefficients were calculated with the coefficient of determination for each of our 180 cases as follows [START_REF] Shamshirband | Ensemble models with uncertainty analysis for multi-day ahead forecasting of chlorophyll a concentration in coastal waters[END_REF][START_REF] Lee | Monthly chlorophyll-a prediction using neurogenetic algorithm for water quality management in Lakes[END_REF][START_REF] Lee | Improved prediction of harmful algal blooms in four Major South Korea's Rivers using deep learning models[END_REF][START_REF] Recknagel | Ecological relationships, thresholds and time-lags determining phytoplankton community dynamics of Lake Kinneret, Israel elucidated by evolutionary computation and wavelets[END_REF][START_REF] Du | Multistep-ahead forecasting of chlorophyll a using a wavelet nonlinear autoregressive network[END_REF][START_REF] Kehoe | Who smells? Forecasting taste and odor in a drinking water reservoir[END_REF]:

𝑅 ! = 1 - 𝑆𝑆 "#$ 𝑆𝑆 %&% = 1 - ∑ (𝑦 ' -𝑦 ) ' )² ( ')* ∑ (𝑦 ' -𝑦 ,) ( ')*

²

where 𝑆𝑆 "#$ is the residual sum of squares, 𝑆𝑆 %&% is the total sum of squares, 𝑛 is the number of observations, 𝑦 ' is the observed data, 𝑦 ) ' is the predicted data and 𝑦 , is the mean of the observed data. An example quantile-quantile plot from the test part is presented in the appendix (Fig. A5).

The highest coefficients of determination were obtained for the 20 minutes and 1 hour frequencies.

The accuracy of the RF model was evaluated for each frequency and lag time in the appendix in Fig. A8. Table A2 shows the error range linked to this Fig. A8. The average coefficient is slightly better for the green curve and R² with no lag time (see annotations). With respect to the frequencies of 12 hours and 1 day, they have the smallest averages. It is significant to note that all curves exhibit the same tendencies; R² generally starts to decrease after at two-month lag. hours, and 1 day, respectively. The annotations show the coefficient of determination with no lag time and the global averages of the coefficient of determination for each frequency. See Table A1 in the appendix for the range of error.

Our results indicate that the RF model has the ability to use the supplementary information, which is contained in the database from high-frequency sampling. As depicted in Fig. 4, the forecast capacities are generally better for sampling frequencies of 20 minutes and 1 hour than those of 12 hours and 1 day. It is also evident that the average R² coefficient is less than 0.4 for a sampling frequency of 1 day. In our previous works, we tested a close forecast strategy using another database from fresh water ecosystems (Yajima and Derot 2018). It was a long-term dataset over a period of 30 years with a bimonthly sampling frequency. With this lower time step, in various cases the coefficients of determination of the forecasted chlorophyll a were below a threshold of 0.5. In the current study with high-frequency database, it is observed that R² stays above this threshold until the 2 months lag, even when the sampling frequency is arterially decreased until 12 hours. Therefore, our findings demonstrate that the pairing of an RF model with a high-frequency dataset from an automatic system yields good forecast results on an annual scale. Water currents and phytoplankton migration have

greater significance in open-ocean and coastal areas than in lakes. This complexity could make it difficult to obtain good forecast results for these types of ecosystems [START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF].

Physicochemical ranking

Once the learning phase has been completed, it is possible to extract the ranking predictor importance from the out-of-bag (OOB) permutated error. Thus, we can understand the relative impact that each predictor has on an RF model during the learning phase. As shown above, the original MAREL Carnot database with a frequency of 20 minutes provided the best forecast results. In order to examine the global ranking predictor importance, we performed an average of the 35 OOB errors for this frequency. The evaluated global ranking is presented in Fig. 5. It is observed that the nutrients appear to have had low impacts. However, it must be noted that owing to the device limitations, with the original time step of 20 minutes, these nutrients were actually recorded with a sampling frequency of 12 hours (Table 1). In regard to the other physicochemical parameters, water temperature had the most influence on these 35 learning phases, closely followed by the pH, and then the dissolved oxygen. Furthermore, the fourth most important predictor is the salinity measured via its proxy for conductivity. Apart from the nutrients, the photosynthetically active radiation (P.A.R) is the predictor with the least influence. In the appendix, this global ranking has also been evaluated for the other sampling frequencies: Fig. A9 for 1 hour, Fig. A10 for 12 hours and Fig. A11 for 1 day. Water temperature, salinity, nutrients, dissolved oxygen, and pH are the water quality indicators that are used in the water framework directive because of their direct impact on biological processes [START_REF] Best | Dissolved oxygen as a physico-chemical supporting element in the Water Framework Directive[END_REF][START_REF] Millero | Chemical oceanography: CRC press[END_REF]). Among the physicochemical parameters, we temperature and pH were observed to be the most important predictors, but the impact of the other predictors, such as dissolved oxygen, turbidity, and salinity, are non-negligible. Furthermore, the sampling frequency and lag time can also strongly impact the predictor ranking, as depicted in Fig. A6, where the out-ofbag importance of the temperature is very low. Despite its relative importance for a frequency of 20 minutes, the temperature alone is not sufficient to predict the chlorophyll a correctly. For this frequency, we obtained an R² without lag that was equal to 0.31, when only the temperature was used as a predictor and other physicochemical parameters were remove. The values of OOB that were extracted from the 35 learning phases with at frequency of 20 minutes were consistent with the water quality indicators, except for the nutrients (Fig 5). Nevertheless, if only the OOB from the databases with a frequency over 12 hours were considered (Fig. A6); the nutrients crucially impacted the learning phase of the RF models. This leads us to believe that the low impact of nutrients shown in this high-frequency database is an artifact caused by recording system limitations.

Consequently, in light of the significant influence of the temperature on the learning phases of the RF models, it considered to have been systematically account for when a parameter directly linked to the primary production is predicted with machine learning based on tree structure. Furthermore, it is important to harmonize all sampling frequencies from automatic devices in order to prevent this type of bias. In this context, when designing or upgrading an automatic station, similar to a MAREL buoy, having several types of sensors, we suggest installing sensors having the highest possible common sampling frequency. This could increase the biological prediction linked to the phytoplankton biomass via a machine learning model. Next, we will study the parallels between the interactions created by the RF model and real biological mechanisms. Although the interactions created during the learning phase of an RF model are difficult to comprehend, it may be possible to obtain some links between these interactions and the biological processes that occur in the ecosystems being studied. In Fig. 6 (upper left), It can be observed that the highest fluorescence data are predicted for temperatures of approximately 11.8°C. This result is consistent with those in previous literature [START_REF] Schoemann | Phaeocystis blooms in the global ocean and their controlling mechanisms: a review[END_REF][START_REF] Jahnke | The light and temperature dependence of growth rate and elemental composition of Phaeocystis globosa Scherffel and P. pouchetii (Har.) Lagerh. in batch cultures[END_REF]). The MAREL Carnot device is located in the English Channel; in this area, the main issue is the harmful algal bloom (HAB) linked to Phaeocystis globosa. For this type of phytoplankton, regardless of whether the light conditions are limited, the optimal growth rate appears to be between 10°C and 14°C [START_REF] Jahnke | The light and temperature dependence of growth rate and elemental composition of Phaeocystis globosa Scherffel and P. pouchetii (Har.) Lagerh. in batch cultures[END_REF][START_REF] Schoemann | Phaeocystis blooms in the global ocean and their controlling mechanisms: a review[END_REF]. Therefore, our ICE analysis of water temperature illustrates that even without prior assumptions, an RF model can account for some real biological processes.

Conclusion

In this study we found that the average coefficient of determination, which is the index of the quality of the forecast, decreases when the sampling frequency increases. The coefficient for the 20minute time step was 0.24 larger than that for the 1-day time step. From our analyses, we observed that the nutrients had a limited impact on the learning phase with the highest sampling frequency. In regard to the water temperature, the averaged OOB error reached 13, while that for the phosphate concentration was only approximately 0.1. Creation of the ICE plot for the water temperature allowed us to illustrate that the RF model predicted the highest fluorescence values of approximately 11.8°C.

Consequently, the results suggest that RF models can use the additional information contained in highfrequency databases. It is supposed that the apparent low influence of the nutrients was a bias due to the difference in sampling frequencies. Moreover, although the RF model has no prior assumptions, it was able to create some interactions closely resembling the biological processes present in our study area.

The decrease in the sampling frequency is not the only factor impacting forecast capacity. It should be kept in mind that different time steps between the input parameters can introduce biases into the learning process of an RF model. Therefore, it is imperative to have harmonized sampling frequencies in datasets from automated devices. Several studies in the environmental science literature have claimed that the pairing between high-frequency or long-term datasets with an RF model could overcome the limitations of conventional models (linear, generalized linear model …) [START_REF] Kehoe | Who smells? Forecasting taste and odor in a drinking water reservoir[END_REF][START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF][START_REF] Rivero-Calle | Multidecadal increase in North Atlantic coccolithophores and the potential role of rising CO2[END_REF]. The results of our study seem to confirm this hypothesis.

Fig. 1 .

 1 Fig. 1. Location of the MAREL Carnot automatic device, in the eastern English Channel at the

Fig. 2 .

 2 Fig. 2. Inter-annual mean (day-scale) of MAREL Carnot raw data for fluorescence and temperature

Fig. 3 .

 3 Fig. 3. Conceptual diagram presenting the methodology used to measure the forecast quality,

Fig. 4 .

 4 Fig. 4. Evolution of forecast performances depending on lag times and sampling frequencies from test

Fig. 5 .

 5 Fig. 5. Ranking of predictor importance based on the average of the out-of-bag (OOB) error, from the

Fig. 6 .

 6 Fig. 6. Individual conditional expectation (ICE) plots for the four most influent predictors with a time

Fig. A3 .

 A3 Fig. A3. Evolution of the out-of-bag error for the year 2007 with lag time of 2 weeks.

Fig. A4 .

 A4 Fig. A4. Evolution of the out-of-bag error for the year 2007 with lag time of 2 months.

Fig. A5 .

 A5 Fig. A5. Quantile-quantile plot from the test part; for the year 2007 with a frequency of 1 hour and a

Fig. A6 .

 A6 Fig. A6. Ranking of predictor importance from the out-of-bag (OOB) error, for the year 2007 this a 768 lag time of 1 day and a sampling frequency of 1 day. 769

Fig. A10 .

 A10 Fig. A10. Ranking of predictor importance based on the average of the out-of-bag (OOB) error, from

Fig. A11 .

 A11 Fig. A11. Ranking of predictor importance based on the average of the out-of-bag (OOB) error, from

Table 1 .

 1 Physicochemical parameters (target signal and predictors) in the original MAREL Carnot 180 database, with number of readings, percentage of missing data between 2005 and 2010, sampling 181 frequency, and their associated units. 182

	Parameters	Number of	Percentage of	Sampling	Units
		readings	missing data	frequency
	Fluorescence	113530	13.60%	20 minutes	FFU
	Water	117176	10.83%	20 minutes	°C
	temperature
	P.A.R	62172	52.68%	20 minutes	µmol/s/m 3
	Conductivity	114114	13.16%	20 minutes	mS/cm
	Dissolved oxygen	111573	15.09%	20 minutes	mg/L
	pH	97556	25.76%	20 minutes	pH
	Turbidity	92992	29.23%	20 minutes	NTU
	Wind direction	103304	21.38%	20 minutes	°
	Wind speed	103716	21.07%	20 minutes	m/s
	Nitrate	1982	45.70%	12 hours	µmol/L
	Phosphate	1908	47.73%	12 hours	µmol/L
	Silicate	1983	45.67%	12 hours	µmol/L

Acknowledgements

This research was funded by a grant from the Japan Society for the Promotion of Science (JSPS).

Derot J. benefited of Postdoctoral Fellowship for Research in Japan. The MAREL Carnot system belongs to a fixed platform network along French coasts called COAST-HF (http://coast-hf.fr). The data presented here can be obtained in the following sites: https://data.coriolis-cotier.org and also the Seanoe site given in Lefebvre et al. (2015).

 --------------------------------------------

Results and discussion

The primary purpose of this study is to demonstrate the capacity of a machine learning model to forecast phytoplankton blooms in coastal areas and to study the impact of the sampling frequency on the forecast performance of the RF model. For that purpose, we artificially reduced the time step and used different lag times with a sliding window strategy. First, we studied the evolution of the coefficients of determination, depending on several lag times and sampling frequencies. Second, we analyzed which predictors had the greatest influence on the learning phase. Subsequently, we compared the interactions created by the RF model with real biological mechanisms.

Sampling frequency and time-lag impacts

The evolution of the forecast performances and the dependence on lag times is depicted in Fig. 4 for the four datasets up to a time period of 3 months. This analysis was only performed on the test part. Each point on the four lines of Fig. 4 is derived from an inter-annual average for the years 2005-2010. For example, the second green point is calculated by averaging these 5 years with a lag time of 1 day. The time axis in Fig. 4 uses a log scale. Therefore, in order to avoid problems with the log of zero, we have put the results for no lag time in the annotations for this figure. The calculated averages of all lag times were included for each sampling frequency. Another point of view with the median instead of average is presented in Fig. A7 in the appendix and the range of error in shown Table A1.

The green line in Fig. 4 represents the inter-annual average lag times depending on the sampling frequency of 20 minutes. Similarly, the blue, red, and magenta lines represent the coefficient of determination averages for the frequencies of 1 hour, 12 hours, and 1 day, respectively. It should be noted that we cannot apply a sliding window of 12 hours for a sampling frequency of 1 day. This is why the first point of the purple curve is missing in the Fig. 4. In the same way, the first point on the red curve, which corresponds to the 12 hours frequency, is equal to its coefficient without lag; it has been retained to maintain a visual coherence.

Nevertheless, our study shows that this pairing strategy can also work in marine ecosystems.

Consequently, in a water body where water quality management is a major societal issue, it is of pivotal importance to highlight the additional value provided by high sample frequency databases generated by automatic devices. The results of this study indicate that the forecast performance of the RF model increases with increasing sampling frequencies. In addition, it should be noted that although some other studies in similar fields have used the pseudo-R² to measure the performance of the RF model, the authors are aware that the coefficient does not assess the true forecast (Large et al. 2015;[START_REF] Teichert | Restoring fish ecological quality in estuaries: implication of interactive and cumulative effects among anthropogenic stressors[END_REF][START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF]. Thus, we split our dataset between a learning part and a test part (Fig. 3), and used the Pearson coefficient to measure the forecast performances. Consequently, the pairing between machine learning models and automatically generated high sample frequency databases could eventually lead to the creation of numerical decision-making models. Such a model could help stakeholders prevent HABs from hindering the economy as well as human health. In the next part of this section, we examine the influence of the predictors on the learning phase.

Learning phase interactions

Machine learning models are often considered "black boxes" because we cannot understand the interaction between the predictor that the model creates during its learning phase. However, it is possible to transform the RF models into "gray boxes" with the partial dependence plot (PDP) and the individual conditional expectation (ICE) plots. In the previous section, it was seen that the water temperature, conductivity, dissolved oxygen, and pH had the most influence on the average in our learning phases. Therefore, we extracted one ICE plot for each of these 4 predictors with a time step of 20 minutes (Fig. 6). The red lines are the PDP, and all the gray lines and the blue points have been derived from the ICE method. In reference to the water temperature, we can see that the RF model predicts high fluorescence values mainly around 11.8°C; there is also a slight increment over 17.0°C.

The other three predictors exhibit a common pattern. That is to say, the predicted values of fluorescence are low until the predictors reach a certain threshold. The results of this study exhibit high predicted fluorescence values for a pH over 8.25, conductivity over 47 mS/cm, and concentration in dissolved oxygen over 9 mg/L. It is also important to note that high fluorescence values are mainly predicted for very high conductivities and pH values. However there is a large spread in the high fluorescence values for the dissolved oxygen from the middle range to the higher value.

Furthermore, some of the automatic systems are equipped with flow cytometers, enabling differentiation between the phytoplankton groups responsible for the HAB [START_REF] Thomas | The predictability of a lake phytoplankton community, over time-scales of hours to years[END_REF].

Therefore, pairing these types of datasets with machine learning models could aid in the creation of numerical decision-making tools that can help stakeholders with water quality management. In the long run, this kind of tool could have a benefit the economy and human health. Within this framework, we are currently exploring the possibilities of applying this type of pairing on an inter-annual scale, in order to increase the lengths of the forecasted periods.