# Benchmarking of ALBA and ABACO-2 models for algaebacteria wastewater treatment

Rebecca Nordio, Francesca Casagli, Enrique Rodríguez-Miranda, José Luis Guzmán, Olivier Bernard, Gabriel Acién

► To cite this version:

Rebecca Nordio, Francesca Casagli, Enrique Rodríguez-Miranda, José Luis Guzmán, Olivier Bernard, et al.. Benchmarking of ALBA and ABACO-2 models for algaebacteria wastewater treatment. Algal Research - Biomass, Biofuels and Bioproducts, 2025, 89, pp.104049. 10.1016/j.algal.2025.104049. hal-05462102

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Submitted on 16 Jan 2026

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Benchmarking of ALBA and ABACO-2 models for algae-

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bacteria wastewater treatment

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Rebecca Nordio<sup>a,b</sup>, Francesca Casagli<sup>d</sup>, Enrique Rodriguez, José Luis Guzmán<sup>b,c</sup>,

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Olivier Bernard<sup>d</sup>, Gabriel Acién<sup>a,b</sup>

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<sup>a</sup> Department of Chemical Engineering, Universidad de Almería, E04120 Almería,

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Spain.

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<sup>b</sup> CIESOL Solar Energy Research Centre, Joint Centre University of Almería-CIEMAT,

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04120 Almería, Spain.

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<sup>c</sup> Department of Informatics, Universidad de Almería, E04120 Almería, Spain.

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<sup>d</sup> GreenOwl, INRIA centre d'Université Côte d'Azur, Sophia-Antipolis F-06902, France.

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* Corresponding author: Rebecca Nordio, rnordio@ual.es

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Abstract

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Microalgae-based wastewater treatment is a promising technology that combines water remediation with biomass production. Mathematical modelling is a powerful tool that can contribute to enhance this technology, by simulating, optimizing, and efficiently managing production systems. In recent years, several microalgae-bacteria models have been developed and validated in various systems and culture media. In this context, the ABACO-2 and ALBA microalgae-bacteria models have been validated at pilot-scale dimensions and over extended periods. However, these digital twins differ significantly in terms of modelling choices, such as their dependency on environmental conditions and nutrient availability, number of parameters, and calibration strategies. This study benchmarks ABACO-2 and ALBA to define their most suitable application fields and identify potential areas for improvement. This objective was achieved by exchanging datasets used for the original validation of the two models (in Almeria for ABACO-2 and in Milan and Narbonne for ALBA), which exhibit significant differences, particularly in environmental conditions and culture medium composition. Both models were validated using the three case studies, and their relative accuracies are presented here. Finally, the main challenges for the efficient scale-up and industrial application are highlighted in terms of data management, parameter calibration, and monitoring capabilities.
## 1. Introduction

Wastewater management remains a pressing global challenge, driven by rapid urbanization, industrial expansion, and growing concerns about water quality [1].

Traditional wastewater treatment processes can return a significant amount of treated water, but at a high environmental cost. These processes have several notable drawbacks, particularly regarding their greenhouse gas emissions, their high energy demand, and the generation of large quantities of residues (e.g., sludge) that require further treatment [2]. In this context, the scientific community is seeking innovative and more sustainable processes that align with the concept of circular economy [3].

Microalgae-based wastewater treatment is a promising and well-established technology for water remediation [4]. One of the main advantages of this bioprocess over classic activated sludge is the self-production of oxygen by microalgae, which can reduce the operational costs associated with aeration by up to 70% [5]. Data from wastewater treatment plants testing this technology in demo facilities report that the energy consumption of classical treatment averages 0.5 kWh·m⁻³, while it can be reduced to 0.1 kWh·m⁻³ using microalgae-based systems [6]. Additionally, they have a smaller environmental footprint as the removed nutrients (phosphorus (P) and nitrogen (N)) is recycled into the microalgal biomass, which can be used in various emerging fields such as fertilizers, bioplastics, and biofuels [7].

Although the nutrient recycling capacity of this process has been proven effective at pilot scale [8], it has not been fully scaled up to the industrial level due to challenges related to cost-effectiveness [9]. For this reason, recent research has focused on improving the cultivation systems through the incorporation of separation units and the implementation of advanced control strategies. The most common photobioreactor is
the raceway and, compared to other open cultivation systems, it can treat a larger
volume of water per unit of land area [10]. Despite its relative simplicity, it has been
shown that operation can be optimized by regulating variables such as dissolved CO2
(via pH), Dissolved Oxygen (DO), temperature, and culture depth. Several studies
have shown that pH and DO significantly impact biomass productivity [11,12] and
overall system stability [13]. Maintaining these variables in an operational range has
proven to be cost-effective.

Algae-based wastewater systems are biologically very complex due to the interactions
among thousands of microbial populations that influence the system's stability and
effectiveness. The capability of managing and controlling efficiently these interactions
determines the success of the biotreatment [14]. Models can help in understanding
and supervising the process dynamics, as well as managing the interactions between
the different microbial populations. They can provide software sensors to on-line track
microbial dynamics and support an on-line optimization strategy, maintaining the
process performance along time despite ongoing environmental fluctuations.

Biological models should meet the dual requirement of accurately describing the
process while minimizing the computational demand and the effort required for
implementation, calibration and simulation. Furthermore, they should undergo
validation using data from real wastewater treatment plants, where nutrient
concentrations permanently fluctuate, especially N and organic matter. However, data
from real-scale applications are limited, given the low number of algae-bacteria based
systems integrated in existing wastewater treatment plants. To date, different
comprehensive microalgae-bacteria models are available in the literature [15–22].
However, there is insufficient evidence to support their reliability when applied to
datasets different from those for which they were originally developed, particularly for
82 climatologies with different ranges of light intensity and temperatures, or for different
83 wastewater composition. On top of this, most of the studies focus on lab scale
84 processes. Assessing the model's capability to predict the process behaviour at larger
85 scale, where the environment fluctuates along the seasons, is still an open and
86 challenging issue.

87 This work aims to evaluate the applicability of two algae-bacteria digital twins, named
88 ALBA [15] and ABACO-2 [16], focusing on their capabilities for forecasting biomass
89 production and nutrient removal. Both models allow to simulate the microbial
90 community dynamics in wastewater in response to environmental factors (e.g., light,
91 temperature) and operational conditions (e.g., pH control, mixing system and
92 wastewater characteristics). They have undergone prior validation using outdoor
93 datasets. ALBA's validation included two annual datasets: the first comes from a 56
94 m² raceway located in Narbonne, France, where synthetic wastewater, simulating
95 municipal wastewater, was used as the culture medium [15]; and the second employed
96 a 3.8 m² raceway located in Milan, Italy, fed with liquid digestate (centrate) [23]. The
97 ABACO-2 model was validated with data from an 80 m² raceway fed with untreated
98 urban wastewater, located in Almeria, Spain [16]. Both ALBA and ABACO-2 have
demonstrated robust predictive capabilities regarding nutrient fluxes and biomass
99 production within their specific outdoor datasets. However, their development included
100 different modelling choices, as bio-process selection, parametrization and the
101 incorporation of specific model states, often strictly related to the modelling objective
102 function. Additionally, the calibration of biological parameters has been influenced by
103 the environmental conditions and weather characteristics of each experimental
104 dataset.
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With this work, the primary objective is to benchmark the ALBA and ABACO-2 models by comparing their performance across the three case studies mentioned before. This analysis will facilitate a discussion of the differences between the two digital twins, both in terms of structure and prediction capabilities. The comparison will also highlight their respective fields of application and provide insights for potential improvements.

Furthermore, the study will focus on the main challenges of simulating microalgae-bacteria systems, particularly those related to parameter calibration and experimental data management. This underscores the need for standardized monitoring campaigns and production systems, enabling the generation of comparable datasets for model calibration, validation, and adaptability.

## 2. Material and Methods

### 2.1. Experimental datasets

The three annual datasets used in this study differ in terms of operational conditions dimension of the production systems, culture media and environmental conditions.

Figure 1 illustrates the three raceway reactors, while Table 1 details the key characteristics of the associated wastewater.

The first dataset was collected from a 56 m² (17 m³) raceway reactor located in Narbonne, France (Figure 1C) [24]. The reactor operated continuously for 443 days (15/05/2018 – 1/08/2019) with a fixed dilution rate of 0.2 day⁻¹. The predominant microalgal strains were *Scenedesmus* sp. and *Chlorella* sp. A synthetic medium simulating municipal wastewater was used as reactor influent, with urea as the primary nitrogen source. The tap water used for diluting the medium was the main provider of inorganic carbon (Table 1). In this case, pH was uncontrolled. The experimental data collected from the reactor included total suspended solids (TSS), chemical oxygen
demand (COD), inorganic nitrogen, Total Nitrogen (TN) and orthophosphates.

Additionally, the algal biomass has been monitored with Optical Density (OD) measurements. See [24] for more details.

The second dataset is sourced from a previous study presented in [25]. The experimental data have been collected from a 3.8 m² (0.88 m³) raceway reactor located in Milan, Italy (Figure 1B). It covers 189 days of raceway operations (31/05/2016 – 6/12/2016) with variable dilution rates. The growth medium consisted of digestate from a biogas plant, with ammonium (NH₄⁺) as the primary nitrogen source (averaging 310 mgN-NH₄·L⁻¹). A notable concentration of nitrate (NO₃⁻) (60 mgN-NO₃·L⁻¹) was also present in the influent. This influent wastewater exhibited the highest organic matter content among the three cases, with an average COD of 490 mgO₂·L⁻¹ (Table 1), even if most of it was in non-biodegradable form. The pH was controlled at 7.5 through CO₂ injection. The experimental data available included TSS and Volatile Suspended Solids (VSS) together with COD (total and soluble). The influent characteristics have been monitored and inorganic nitrogen (ammonium, nitrate and nitrite), Total Nitrogen and Phosphorus have been measured, while the algal biomass was estimated through OD. See [25] for more details.

Finally, the third dataset was obtained from an 80 m² (12 m³) raceway reactor located in Almeria, Spain (Figure 1A). It covers 206 days (16/05/2022 – 16/11/2022) of semi-continuous operations at a fixed dilution rate of 0.2 day⁻¹. The growth medium was primary urban wastewater, filtered using industrial 200 µm filter. The NH₄⁺ was the main nitrogen source (averaging 120 mgN-NH₄·L⁻¹), while the influent showed a negligible NO₃⁻ concentration (3 mgN-NO₃·L⁻¹ on average). The average recorded COD was 320 mgO₂·L⁻¹ (Table 1). Regarding reactor operation, pH was automatically controlled through on-demand CO₂ injection, serving as the primary source of
inorganic carbon. Additionally, compressed air was injected into the sump to strip
excess dissolved oxygen. The available experimental data included dry weight
measurements for evaluating the total biomass (algae and bacteria), the influent
characteristics in terms of NH₄, NO₃, PO₄ and COD was evaluated with
spectrophotometric methods. We refer to [16] for more details.

Besides the variations in wastewater characteristics and raceway operations, the
Narbonne, Milan, and Almeria datasets exhibit significant differences in environmental
conditions, particularly in solar radiation and temperature. Acknowledging these
differences is crucial, as raceways are outdoor systems, and environmental factors
significantly influence biological kinetics, thereby impacting biomass productivity and
nutrient recovery efficiency. Figure 2 illustrates the Photosynthetically Active Radiation
(PAR) and temperature distribution for each dataset. As expected from the
geographical locations, Almeria experiences higher temperatures and solar radiation
levels, with winter temperatures never below 8°C. The data distribution for temperature
in Almeria remains within a range of 15-38°C (Figure 2A), while PRA was uniformly
distributed across the entire range of values (Figure 2B). On the other hand, Milan and
Narbonne experience colder climates, with winter temperatures reaching low values
closed to zero. Consequently, these two datasets include a wider temperature range
of 0-30°C (Figure 2A). Similar to the Almeria dataset, Narbonne exhibits a uniform
distribution of PAR, while the Milan dataset recorded lower PAR intensities (Figure
2B).

## 2.2. Model calibration

The ABACO-2 model has been calibrated for each dataset presented in this study. The
calibrations period included 28/04/2022-15/2022, 9/08/2022-15/08/2022, 1/11/2022-
179 15/11/2022 for Almeria dataset; 6/08/2018-1/09/2018, 1/11/2018-15/11/2018,
180 15/06/2019-20/06/2019 for Narbonne dataset and 15/06/2016-20/06/2016, 1/09/2016-
181 10/09/2016, 1/12/2016-6/12/2016 for Milan dataset. The calibration of parameters has
182 been carried by minimizing the loss function (1), using "Nelder-Mead" algorithm
183 available in the Scypi optimization tool of Python [26]:

$$Obj = \sum \left( \frac{(y_{sim} - y_{exp})}{\sigma_{exp}} \right)^2 \quad (1)$$

185 Where ysim is the model output, yexp the experimental data and σexp is the experimental
186 standard deviation. The nominal and calibrated parameter values are reported in Table
187 2 and discussed in the following sections.

188 Conversely, the ALBA model was calibrated only over a subset of data from Narbonne
189 case study, covering the period between 2/10/2018-21/10/2018, 1/01/2019-
190 10/01/2019. The model calibration was conducted using the identification toolbox of
191 AQUASIM using the objective function (1) computed for DO and pH. A detailed
192 description of the calibration methodology for both models on their original datasets,
193 together with the original parameter values, is available in the Supporting Information.

## 2.3. Model accuracy and other statistical methods

195 The normalized root mean squared error (NRMSE) [27] and Thiel's Inequality
196 Coefficient (TIC) [28] were calculated using equations (2) and (3):

$$NRMSE = \frac{\sqrt{\frac{\sum(y_{sim} - y_{exp})^2}{N}}}{(y_{exp,max} - y_{exp,min})} \quad (2)$$

$$TIC = \frac{\sqrt{\sum(y_{sim} - y_{exp})^2}}{\sum y_{sim}^2 + \sum y_{exp}^2} \quad (3)$$
Where $y_{sim}$ is the model output, $y_{exp}$ the experimental data, while $y_{exp,max}$ and $y_{exp,min}$ is the max and the min values inside the experimental dataset. A TIC value below 0.3 indicates a good agreement between the experimental data and the model predictions. Results are summarized in Table 3 and 8 and discussed in the following section. Table 3 presents the errors computed for each model using its respective validation dataset. In contrast, Table 8 reports the errors calculated on a shared validation subset, obtained by excluding all calibration data used from both models.

In order to classify the different environmental conditions associated to each case study, the dataset dimensionalities have been reduced with a Principle Component Analysis (PCA) using Python programming language and Skylearn package.

## 3. State of the Art in modelling algae-bacteria systems

On top of ABACO-2 and ALBA, several algae-bacteria have been developed in the field of microalgae-based wastewater treatment. Table 4 compares the main models, including River Water Quality Model (RWQM1) [20], Zambrano [19], BIO_ALGAE [29] and the one proposed by Aparicio in [22]. They are based on various structures, supported by experimental data from different processes (from lab to outdoor), and their validations differ by the amount of data, their nature and duration.

The RWQM1, one of the earliest microalgae-bacteria models, was developed to guide water management in rivers. It describes the interaction between algae and three bacteria populations (heterotrophic, Ammonium Oxidizing Bacteria (AOB), and Nitrite Oxidizing Bacteria (NOB)) across 22 biological processes, including aerobic and anoxic bacteria growth, hydrolysis, and chemical equilibrium. However, the RWQM1's complexity and potential over-parametrization arise from the inclusion of a large number of biological parameters (120) [30].
More recently, the Zambrano model was developed as a simplified model for algae-bacteria dynamics in photo-bioreactors. It considers only two microbial populations (generically classified as algae and bacteria) and incorporates a limited number of state variables (6) and biological processes (5). Additionally, the Zambrano model was validated using experimental data obtained from 1L cylindrical photobioreactor fed with municipal wastewater over a 6-day period (Table 4). Despite demonstrating good accuracy within the specific pH and temperature ranges where it was validated and calibrated, the model's applicability should be considered limited to those conditions [19].

The BIO-ALGAE model has been proposed by Solimeno et al. [29] and later improved in [18]. This model represents a comprehensive microalgae-bacteria model, encompassing a large number of processes (18), including aerobic and anoxic growth of heterotrophic bacteria, growth of two groups of nitrifiers, endogenous respiration, and hydrolysis (19 state variables). Despite the demonstrated good accuracy, the BIOALGAE2 model validation was conducted over a limited period (8 days) using a 14 L cylindrical photobioreactor fed with municipal wastewater, while the BIOALGAE 1 was validated with a raceway reactor of 1 m³ over a longer period (175 days).

Finally, Aparicio et al. proposed a novel integrated model applied to outdoor membrane photobioreactors [22], coupling the BNRM2 model [31] with the microalgal model proposed by Viruela et al. [32]. The main novelty of this model is the inclusion of chemical processes such as phosphorus precipitation and microalgae inhibition by nitrite (NO₂⁻). It includes a large number of processes (38) and parameters (170), incorporating micronutrients like magnesium, iron, and potassium as state variables. It underwent validation over 30 days for a flat panel photobioreactor coupled to a membrane filtration system (MPBR), with a high degree of accuracy.
## 3.1. Structural comparison of ABACO-2 and ALBA

ABACO-2 and ALBA are two comprehensive algae-bacteria models predicting biomass production and nutrient evolution depending on environmental and operational conditions. Both digital twins were previously validated over extended periods using yearlong datasets from pilot-scale systems. However, they differ significantly in terms of modelling choices and, in particular, by the mathematical functions used to describe microbial growth rates.

The ALBA model is a fully predictive model, as it includes sub-models predicting temperature and pH evolutions. It describes interactions among microalgae, heterotrophic bacteria, and two groups of nitrifiers (AOB and NOB). The ALBA model encompasses a wide range of biological processes (19 in total), including anoxic growth of heterotrophic bacteria in $NO_3^-$, two different processes for endogenous respiration and decay for each microorganism, as well as organic matter hydrolysis and urea ammonification. Consequently, the ALBA model exhibits greater complexity compared to the ABACO-2 model, which neglects some of these processes. The ABACO-2 includes 7 biological processes and 8 state variables (Table 4), including microalgae, heterotrophic bacteria, and a single consortium of nitrifying bacteria that oxidize $NH_4^+$ directly into $NO_3^-$ (one step nitrification). This simplification is based on the experimental observation of low concentrations of $NO_2^-$ in the cultures cultivated in Almeria. Furthermore, the ABACO-2 model handles substrate limitation using a multiplicative substrate limitation kinetic approach, as proposed by the traditional Activated Sludge Model (ASM) [33]. Alternatively, the ALBA model implements a minimum function for limiting substrates, where only the most limiting one is driving the overall biological kinetics.
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### 3.1.1. Effect of operational variables

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Both models consider the multiple effects of temperature, pH, DO, and nutrient availability on algae and bacteria growth dynamics. However, these dependencies are often modelled using different functions. For instance, ALBA implements the equation proposed by Bernard & Rémond, 2012 [34], to model algae growth dependency on light intensity, with photoinhibition at high light, as described in equation (4), where $a$ represents the initial slope of the light response curve and $I_{opt}$ is the irradiance at which growth is maximal with respect to light. Alternatively, the ABACO-2 employs the function proposed by Grima et al., 1994 [35] described in equation (5), where $I_k$ represents the irradiance necessary to reach half of the maximum growth rate, while $n$ is the shape parameter. In addition, the ALBA model averages the light intensity along depth using the Lambert-Beer equation [36], while in ABACO-2, the average light is calculated as a function of the extinction coefficient and the biomass concentration [37]. A comparison between the two functions is presented in Figure 3A.

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$$ \overline{\mu(I)} = \frac{I}{1 + \frac{\mu_{max}}{a} \left( \frac{I}{I_{opt}} - 1 \right)^2} \quad (4) $$

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$$ \mu(I) = \frac{I^n}{I_k^n + I^n} \quad (5) $$

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These differences also extend to the handling of pH dependencies. Their pH modelling differ, as represented in Figure 3 B, C, D. The ABACO-2 model employs the Cardinal pH Model with Inflection (CPMI), whereas the ALBA model utilizes the pH model proposed by Rosso et al., 1995 (CPM) [38]. The effect of temperature on the microbial kinetics is represented for both by the Cardinal Temperature Model with Inflection (CTMI) [39], including a minimal temperature under which there is no growth, an
optimal temperature and a temperature beyond which growth is no more possible.
Additionally, both models account for inhibition effects resulting from high
concentrations of DO and ammonium/ammonia, but they employ different equations
for these inhibitions. In the case of the ABACO-2 model, dissolved oxygen inhibition is
modelled using a hyperbolic tangent function proposed by Costache et al., 2013 [40]
as shown in equation (6), Where $S_{O_2,max}$ represents the oxygen concentration at which
photosynthesis is completely inhibited. Furthermore, the ammonium inhibition is
described with the Haldane function, including an inhibition constant $K_i$, as described
in equation (7).

$$ \overline{\mu(O_2)_{alg}} = 1 - \left( \frac{S_{O_2}}{S_{O_2,max}} \right)^z \quad (6) $$

$$ \overline{\mu(NH_4)} = \frac{S_{NH_4}}{S_{NH_4} + K_{s,NH_4} + \frac{(S_{NH_4})^2}{K_{I,NH_4}}} \quad (7) $$

On the contrary, in the ALBA model, the effect of oxygen inhibition is modelled using
the S-shaped dose-response inhibition curve (Hill model), as described in (8), where
EC₅₀,₀₂ represents the oxygen concentration causing 50% inhibition of the
photosynthetic activity. Similarly, the inhibition by ammonia is implemented with a non-
competitive inhibition model described in (9), where EC₅₀,NH₃ represents the inhibition
parameter that causes the 50% inhibition of the photosynthetic activity, as proposed
by Rosso et al., 2020 [41].

$$ \overline{\mu(O_2)_{alg}} = \frac{EC_{50,O_2}^n}{S_{O_2}^n + EC_{50,O_2}^n} \quad (8) $$

$$ \overline{\mu(NH_3)} = \frac{1}{1 + \left( \frac{NH_3}{EC_{50,NH_3}} \right)^n} \quad (9) $$
### 3.1.2. Nutrients uptake

Beyond the differences in modelling environmental factors, the representation of nutrient consumption by microorganisms also varies considerably between ABACO-2 and ALBA. In line with the ASM approach, the ALBA model defines a stoichiometric matrix dependent on the reference composition of algae and bacteria. This classical approach assumes a constant composition of algal biomass, resulting from an uptake of nutrients proportional to growth. While this ensures elemental mass continuity, it does not account for the varying nutrient yields, which are influenced by various operational and environmental factors such as nutrient availability, pH, temperature, and light. This phenomenon was first identified by Droop (1968) [42], resulting in the change of the internal quota as a function of the environment. Modelling nutrient yields is complex, but it is a key distinction characterizing microalgae-bacteria from activated sludge systems. The ABACO-2 model introduces a novel approach in the context of comprehensive microalgae-bacteria models by incorporating nutrient yields as a function of the nutrient concentration in the medium, following the equation proposed by Zurano et al., 2021 [43] (10). This approach assumes a non-constant composition of algal biomass, offering a more realistic representation of nutrient uptake dynamics.

$$Y_{s,alg} = \left[ \frac{Y_{max} S^{t_s}}{S_N^{t_s} K_{s,Y_s}^{t_s}} \right] + \left[ \frac{(S - S_{max}) (S - S_{min})^2}{(S_{opt} - S_{min}) \left( \left( (S_{opt} - S_{min})(S_N - S_{opt}) \right) - \left( (S_{opt} - S_{max})(S_{opt} + S_{min} - 2S) \right) \right)} \right] (10)$$

Additionally, the ABACO-2 model enhances the Monod equations by incorporating an "assimilation" factor, α, which represents the ability of microalgae to accumulate nutrients. This modification allows to predict growth even right after nutrient have been exhausted from the medium, in line with the Droop model [42]. Typically, achieving this level of detail requires more complex models, increasing computational demands and needing extensive experimental data for calibration. In contrast, the ABACO-2 model
simplifies this process by calculating the substrates used in the Monod functions as the sum of the nutrient concentration in the medium and the nutrients assimilated into the biomass (equations (11) and (12)). It assumes that the maximum nitrogen concentration in the biomass is 10%, while phosphorus is 2%.

$$S_N = S_{N,medium} + X_{alg} \cdot 0.1 \cdot \alpha \quad (11)$$

$$S_P = S_{P,medium} + X_{alg} \cdot 0.02 \cdot \alpha \quad (12)$$

In conclusion to the comparison analysis, the biological parameters for both models were primarily calibrated using data collected over one month of experiments conducted across different seasons (Table 4, Section 5 of supporting information). Additionally, sensitivity and model uncertainty analyses were performed in both cases.

# 4. Benchmarking ABACO2 and ALBA

## 4.1. Model validation

This section presents the simulation results from the ABACO-2 and ALBA models for the Almeria, Narbonne, and Milan datasets. Figures 4, 6, and 8 illustrate validation graphs for ABACO-2, while Figures 5, 7, and 9 show results for ALBA. In all graphs, continuous lines represent simulations, while dots represent experimental data. In addition, the calibration data have been indicated with a yellow bar under the time axis. Table 3 presents the NRMSE and TIC values for each simulation. Some ABACO-2 model parameters were recalibrated (Table 2) for each dataset to achieve satisfactory results. Further discussion on model calibration is provided in the next sections. A summary of the main results from the analysis that follows is in Table 6.

### 4.1.1. Almeria data set
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Figures 4A and 5A illustrate the evolution of total biomass within the Almeria system.

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Total biomass was experimentally determined by dry weight (DW) measurements and can be approximated as the sum of algal and bacterial contributions. Biomass variation, primarily driven by microalgae [44] was influenced by environmental conditions such as solar radiation and temperature, ranging from 0.7 gDW·L⁻¹ in spring to 1.5 gDW·L⁻¹ in summer, with a sharp decrease to 0.3 gDW·L⁻¹ during autumn. Both the ALBA and ABACO-2 models provided simulations with similar errors (NRMSE = 0.21, 0.25; TIC = 0.16, 0.17 for ABACO-2 and ALBA, respectively), with a slightly higher error for the ALBA model, which was less accurate in representing the system during summer. This lack of accuracy results from the fact that the ALBA model was not recalibrated, unlike ABACO-2, which was calibrated for each case study. Therefore, the reduced accuracy at specific times can be attributed to the calibration phase, carried out on datasets exploiting lower summer temperatures and solar radiation values.

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Regarding the nitrogen dynamics, Figures 4B and 5B depict the evolution of NH₄⁺, while Figures 4C and 5C show the evolution of NO₃⁻. Both models simulated NH₄⁺ with peaks at specific times of the day reflecting semi-continuous system operation with a high NH₄⁺ load (20 g·m⁻³·day⁻¹) introduced punctually during each daily dilution cycle (0.2 day⁻¹). For this reason, accurately simulating the fast dynamics of NH₄⁺ was particularly challenging. Despite this, both models returned acceptable NRMSE values (0.14 for ABACO-2 and 0.24 for ALBA), although the TIC values were high, both exceeding 0.3 (0.53 for ABACO-2 and 0.55 for ALBA). In this system, NH₄⁺, was primarily consumed by microalgae in competition with nitrifiers, which produced NO₃⁻ during the nitrification process. Complete nitrification was achieved, as negligible NO₂⁻ levels (5 mgN·NO₂·L⁻¹ on average) were measured in the culture. Simultaneously, NO₃⁻
accumulation remained below 100 gNO3·m⁻³ for most of the months, with an increase up to 400 gNO3·m⁻³ observed during autumn, likely due to lower algal concentrations and a temporary aeration system failure, favouring NO3⁻ accumulation. In this scenario, the ABACO-2 model demonstrated slightly better accuracy, with an NRMSE of 0.16 and a TIC of 0.23, compared to ALBA's NRMSE of 0.26 and TIC of 0.3.

Figures 4D and 5D illustrate the dissolved oxygen concentration. Despite the presence of an external aeration flow designed to strip out oxygen and mitigate algal inhibition, the DO reached up to 25 mgO2·L⁻¹ during the day, due to the strong photosynthetic activity, decreasing to near anoxic conditions at night. Both the ABACO-2 and ALBA models successfully captured the overall variation and daily oscillations of dissolved oxygen between day and night (NRMSE = 0.14, 0.24; TIC = 0.21, 0.33 for ABACO-2 and ALBA, respectively). Similar to the biomass concentration results, the ALBA model performances degraded during the summer season, due to the lower algal biomass predicted at higher temperature.

Finally, Figures 4E and 5E illustrate the evolution of soluble organic matter, defined as BSMO (Biodegradable Soluble Organic Matter) in this study. The BSMO represents the organic matter directly oxidized by heterotrophic bacteria. In this case, the influent was sourced from urban wastewater, with BSMO estimated to constitute 80% of the total inlet COD. The prediction of this variable was again better performed by both models (NRMSE = 0.16, 0.21; TIC = 0.14, 0.24 for ABACO-2 and ALBA, respectively).

### 4.1.2. Milan dataset

Figures 6A and 7A provide an overview of the algal biomass concentration (galg·m⁻³) evolution across the Milan dataset. It was experimentally determined by correlating Volatile Suspended Solids (VSS) with the optical density (OD) at 680 nm [16]. An initial
rise in algae concentration (0.3 to 0.7 $g_{alg} \cdot L^{-1}$) was followed by an unexpected decline during summer (0.1 $g_{alg} \cdot L^{-1}$), due to the temporary installation and subsequent removal of a shading net installed to reduce the effect of photoinhibition [25]. Both models accurately predicted algal concentration (NRMSE = 0.19, 0.11; TIC = 0.14, 0.18 for ABACO-2 and ALBA, respectively). Upon closer examination of the simulations, ABACO-2 demonstrates superior performance during autumn seasons, mainly attributed to the recalibration of cardinal temperature parameters for the different microbial population. Conversely, the ALBA model adeptly captures biomass fluctuations over shorter time intervals.

Figures 6B and 7B show the fluctuation of ammonium levels in the medium, ranging widely from 0 to 150 $g_{NH_4} \cdot L^{-1}$. Both models yielded similar simulation results (NRMSE = 0.31, 0.16; TIC = 0.34, 0.31 for ABACO-2 and ALBA, respectively). The higher TIC values, particularly for ABACO-2, highlights the complexity of modelling $NH_4^+$ dynamics which is involved in several microbial activities. Interestingly, the decrease in algal concentration during summer did not notably affect $NH_4^+$ accumulation, indicating that nitrifiers were the main responsible for its removal [15]. Moreover, nitrifiers drove $NO_3^-$ accumulation, reaching 300 $g_{NO_3} \cdot L^{-1}$ (Figures 6C, 7C). Previous studies have confirmed complete nitrification occurring approximately 70 days after the startup [23]. Since the ABACO-2 considers one step nitrification, converting $NH_4^+$ directly to $NO_3^-$, its accuracy is reduced at the beginning of the simulation. Nevertheless, both models result in similar $NO_3^-$ error and correlation values (NRMSE = 0.21, 0.2; TIC = 0.3, 0.18 for ABACO-2 and ALBA, respectively).

Figures 6D and 7D show simulation results for DO. The Milan case study showed a narrower DO range (5 to 20 $mgo_2 \cdot L^{-1}$) compared to Almeria, likely due to lower algal productivity, a more efficient mixing system ($K_{la} = 34 h^{-1}$), and the smaller raceway
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dimensions. Both models accurately predicted DO levels (NRMSE = 0.17, 0.088; TIC = 0.15, 0.15), effectively capturing the shape and oscillations of DO for most of the considered period.

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Finally, Figures 6E and 7E depict the simulations of BSMO. For this digestate derived influent, previous analyses estimated BSMO to constitute 28% of the total COD [45].

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The ALBA model demonstrated superior accuracy in predicting BSMO levels (NRMSE = 0.4, 0.1; TIC = 0.18, 0.05 for ABACO-2 and ALBA, respectively), likely due to its more detailed representation of organic matter components (soluble, particulate, readily and slowly biodegradable) and hydrolysis processes. On the contrary, the ABACO-2 model only assumes a fixed amount of COD consumed by heterotrophic bacteria. While less accurate, ABACO-2 still captured the overall BSMO dynamics.

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### 4.1.3. Narbonne dataset

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Figures 8A and 9A represent the algal biomass concentration in the Narbonne reactor. Algal biomass concentration, estimated by correlating TSS with OD at 680 nm, fluctuated in response to seasonal changes in solar radiation and temperature, reaching 0.05 $g_{alg} \cdot L^{-1}$ in winter and 0.4 $g_{alg} \cdot L^{-1}$ in summer. Both models simulated algal biomass, with similar trends (TIC=0.18 for ABACO-2, 0.11 for ALBA). However, ABACO-2 showed lower accuracy (NRMSE: 0.5 vs. 0.27 for ALBA), especially during colder months (December to February).

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For almost the entire period, $NH_4^+$ was fully consumed, except in winter when lower microalgal activity led to decreased uptake. Conversely, a substantial accumulation of $NO_3^-$ was observed ranging from 0 to 150 $g_{NO3} \cdot L^{-1}$. In this case, full nitrification was achieved 20 days after startup [15]. Both models demonstrated similar accuracy in simulating $NO_3^-$, with comparable NRMSE (0.38, 0.21 for ABACO-2 and ALBA) and

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TIC (0.5, 0.23 for ABACO-2 and ALBA) values. However, the ABACO-2 model was less accurate during the initial simulation stages, as it does not consider the generation of NO₂⁻ by AOB. Both models exhibited lower accuracy when simulating NH₄⁺, highlighting again the challenge of obtaining accurate simulations for this component (NRMSE=0.25, 0.21, TIC=0.55, 0.42 for ABACO-2 and ALBA respectively).

Both models effectively captured DO dynamics (Figures 8D, 9D), reaching a good accuracy (NRMSE = 0.15, 0.15; TIC = 0.1, 0.01 for ABACO-2 and ALBA, respectively).

Finally, Figures 8E and 9E show the evolution of BSMO within the culture. Similar to the Milan case, ABACO-2 showed lower accuracy for BSMO (NRMSE= 0.5; TIC= 0.5) compared to ALBA (NRMSE= 0.27; TIC= 0.3).

#### 4.1.4. Model performance summary

Table 5 compares the qualitative performance of the two models considering all the state variables. None of the models consistently outperforms the other across all scenarios. Instead, each demonstrates specific strengths and weaknesses depending on the variable being predicted and the characteristics of each dataset. Furthermore, Table 3 shows the average NRMSE and TIC of both models across the three datasets.

Overall, both performed best on the Milan case study. It probably results from the simpler nature of this smaller pilot system, closer to a laboratory setting and operated on a shorter period of time. On the contrary, simulating larger datasets coming from pilot-scale systems closer to industrial settings proved to be more challenging. For these cases, ALBA performed better on the Narbonne dataset, while ABACO-2 on the Almeria dataset. This not surprising, as these were the original datasets supporting their respective developments. Furthermore, NH₄⁺ and BSMO were the most difficult variables to simulate across all the cases.
483 5. Discussion

484 5.1. Application fields and further improvements

485 Comparing the performances of ABACO-2 and ALBA models highlights areas for
486 potential improvement, and the differences in performance reflect the distinct specific
487 purpose of each model.

488 For instance, ABACO-2 produced better simulations of algal biomass evolution,
489 although its accuracy in winter seasons could be improved. Conversely, ALBA
490 demonstrated a greater ability to track nitrogen evolution and BSMO. These results
491 align with the distinct goals for which each model was originally developed. ALBA aims
492 to extend traditional ASM models for wastewater treatment by incorporating
493 microalgae as an additional microorganism. In contrast, ABACO-2 focuses on
494 describing microalgae production systems using nutrients contained in wastewaters
495 as growth medium. This difference in objectives is particularly evident when focusing
496 on the different modelling approaches used for nutrient yields and the composition of
497 algal biomass. For ABACO-2, modelling algal biomass is central, and for this reason,
498 it introduces dynamics in yield modelling, while variables like COD reduction, which
499 are fundamental in wastewater treatment, are less emphasized and more relevant for
500 the ALBA model.

501 Additionally, ALBA proved more accurate in predicting nitrogen evolution in some
502 cases, likely due to its consideration of two distinct nitrifier groups and the ability to
503 simulate NO₂⁻. Conversely, ABACO-2 hypotheses a single step nitrification, leading to
504 less accurate simulations, particularly during the system startup phase. The
505 assumption of full nitrification can be considered valid for Almería case study, where
506 the high concentration of oxygen combined with the high temperatures favour the
507 oxidation of NO₂⁻ to NO₃⁻. However, to enhance ABACO-2's applicability, it will be
508 necessary to enable the simulation of the two groups of nitrifying bacteria in each
509 specific case. Furthermore, ABACO-2 could be improved by including the modelling
510 of the relationship between inorganic carbon, microalgal growth, and pH evolution.
511 Previous studies show that when pH is controlled and alkalinity is adequate, inorganic
512 carbon is not limited [46], but it can become drastically limiting without pH control [12].

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5.2. Transition to standard algae-bacteria models: challenges in model
calibration and data integration.

515 Advanced modelling can help to better reveal and exploit the widely recognized
516 potential of algae-bacteria systems for wastewater remediation. These systems are
517 complex, with a dynamic metabolic interplay between microorganisms involved in
518 nutrient removal and toxic compounds degradation. The literature presents several
519 studies that describe the growth dynamics of the main populations present in
520 wastewater, mainly nitrifying and heterotrophic bacteria [47]. However, managing
521 these interactions to achieve optimal water treatment and biomass production at
522 industrial scale remains a complex challenge. Over the years, several experimental
523 applications have been proposed for evaluating the most relevant microbial
524 populations in wastewater, such as flow cytometry [48], respirometric [44] or Next
525 Generation Sequencing [49] methodologies. However, these techniques are resource
526 and time consuming. A model-based approach serves as a valuable complement to
527 limited experimental records by providing a mathematical description of the biological
528 system, allowing the prediction of algae-bacteria dynamics, and the nutrient evolution
529 in wastewater.
One of the most significant challenges for scaling-up algae-bacteria systems is to more accurately understand and predict these complex dynamics under different environmental and operational conditions. Digital twins will definitely be instrumental for this perspective, and this means that standardized modelling frameworks must be adopted. Standardization involves defining uniform protocols for identifying key system parameters, such as growth kinetics, substrate uptake rates, light availability, and oxygen transfer dynamics, which influence both algal photosynthetic activity and bacterial respiration.

In contrast to algae-bacteria systems, standardized modelling protocols for conventional bioremediation processes, such as activated sludge, are more established and have been widely applied at industrial scale. These protocols, proposed by the International Water Association (IWA), are outlined in the Activated Sludge Models (ASM1, ASM2, and ASM3) [50]. These models embed different levels of complexity, depending on their intended use, such as one- or two-step nitrification, inclusion of phosphate uptake mechanisms, and the modelling of organic matter cycling. Despite substantial advances in experimental knowledge and modelling of algae-bacteria systems over the past two decades, the development of standardized modelling approaches remains a primary objective to improve model reproducibility and scalability. A major obstacle to this goal is the limited accessibility of common platforms for sharing experimental data and benchmarking models. More experimental campaigns are needed to better characterize the dynamics of these system, and especially to get more insight into the evolution of the various microbial species. Data recorded on industrial-scale plants, are often not publicly available or are inconsistently reported. This inconsistency arises from the use of different experimental techniques to measure the same parameters, leading to non-
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comparable data across different monitoring campaigns and eventually make the
model comparison tricky. Data scarcity complicates the implementation of calibration
and validation protocols, limiting the transferability and reliability of models in real-
world applications. Facilitating the exchange of experimental data is therefore a crucial
component of standardizing modelling frameworks.

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In addition to collaborative efforts to develop shared database, the dissemination of
model codes implemented in open-source programming languages (e.g., Python,
Julia, Jax) and the establishment of benchmarks for parameter estimation and model
prediction evaluation would significantly enhance model comparison, reproducibility,
and scalability. Sharing the calibration tools together with the model is also
instrumental for an efficient model reuse [51]. Moreover, the incorporation of emerging
tools, such as machine learning techniques (e.g., neural networks, symbolic
regressions), has the potential to further improve prediction accuracy and optimize
system performances. A standardized modelling approach not only supports
comparative studies and scalability but also accelerates the development of robust,
efficient, and adaptable solutions for wastewater treatment applications.

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The objective of this study was to progress in this direction providing a comparative
evaluation of the ALBA and ABACO2 models, with the aim of testing both models on
independent datasets, different from those on which they were originally calibrated, in
order to assess their extrapolation capability. This analysis provides crucial insights
into the suitability of each model for different case studies and objective functions.
Nonetheless, this research should be expanded within a broader framework,
incorporating a wider range of algae-bacteria models for comparative analysis. Such
an approach would facilitate the establishment of standardized modelling protocols for

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algae-bacteria systems, thereby supporting the optimization and scaling-up of this
biotechnology for wastewater treatment applications.

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**5.2.1. Standardization challenges**

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**5.2.1.1. Experimental data**

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As an example of typical challenges for standardizing data recorded during different
monitoring campaigns, Table 7 highlights the differences between the experimental
data used for Almeria, Milan and Narbonne case studies. The most significant
discrepancies lie in the evaluation and interpretation of the biomass concentration.

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Specifically, the Almeria dataset uses a dry weight methodology, expressed in g<sub>dw</sub>·m<sup>-3</sup>, encompassing both bacterial and microalgal contributions. Conversely, in the Narbonne and Milan datasets, algal concentration is expressed in g<sub>COD</sub>·m<sup>-3</sup> and estimated through a correlation of OD and VSS. Moreover, the total biomass (algae plus bacteria) is evaluated as Total Suspended Solids (TSS), expressed in g<sub>COD</sub>·m<sup>-3</sup>.

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These quantities all implicitly assume that microbial biomasses dominate the organic particulates, and none of them distinguishes microalgae and bacteria. Additionally, the nutrient concentrations have been evaluated with different spectrophotometric methodologies associated to different units. These discrepancies are challenging for establishing and developing standard algae-bacteria model, as they introduce complexities in data interpretation and model calibration.

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**5.2.1.2. Calibration and validation methods**

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In addition to standardizing monitoring culture campaigns, the models' applicability can be extended to new datasets if there is a clear definition of the calibration and validation procedure when transitioning to new case studies. Table 2 lists the 24 parameters that underwent additional calibration to achieve satisfactory accuracy for

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603 ABACO-2 over the Milan and Narbonne datasets. Despite the ABACO-2 model's large
604 number of parameters (79 in total), only a small subset required recalibration, selected
605 after performing a sensitivity analysis, as presented in [16]. This subset includes the
606 maximum growth rate and decay rate for each microbial population, the cardinal
607 parameters for temperature and pH, and, exclusively for the Milan dataset, the yield
608 of NO₃⁻ generation by nitrifying bacteria. The need for recalibrating parameters such
609 as maximum growth rates and decay rates suggests potential variations in microbial
610 populations across the three systems, likely influenced by differing influent sources
611 and characteristics. Cardinal parameters, as the optimal, maximum and minimum
612 temperature and pH values, significantly influence biokinetic rates and simulation
613 accuracy, therefore they should be carefully identified. Notably, to achieve good
614 accuracy in the Milan and Narbonne datasets, where temperature values were
615 reaching negative pics over the autumn/winter season, it was necessary to adapt the
616 minimum temperature parameter of the CTMI (Tmin). Additionally, since pH in the
617 Narbonne raceway was not controlled, and was reaching high values, the pH cardinal
618 parameters had to be adapted to adequately simulate this range.

619 Conversely, the ALBA model was applied to the three datasets without biological
620 parameter recalibration. However, it is likely that a fast and standardized calibration
621 procedure for ALBA's main sensitive parameters would also have been beneficial for
622 better simulating outdoor raceways exposed to higher temperatures and solar fluxes.
623 In this case, a new sensitivity analysis would be also necessary, as the most sensitive
624 parameters can vary depending on the specific environmental conditions, since the
625 microbial populations have different metabolic response to environmental changes.
626 However, the capacity of the ALBA model to perform with a high accuracy over the
627 Almeria dataset without recalibrating the biological parameters can be explained by
the fact that it encompasses numerous processes and kinetics, allowing for a more
comprehensive and general approach compared to the ABACO-2. This raises another
important consideration in microalgae-wastewater treatment model development:
balancing computational demand, complexity, and accuracy. Although ALBA
demonstrates greater comprehensiveness compared to ABACO-2, its increased
number of equations and processes considered may present challenges in practical
implementation, particularly for developing models for optimization and automatic
control. Conversely, a model like ABACO-2 including less processes and variables
offers advantages in terms of interpretability and ease of implementation.
Nevertheless, to ensure predictability, it requires calibration for each new dataset. On
the other hand, while biological parameters did not require recalibration in the ALBA
model, operational parameters (e.g., mass transfer coefficient, liquid depth, and light
extinction coefficient) needed to be accurately adjusted to each configuration. The light
extinction coefficient, crucial for simulating the amount of light available for microalgae
growth, was set to the experimentally measured value in the Almeria raceway [52].
Indeed, this coefficient is highly influenced by wastewater characteristics and liquid
depth, which was considerably lower in Almeria (15 cm) compared to Milan (21 cm)
and Narbonne (28 cm). However, the primary challenge was simulating the operational
processes involving gas-liquid exchange. In practice, the air injection system was
included in the model in addition to the already implemented pH control through CO2
injection and the natural exchange of CO2 and O2 with the atmosphere. This required
the use of four different mass transfer coefficient values obtained from experimental
measurements. Two of these values were determined by the reactor specific injection
system and were typically much higher than those describing natural exchange with
the atmosphere, which are primarily influenced by the reactor mixing system.
Furthermore, the main challenge was accurately smoothing and integrating the injected air flow dynamics. This was done by adapting the mass transfer coefficient, which varied continuously due to the measured dissolved oxygen concentration and the activation of the pH control system. Finally, the experimental management of CO2 and air injection systems changed several times during the campaign, further complicating the reproduction of their rapid dynamics. The simulation results of algal biomass production revealed that accurately reproducing these gas-liquid exchanges was crucial for correctly simulating algae growth kinetics.

Another key challenge in standardizing the validation and comparison of different models is determining how best to assess their performance when they are calibrated on different datasets. Tables 3 and 8 present two distinct approaches: evaluating each model solely on its respective validation data (Table 3) or using a common validation dataset for both models (Table 8). The first approach provides an assessment of individual model performance, but direct comparisons may lack rigor since the performance indexes are computed on different amounts of data. Conversely, the second method offers a more standardized comparison but introduces bias by systematically excluding validation data for one model if it has been used for calibrating the other. This exclusion may lead to an uneven assessment of model performance, as it removes data points where a model might demonstrate strong predictive capability, potentially underestimating its accuracy. The absence of a widely accepted methodology for selecting validation datasets presents a significant challenge in complex model comparisons. This study provides a preliminary evaluation of this issue, highlighting the need for further investigation to advance the standardization of model validation in wastewater treatment applications.
The results in Table 8, compared to those in Table 3, show an overall increase in NRMSE for both models across all datasets then comparing them in the same data set (without any data used for calibrating one of the models). However, the main conclusions regarding relative model performance, as discussed in Section 4, remain valid. Notably, the TIC values remained unchanged across both validation methods, suggesting that TIC may be the most robust metric for comparing models calibrated on different amounts and types of data.

### 5.2.2. Exploring significantly different environmental conditions

It is fundamental to challenge models with several data sets to demonstrate their universality and ability to accurately predict the behaviour of algae-bacteria systems in a large range of climatologies and processes. The experimental campaigns used for benchmarking the models encompass processes from 3.8 m² to 80 m² conducted under different climatic conditions. Figure 10 illustrates the PCA analysis conducted on the model input variables across the three datasets. The first component reveals that culture height and $NH_4^+$ concentration account for the highest variance. This result can be explained by the fact that the Narbonne case study was dominated by lower amount of ammonium, since the primary source of nitrogen was urea. Conversely, the second component highlights solar radiation, temperature, pH, and DO as the most relevant input variables. This analysis emphasizes that influent characteristics and composition are less critical for model prediction, aligning with the previous analysis showing nutrient yields as less sensitive and not requiring recalibration. Instead, environmental conditions and reactor operation has a greater influence, justifying the need to recalibrate temperature and pH cardinal parameters when transitioning between datasets. Moreover, culture height significantly influences the simulation accuracy. Considering these results, when developing a model, these identified input
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variables should be prioritized and meticulously monitored to ensure optimal model
performance.

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### 5.3. Bridging the gap between models and industrial reality: the future of algae-bacteria bioprocess modelling

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Full scale up is one of the main challenges that algae biorefineries are still facing [53]. Bridging the gap between laboratory observations and the realities of industrial-scale production can strongly benefit from modelling advances. Digital twins can inspire more efficient reactors design based on fluxes estimations, improved nutrient removal and biomass production. The ALBA and ABACO-2 models have proven to be effective tools for the description and simulation of these systems at pilot-scale. However, their application in real industrial scenarios will only be possible after further research and validation. For instance, none of the models available in the literature has been validated in large-scale reactors exceeding 1000 m² due to the limited number of industrial facilities in operation and the available experimental data.

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Furthermore, there are other limitations regarding the experimental data that constrain the effective validation and proof of accuracy of these models. For example, there are currently no straightforward techniques to distinguish between algal and bacterial contributions to biomass in $g·L^{-1}$ that can be easily implemented in a model. Therefore, future efforts should prioritize developing experimental protocols for biomass fractionation. Additionally, future research should focus on investigating algae nutrient yield and uptake. Specifically, it will be necessary to clarify the influence of light intensity, temperature, and dissolved oxygen, and to model these dependencies that can be integrated into biological framework.
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Accurately modelling algae-bacteria systems will open the way for the digitalization of these systems. Digitalization, automation, and automatic controls are fundamental for reducing costs, energy consumption, and labour, significantly enhancing the design and optimization of microalgae-bacteria consortia processes and accelerating their integration into Water Resource Recovery Facilities (WRRFs). In this context, there is a need for the development of user-friendly algae-bacteria simulation platform running various digital twins. This development will require in parallel standardized monitoring protocols across facilities, ensuring data comparability and facilitating model calibration and validation. This study has shown that robust calibration procedures are crucial for adapting models to new datasets. It presents an initial evaluation of which parameters necessitate further calibration when transitioning between case studies, highlighting the need for additional research in this area.

Finally, beyond addressing these immediate challenges, it will be necessary to enhance the stability and water disinfection capabilities of algae-bacteria systems. Microorganisms such as rotifers and fungi typically represent a challenge for the stability of these systems, causing their sudden crash [54,55]. For this reason, developing theoretical tools to support the early detection of algae predators and to prevent the biomass loss is crucial for enhancing their stability. Similarly, there is a growing interest in the identification of pathogenic bacteria and their inactivation to assess the disinfection capacity of the systems and meet the regulatory requirements imposed by the EU [56]. In future work, models should support the automatic detection and diagnosis of algae predators and pathogenic bacteria to rapidly react and take the proper actions. While this would increase model complexity, it could be achieved through novel modelling strategies such as data-driven or hybrid models. In addition, this integration necessitates advances in monitoring technologies, including online
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sensors or laboratory tests, to automatically detect the discrepancies in model predictions due to the presence of contaminants.

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## Conclusions

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The comparative benchmarking of the ALBA and ABACO-2 models has elucidated their relative strengths and areas for further refinement. Cross-validation across three distinct datasets revealed that, despite their structural differences, both models demonstrate good predictive capacity. The ABACO-2 seemed to have stronger predictive capabilities of the biomass concentration, but simplified nitrification model can be a limiting factor when it comes to accurately simulating $NH_4^+$ dynamics and initial $NO_3^-$ production. On the other hand, the ALBA model performs better in the prediction of the N forms and the organic matter. Furthermore, the ABACO-2 model required parameter recalibration when applied to different datasets. The key parameters requiring recalibration in ABACO-2 were primarily related to the prediction of biomass growth kinetics, as the maximum growth rates and the cardinal parameters for temperature and pH. Differently, the ALBA model, offered a more comprehensive and generalizable approach, and recalibration was not needed, apart for key operational parameters related to the mixing system and the liquid depth applied in the reactor. Further research should focus on refining calibration procedures and developing standardized monitoring protocols to facilitate data comparability across different systems. It will therefore be possible to develop a standardized model that will help drive forward the digitization of these systems, improving their efficiency from design to on-line supervision and control.

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## Credit authorship contribution statement
773 **R. Nordio**: Investigation, Formal Analysis, Validation, Software, Data Curation, Visualization, Writing – Original Draft; **F. Casagli**: Investigation, Formal Analysis, Validation, Software, Data Curation, Visualization, Writing – Original Draft; **E. Rodríguez-Miranda**: Investigation, Formal Analysis, Software; **J. L. Guzmán**: Conceptualization, Supervision, Writing - Review & Editing, Funding Acquisition; **O. Bernard**: Conceptualization, Supervision, Writing - Review & Editing, Funding Acquisition; **G. Acien**: Conceptualization, Supervision, Writing - Review & Editing, Funding Acquisition.

781 Acknowledgements

782 This research was funded by the H2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement (project: Digitalisation, 955520). and 783 by the H2020 Research and Innovation Framework Programme (REALM, 784 101060991). F. Casagli and O. Bernard thank the support of the ANR BARRIER 785 project (ANR-22-CE34-0021). Furthermore, all the authors thank Politecnico di Milano 786 and INRAE-LBE for the experimental data provided. 787

788 Tables

<table><caption>789 Table 1: Influent composition comparison between Almeria, Narbonne and Milan datasets</caption><thead><tr><th>Nutrients</th><th>Almeria<br>[mg·L<sup>-1</sup>]</th><th>Narbonne<br>[mg·L<sup>-1</sup>]</th><th>Milan<br>[mg·L<sup>-1</sup>]</th></tr></thead><tbody><tr><td>N-NH<sub>4</sub><sup>+</sup></td><td>118±100</td><td>8±2</td><td>422±111</td></tr><tr><td>N-NO<sub>3</sub><sup>-</sup></td><td>0.45±4</td><td>0.22±1</td><td>60±12</td></tr><tr><td>P-PO<sub>4</sub><sup>3-</sup></td><td>10±26</td><td>13±3</td><td>41±13</td></tr><tr><td>Urea</td><td>-</td><td>68±12</td><td>-</td></tr><tr><td>COD<sub>tot</sub></td><td>322±160</td><td>378±57</td><td>490±107</td></tr></tbody></table>

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<table><caption>Table 2: List of parameters recalibrated of the ABACO-2 model</caption><thead><tr><th colspan="5">ABACO-2</th></tr><tr><th>Parameter</th><th>Units</th><th>Original values</th><th>Milan</th><th>Narbonne</th></tr></thead><tbody><tr><td>μ<sub>max,alg</sub></td><td>day<sup>-1</sup></td><td>1.5</td><td>1.2</td><td>1.5</td></tr><tr><td>μ<sub>max,nit</sub></td><td>day<sup>-1</sup></td><td>0.75</td><td>0.28</td><td>0.56</td></tr><tr><td>μ<sub>max,het</sub></td><td>day<sup>-1</sup></td><td>3.4</td><td>0.5</td><td>0.5</td></tr><tr><td>m<sub>nit</sub></td><td>day<sup>-1</sup></td><td>0.05 μ<sub>max,nit</sub></td><td>0.22 μ<sub>max,nit</sub></td><td>0.2 μ<sub>max,nit</sub></td></tr><tr><td>m<sub>het</sub></td><td>day<sup>-1</sup></td><td>0.2 μ<sub>max,het</sub></td><td>0.55 μ<sub>max,het</sub></td><td>0.2 μ<sub>max,het</sub></td></tr><tr><td>T<sub>opt</sub>, T<sub>min</sub>, T<sub>max</sub> (alg)</td><td>°C</td><td>20,-10,42</td><td>20,-10,42</td><td>20,-15,40</td></tr><tr><td>T<sub>opt</sub>, T<sub>min</sub>, T<sub>max</sub> (nit)</td><td>°C</td><td>20,-8,40</td><td>23,-8,45</td><td>21,-7,35</td></tr><tr><td>T<sub>opt</sub>, T<sub>min</sub>, T<sub>max</sub> (het)</td><td>°C</td><td>25,-3,42</td><td>25,-3,40</td><td>20,-10,40</td></tr><tr><td>pH<sub>opt</sub>, pH<sub>min</sub>, pH<sub>max</sub> (alg)</td><td>—</td><td>8.5, 1.8,12.9</td><td>8.4, 2,12</td><td>8.4, 2,12</td></tr><tr><td>pH<sub>opt</sub>, pH<sub>min</sub>, pH<sub>max</sub> (nit)</td><td>—</td><td>9, 2,13.4</td><td>7.5,5.5,10</td><td>7.5,5.5,10</td></tr><tr><td>pH<sub>opt</sub>, pH<sub>min</sub>, pH<sub>max</sub> (het)</td><td>—</td><td>9, 6,12</td><td>7.5,5,13</td><td>8,5,12</td></tr><tr><td>Y<sub>NO<sub>3</sub>,nit</sub></td><td>g<sub>NO<sub>3</sub></sub> · g<sub>nit</sub><sup>-1</sup></td><td>26.7</td><td>10</td><td>26.7</td></tr></tbody></table>

<table><caption>Table 3: NRMSE and TIC computed from ABACO-2 and ALBA simulations considering only their respective validation data sets (calibration periods have been discarded).</caption><thead><tr><th rowspan="2"></th><th colspan="3">ABACO-2</th><th colspan="3">ALBA</th></tr><tr><th colspan="3">NRMSE</th><th colspan="3">TIC</th></tr><tr><th></th><th>Milan</th><th>Narbonne</th><th>Almeria</th><th>Milan</th><th>Narbonne</th><th>Almeria</th></tr></thead><tbody><tr><td>X<sub>alg</sub>/X<sub>tot</sub></td><td>0.19</td><td>0.5</td><td>0.21</td><td>0.11</td><td>0.18</td><td>0.16</td></tr><tr><td>S<sub>NH4</sub></td><td>0.31</td><td>0.25</td><td>0.22</td><td>0.34</td><td>0.55</td><td>0.55</td></tr><tr><td>S<sub>NO3</sub></td><td>0.21</td><td>0.38</td><td>0.16</td><td>0.3</td><td>0.44</td><td>0.15</td></tr><tr><td>S<sub>BSMO</sub></td><td>0.4</td><td>0.5</td><td>0.16</td><td>0.18</td><td>0.5</td><td>0.21</td></tr><tr><td>S<sub>DO</sub></td><td>0.17</td><td>0.15</td><td>0.14</td><td>0.15</td><td>0.1</td><td>0.21</td></tr></tbody></table><table><thead><tr><th colspan="3">NRMSE</th><th colspan="3">TIC</th></tr><tr><th>Milan</th><th>Narbonne</th><th>Almeria</th><th>Milan</th><th>Narbonne</th><th>Almeria</th></tr></thead><tbody><tr><td>0.19</td><td>0.5</td><td>0.21</td><td>0.11</td><td>0.18</td><td>0.16</td></tr><tr><td>0.31</td><td>0.25</td><td>0.22</td><td>0.34</td><td>0.55</td><td>0.55</td></tr><tr><td>0.21</td><td>0.38</td><td>0.16</td><td>0.3</td><td>0.44</td><td>0.15</td></tr><tr><td>0.4</td><td>0.5</td><td>0.16</td><td>0.18</td><td>0.5</td><td>0.21</td></tr><tr><td>0.17</td><td>0.15</td><td>0.14</td><td>0.15</td><td>0.1</td><td>0.21</td></tr></tbody></table>
<table><caption>Table 4: Comparison between main algae-bacteria models available</caption><thead><tr><th></th><th>RWQM1</th><th>Zambrano</th><th>BIO_ALGAE 1</th><th>BIO_ALGAE 2</th><th>ABACO</th><th>Aparicio model</th><th>ABACO-2</th><th>ALBA</th></tr></thead><tbody><tr><td>Reference</td><td>[20]</td><td>[19]</td><td>[29]</td><td>[18]</td><td>[17]</td><td>[22]</td><td>[16]</td><td>[15]</td></tr><tr><td>State variables</td><td>24</td><td>6</td><td>19</td><td>19</td><td>7</td><td>32</td><td>8</td><td>17</td></tr><tr><td>Biological processes</td><td>22</td><td>5</td><td>18</td><td>22</td><td>4</td><td>38</td><td>7</td><td>19</td></tr><tr><td>Parameters</td><td>120</td><td>23</td><td>94</td><td>108</td><td>57</td><td>170</td><td>79</td><td>72</td></tr><tr><td>Growth kinetic type</td><td>Multiplicative</td><td>Multiplicative</td><td>Multiplicative</td><td>Multiplicative</td><td>Multiplicative</td><td>Multiplicative</td><td>Multiplicative</td><td>Multiplicative / minimum</td></tr><tr><td>Microbial populations</td><td>Algae, AOB, NOB, Het</td><td>Algae, bacteria</td><td>Algae, AOB, NOB, Het</td><td>Algae, AOB, NOB, Het</td><td>Algae, Nit, Het</td><td>Algae, AOB, NOB, Het</td><td>Algae, Nit, Het</td><td>Algae, AOB, NOB, Het</td></tr><tr><td>N-forms</td><td>NH<sub>3</sub>,NH<sub>4</sub><sup>+</sup>,NO<sub>3</sub><sup>-</sup> NO<sub>2</sub><sup>-</sup></td><td>NH<sub>4</sub><sup>+</sup>,NO<sub>3</sub><sup>-</sup></td><td>NH<sub>3</sub>,NH<sub>4</sub><sup>+</sup>,NO<sub>3</sub><sup>-</sup> NO<sub>2</sub><sup>-</sup></td><td>NH<sub>3</sub>,NH<sub>4</sub><sup>+</sup>,NO<sub>3</sub><sup>-</sup> NO<sub>2</sub><sup>-</sup></td><td>NH<sub>4</sub><sup>+</sup>,NO<sub>3</sub><sup>-</sup></td><td>NH<sub>3</sub>,NH<sub>4</sub><sup>+</sup>,N O<sub>3</sub><sup>-</sup>NO<sub>2</sub><sup>-</sup></td><td>NH<sub>4</sub><sup>+</sup>,NO<sub>3</sub><sup>-</sup></td><td>N<sub>org</sub>,NH<sub>3</sub>,NH<sub>4</sub><sup>+</sup>, NO<sub>3</sub><sup>-</sup>, NO<sub>2</sub><sup>-</sup>,HNO<sub>2</sub>, HNO<sub>3</sub>,N<sub>2</sub></td></tr><tr><td>P-forms</td><td>H<sub>2</sub>PO<sub>4</sub><sup>-</sup>,HPO<sub>4</sub><sup>2-</sup></td><td>-</td><td>PO<sub>4</sub><sup>3-</sup></td><td>PO<sub>4</sub><sup>3-</sup></td><td>PO<sub>4</sub><sup>3-</sup></td><td>PO<sub>4</sub><sup>3-</sup></td><td>PO<sub>4</sub><sup>3-</sup></td><td>H<sub>3</sub>PO<sub>4</sub>,H<sub>2</sub>PO<sub>4</sub><sup>-</sup>,HPO<sub>4</sub><sup>2-</sup>, PO<sub>4</sub><sup>3-</sup></td></tr><tr><td>Nutrient consumption</td><td>Stoichiometric coefficients</td><td>Stoichiometric coefficients</td><td>Stoichiometric coefficients</td><td>Stoichiometric coefficients</td><td>Stoichiometric coefficients</td><td>Stoichiometric coefficients</td><td>Yield coefficients</td><td>Stoichiometric coefficients</td></tr><tr><td>PAR model</td><td>Steele</td><td>Monod</td><td>Eliers & Peters</td><td>Eliers & Peters</td><td>Molina</td><td>Steele</td><td>Molina</td><td>Bernard & Ramon</td></tr><tr><td>T growth dependence</td><td>Arrhenius</td><td>-</td><td>Arrhenius</td><td>CTMI</td><td>CTMI</td><td>Arrhenius</td><td>CTMI</td><td>CTMI</td></tr><tr><td>pH growth dependence</td><td>-</td><td>-</td><td>-</td><td>CPMI</td><td>CPMI</td><td>Monod with inhibition</td><td>CPMI</td><td>CPM</td></tr><tr><td>Ammonification</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>yes</td></tr><tr><td>DO inhibition</td><td>-</td><td>-</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td></tr><tr><td>NH<sub>3</sub> inhibition</td><td>-</td><td>-</td><td>-</td><td>yes</td><td>yes</td><td>-</td><td>yes</td><td>yes</td></tr><tr><td>Gas-liquid mass transfer</td><td>O<sub>2</sub></td><td>O<sub>2</sub></td><td>O<sub>2</sub>, CO<sub>2</sub>,NH<sub>3</sub></td><td>O<sub>2</sub>, CO<sub>2</sub>,NH<sub>3</sub></td><td>-</td><td>O<sub>2</sub>, CO<sub>2</sub>,NH<sub>3</sub>, N<sub>2</sub></td><td>O<sub>2</sub></td><td>O<sub>2</sub>, CO<sub>2</sub>,NH<sub>3</sub>, evaporation</td></tr><tr><td>Reactor type</td><td>River environment</td><td>Cylindrical</td><td>Raceway</td><td>Cylindrical</td><td>Cylindrical</td><td>MPBR</td><td>Raceway</td><td>Raceway</td></tr><tr><td>Reactor volume/ installation</td><td>Outdoor</td><td>Indoor, 1L</td><td>Outdoor, 1 m<sup>3</sup></td><td>Indoor, 4L</td><td>Indoor, 1L</td><td>Outdoor, 0.23 m<sup>3</sup></td><td>Outdoor, 12m<sup>3</sup></td><td>Outdoor, 17 m<sup>3</sup>, 1m<sup>3</sup></td></tr></tbody></table>
<table><thead><tr><th></th><th>Influent</th><th>Wastewater discharge</th><th>Municipal wastewater</th><th>Municipal wastewater</th><th>Municipal wastewater</th><th>Municipal wastewater</th><th>Permeate</th><th>Municipal wastewater</th><th>Sinthetic wastewater, digestate</th></tr></thead><tbody><tr><td rowspan="2">Experimental data</td><td>Calibration dataset</td><td>-</td><td>n.d</td><td>4 days</td><td>8 days</td><td>7 days</td><td>20 days</td><td>41 days</td><td>30 days</td></tr><tr><td>Validation dataset</td><td>-</td><td>6 days</td><td>175 days</td><td>8 days</td><td>21 days</td><td>25 days</td><td>206 days</td><td>413, 189 days</td></tr><tr><td rowspan="3">Validation</td><td>Sensitivity analysis</td><td>yes</td><td>yes</td><td>yes</td><td>-</td><td>-</td><td>yes</td><td>yes</td><td>yes</td></tr><tr><td>Parameters uncertainty</td><td>yes</td><td>yes</td><td>-</td><td>-</td><td>-</td><td>yes</td><td>yes</td><td>yes</td></tr><tr><td>Model uncertainty</td><td>yes</td><td>-</td><td>-</td><td>-</td><td>-</td><td>yes</td><td>yes</td><td>yes</td></tr></tbody></table>

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<table><caption>Table 5: Summary of ABACO-2 and ALBA performances across all the state of variables</caption><thead><tr><th>Variable</th><th>Dataset</th><th>ALBA</th><th>ABACO-2</th><th>Observations</th></tr></thead><tbody><tr><td>X<sub>tot</sub></td><td>Almeria</td><td>Less accurate during summer</td><td>Good overall performance</td><td>Can be considered as the sum of algae and bacteria, experimentally estimated as dry weight for ABACO-2 and TSS for ALBA</td></tr><tr><td>X<sub>alg</sub></td><td>Narbonne, Milan</td><td>Good predictions It captures short-term oscillations in the Milan dataset.</td><td>Less accurate for Narbonne. Good predictions for Milan, especially in winter.</td><td>Experimentally estimated through the correlation of VSS and DO</td></tr><tr><td>S<sub>NH4</sub></td><td>Almeria, Narbonne, Milan</td><td>Overall good performance but high TIC values (exceeding 0.3). Less accurate in Almeria.</td><td>Overall good performance but high TIC values (exceeding 0.3). Less accurate in Narbonne.</td><td>Overall challenging to simulate since its presence in all the processes and its consumption by all the microorganisms</td></tr><tr><td>S<sub>NO3</sub></td><td>Almeria, Narbonne, Milan</td><td>Good overall performance but higher NRMSE values than the other variables. Performs better in Milan and Narbonne</td><td>Less accurate especially for Milan and Narbonne and in-process startups due to the simplified nitrification model. Performs better in Almeria</td><td>Full nitrification after 70 days in Milan and after 20 days in Narbonne. Full nitrification over all the Almeria dataset.</td></tr><tr><td>S<sub>BSMO</sub></td><td>Almeria, Narbonne, Milan</td><td>Overall more accurate especially for Narbonne and Milan given its more detailed model for COD fractionation.</td><td>Performs better for the Almeria dataset.</td><td>80% of COD<sub>tot</sub> for Almeria, 28% of COD<sub>tot</sub> for Milan, 56% of COD<sub>tot</sub> for Narbonne</td></tr><tr><td>S<sub>DO</sub></td><td>Almeria, Narbonne, Milan</td><td>Good overall performance, capturing short and long-term oscillations. Less accurate during summer in Almeria</td><td>Good overall performance, capturing short and long-term oscillations. Higher TIC for the Narbonne dataset</td><td>Higher oscillations registered in Almeria closer to inhibition for algae. Better air desorption in Milan.</td></tr></tbody></table>

<table><caption>Table 6: Average NRMSE and TIC values across the three datasets</caption><thead><tr><th></th><th>ABACO-2</th><th>ALBA</th></tr></thead><tbody><tr><th colspan="3" style="text-align: center;">NRMSE</th></tr><tr><td>Milan</td><td>0.25</td><td>0.15</td></tr><tr><td>Narbonne</td><td>0.36</td><td>0.22</td></tr><tr><td>Almeria</td><td>0.18</td><td>0.24</td></tr><tr><th colspan="3" style="text-align: center;">TIC</th></tr><tr><td>Milan</td><td>0.21</td><td>0.17</td></tr><tr><td>Narbonne</td><td>0.36</td><td>0.22</td></tr><tr><td>Almeria</td><td>0.25</td><td>0.31</td></tr></tbody></table>
<table><caption>Table 7: Experimental data for ABACO-2 and ALBA model</caption><thead><tr><th rowspan="2"></th><th colspan="2">Almeria dataset</th><th colspan="2">Narbonne, Milan datasets</th></tr><tr><th>Method</th><th>Units</th><th>Method</th><th>Units</th></tr></thead><tbody><tr><td>Ammonium</td><td>Spectrophotometric method using the Nessler reactive</td><td>g<sub>NH4</sub>·m<sup>-3</sup></td><td>Spectrophotometric method using Hach-Lange kits LCK303</td><td>g<sub>N-NH4</sub>·m<sup>-3</sup></td></tr><tr><td>Nitrate</td><td>Spectrophotometric method - 220 and 275 nm</td><td>g<sub>NO3</sub>·m<sup>-3</sup></td><td>Spectrophotometric method using Hach-Lange kits LCK341</td><td>g<sub>N-NO3</sub>·m<sup>-3</sup></td></tr><tr><td>Phosphate</td><td>spectrophotometric method using a phosphor-vanado-molybdate complex</td><td>g<sub>PO4</sub>·m<sup>-3</sup></td><td>Spectrophotometric method using Hach-Lange kits LCK348</td><td>g<sub>P-PO4</sub>·m<sup>-3</sup></td></tr><tr><td>Algae biomass</td><td>-</td><td>-</td><td>Correlation between OD<sub>680</sub> and VSS</td><td>g<sub>COD</sub>·m<sup>-3</sup></td></tr><tr><td>Total biomass</td><td>Dry weight</td><td>g<sub>DW</sub>·m<sup>-3</sup></td><td>TSS</td><td>g<sub>COD</sub>·m<sup>-3</sup></td></tr><tr><td>Oxygen</td><td>Sensor probe</td><td>%-Sat</td><td>Sensor probe</td><td>g<sub>O2</sub>·m<sup>-3</sup></td></tr></tbody></table>

<table><caption>Table 8: NRMSE and TIC computed for ABACO-2 and ALBA using data for validation which were not used for calibrating any of the models.</caption><thead><tr><th rowspan="3"></th><th colspan="6">ABACO-2</th><th colspan="6">ALBA</th></tr><tr><th colspan="3">NRMSE</th><th colspan="3">TIC</th><th colspan="3">NRMSE</th><th colspan="3">TIC</th></tr><tr><th>Milan<br>(as in Table3)</th><th>Narbonne<br>(as in Table3)</th><th>Almeria<br>(as in Table3)</th><th>Milan<br>(as in Table3)</th><th>Narbonne<br>(as in Table3)</th><th>Almeria<br>(as in Table3)</th><th>Milan<br>(as in Table3)</th><th>Narbonne<br>(as in Table3)</th><th>Almeria<br>(as in Table3)</th><th>Milan<br>(as in Table3)</th><th>Narbonne<br>(as in Table3)</th><th>Almeria<br>(as in Table3)</th></tr></thead><tbody><tr><td>X<sub>alg</sub>/X<sub>tot</sub></td><td>0.19</td><td>0.6</td><td>0.21</td><td>0.11</td><td>0.2</td><td>0.16</td><td>0.38</td><td>0.45</td><td>0.38</td><td>0.19</td><td>0.15</td><td>0.17</td></tr><tr><td>S<sub>NH4</sub></td><td>0.31</td><td>0.26</td><td>0.22</td><td>0.34</td><td>0.4</td><td>0.55</td><td>0.24</td><td>0.34</td><td>0.6</td><td>0.33</td><td>0.5</td><td>0.52</td></tr><tr><td>S<sub>NO3</sub></td><td>0.21</td><td>0.6</td><td>0.16</td><td>0.3</td><td>0.4</td><td>0.15</td><td>0.38</td><td>0.48</td><td>0.33</td><td>0.21</td><td>0.24</td><td>0.38</td></tr><tr><td>S<sub>BSMO</sub></td><td>0.5</td><td>0.5</td><td>0.16</td><td>0.18</td><td>0.4</td><td>0.21</td><td>0.29</td><td>0.4</td><td>0.36</td><td>0.06</td><td>0.3</td><td>0.24</td></tr><tr><td>S<sub>DO</sub></td><td>0.17</td><td>0.17</td><td>0.14</td><td>0.15</td><td>0.1</td><td>0.21</td><td>0.12</td><td>0.21</td><td>?</td><td>0.14</td><td>0.12</td><td>0.33</td></tr></tbody></table>
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<figure><img src="image_2.png" /></figure>

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<caption>Figure 1: Demonstrative raceway reactors used to validate the ALBA/ABACO model: A) raceway of 80 m² located in Almería, Spian; B) raceway of 3.8 m² located in Milan, Italy; C) raceway reactor of 56 m² located in Narbonne, France</caption>

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<figure><img src="image_3.png" /></figure>

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<caption>Figure 2: Data frequency in Narbonne, Milan and Almería datasets: A) Data frequency in Temperature (°C), B) Data frequency in solar radiation (µE·m⁻²·s⁻¹)</caption>

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<figure><img src="image_4.png" /><figcaption>Figure 3: Comparison of the growth rate functions between ABACO-2 and ALBA. A) Light response; B) pH response for algae; C) pH response for heterotrophic bacteria; D) pH response for nitrifying bacteria</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 4: Validation of ABACO-2 over Almeria dataset. The calibration periods are indicated in the x-axes with a yellow bar.</figcaption></figure>

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<figure><img src="image_6.png" /><figcaption>Figure 5: Validation of ALBA over Almeria dataset</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 6: Validation of ABACO-2 over Milan dataset. The calibration periods are indicated in the x-axes with a yellow bar.</figcaption></figure>

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<figure><img src="image_8.png" /><figcaption>Figure 7: Validation of ALBA model over Milan dataset</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 8: Validation of ABACO-2 model over Narbonne dataset. The calibration periods are indicated in the x-axes with a yellow bar.</figcaption></figure>

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<figure><img src="image_10.png" /><figcaption>Figure 9: Validation of ALBA model over Narbonne dataset. The calibration periods are indicated in the x-axes with a yellow bar.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 10: PCA analysis of input data</figcaption></figure>

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