The municipal wastewater treatment plant (WWTP) North of San Luis Potosí, SLP, Mexico, (Planta Norte) is located at the northeast of the city of the same name, at 22˚12'24" of north latitude and 100˚56'49" of west longitude, and 1848 m of elevation. It is a train of four aerated lagoons in series, with an average operation flowrate of 23,126 m³/d for the studied period (2004-2010). Figure 1 (elaborated in this research) shows a schematic diagram of the Planta Norte with a brief mention of the main equipment. Details of the plant and, specifically, the primary lagoon are given elsewhere [4] .

Regular sampling and data recording was performed by Proagua by obtaining grab samples of the WWTP influent and effluent every 4 h, starting at 00:00, recording the date, time, point of monitoring and the instant flowrate. Daily composite samples were prepared from the grab samples, in accordance with the NMX-AA-003- 1980 standard [5] . Composite samples were analyzed for total suspended solids (TSS), volatile suspended solids (VSS); chemical oxygen demand (COD) and biological oxygen demand (BOD₅) in accordance with the NMX- AA-034-SCFI-2001, NMX-AA-030/1-SCFI-2012, NMX-AA-028-SCFI-2001 standards [6] - [8] , respectively. In addition, on Monday and Thursday the same parameters were analyzed at the effluent of each lagoon.

In the scope of AFL dynamic modeling, there are very few studies published on the scientific literature, most focused primarily on hydrodynamic aspects [9] - [17] , other models include the wastewater composition and their transformation processes, but in most of these models the complexity is such that they require advanced waste-

water characterization as well as specialized software [18] - [27] . Despite their complexity, these models have not been able to describe the complex behavior of organic matter/oxygen demand in the AFL in a precise or proper manner. This problem motivated the evaluation of existing, simpler aerated lagoon models, based on aggregated organic matter or oxygen demand components. The goal is to determine if they are able to provide a reasonable description of the lagoon behavior at a lower modeling cost.

In the next subsections, three AFL dynamic models (in non-steady state) from the literature are presented [25] [26] [28] . They have been chosen for evaluation in this study.

All the mentioned models were built and implemented in MATLAB^®/Simulink^®, their calibrations were performed with the Parameter Estimation tool, by the conjugated gradient optimization method, and using the sum of squared errors of the effluent oxygen demand (measured vs. estimated) as cost function. For this purpose, a period of two consecutive data years (2007-2008) was taken as calibration period and the rest of the time series was used as validation period, this calibration period was chosen due to during this, abrupt oscillations in the influent flowrate occurs with less frequency, in comparing to the rest of the time series.

Once resolved the dimensional inconsistencies, the model was executed and its parameters were calibrated. The measured and estimated BOD concentrations at the effluent of the lagoon are presented in Figure 2. The model obtains 0.528 of R² with RMSE of 11.9 mg/L for calibration, and 0.345 with 17.6 mg/L for validation, respectively. Table 1 shows the model parameter values (initial and adjusted).

In Figure 2 it can be noticed that although the model describes well the average behavior of BOD in the first

part of the simulation period (2004-2008), the fluctuations in the measured data are not represented by the model, especially in the specific cases of sudden increases or decreases (pulses) in the effluent BOD concentration of the lagoon, which are associated to rain-induced influent flow peaks. Furthermore, in the last part of the time series (2009-2010), where the concentration variation range is the widest of all the time series, the model clearly overestimates the effluent concentrations. This occurs through both higher-than-observed peaks and shallower-than-observed valleys, as well as through periods of general model overestimation. Regarding the parameters of the model, Table 1 shows that the adjusted values are very different to the typical ones; this may be due― among other causes―to the difference in environmental and operation conditions between Manitoba (Canada) and San Luis Potosí (Mexico), or to the fact that the model does not consider the kinetics of biomass responsible for degradation of the substrate, nor the responsible for sludge fermentation. No reference values or interval was provided for the model parameters by the author in the original study.

While the Bemister model [28] visibly follows the general effluent BOD trend―especially during the calibration period―the degree of fit can be considered insufficient in terms of R² and RMSE. This is especially true for the validation period and―visibly―around the sharp perturbations appearing in several years during summer/ fall, the latter being associated to intense rain episodes or periods. Another fact to consider is that the Bemister model [28] does not include an oxygen balance, neither the effect of oxygen concentration in the substrate kinetics. While complete-mix aerated lagoons have been traditionally designed using substrate and biomass equations assuming no oxygen limitation―e.g. [34] [35] ―dissolved oxygen in aerated facultative lagoons can be low or very low. At the studied plant, effluent dissolved oxygen (DO) ranged 0.0 - 2.9 mg/L (average 0.49 mg/L) [26] . Since a typical Monod half-saturation constant value for oxygen in ASM1 is K_O,H = 0.2 mg/L [36] , the average DO at the lagoon fell in the region where the biodegradation kinetics is still affected by the DO level. So, considering the effect of oxygen limitation could improve the model adequacy. Other aspects that could affect the model performance and are not included in the model are: the actual non-completemix flow in each section of the lagoon, the nitrogen dynamics, and unaccounted effects of intense rains and their associated flow peaks on the primary lagoon performance.

The model considers k_L,20 = 0.002 and s_ρ= 0.4, according to a study by [37] . In this study, the Bemister model [28] was tested considering that those parameters could also be identified according to the differences in climatic and operation conditions of the stabilization pond studied by [37] , with respect to the “Planta Norte” primary AFL. The results were: 0.575 of R² with RMSE of 11.4 mg/L for calibration, and 0.362 with 17.2 mg/L for validation, respectively; Table 1 displays the parameter values obtained for this modification to the original model (see “adapted, recalibrated” in Table 1). The estimated BOD effluent is showed in the Figure 1 as BODest, 2; in this figure a significant difference between the original model and adapted is not appreciated. However, the degree of fit in the second case (adapted version) itself increased, this verifies that the assumption made (k_L,20 and s_ρ with different values than originally proposed) is partially correct.

The measured and estimated effluent BOD concentrations are presented in Figure 3. This model achieved a determination coefficient of 0.489 and RMSE of 13.0 mg/L in calibration, and 0.290 with 18.9 mg/L for validation period, respectively. Table 2 shows the parameter values (typical and adjusted). The estimated parameters are remarkably similar to those of the original model.

It can be seen, in Figure 3, a similar behavior to that obtained by the Bemister model [28] for the description of the AFL effluent BOD; however its fit index is lower, and the overestimation at the final period of the time series is greater than that obtained with the Bemister model [28] . For both models, the degree of fit can be considered insufficient, especially for the validation period, and the same considerations on lagoon processes not included in the model can be applied to Chagnon’s model [29] too.

The results of measured and estimated BOD and VSS concentrations for the lagoon effluent are presented in Figure 4. For BOD, this model achieved R² of 0.242 with RMSE of 16.8 mg/L for the calibration period, and 0.230 with 19.6 mg/L for the validation, respectively; while for VSS, it obtains R² of 0.078 with 35.8 mg/L of RMSE for the calibration period, and 0.236 with 29.7 mg/L for validation, respectively. The model parameters

^*Data estimated from [38] .

values (initial and adjusted) are shown in Table 3. In this case, the model consistently underestimates BOD (112.9 mg/L for estimates vs. 119.9 mg/L for measured data, on average) and, especially, VSS (79.8 mg/L for estimates vs. 104.4 mg/L for measured data, on average).

This model presents the poorest fit value of the study. In Figure 4, it can be observed that this model is not able to describe the wide, months long fluctuations in the BOD concentration at the AFL effluent, much less is suitable to represent the sharp pulses observed in the measured lagoon behavior, associated to rain episodes. The model VSS performance is even poorer, with the model estimates clearly departing below the measured data. The considerations done above for the other two models are also applicable here, but the assumption of complete mix is critical when modeling a partially settleable component like VSS. While BOD―soluble or particulate―will largely be biodegraded in the lagoon through a combination of hydrolysis/fermentation and soluble substrate uptake, assuming that VSS will not settle will tend to yield too high modeled VSS, resulting in higher modeled biodegradation rates (since VSS also represents biomass) and lower modeled BOD effluent. When minimizing errors in parameter estimation, the procedure will try to reduce the VSS modeled concentration, by increasing K_d (0.60 d⁻¹, very high) and μ_m (1.17 d⁻¹). This can give some relief to the BOD lack of fit, but results in a very poor representation of VSS.

Another cause in the lack of fit of this model may be the fact that it does not consider the variation of the parameters with respect to the lagoon temperature, being that according to [39] , the kinetic parameters of a model based on biological processes, “per se” are temperature dependent. In Table 3, it can be seen that the adjusted parameter values differ from the identified by the model author; this may be due to the type of substrate utilized by the original model (wastewater from a winery industry) and the substrate and operating conditions of the primary AFL of the “Planta Norte”, are very different.

The temperature effect on the model parameters was proved using the Arrhenius correction as follows, in accordance with [39] :. The modified model achieved R² of 0.409 with RMSE of 14.0 mg/L for the calibration period, and 0.281 with 19.1 mg/L for the validation, respectively; while for VSS, it obtained an R² of 0.062 with 21.7 mg/L of RMSE for the calibration period, and 0.273 with 24.9 mg/L for validation, respectively. Its calibrated parameters values are shown in Table 3 (see “modified, recalibrated”). The proposed modifications enhanced the model degree of fit (from 0.242 to 0.409 of R²), mitigating the underestimation of the BOD (120.1 mg/L for estimates and 119.9 mg/L for measured data, on average) and, particularly, for VSS (107.8 mg/L for estimates and 104.4 mg/L for measured data,

on average). However, the fit still remains from poor to moderate. The estimated concentrations at the lagoon effluent are also shown in Figure 4 as BODest, 2 and VSSest, 2, where it can be observed that the modified model―though insufficiently―describes the variation of the measured data in a better way than the original model, specially, for the behavior of the effluent VSS.

Finally, the three simple AFL models founded in the literature showed a poor to moderate fit when applied to the operational data of the “Planta Norte” (WWTP) in San Luis Potosí. This can be observed in Table 4, which summarizes the degree of fit (expressed as R²) obtained with each model as well as its associated error (as RMSE) for BOD determination and VSS for the Montalvo et al. model [31] , and its modified version, for the selected calibration and validation periods. This table shows that the model with the best fit of all is to the adapted version of the Bemister model [28] . However, it presents an overestimation of effluent concentration specifically at periods when the rains are heavy and persistent. In summary none of the three models provided a good representation of the lagoon effluent BOD.

It is worth mentioning that two additional calibration periods (2004-2005 and 2005-2006) for the three models were tested, finding that it is in the selected period (2007-2008) in which a best fit was obtained in the description of the BOD behavior, this was verified at all three models.

The evaluation and comparisons made in this research allow confirming that oxygen demand behavior description in AFL requires further investigation for the development of better simple models that can be applied at full-scale plants for different objectives such as, effluent quality control or aeration control.