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espanolIntroduccion: Laguna Cartagena (LC), es un humedal en Lajas, Puerto Rico, que ha sido afectado negativamente por nutrientes, principalmente escorrentia de fosforo de las actividades agricolas hasta el final del cultivo de la cana de azucar a fines del siglo XX. Estas condiciones han propiciado que, la concentracion de P permaneciera alta en un estado hipereutrofico, el cual era irremediable incluso despues de una reduccion de 5 veces en la concentracion de nutrientes del agua fuente. Objetivo: El objetivo principal de este articulo de investigacion es aplicar dos metodos matematicos diferentes para evaluar el nivel de eutrofizacion de un humedal en Puerto Rico. Metodologia: El Metodo de Agrupamiento de Grises (GCM) se uso para clasificar el estado eutrofico de LC aplicando los estandares troficos internacional y chino y dos parametros, Fosforo Total (TP) y Nitrogeno Total (TN). La media de TP y TN en el sustrato del fondo consolidado de LC y las muestras de floculencia se utilizaron para clasificar LC. Para analizar si LC puede recuperarse, se utilizo fosforo reactivo soluble (SRP) y TP a partir de muestras de agua a la entrada, salida y centro de LC para modelar (ecuacion diferencial) la entrada y perdida de fosforo en LC y determinar si existe un punto de equilibrio. El analisis GCM clasifico a la LC como un humedal eutrofico utilizando el estandar internacional e hipereutrofico utilizando el estandar chino. Resultados: La clasificacion del estado trofico no presento variaciones con el uso del sustrato de fondo consolidado versus las muestras de floculencia. El modelo de ecuaciones diferenciales mostro que los niveles de SRP y TP dentro de LC fueron mas altos que los niveles de SRP y TP que entran en LC, lo que podria ser causado por un proceso de reciclaje de nutrientes dentro de LC que puede predecir el fracaso de los esfuerzos de remediacion. Se encontro un punto de equilibrio a nivel eutrofico, lo que significa que incluso si hay una reduccion en la entrada de fosforo, no habra un cambio en el estado eutrofico de LC. Conclusiones: El estandar trofico chino indico que la LC estaba en un estado hipertrofico. Se encontraron resultados similares usando el estandar internacional. El modelo de ecuaciones diferenciales mostro que LC es irreversible. EnglishIntroduction: Laguna Cartagena (LC), a wetland in Lajas, Puerto Rico, has been negatively impacted by nutrients, mainly phosphorus run-off from agricultural activities until the end of sugar cane cultivation in the late 1900s. This led to P concentration remain high at hypereutrophic state that was irremediable even after a 5-fold reduction in source water nutrient concentration. Objective: The main goal of this research paper is to apply two different mathematical approaches to assess the eutrophication level of a wetland in Puerto Rico. Method: Grey Cluster Method (GCM) was used to classify LC’s eutrophic state by applying the International and Chinese trophic standards and two parameters, total phosphorous (TP) and total nitrogen (TN). Mean TP and TN from LC consolidated bottom substrate and flocculence samples were used to classify LC. To address whether LC can recover, soluble reactive phosphorus (SRP) and TP from LC inlet, outlet and center water samples were used to model (differential equation) the input and loss of phosphorus in LC and determine whether an equilibrium point exists. GCM analysis classified LC as a eutrophic wetland using the International standard and hypereutrophic using the Chinese standard. Results: Trophic state classification did not vary with use of consolidated bottom substrate versus flocculence samples. The differential equation model showed that SRP and TP levels within LC were higher than levels of SRP and TP entering LC, which could be caused by a nutrient recycling process within LC that may predict failure of remediation efforts. An equilibrium point was found at the eutrophic level, which means that even if there is a reduction in phosphorus input, there will not be a change in LC’s eutrophic state. Conclusions: Chinese trophic standard indicated LC was in a hypertrophic state. Similar results were found using the international standard. The differential equation model showed that LC is irreversible.

Two mathematical approaches to study the phosphorus eutrophication of a wetland in Puerto Rico