NPZ Models of Plankton Dynamics: Their Construction, Coupling to Physics, and Application

Nutrient-phytoplankton-zooplankton (NPZ) models have been in use in oceanography for at least three decades, and are still a common research tool. Given the discoveries of the last two decades, particularly concerning the role of bacteria in the plankton, there are questions as to whether NPZ models can still be supported as a useful tool in planktonic research. Here I review the construction of NPZ models, and some of the physical platforms they have been coupled to. I then discuss the applications of NPZ-physical models, and conclude that they still constitute an important and viable research tool, provided that the questions being explored are clearly stated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Microcoleus autumnalis and filamentous algae-dominated mats and chlorophyll-a increase with agricultural land use but respond differently to associated nutrient and sediment enrichment

ABSTRACT

This study investigated the impact of pastoral land use and nutrient and fine sediment inputs on Microcoleus autumnalis and filamentous algae-dominated mats, and benthic chlorophyll-a in streams (lower North Island, New Zealand). Surveying and sampling was undertaken monthly at 61 sites spanning a wide gradient in catchment cover and environmental conditions. Two boosted regression tree models were built. The first models included pastoral land cover and five environmental variables as predictors. In the second model pastoral land cover was replaced by nutrient/sediment data. The abundance of the two mat types and chlorophyll-a increased when pastoral land cover was between 20% and 70% (model 1). Replacement of pastoral land cover by nutrient/sediment data (model 2) slightly improved the model fit for all three periphyton variables. Microcoleus autumnalis-dominant mats increased with dissolved inorganic nitrogen concentrations up to ca. 0.6?mg?L^?1, and in streams with more frequent flushes. In contrast, filamentous algal-dominated mats increased with turbidity, and in streams with less frequent flushes. Chlorophyll-a generally followed the response of the dominant periphyton type. Increased knowledge on responses of specific periphyton types, rather than total biomass, to environmental variables is essential to guide effective management strategies.     

Wave reflection from partially perforated-wall caisson breakwater

In 1995, Suh and Park developed a numerical model that computes the reflection of regular waves from a fully perforated-wall caisson breakwater. This paper describes how to apply this model to a partially perforated-wall caisson and irregular waves. To examine the performance of the model, existing experimental data are used for regular waves, while a laboratory experiment is conducted in this study for irregular waves. The numerical model based on a linear wave theory tends to over-predict the reflection coefficient of regular waves as the wave nonlinearity increases, but such an over-prediction is not observed in the case of irregular waves. For both regular and irregular waves, the numerical model slightly over- and under-predicts the reflection coefficients at larger and smaller values, respectively, because the model neglects the evanescent waves near the breakwater.     

The dynamic behaviour of a river-dominated tidal inlet, River Murray, Australia

Australia's largest river, the River Murray, discharges to the southern ocean through a coastal lagoon and river-dominated tidal inlet. Increased water extractions upstream for irrigation have led to significantly reduced flows at the mouth and, as a result, the area is undergoing rapid change, particularly with regard to the rate at which sediment is being transported into the lagoon. Based on detailed and accurate bathymetric surveys it has been possible to estimate that the rate of lagoon in-filling is of the order of 100,000 m³ per year for the period June 2000 to May 2003, although the actual rate shows significant year to year variability. Dredging of the lagoon commenced in 2000 in an attempt to reverse the trend.In an effort to understand the behaviour of the inlet a one-dimensional numerical model of the inlet has been developed. The model extends the original of van de Kreeke by including a dynamic inlet throat area based on predicted river flows and a sediment transport module to predict the resulting net sediment transport. Comparisons with water level data collected on both the ocean and lagoon sides of the mouth have shown that the model is able to predict the attenuation and lag of the tidal signal reasonably well. The sediment transport model was based on predicted sediment concentrations in the surf zone and was found to predict the rate of sediment in-filling to an acceptable level of accuracy. It is envisaged that the model will be a useful management tool, especially since it is possible to manipulate river discharges to the mouth.     

A singular evolutive extended Kalman filter to assimilate ocean color data in a coupled physical–biochemical model of the North Atlantic ocean

Within the European DIADEM project, a data assimilation system for coupled ocean circulation and marine ecosystem models has been implemented for the North Atlantic and the Nordic Seas. One objective of this project is to demonstrate the relevance of sophisticated methods to assimilate satellite data such as altimetry, surface temperature and ocean color, into realistic ocean models. In this paper, the singular evolutive extended Kalman (SEEK) filter, which is an advanced assimilation scheme where three-dimensional, multivariate error statistics are taken into account, is used to assimilate ocean color data into the biological component of the coupled system. The marine ecosystem model, derived from the FDM model [J. Mar. Res. 48 (1990) 591], includes 11 nitrogen and carbon compartments and describes the synthesis of organic matter in the euphotic zone, its consumption by animals of upper trophic levels, and the recycling of detritic material in the deep ocean. The circulation model coupled to the ecosystem is the Miami isopycnic coordinate ocean model (MICOM), which covers the Atlantic and the Arctic Oceans with an enhanced resolution in the North Atlantic basin. The model is forced with realistic ECMWF ocean/atmosphere fluxes, which permits to resolve the seasonal variability of the circulation and mixed layer properties. In the twin assimimation experiments reported here, the predictions of the coupled model are corrected every 10 days using pseudo-measurements of surface phytoplankton as a substitute to chlorophyll concentrations measured from space. The diagnostics of these experiments indicate that the assimilation is feasible with a reduced-order Kalman filter of small rank (of order 10) as long as a sufficiently good identification of the error structure is available. In addition, the control of non-observed quantities such as zooplankton and nitrate concentrations is made possible, owing to the multivariate nature of the analysis scheme. However, a too severe truncation of the error sub-space downgrades the propagation of surface information below the mixed layer. The reduction of the actual state vector to the surface layers is therefore investigated to improve the estimation process in the perspective of sea-viewing wide field-of-view sensor (SeaWiFS) data assimilation experiments.     

Intercomparison of coastal area morphodynamic models

Five different coastal area morphodynamic models have been set up to run on the same offshore breakwater layout and an intercomparison carried out on the hydrodynamic and morphodynamic output produced by each scheme. In addition, the predicted morphodynamics was checked against available laboratory and field data.It is concluded that the models are capable of producing realistic estimates for the dominant morphodynamic features associated with offshore breakwaters. Coupling of the wave, current and sediment transport components of each scheme is shown to yield bathymetry which attains a state of equilibrium, unlike models which are based on the initial transport field only.     

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E _Y = (X−E _X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E _Y and E _X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.     

Use of unit response functions for management of regional multilayered aquifers: application to the North Aquitaine Tertiary system (France)

Although there are many numerical applications used in aquifer management, few methodologies seem to be sufficiently adapted to provide solutions for regional-scale problems. Their applications for multilayered aquifers are also too limited. A new groundwater management tool adapted to such large physical systems has been developed, using the unit response function (URF) approach. This tool is based on the link between a numerical groundwater flow model and a mathematical optimisation tool. Pre- and post processing are based on a geographical information system (GIS). The developed tool has been applied to a real management case—the regional Aquitaine multilayered aquifer (France). A representative hydrodynamic model was built using MODFLOW 2000 code. First tests show that the linearity condition needed for the application of URF methodology is respected despite the high complexity of the system. Two management scenarios were tested. Optimal solutions thus obtained allow for viable exploitation alternatives to be proposed, which integrate complex environmental constraints.

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Résumé Malgré un nombre important d’applications existant dans le domaine de la gestion des aquifères, peu de méthodologies semblent adaptées pour proposer des solutions à des problèmes réels de dimension régionale. Leurs application pour des systèmes multicouches sont souvent trop limitées. Un outil de gestion adapté à ces systèmes de large taille a été développé, basé sur la théorie des Fonctions de Réponses Unitaires (FRU). Cet outil est basé sur le couplage d’un modèle numérique d’écoulement et d’un code d’optimisation mathématique. Les entrées et sorties du modèle sont réalisées à l’aide d’un Système d’Information Géographique (SIG). L’outil développé est appliqué à un cas de gestion réel—le système aquifère régional multicouche aquitain (France). Un modèle hydrodynamique représentatif a été construit, basé sur le code MODFLOW 2000. Les premiers tests montrent que les conditions de linéarité nécessaires à l’application de la méthode FRU sont respectées, malgré l’importante complexité du système. Deux scénarii de gestion sont testés. Les solutions optimales ainsi obtenues permettent de proposer des solutions d’exploitation alternatives viables, intégrant des contraintes environnementales complexes.

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Resumen Aunque hay muchas aplicaciones numéricas usadas en la gestión de acuíferos, unas pocas metodologías parecen estar adaptadas suficientemente para dar las soluciones a los problemas de escala regional. También son limitadas sus aplicaciones para los acuíferos multicapa. Se ha desarrollado una nueva herramienta para el manejo del agua subterránea, adaptada a tales sistemas físicos grandes, usando el avance de la Función de Respuesta Unitaria (URF). Esta herramienta se basa en la combinación entre un modelo numérico de flujo de agua subterránea y una herramienta de optimización matemática. El pre-proceso y el post-proceso se basan en un Sistema de Información Geográfico (GIS). La herramienta desarrollada se ha aplicado a un caso real de manejo en el acuífero regional multicapa de Aquitania (Francia). Se construyó un modelo hidrodinámico representativo, que usó el código MODFLOW 2000. Las primeras pruebas muestran que la condición de linearidad, necesaria para la aplicación de la metodología URF, se respeta a pesar de la complejidad alta del sistema. Se probaron dos escenarios de manejo. Las soluciones óptimas así obtenidas permiten la proyección de alternativas viables de explotación, las cuales integran restricciones medioambientales complejas.