Modelling cyanobacteria in shallow coastal seas

There is an increasing need to describe cyanobacteria bloom dynamics using ecosystem models. We consider two fundamentally different ways how cyanobacteria are currently implemented: a simple approach without explicit consideration of the life cycle which assumes that cyanobacteria grow due to nitrogen fixation alone and an advanced approach that computes the succession of four different stages of the cyanobacteria life cycle based on internal quotas of energy and nitrogen. To qualitatively and quantitatively intercompare these different approaches and with observations, we use the Baltic Sea ecosystem model ERGOM coupled to the one-dimensional water column model GOTM. Four experiments are carried out: three, using the simple approach with either (a) a prescribed constant minimum production, (b) no minimum value or (c) a prescribed constant minimum concentration, and one with (d) the full predictive life cycle. The model data of 35 years (1970-2005) are analyzed for the timing of the bloom, the interannual variability, the annual mean nitrogen fixation rates and the effect of cyanobacteria on eukaryotic phytoplankton. The results show significant differences. In the climatological seasonal mean, only the advanced approach which resolves the life cycle produces a realistic bloom onset and duration. The interannual variability of blooms is unrealistically small in the experiments with a prescribed minimum value. Annual mean nitrogen fixation rates diverge by up to 30% between the four model solutions. Finally, the representation of the cyanobacteria also influences the seasonal cycle of eukaryotic phytoplankton, i.e., flagellates. This study demonstrates that the way how cyanobacteria are implemented in coupled biological-physical models strongly determines the fluxes into the system and between the individual compartments.     

A boundary value approach for estuarine water quality modelling with results for Jamaica Bay,New York

Results of water quality modelling for Jamaica Bay, a New York estuary with a large hydraulic circulation, are presented. The two-dimensional topology is approximated by a set of coupled one-dimensional subsystems. The long term steady state water quality problem is then reformulated as a multi-point boundary value problem for ordinary differential equations. Piecewise constant dispersion parameters are estimated from salinity data.A sequential algorithm based on parallel shooting is developed for solving the multipoint problem. The method, which simplifies handling of feedforward and feedback reaction kinetics, is equivalent to employing a high order finite difference technique with the subsequent enhanced accuracy.Results of model verification for uncoupled variables — salinity, coliform, total soluble phosphorus, and coupled variables for nitrogen (organic and ammonia) and BOD-DO for Jamaica Bay are discussed.     

Simulation of NO and N2O emissions from a spruce forest during a freeze/thaw event using an N-flux submodel from the PnET-N-DNDC model integrated to CoupModel

The amount of nitrogen gases (N₂O, NO and N₂) emitted from forest soils depends on interactions between soil properties, climatic factors and soil management. To increase the understanding of nitrogen processes in soil ecosystems, two dynamic models, CoupModel (coupled heat and mass transfer model for soil–plant–atmosphere systems) and the denitrification–decomposition (DNDC) model were selected. Both are dynamic models with different submodels for soil, vegetation, hydrology and climate system. CoupModel has a higher degree of detail on soil physical and abiotic components, whereas the DNDC model contains details of microbiological processes involved in production of nitrogen gases. To improve the previous simple submodel of nitrogen emission in CoupModel, we included a submodel corresponding to the forest version of DNDC containing photosynthesis/evapotranspiration-nitrogen (PnET-N-DNDC model).     

A two-dimensional numerical model for eutrophication in Baiyangdian Lake

Hydrodynamic, physical, and biochemical processes in the Baiyangdian Lake water environment were analyzed comprehensively. An eutrophication ecodynamics model including the effects of reed resistance on flow was coupled with the hydrodynamics governing equations. An improvement on the Water Quality Analysis Simulation Program (WASP, a modeling system introduced by the US Environmental Protection Agency) is established, which uses the zooplankton kinetic equation. The model simulates water quality constituents associated with eutrophication in the lake, including phytoplankton, zooplankton, nitrogen, phosphorus, dissolved oxygen, and others. Various kinetic coefficients were calibrated using measured data or information from relevant literature, to study eutrophication in the lake. The values calculated by the calibrated model agree well with field data, including ammonia nitrogen, total nitrogen, total phosphorus and dissolved oxygen. Changes related to nutrition and dissolved oxygen during the processes were simulated. The present model describes the temporal variation of water quality in Baiyangdian Lake with reasonable accuracy. Deviations between model-simulated and observed values are discussed. As an ideal tool for environmental management of the lake, this model can be used to predict its water quality, and be used in research to examine the eutrophication process.     

Modelling seasonal dynamics of biomasses and nitrogen contents in a seagrass meadow (Zostera noltii Hornem.): application to the Thau lagoon (French Mediterranean coast)

Anumerical deterministic model for a seagrass ecosystem (Zostera noltii meadows) has been developed for the Thau lagoon. It involves both above- and belowground seagrass biomasses, nitrogen quotas and epiphytes. Driving variables are light intensity, wind speed, rain data and water temperature. This seagrass model has been coupled to another biological model in order to simulate the relative contributions of each primary producer to: (i) the total ecosystem production, (ii) the impact on inorganic nitrogen and (iii) the fluxes towards the detritus compartment. As a first step in the modelling of seagrass beds in the Thau lagoon, the model has a vertical structure based on four boxes (a water box on top of three sediment boxes) and the horizontal variability is neglected until now. This simple box structure is nevertheless representative for the shallow depth Z. noltii meadows, spread over large areas at the lagoon periphery.After calibration, simulation results have been compared with in situ measurements and have shown that the model is able to reproduce the general pattern of biomasses and nitrogen contents seasonal dynamics. Moreover, results show that, in such shallow ecosystems, seagrasses remain the most productive compartment when compared with epiphytes or phytoplankton productions, and that seagrasses, probably due to their ability in taking nutrients in the sediment, have a lower impact on nutrient concentration in the water column than the phytoplankton. Furthermore, in spite of active mechanisms of internal nitrogen redistribution and reclamation, the occurrence of a nitrogen limitation of the seagrass growth during summer, already mentioned in the literature, have also been pointed out by the model. Finally, simulations seems to point out that epiphytes and phytoplankton could compete for nitrogen in the water column, while a competition for light resources seems to be more likely between epiphytes and seagrasses.     

Herbivores enable plant survival under nutrient limited conditions in a model grazing system

We make a theoretical study of nitrogen cycling in a model of a grazing system with five compartments. The rates of uptake of nutrient by plants and herbivores are allowed nonlinear forms which involve no a priori assumptions about whether the system is subject to top-down or bottom-up control. We derive a method of piecewise linear approximation which allows analytical study of the system. We then use this method to investigate the properties of the equilibrium states of the system, and in particular whether the system favours donor- or recipient-control, the grazing optimization problem, and the potential benefits of herbivory to plant growth. We are able to generalise our results to all uptake functions of the same qualitative class as those considered, and to show that in general the system will tend to a stable equilibrium state of donor-controlled herbivory. In this model, the presence of the ‘right’ class of herbivore is not only beneficial to plant growth in certain circumstances, but can be essential to their survival, allowing plants to co-exist with herbivores under conditions in which they would be unable to survive alone.     

Nitrogen and plankton dynamics in the lagoon of Venice

The nitrogen cycle in the lagoon of Venice, which is the largest Italian lagoon, was investigated by means of a 3D fully coupled transport – water quality model, which had been validated against a substantial amount of real-world data. Nitrogen fluxes among different ecosystem compartments were computed for each month of a reference year, and for each one of the three sub-basins into which the lagoon is conventionally subdivided. The computation included the loads of nitrogen discharged by the tributaries, the direct inputs from the industrial area and the city of Venice, the atmospheric loads, the fluxes at the three lagoon inlets and the internal fluxes between sediment and water compartments and among the three sub-basins. The results of the analysis show that the lagoon, as a whole, exports nitrogen towards the sea. Approximately 4000 tN/year are recycled by the system, while 4640 tN/year is the net input from the drainage basin and the other sources, thus leading to about 8640 tN/year of dissolved inorganic nitrogen that enter the water compartment. Around half of the this amount is used by primary producers, one fourth is exported towards the sea, and one fourth is transferred into the sediment compartment, or lost to atmosphere. These findings suggest that the exchanges through the inlets play an important role in keeping nitrogen concentration at an acceptable level. A more detailed analysis of the model results shows that the non-homogeneous spatial distribution of tributary discharges and point sources is the main cause of the differences in the ecosystem response and water quality among the three sub-basins. Nutrient poorer sub-basins fix a ration of available inorganic nutrient higher than nutrient rich ones. However, they are more efficient in transferring the biomass to the highest trophic levels. Results also include estimates of fluxes that were not quantified so far (such as grazing and recycling), and a validated model, which could have a practical use, for example for assessing implications of reduction of nutrient loads.     

A σ-coordinate transport model coupled with rotational boussinesq-type equations

This paper describes a σ-coordinate scalar transport model coupled with a Boussinesq-type hydrodynamic model. The Boussinesq model has the ability to calculate both three-dimensional velocity distributions and the water surface motion. To capture ‘dispersion’ processes in open channel flow, horizontal vorticity effects induced by a bottom shear stress are included in the Boussinesq model. Thus, a reasonable representation of vertical flow structure can be captured in shallow and wavy flow fields. To solve the coupled Boussinesq and scalar transport system, a finite-volume method, based on a Godunov-type scheme with the HLL Riemann solver, is employed. Basic advection and advection–diffusion numerical tests in a non-rectangular domain were carried out and the computed results show good agreement with analytic solutions. With quantitative comparisons of dispersion experiments in an open channel, it is verified that the proposed coupled model is appropriate for both near and far field scalar transport predictions. From numerical simulations in the surf zone, physically reasonable results showing expected vertical variation are obtained.     

A vertical-compressed three-dimensional ecological model in Lake Taihu, China

A three-dimensional ecological model on the basis of the analyses of environmental characteristics is set up for Lake Taihu, one of the largest shallow lakes in China. The hydrodynamic processes, nutrient cycling, chemical processes and biological processes are integrated in the model. Model state variables include: water current, surface displacement, nutrients of nitrogen and phosphorus, as well as their different forms such as ammonia nitrogen, nitrate nitrogen, phosphate phosphorus, etc., biomasses of macroplankton, phytoplankton, zooplankton and fish, and also the nutrient levels of macroplankton and phytoplankton. A nutrient budget and sediment transformation are also coupled in the model. The data from January 17, 1997 to January 18, 1998 are use to calibrate the model. The model results have shown good agreement with the observations. It implies that the model could be used for the lake environmental management and research for examining the processes and determining the water quality. The reasons of deviations between the modelled results and the observed values are also discussed. There are six factors that explain the deviations of the modelled results from the observed values and they can be grouped into two sets. One set of problems is associated with the standard deviation introduced by sampling and analyses. The second set of problems can be solved by introduction of processes lacking in the present model (resuspension, phytoplankton transportation mode under the wind with low speed, shifts in species composition and varied size of phytoplankton and zooplankton). The latter two processes should be included in the model at a later stage by integration of a structurally dynamic approach into the three-dimensional model.     

SPACSYS: Integration of a 3D root architecture component to carbon, nitrogen and water cycling—Model description

It is an ongoing challenge to develop and demonstrate management practices that increase the sustainability of agricultural systems. Soil carbon and nitrogen dynamics directly affect soil quality, crop productivity and environmental impacts. Root systems are central to the acquisition of water and nutrients by plants, but are also a major pathway for the inputs of carbon and nutrients to soil. The complexity of both biotic and abiotic interactions, combined with stochastic changes in root architecture, makes it difficult to understand below-ground dynamics on the basis of experimentation alone. The integration of dynamic models of above-ground growth, three-dimensional root system demography, and interactions between plants and the environment, into one single model is a major challenge because of the complexity of the systems.In order to understand the interaction between a plant and the environment, it is advantageous to develop a model framework to integrate submodels that simulate various plant and environmental components. The objective of this paper is to outline a mechanistic and process-based model, which is capable of simulating interactions among environmental conditions around plants, plant growth and development, nitrogen and carbon cycles, with a three-dimensional root system submodel as an interface.The model presented in this paper is a mixed dimensional, multi-layer, field scale, weather-driven and daily time-step dynamic simulation model. The current version includes a plant growth and development component, a nitrogen cycling component, a carbon cycling component, plus a soil water component that includes representation of water flow to field drains as well as downwards through the soil layers, together with a heat transfer component. The components themselves and linkage among components are designed using object-oriented techniques, which makes the model robust, understandable and reusable. The components are implemented in the C++ programming language, and inputs and outputs of all components are organised as a database in either Microsoft^® SQL Server 2000, Access 2000 or MySQL5.0. Root architecture is visualised by using the OpenGL graphics system. Preliminary validation with two separate experimental datasets shows that the model can reasonably simulate root systems, nitrogen cycling, water movement and plant growth.     

A hierarchical analysis of terrestrial ecosystem model Biome-BGC: Equilibrium analysis and model calibration

The increasing complexity of ecosystem models represents a major difficulty in tuning model parameters and analyzing simulated results. To address this problem, this study develops a hierarchical scheme that simplifies the Biome-BGC model into three functionally cascaded tiers and analyzes them sequentially. The first-tier model focuses on leaf-level ecophysiological processes; it simulates evapotranspiration and photosynthesis with prescribed leaf area index (LAI). The restriction on LAI is then lifted in the following two model tiers, which analyze how carbon and nitrogen is cycled at the whole-plant level (the second tier) and in all litter/soil pools (the third tier) to dynamically support the prescribed canopy. In particular, this study analyzes the steady state of these two model tiers by a set of equilibrium equations that are derived from Biome-BGC algorithms and are based on the principle of mass balance. Instead of spinning-up the model for thousands of climate years, these equations are able to estimate carbon/nitrogen stocks and fluxes of the target (steady-state) ecosystem directly from the results obtained by the first-tier model. The model hierarchy is examined with model experiments at four AmeriFlux sites. The results indicate that the proposed scheme can effectively calibrate Biome-BGC to simulate observed fluxes of evapotranspiration and photosynthesis; and the carbon/nitrogen stocks estimated by the equilibrium analysis approach are highly consistent with the results of model simulations. Therefore, the scheme developed in this study may serve as a practical guide to calibrate/analyze Biome-BGC; it also provides an efficient way to solve the problem of model spin-up, especially for applications over large regions. The same methodology may help analyze other similar ecosystem models as well.     

Nitrogen source apportionment—a comparison between a dynamic and a statistical model

A dynamic model, HBV-N, and a statistical model, MESAW, for nitrogen source apportionment were compared regarding model performance, model uncertainty and user applicability. The HBV-N model simulates continuous series of nitrogen concentrations with meteorological data and sub-basin characteristics as input. Diffuse nitrogen emissions are defined as regional model parameters which are calibrated by comparison of observed and simulated nitrogen data. The MESAW model uses nitrogen loads for a fixed time interval at each monitoring site as response variable and sub-basin characteristics as explanatory variables to estimate diffuse nitrogen emissions through non-linear regression analysis. The two models were applied in the Matsalu Bay watershed (3640 km²) in Estonia and the same land use and point sources data were used as input. Both models gave similar levels of diffuse total nitrogen emissions and retention rates, which also fit well with previous estimates made in Estonia and Scandinavia. A sensitivity analysis of the model parameters also showed similar uncertainty levels, which indicated that the model uncertainty was more dependent on the availability of nitrogen data and land cover distribution than the choice of model. Furthermore, the sensitivity analysis showed a parameter interdependency in both models, which implied the risk of compensation between estimated diffuse emissions and retention. In conclusion, however, the study showed that both models were capable of estimating nitrogen leakage from the dominating land classes and giving reliable source apportionment from the available input data. The study indicated that the HBV-N model has its advantage in assessments where detailed outputs are needed and when run-off data are limited, while the statistical MESAW model has its advantage in extensive studies since it is easily applied to large watersheds that have dense monitoring networks.     

Modeling the influence of precipitation and nitrogen deposition on forest understory fuel connectivity in Sierra Nevada mixed-conifer forest

Climate change models for California's Sierra Nevada predict greater inter-annual variability in precipitation over the next 50 years. These increases in precipitation variability coupled with increases in nitrogen deposition from fossil fuel consumption are likely to result in increased productivity levels and significant increases in forest understory fuel loads. Higher understory plant biomass contributes to fuel connectivity and may increase future fire size and severity in the Sierra Nevada. The objective of this research was to develop and test a model to determine how changing precipitation and nitrogen deposition levels affect shrub and herb biomass production, and to determine how often prescribed fire would be needed to counter increasing fuel loads. Model outputs indicate that under an increasing precipitation scenario significant increases in shrub and herb biomass occur that can be counteracted by decreasing the fire return interval to 10 years. Under a scenario with greater inter-annual variability in precipitation and increased nitrogen deposition, implementing fire treatments at an interval equivalent to the historical range of 15–30 years maintains understory vegetation fuel loads at levels comparable to the control.     

Assessment of nitrogen leaching from arable land in large river basins: Part I. Simulation experiments using a process-based model

A two-step procedure for analysing nitrogen leaching from arable land in large river basins is suggested: (1) application of a process-based dynamic model for a set of representative conditions in a large river basin to simulate water and nitrogen fluxes and (2) development of a fuzzy-rule based metamodel using the simulated nitrogen fluxes in Step 1 as a training set. After that the metamodel can be used for rapid assessment of water quality inside the considered ranges of parameters, describing natural conditions and management practices. This paper describes Step 1 of the procedure. Step 2 is described in an accompanying paper (Haberlandt et al., Ecological Modelling 150 (3) (2002) 277–294). The advantage of this approach is that it combines the ‘process-based foundation’ with the resulting simplicity of the metamodel. Simulation experiments for analysing nitrogen (N) leaching from arable land were performed using the Soil and Water Integrated Model (SWIM) for a set of representative conditions in the Saale basin (23 687 km²) in Central Europe. The Saale River is one of the main tributaries of the Elbe. In advance, hydrological validation of the model was done for the whole Saale basin and validation of nitrogen dynamics was fulfilled in two mesoscale sub-basins of the Elbe. For the simulation experiments the drainage basin area was sub-divided into five climate zones and nine representative soil classes were chosen. The basic rotation and fertilisation schemes were established using regional information obtained from literature. In addition, the effects of changing the basic rotation to more/less intensive ones and changing fertilisation rates by 50% increase/decrease were studied. The ranges of simulated nitrogen fluxes for the basic rotation and fertilisation schemes are comparable to available regional estimates and differences between sub-regions and soils are plausible. The relative importance of natural and anthropogenic factors affecting nitrogen leaching for the Saale River basin was as follows: (1) soil, (2) climate, (3) fertilisation rate and (4) crop rotation. The simulation experiments provide a basis for a fuzzy-rule based metamodel approach, which aims at rapid water quality assessment of large regions.     

Quantification and Index of Non-Point Source Pollution in Taihu Lake Region with GIS

The contribution of phosphorus and nitrogen from non-point source pollution (NPS) in the Taihu Lake region was investigated through case study and surveying in the town of Xueyan, From experimental results coupled with survey and statistics in the studied area, the distribution of nitrogen and phosphorus input to the water body is achieved from four main sources: agricultural land, village, the town center and the poultry factory. The results showed that about 38% of total phosphorus (TP) and 48% of total nitrogen (TN) discharged is from agricultural land, 33% of TP and 40% TN from village residents, 25% of TP and 10% of TN from the town center and 4% of TP and 2% of TN from the poultry factory.The Agricultural Non-point Pollution Potential Index (APPI) system for identifying and ranking critical areas of NPS was established with a Geographic Information Systems (GIS)-based technology. Quantification of the key factors in non-point sources pollution was carried out utilizing the following: Sediment Production Index (SPI), Runoff Index (RI), People and Animal Loading Index (PALI) and Chemical Use Index (CUI). These are the core parts of the model, and the weighting factor of each index was evaluated according the results of quantification. The model was successfully applied for evaluating APPI in Xueyan. Results from the model showed that the critical area identified for NPS control in Xueyan. The model has several advantages including: requiring fewer parameters, easy acquirement of these parameters, friendly interface, and convenience of operation. In addition it is especially useful for identifying critical areas of NPS when the basic data are not fully accessible, which is the present situation in China.     

Impact of microphytobenthos on the sediment biogeochemical cycles: A modeling approach

In marine biogeochemical modeling, the sediment is usually represented by diagenetic models, but in shallow ecosystems these models are incomplete, because they do not take into account the benthic primary production. While microphytobenthos (MPB) is known to strongly impact mineralization pathways and nutrient fluxes, MPB is rarely integrated as an explicit variable. To investigate the impact of microphytobenthos on early diagenesis in sediment, we built a fine-scale dynamic model, based on the diagenetic model OMEXDIA and including MPB and associated processes. The model outputs were similar to a data set of MPB-colonized sediment sampled in Florida Bay, suggesting that the model can recreate a realistic situation. The model showed that MPB activities induced a strong diurnal rhythm on concentration profiles, fluxes, and mineralization processes. When MPB was present at the sediment surface, the total mineralization was strongly enhanced thanks to the supply of labile organic matter. In contrast, coupled nitrification–denitrification was inhibited by a factor of 3.8. This inhibition can be explained by the competition for nitrate and ammonium between MPB and bacteria. Nitrogen uptake of MPB represented 96% of the daily supply of dissolved inorganic nitrogen. This was more than 50 times greater than N consumption by denitrification. With MPB, sediment nitrogen flux to the water column was reduced by a factor of 70, suggesting that sediment colonized by MPB represents a minor source of nutrients for phytoplankton and bacterioplankton. Results showed that current diagenetic models are not well-suited for shallow ecosystems with significant MPB primary production.     

Quantification and index of non-point source pollution in Taihu Lake region with GIS

The contribution of phosphorus and nitrogen from non-point source pollution (NPS) in the Taihu Lake region was investigated through case study and surveying in the town of Xueyan, From experimental results coupled with survey and statistics in the studied area, the distribution of nitrogen and phosphorus input to the water body is achieved from four main sources: agricultural land, village, the town center and the poultry factory. The results showed that about 38% of total phosphorus (TP) and 48% of total nitrogen (TN) discharged is from agricultural land, 33% of TP and 40% TN from village residents, 25% of TP and 10% of TN from the town center and 4% of TP and 2% of TN from the poultry factory. The Agricultural Non-point Pollution Potential Index (APPI) system for identifying and ranking critical areas of NPS was established with a Geographic Information Systems (GIS)-based technology. Quantification of the key factors in non-point sources pollution was carried out utilizing the following: Sediment Production Index (SPI), Runoff Index (RI), People and Animal Loading Index (PALI) and Chemical Use Index (CUI). These are the core parts of the model, and the weighting factor of each index was evaluated according the results of quantification. The model was successfully applied for evaluating APPI in Xueyan. Results from the model showed that the critical area identified for NPS control in Xueyan. The model has several advantages including: requiring fewer parameters, easy acquirement of these parameters, friendly interface, and convenience of operation. In addition it is especially useful for identifying critical areas of NPS when the basic data are not fully accessible, which is the present situation in China.     

A simulation model for the effects of burning on the phosphorus and nitrogen cycle of a heathland ecosystem

In this paper, a simulation model is presented for nutrient cycling in heathland ecosystems. The results of simulations are compared with field data of phosphorus and nitrogen accumulation in different compartments of the system in the years after burning, given in the literature on this subject (Chapman, 1967; 1970). It is shown that for the cycling of P the system returns slowly to equilibrium after an initial disturbance. The time span of about 30 years that is required to reach equilibrium is in agreement with the field data. However, P accumulation in living above-ground biomass and litter is overestimated by the model in the first years after burning. Nitrogen accumulation in biomass and litter is systematically underestimated by the model.The results are discussed with reference to the processes in nutrient cycling that are insufficiently understood, and with reference to the management of heathlands.     

Analysis of spatial and temporal patterns in a large reservoir using water quality and hydrodynamic modeling

Effective management of reservoir water resources demands a good command of ecological processes in the waterbody. In this work the three-dimensional finite element hydrodynamic model RMA10 was coupled to an eutrophication model. The models were used together with a methodology for loads estimation to foster the understanding of such processes in the largest reservoir in Western Europe—the Alqueva. Nutrient enrichment and eutrophication are water quality concerns in this man-made impoundment. A total phosphorus and nitrogen loads quantification methodology was developed to estimate the inputs in the reservoir, using point and non-point source data.Field data (including water temperature, wind, water elevation, chlorophyll-a, nutrient concentration and dissolved oxygen) and estimated loads were used as forcing for simulations.The analysis of the modeling results shows that spatial and temporal distributions for water temperature, chlorophyll-a, dissolved oxygen and nutrients are consistent with measured in situ data.Modeling results allowed the identification of likely key impact factors on the water quality of the Alqueva reservoir. It is shown that the particular geomorphological and hydrological characteristics of the reservoir together with local climate features are responsible for the existence of distinct ecological regions within the reservoir.     

Choosing classes for size projection matrix models

Projection matrix models are intensely used in ecology to model the dynamics of structured populations. When dealing with size-structured populations, there is no satisfactory algorithm to partition size into discrete classes. We show that the Vandermeer-Moloney algorithm for choosing classes is inconsistent with the Usher model, and systematically selects the finest classes. Considering that the matrix model is a discrete approximation of a continuous model, we define an approximation error as the sum of a distribution error (the difference between the discrete distribution and its continuous counterpart), and a sample error. The optimal partition of size into classes is the one that minimizes the approximation error. This method for choosing classes also shows that the choice of the class width cannot be disconnected from the choice of the time step. When applied to 520 trees of Dicorynia guianensis in French Guiana, this algorithm identified 8 classes of 11.4 cm in width, which is in agreement with the empirical choice of foresters.