Quantifying uncertainty in high-resolution coupled hydrodynamic-ecosystem models

Marine ecosystem models are becoming increasingly complex and sophisticated, and are being used to estimate the effects of future changes in the earth system with a view to informing important policy decisions. Despite their potential importance, far too little attention has been, and is generally, paid to model errors and the extent to which model outputs actually relate to real-world processes. With the increasing complexity of the models themselves comes an increasing complexity among model results. If we are to develop useful modelling tools for the marine environment we need to be able to understand and quantify the uncertainties inherent in the simulations. Analysing errors within highly multivariate model outputs, and relating them to even more complex and multivariate observational data, are not trivial tasks. Here we describe the application of a series of techniques, including a 2-stage self-organising map (SOM), non-parametric multivariate analysis, and error statistics, to a complex spatio-temporal model run for the period 1988–1989 in the Southern North Sea, coinciding with the North Sea Project which collected a wealth of observational data. We use model output, large spatio-temporally resolved data sets and a combination of methodologies (SOM, MDS, uncertainty metrics) to simplify the problem and to provide tractable information on model performance. The use of a SOM as a clustering tool allows us to simplify the dimensions of the problem while the use of MDS on independent data grouped according to the SOM classification allows us to validate the SOM. The combination of classification and uncertainty metrics allows us to pinpoint the variables and associated processes which require attention in each region. We recommend the use of this combination of techniques for simplifying complex comparisons of model outputs with real data, and analysis of error distributions.     

Environmental factors which affect growth of Japanese common squid, Todarodes pacificus, analyzed by a bioenergetics model coupled with a lower trophic ecosystem model

Bioenergetics model is applied to Japanese common squid, Todarodes pacificus. The temporal change of wet weight of common squid, which migrates in the Sea of Japan, is simulated. The time dependent horizontal distribution of prey is calculated a priori by 3-D coupled physical–biological model. The biological model NEMURO (North Pacific Ecosystem Model for Understanding Regional Oceanography) is used to simulate the lower-trophic ecosystem including three kinds of zooplankton biomass two of which is used as prey of common squid. A bioenergetics model reproduced appropriate growth curve of common squid, migrating in the North Pacific and the Sea of Japan. The results show that the wet weight of common squid in the northern Sea of Japan is heavier than that migrating in the central Sea of Japan, because prey density of the northern Sea of Japan is higher than that of the central Sea of Japan. We also investigate the wet weight anomaly for a global warming scenario. In this case, wet weight of common squid decreases because water temperature exceeds the optimum temperature for common squid. This result indicates that migration route and spawning area of common squid might change with global warming.     

Description of a flexible and extendable physical–biogeochemical model system for the water column

A modelling system for coupled physical–biogeochemical simulations in the water column is presented here. The physical model component allows for a number of different statistical turbulence closure schemes, ranging from simple algebraic closures to two-equation turbulence models with algebraic second-moment closures. The biogeochemical module consists of models which are based on a number of state variables represented by their ensemble averaged concentrations. Specific biogeochemical models may range from simple NPZ (nutrient–phytoplankton–zooplankton) to complex ecosystem models. Recently developed modified Patankar solvers for ordinary differential equations allow for stable discretisations of the production and destruction terms guaranteeing conservative and non-negative solutions. The increased stability of these new solvers over explicit solvers is demonstrated for a plankton spring bloom simulation. The model system is applied to marine ecosystem dynamics the Northern North Sea and the Central Gotland Sea. Two different biogeochemical models are applied, a conservative nitrogen-based model to the North Sea, and a more complex model including an oxygen equation to the Baltic Sea, allowing for the reproduction of chemical processes under anoxic conditions. For both applications, earlier model results obtained with slightly different model setups could be basically reproduced. It became however clear that the choice for ecosystem model parameters such as maximum phytoplankton growth rates does strongly depend on the physical model parameters (such as turbulence closure models or external forcing).     

Application of an Ensemble Kalman filter to a 1-D coupled hydrodynamic-ecosystem model of the Ligurian Sea

The Ensemble Kalman filter (EnKF) has been applied to a 1-D complex ecosystem model coupled with a hydrodynamic model of the Ligurian Sea. In order to improve the performance of the EnKF, an ensemble subsampling strategy has been used to better represent the covariance matrices and a pre-analysis step for correcting the non-normality of the members distribution has been implemented. Twin experiments have been realized to assess the performance of the developed tool and a real data assimilation experiment has been conducted to hindcast the ecosystem at the Dyfamed site during the year 2000. Finally the performance of the EnKF has been compared with a Singular Evolutive Extended Kalman (SEEK) filter with a fixed basis. We conclude that, on one hand, there is a benefit in using the subsampling strategy and the lognormal transformation with the EnKF, and on the other hand, this filter presents better performance than the fixed basis version of the SEEK filter. However, it also incurs a large computational cost.     

Monitoring marine plankton ecosystems: Identification of the most relevant indicators of the state of an ecosystem

The number of variables involved in the monitoring of an ecosystem can be high and often one of the first stages in the analysis is to reduce the number of variables. We describe a method developed for geological purposes, using the information theory, that enables selection of the most relevant variables. This technique also allows the examination of the asymmetrical relationships between variables. Applied to a set of physical and biological variables (plankton assemblages in four areas of the North Sea), the method shows that biological variables are more informative than physical variables although the controlling factors are mainly physical (sea surface temperature in winter and spring). Among biological variables, diversity measures and warm-water species assemblages are informative for the state of the North Sea pelagic ecosystems while among physical variables sea surface temperature in late winter and early spring are highly informative. Although often used in bioclimatology, the utilisation of the North Atlantic Oscillation (NAO) index does not seem to provide a lot of information. The method reveals that only the extreme states of this index has an influence on North Sea pelagic ecosystems. The substantial and persistent changes that were detected in the dynamic regime of the North Sea ecosystems and called regime shift are detected by the method and corresponds to the timing of other shifts described in the literature for some European Systems such as the Baltic and the Mediterranean Sea when both physical and biological variables are considered.     

Resolving the impact of short-term variations in physical processes impacting on the spawning environment of eastern Baltic cod: application of a 3-D hydrodynamic model

Variations in oxygen conditions below the permanent halocline influence the ecosystem of the Baltic Sea through a number of mechanisms. In this study, we examine the effects of physical forcing on variations in the volume of deep oxygenated water suitable for reproductive success of central Baltic cod. Recent research has identified the importance of inflows of saline and oxygenated North Sea water into the Baltic Sea for the recruitment of Baltic cod. However, other processes have been suggested to modify this reproduction volume including variations in timing and volume of terrestrial runoff, variability of the solubility of oxygen due to variations in sea surface temperature as well as the influence of variations in wind stress. In order to examine the latter three mechanisms, we have performed simulations utilizing the Kiel Baltic Sea model for a period of a weak to moderate inflow of North Sea water into the Baltic, modifying wind stress, freshwater runoff and thermal inputs. The model is started from three-dimensional fields of temperature, salinity and oxygen obtained from a previous model run and forced by realistic atmospheric conditions. Results of this realistic reference run were compared to runs with modified meteorological forcing conditions and river runoff.From these simulations, it is apparent that processes other than major Baltic inflows have the potential to alter the reproduction volume of Baltic cod. Low near-surface air temperatures in the North Sea, the Skagerrak/Kattegat area and in the western Baltic influence the water mass properties (high oxygen solubility). Eastward oriented transports of these well-oxygenated highly saline water masses may have a significant positive impact on the Baltic cod reproduction volume in the Bornholm Basin.Finally, we analysed how large scale and local atmospheric forcing conditions are related to the identified major processes affecting the reproduction volume.     

A numerical transport model for predicting the distributions of Cd, Cu, Ni, Pb and Zn in the southern North Sea: the sensitivity of model results to the uncertainties in the magnitudes of metal inputs

A new transport model for metals (named NOSTRADAMUS) has been developed to predict concentrations and distributions of Cd, Cu, Ni, Pb and Zn in the southern North Sea. NOSTRADAMUS is comprised of components for water, inorganic and organic suspended particulate matter transport; a primary production module contributes to the latter component. Metal exchange between dissolved (water) and total suspended particulate matter (inorganic + organic) phases is driven by distribution coefficients. Transport is based on an existent 2-D vertically integrated model, incorporating a 35 × 35 km grid. NOSTRADAMUS is largely driven by data obtained during the Natural Environment Research Council North Sea Project (NERC NSP). The sensitivity of model predictions to uncertainties in the magnitudes of metal inputs has been tested. Results are reported for a winter period (January 1989) when plankton production was low. Simulated ranges in concentrations in regions influenced by the largest inflows, i.e. the NE English coast and the Southern Bight, are similar to the ranges in the errors of the concentrations estimated at the northern and southern open sea boundaries of the model. Inclusion of uncertainties with respect to atmospheric (up to ± 54%) and riverine (± 30%) inputs makes little difference to the calculated concentrations of both dissolved and particulate fractions within the southern North Sea. When all the errors associated with the inputs are included there is good agreement between computed and observed concentrations, and that for dissolved and particulate Cd, Cu and Zn, and dissolved Ni and Pb, many of the observations fall within, or are close to, the range of values generated by the model. For particulate Pb, model simulations predict concentrations of the right order, but do not reproduce the large scatter in actual concentrations, with simulated concentrations showing a bias towards lower values compared to those observed. A factor which could have contributed to observed concentrations, and which is not included in the model, is considered to be a substantial benthic input of dissolved lead during this winter period, coupled to a rapid and extensive scavenging of the dissolved lead to particles. Significant reductions in riverine and aeolian inputs of total Cd and Cu of 70% and 50%, respectively, consistent with aims of North Sea Conferences, are predicted to lead to minor decreases (~ 10%) in water column concentrations of dissolved and particulate Cd and Cu, except near river sources, where maximum reductions of ~ 30–40% may occur.     

An eddy-permitting, coupled ecosystem-circulation model of the Arabian Sea: comparison with observations

A nitrogen-based, pelagic ecosystem model has been coupled with an eddy-permitting ocean general circulation model of the Arabian Sea, and the results are compared with observations. The seasonal variability simulated by the model is in good agreement with observations: during the southwest monsoon season, phytoplankton increases in the western Arabian Sea due to upwelling along the coast; during the northeast monsoon season, phytoplankton abundance is large in the northern Arabian Sea because of the enhanced nitrate entrained by relatively deep vertical mixing. Two major differences are, however, found in the basin-wide comparison between model results and observations: an unrealistic nitrate maximum in the subsurface layer of the northern Arabian Sea and too low primary production in oligotrophic regimes. The former may be attributed to the lack of denitrification in the model. Possible causes for the latter include the present model's underestimation of fast nutrient recycling, the neglect of carbon fixation decoupled from nitrogen uptake and of nitrogen fixation, and inadequate nitrate entrainment by mixed layer deepening. The rate at which simulated nitrate increases in the northern Arabian Sea is 11–24 TgN/year, and should correspond to the denitrification rate integrated over the northern Arabian Sea assuming that the loss of nitrogen through denitrification is balanced by advective input. The model does not reproduce the observed phytoplankton bloom in the late southwest monsoon season. Possible causes are that the mixed layer may be too shallow in summer and that the horizontal transport of nitrate from the coast of Oman may be too weak. Sensitivity experiments demonstrate a strong dependence of the simulated primary productivity on the vertical mixing scheme and on the inclusion of a fast recycling loop in the ecosystem model.     

On the key role of nutrient data to constrain a coupled physical–biogeochemical assimilative model of the North Atlantic Ocean

A sequential assimilative system has been implemented into a coupled physical–biogeochemical model (CPBM) of the North Atlantic basin at eddy-permitting resolution (1/4°), with the long-term goal of estimating the basin scale patterns of the oceanic primary production and their seasonal variability. The assimilation system, which is based on the SEEK filter [Brasseur, P., Verron, J., 2006. The SEEK filter method for data assimilation in oceanography: a synthesis. Ocean Dynamics. doi: 10.1007/s10236-006-0080-3], has been adapted to this CPBM in order to control the physical and biogeochemical components of the coupled model separately or in combination. The assimilated data are the satellite Topex/Poseidon and ERS altimetric data, the AVHRR Sea Surface Temperature observations, and the Levitus climatology for salinity, temperature and nitrate.In the present study, different assimilation experiments are conducted to assess the relative usefulness of the assimilated data to improve the representation of the primary production by the CPBM. Consistently with the results obtained by Berline et al. [Berline, L., Brankart, J-M., Brasseur, P., Ourmières, Y., Verron, J., 2007. Improving the physics of a coupled physical–biogeochemical model of the North Atlantic through data assimilation: impact on the ecosystem. J. Mar. Syst. 64 (1–4), 153–172] with a comparable assimilative model, it is shown that the assimilation of physical data alone can improve the representation of the mixed layer depth, but the impact on the ecosystem is rather weak. In some situations, the physical data assimilation can even worsen the ecosystem response for areas where the prior nutrient distribution is significantly incorrect. However, these experiments also show that the combined assimilation of physical and nutrient data has a positive impact on the phytoplankton patterns by comparison with SeaWiFS ocean colour data, demonstrating the good complementarity between SST, altimetry and in situ nutrient data. These results suggest that more intensive in situ measurements of biogeochemical nutrients are urgently needed at basin scale to initiate a permanent monitoring of oceanic ecosystems.     

Optimal interpolation of sea surface temperature for the North Sea and Baltic Sea

Sea surface temperature fields of the North Sea and Baltic Sea have been constructed for the year 2001 using a multiplatform Optimal Interpolation scheme. The analyzed fields are constructed every 12 h on a 10 km spatial grid. The product is based upon observations from the three NOAA satellites 12, 14 and 16 together with a large amount of in situ observations. Space dependent covariance functions are estimated from the satellite observations and account for spatial and temporal lags. Several independent methods have been used to assess the error on the sea surface temperature product. Compared against independent in situ observations, the mean RMS difference for the year 2001 is 0.78 °C. The spatial distribution of the errors reveals that the Baltic Sea in general show higher errors than the North Sea. The error statistics throughout the year show a temporal variation of the errors with maximum during summer and winter. Tests with a varying number of satellite observations show that the accuracy of the satellite observations is the most important parameter in terms of reducing the errors on the interpolated sea surface temperature product.     

Modelling Pseudocalanus elongatus stage-structured population dynamics embedded in a water column ecosystem model for the northern North Sea

This paper outlines an approach to couple a structured zooplankton population model with state variables for eggs, nauplii, two copepodites stages and adults adapted to Pseudocalanus elongatus into the complex marine ecosystem model ECOHAM2 with 13 state variables resolving the carbon and nitrogen cycle. Different temperature and food scenarios derived from laboratory culture studies were examined to improve the process parameterisation for copepod stage dependent development processes. To study annual cycles under realistic weather and hydrographic conditions, the coupled ecosystem–zooplankton model is applied to a water column in the northern North Sea. The main ecosystem state variables were validated against observed monthly mean values. Then vertical profiles of selected state variables were compared to the physical forcing to study differences between zooplankton as one biomass state variable or partitioned into five population state variables. Simulated generation times are more affected by temperature than food conditions except during the spring phytoplankton bloom. Up to six generations within the annual cycle can be discerned in the simulation.     

Application of the Grey topological method to predict the effects of ship pitching

Ship motion, with six degrees of freedom, is a complex stochastic process. Sea wind and waves are the primary influencing factors. Prediction of ship motion is significant for ship navigation. To eliminate errors, a path prediction model incorporating ship pitching was developed using the Gray topological method, after analyzing ship pitching motions. With the help of simple introduction to Gray system theory, we selected a group of threshold values. Based on an analysis of ship pitch angle sequences over 40 second intervals, a Grey metabolism GM（1,1） model was established according to the time-series which every threshold corresponded to. Forecasting future ship motion with the GM （1,1） model allowed drawing of the forecast curve with effective forecasting points. The precision of the test results show that the model is accurate, and the forecast results are reliable.     

A box model for North-East Atlantic coastal waters compared with radioactive tracers

A box model for the estimation of doses to members of the public from discharges of radioactivity into North-East Atlantic coastal waters has been used to predict annual means of radionuclide seawater concentrations which have been compared with measured data of tracer radionuclides, ¹³⁷Cs, ⁹⁹Tc and ¹²⁵Sb. Discharges of these radionuclides into the sea from the nuclear reprocessing plants Sellafield in the UK and La Hague in France have been used as input to the model. Fallout of ¹³⁷Cs from atmospheric nuclear weapons tests and fallout of ¹³⁷Cs from the Chernobyl accident into the Baltic Sea have been taken into account. A large proportion of the measured data was collected during the CEC MAST-900052 project which is concerned with the utilization of radionuclides as tracers for water movements. The data cover the time period 1972–1992. A comparison between predicted and measured concentrations of radionuclides in seawater indicated the need to improve the model with respect to mixing conditions in the English Channel and water transport from the North Sea to the Baltic Sea via the Skagerrak, the Kattegat and the Belt Sea. Improvements were made using the data for ¹³⁷Cs and ⁹⁹Tc and involved adjustments of the mixing conditions (water exchange rates) between adjacent water boxes while keeping the net advective water fluxes of the model unaltered. The results of the modified version of the model have been compared with observed values. The comparison shows a somewhat better agreement for ¹³⁷Cs and ¹²⁵Sb than for ⁹⁹Tc which is believed to be due to the lower reliability of the ⁹⁹Tc discharge data from Sellafield in 1978. An analysis of the predicted-to-observed seawater concentrations indicates an overall predictive accuracy of the model of 0.9 corresponding to a 10% underestimation and a predictive precision of about a factor of 2.5 at a confidence level of 95%. The ¹²⁵Sb data, which are independent of the tuning of the model, support the general conclusions about the model predictions of radionuclide concentrations in seawater.     

Forecast verification of a 3D model of the Mediterranean Sea. The use of discrete wavelet transforms and EOFs in the skill assessment of spatial forecasts

The quality assessment of a nested model system of the Mediterranean Sea is realised. The model has two zooms in the Provençal Basin and in the Ligurian Sea, realised with a two-way nesting approach. The experiment lasts for nine weeks, and at each week sea surface temperature (SST) and sea level anomaly are assimilated. The quality assessment of the surface temperature is done in a spatio-temporal approach, to take into account the high complexity of the SST distribution. We focus on the multi-scale nature of oceanic processes using two powerful tools for spatio-temporal analysis, wavelets and Empirical Orthogonal Functions (EOFs). We apply two-dimensional wavelets to decompose the high-resolution model and observed SST into different spatial scales. The Ligurian Sea model results are compared to observations at each of those spatial scales, with special attention on how the assimilation affects the model behaviour. We also use EOFs to assess the similarities between the Mediterranean Sea model and the observed SST. The results show that the assimilation mainly affects the model large-scale features, whereas the small scales show little or no improvement and sometimes, even a decrease in their skill. The multiresolution analysis reveals the connection between large- and small-scale errors, and how the choice of the maximum correlation length of the assimilation scheme affects the distribution of the model error among the different spatial scales.     

Planktonic community structure and carbon cycling in the Arabian Sea as a result of monsoonal forcing: the application of a generic model

The Arabian Sea exhibits a complex pattern of biogeochemical and ecological dynamics, which vary both seasonally and spatially. These dynamics have been studied using a one-dimensional vertical hydrodynamic model coupled to a complex ecosystem model, simulating the annual cycle at three contrasting stations. These stations are characterised by seasonally upwelling, mixed-layer-deepening and a-seasonal oligotrophic conditions, respectively, and coincide with extensively measured stations on the two JGOFS ARABESQUE cruises in 1994. The model reproduces many spatial and temporal trends in production, biomass, physical and chemical properties, both qualitatively and quantitatively and so gives insight into the main mechanisms responsible for the biogeochemical and ecological complexity. Monsoonal systems are typified by classical food web dynamics, whilst intermonsoonal and oligotrophic systems are dominated by the microbial loop. The ecosystem model (ERSEM), developed for temperate regions, is found to be applicable to the Arabian Sea system with little reparameterisation. Differences in in-situ physical forcing are sufficient to recreate contrasting eutrophic and oligotrophic systems, although the lack of lateral terms are probably the greatest source of error in the model. Physics, nutrients, light and grazing are all shown to play a role in controlling production and community structure. Small-celled phytoplanktons are predicted to be dominant and sub-surface chlorophyll maxima are robust centers of production during intermonsoon periods. Analysis of carbon fluxes indicate that physically driven outgassing of CO₂ predominates in monsoonal upwelling systems but ecological activity may significantly moderate CO₂ outgassing in the Arabian Sea interior.     

Modelling the spatial and temporal variability of the Cretan Sea ecosystem

The ecosystem function of the oligotrophic Cretan Sea is explored through the development and application of a 3D ecological model. The simulation system comprises of two on-line coupled submodels: the 3D Princeton Ocean Model (POM) and the 1D European Regional Seas Ecosystem Model (ERSEM) adapted to the Cretan Sea. For the tuning and initialisation of the ecosystem parameters, the 1D version of the biogeochemical model is used.After a model spin up period of 10 years to reach a quasi-steady state, the results from an annual simulation are presented. A cost function is used as validation method for the comparison of model results with field data. The estimated annual primary and bacteria production are found to be in the range of the reported values. Simulation results are in good agreement with in situ data illustrating the role of the physical processes in determining the evolution and variability of the ecosystem.     

Ballast Water Risk Indication for the North Sea

The ballast water from ships carries marine organisms that have invasive potential. The International Maritime Organization Ballast Water Management Convention (2004) requires ballast water exchange or ballast water management (BWM) systems either onboard or ashore. Ships can be exempted on the basis of risk assessment, when exclusively sailing between specific ports or in an enclosed area. In reply to our questionnaire, the shipping sector argues that the North Sea is ecologically homogeneous and exemptions could therefore be granted. This paper proposes that the North Sea area is, in fact, not homogeneous in terms of hydrographical and biological conditions; therefore, ballast water is a relevant transport mechanism for organisms. Within the North Sea, the short shipping routes indicate a high risk for survival. We examined actual simulation models for ballast water risk assessment in the North Sea, and we have identified the major parameters that need to be included in such models. These models provided a basis; they further need to be combined and adapted for the purpose of evaluating the rationale for an exemption. We concluded that exemptions from BWM are not recommended for the North Sea area. Anticipating the Ballast Water Management Convention, ship owners might do well to study possibilities for installing BWM systems onboard.     

南海北部湾台风浪数值模拟方法研究

对第三代近岸海浪数值模式SWAN控制方程进行简要介绍,并利用由藤田和高桥公式相互嵌套的方法提供了台风风场,用SWAN模式采用大小模型范围嵌套的方式对影响南海北部湾海域的8303号台风浪过程进行了模拟验证,并利用该模式预报了该海域在不同台风作用下的台风浪过程.结果表明,模拟结果与实际海浪观测资料吻合较好,计算预报结果可以为该海域台风浪防灾等提供较为重要的参考.     

High-resolution synthetic monitoring by a 4-dimensional variational data assimilation system in the northwestern North Pacific

A data assimilation system is applied to the integrated monitoring of oceanic states in the northwestern North Pacific by combining a high resolution ocean general circulation model with an adjoint method. A comparison of assimilation results with observations shows that the system is better able to represent synoptic features of ocean circulation than do models or data alone. Furthermore, meso-scale features associated with frontal structures and eddies, which are often seen in the Kuroshio and Oyashio extension regions and the Sea of Japan, are better defined in the assimilation results. These features suggest that our 4D-VAR high-resolution data assimilation system is capable of providing time series data which satisfy the model physics and fit the observations, and hence the ocean state derived from our system has greater information content than that obtained from earlier methods.     

An appropriate unidirectional wave spectrum model for the Strait of Hormuz

The objective of this paper is to introduce an appropriate unidirectional wave spectrum model for the Strait of Hormuz. The research is focused on assessing performance of standard wave spectrum models in the region. By evaluating such models based on valuable measurement data recently published, the calibration procedure has been conducted on such standard models to reach a better concordance between a modified standard spectral model and observed field spectra. The calibration is performed initially with respect to four distinct directions related to four available measurement stations. So, it results in four sets of coefficients for a nominated model. Next, it is continued to reach just one model insensitive to directions. Results clearly showed that the International Towing Tank Conference (ITTC) model is more appropriate than Joint North Sea Wave Project (JONSWAP) and Pierson and Moskowitz (PM) models in this area, even without any calibration. However, modifications have been successful on improving the conformity of the model.