Two-particle models for the estimation of the mean and standard deviation of concentrations in coastal waters

In this paper we study the mean and standard deviation of concentrations using random walk models. Two-particle models that takes into account the space correlation of the turbulence are introduced and some properties of the distribution of the particle concentration are studied. In order to reduce the CPU time of the calculation a new estimator based on reverse time diffusion is applied. This estimator has been introduced recently by Milstein, Schoenmakers, and Spokoiny (2004). Some numerical aspects of the implementation are discussed for relative simple test problems and finally a realistic application to predict the spreading of the pollutant in the Dutch coastal zone is described

Lagrangian ocean analysis: fundamentals and practices

Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing

RANDOM WALK MODEL IN CASE OF ISO-AND DIAPYCNAL DIFFUSION

Abstract. In order to efficiently simulate the advection-diffusion processes along and across density surfaces, we need to deal with the diffusivity tensor containing off-diagonal element

Assessing Lagrangian schemes for simulating diffusion on non-flat isopycnal surfaces

In large-scale ocean flows diffusion mostly occurs along the density surfaces and its representation resorts to the Redi isopycnal diffusivity tensor containing off-diagonal terms. This study focuses on the Lagrangian/particle framework for simulating such diffusive processes. A two-dimensional idealised test case for purely isopycnal diffusion on non-flat isopycnal surfaces is considered. Implementation of the higher order strong Euler, Milstein and order 1.5 Taylor schemes on our idealised test case shows that the higher order strong schemes produce the better pathwise approximations. The effective spurious diapycnal diffusivity is measured for each Lagrangian scheme under consideration. The propensity of the particles to move away from the isopycnal surface on which they were released is also measured. This shows that for non-flat isopycnals the order of convergence of the Euler scheme is not sufficient to achieve the desired accuracy. However, the Milstein scheme seems to be a good choice to achieve in an efficient way a fairly accurate result

Residence time in a semi-enclosed domain from the solution of an adjoint problem

The residence time measures the time spent by a water parcel or a pollutant in a given water body and is therefore a widely used concept in environmental studies. While many previous studies rely on severe hypotheses (assuming stationarity of the flow and/or neglecting diffusion) to evaluate the residence time, the paper introduces a general method for computing the residence time and/or the mean residence time without such simplifying hypotheses. The method is based on the resolution of an adjoint advection-diffusion problem and is therefore primarily meant to be used with numerical models. The method and its implications are first introduced using a simplified one-dimensional analytical model. The approach is then applied to the diagnostic of the three-dimensional circulation on the Northwest European Continental Shelf. (C) 2004 Elsevier Ltd. All rights reserved

Estimating NO_x LOTOS-EUROS CTM Emission Parameters over the Northwest of South America through 4DEnVar TROPOMI NO₂ Assimilation

In this work, we present the development of a 4D-Ensemble-Variational (4DEnVar) data assimilation technique to estimate NOx top-down emissions using the regional chemical transport model LOTOS-EUROS with the NO2 observations from the TROPOspheric Monitoring Instrument (TROPOMI). The assimilation was performed for a domain in the northwest of South America centered over Colombia, and includes regions in Panama, Venezuela and Ecuador. In the 4DEnVar approach, the implementation of the linearized and adjoint model are avoided by generating an ensemble of model simulations and by using this ensemble to approximate the nonlinear model and observation operator. Emission correction parameters’ locations were defined for positions where the model simulations showed significant discrepancies with the satellite observations. Using the 4DEnVar data assimilation method, optimal emission parameters for the LOTOS-EUROS model were estimated, allowing for corrections in areas where ground observations are unavailable and the region’s emission inventories do not correctly reflect the current emissions activities. The analyzed 4DEnVar concentrations were compared with the ground measurements of one local air quality monitoring network and the data retrieved by the satellite instrument Ozone Monitoring Instrument (OMI). The assimilation had a low impact on NO2 surface concentrations reducing the Mean Fractional Bias from 0.45 to 0.32, primordially enhancing the spatial and temporal variations in the simulated NO2 fields

Curriculum vitae of the LOTOS–EUROS (v2.0) chemistry transport model

The development and application of chemistry transport models has a long tradition. Within the Netherlands the LOTOS–EUROS model has been developed by a consortium of institutes, after combining its independently developed predecessors in 2005. Recently, version 2.0 of the model was released as an open-source version. This paper presents the curriculum vitae of the model system, describing the model's history, model philosophy, basic features and a validation with EMEP stations for the new benchmark year 2012, and presents cases with the model's most recent and key developments. By setting the model developments in context and providing an outlook for directions for further development, the paper goes beyond the common model description. With an origin in ozone and sulfur modelling for the models LOTOS and EUROS, the application areas were gradually extended with persistent organic pollutants, reactive nitrogen, and primary and secondary particulate matter. After the combination of the models to LOTOS–EUROS in 2005, the model was further developed to include new source parametrizations (e.g. road resuspension, desert dust, wildfires), applied for operational smog forecasts in the Netherlands and Europe, and has been used for emission scenarios, source apportionment, and long-term hindcast and climate change scenarios. LOTOS–EUROS has been a front-runner in data assimilation of ground-based and satellite observations and has participated in many model intercomparison studies. The model is no longer confined to applications over Europe but is also applied to other regions of the world, e.g. China. The increasing interaction with emission experts has also contributed to the improvement of the model's performance. The philosophy for model development has always been to use knowledge that is state of the art and proven, to keep a good balance in the level of detail of process description and accuracy of input and output, and to keep a good record on the effect of model changes using benchmarking and validation. The performance of v2.0 with respect to EMEP observations is good, with spatial correlations around 0.8 or higher for concentrations and wet deposition. Temporal correlations are around 0.5 or higher. Recent innovative applications include source apportionment and data assimilation, particle number modelling, and energy transition scenarios including corresponding land use changes as well as Saharan dust forecasting. Future developments would enable more flexibility with respect to model horizontal and vertical resolution and further detailing of model input data. This includes the use of different sources of land use characterization (roughness length and vegetation), detailing of emissions in space and time, and efficient coupling to meteorology from different meteorological models