The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity

International audienceRandom walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continuous change in diffusivity may be represented by a discontinuity. The random walk model based on backward Îto calculus can be used for these problems. This model was proposed by LaBolle et al. (2000). The latter is best suited to the problems under consideration. It is then applied for two test cases with discontinuous diffusivity, highlighting the advantages of this method

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

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

Nonlinearity in Data Assimilation Applications: A Practical Method for Analysis

A new method to quantify the nonlinearity of data assimilation problems is proposed. The method includes the effects of system errors, measurement errors, observational network, and sampling interval. It is based on computation of the first neglected term in a "Taylor" series expansion of the errors introduced by an extended Kalman filter, and can be computed at very little cost when one is already applying a second-order (or higher order) Kalman filter or an ensemble Kalman filter. The nonlinearity measure proposed here can be used to classify the "hardness" of the problem and predict the failure of data assimilation algorithms. In this manner it facilitates the comparison of data assimilation algorithms and applications