Lagrangian validation of numerical drifter trajectories using drifting buoys: Application to the Agulhas system

The skill of numerical Lagrangian drifter trajectories in three numerical models is assessed by comparing these numerically obtained paths to the trajectories of drifting buoys in the real ocean. The skill assessment is performed using the two-sample Kolmogorov–Smirnov statistical test. To demonstrate the assessment procedure, it is applied to three different models of the Agulhas region. The test can either be performed using crossing positions of one-dimensional sections in order to test model performance in specific locations, or using the total two-dimensional data set of trajectories. The test yields four quantities: a binary decision of model skill, a confidence level which can be used as a measure of goodness-of-fit of the model, a test statistic which can be used to determine the sensitivity of the confidence level, and cumulative distribution functions that aid in the qualitative analysis. The ordering of models by their confidence levels is the same as the ordering based on the qualitative analysis, which suggests that the method is suited for model validation. Only one of the three models, a 1/10° two-way nested regional ocean model, might have skill in the Agulhas region. The other two models, a 1/2° global model and a 1/8° assimilative model, might have skill only on some sections in the region

A Riemann solver for compressible flow of a real gas in a Lagrangian frame

An approximate Riemann solver is presented for the compressible flow equations with a general (convex) equation of state in a Lagrangian frame of reference.

Cylindrically symmetric flows in a Lagrangian frame

An approximate Riemann solver, in a Lagrangian frame of reference, is presented for the compressible flow equations with cylindrical and spherical symmetry, including flow in a duct of variable cross section. The scheme is applied to a cylindrically symmetric problem involving the interaction of shocks.

Evaluation of a Lagrangian box model using field measurements from EASE (Eastern Atlantic Summer Experiment) 1996

The Cambridge Tropospheric Trajectory model of Chemistry and Transport (CiTTyCAT), a Lagrangian chemistry model, has been evaluated using atmospheric chemical measurements collected during the East Atlantic Summer Experiment 1996 (EASE '96). This field campaign was part of the UK Natural Environment Research Council's (NERC) Atmospheric Chemistry Studies in the Oceanic Environment (ACSOE) programme, conducted at Mace Head, Republic of Ireland, during July and August 1996. The model includes a description of gas-phase tropospheric chemistry, and simple parameterisations for surface deposition, mixing from the free troposphere and emissions. The model generally compares well with the measurements and is used to study the production and loss of O3 under a variety of conditions. The mean difference between the hourly O3 concentrations calculated by the model and those measured is 0.6 ppbv with a standard deviation of 8.7 ppbv. Three specific air-flow regimes were identified during the campaign – westerly, anticyclonic (easterly) and south westerly. The westerly flow is typical of background conditions for Mace Head. However, on some occasions there was evidence of long-range transport of pollutants from North America. In periods of anticyclonic flow, air parcels had collected emissions of NOx and VOCs immediately before arriving at Mace Head, leading to O3 production. The level of calculated O3 depends critically on the precise details of the trajectory, and hence on the emissions into the air parcel. In several periods of south westerly flow, low concentrations of O3 were measured which were consistent with deposition and photochemical destruction inside the tropical marine boundary layer.

A Lagrangian model of air-mass photochemistry and mixing using a trajectory ensemble: the Cambridge Tropospheric Trajectory model of Chemistry And Transport (CiTTyCAT) version 4.2

A Lagrangian model of photochemistry and mixing is described (CiTTyCAT, stemming from the Cambridge Tropospheric Trajectory model of Chemistry And Transport), which is suitable for transport and chemistry studies throughout the troposphere. Over the last five years, the model has been developed in parallel at several different institutions and here those developments have been incorporated into one "community" model and documented for the first time. The key photochemical developments include a new scheme for biogenic volatile organic compounds and updated emissions schemes. The key physical development is to evolve composition following an ensemble of trajectories within neighbouring air-masses, including a simple scheme for mixing between them via an evolving "background profile", both within the boundary layer and free troposphere. The model runs along trajectories pre-calculated using winds and temperature from meteorological analyses. In addition, boundary layer height and precipitation rates, output from the analysis model, are interpolated to trajectory points and used as inputs to the mixing and wet deposition schemes. The model is most suitable in regimes when the effects of small-scale turbulent mixing are slow relative to advection by the resolved winds so that coherent air-masses form with distinct composition and strong gradients between them. Such air-masses can persist for many days while stretching, folding and thinning. Lagrangian models offer a useful framework for picking apart the processes of air-mass evolution over inter-continental distances, without being hindered by the numerical diffusion inherent to global Eulerian models. The model, including different box and trajectory modes, is described and some output for each of the modes is presented for evaluation. The model is available for download from a Subversion-controlled repository by contacting the corresponding authors.

A Lagrangian analysis of ice-supersaturated air over the North Atlantic

Understanding the nature of air parcels that exhibit ice-supersaturation is important because they are the regions of potential formation of both cirrus and aircraft contrails, which affect the radiation balance. Ice-supersaturated air parcels in the upper troposphere and lower stratosphere over the North Atlantic are investigated using Lagrangian trajectories. The trajectory calculations use ERA-Interim data for three winter and three summer seasons, resulting in approximately 200,000 trajectories with ice-supersaturation for each season. For both summer and winter, the median duration of ice-supersaturation along a trajectory is less than 6 hours. 5% of air which becomes ice-supersaturated in the troposphere, and 23% of air which becomes ice-supersaturated in the stratosphere will remain ice-supersaturated for at least 24 hours. Weighting the ice-supersaturation duration with the observed frequency indicates the likely overall importance of the longer duration ice-supersaturated trajectories. Ice-supersaturated air parcels typically experience a decrease in moisture content while ice-supersaturated, suggesting that cirrus clouds eventually form in the majority of such air. A comparison is made between short-lived (less than 24 h) and long-lived (greater than 24 h) ice-supersaturated air flows. For both air flows, ice-supersaturation occurs around the northernmost part of the trajectory. Short-lived ice-supersaturated air flows show no significant differences in speed or direction of movement to subsaturated air parcels. However, long-lived ice-supersaturated air occurs in slower moving air flows, which implies that they are not associated with the fastest moving air through a jet stream.

Mechanisms underlying temperature extremes in Iberia: a Lagrangian perspective

The mechanisms underlying the occurrence of temperature extremes in Iberia are analysed considering a Lagrangian perspective of the atmospheric flow, using 6-hourly ERA-Interim reanalysis data for the years 1979–2012. Daily 2-m minimum temperatures below the 1st percentile and 2-m maximum temperatures above the 99th percentile at each grid point over Iberia are selected separately for winter and summer. Four categories of extremes are analysed using 10-d backward trajectories initialized at the extreme temperature grid points close to the surface: winter cold (WCE) and warm extremes (WWE), and summer cold (SCE) and warm extremes (SWE). Air masses leading to temperature extremes are first transported from the North Atlantic towards Europe for all categories. While there is a clear relation to large-scale circulation patterns in winter, the Iberian thermal low is important in summer. Along the trajectories, air mass characteristics are significantly modified through adiabatic warming (air parcel descent), upper-air radiative cooling and near-surface warming (surface heat fluxes and radiation). High residence times over continental areas, such as over northern-central Europe for WCE and, to a lesser extent, over Iberia for SWE, significantly enhance these air mass modifications. Near-surface diabatic warming is particularly striking for SWE. WCE and SWE are responsible for the most extreme conditions in a given year. For WWE and SCE, strong temperature advection associated with important meridional air mass transports are the main driving mechanisms, accompanied by comparatively minor changes in the air mass properties. These results permit a better understanding of mechanisms leading to temperature extremes in Iberia.

A Lagrangian identification of major sources of moisture over Central Brazil and La Plata Basin

[1] This work examines the main sources of moisture over Central Brazil and La Plata Basin during the year through a new Lagrangian diagnosis method which identifies the humidity contributions to the moisture budget over a region. This methodology computes budgets of evaporation minus precipitation by calculating changes in the specific humidity along back-trajectories for the previous 10 d. The origin of all air masses residing over each region was tracked during a period of 5 years (2000-2004). These regions were selected because they coincide with two centers of action of a known dipole precipitation variability mode observed in different temporal scales (from intra seasonal up to inter decadal timescales) and are related to the climatic variability of the South American Monsoon System. The results suggested the importance of the tropical south Atlantic as a moisture source for Central Brazil, and of recycling for La Plata basin. It seems that the Tropical South Atlantic plays an important role as a moisture source for Central Brazil and La Plata basin along the year, particularly during the austral summer. The north Atlantic is also an additional source for both regions during the austral summer.

Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem

A new approach for solving the optimal power flow (OPF) problem is established by combining the reduced gradient method and the augmented Lagrangian method with barriers and exploring specific characteristics of the relations between the variables of the OPF problem. Computer simulations on IEEE 14-bus and IEEE 30-bus test systems illustrate the method. (c) 2007 Elsevier Inc. All rights reserved.

A Lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem

Industrial production processes involving both lot-sizing and cutting stock problems are common in many industrial settings. However, they are usually treated in a separate way, which could lead to costly production plans. In this paper, a coupled mathematical model is formulated and a heuristic method based on Lagrangian relaxation is proposed. Computational results prove its effectiveness. (C) 2009 Elsevier B.V. All rights reserved.

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the epsilon(k)-global minimization of the Augmented Lagrangian with simple constraints, where epsilon(k) -> epsilon. Global convergence to an epsilon-global minimizer of the original problem is proved. The subproblems are solved using the alpha BB method. Numerical experiments are presented.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.