Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation

The weak-constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The well-known result that for Gaussian error statistics the minimum of the weak-constraint inverse is equal to the maximum-likelihood estimate is rederived. Then several methods based on ensemble statistics that can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. they also avoid iterative searches in a Hilbert space, and error estimates can be obtained without much additional computational effort. the feasibility of the new methods is illustrated in a two-layer quasigeostrophic model.

Assimilation of Geosat Altimeter Data for the Agulhas Current Using the Ensemble Kalman Filter with a Quasigeostrophic Model

The ring-shedding process in the Agulhas Current is studied using the ensemble Kalman filter to assimilate geosat altimeter data into a two-layer quasigeostrophic ocean model. The properties of the ensemble Kalman filter are further explored with focus on the analysis scheme and the use of gridded data. The Geosat data consist of 10 fields of gridded sea-surface height anomalies separated 10 days apart that are added to a climatic mean field. This corresponds to a huge number of data values, and a data reduction scheme must be applied to increase the efficiency of the analysis procedure. Further, it is illustrated how one can resolve the rank problem occurring when a too large dataset or a small ensemble is used.

Aspects of particle filtering in high-dimensional spaces

Nonlinear data assimilation is high on the agenda in all fields of the geosciences as with ever increasing model resolution and inclusion of more physical (biological etc.) processes, and more complex observation operators the data-assimilation problem becomes more and more nonlinear. The suitability of particle filters to solve the nonlinear data assimilation problem in high-dimensional geophysical problems will be discussed. Several existing and new schemes will be presented and it is shown that at least one of them, the Equivalent-Weights Particle Filter, does indeed beat the curse of dimensionality and provides a way forward to solve the problem of nonlinear data assimilation in high-dimensional systems.

Increasing frequency of extreme El Niño events due to greenhouse warming

El Niño events are a prominent feature of climate variability with global climatic impacts. The 1997/98 episode, often referred to as ‘the climate event of the twentieth century’1, 2, and the 1982/83 extreme El Niño3, featured a pronounced eastward extension of the west Pacific warm pool and development of atmospheric convection, and hence a huge rainfall increase, in the usually cold and dry equatorial eastern Pacific. Such a massive reorganization of atmospheric convection, which we define as an extreme El Niño, severely disrupted global weather patterns, affecting ecosystems4, 5, agriculture6, tropical cyclones, drought, bushfires, floods and other extreme weather events worldwide3, 7, 8, 9. Potential future changes in such extreme El Niño occurrences could have profound socio-economic consequences. Here we present climate modelling evidence for a doubling in the occurrences in the future in response to greenhouse warming. We estimate the change by aggregating results from climate models in the Coupled Model Intercomparison Project phases 3 (CMIP3; ref. 10) and 5 (CMIP5; ref. 11) multi-model databases, and a perturbed physics ensemble12. The increased frequency arises from a projected surface warming over the eastern equatorial Pacific that occurs faster than in the surrounding ocean waters13, 14, facilitating more occurrences of atmospheric convection in the eastern equatorial region.

A systematic method of parameterisation estimation using data assimilation

In numerical weather prediction, parameterisations are used to simulate missing physics in the model. These can be due to a lack of scientific understanding or a lack of computing power available to address all the known physical processes. Parameterisations are sources of large uncertainty in a model as parameter values used in these parameterisations cannot be measured directly and hence are often not well known; and the parameterisations themselves are also approximations of the processes present in the true atmosphere. Whilst there are many efficient and effective methods for combined state/parameter estimation in data assimilation (DA), such as state augmentation, these are not effective at estimating the structure of parameterisations. A new method of parameterisation estimation is proposed that uses sequential DA methods to estimate errors in the numerical models at each space-time point for each model equation. These errors are then fitted to pre-determined functional forms of missing physics or parameterisations that are based upon prior information. We applied the method to a one-dimensional advection model with additive model error, and it is shown that the method can accurately estimate parameterisations, with consistent error estimates. Furthermore, it is shown how the method depends on the quality of the DA results. The results indicate that this new method is a powerful tool in systematic model improvement.

Implicit equal-weights particle filter

Filter degeneracy is the main obstacle for the implementation of particle filter in non-linear high-dimensional models. A new scheme, the implicit equal-weights particle filter (IEWPF), is introduced. In this scheme samples are drawn implicitly from proposal densities with a different covariance for each particle, such that all particle weights are equal by construction. We test and explore the properties of the new scheme using a 1,000-dimensional simple linear model, and the 1,000-dimensional non-linear Lorenz96 model, and compare the performance of the scheme to a Local Ensemble Kalman Filter. The experiments show that the new scheme can easily be implemented in high-dimensional systems and is never degenerate, with good convergence properties in both systems.

Translation, decay and splitting of Agulhas rings in the southeastern Atlantic Ocean

All Agulhas rings that were spawned at the Agulhas retrofiec- tion between 1993 and 1996 (a total of 21 rings) have been monitored using TOPEX/Poseidon satellite altimetry and followed as they moved through the southeastern Atlantic Ocean, decayed, interacted with bottom topography and each other, or dissipated completely. Rings preferentially crossed the Walvis Ridge at its deepest parts. After having crossed this ridge they have lower translational speeds, and their decay rate decreases markedly. Half the decay of long-lived rings takes place in the first 5 months of their lifetimes. In addition to the strong decay of rings in the Cape Basin, about one third of the observed rings do not seem to leave this region at all but totally disintegrate here. The interaction of rings with bottom topography, in particular with the Verna Seamount, is shown frequently to cause splitting of rings. This will enhance mixing of the rings' Indian Ocean water into that of the southern Atlantic. This localized mixing may well provide a considerable source of warm and salty Indian Ocean water into the Atlantic overturning circulation.

Upstream control of Agulhas Ring shedding

Rings shed in the Agulhas Retroflection region play an important role in the global thermohaline circulation. The shedding of these rings has been considered very irregular. In this paper, we present evidence for remote control of the timing and frequency of the ring shedding events. This turns out to be a far more regular process, at a frequency of 4–5 cycles per year. The movement of the Agulhas Retroflection, and thereby the shedding of rings, is timed by incoming eddies from the upstream regions. Eddies from the Mozambique Channel, and from the East Madagascar current reach the retroflection region at the frequency of 4–5 times per year. The existence of these eddies can be related to incoming Rossby waves that cross the Indian Ocean and reach the Agulhas Current system. These may in turn be part of a basin-wide oscillation. The irregularity found in ring shedding statistics can be ascribed to processes occurring between the actual shedding and the first unambiguous observation of a separated ring.

Eddies and variability in the Mozambique Channel

Between 1995 and 2000, on average 4 eddies per year are observed from satellite altimetry to propagate southward through the Mozambique Channel, into the upstream Agulhas region. Further south, these eddies have been found to control the timing and frequenc yof Agulhas ring shedding. Within the Mozambique Channel, anomalous SSH amplitudes rise to 30 cm ; in agreement with in situ measured velocities. Comparison of an observed velocit ysection with GCM model results shows that the Mozambique Channel eddies in these models are too surface intensified. Also, the number of eddies formed in the models is in disagreement with our observational analysis. Moored current meter measurements observing the passage of three eddies in 2000 are extended to a 5-year time series b yreferencing the anomalous surface currents estimated from altimeter data to a s ynoptic LADCP velocit y measurement. The results show intermittent edd ypassage at the mooring location. A statistical analysis of SSH observations in different parts of the Mozambique Channel shows a southward decrease of the dominant frequency of the variability, going from 7 per year in the extension of the South Equatorial Current north of Madagascar to 4 per year south of Madagascar. The observations suggest that frequency reduction is related to the Rossb ywaves coming in from the east

A parallel data assimilation model for oceanographic observations

In this paper we describe the development of a program that aims at the optimal integration of observed data in an oceanographic model describ

Results of Joint Experiments and other IAEA activities on research using small tokamaks

This paper presents an overview of the results obtained during the Joint Experiments organized in the framework of the IAEA Coordinated Research Project on `Joint Research Using Small Tokamaks` that have been carried out on the tokamaks CASTOR at IPP Prague, Czech Republic (2005), T-10 at RRC `Kurchatov Institute`, Moscow, Russia (2006), and the most recent one at ISTTOK at IST, Lisbon, Portugal, in 2007. Experimental programmes were aimed at diagnosing and characterizing the core and the edge plasma turbulence in a tokamak in order to investigate correlations between the occurrence of transport barriers, improved confinement, electric fields and electrostatic turbulence using advanced diagnostics with high spatial and temporal resolution. On CASTOR and ISTTOK, electric fields were generated by biasing an electrode inserted into the edge plasma and an improvement of the global particle confinement induced by the electrode positive biasing has been observed. Geodesic acoustic modes were studied using heavy ion beam diagnostics on T-10 and ISTTOK and correlation reflectometry on T-10. ISTTOK is equipped with a gallium jet injector and the technical feasibility of gallium jets interacting with plasmas has been investigated in pulsed and ac operation. The first Joint Experiments have clearly demonstrated that small tokamaks are suitable for broad international cooperation to conduct dedicated joint research programmes. Other activities within the IAEA Coordinated Research Project on Joint Research Using Small Tokamaks are also overviewed.

Thyroid status, but not insulin status, affects expression of avian uncoupling protein mRNA in chicken

The aim of this study was to investigate the hormonal regulation of the avian homolog of mammalian uncoupling protein (avUCP) by studying the impact of thyroid hormones and insulin on avUCP mRNA expression in chickens (Gallus gallus). For 3 wk, chicks received either a standard diet (control group), or a standard diet supplemented with triiodothyronine (T-3; T3 group) or with the thyroid gland inhibitor methimazole (MMI group). A fourth group received injections of the deiodinase inhibitor iopanoic acid (IOP group). During the 4th wk of age, all animals received two daily injections of either human insulin or saline solution. The results indicate a twofold overexpression of avUCP mRNA in gastrocnemius muscle of T3 birds and a clear downregulation (-74%) in MMI chickens compared with control chickens. Insulin injections had no significant effect on avUCP mRNA expression in chickens. This study describes for the first time induction of avUCP mRNA expression by the thermogenic hormone T3 in chickens and supports a possible involvement of avUCP in avian thermogenesis.