An Ensemble Smoother with Error Estimates

A smoother introduced earlier by van Leeuwen and Evensen is applied to a problem in which real obser vations are used in an area with strongly nonlinear dynamics. The derivation is new , but it resembles an earlier derivation by van Leeuwen and Evensen. Again a Bayesian view is taken in which the prior probability density of the model and the probability density of the obser vations are combined to for m a posterior density . The mean and the covariance of this density give the variance-minimizing model evolution and its errors. The assumption is made that the prior probability density is a Gaussian, leading to a linear update equation. Critical evaluation shows when the assumption is justified. This also sheds light on why Kalman filters, in which the same ap- proximation is made, work for nonlinear models. By reference to the derivation, the impact of model and obser vational biases on the equations is discussed, and it is shown that Bayes’ s for mulation can still be used. A practical advantage of the ensemble smoother is that no adjoint equations have to be integrated and that error estimates are easily obtained. The present application shows that for process studies a smoother will give superior results compared to a filter , not only owing to the smooth transitions at obser vation points, but also because the origin of features can be followed back in time. Also its preference over a strong-constraint method is highlighted. Further more, it is argued that the proposed smoother is more efficient than gradient descent methods or than the representer method when error estimates are taken into account

Analysis Scheme in the Ensemble Kalman Filter

This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter . I t i s shown that the obser vations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the obser vations and generate an ensemble of obser vations that then is used in updating the ensemble of model states. T raditionally , this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low . This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach

Diagnosing observation error correlations for Doppler radar radial winds in the Met Office UKV model using observation-minus-background and observation-minus-analysis statistics

With the development of convection-permitting numerical weather prediction the efficient use of high resolution observations in data assimilation is becoming increasingly important. The operational assimilation of these observations, such as Dopplerradar radial winds, is now common, though to avoid violating the assumption of un- correlated observation errors the observation density is severely reduced. To improve the quantity of observations used and the impact that they have on the forecast will require the introduction of the full, potentially correlated, error statistics. In this work, observation error statistics are calculated for the Doppler radar radial winds that are assimilated into the Met Office high resolution UK model using a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. This is the first in-depth study using the diagnostic to estimate both horizontal and along-beam correlated observation errors. By considering the new results obtained it is found that the Doppler radar radial wind error standard deviations are similar to those used operationally and increase as the observation height increases. Surprisingly the estimated observation error correlation length scales are longer than the operational thinning distance. They are dependent on both the height of the observation and on the distance of the observation away from the radar. Further tests show that the long correlations cannot be attributed to the use of superobservations or the background error covariance matrix used in the assimilation. The large horizontal correlation length scales are, however, in part, a result of using a simplified observation operator.

Atmospheric impact of Arctic Sea ice loss in a coupled ocean–atmosphere simulation

The atmospheric response to an idealized decline in Arctic sea ice is investigated in a novel fully coupled climate model experiment. In this experiment two ensembles of single-year model integrations are performed starting on 1 April, the approximate start of the ice melt season. By perturbing the initial conditions of sea ice thickness (SIT), declines in both sea ice concentration and SIT, which result in sea ice distributions that are similar to the recent sea ice minima of 2007 and 2012, are induced. In the ice loss regions there are strong (~3 K) local increases in sea surface temperature (SST); additionally, there are remote increases in SST in the central North Pacific and subpolar gyre in the North Atlantic. Over the central Arctic there are increases in surface air temperature (SAT) of ~8 K due to increases in ocean–atmosphere heat fluxes. There are increases in SAT over continental North America that are in good agreement with recent changes as seen by reanalysis data. It is estimated that up to two-thirds of the observed increase in SAT in this region could be related to Arctic sea ice loss. In early summer there is a significant but weak atmospheric circulation response that projects onto the summer North Atlantic Oscillation (NAO). In early summer and early autumn there is an equatorward shift of the eddy-driven jet over the North Atlantic as a result of a reduction in the meridional temperature gradients. In winter there is no projection onto a particular phase of the NAO.

Ocean heat content variability and change in an ensemble of ocean reanalyses

Accurate knowledge of the location and magnitude of ocean heat content (OHC) variability and change is essential for understanding the processes that govern decadal variations in surface temperature, quantifying changes in the planetary energy budget, and developing constraints on the transient climate response to external forcings. We present an overview of the temporal and spatial characteristics of OHC variability and change as represented by an ensemble of dynamical and statistical ocean reanalyses (ORAs). Spatial maps of the 0–300 m layer show large regions of the Pacific and Indian Oceans where the interannual variability of the ensemble mean exceeds ensemble spread, indicating that OHC variations are well-constrained by the available observations over the period 1993–2009. At deeper levels, the ORAs are less well-constrained by observations with the largest differences across the ensemble mostly associated with areas of high eddy kinetic energy, such as the Southern Ocean and boundary current regions. Spatial patterns of OHC change for the period 1997–2009 show good agreement in the upper 300 m and are characterized by a strong dipole pattern in the Pacific Ocean. There is less agreement in the patterns of change at deeper levels, potentially linked to differences in the representation of ocean dynamics, such as water mass formation processes. However, the Atlantic and Southern Oceans are regions in which many ORAs show widespread warming below 700 m over the period 1997–2009. Annual time series of global and hemispheric OHC change for 0–700 m show the largest spread for the data sparse Southern Hemisphere and a number of ORAs seem to be subject to large initialization ‘shock’ over the first few years. In agreement with previous studies, a number of ORAs exhibit enhanced ocean heat uptake below 300 and 700 m during the mid-1990s or early 2000s. The ORA ensemble mean (±1 standard deviation) of rolling 5-year trends in full-depth OHC shows a relatively steady heat uptake of approximately 0.9 ± 0.8 W m−2 (expressed relative to Earth’s surface area) between 1995 and 2002, which reduces to about 0.2 ± 0.6 W m−2 between 2004 and 2006, in qualitative agreement with recent analysis of Earth’s energy imbalance. There is a marked reduction in the ensemble spread of OHC trends below 300 m as the Argo profiling float observations become available in the early 2000s. In general, we suggest that ORAs should be treated with caution when employed to understand past ocean warming trends—especially when considering the deeper ocean where there is little in the way of observational constraints. The current work emphasizes the need to better observe the deep ocean, both for providing observational constraints for future ocean state estimation efforts and also to develop improved models and data assimilation methods.

Southern Ocean isopycnal mixing and ventilation changes driven by winds

Observed and predicted changes in the strength of the westerly winds blowing over the Southern Ocean have motivated a number of studies of the response of the Antarctic Circumpolar Current and Southern Ocean Meridional Overturning Circulation (MOC) to wind perturbations and led to the discovery of the``eddy-compensation" regime, wherein the MOC becomes insensitive to wind changes. In addition to the MOC, tracer transport also depends on mixing processes. Here we show, in a high-resolution process model, that isopycnal mixing by mesoscale eddies is strongly dependent on the wind strength. This dependence can be explained by mixing-length theory and is driven by increases in eddy kinetic energy; the mixing length does not change strongly in our simulation. Simulation of a passive ventilation tracer (analogous to CFCs or anthropogenic CO$_2$) demonstrates that variations in tracer uptake across experiments are dominated by changes in isopycnal mixing, rather than changes in the MOC. We argue that, to properly understand tracer uptake under different wind-forcing scenarios, the sensitivity of isopycnal mixing to winds must be accounted for.

First-order turbulence closure for modelling complex canopy flows

Simple first-order closure remains an attractive way of formulating equations for complex canopy flows when the aim is to find analytic or simple numerical solutions to illustrate fundamental physical processes. Nevertheless, the limitations of such closures must be understood if the resulting models are to illuminate rather than mislead. We propose five conditions that first-order closures must satisfy then test two widely used closures against them. The first is the eddy diffusivity based on a mixing length. We discuss the origins of this approach, its use in simple canopy flows and extensions to more complex flows. We find that it satisfies most of the conditions and, because the reasons for its failures are well understood, it is a reliable methodology. The second is the velocity-squared closure that relates shear stress to the square of mean velocity. Again we discuss the origins of this closure and show that it is based on incorrect physical principles and fails to satisfy any of the five conditions in complex canopy flows; consequently its use can lead to actively misleading conclusions.

Langmuir turbulence and surface heating in the ocean surface boundary layer

This study uses large-eddy simulation to investigate the structure of the ocean surface boundary layer (OSBL) in the presence of Langmuir turbulence and stabilizing surface heat fluxes. The OSBL consists of a weakly stratified layer, despite a surface heat flux, above a stratified thermocline. The weakly stratified (mixed) layer is maintained by a combination of a turbulent heat flux produced by the wave-driven Stokes drift and downgradient turbulent diffusion. The scaling of turbulence statistics, such as dissipation and vertical velocity variance, is only affected by the surface heat flux through changes in the mixed layer depth. Diagnostic models are proposed for the equilibrium boundary layer and mixed layer depths in the presence of surface heating. The models are a function of the initial mixed layer depth before heating is imposed and the Langmuir stability length. In the presence of radiative heating, the models are extended to account for the depth profile of the heating.

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.

Relational architecture and relational capability: organisational levers to support strategic supplier relationships

The resource based view of strategy suggests that competitiveness in part derives from a firms ability to collaborate with a subset of its supply network to co-create highly valued products and services. This relational capability relies on a foundational intra and inter-organisational architecture, the manifestation of strategic, people, and process decisions facilitating the interface between the firm and its strategic suppliers. Using covariance-based structural equation modelling we examine the relationships between internal and external features of relational architecture, and their relationship with relational capability and relational quality. This is undertaken on data collected by mail survey. We find significant relationships between both internal and external relational architecture and relational capability and between relational capability and relational quality. Novel constructs for internal and external elements of relational architecture are specified to demonstrate their positive influence on relational capability and relationship quality.

Sparse density estimation on multinomial manifold combining local component analysis

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion combining local component analysis for the finite mixture model. We start with a Parzen window estimator which has the Gaussian kernels with a common covariance matrix, the local component analysis is initially applied to find the covariance matrix using expectation maximization algorithm. Since the constraint on the mixing coefficients of a finite mixture model is on the multinomial manifold, we then use the well-known Riemannian trust-region algorithm to find the set of sparse mixing coefficients. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Additive genetic relationships between scrotal circumference, heifer pregnancy, and stayability in Nellore cattle

Scrotal circumference data from 47,605 Nellore young bulls, measured at around 18 mo of age (SC18), were analyzed simultaneously with 27,924 heifer pregnancy (HP) and 80,831 stayability (STAY) records to estimate their additive genetic relationships. Additionally, the possibility that economically relevant traits measured directly in females could replace SC18 as a selection criterion was verified. Heifer pregnancy was defined as the observation that a heifer conceived and remained pregnant, which was assessed by rectal palpation at 60 d. Females were exposed to sires for the first time at about 14 mo of age (between 11 and 16 mo). Stayability was defined as whether or not a cow calved every year up to 5 yr of age, when the opportunity to breed was provided. A Bayesian linear-threshold-threshold analysis via Gibbs sampler was used to estimate the variance and covariance components of the multitrait model. Heritability estimates were 0.42 +/- 0.01, 0.53 +/- 0.03, and 0.10 +/- 0.01, for SC18, HP, and STAY, respectively. The genetic correlation estimates were 0.29 +/- 0.05, 0.19 +/- 0.05, and 0.64 +/- 0.07 between SC18 and HP, SC18 and STAY, and HP and STAY, respectively. The residual correlation estimate between HP and STAY was -0.08 +/- 0.03. The heritability values indicate the existence of considerable genetic variance for SC18 and HP traits. However, genetic correlations between SC18 and the female reproductive traits analyzed in the present study can only be considered moderate. The small residual correlation between HP and STAY suggests that environmental effects common to both traits are not major. The large heritability estimate for HP and the high genetic correlation between HP and STAY obtained in the present study confirm that EPD for HP can be used to select bulls for the production of precocious, fertile, and long-lived daughters. Moreover, SC18 could be incorporated in multitrait analysis to improve the prediction accuracy for HP genetic merit of young bulls.

New perspectives on the synoptic and mesoscale structure of Hurricane Catarina

This work explores in detail synoptic and mesoscale features of Hurricane Catarina during its life cycle from a decaying baroclinic wave to a tropical depression that underwent tropical transition (TT) and finally to a Category 2 hurricane at landfall over Santa Catarina State coast, southern Brazil. This unique system caused 11 deaths mostly off the Brazilian coast and an estimated half billion dollars in damage in a matter of a few hours on 28 March 2004. Although the closest meteorological station available was tens of kilometres away from the eye, in situ meteorological measurements provided by a work-team sent to the area where the eye made landfall unequivocally reproduces the tropical signature with category 2 strength, adding to previous analysis where this data was not available. Further analyses are based mostly on remote sensing data available at the time of the event. A classic dipole blocking set synoptic conditions for Hurricane Catarina to develop, dynamically contributing to the low wind shear observed. On the other hand, on its westward transit, large scale subsidence limited its strength and vertical development. Catarina had relatively cool SST conditions, but this was mitigated by favourable air-sea fluxes leading to latent heat release-driven processes during the mature phase. The ocean`s dynamic topography also suggested the presence of nearby warm core rings which may have facilitated the transition and post-transition intensification. Since there were no records of such a system at least in the past 30 years and given that SSTs were generally below 26 degrees C and vertical shear was usually strong, despite all satellite data available, the system was initially classified as an extratropical cyclone. Here we hypothesise that this categorization was based oil inadequate regional scale model outputs which did not account for the importance of the latent heat fluxes over the ocean. Hurricane Catarina represents a dramatic event on weather systems in South America. It has attracted attention worldwide and poses questions as whether or not it is a symptom of global warming. (C) 2009 Elsevier B.V. All rights reserved.

An analysis of the environmental energetics associated with the transition of the first South Atlantic hurricane

This study presents the first analysis of the energetics associated with a hybrid cyclone`s transition in the Southern Hemisphere, Hurricane Catarina ( March 2004). Catarina has earned a place in history as the first documented South Atlantic hurricane, but its unusual tropical transition is still poorly understood. Here we show that Catarina`s transition was preceded by marked environmental changes in the Lorenz energy cycle, with an abrupt shift from a baroclinic to a predominantly barotropic state. Such changes help to explain the unusual vortex`s growth until its transition was completed. Although the vortex`s energy flux is not explicitly calculated, a likely mechanism linking the environmental energetics with Catarina is the extraction of eddy kinetic energy from horizontal momentum and heat transfers within the through component of the blocking. The results advance the understanding of this rare event and suggest that the technique has a great potential to study transitioning systems in general.