Decadal climate prediction: an update from the trenches

This paper provides an update on research in the relatively new and fast-moving field of decadal climate prediction, and addresses the use of decadal climate predictions not only for potential users of such information but also for improving our understanding of processes in the climate system. External forcing influences the predictions throughout, but their contributions to predictive skill become dominant after most of the improved skill from initialization with observations vanishes after about six to nine years. Recent multi-model results suggest that there is relatively more decadal predictive skill in the North Atlantic, western Pacific, and Indian Oceans than in other regions of the world oceans. Aspects of decadal variability of SSTs, like the mid-1970s shift in the Pacific, the mid-1990s shift in the northern North Atlantic and western Pacific, and the early-2000s hiatus, are better represented in initialized hindcasts compared to uninitialized simulations. There is evidence of higher skill in initialized multi-model ensemble decadal hindcasts than in single model results, with multi-model initialized predictions for near term climate showing somewhat less global warming than uninitialized simulations. Some decadal hindcasts have shown statistically reliable predictions of surface temperature over various land and ocean regions for lead times of up to 6-9 years, but this needs to be investigated in a wider set of models. As in the early days of El Niño-Southern Oscillation (ENSO) prediction, improvements to models will reduce the need for bias adjustment, and increase the reliability, and thus usefulness, of decadal climate predictions in the future.

Sparse probability density function estimation using the minimum integrated square error

We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of kernels and the estimation of mixing weights. The proposed approach is simple to implement and the associated computational cost is very low. Specifically, the complexity of our algorithm is in the order of the number of training data N, which is much lower than the order of N2 offered by the best existing sparse kernel density estimators. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to those of the classical Parzen window estimate and other existing sparse kernel density estimators.

On Hamiltonian balanced dynamics and the slowest invariant manifold

The concept of a slowest invariant manifold is investigated for the five-component model of Lorenz under conservative dynamics. It is shown that Lorenz's model is a two-degree-of-freedom canonical Hamiltonian system, consisting of a nonlinear vorticity-triad oscillator coupled to a linear gravity wave oscillator, whose solutions consist of regular and chaotic orbits. When either the Rossby number or the rotational Froude number is small, there is a formal separation of timescales, and one can speak of fast and slow motion. In the same regime, the coupling is weak, and the Kolmogorov–Arnold-Moser theorem is shown to apply. The chaotic orbits are inherently unbalanced and are confined to regions sandwiched between invariant tori consisting of quasi-periodic regular orbits. The regular orbits generally contain free fast motion, but a slowest invariant manifold may be geometrically defined as the set of all slow cores of invariant tori (defined by zero fast action) that are smoothly related to such cores in the uncoupled system. This slowest invariant manifold is not global; in fact, its structure is fractal; but it is of nearly full measure in the limit of weak coupling. It is also nonlinearly stable. As the coupling increases, the slowest invariant manifold shrinks until it disappears altogether. The results clarify previous definitions of a slowest invariant manifold and highlight the ambiguity in the definition of “slowness.” An asymptotic procedure, analogous to standard initialization techniques, is found to yield nonzero free fast motion even when the core solutions contain none. A hierarchy of Hamiltonian balanced models preserving the symmetries in the original low-order model is formulated; these models are compared with classic balanced models, asymptotically initialized solutions of the full system and the slowest invariant manifold defined by the core solutions. The analysis suggests that for sufficiently small Rossby or rotational Froude numbers, a stable slowest invariant manifold can be defined for this system, which has zero free gravity wave activity, but it cannot be defined everywhere. The implications of the results for more complex systems are discussed.

Balance model for equatorial long waves

Geophysical fluid models often support both fast and slow motions. As the dynamics are often dominated by the slow motions, it is desirable to filter out the fast motions by constructing balance models. An example is the quasi geostrophic (QG) model, which is used widely in meteorology and oceanography for theoretical studies, in addition to practical applications such as model initialization and data assimilation. Although the QG model works quite well in the mid-latitudes, its usefulness diminishes as one approaches the equator. Thus far, attempts to derive similar balance models for the tropics have not been entirely successful as the models generally filter out Kelvin waves, which contribute significantly to tropical low-frequency variability. There is much theoretical interest in the dynamics of planetary-scale Kelvin waves, especially for atmospheric and oceanic data assimilation where observations are generally only of the mass field and thus do not constrain the wind field without some kind of diagnostic balance relation. As a result, estimates of Kelvin wave amplitudes can be poor. Our goal is to find a balance model that includes Kelvin waves for planetary-scale motions. Using asymptotic methods, we derive a balance model for the weakly nonlinear equatorial shallow-water equations. Specifically we adopt the ‘slaving’ method proposed by Warn et al. (Q. J. R. Meteorol. Soc., vol. 121, 1995, pp. 723–739), which avoids secular terms in the expansion and thus can in principle be carried out to any order. Different from previous approaches, our expansion is based on a long-wave scaling and the slow dynamics is described using the height field instead of potential vorticity. The leading-order model is equivalent to the truncated long-wave model considered previously (e.g. Heckley & Gill, Q. J. R. Meteorol. Soc., vol. 110, 1984, pp. 203–217), which retains Kelvin waves in addition to equatorial Rossby waves. Our method allows for the derivation of higher-order models which significantly improve the representation of Rossby waves in the isotropic limit. In addition, the ‘slaving’ method is applicable even when the weakly nonlinear assumption is relaxed, and the resulting nonlinear model encompasses the weakly nonlinear model. We also demonstrate that the method can be applied to more realistic stratified models, such as the Boussinesq model.

Ensemble transform Kalman-Bucy filters

Two recent works have adapted the Kalman–Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman–Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

Time valued life cycle greenhouse gas emissions from buildings

The UK has adopted legally binding carbon reduction targets of 34% by 2020 and 80% by 2050 (measured against the 1990 baseline). Buildings are estimated to be responsible for more than 50% of greenhouse gas (GHG) emissions in the UK. These consist of both operational, produced during use, and embodied, produced during manufacture of materials and components, and during construction, refurbishments and demolition. A brief assessment suggests that it is unlikely that UK emission reduction targets can be met without substantial reductions in both Oc and Ec. Oc occurs over the lifetime of a building whereas the bulk of Ec occurs at the start of a building’s life. A time value for emissions could influence the decision making process when it comes to comparing mitigation measures which have benefits that occur at different times. An example might be the choice between building construction using low Ec construction materials versus building construction using high Ec construction materials but with lower Oc, although the use of high Ec materials does not necessarily imply a lower Oc. Particular time related issues examined here are: the urgency of the need to achieve large emissions reductions during the next 10 to 20 years; the earlier effective action is taken, the less costly it will be; future reduction in carbon intensity of energy supply; the carbon cycle and relationship between the release of GHG’s and their subsequent concentrations in the atmosphere. An equation is proposed, which weights emissions according to when they occur during the building life cycle, and which effectively increases Ec as a proportion of the total, suggesting that reducing Ec is likely to be more beneficial, in terms of climate change, for most new buildings. Thus, giving higher priority to Ec reductions is likely to result in a bigger positive impact on climate change and mitigation costs.

Pooling of forecasts

We consider forecasting using a combination, when no model coincides with a non-constant data generation process (DGP). Practical experience suggests that combining forecasts adds value, and can even dominate the best individual device. We show why this can occur when forecasting models are differentially mis-specified, and is likely to occur when the DGP is subject to location shifts. Moreover, averaging may then dominate over estimated weights in the combination. Finally, it cannot be proved that only non-encompassed devices should be retained in the combination. Empirical and Monte Carlo illustrations confirm the analysis.

Efficient fully nonlinear data assimilation for geophysical fluid dynamics

A potential problem with Ensemble Kalman Filter is the implicit Gaussian assumption at analysis times. Here we explore the performance of a recently proposed fully nonlinear particle filter on a high-dimensional but simplified ocean model, in which the Gaussian assumption is not made. The model simulates the evolution of the vorticity field in time, described by the barotropic vorticity equation, in a highly nonlinear flow regime. While common knowledge is that particle filters are inefficient and need large numbers of model runs to avoid degeneracy, the newly developed particle filter needs only of the order of 10-100 particles on large scale problems. The crucial new ingredient is that the proposal density cannot only be used to ensure all particles end up in high-probability regions of state space as defined by the observations, but also to ensure that most of the particles have similar weights. Using identical twin experiments we found that the ensemble mean follows the truth reliably, and the difference from the truth is captured by the ensemble spread. A rank histogram is used to show that the truth run is indistinguishable from any of the particles, showing statistical consistency of the method.

Assimilation of sea-ice concentration in a global climate model — physical and statistical aspects

We investigate the initialization of Northern-hemisphere sea ice in the global climate model ECHAM5/MPI-OM by assimilating sea-ice concentration data. The analysis updates for concentration are given by Newtonian relaxation, and we discuss different ways of specifying the analysis updates for mean thickness. Because the conservation of mean ice thickness or actual ice thickness in the analysis updates leads to poor assimilation performance, we introduce a proportional dependence between concentration and mean thickness analysis updates. Assimilation with these proportional mean-thickness analysis updates significantly reduces assimilation error both in identical-twin experiments and when assimilating sea-ice observations, reducing the concentration error by a factor of four to six, and the thickness error by a factor of two. To understand the physical aspects of assimilation errors, we construct a simple prognostic model of the sea-ice thermodynamics, and analyse its response to the assimilation. We find that the strong dependence of thermodynamic ice growth on ice concentration necessitates an adjustment of mean ice thickness in the analysis update. To understand the statistical aspects of assimilation errors, we study the model background error covariance between ice concentration and ice thickness. We find that the spatial structure of covariances is best represented by the proportional mean-thickness analysis updates. Both physical and statistical evidence supports the experimental finding that proportional mean-thickness updates are superior to the other two methods considered and enable us to assimilate sea ice in a global climate model using simple Newtonian relaxation.

Costing conservation: an expert appraisal of the pollinator habitat benefits of England’s entry level stewardship

Pollination services provided by insects play a key role in English crop production and wider ecology. Despite growing evidence of the negative effects of habitat loss on pollinator populations, limited policy support is available to reverse this pressure. One measure that may provide beneficial habitat to pollinators is England’s entry level stewardship agri-environment scheme. This study uses a novel expert survey to develop weights for a range of models which adjust the balance of Entry Level Stewardship options within the current area of spending. The annual costs of establishing and maintaining these option compositions were estimated at £59.3–£12.4 M above current expenditure. Although this produced substantial reduction in private cost:benefit ratios, the benefits of the scheme to pollinator habitat rose by 7–140 %; significantly increasing the public cost:benefit ratio. This study demonstrates that the scheme has significant untapped potential to provide good quality habitat for pollinators across England, even within existing expenditure. The findings should open debate on the costs and benefits of specific entry level stewardship management options and how these can be enhanced to benefit both participants and biodiversity more equitably.

Complex-valued B-spline neural networks for modeling and inverting Hammerstein systems

Many communication signal processing applications involve modelling and inverting complex-valued (CV) Hammerstein systems. We develops a new CV B-spline neural network approach for efficient identification of the CV Hammerstein system and effective inversion of the estimated CV Hammerstein model. Specifically, the CV nonlinear static function in the Hammerstein system is represented using the tensor product from two univariate B-spline neural networks. An efficient alternating least squares estimation method is adopted for identifying the CV linear dynamic model’s coefficients and the CV B-spline neural network’s weights, which yields the closed-form solutions for both the linear dynamic model’s coefficients and the B-spline neural network’s weights, and this estimation process is guaranteed to converge very fast to a unique minimum solution. Furthermore, an accurate inversion of the CV Hammerstein system can readily be obtained using the estimated model. In particular, the inversion of the CV nonlinear static function in the Hammerstein system can be calculated effectively using a Gaussian-Newton algorithm, which naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. The effectiveness of our approach is demonstrated using the application to equalisation of Hammerstein channels.

Oral treatment of chickens with Lactobacillus reuteri LM1 reduces Brachyspira pilosicoli-induced pathology

Avian intestinal spirochaetosis (AIS) results from the colonization of the caeca and colon of poultry by pathogenic Brachyspira, notably Brachyspira pilosicoli. Following the ban on the use of antibiotic growth promoters in the European Union in 2006, the number of cases of AIS has increased, which, alongside emerging antimicrobial resistance in Brachyspira, has driven renewed interest in alternative intervention strategies. Lactobacillus-based probiotics have been shown to protect against infection with common enteric pathogens in livestock. Our previous studies have shown that Lactobacillus reuteri LM1 antagonizes aspects of the pathobiology of Brachyspira in vitro. Here, we showed that L. reuteri LM1 mitigates the clinical symptoms of AIS in chickens experimentally challenged with B. pilosicoli. Two groups of 15 commercial laying hens were challenged experimentally by oral gavage with B. pilosicoli B2904 at 18 weeks of age; one group received unsupplemented drinking water and the other received L. reuteri LM1 in drinking water from 1 week prior to challenge with Brachyspira and thereafter for the duration of the study. This treatment regime was protective. Specifically, B. pilosicoli was detected by culture in fewer birds, bird weights were higher, faecal moisture contents were significantly lower (P<0.05) and egg production as assessed by egg weight and faecal staining score was improved (P<0.05). Also, at post-mortem examination, significantly fewer B. pilosicoli were recovered from treated birds (P<0.05), with only mild–moderate histopathological changes observed. These data suggest that L. reuteri LM1 may be a useful tool in the control of AIS.

Dissecting the illegal ivory trade: an analysis of ivory seizures data

Reliable evidence of trends in the illegal ivory trade is important for informing decision making for elephants but it is difficult to obtain due to the covert nature of the trade. The Elephant Trade Information System, a global database of reported seizures of illegal ivory, holds the only extensive information on illicit trade available. However inherent biases in seizure data make it difficult to infer trends; countries differ in their ability to make and report seizures and these differences cannot be directly measured. We developed a new modelling framework to provide quantitative evidence on trends in the illegal ivory trade from seizures data. The framework used Bayesian hierarchical latent variable models to reduce bias in seizures data by identifying proxy variables that describe the variability in seizure and reporting rates between countries and over time. Models produced bias-adjusted smoothed estimates of relative trends in illegal ivory activity for raw and worked ivory in three weight classes. Activity is represented by two indicators describing the number of illegal ivory transactions--Transactions Index--and the total weight of illegal ivory transactions--Weights Index--at global, regional or national levels. Globally, activity was found to be rapidly increasing and at its highest level for 16 years, more than doubling from 2007 to 2011 and tripling from 1998 to 2011. Over 70% of the Transactions Index is from shipments of worked ivory weighing less than 10 kg and the rapid increase since 2007 is mainly due to increased consumption in China. Over 70% of the Weights Index is from shipments of raw ivory weighing at least 100 kg mainly moving from Central and East Africa to Southeast and East Asia. The results tie together recent findings on trends in poaching rates, declining populations and consumption and provide detailed evidence to inform international decision making on elephants.

Effect of fall-grazed sericea lespedeza (Lespedeza cuneata) on gastrointestinal nematode infections of growing goats

High prevalence of anthelmintic-resistant gastrointestinal nematodes (GIN) in goats has increased pressure to find effective, alternative non-synthetic control methods, one of which is adding forage of the high condensed tannin (CT) legume sericea lespedeza (SL; Lespedeza cuneata) to the animal's diet. Previous work has demonstrated good efficacy of dried SL (hay, pellets) against small ruminant GIN, but information is lacking on consumption of fresh SL, particularly during the late summer–autumn period in the southern USA when perennial warm-season grass pastures are often low in quality. A study was designed to determine the effects of autumn (September–November) consumption of fresh SL forage, grass pasture (predominantly bermudagrass, BG; Cynodon dactylon), or a combination of SL + BG forage by young goats [intact male Spanish kids, 9 months old (20.7 ± 1.1 kg), n = 10/treatment group] on their GIN infection status. Three forage paddocks (0.40 ha) were set up at the Fort Valley State University Agricultural Research Station (Fort Valley, GA) for an 8-week trial. The goats in each paddock were supplemented with a commercial feed pellet at 0.45 kg/head/d for the first 4 weeks of the trial, and 0.27 kg/head/d for the final 4 weeks. Forage samples taken at the start of the trial were analyzed for crude protein (CP), neutral detergent fiber (NDF), and acid detergent fiber (ADF) content, and a separate set of SL samples was analyzed for CT in leaves, stems, and whole plant using the benzyl mercaptan thiolysis method. Animal weights were taken at the start and end of the trial, and fecal and blood samples were collected weekly for determination of fecal egg counts (FEC) and packed cell volume (PCV), respectively. Adult GIN was recovered from the abomasum and small intestines of all goats at the end of the experiment for counting and speciation. The CP levels were highest for SL forage, intermediate for SL + BG, and lowest for BG forage samples, while NDF and ADF values were the opposite, with highest levels in BG and lowest in SL forage samples. Sericea lespedeza leaves had more CT than stems (16.0 g vs. 3.3 g/100 g dry weight), a slightly higher percentage of PDs (98% vs. 94%, respectively) and polymers of larger mean degrees of polymerization (42 vs. 18, respectively). There were no differences in average daily gain or blood PCV between the treatment groups, but SL goats had lower FEC (P < 0.05) than the BG or SL + BG forage goats throughout most of the trial. The SL + BG goats had lower FEC than the BG forage animals by the end of the trial (week 8, P < 0.05). The SL goats had lower numbers (P < 0.05) of male Haemonchus contortus and tended to have fewer female (P < 0.10) and total (P < 0.07) H. contortus compared with the BG goats. The predominant GIN in all the goats was Trichostrongylus colubriformis (73% of total GIN). As a low-input forage with activity against pathogenic GIN (H. contortus), SL has a potential to reduce producers’ dependence upon synthetic anthelmintics and also to fill the autumn ‘window’ in good-quality fresh forages for goat grazing in the southern USA.