Understanding the processes governing climate variability and change, climate predictability and the probability of extreme events

The purpose of Research Theme 4 (RT4) was to advance understanding of the basic science issues at the heart of the ENSEMBLES project, focusing on the key processes that govern climate variability and change, and that determine the predictability of climate. Particular attention was given to understanding linear and non-linear feedbacks that may lead to climate surprises,and to understanding the factors that govern the probability of extreme events. Improved understanding of these issues will contribute significantly to the quantification and reduction of uncertainty in seasonal to decadal predictions and projections of climate change. RT4 exploited the ENSEMBLES integrations (stream 1) performed in RT2A as well as undertaking its own experimentation to explore key processes within the climate system. It was working at the cutting edge of problems related to climate feedbacks, the interaction between climate variability and climate change � especially how climate change pertains to extreme events, and the predictability of the climate system on a range of time-scales. The statisticalmethodologies developed for extreme event analysis are new and state-of-the-art. The RT4-coordinated experiments, which have been conducted with six different atmospheric GCMs forced by common timeinvariant sea surface temperature (SST) and sea-ice fields (removing some sources of inter-model variability), are designed to help to understand model uncertainty (rather than scenario or initial condition uncertainty) in predictions of the response to greenhouse-gas-induced warming. RT4 links strongly with RT5 on the evaluation of the ENSEMBLES prediction system and feeds back its results to RT1 to guide improvements in the Earth system models and, through its research on predictability, to steer the development of methods for initialising the ensembles

The role of mean ocean salinity in climate

We describe numerical simulations designed to elucidate the role of mean ocean salinity in climate. Using a coupled atmosphere-ocean general circulation model, we study a 100-year sensitivity experiment in which the global-mean salinity is approximately doubled from its present observed value, by adding 35 psu everywhere in the ocean. The salinity increase produces a rapid global-mean sea-surface warming of C within a few years, caused by reduced vertical mixing associated with changes in cabbeling. The warming is followed by a gradual global-mean sea-surface cooling of C within a few decades, caused by an increase in the vertical (downward) component of the isopycnal diffusive heat flux. We find no evidence of impacts on the variability of the thermohaline circulation (THC) or El Niño/Southern Oscillation (ENSO). The mean strength of the Atlantic meridional overturning is reduced by 20% and the North Atlantic Deep Water penetrates less deeply. Nevertheless, our results dispute claims that higher salinities for the world ocean have profound consequences for the thermohaline circulation. In additional experiments with doubled atmospheric carbon dioxide, we find that the amplitude and spatial pattern of the global warming signal are modified in the hypersaline ocean. In particular, the equilibrated global-mean sea-surface temperature increase caused by doubling carbon dioxide is reduced by 10%. We infer the existence of a non-linear interaction between the climate responses to modified carbon dioxide and modified salinity.

Understanding African easterly waves: a moist singular vector approach

Moist singular vectors (MSV) have been applied successfully to predicting mid-latitude storms growing in association with latent heat of condensation. Tropical cyclone sensitivity has also been assessed. Extending this approach to more general tropical weather systems here, MSVs are evaluated for understanding and predicting African easterly waves, given the importance of moist processes in their development. First results, without initial moisture perturbations, suggest MSVs may be used advantageously. Perturbations bear similar structural and energy profiles to previous idealised non-linear studies and observations. Strong sensitivities prevail in the metrics and trajectories chosen, and benefits of initial moisture perturbations should be appraised. Copyright © 2009 Royal Meteorological Society

Effects of fluctuating daily surface fluxes on the time-mean oceanic circulation

The effect of fluctuating daily surface fluxes on the time-mean oceanic circulation is studied using an empirical flux model. The model produces fluctuating fluxes resulting from atmospheric variability and includes oceanic feedbacks on the fluxes. Numerical experiments were carried out by driving an ocean general circulation model with three different versions of the empirical model. It is found that fluctuating daily fluxes lead to an increase in the meridional overturning circulation (MOC) of the Atlantic of about 1 Sv and a decrease in the Antarctic circumpolar current (ACC) of about 32 Sv. The changes are approximately 7% of the MOC and 16% of the ACC obtained without fluctuating daily fluxes. The fluctuating fluxes change the intensity and the depth of vertical mixing. This, in turn, changes the density field and thus the circulation. Fluctuating buoyancy fluxes change the vertical mixing in a non-linear way: they tend to increase the convective mixing in mostly stable regions and to decrease the convective mixing in mostly unstable regions. The ACC changes are related to the enhanced mixing in the subtropical and the mid-latitude Southern Ocean and reduced mixing in the high-latitude Southern Ocean. The enhanced mixing is related to an increase in the frequency and the depth of convective events. As these events bring more dense water downward, the mixing changes lead to a reduction in meridional gradient of the depth-integrated density in the Southern Ocean and hence the strength of the ACC. The MOC changes are related to more subtle density changes. It is found that the vertical mixing in a latitudinal strip in the northern North Atlantic is more strongly enhanced due to fluctuating fluxes than the mixing in a latitudinal strip in the South Atlantic. This leads to an increase in the density difference between the two strips, which can be responsible for the increase in the Atlantic MOC.

Biogenic nitric oxide emissions from soils: impact on NOx and ozone over West Africa during AMMA (African Monsoon Multidisciplinary Analysis) - Modelling study

Nitrogen oxide biogenic emissions from soils are driven by soil and environmental parameters. The relationship between these parameters and NO fluxes is highly non linear. A new algorithm, based on a neural network calculation, is used to reproduce the NO biogenic emissions linked to precipitations in the Sahel on the 6 August 2006 during the AMMA campaign. This algorithm has been coupled in the surface scheme of a coupled chemistry dynamics model (MesoNH Chemistry) to estimate the impact of the NO emissions on NOx and O3 formation in the lower troposphere for this particular episode. Four different simulations on the same domain and at the same period are compared: one with anthropogenic emissions only, one with soil NO emissions from a static inventory, at low time and space resolution, one with NO emissions from neural network, and one with NO from neural network plus lightning NOx. The influence of NOx from lightning is limited to the upper troposphere. The NO emission from soils calculated with neural network responds to changes in soil moisture giving enhanced emissions over the wetted soil, as observed by aircraft measurements after the passing of a convective system. The subsequent enhancement of NOx and ozone is limited to the lowest layers of the atmosphere in modelling, whereas measurements show higher concentrations above 1000 m. The neural network algorithm, applied in the Sahel region for one particular day of the wet season, allows an immediate response of fluxes to environmental parameters, unlike static emission inventories. Stewart et al (2008) is a companion paper to this one which looks at NOx and ozone concentrations in the boundary layer as measured on a research aircraft, examines how they vary with respect to the soil moisture, as indicated by surface temperature anomalies, and deduces NOx fluxes. In this current paper the model-derived results are compared to the observations and calculated fluxes presented by Stewart et al (2008).

Effectiveness of landmark analysis for establishing locality in p2p networks

Locality to other nodes on a peer-to-peer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multi-dimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and non-linear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model with a typical power-law distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required.

Anharmonic force constant calculations

The relationship of the anharmonic force constants in curvilinear internal coordinates to the observed vibration-rotation spectrum of a molecule is reviewed. A simplified method of setting up the required non-linear coordinate transformations is described: this makes use of an / tensor, which is a straightforward generalization of the / matrix used in the customary description of harmonic force constant calculations. General formulae for the / tensor elements, in terms of the familiar L matrix elements, are presented. The use of non-linear symmetry coordinates and redundancies are described. Sample calculations on the water and ammonia molecules are reported.

Redundant coordinates in harmonic force-field calculations

Redundancy relations between vibrational coordinates may be linear (as for rectilinear coordinates used in deriving a G matrix), or non-linear (as for curvilinear coordinates used in formulating model force fields). It is shown that geometrically defined internal coordinates are necessarily curvilinear. Hence it is shown that linear force constants can occur in model force field calculations involving redundant coordinates, in disagreement with the recent proposal of Gussoni and Zerbi.

The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

Statistical downscaling of river flows

An extensive statistical ‘downscaling’ study is done to relate large-scale climate information from a general circulation model (GCM) to local-scale river flows in SW France for 51 gauging stations ranging from nival (snow-dominated) to pluvial (rainfall-dominated) river-systems. This study helps to select the appropriate statistical method at a given spatial and temporal scale to downscale hydrology for future climate change impact assessment of hydrological resources. The four proposed statistical downscaling models use large-scale predictors (derived from climate model outputs or reanalysis data) that characterize precipitation and evaporation processes in the hydrological cycle to estimate summary flow statistics. The four statistical models used are generalized linear (GLM) and additive (GAM) models, aggregated boosted trees (ABT) and multi-layer perceptron neural networks (ANN). These four models were each applied at two different spatial scales, namely at that of a single flow-gauging station (local downscaling) and that of a group of flow-gauging stations having the same hydrological behaviour (regional downscaling). For each statistical model and each spatial resolution, three temporal resolutions were considered, namely the daily mean flows, the summary statistics of fortnightly flows and a daily ‘integrated approach’. The results show that flow sensitivity to atmospheric factors is significantly different between nival and pluvial hydrological systems which are mainly influenced, respectively, by shortwave solar radiations and atmospheric temperature. The non-linear models (i.e. GAM, ABT and ANN) performed better than the linear GLM when simulating fortnightly flow percentiles. The aggregated boosted trees method showed higher and less variable R2 values to downscale the hydrological variability in both nival and pluvial regimes. Based on GCM cnrm-cm3 and scenarios A2 and A1B, future relative changes of fortnightly median flows were projected based on the regional downscaling approach. The results suggest a global decrease of flow in both pluvial and nival regimes, especially in spring, summer and autumn, whatever the considered scenario. The discussion considers the performance of each statistical method for downscaling flow at different spatial and temporal scales as well as the relationship between atmospheric processes and flow variability.

Estimation of the stoichiometry of volatile fatty acid production in the rumen of lactating cows

The purpose of this study was to improve the prediction of the quantity and type of Volatile Fatty Acids (VFA) produced from fermented substrate in the rumen of lactating cows. A model was formulated that describes the conversion of substrate (soluble carbohydrates, starch, hemi-cellulose, cellulose, and protein) into VFA (acetate, propionate, butyrate, and other VFA). Inputs to the model were observed rates of true rumen digestion of substrates, whereas outputs were observed molar proportions of VFA in rumen fluid. A literature survey generated data of 182 diets (96 roughage and 86 concentrate diets). Coefficient values that define the conversion of a specific substrate into VFA were estimated meta-analytically by regression of the model against observed VFA molar proportions using non-linear regression techniques. Coefficient estimates significantly differed for acetate and propionate production in particular, between different types of substrate and between roughage and concentrate diets. Deviations of fitted from observed VFA molar proportions could be attributed to random error for 100%. In addition to regression against observed data, simulation studies were performed to investigate the potential of the estimation method. Fitted coefficient estimates from simulated data sets appeared accurate, as well as fitted rates of VFA production, although the model accounted for only a small fraction (maximally 45%) of the variation in VFA molar proportions. The simulation results showed that the latter result was merely a consequence of the statistical analysis chosen and should not be interpreted as an indication of inaccuracy of coefficient estimates. Deviations between fitted and observed values corresponded to those obtained in simulations. (c) 2005 Elsevier Ltd. All rights reserved.

Modelling effects of prolonged conditioning on dormancy and germination of Striga hermonthica

The impact of environment on the germination biology of the parasite was studied in the laboratory with seeds conditioned at various water potentials, urea concentrations and at 17.5 to 37.5°C for up to 133 days. Maximum germination was observed at 20 to 25°C. Water stress and urea suppressed maximum germination. The final percentage germination response to period of conditioning showed a non-linear relationship and suggests the release of seeds from dormancy during the initial period and later on dormancy induction. Germination percentage increased with increase in conditioning period to a threshold and remained stable for variable periods followed by a decline with further extension of conditioning time. The decline in germination finally terminated in zero germination in most treatments before the end of experimentation. The investigated factors of temperature, water potential and urea showed clear effects on the expression of dormancy pattern of the parasite. The effects of water potential and urea were viewed as modifying a primary response of seeds to temperature during conditioning. The changes in germinability potential during conditioning were consistent with the hypothesis that dormancy periods are normally distributed within seed populations and that loss of primary dormancy precedes induction of secondary dormancy. Hence an additive mathematical model of loss of primary dormancy and induction of secondary as affected by environment was developed as: G = {[Φ-1 (Kp+ (po+pnN+pwW) (T-Tb) t)]-[Φ-1 (Ks+ ((swW+sa)+sorT)t)]}[Φ-1(aT2+bT+c+cwW)].

Describing long-term trends in precipitation using generalized additive models

With the current concern over climate change, descriptions of how rainfall patterns are changing over time can be useful. Observations of daily rainfall data over the last few decades provide information on these trends. Generalized linear models are typically used to model patterns in the occurrence and intensity of rainfall. These models describe rainfall patterns for an average year but are more limited when describing long-term trends, particularly when these are potentially non-linear. Generalized additive models (GAMS) provide a framework for modelling non-linear relationships by fitting smooth functions to the data. This paper describes how GAMS can extend the flexibility of models to describe seasonal patterns and long-term trends in the occurrence and intensity of daily rainfall using data from Mauritius from 1962 to 2001. Smoothed estimates from the models provide useful graphical descriptions of changing rainfall patterns over the last 40 years at this location. GAMS are particularly helpful when exploring non-linear relationships in the data. Care is needed to ensure the choice of smooth functions is appropriate for the data and modelling objectives. (c) 2008 Elsevier B.V. All rights reserved.

When are ant-attractant devices a worthwhile investment? Vicia faba extrafloral nectaries and Lasius niger ants

Most studies aiming to determine the beneficial effect of ants on plants simply consider the effects of the presence or exclusion of ants on plant yield. This approach is often inadequate, however, as ants interact with both non-tended herbivores and tended Homoptera. Moreover, the interaction with these groups of organisms is dependent on ant density, and these functional relationships are likely to be non-linear. A model is presented here that segregates plant herbivores into two categories depending on the sign of their numerical response to ants (myrmecophiles increase with ants, non-tended herbivores decline). The changes in these two components of herbivores with increasing ant density and the resulting implications for ant-plant mutualisms are considered. It emerges that a wide range of ant densities needs to be considered as the interaction sign (mutualism or parasitism) and strength is likely to change with ant density. The model is used to interpret the results of an experimental study that varied levels of Aphis fabae infestation and Lasius niger ant attendance on Vicia faba bean plants. Increasing ant density consistently reduced plant fitness and thus, in this location, the interaction between the ants and the plant can be considered parasitic. In the Vicia faba system, these costs of ants are unlikely to be offset by other beneficial agents (e.g., parasitoids), which also visit extrafloral nectaries.

GeneMCL in microarray analysis

Accurately and reliably identifying the actual number of clusters present with a dataset of gene expression profiles, when no additional information on cluster structure is available, is a problem addressed by few algorithms. GeneMCL transforms microarray analysis data into a graph consisting of nodes connected by edges, where the nodes represent genes, and the edges represent the similarity in expression of those genes, as given by a proximity measurement. This measurement is taken to be the Pearson correlation coefficient combined with a local non-linear rescaling step. The resulting graph is input to the Markov Cluster (MCL) algorithm, which is an elegant, deterministic, non-specific and scalable method, which models stochastic flow through the graph. The algorithm is inherently affected by any cluster structure present, and rapidly decomposes a graph into cohesive clusters. The potential of the GeneMCL algorithm is demonstrated with a 5730 gene subset (IGS) of the Van't Veer breast cancer database, for which the clusterings are shown to reflect underlying biological mechanisms. (c) 2005 Elsevier Ltd. All rights reserved.