Comparison of stochastic parametrization approaches in a single-column model

We discuss and test the potential usefulness of single-column models (SCMs) for the testing of stchastic physics schemes that have been proposed for use in general circulation models (GCMs). We argue that although single column tests cannot be definitive in exposing the full behaviour of a stochastic method in the full GCM, and although there are differences between SCM testing of deterministic and stochastic methods, nonetheless SCM testing remains a useful tool. It is necessary to consider an ensemble of SCM runs produced by the stochastic method. These can be usefully compared to deterministic ensembles describing initial condition uncertainty and also to combinations of these (with structural model changes) into poor man's ensembles. The proposed methodology is demonstrated using an SCM experiment recently developed by the GCSS community, simulating the transitions between active and suppressed periods of tropical convection.

Sensitivity of tropospheric forecasts to stratospheric initial conditions

A number of recent papers in the atmospheric science literature have suggested that a dynamical link exists between the stratosphere and troposphere. Numerical modelling studies have shown that the troposphere has a time-mean response to changes to the stratospheric climatological state. In this study the response of the troposphere to an imposed transient stratospheric change is examined. The study uses a high horizontal and vertical resolution numerical weather-prediction model. Experiments compare the tropospheric forecasts of two medium-range forecast ensembles which have identical tropospheric initial conditions and different stratospheric initial conditions. In three case studies described here, stratospheric initial conditions have a statistically significant impact on the tropospheric flow. The mechanism for this change involves, in its most basic step, a change to tropospheric synoptic-scale systems. A consistent change to the tropospheric synoptic-scale systems occurs in response to the stratospheric initial conditions. The aggregated impact of changes to individual synoptic systems maps strongly onto the structure of the Arctic Oscillation, particularly over the North Atlantic storm track. The relationship between the stratosphere and troposphere, while apparent in Arctic Oscillation diagnostics, does not occur on coherent, hemispheric scales.

Can the dynamical impact of the stratosphere on the troposphere be described by large-scale adjustment to the stratospheric PV distribution?

Recent numerical experiments have demonstrated that the state of the stratosphere has a dynamical impact on the state of the troposphere. To account for such an effect, a number of mechanisms have been proposed in the literature, all of which amount to a large-scale adjustment of the troposphere to potential vorticity (PV) anomalies in the stratosphere. This paper analyses whether a simple PV adjustment suffices to explain the actual dynamical response of the troposphere to the state of the stratosphere, the actual response being determined by ensembles of numerical experiments run with an atmospheric general-circulation model. For this purpose, a new PV inverter is developed. It is shown that the simple PV adjustment hypothesis is inadequate. PV anomalies in the stratosphere induce, by inversion, flow anomalies in the troposphere that do not coincide spatially with the tropospheric changes determined by the numerical experiments. Moreover, the tropospheric anomalies induced by PV inversion are on a larger scale than the changes found in the numerical experiments, which are linked to the Atlantic and Pacific storm-tracks. These findings imply that the impact of the stratospheric state on the troposphere is manifested through the impact on individual synoptic-scale systems and their self-organization in the storm-tracks. Changes in these weather systems in the troposphere are not merely synoptic-scale noise on a larger scale tropospheric response, but an integral part of the mechanism by which the state of the stratosphere impacts that of the troposphere.

Comparison of stochastic parameterisation approaches in a single-column model

We discuss and test the potential usefulness of single-column models (SCMs) for the testing of stochastic physics schemes that have been proposed for use in general circulation models (GCMs). We argue that although single column tests cannot be definitive in exposing the full behaviour of a stochastic method in the full GCM, and although there are differences between SCM testing of deterministic and stochastic methods, SCM testing remains a useful tool. It is necessary to consider an ensemble of SCM runs produced by the stochastic method. These can be usefully compared to deterministic ensembles describing initial condition uncertainty and also to combinations of these (with structural model changes) into poor man's ensembles. The proposed methodology is demonstrated using an SCM experiment recently developed by the GCSS (GEWEX Cloud System Study) community, simulating transitions between active and suppressed periods of tropical convection.

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

Understanding land-sea warming contrast in response to increasing greenhouse gases. Part I: Transient adjustment

Climate model simulations consistently show that surface temperature over land increases more rapidly than over sea in response to greenhouse gas forcing. The enhanced warming over land is not simply a transient effect caused by the land–sea contrast in heat capacities, since it is also present in equilibrium conditions. This paper elucidates the transient adjustment processes over time scales of days to weeks of the surface and tropospheric climate in response to a doubling of CO2 and to changes in sea surface temperature (SST), imposed separately and together, using ensembles of experiments with an atmospheric general circulation model. These adjustment processes can be grouped into three stages: immediate response of the troposphere and surface processes (day 1), fast adjustment of surface processes (days 2–5), and adjustment of the whole troposphere (days 6–20). Some land surface warming in response to doubled CO2 (with unchanged SSTs) occurs immediately because of increased downward longwave radiation. Increased CO2 also leads to reduced plant stomatal resistance and hence restricted evaporation, which increases land surface warming in the first day. Rapid reductions in cloud amount lead in the next few days to increased downward shortwave radiation and further warming, which spreads upward from the surface, and by day 5 the surface and tropospheric response is statistically consistent with the equilibrium value. Land surface warming in response to imposed SST change (with unchanged CO2) is slower. Tropospheric warming is advected inland from the sea, and over land it occurs at all levels together rather than spreading upward from the surface. The atmospheric response to prescribed SST change in about 20 days is statistically consistent with the equilibrium value, and the warming is largest in the upper troposphere over both land and sea. The land surface warming involves reduction of cloud cover and increased downward shortwave radiation, as in the experiment with CO2 change, but in this case it is due to the restriction of moisture supply to the land (indicated by reduced soil moisture), whereas in the CO2 forcing experiment it is due to restricted evaporation despite increased moisture supply (indicated by increased soil moisture). The warming over land in response to SST change is greater than over the sea and is the dominant contribution to the land–sea warming contrast under enhanced CO2 forcing.

Climate predictability in the second year

In this paper, the predictability of climate arising from ocean heat content (OHC) anomalies is investigated in the HadCM3 coupled atmosphere–ocean model. An ensemble of simulations of the twentieth century are used to provide initial conditions for a case study. The case study consists of two ensembles started from initial conditions with large differences in regional OHC in the North Atlantic, the Southern Ocean and parts of the West Pacific. Surface temperatures and precipitation are on average not predictable beyond seasonal time scales, but for certain initial conditions there may be longer predictability. It is shown that, for the case study examined here, some aspects of tropical precipitation, European surface temperatures and North Atlantic sea-level pressure are potentially predictable 2 years ahead. Predictability also exists in the other case studies, but the climate variables and regions, which are potentially predictable, differ. This work was done as part of the Grid for Coupled Ensemble Prediction (GCEP) eScience project.

Dynamic scaling of bred vectors in spatially extended chaotic systems

We unfold a profound relationship between the dynamics of finite-size perturbations in spatially extended chaotic systems and the universality class of Kardar-Parisi-Zhang (KPZ). We show how this relationship can be exploited to obtain a complete theoretical description of the bred vectors dynamics. The existence of characteristic length/time scales, the spatial extent of spatial correlations and how to time it, and the role of the breeding amplitude are all analyzed in the light of our theory. Implications to weather forecasting based on ensembles of initial conditions are also discussed.

Design and analysis of climate model experiments for the efficient estimation of anthropogenic signals

Presented herein is an experimental design that allows the effects of several radiative forcing factors on climate to be estimated as precisely as possible from a limited suite of atmosphere-only general circulation model (GCM) integrations. The forcings include the combined effect of observed changes in sea surface temperatures, sea ice extent, stratospheric (volcanic) aerosols, and solar output, plus the individual effects of several anthropogenic forcings. A single linear statistical model is used to estimate the forcing effects, each of which is represented by its global mean radiative forcing. The strong colinearity in time between the various anthropogenic forcings provides a technical problem that is overcome through the design of the experiment. This design uses every combination of anthropogenic forcing rather than having a few highly replicated ensembles, which is more commonly used in climate studies. Not only is this design highly efficient for a given number of integrations, but it also allows the estimation of (nonadditive) interactions between pairs of anthropogenic forcings. The simulated land surface air temperature changes since 1871 have been analyzed. The changes in natural and oceanic forcing, which itself contains some forcing from anthropogenic and natural influences, have the most influence. For the global mean, increasing greenhouse gases and the indirect aerosol effect had the largest anthropogenic effects. It was also found that an interaction between these two anthropogenic effects in the atmosphere-only GCM exists. This interaction is similar in magnitude to the individual effects of changing tropospheric and stratospheric ozone concentrations or to the direct (sulfate) aerosol effect. Various diagnostics are used to evaluate the fit of the statistical model. For the global mean, this shows that the land temperature response is proportional to the global mean radiative forcing, reinforcing the use of radiative forcing as a measure of climate change. The diagnostic tests also show that the linear model was suitable for analyses of land surface air temperature at each GCM grid point. Therefore, the linear model provides precise estimates of the space time signals for all forcing factors under consideration. For simulated 50-hPa temperatures, results show that tropospheric ozone increases have contributed to stratospheric cooling over the twentieth century almost as much as changes in well-mixed greenhouse gases.

Geostatistical analysis of rainfall

Rainfall can be modeled as a spatially correlated random field superimposed on a background mean value; therefore, geostatistical methods are appropriate for the analysis of rain gauge data. Nevertheless, there are certain typical features of these data that must be taken into account to produce useful results, including the generally non-Gaussian mixed distribution, the inhomogeneity and low density of observations, and the temporal and spatial variability of spatial correlation patterns. Many studies show that rigorous geostatistical analysis performs better than other available interpolation techniques for rain gauge data. Important elements are the use of climatological variograms and the appropriate treatment of rainy and nonrainy areas. Benefits of geostatistical analysis for rainfall include ease of estimating areal averages, estimation of uncertainties, and the possibility of using secondary information (e.g., topography). Geostatistical analysis also facilitates the generation of ensembles of rainfall fields that are consistent with a given set of observations, allowing for a more realistic exploration of errors and their propagation in downstream models, such as those used for agricultural or hydrological forecasting. This article provides a review of geostatistical methods used for kriging, exemplified where appropriate by daily rain gauge data from Ethiopia.

A model study of factors influencing projected changes in regional sea level over the 21st century

In addition to projected increases in global mean sea level over the 21st century, model simulations suggest there will also be changes in the regional distribution of sea level relative to the global mean. There is a considerable spread in the projected patterns of these changes by current models, as shown by the recent Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment (AR4). This spread has not reduced from that given by the Third Assessment models. Comparison with projections by ensembles of models based on a single structure supports an earlier suggestion that models of similar formulation give more similar patterns of sea level change. Analysing an AR4 ensemble of model projections under a business-as-usual scenario shows that steric changes (associated with subsurface ocean density changes) largely dominate the sea level pattern changes. The relative importance of subsurface temperature or salinity changes in contributing to this differs from region to region and, to an extent, from model-to-model. In general, thermosteric changes give the spatial variations in the Southern Ocean, halosteric changes dominate in the Arctic and strong compensation between thermosteric and halosteric changes characterises the Atlantic. The magnitude of sea level and component changes in the Atlantic appear to be linked to the amount of Atlantic meridional overturning circulation (MOC) weakening. When the MOC weakening is substantial, the Atlantic thermosteric patterns of change arise from a dominant role of ocean advective heat flux changes.

The impact of finer-resolution air-sea coupling on the intraseasonal oscillation of the Indian monsoon

The new HadKPP atmosphere–ocean coupled model is described and then used to determine the effects of sub-daily air–sea coupling and fine near-surface ocean vertical resolution on the representation of the Northern Hemisphere summer intra-seasonal oscillation. HadKPP comprises the Hadley Centre atmospheric model coupled to the K Profile Parameterization ocean-boundary-layer model. Four 30-member ensembles were performed that varied in oceanic vertical resolution between 1 m and 10 m and in coupling frequency between 3 h and 24 h. The 10 m, 24 h ensemble exhibited roughly 60% of the observed 30–50 day variability in sea-surface temperatures and rainfall and very weak northward propagation. Enhancing either only the vertical resolution or only the coupling frequency produced modest improvements in variability and only a standing intra-seasonal oscillation. Only the 1 m, 3 h configuration generated organized, northward-propagating convection similar to observations. Sub-daily surface forcing produced stronger upper-ocean temperature anomalies in quadrature with anomalous convection, which likely affected lower-atmospheric stability ahead of the convection, causing propagation. Well-resolved air–sea coupling did not improve the eastward propagation of the boreal summer intra-seasonal oscillation in this model. Upper-ocean vertical mixing and diurnal variability in coupled models must be improved to accurately resolve and simulate tropical sub-seasonal variability. In HadKPP, the mere presence of air–sea coupling was not sufficient to generate an intra-seasonal oscillation resembling observations.

Spatiotemporal behavior of the TIGGE medium-range ensemble forecasts

Using the recently-developed mean–variance of logarithms (MVL) diagram, together with the TIGGE archive of medium-range ensemble forecasts from nine different centres, an analysis is presented of the spatiotemporal dynamics of their perturbations, showing how the differences between models and perturbation techniques can explain the shape of their characteristic MVL curves. In particular, a divide is seen between ensembles based on singular vectors or empirical orthogonal functions, and those based on bred vector, Ensemble Transform with Rescaling or Ensemble Kalman Filter techniques. Consideration is also given to the use of the MVL diagram to compare the growth of perturbations within the ensemble with the growth of the forecast error, showing that there is a much closer correspondence for some models than others. Finally, the use of the MVL technique to assist in selecting models for inclusion in a multi-model ensemble is discussed, and an experiment suggested to test its potential in this context.

A simple, coherent framework for partitioning uncertainty in climate predictions

A simple and coherent framework for partitioning uncertainty in multi-model climate ensembles is presented. The analysis of variance (ANOVA) is used to decompose a measure of total variation additively into scenario uncertainty, model uncertainty and internal variability. This approach requires fewer assumptions than existing methods and can be easily used to quantify uncertainty related to model-scenario interaction - the contribution to model uncertainty arising from the variation across scenarios of model deviations from the ensemble mean. Uncertainty in global mean surface air temperature is quantified as a function of lead time for a subset of the Coupled Model Intercomparison Project phase 3 ensemble and results largely agree with those published by other authors: scenario uncertainty dominates beyond 2050 and internal variability remains approximately constant over the 21st century. Both elements of model uncertainty, due to scenario-independent and scenario-dependent deviations from the ensemble mean, are found to increase with time. Estimates of model deviations that arise as by-products of the framework reveal significant differences between models that could lead to a deeper understanding of the sources of uncertainty in multi-model ensembles. For example, three models are shown diverging pattern over the 21st century, while another model exhibits an unusually large variation among its scenario-dependent deviations.

Efficient non-linear data assimilation in geophysical fluid dynamics

New ways of combining observations with numerical models are discussed in which the size of the state space can be very large, and the model can be highly nonlinear. Also the observations of the system can be related to the model variables in highly nonlinear ways, making this data-assimilation (or inverse) problem highly nonlinear. First we discuss the connection between data assimilation and inverse problems, including regularization. We explore the choice of proposal density in a Particle Filter and show how the ’curse of dimensionality’ might be beaten. In the standard Particle Filter ensembles of model runs are propagated forward in time until observations are encountered, rendering it a pure Monte-Carlo method. In large-dimensional systems this is very inefficient and very large numbers of model runs are needed to solve the data-assimilation problem realistically. In our approach we steer all model runs towards the observations resulting in a much more efficient method. By further ’ensuring almost equal weight’ we avoid performing model runs that are useless in the end. Results are shown for the 40 and 1000 dimensional Lorenz 1995 model.