Ensemble forecasts of a flood-producing storm: comparison of the influence of model-state perturbations and parameter modifications

High-resolution ensemble simulations (Δx = 1 km) are performed with the Met Office Unified Model for the Boscastle (Cornwall, UK) flash-flooding event of 16 August 2004. Forecast uncertainties arising from imperfections in the forecast model are analysed by comparing the simulation results produced by two types of perturbation strategy. Motivated by the meteorology of the event, one type of perturbation alters relevant physics choices or parameter settings in the model's parametrization schemes. The other type of perturbation is designed to account for representativity error in the boundary-layer parametrization. It makes direct changes to the model state and provides a lower bound against which to judge the spread produced by other uncertainties. The Boscastle has genuine skill at scales of approximately 60 km and an ensemble spread which can be estimated to within ∼ 10% with only eight members. Differences between the model-state perturbation and physics modification strategies are discussed, the former being more important for triggering and the latter for subsequent cell development, including the average internal structure of convective cells. Despite such differences, the spread in rainfall evaluated at skilful scales is shown to be only weakly sensitive to the perturbation strategy. This suggests that relatively simple strategies for treating model uncertainty may be sufficient for practical, convective-scale ensemble forecasting.

Separating the dynamical effects of climate change and ozone depletion. Part II: Southern Hemisphere troposphere

The separate effects of ozone depleting substances (ODSs) and greenhouse gases (GHGs) on forcing circulation changes in the Southern Hemisphere extratropical troposphere are investigated using a version of the Canadian Middle Atmosphere Model (CMAM) that is coupled to an ocean. Circulation-related diagnostics include zonal wind, tropopause pressure, Hadley cell width, jet location, annular mode index, precipitation, wave drag, and eddy fluxes of momentum and heat. As expected, the tropospheric response to the ODS forcing occurs primarily in austral summer, with past (1960-99) and future (2000-99) trends of opposite sign, while the GHG forcing produces more seasonally uniform trends with the same sign in the past and future. In summer the ODS forcing dominates past trends in all diagnostics, while the two forcings contribute nearly equally but oppositely to future trends. The ODS forcing produces a past surface temperature response consisting of cooling over eastern Antarctica, and is the dominant driver of past summertime surface temperature changes when the model is constrained by observed sea surface temperatures. For all diagnostics, the response to the ODS and GHG forcings is additive: that is, the linear trend computed from the simulations using the combined forcings equals (within statistical uncertainty) the sum of the linear trends from the simulations using the two separate forcings. Space time spectra of eddy fluxes and the spatial distribution of transient wave drag are examined to assess the viability of several recently proposed mechanisms for the observed poleward shift in the tropospheric jet.

European plant phenology and climate as seen in a 20-year AVHRR land-surface parameter dataset

Vegetation distribution and state have been measured since 1981 by the AVHRR (Advanced Very High Resolution Radiometer) instrument through satellite remote sensing. In this study a correction method is applied to the Pathfinder NDVI (Normalized Difference Vegetation Index) data to create a continuous European vegetation phenology dataset of a 10-day temporal and 0.1° spatial resolution; additionally, land surface parameters for use in biosphere–atmosphere modelling are derived. The analysis of time-series from this dataset reveals, for the years 1982–2001, strong seasonal and interannual variability in European land surface vegetation state. Phenological metrics indicate a late and short growing season for the years 1985–1987, in addition to early and prolonged activity in the years 1989, 1990, 1994 and 1995. These variations are in close agreement with findings from phenological measurements at the surface; spring phenology is also shown to correlate particularly well with anomalies in winter temperature and winter North Atlantic Oscillation (NAO) index. Nevertheless, phenological metrics, which display considerable regional differences, could only be determined for vegetation with a seasonal behaviour. Trends in the phenological phases reveal a general shift to earlier (−0.54 days year−1) and prolonged (0.96 days year−1) growing periods which are statistically significant, especially for central Europe.

Downscaling from GCM precipitation: a benchmark for dynamical and statistical downscaling methods

A precipitation downscaling method is presented using precipitation from a general circulation model (GCM) as predictor. The method extends a previous method from monthly to daily temporal resolution. The simplest form of the method corrects for biases in wet-day frequency and intensity. A more sophisticated variant also takes account of flow-dependent biases in the GCM. The method is flexible and simple to implement. It is proposed here as a correction of GCM output for applications where sophisticated methods are not available, or as a benchmark for the evaluation of other downscaling methods. Applied to output from reanalyses (ECMWF, NCEP) in the region of the European Alps, the method is capable of reducing large biases in the precipitation frequency distribution, even for high quantiles. The two variants exhibit similar performances, but the ideal choice of method can depend on the GCM/reanalysis and it is recommended to test the methods in each case. Limitations of the method are found in small areas with unresolved topographic detail that influence higher-order statistics (e.g. high quantiles). When used as benchmark for three regional climate models (RCMs), the corrected reanalysis and the RCMs perform similarly in many regions, but the added value of the latter is evident for high quantiles in some small regions.

Statistical decadal predictions for sea surface temperatures: a benchmark for dynamical GCM predictions

Accurate decadal climate predictions could be used to inform adaptation actions to a changing climate. The skill of such predictions from initialised dynamical global climate models (GCMs) may be assessed by comparing with predictions from statistical models which are based solely on historical observations. This paper presents two benchmark statistical models for predicting both the radiatively forced trend and internal variability of annual mean sea surface temperatures (SSTs) on a decadal timescale based on the gridded observation data set HadISST. For both statistical models, the trend related to radiative forcing is modelled using a linear regression of SST time series at each grid box on the time series of equivalent global mean atmospheric CO2 concentration. The residual internal variability is then modelled by (1) a first-order autoregressive model (AR1) and (2) a constructed analogue model (CA). From the verification of 46 retrospective forecasts with start years from 1960 to 2005, the correlation coefficient for anomaly forecasts using trend with AR1 is greater than 0.7 over parts of extra-tropical North Atlantic, the Indian Ocean and western Pacific. This is primarily related to the prediction of the forced trend. More importantly, both CA and AR1 give skillful predictions of the internal variability of SSTs in the subpolar gyre region over the far North Atlantic for lead time of 2 to 5 years, with correlation coefficients greater than 0.5. For the subpolar gyre and parts of the South Atlantic, CA is superior to AR1 for lead time of 6 to 9 years. These statistical forecasts are also compared with ensemble mean retrospective forecasts by DePreSys, an initialised GCM. DePreSys is found to outperform the statistical models over large parts of North Atlantic for lead times of 2 to 5 years and 6 to 9 years, however trend with AR1 is generally superior to DePreSys in the North Atlantic Current region, while trend with CA is superior to DePreSys in parts of South Atlantic for lead time of 6 to 9 years. These findings encourage further development of benchmark statistical decadal prediction models, and methods to combine different predictions.

Bayesian parameter estimation for latent Markov random fields and social networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.

Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

The importance of friction in mountain wave drag amplification by Scorer parameter resonance

A mechanism for amplification of mountain waves, and their associated drag, by parametric resonance is investigated using linear theory and numerical simulations. This mechanism, which is active when the Scorer parameter oscillates with height, was recently classified by previous authors as intrinsically nonlinear. Here it is shown that, if friction is included in the simplest possible form as a Rayleigh damping, and the solution to the Taylor-Goldstein equation is expanded in a power series of the amplitude of the Scorer parameter oscillation, linear theory can replicate the resonant amplification produced by numerical simulations with some accuracy. The drag is significantly altered by resonance in the vicinity of n/l_0 = 2, where l_0 is the unperturbed value of the Scorer parameter and n is the wave number of its oscillation. Depending on the phase of this oscillation, the drag may be substantially amplified or attenuated relative to its non-resonant value, displaying either single maxima or minima, or double extrema near n/l_0 = 2. Both non-hydrostatic effects and friction tend to reduce the magnitude of the drag extrema. However, in exactly inviscid conditions, the single drag maximum and minimum are suppressed. As in the atmosphere friction is often small but non-zero outside the boundary layer, modelling of the drag amplification mechanism addressed here should be quite sensitive to the type of turbulence closure employed in numerical models, or to computational dissipation in nominally inviscid simulations.

Separating the dynamical effects of climate change and ozone depletion. Part I: Southern Hemisphere stratosphere

A version of the Canadian Middle Atmosphere Model that is coupled to an ocean is used to investigate the separate effects of climate change and ozone depletion on the dynamics of the Southern Hemisphere (SH) stratosphere. This is achieved by performing three sets of simulations extending from 1960 to 2099: 1) greenhouse gases (GHGs) fixed at 1960 levels and ozone depleting substances (ODSs) varying in time, 2) ODSs fixed at 1960 levels and GHGs varying in time, and 3) both GHGs and ODSs varying in time. The response of various dynamical quantities to theGHGand ODS forcings is shown to be additive; that is, trends computed from the sum of the first two simulations are equal to trends from the third. Additivity is shown to hold for the zonal mean zonal wind and temperature, the mass flux into and out of the stratosphere, and the latitudinally averaged wave drag in SH spring and summer, as well as for final warming dates. Ozone depletion and recovery causes seasonal changes in lower-stratosphere mass flux, with reduced polar downwelling in the past followed by increased downwelling in the future in SH spring, and the reverse in SH summer. These seasonal changes are attributed to changes in wave drag caused by ozone-induced changes in the zonal mean zonal winds. Climate change, on the other hand, causes a steady decrease in wave drag during SH spring, which delays the breakdown of the vortex, resulting in increased wave drag in summer

Dynamical and cloud-radiation feedbacks in El Niño and greenhouse warming

An El Niño-like steady response is found in a greenhouse warming simulation resulting from coupled ocean-atmosphere dynamical feedbacks similar to those producing the present-day El Niños. There is a strong negative cloud-radiation feedback on the sea surface temperature (SST) anomaly associated with this enhanced eastern equatorial Pacific warm pattern. However, this negative feedback is overwhelmed by the positive dynamical feedbacks and cannot diminish the sensitivity of the tropical SST to enhanced greenhouse gas concentrations. The enhanced eastern-Pacific warming in the coupled ocean-atmosphere system suggests that coupled dynamics can strengthen this sensitivity.

An experiment in the Assimilation of Data in Dynamical Analysis

A system for continuous data assimilation is presented and discussed. To simulate the dynamical development a channel version of a balanced barotropic model is used and geopotential (height) data are assimilated into the models computations as data become available. In the first experiment the updating is performed every 24th, 12th and 6th hours with a given network. The stations are distributed at random in 4 groups in order to simulate 4 areas with different density of stations. Optimum interpolation is performed for the difference between the forecast and the valid observations. The RMS-error of the analyses is reduced in time, and the error being smaller the more frequent the updating is performed. The updating every 6th hour yields an error in the analysis less than the RMS-error of the observation. In a second experiment the updating is performed by data from a moving satellite with a side-scan capability of about 15°. If the satellite data are analysed at every time step before they are introduced into the system the error of the analysis is reduced to a value below the RMS-error of the observation already after 24 hours and yields as a whole a better result than updating from a fixed network. If the satellite data are introduced without any modification the error of the analysis is reduced much slower and it takes about 4 days to reach a comparable result to the one where the data have been analysed.