Very large inverse problems in atmosphere and ocean modelling

For the very large nonlinear dynamical systems that arise in a wide range of physical, biological and environmental problems, the data needed to initialize a numerical forecasting model are seldom available. To generate accurate estimates of the expected states of the system, both current and future, the technique of ‘data assimilation’ is used to combine the numerical model predictions with observations of the system measured over time. Assimilation of data is an inverse problem that for very large-scale systems is generally ill-posed. In four-dimensional variational assimilation schemes, the dynamical model equations provide constraints that act to spread information into data sparse regions, enabling the state of the system to be reconstructed accurately. The mechanism for this is not well understood. Singular value decomposition techniques are applied here to the observability matrix of the system in order to analyse the critical features in this process. Simplified models are used to demonstrate how information is propagated from observed regions into unobserved areas. The impact of the size of the observational noise and the temporal position of the observations is examined. The best signal-to-noise ratio needed to extract the most information from the observations is estimated using Tikhonov regularization theory. Copyright © 2005 John Wiley & Sons, Ltd.

The cumulus-capped boundary layer. I: Modelling transports in the cloud layer

Scalar-flux budgets have been obtained from large-eddy simulations (LESs) of the cumulus-capped boundary layer. Parametrizations of the terms in the budgets are discussed, and two parametrizations for the transport term in the cloud layer are proposed. It is shown that these lead to two models for scalar transports by shallow cumulus convection. One is equivalent to the subsidence detrainment form of convective tendencies obtained from mass-flux parametrizations of cumulus convection. The second is a flux-gradient relationship that is similar in form to the non-local parametrizations of turbulent transports in the dry-convective boundary layer. Using the fluxes of liquid-water potential temperature and total water content from the LES, it is shown that both models are reasonable diagnostic relations between fluxes and the vertical gradients of the mean fields. The LESs used in this study are for steady-state convection and it is possible to treat the fluxes of conserved thermodynamic variables as independent, and ignore the effects of condensation. It is argued that a parametrization of cumulus transports in a model of the cumulus-capped boundary layer should also include an explicit representation of condensation. A simple parametrization of the liquid-water flux in terms of conserved variables is also derived.

Observations of the depth of ice particle evaporation beneath frontal cloud to improve NWP modelling

The evaporation (sublimation) of ice particles beneath frontal ice cloud can provide a significant source of diabatic cooling which can lead to enhanced slantwise descent below the frontal surface. The strength and vertical extent of the cooling play a role in determining the dynamic response of the atmosphere, and an adequate representation is required in numerical weather-prediction (NWP) models for accurate forecasts of frontal dynamics. In this paper, data from a vertically pointing 94 GHz radar are used to determine the characteristic depth-scale of ice particle sublimation beneath frontal ice cloud. A statistical comparison is made with equivalent data extracted from the NWP mesoscale model operational at the Met Office, defining the evaporation depth-scale as the distance for the ice water content to fall to 10% of its peak value in the cloud. The results show that the depth of the ice evaporation zone derived from observations is less than 1 km for 90% of the time. The model significantly overestimates the sublimation depth-scales by a factor of between two and three, and underestimates the local ice water content by a factor of between two and four. Consequently the results suggest the model significantly underestimates the strength of the evaporative cooling, with implications for the prediction of frontal dynamics. A number of reasons for the model discrepancy are suggested. A comparison with radiosonde relative humidity data suggests part of the overestimation in evaporation depth may be due to a high RH bias in the dry slot beneath the frontal cloud, but other possible reasons include poor vertical resolution and deficiencies in the evaporation rate or ice particle fall-speed parametrizations.

Modelling seasonally varying data: A case study for sudden infant death syndrome (SIDS)

Many time series are measured monthly, either as averages or totals, and such data often exhibit seasonal variability-the values of the series are consistently larger for some months of the year than for others. A typical series of this type is the number of deaths each month attributed to SIDS (Sudden Infant Death Syndrome). Seasonality can be modelled in a number of ways. This paper describes and discusses various methods for modelling seasonality in SIDS data, though much of the discussion is relevant to other seasonally varying data. There are two main approaches, either fitting a circular probability distribution to the data, or using regression-based techniques to model the mean seasonal behaviour. Both are discussed in this paper.

PRISM and ENES: a European approach to Earth system modelling

Europe's widely distributed climate modelling expertise, now organized in the European Network for Earth System Modelling (ENES), is both a strength and a challenge. Recognizing this, the European Union's Program for Integrated Earth System Modelling (PRISM) infrastructure project aims at designing a flexible and friendly user environment to assemble, run and post-process Earth System models. PRISM was started in December 2001 with a duration of three years. This paper presents the major stages of PRISM, including: (1) the definition and promotion of scientific and technical standards to increase component modularity; (2) the development of an end-to-end software environment (graphical user interface, coupling and I/O system, diagnostics, visualization) to launch, monitor and analyse complex Earth system models built around state-of-art community component models (atmosphere, ocean, atmospheric chemistry, ocean bio-chemistry, sea-ice, land-surface); and (3) testing and quality standards to ensure high-performance computing performance on a variety of platforms. PRISM is emerging as a core strategic software infrastructure for building the European research area in Earth system sciences. Copyright (c) 2005 John Wiley & Sons, Ltd.