A note on atmospheric predictability

Using the method of Lorenz (1982), we have estimated the predictability of a recent version of the European Center for Medium-Range Weather Forecasting (ECMWF) model using two different estimates of the initial error corresponding to 6- and 24-hr forecast errors, respectively. For a 6-hr forecast error of the extratropical 500-hPa geopotential height field, a potential increase in forecast skill by more than 3 d is suggested, indicating a further increase in predictability by another 1.5 d compared to the use of a 24-hr forecast error. This is due to a smaller initial error and to an initial error reduction resulting in a smaller averaged growth rate for the whole 7-d forecast. A similar assessment for the tropics using the wind vector fields at 850 and 250 hPa suggests a huge potential improvement with a 7-d forecast providing the same skill as a 1-d forecast now. A contributing factor to the increase in the estimate of predictability is the apparent slow increase of error during the early part of the forecast.

Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.

Data assimilation: From photon counts to Earth System forecasts

Data assimilation – the set of techniques whereby information from observing systems and models is combined optimally – is rapidly becoming prominent in endeavours to exploit Earth Observation for Earth sciences, including climate prediction. This paper explains the broad principles of data assimilation, outlining different approaches (optimal interpolation, three-dimensional and four-dimensional variational methods, the Kalman Filter), together with the approximations that are often necessary to make them practicable. After pointing out a variety of benefits of data assimilation, the paper then outlines some practical applications of the exploitation of Earth Observation by data assimilation in the areas of operational oceanography, chemical weather forecasting and carbon cycle modelling. Finally, some challenges for the future are noted.

The Convective Storm Initiation Project

The Convective Storm Initiation Project (CSIP) is an international project to understand precisely where, when, and how convective clouds form and develop into showers in the mainly maritime environment of southern England. A major aim of CSIP is to compare the results of the very high resolution Met Office weather forecasting model with detailed observations of the early stages of convective clouds and to use the newly gained understanding to improve the predictions of the model. A large array of ground-based instruments plus two instrumented aircraft, from the U.K. National Centre for Atmospheric Science (NCAS) and the German Institute for Meteorology and Climate Research (IMK), Karlsruhe, were deployed in southern England, over an area centered on the meteorological radars at Chilbolton, during the summers of 2004 and 2005. In addition to a variety of ground-based remote-sensing instruments, numerous rawin-sondes were released at one- to two-hourly intervals from six closely spaced sites. The Met Office weather radar network and Meteosat satellite imagery were used to provide context for the observations made by the instruments deployed during CSIP. This article presents an overview of the CSIP field campaign and examples from CSIP of the types of convective initiation phenomena that are typical in the United Kingdom. It shows the way in which certain kinds of observational data are able to reveal these phenomena and gives an explanation of how the analyses of data from the field campaign will be used in the development of an improved very high resolution NWP model for operational use.

Stochastic modelling of rainfall from satellite data

Satellite-based rainfall monitoring is widely used for climatological studies because of its full global coverage but it is also of great importance for operational purposes especially in areas such as Africa where there is a lack of ground-based rainfall data. Satellite rainfall estimates have enormous potential benefits as input to hydrological and agricultural models because of their real time availability, low cost and full spatial coverage. One issue that needs to be addressed is the uncertainty on these estimates. This is particularly important in assessing the likely errors on the output from non-linear models (rainfall-runoff or crop yield) which make use of the rainfall estimates, aggregated over an area, as input. Correct assessment of the uncertainty on the rainfall is non-trivial as it must take account of • the difference in spatial support of the satellite information and independent data used for calibration • uncertainties on the independent calibration data • the non-Gaussian distribution of rainfall amount • the spatial intermittency of rainfall • the spatial correlation of the rainfall field This paper describes a method for estimating the uncertainty on satellite-based rainfall values taking account of these factors. The method involves firstly a stochastic calibration which completely describes the probability of rainfall occurrence and the pdf of rainfall amount for a given satellite value, and secondly the generation of ensemble of rainfall fields based on the stochastic calibration but with the correct spatial correlation structure within each ensemble member. This is achieved by the use of geostatistical sequential simulation. The ensemble generated in this way may be used to estimate uncertainty at larger spatial scales. A case study of daily rainfall monitoring in the Gambia, west Africa for the purpose of crop yield forecasting is presented to illustrate the method.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Data assimilation for morphodynamic prediction and predictability

This paper gives an overview of the project Changing Coastlines: data assimilation for morphodynamic prediction and predictability. This project is investigating whether data assimilation could be used to improve coastal morphodynamic modeling. The concept of data assimilation is described, and the benefits that data assimilation could bring to coastal morphodynamic modeling are discussed. Application of data assimilation in a simple 1D morphodynamic model is presented. This shows that data assimilation can be used to improve the current state of the model bathymetry, and to tune the model parameter. We now intend to implement these ideas in a 2D morphodynamic model, for two study sites. The logistics of this are considered, including model design and implementation, and data requirement issues. We envisage that this work could provide a means for maintaining up-to-date information on coastal bathymetry, without the need for costly survey campaigns. This would be useful for a range of coastal management issues, including coastal flood forecasting.

Aerosol optical depths over North Africa: 2. Modeling and model validation

An operational dust forecasting model is developed by including the Met Office Hadley Centre climate model dust parameterization scheme, within a Met Office regional numerical weather prediction (NWP) model. The model includes parameterizations for dust uplift, dust transport, and dust deposition in six discrete size bins and provides diagnostics such as the aerosol optical depth. The results are compared against surface and satellite remote sensing measurements and against in situ measurements from the Facility for Atmospheric Airborne Measurements for a case study when a strong dust event was forecast. Comparisons are also performed against satellite and surface instrumentation for the entire month of August. The case study shows that this Saharan dust NWP model can provide very good guidance of dust events, as much as 42 h ahead. The analysis of monthly data suggests that the mean and variability in the dust model is also well represented.

Running Climate Models On The NERC Cluster Grid Using G-Rex

Compute grids are used widely in many areas of environmental science, but there has been limited uptake of grid computing by the climate modelling community, partly because the characteristics of many climate models make them difficult to use with popular grid middleware systems. In particular, climate models usually produce large volumes of output data, and running them usually involves complicated workflows implemented as shell scripts. For example, NEMO (Smith et al. 2008) is a state-of-the-art ocean model that is used currently for operational ocean forecasting in France, and will soon be used in the UK for both ocean forecasting and climate modelling. On a typical modern cluster, a particular one year global ocean simulation at 1-degree resolution takes about three hours when running on 40 processors, and produces roughly 20 GB of output as 50000 separate files. 50-year simulations are common, during which the model is resubmitted as a new job after each year. Running NEMO relies on a set of complicated shell scripts and command utilities for data pre-processing and post-processing prior to job resubmission. Grid Remote Execution (G-Rex) is a pure Java grid middleware system that allows scientific applications to be deployed as Web services on remote computer systems, and then launched and controlled as if they are running on the user's own computer. Although G-Rex is general purpose middleware it has two key features that make it particularly suitable for remote execution of climate models: (1) Output from the model is transferred back to the user while the run is in progress to prevent it from accumulating on the remote system and to allow the user to monitor the model; (2) The client component is a command-line program that can easily be incorporated into existing model work-flow scripts. G-Rex has a REST (Fielding, 2000) architectural style, which allows client programs to be very simple and lightweight and allows users to interact with model runs using only a basic HTTP client (such as a Web browser or the curl utility) if they wish. This design also allows for new client interfaces to be developed in other programming languages with relatively little effort. The G-Rex server is a standard Web application that runs inside a servlet container such as Apache Tomcat and is therefore easy to install and maintain by system administrators. G-Rex is employed as the middleware for the NERC1 Cluster Grid, a small grid of HPC2 clusters belonging to collaborating NERC research institutes. Currently the NEMO (Smith et al. 2008) and POLCOMS (Holt et al, 2008) ocean models are installed, and there are plans to install the Hadley Centre’s HadCM3 model for use in the decadal climate prediction project GCEP (Haines et al., 2008). The science projects involving NEMO on the Grid have a particular focus on data assimilation (Smith et al. 2008), a technique that involves constraining model simulations with observations. The POLCOMS model will play an important part in the GCOMS project (Holt et al, 2008), which aims to simulate the world’s coastal oceans. A typical use of G-Rex by a scientist to run a climate model on the NERC Cluster Grid proceeds as follows :(1) The scientist prepares input files on his or her local machine. (2) Using information provided by the Grid’s Ganglia3 monitoring system, the scientist selects an appropriate compute resource. (3) The scientist runs the relevant workflow script on his or her local machine. This is unmodified except that calls to run the model (e.g. with “mpirun”) are simply replaced with calls to "GRexRun" (4) The G-Rex middleware automatically handles the uploading of input files to the remote resource, and the downloading of output files back to the user, including their deletion from the remote system, during the run. (5) The scientist monitors the output files, using familiar analysis and visualization tools on his or her own local machine. G-Rex is well suited to climate modelling because it addresses many of the middleware usability issues that have led to limited uptake of grid computing by climate scientists. It is a lightweight, low-impact and easy-to-install solution that is currently designed for use in relatively small grids such as the NERC Cluster Grid. A current topic of research is the use of G-Rex as an easy-to-use front-end to larger-scale Grid resources such as the UK National Grid service.