A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

The impact of climate change on daily precipitation statistics for Jordan and Israel

A regional climate model is used to investigate changes in Israel and Jordan precipitation at the end of the 21st century on daily to monthly timescales. The model predicts that this region will get significantly drier at the peak of the rainy season, reflecting a reduction in both the frequency and duration of rainy events. These changes may be associated with a reduction in the strength of the Mediterranean storm track

A singular vector perspective of 4D-Var: Filtering and interpolation

Four-dimensional variational data assimilation (4D-Var) combines the information from a time sequence of observations with the model dynamics and a background state to produce an analysis. In this paper, a new mathematical insight into the behaviour of 4D-Var is gained from an extension of concepts that are used to assess the qualitative information content of observations in satellite retrievals. It is shown that the 4D-Var analysis increments can be written as a linear combination of the singular vectors of a matrix which is a function of both the observational and the forecast model systems. This formulation is used to consider the filtering and interpolating aspects of 4D-Var using idealized case-studies based on a simple model of baroclinic instability. The results of the 4D-Var case-studies exhibit the reconstruction of the state in unobserved regions as a consequence of the interpolation of observations through time. The results also exhibit the filtering of components with small spatial scales that correspond to noise, and the filtering of structures in unobserved regions. The singular vector perspective gives a very clear view of this filtering and interpolating by the 4D-Var algorithm and shows that the appropriate specification of the a priori statistics is vital to extract the largest possible amount of useful information from the observations. Copyright © 2005 Royal Meteorological Society

Mean flow and turbulence statistics over groups of urban-like cubical obstacles

Direct numerical simulations of turbulent flow over regular arrays of urban-like, cubical obstacles are reported. Results are analysed in terms of a formal spatial averaging procedure to enable interpretation of the flow within the arrays as a canopy flow, and of the flow above as a rough wall boundary layer. Spatial averages of the mean velocity, turbulent stresses and pressure drag are computed. The statistics compare very well with data from wind-tunnel experiments. Within the arrays the time-averaged flow structure gives rise to significant 'dispersive stress' whereas above the Reynolds stress dominates. The mean flow structure and turbulence statistics depend significantly on the layout of the cubes. Unsteady effects are important, especially in the lower canopy layer where turbulent fluctuations dominate over the mean flow.

Electronic marking of statistics assessments for bioscience students

We describe the main features of a program written to perform electronic marking of quantitative or simple text questions. One of the main benefits is that it can check answers for being consistent with earlier errors, so can cope with a range of numerical questions. We summarise our experience of using it in a statistics course taught to 200 bioscience students.

The best of both worlds: Producing national statistics using participatory methods

This paper presents our experience with combining statistical principles and participatory methods to generate national statistics. The methodology was developed in Malawi during 1999–2002. We demonstrate that if PRA is combined with statistical principles (including probability-based sampling and standardization), it can produce total population statistics and estimates of the proportion of households with certain characteristics (e.g., poverty). It can also provide quantitative data on complex issues of national importance such as poverty targeting. This approach is distinct from previous PRA-based approaches, which generate numbers at community level but only provide qualitative information at national level.

Performance statistics of a head-operated force-reflecting rehabilitation robot system

Researchers in the rehabilitation engineering community have been designing and developing a variety of passive/active devices to help persons with limited upper extremity function to perform essential daily manipulations. Devices range from low-end tools such as head/mouth sticks to sophisticated robots using vision and speech input. While almost all of the high-end equipment developed to date relies on visual feedback alone to guide the user providing no tactile or proprioceptive cues, the “low-tech” head/mouth sticks deliver better “feel” because of the inherent force feedback through physical contact with the user's body. However, the disadvantage of a conventional head/mouth stick is that it can only function in a limited workspace and the performance is limited by the user's strength. It therefore seems reasonable to attempt to develop a system that exploits the advantages of the two approaches: the power and flexibility of robotic systems with the sensory feedback of a headstick. The system presented in this paper reflects the design philosophy stated above. This system contains a pair of master-slave robots with the master being operated by the user's head and the slave acting as a telestick. Described in this paper are the design, control strategies, implementation and performance evaluation of the head-controlled force-reflecting telestick system.

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.

A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, Pf. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.