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.

Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

Bond graph models of DC-DC converters operating in both CCM and DCM

In this paper, Bond Graphs are employed to develop a novel mathematical model of conventional switched-mode DC-DC converters valid for both continuous and discontinuous conduction modes. A unique causality bond graph model of hybrid models is suggested with the operation of the switch and the diode to be represented by a Modulated Transformer with a binary input and a resistor with fixed conductance causality. The operation of the diode is controlled using an if-then function within the model. The extracted hybrid model is implemented on a Boost and Buck converter with their operations to change from CCM to DCM and to return to CCM. The vector fields of the models show validity in a wide operation area and comparison with the simulation of the converters using PSPICE reveals high accuracy of the proposed model, with the Normalised Root Means Square Error and the Maximum Absolute Error remaining adequately low. The model is also experimentally tested on a Buck topology.

Proof of concept of automated mapping of weeds in arable fields

The project investigated whether it would be possible to remove the main technical hindrance to precision application of herbicides to arable crops in the UK, namely creating geo-referenced weed maps for each field. The ultimate goal is an information system so that agronomists and farmers can plan precision weed control and create spraying maps. The project focussed on black-grass in wheat, but research was also carried out on barley and beans and on wild-oats, barren brome, rye-grass, cleavers and thistles which form stable patches in arable fields. Farmers may also make special efforts to control them. Using cameras mounted on farm machinery, the project explored the feasibility of automating the process of mapping black-grass in fields. Geo-referenced images were captured from June to December 2009, using sprayers, a tractor, combine harvesters and on foot. Cameras were mounted on the sprayer boom, on windows or on top of tractor and combine cabs and images were captured with a range of vibration levels and at speeds up to 20 km h-1. For acceptability to farmers, it was important that every image containing black-grass was classified as containing black-grass; false negatives are highly undesirable. The software algorithms recorded no false negatives in sample images analysed to date, although some black-grass heads were unclassified and there were also false positives. The density of black-grass heads per unit area estimated by machine vision increased as a linear function of the actual density with a mean detection rate of 47% of black-grass heads in sample images at T3 within a density range of 13 to 1230 heads m-2. A final part of the project was to create geo-referenced weed maps using software written in previous HGCA-funded projects and two examples show that geo-location by machine vision compares well with manually-mapped weed patches. The consortium therefore demonstrated for the first time the feasibility of using a GPS-linked computer-controlled camera system mounted on farm machinery (tractor, sprayer or combine) to geo-reference black-grass in winter wheat between black-grass head emergence and seed shedding.