Precipitation is highly variable in space and time; hence, rain gauge time series generally exhibit additional random small-scale variability compared to area averages. Therefore, differences between daily precipitation statistics simulated by climate models and gauge observations are generally not only caused by model biases, but also by the corresponding scale gap. Classical bias correction methods, in general, cannot bridge this gap; they do not account for small-scale random variability and may produce artifacts. Here, stochastic model output statistics is proposed as a bias correction framework to explicitly account for random small-scale variability. Daily precipitation simulated by a regional climate model (RCM) is employed to predict the probability distribution of local precipitation. The pairwise correspondence between predictor and predictand required for calibration is ensured by driving the RCM with perfect boundary conditions. Wet day probabilities are described by a logistic regression, and precipitation intensities are described by a mixture model consisting of a gamma distribution for moderate precipitation and a generalized Pareto distribution for extremes. The dependence of the model parameters on simulated precipitation is modeled by a vector generalized linear model. The proposed model effectively corrects systematic biases and correctly represents local-scale random variability for most gauges. Additionally, a simplified model is considered that disregards the separate tail model. This computationally efficient model proves to be a feasible alternative for precipitation up to moderately extreme intensities. The approach sets a new framework for bias correction that combines the advantages of weather generators and RCMs.

An idealized fluid model of convective-scale numerical weather prediction, intended for use in inexpensive data assimilation experiments, is described here and its distinctive dynamics are investigated. The model modifies the rotating shallow water equations to include some simplified dynamics of cumulus convection and associated precipitation, extending and improving the model of Würsch and Craig. Changes to this original model are the removal of ad hoc diffusive terms and the addition of Coriolis rotation terms, leading to a so-called 1.5-dimensional model. Despite the non-trivial modifications to the parent equations, it is shown that this shallow water type model remains hyperbolic in character and can be integrated accordingly using a discontinuous Galerkin finite element method for nonconservative hyperbolic systems of partial differential equations. Combined with methods to ensure well-balancedness and nonnegativity, the resulting numerical solver is novel, efficient and robust. Classical numerical experiments in the shallow water theory, such as the Rossby geostrophic adjustment and flow over topography, are reproduced for the standard shallow water model and used to highlight the modified dynamics of the new model. In particular, it exhibits important aspects of convective-scale dynamics relating to the disruption of large-scale balance and is able to simulate other features related to convecting and precipitating weather systems. Our analysis here and preliminary results suggest that the model is well suited for efficiently and robustly investigating data assimilation schemes in an idealized 'convectivescale' forecast assimilation framework.

The goals of this paper are threefold, namely to: (i) define the rarely used concept of flood-excess volume (FEV) as the flood volume above a chosen river-level threshold of flooding; (ii) show how to estimate FEV for the Boxing Day Flood of 2015 of the River Aire; and, (iii) analyse the use of FEV in evaluating a hypothetical flood-alleviation scheme (FASII + ) for the River Aire, largely based on the actual Leeds' Flood-Alleviation Scheme II (FASII). Techniques employed are data analysis combined with general river hydraulics and estimation using bounds. By expressing FEV equivalently in terms of a square lake with a certain side-length and depth (of one to a few metres), with the same capacity, it becomes easy to visualise its dimensions and compare it with those of the river valley considered.FEV analysis provides cost-effective estimates of new flood-mitigation measures, either prior to or in tandem with more detailed hydrodynamic numerical and laboratory modelling of river flows. It is used to illuminate five different scenarios of flood mitigation for our new FASII + , with each scenario involving a combination of higher (than existing) flood-defence walls and enhanced flood-plain storage sites both closer to and further upstream of Leeds. An integral part of this approach is a cost-benefit analysis. For policy makers, a further advantage of FEV is that it can be used to analyse and choose between flood-mitigation measures in a direct and visual manner, thereby offering better prospects of being understood by a wide, particularly non-technical, audience and city-council planning departments.

This paper explores an analytic, geometric approach to finding optimal routes for commercial formation flight. A weighted extension of the classical Fermat point problem is used to develop a scalable methodology for the formation routing problem, enabling quick calculation of formation costs. This rapid evaluation allows the large-scale fleet assignment problem to be solved via a mixed integer linear program in reasonable time. Weighting schemes for aircraft performance characteristics are first introduced and then extended to allow for differential rates of fuel burn. Finally, a case study for 210 transatlantic flight routes is presented, with results showing possible average fuel-burn savings against solo flight of around 8.7% for formations of two and 13.1% for formations of up to three.

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