Reduced space optimal interpolation of daily rain gauge precipitation in Switzerland

The coarse spacing of automatic rain gauges complicates near-real- time spatial analyses of precipitation. We test the possibility of improving such analyses by considering, in addition to the in situ measurements, the spatial covariance structure inferred from past observations with a denser network. To this end, a statistical reconstruction technique, reduced space optimal interpolation (RSOI), is applied over Switzerland, a region of complex topography. RSOI consists of two main parts. First, principal component analysis (PCA) is applied to obtain a reduced space representation of gridded high- resolution precipitation fields available for a multiyear calibration period in the past. Second, sparse real-time rain gauge observations are used to estimate the principal component scores and to reconstruct the precipitation field. In this way, climatological information at higher resolution than the near-real-time measurements is incorporated into the spatial analysis. PCA is found to efficiently reduce the dimensionality of the calibration fields, and RSOI is successful despite the difficulties associated with the statistical distribution of daily precipitation (skewness, dry days). Examples and a systematic evaluation show substantial added value over a simple interpolation technique that uses near-real-time observations only. The benefit is particularly strong for larger- scale precipitation and prominent topographic effects. Small-scale precipitation features are reconstructed at a skill comparable to that of the simple technique. Stratifying the reconstruction method by the types of weather type classifications yields little added skill. Apart from application in near real time, RSOI may also be valuable for enhancing instrumental precipitation analyses for the historic past when direct observations were sparse.

Characterising North Atlantic weather patterns for climate-optimal aircraft routing

Daily weather patterns over the North Atlantic are classified into relevant types: typical weather patterns that may characterize the range of climate impacts from aviation in this region, for both summer and winter. The motivation is to provide a set of weather types to facilitate an investigation of climate-optimal aircraft routing of trans-Atlantic flights (minimizing the climate impact on a flight-by-flight basis). Using the New York to London route as an example, the time-optimal route times are shown to vary by over 60 min, to take advantage of strong tailwinds or avoid headwinds, and for eastbound routes latitude correlates well with the latitude of the jet stream. The weather patterns are classified by their similarity to the North Atlantic Oscillation and East Atlantic teleconnection patterns. For winter, five types are defined; in summer, when there is less variation in jet latitude, only three types are defined. The types can be characterized by the jet strength and position, and therefore the location of the time-optimal routes varies by type. Simple proxies for the climate impact of carbon dioxide, ozone, water vapour and contrails are defined, which depend on parameters such as the route time, latitude and season, the time spent flying in the stratosphere, and the distance over which the air is supersaturated with respect to ice. These proxies are then shown to vary between weather types and between eastbound and westbound routes.

Semi-dwarfing (Rht-B1b) improves nitrogen-use efficiency in wheat, but not at economically optimal levels of nitrogen availability

A UK field experiment compared a complete factorial combination of three backgrounds (cvs Mercia, Maris Huntsman and Maris Widgeon), three alleles at the Rht-B1 locus as Near Isogenic Lines (NILs: rht-B1a (tall), Rht-B1b (semi-dwarf), Rht-B1c (severe dwarf)) and four nitrogen (N) fertilizer application rates (0, 100, 200 and 350 kg N/ha). Linear+exponential functions were fitted to grain yield (GY) and nitrogen-use efficiency (NUE; GY/available N) responses to N rate. Averaged over N rate and background Rht-B1b conferred significantly (P<0.05) greater GY, NUE, N uptake efficiency (NUpE; N in above ground crop / available N) and N utilization efficiency (NUtEg; GY / N in above ground crop) compared with rht-B1a and Rht-B1c. However the economically optimal N rate (Nopt) for N:grain price ratios of 3.5:1 to 10:1 were also greater for Rht-B1b, and because NUE, NUpE and NUtE all declined with N rate, Rht-Blb failed to increase NUE or its components at Nopt. The adoption of semi-dwarf lines in temperate and humid regions, and the greater N rates that such adoption justifies economically, greatly increases land-use efficiency, but not necessarily, NUE.

Optimal hedging with higher moments

This study proposes a utility-based framework for the determination of optimal hedge ratios (OHRs) that can allow for the impact of higher moments on hedging decisions. We examine the entire hyperbolic absolute risk aversion family of utilities which include quadratic, logarithmic, power, and exponential utility functions. We find that for both moderate and large spot (commodity) exposures, the performance of out-of-sample hedges constructed allowing for nonzero higher moments is better than the performance of the simpler OLS hedge ratio. The picture is, however, not uniform throughout our seven spot commodities as there is one instance (cotton) for which the modeling of higher moments decreases welfare out-of-sample relative to the simpler OLS. We support our empirical findings by a theoretical analysis of optimal hedging decisions and we uncover a novel link between OHRs and the minimax hedge ratio, that is the ratio which minimizes the largest loss of the hedged position. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark

A tutorial on pseudospectral methods for computational optimal control

[English] This paper is a tutorial introduction to pseudospectral optimal control. With pseudospectral methods, a function is approximated as a linear combination of smooth basis functions, which are often chosen to be Legendre or Chebyshev polynomials. Collocation of the differential-algebraic equations is performed at orthogonal collocation points, which are selected to yield interpolation of high accuracy. Pseudospectral methods directly discretize the original optimal control problem to recast it into a nonlinear programming format. A numerical optimizer is then employed to find approximate local optimal solutions. The paper also briefly describes the functionality and implementation of PSOPT, an open source software package written in C++ that employs pseudospectral discretization methods to solve multi-phase optimal control problems. The software implements the Legendre and Chebyshev pseudospectral methods, and it has useful features such as automatic differentiation, sparsity detection, and automatic scaling. The use of pseudospectral methods is illustrated in two problems taken from the literature on computational optimal control. [Portuguese] Este artigo e um tutorial introdutorio sobre controle otimo pseudo-espectral. Em metodos pseudo-espectrais, uma funcao e aproximada como uma combinacao linear de funcoes de base suaves, tipicamente escolhidas como polinomios de Legendre ou Chebyshev. A colocacao de equacoes algebrico-diferenciais e realizada em pontos de colocacao ortogonal, que sao selecionados de modo a minimizar o erro de interpolacao. Metodos pseudoespectrais discretizam o problema de controle otimo original de modo a converte-lo em um problema de programa cao nao-linear. Um otimizador numerico e entao empregado para obter solucoes localmente otimas. Este artigo tambem descreve sucintamente a funcionalidade e a implementacao de um pacote computacional de codigo aberto escrito em C++ chamado PSOPT. Tal pacote emprega metodos de discretizacao pseudo-spectrais para resolver problemas de controle otimo com multiplas fase. O PSOPT permite a utilizacao de metodos de Legendre ou Chebyshev, e possui caractersticas uteis tais como diferenciacao automatica, deteccao de esparsidade e escalonamento automatico. O uso de metodos pseudo-espectrais e ilustrado em dois problemas retirados da literatura de controle otimo computacional.

Optimal growth strategies when mortality and production rates are size-dependent

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.

Robust pole assignment and optimal stability margins

A robust pole assignment by linear state feedback is achieved in state-space representation by selecting a feedback which minimises the conditioning of the assigned eigenvalues of the closed-loop system. It is shown here that when this conditioning is minimised, a lower bound on the stability margin in the frequency domain is maximised.