A note on the analysis error associated with 3D-FGAT

The analysis-error variance of a 3D-FGAT assimilation is examined analytically using a simple scalar equation. It is shown that the analysis-error variance may be greater than the error variances of the inputs. The results are illustrated numerically with a scalar example and a shallow-water model.

A Note on Dividing Integers by Two

This note describes a simple method of dividing all integers, positive and negative, by two when represented in two's complement arithmetic.

Idealized SST anomaly regional climate model experiments: a note of caution

To date, a number of studies have focused on the influence of sea surface temperature (SST) on global and regional rainfall variability, with the majority of these focusing on certain ocean basins e.g. the Pacific, North Atlantic and Indian Ocean. In contrast, relatively less work has been done on the influence of the central South Atlantic, particularly in relation to rainfall over southern Africa. Previous work by the authors, using reanalysis data and general circulation model (GCM) experiments, has suggested that cold SST anomalies in the central southern Atlantic Ocean are linked to an increase in rainfall extremes across southern Africa. In this paper we present results from idealised regional climate model (RCM) experiments forced with both positive and negative SST anomalies in the southern Atlantic Ocean. These experiments reveal an unexpected response of rainfall over southern Africa. In particular it was found that SST anomalies of opposite sign can cause similar rainfall responses in the model experiments, with isolated increases in rainfall over central southern Africa as well as a large region of drying over the Mozambique Channel. The purpose of this paper is to highlight this finding and explore explanations for the behaviour of the climate model. It is suggested that the observed changes in rainfall might result from the redistribution of energy (associated with upper level changes to Rossby waves) or, of more concern, model error, and therefore the paper concludes that the results of idealised regional climate models forced with SST anomalies should be viewed cautiously.

Decision theory and real estate development: a note on uncertainty

Real estate development appraisal is a quantification of future expectations. The appraisal model relies upon the valuer/developer having an understanding of the future in terms of the future marketability of the completed development and the future cost of development. In some cases the developer has some degree of control over the possible variation in the variables, as with the cost of construction through the choice of specification. However, other variables, such as the sale price of the final product, are totally dependent upon the vagaries of the market at the completion date. To try to address the risk of a different outcome to the one expected (modelled) the developer will often carry out a sensitivity analysis on the development. However, traditional sensitivity analysis has generally only looked at the best and worst scenarios and has focused on the anticipated or expected outcomes. This does not take into account uncertainty and the range of outcomes that can happen. A fuller analysis should include examination of the uncertainties in each of the components of the appraisal and account for the appropriate distributions of the variables. Similarly, as many of the variables in the model are not independent, the variables need to be correlated. This requires a standardised approach and we suggest that the use of a generic forecasting software package, in this case Crystal Ball, allows the analyst to work with an existing development appraisal model set up in Excel (or other spreadsheet) and to work with a predetermined set of probability distributions. Without a full knowledge of risk, developers are unable to determine the anticipated level of return that should be sought to compensate for the risk. This model allows the user a better understanding of the possible outcomes for the development. Ultimately the final decision will be made relative to current expectations and current business constraints, but by assessing the upside and downside risks more appropriately, the decision maker should be better placed to make a more informed and “better”.

A note on estimating market–based minimum capital risk requirements: a multivariate GARCH approach

Internal risk management models of the kind popularized by J. P. Morgan are now used widely by the world’s most sophisticated financial institutions as a means of measuring risk. Using the returns on three of the most popular futures contracts on the London International Financial Futures Exchange, in this paper we investigate the possibility of using multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models for the calculation of minimum capital risk requirements (MCRRs). We propose a method for the estimation of the value at risk of a portfolio based on a multivariate GARCH model. We find that the consideration of the correlation between the contracts can lead to more accurate, and therefore more appropriate, MCRRs compared with the values obtained from a univariate approach to the problem.

A note on the use of spreadsheet optimisers in real estate analysis

Modern Portfolio Theory (MPT) has been advocated as a more rational approach to the construction of real estate portfolios. The application of MPT can now be achieved with relative ease using the powerful facilities of modern spreadsheet, and does not necessarily need specialist software. This capability is to be found in the use of an add-in Tool now found in several spreadsheets, called an Optimiser or Solver. The value in using this kind of more sophisticated analysis feature of spreadsheets is increasingly difficult to ignore. This paper examines the use of the spreadsheet Optimiser in handling asset allocation problems. Using the Markowitz Mean-Variance approach, the paper introduces the necessary calculations, and shows, by means of an elementary example implemented in Microsoft's Excel, how the Optimiser may be used. Emphasis is placed on understanding the inputs and outputs from the portfolio optimisation process, and the danger of treating the Optimiser as a Black Box is discussed.

A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols

We characterize the essential spectra of Toeplitz operators Ta on weighted Bergman spaces with matrix-valued symbols; in particular we deal with two classes of symbols, the Douglas algebra C+H∞ and the Zhu class Q := L∞ ∩VMO∂ . In addition, for symbols in C+H∞ , we derive a formula for the index of Ta in terms of its symbol a in the scalar-valued case, while in the matrix-valued case we indicate that the standard reduction to the scalar-valued case fails to work analogously to the Hardy space case. Mathematics subject classification (2010): 47B35,

A note on an integration by parts formula for the generators of uniform translations on configuration space

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on Rd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.

Technical Note: The normal quantile transformation and its application in a flood forecasting system.

The Normal Quantile Transform (NQT) has been used in many hydrological and meteorological applications in order to make the Cumulated Distribution Function (CDF) of the observed, simulated and forecast river discharge, water level or precipitation data Gaussian. It is also the heart of the meta-Gaussian model for assessing the total predictive uncertainty of the Hydrological Uncertainty Processor (HUP) developed by Krzysztofowicz. In the field of geo-statistics this transformation is better known as the Normal-Score Transform. In this paper some possible problems caused by small sample sizes when applying the NQT in flood forecasting systems will be discussed and a novel way to solve the problem will be outlined by combining extreme value analysis and non-parametric regression methods. The method will be illustrated by examples of hydrological stream-flow forecasts.

Non-concordance between genetic profiles of olive oil and fruit: a cautionary note to the use of DNA markers for provenance testing.

To investigate the contribution of paternal alleles to the DNA content of olive oil, genetic analyses of olive DNA samples from fruits, leaves, and oil derived from the same tree (cv. Leccino) were carried out. DNA extracted from maternal tissues--leaves and flesh--from different fruits showed identical genetic profiles using a set of DNA markers. Additional simple sequence repeat (SSR) alleles, not found in the maternal samples, were amplified in the embryos (stone), and they were also detected in DNA extracted from the paste obtained by crushing whole fruits and from the oil pressed from this material. These results demonstrate that the DNA profile obtained from olive oil is likely to represent a composite profile of the maternal alleles juxtaposed with alleles contributed by various pollen donors. Therefore, care needs to be taken in the interpretation of DNA profiles obtained from DNA extracted from oil for resolving provenance and authenticity issues.