Sampling errors of correlograms with and without sample mean removal for higher-order complex white noise with arbitrary mean

We derive the bias, variance, covariance, and mean square error of the standard lag windowed correlogram estimator both with and without sample mean removal for complex white noise with an arbitrary mean. We find that the arbitrary mean introduces lag dependent covariance between different lags of the correlogram estimates in spite of the lack of covariance in white noise for non-zeros lags. We provide a heuristic rule for when the sample mean should be, and when it should not be, removed if the true mean is not known. The sampling properties derived here are useful is assesing the general statistical performance of autocovariance and autocorrelation estimators in different parameter regimes. Alternatively, the sampling properties could be used as bounds on the detection of a weak signal in general white noise.Comment: 11 pages, 2 figures, To be published in Journal of Time Series Analysi

Deriving the sampling errors of correlograms for general white noise

We derive the second-order sampling properties of certain autocovariance and autocorrelation estimators for sequences of independent and identically distributed samples. Specifically, the estimators we consider are the classic lag windowed correlogram, the correlogram with subtracted sample mean, and the fixed-length summation correlogram. For each correlogram we derive explicit formulas for the bias, covariance, mean square error and consistency for generalised higher-order white noise sequences. In particular, this class of sequences may have non-zero means, be complexed valued and also includes non-analytical noise signals. We find that these commonly used correlograms exhibit lag dependent covariance despite the fact that these processes are white and hence by definition do not depend on lag.Comment: Submitted to Biometrik

Revisiting the radio interferometer measurement equation. IV. A generalized tensor formalism

The radio interferometer measurement equation (RIME), especially in its 2x2 form, has provided a comprehensive matrix-based formalism for describing classical radio interferometry and polarimetry, as shown in the previous three papers of this series. However, recent practical and theoretical developments, such as phased array feeds (PAFs), aperture arrays (AAs) and wide-field polarimetry, are exposing limitations of the formalism. This paper aims to develop a more general formalism that can be used to both clearly define the limitations of the matrix RIME, and to describe observational scenarios that lie outside these limitations. Some assumptions underlying the matrix RIME are explicated and analysed in detail. To this purpose, an array correlation matrix (ACM) formalism is explored. This proves of limited use; it is shown that matrix algebra is simply not a sufficiently flexible tool for the job. To overcome these limitations, a more general formalism based on tensors and the Einstein notation is proposed and explored both theoretically, and with a view to practical implementations. The tensor formalism elegantly yields generalized RIMEs describing beamforming, mutual coupling, and wide-field polarimetry in one equation. It is shown that under the explicated assumptions, tensor equations reduce to the 2x2 RIME. From a practical point of view, some methods for implementing tensor equations in an optimal way are proposed and analysed. The tensor RIME is a powerful means of describing observational scenarios not amenable to the matrix RIME. Even in cases where the latter remains applicable, the tensor formalism can be a valuable tool for understanding the limits of such applicability.Comment: 16 pages, no figures, accepted by A&

AMMONIA EMISSIONS FROM ARABLE LANDS IN PO VALLEY: METHODOLOGIES, DYNAMICS AND QUANTIFICATION.

Although the Po Valley (north Italy) is considered one of the most important ammonia (NH3) emitting regions in Europe, few data are available for an evaluation of the ammonia budget at field level in arable lands. Here the NH3 losses were quantify, considering different measurement and estimation approach, fertilisers and agronomic managements. The outputs of two concentration based-inverse dispersion models, together a mechanistic model were assessed with the direct measurements of ammonia fluxes by the micrometeorological technique eddy covariance, at hourly, daily and seasonal scales. A discussion on advantages, disadvantages and performances of each model is given in order to determine the most suitable method able to evaluate the ammonia emission in Po Valley at field scale. The selected inverse dispersion models were assessed in their uncertainty to quantify ammonia emissions rates, and their significance with regards to the Italian context. Moreover emissions from cattle slurry and urea application were performed in seven field trials in three different locations of Po Valley, in order to evaluate the best practices in reducing NH3 loss from arable land. The emission factors relative to different agronomical practices (slurry injection, slurry surface spreading with and without incorporation, urea surface spreading) are given, taking into account the main factors affecting the NH3 volatilization phenomenon and describing its dynamics

Revisiting the radio interferometer measurement equation. I. A full-sky Jones formalism

Since its formulation by Hamaker et al., the radio interferometer measurement equation (RIME) has provided a rigorous mathematical basis for the development of novel calibration methods and techniques, including various approaches to the problem of direction-dependent effects (DDEs). This series of papers aims to place recent developments in the treatment of DDEs into one RIME-based mathematical framework, and to demonstrate the ease with which the various effects can be described and understood. It also aims to show the benefits of a RIME-based approach to calibration. Paper I re-derives the RIME from first principles, extends the formalism to the full-sky case, and incorporates DDEs. Paper II then uses the formalism to describe self-calibration, both with a full RIME, and with the approximate equations of older software packages, and shows how this is affected by DDEs. It also gives an overview of real-life DDEs and proposed methods of dealing with them. Applying this to WSRT data (Paper III) results in a noise-limited image of the field around 3C 147 with a very high dynamic range (1.6 million), and none of the off-axis artifacts that plague regular selfcal. The resulting differential gain solutions contain significant information on DDEs, and can be used for iterative improvements of sky models. Perhaps most importantly, sources as faint as 2 mJy have been shown to yield meaningful differential gain solutions, and thus can be used as potential calibration beacons in other DDE-related schemes.Comment: 12 pages, no figures, published in A&

On the similarity of Information Energy to Dark Energy

Information energy is shown here to have properties similar to those of dark energy. The energy associated with each information bit of the universe is found to be defined identically to the characteristic energy of a cosmological constant. Two independent methods are used to estimate the universe information content of ~10^91 bits, a value that provides an information energy total comparable to that of the dark energy. Information energy is also found to have a significantly negative equation of state parameter, w < -0.4, and thus exerts a negative pressure, similar to dark energy.Comment: 5 pages, no figures, no table

Evaluation of total and bioavailable heavy metals and other soilrelated variables in a rice paddy after the application of defecation lime

A two-year experiment was carried out in a paddy field to investigate the effects of the use of defecation lime derived from treated sewage sludge on soil total and soil phytoavailable heavy metals concentration. Heavy metals concentration was determined also in raw rice. Four treatments were arranged in a completely randomized block design: not fertilised (T0), organic fertilisation + chemical fertilisers (T1), defecation lime + chemical fertilisers (T2), defecation lime at pre-sowing (T3). For T3, the pH value increased significantly at the end of the second year, increasing from 5.8 to 6.11. T3 resulted in the highest soil organic carbon content (9.4 g kg-1), suggesting the potential of defecation lime both as soil corrective material and soil amendment. The application of defecation lime in the paddy field did not result in an increased phytoavailable amount of heavy metals in soil

Tecnica di misura dei fenomeni di ruscellamento superficiale

Il suolo \ue8 una risorsa non rinnovabile capace di assicurare funzioni essenziali non solo a livello ambientale ma anche sociale ed economico, assumendo quindi un ruolo centrale nel contesto di sostenibilit\ue0 dell\u2019agricoltura. Tuttavia il suolo \ue8 soggetto ad un continuo degrado dovuto in particolare al fenomeno dell\u2019erosione che non solo ne influenza negativamente le propriet\ue0 nutritive ma diventa una potenziale fonte di inquinamento per le acque superficiali. I fenomeni erosivi sono influenzati da notevoli fattori che il pi\uf9 delle volte vengono meglio descritti se studiati a scala di campo, piuttosto che a piccola scala. Inoltre gli alti costi degli strumenti e la quantit\ue0 enorme di ruscellato limitano il pi\uf9 delle volte il numero di siti che possono essere studiati. Sono stati quindi sperimentati strumenti, per parcelle di pi\uf9 ampia superficie, che permettono di ripartire l\u2019acqua ed il ruscellato e di ridurre in questo modo il campione raccolto mantenendolo rappresentativo. In questo lavoro viene presentata l\u2019applicazione pratica di uno di questi strumenti di misura opportunamente adattato che permette con ampia soluzione temporale di monitorare i fenomeni di ruscellamento superficiale a scala di campo