Hydrochemical processes in lowland rivers: insights from in situ, high-resolution monitoring

This paper introduces new insights into the hydrochemical functioning of lowland river systems using field-based spectrophotometric and electrode technologies. The streamwater concentrations of nitrogen species and phosphorus fractions were measured at hourly intervals on a continuous basis at two contrasting sites on tributaries of the River Thames – one draining a rural catchment, the River Enborne, and one draining a more urban system, The Cut. The measurements complement those from an existing network of multi-parameter water quality sondes maintained across the Thames catchment and weekly monitoring based on grab samples. The results of the sub-daily monitoring show that streamwater phosphorus concentrations display highly complex dynamics under storm conditions dependent on the antecedent catchment wetness, and that diurnal phosphorus and nitrogen cycles occur under low flow conditions. The diurnal patterns highlight the dominance of sewage inputs in controlling the streamwater phosphorus and nitrogen concentrations at low flows, even at a distance of 7 km from the nearest sewage treatment works in the rural River Enborne. The time of sample collection is important when judging water quality against ecological thresholds or standards. An exhaustion of the supply of phosphorus from diffuse and multiple septic tank sources during storm events was evident and load estimation was not improved by sub-daily monitoring beyond that achieved by daily sampling because of the eventual reduction in the phosphorus mass entering the stream during events. The results highlight the utility of sub-daily water quality measurements and the discussion considers the practicalities and challenges of in situ, sub-daily monitoring.

Smoothness of scale functions for spectrally negative Lévy processes

Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes and often appear in the context of martingale relations. These relations are often require excursion theory rather than Itô calculus. The reason for the latter is that standard Itô calculus is only applicable to functions with a sufficient degree of smoothness and knowledge of the precise degree of smoothness of scale functions is seemingly incomplete. The aim of this article is to offer new results concerning properties of scale functions in relation to the smoothness of the underlying Lévy measure. We place particular emphasis on spectrally negative Lévy processes with a Gaussian component and processes of bounded variation. An additional motivation is the very intimate relation of scale functions to renewal functions of subordinators. The results obtained for scale functions have direct implications offering new results concerning the smoothness of such renewal functions for which there seems to be very little existing literature on this topic.

Small time two-sided LIL behavior for Lévy processes at zero

We wish to characterize when a Lévy process X t crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of sup t→0|X t |/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that sup t→0 |X t |/b(t) = 1.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.

On the variability of the surface environment response to synoptic forcing over complex terrain: a multivariate data analysis approach

Synoptic climatology relates the atmospheric circulation with the surface environment. The aim of this study is to examine the variability of the surface meteorological patterns, which are developing under different synoptic scale categories over a suburban area with complex topography. Multivariate Data Analysis techniques were performed to a data set with surface meteorological elements. Three principal components related to the thermodynamic status of the surface environment and the two components of the wind speed were found. The variability of the surface flows was related with atmospheric circulation categories by applying Correspondence Analysis. Similar surface thermodynamic fields develop under cyclonic categories, which are contrasted with the anti-cyclonic category. A strong, steady wind flow characterized by high shear values develops under the cyclonic Closed Low and the anticyclonic H–L categories, in contrast to the variable weak flow under the anticyclonic Open Anticyclone category.

Regulation of surface water quality in a Cretaceous chalk catchment, UK: an assessment of the relative importance of instream and wetland processes

To investigate the relative importance of instream nutrient spiralling and wetland transformation processes on surface water quality, total nitrogen (TN) and total phosphorus (TP) concentrations in a 200 m reach of the River Lambourn in the south-east of England were monitored over a 2-year period. In addition, the soil pore water nutrient dynamics in a riparian ecosystem adjacent to the river were investigated. Analysis of variance indicated that TN, TP and suspended sediment concentrations recorded upstream of the wetland were statistically significantly higher (P<0.05) than those downstream of the site. Such results suggest that the wetland was performing a nutrient retention function. Indeed, analysis of soil pore waters within the site show that up to 85% of TN and 70% of TP was removed from water flowing through the wetland during baseflow conditions, thus supporting the theory that the wetland played an important role in the regulation of surface water quality at the site. However, the small variations observed (0.034 mg TN l-1 and 0.031 mg P l-1) are consistent with the theory of nutrient spiralling suggesting that both instream and wetland retention processes have a causal effect on surface water quality.

Epoch-specific functional networks involved in working memory

Working memory (WM) is not a unitary construct. There are distinct processes involved in encoding information, maintaining it on-line, and using it to guide responses. The anatomical configurations of these processes are more accurately analyzed as functionally connected networks than collections of individual regions. In the current study we analyzed event-related functional magnetic resonance imaging (fMRI) data from a Sternberg Item Recognition Paradigm WM task using a multivariate analysis method that allowed the linking of functional networks to temporally-separated WM epochs. The length of the delay epochs was varied to optimize isolation of the hemodynamic response (HDR) for each task epoch. All extracted functional networks displayed statistically significant sensitivity to delay length. Novel information extracted from these networks that was not apparent in the univariate analysis of these data included involvement of the hippocampus in encoding/probe, and decreases in BOLD signal in the superior temporal gyrus (STG), along with default-mode regions, during encoding/delay. The bilateral hippocampal activity during encoding/delay fits with theoretical models of WM in which memoranda held across the short term are activated long-term memory representations. The BOLD signal decreases in the STG were unexpected, and may reflect repetition suppression effects invoked by internal repetition of letter stimuli. Thus, analysis methods focusing on how network dynamics relate to experimental conditions allowed extraction of novel information not apparent in univariate analyses, and are particularly recommended for WM experiments for which task epochs cannot be randomized.

The sample autocorrelation function and the detection of long-memory processes

The detection of long-range dependence in time series analysis is an important task to which this paper contributes by showing that whilst the theoretical definition of a long-memory (or long-range dependent) process is based on the autocorrelation function, it is not possible for long memory to be identified using the sum of the sample autocorrelations, as usually defined. The reason for this is that the sample sum is a predetermined constant for any stationary time series; a result that is independent of the sample size. Diagnostic or estimation procedures, such as those in the frequency domain, that embed this sum are equally open to this criticism. We develop this result in the context of long memory, extending it to the implications for the spectral density function and the variance of partial sums of a stationary stochastic process. The results are further extended to higher order sample autocorrelations and the bispectral density. The corresponding result is that the sum of the third order sample (auto) bicorrelations at lags h,k≥1, is also a predetermined constant, different from that in the second order case, for any stationary time series of arbitrary length.

Crossbred cow adoption and milk market participation in a multivariate count data framework

Cross-bred cow adoption is an important and potent policy variable precipitating subsistence household entry into emerging milk markets. This paper focuses on the problem of designing policies that encourage and sustain milkmarket expansion among a sample of subsistence households in the Ethiopian highlands. In this context it is desirable to measure households’ ‘proximity’ to market in terms of the level of deficiency of essential inputs. This problem is compounded by four factors. One is the existence of cross-bred cow numbers (count data) as an important, endogenous decision by the household; second is the lack of a multivariate generalization of the Poisson regression model; third is the censored nature of the milk sales data (sales from non-participating households are, essentially, censored at zero); and fourth is an important simultaneity that exists between the decision to adopt a cross-bred cow, the decision about how much milk to produce, the decision about how much milk to consume and the decision to market that milk which is produced but not consumed internally by the household. Routine application of Gibbs sampling and data augmentation overcome these problems in a relatively straightforward manner. We model the count data from two sites close to Addis Ababa in a latent, categorical-variable setting with known bin boundaries. The single-equation model is then extended to a multivariate system that accommodates the covariance between crossbred-cow adoption, milk-output, and milk-sales equations. The latent-variable procedure proves tractable in extension to the multivariate setting and provides important information for policy formation in emerging-market settings

Diabatic processes modifying potential vorticity in a North Atlantic cyclone

Potential vorticity (PV) succinctly describes the evolution of large-scale atmospheric flow because of its material conservation and invertibility properties. However, diabatic processes in extratropical cyclones can modify PV and influence both mesoscale weather and the evolution of the synoptic-scale wave pattern. In this investigation, modification of PV by diabatic processes is diagnosed in a Met Office Unified Model (MetUM) simulation of a North Atlantic cyclone using a set of PV tracers. The structure of diabatic PV within the extratropical cyclone is investigated and linked to the processes responsible for it. On the mesoscale, a tripole of diabatic PV is generated across the tropopause fold extending down to the cold front. The structure results from a dipole in heating across the frontal interface due to condensation in the warm conveyor belt flanking the upper side of the fold and evaporation of precipitation in the dry intrusion and below. On isentropic surfaces intersecting the tropopause, positive diabatic PV is generated on the stratospheric side, while negative diabatic PV is generated on the tropospheric side. The stratospheric diabatic PV is generated primarily by long-wave cooling which peaks at the tropopause itself due to the sharp gradient in humidity there. The tropospheric diabatic PV originates locally from the long-wave radiation and non-locally by advection out of the top of heating associated with the large-scale cloud, convection and boundary layer schemes. In most locations there is no diabatic modification of PV at the tropopause itself but diabatic PV anomalies would influence the tropopause indirectly through the winds they induce and subsequent advection. The consequences of this diabatic PV dipole for the evolution of synoptic-scale wave patterns are discussed.