A functional coefficient model view of the Feldstein–Horioka puzzle

What does the saving–investment (SI) relation really measure and how should the SI relation be measured? These are two of the most discussed issues triggered by the so-called Feldstein–Horioka puzzle. Based on panel data we introduce a new variant of functional coefficient models that allows to separate long and short to medium run parameter dependence. The new modeling framework is applied to uncover the determinants of the SI relation. Macroeconomic state variables such as openness, the age dependency ratio, government current and consumption expenditures are found to affect the SI relation significantly in the long run.

Local gratings due to angular hole burning in a photorefractive polymer

We investigate the processes involved in writing real-time holographic gratings in a photorefractive polymer (PRP) that incorporates an azo-dye. In such systems there may be gratings due to mechanisms associated with trans–cis isomerization (angular hole burning (AHB) and/or angular redistribution), which appear in addition to those arising from the photorefractive (PR) effect. The work presented here helps to understand the interactions which may occur between these different gratings. The formation of local gratings due to mechanisms associated with photoisomerization is studied, in a new PRP based on the photoconductor poly(N-vinylcarbazole):2, 4, 7-trinitro-9-fluorenone, plasticized with N-ethylcarbazole. The polymer includes the azo-dye 4-nitro-4'-pentyloxy-azobenzene and we observe both PR and photoisomerization gratings. The gratings are shown to be both polarization-sensitive and reversible. The presence of the photoisomerization gratings (which diffract almost as strongly as the PR gratings) significantly affects the field-dependent diffractive behaviour of the composite. A measurement of the lifetime of the cis state is made (τcis = 38 s) using photoinduced dichroism. This is close to the decay time constant of the local gratings (τdecay = 42 s), and it is suggested that the local grating mechanism is AHB of the azo-dye. This is the first time (to the knowledge of the authors) that a local grating due to AHB has been demonstrated in a PRP.

Catchment phosphorous losses: an export coefficient modelling approach with scenario analysis for water management

This paper presents the development of an export coefficient model to characterise the rates and sources of P export from land to water in four reservoir systems located in a semi-arid rural region in southern of Portugal. The model was developed to enable effective management of these important water resource systems under the EU Water Framework Directive. This is the first time such an approach has been fully adapted for the semi-arid systems typical of Mediterranean Europe. The sources of P loading delivered to each reservoir from its catchment were determined and scenario analysis was undertaken to predict the likely impact of catchment management strategies on the scale of rate of P loading delivered to each water body from its catchment. The results indicate the importance of farming and sewage treatment works/collective septic tanks discharges as the main contributors to the total diffuse and point source P loading delivered to the reservoirs, respectively. A reduction in the total P loading for all study areas would require control of farming practices and more efficient removal of P from human wastes prior to discharge to surface waters. The scenario analysis indicates a strategy based solely on reducing the agricultural P surplus may result in only a slow improvement in water quality, which would be unlikely to support the generation of good ecological status in reservoirs. The model application indicates that a reduction of P-inputs to the reservoirs should first focus on reducing P loading from sewage effluent discharges through the introduction of tertiary treatment (P-stripping) in all major residential areas. The fully calibrated export coefficient modelling approach transferred well to semi-arid regions, with the only significant limitation being the availability of suitable input data to drive the model. Further studies using this approach in semi-arid catchments are now needed to increase the knowledge of nutrient export behaviours in semi-arid regions.

Evaluation and management of the impact of land use change on the nitrogen and phosphorus load delivered to surface waters: the export coefficient modelling approach

A manageable, relatively inexpensive model was constructed to predict the loss of nitrogen and phosphorus from a complex catchment to its drainage system. The model used an export coefficient approach, calculating the total nitrogen (N) and total phosphorus (P) load delivered annually to a water body as the sum of the individual loads exported from each nutrient source in its catchment. The export coefficient modelling approach permits scaling up from plot-scale experiments to the catchment scale, allowing application of findings from field experimental studies at a suitable scale for catchment management. The catchment of the River Windrush, a tributary of the River Thames, UK, was selected as the initial study site. The Windrush model predicted nitrogen and phosphorus loading within 2% of observed total nitrogen load and 0.5% of observed total phosphorus load in 1989. The export coefficient modelling approach was then validated by application in a second research basin, the catchment of Slapton Ley, south Devon, which has markedly different catchment hydrology and land use. The Slapton model was calibrated within 2% of observed total nitrogen load and 2.5% of observed total phosphorus load in 1986. Both models proved sensitive to the impact of temporal changes in land use and management on water quality in both catchments, and were therefore used to evaluate the potential impact of proposed pollution control strategies on the nutrient loading delivered to the River Windrush and Slapton Ley

The Natural History of Slapton Ley Nature Reserve XVIII: nitrogen and phosphorus losses from the catchment - an export coefficient modelling approach

Nitrogen and phosphorus losses from the catchment of Slapton Ley, a small coastal lake in SW England, were calculated using an adaptation of a model developed by Jorgensen (1980). A detailed survey of the catchment revealed that its land use is dominated by both permanent and temporary grassland (respectively 38 and 32% of its total area), and that the remainder is made up of the cultivation of cereals and field vegetables, and market gardening. Livestock numbers in the catchment constitute ca. 6600 head of cattle, 10,000 sheep, 590 pigs, 1700 poultry and 58 horses. The permanent human population of the area is ca. 2000, served by two small gravity-fed sewage treatment works (STWs). Inputs to, and losses from, farmland in the catchment were computed using Jorgensen’s model, and coefficients derived from the data of Cooke (1976), Gostick (1982), Rast and Lee (1983) and Vollenweider (1968). Allowing for outputs from STWs, the total annual external load of N and P upon Slapton Ley is 160 t (35 kg ha-1) a-1 N, and 4.8 t (1.05 kg ha-1) a-1 P. Accordingly to Vollenweider (1968, 1975), such loadings exceed OECD permissible level by a factor of ca. 50 in the case of N, and ca. 5 in that of P. In order to reduce nutrient loads, attention would need to be paid to both STW and agricultural sources.

Correlations between two sets of angular relation equations

It is shown here that the angular relation equations between direct and reciprocal vectors are very similar to the angular relation equations in Euler's theorem. These two sets of equations are usually treated separately as unrelated equations in different fields. In this careful study, the connection between the two sets of angular equations is revealed by considering the cosine rule for the spherical triangle. It is found that understanding of the correlation is hindered by the facts that the same variables are defined differently and different symbols are used to represent them in the two fields. Understanding the connection between different concepts is not only stimulating and beneficial, but also a fundamental tool in innovation and research, and has historical significance. The background of the work presented here contains elements of many scientific disciplines. This work illustrates the common ground of two theories usually considered separately and is therefore of benefit not only for its own sake but also to illustrate a general principle that a theory relevant to one discipline can often be used in another. The paper works with chemistry related concepts using mathematical methodologies unfamiliar to the usual audience of mainstream experimental and theoretical chemists.

Angular momentum conservation and gravity wave drag parameterization: implications for climate models

The robustness of the parameterized gravity wave response to an imposed radiative perturbation in the middle atmosphere is examined. When momentum is conserved and for reasonable gravity wave drag parameters, the response to a polar cooling induces polar downwelling above the region of the imposed cooling, with consequent adiabatic warming. This response is robust to changes in the gravity wave source spectrum, background flow, gravity wave breaking criterion, and model lid height. When momentum is not conserved, either in the formulation or in the implementation of the gravity wave drag parameterization, the response becomes sensitive to the above-mentioned factors—in particular to the model lid height. The spurious response resulting from nonconservation is found to be nonnegligible in terms of the total gravity wave drag–induced downwelling.

The angular momentum constraint on climate sensitivity and downward influence in the middle atmosphere

It is shown that under reasonable assumptions, conservation of angular momentum provides a strong constraint on gravity wave drag feedbacks to radiative perturbations in the middle atmosphere. In the time mean, radiatively induced temperature perturbations above a given altitude z cannot induce changes in zonal mean wind and temperature below z through feedbacks in gravity wave drag alone (assuming an unchanged gravity wave source spectrum). Thus, despite the many uncertainties in the parameterization of gravity wave drag, the role of gravity wave drag in middle-atmosphere climate perturbations may be much more limited than its role in climate itself. This constraint limits the possibilities for downward influence from the mesosphere. In order for a gravity wave drag parameterization to respect the momentum constraint and avoid spurious downward influence, any nonzero parameterized momentum flux at a model lid must be deposited within the model domain, and there must be no zonal mean sponge layer. Examples are provided of how violation of these conditions leads to spurious downward influence. For planetary waves, the momentum constraint does not prohibit downward influence, but it limits the mechanisms by which it can occur: in the time mean, downward influence from a radiative perturbation can only arise through changes in reflection and meridional propagation properties of planetary waves.

Determination of the gas diffusion coefficient of a peat grassland soil

Peatland habitats are important carbon stocks that also have the potential to be significant sources of greenhouse gases, particularly when subject to changes such as artificial drainage and application of fertilizer. Models aiming to estimate greenhouse gas release from peatlands require an accurate estimate of the diffusion coefficient of gas transport through soil (Ds). The availability of specific measurements for peatland soils is currently limited. This study measured Ds for a peat soil with an overlying clay horizon and compared values with those from widely available models. The Ds value of a sandy loam reference soil was measured for comparison. Using the Currie (1960) method, Ds was measured between an air-filled porosity (ϵ) range of 0 and 0.5 cm3 cm−3. Values of Ds for the peat cores ranged between 3.2 × 10−4 and 4.4 × 10−3 m2 hour−1, for loamy clay cores between 0 and 4.7 × 10−3 m2 hour−1 and for the sandy reference soil they were between 5.4 × 10−4 and 3.4 × 10−3 m2 hour−1. The agreement of measured and modelled values of relative diffusivity (Ds/D0, with D0 the diffusion coefficient through free air) varied with soil type; however, the Campbell (1985) model provided the best replication of measured values for all soils. This research therefore suggests that the use of the Campbell model in the absence of accurately measured Ds and porosity values for a study soil would be appropriate. Future research into methods to reduce shrinkage of peat during measurement and therefore allow measurement of Ds for a greater range of ϵ would be beneficial.

A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

Simulations of angular momentum evolution in wind-fed CV precursors

It is thought that the secondary stars in cataclysmic variables (CVs) may undergo a period of mass loss in the form of a wind during the evolution of the system (Mullan et al. 1992). This wind is thought to magnetically brake the secondary star with a time-scale ~ 10^8 yr (e.g. van Paradijs 1986). When the secondary’s spin has been brought close to synchronism with the orbit it is possible for tidal torques to lock the secondary in synchronous rotation.

Synergistic angular and spectral estimation of aerosol properties using CHRIS/PROBA-1 and simulated Sentinel-3~data

A method has been developed to estimate Aerosol Optical Depth (AOD), Fine Mode Fraction (FMF) and Single Scattering Albedo (SSA) over land surfaces using simulated Sentinel-3 data. The method uses inversion of a coupled surface/atmosphere radiative transfer model, and includes a general physical model of angular surface reflectance. An iterative process is used to determine the optimum value of the aerosol properties providing the best fit of the corrected reflectance values for a number of view angles and wavelengths with those provided by the physical model. A method of estimating AOD using only angular retrieval has previously been demonstrated on data from the ENVISAT and PROBA-1 satellite instruments, and is extended here to the synergistic spectral and angular sampling of Sentinel-3 and the additional aerosol properties. The method is tested using hyperspectral, multi-angle Compact High Resolution Imaging Spectrometer (CHRIS) images. The values obtained from these CHRIS observations are validated using ground based sun-photometer measurements. Results from 22 image sets using the synergistic retrieval and improved aerosol models show an RMSE of 0.06 in AOD, reduced to 0.03 over vegetated targets.

Synergistic angular and spectral estimation of aerosol properties using CHRIS/PROBA-1 and simulated Sentinel-3 data

We develop a method to derive aerosol properties over land surfaces using combined spectral and angular information, such as available from ESA Sentinel-3 mission, to be launched in 2015. A method of estimating aerosol optical depth (AOD) using only angular retrieval has previously been demonstrated on data from the ENVISAT and PROBA-1 satellite instruments, and is extended here to the synergistic spectral and angular sampling of Sentinel-3. The method aims to improve the estimation of AOD, and to explore the estimation of fine mode fraction (FMF) and single scattering albedo (SSA) over land surfaces by inversion of a coupled surface/atmosphere radiative transfer model. The surface model includes a general physical model of angular and spectral surface reflectance. An iterative process is used to determine the optimum value of the aerosol properties providing the best fit of the corrected reflectance values to the physical model. The method is tested using hyperspectral, multi-angle Compact High Resolution Imaging Spectrometer (CHRIS) images. The values obtained from these CHRIS observations are validated using ground-based sun photometer measurements. Results from 22 image sets using the synergistic retrieval and improved aerosol models show an RMSE of 0.06 in AOD, reduced to 0.03 over vegetated targets.

Independent uncertainty estimates for coefficient based sea surface temperature retrieval from the Along-Trck Scanning Radiometer instruments

We establish a methodology for calculating uncertainties in sea surface temperature estimates from coefficient based satellite retrievals. The uncertainty estimates are derived independently of in-situ data. This enables validation of both the retrieved SSTs and their uncertainty estimate using in-situ data records. The total uncertainty budget is comprised of a number of components, arising from uncorrelated (eg. noise), locally systematic (eg. atmospheric), large scale systematic and sampling effects (for gridded products). The importance of distinguishing these components arises in propagating uncertainty across spatio-temporal scales. We apply the method to SST data retrieved from the Advanced Along Track Scanning Radiometer (AATSR) and validate the results for two different SST retrieval algorithms, both at a per pixel level and for gridded data. We find good agreement between our estimated uncertainties and validation data. This approach to calculating uncertainties in SST retrievals has a wider application to data from other instruments and retrieval of other geophysical variables.