Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

Variability of the Atlantic thermohaline circulation described by three-dimensional empirical orthogonal functions

We describe the use of bivariate 3d empirical orthogonal functions (EOFs) in characterising low frequency variability of the Atlantic thermohaline circulation (THC) in the Hadley Centre global climate model, HadCM3. We find that the leading two modes are well correlated with an index of the meridional overturning circulation (MOC) on decadal timescales, with the leading mode alone accounting for 54% of the decadal variance. Episodes of coherent oscillations in the sub-space of the leading EOFs are identified; these episodes are of great interest for the predictability of the THC, and could indicate the existence of different regimes of natural variability. The mechanism identified for the multi-decadal variability is an internal ocean mode, dominated by changes in convection in the Nordic Seas, which lead the changes in the MOC by a few years. Variations in salinity transports from the Arctic and from the North Atlantic are the main feedbacks which control the oscillation. This mode has a weak feedback onto the atmosphere and hence a surface climatic influence. Interestingly, some of these climate impacts lead the changes in the overturning. There are also similarities to observed multi-decadal climate variability.

A comparison of diatom phosphorus transfer functions and export coefficient models as tools for reconstructing lake nutrient histories

1. We compared the baseline phosphorus (P) concentrations inferred by diatom-P transfer functions and export coefficient models at 62 lakes in Great Britain to assess whether the techniques produce similar estimates of historical nutrient status. 2. There was a strong linear relationship between the two sets of values over the whole total P (TP) gradient (2-200 mu g TP L-1). However, a systematic bias was observed with the diatom model producing the higher values in 46 lakes (of which values differed by more than 10 mu g TP L-1 in 21). The export coefficient model gave the higher values in 10 lakes (of which the values differed by more than 10 mu g TP L-1 in only 4). 3. The difference between baseline and present-day TP concentrations was calculated to compare the extent of eutrophication inferred by the two sets of model output. There was generally poor agreement between the amounts of change estimated by the two approaches. The discrepancy in both the baseline values and the degree of change inferred by the models was greatest in the shallow and more productive sites. 4. Both approaches were applied to two lakes in the English Lake District where long-term P data exist, to assess how well the models track measured P concentrations since approximately 1850. There was good agreement between the pre-enrichment TP concentrations generated by the models. The diatom model paralleled the steeper rise in maximum soluble reactive P (SRP) more closely than the gradual increase in annual mean TP in both lakes. The export coefficient model produced a closer fit to observed annual mean TP concentrations for both sites, tracking the changes in total external nutrient loading. 5. A combined approach is recommended, with the diatom model employed to reflect the nature and timing of the in-lake response to changes in nutrient loading, and the export coefficient model used to establish the origins and extent of changes in the external load and to assess potential reduction in loading under different management scenarios. 6. However, caution must be exercised when applying these models to shallow lakes where the export coefficient model TP estimate will not include internal P loading from lake sediments and where the diatom TP inferences may over-estimate TP concentrations because of the high abundance of benthic taxa, many of which are poor indicators of trophic state.

A comparison of the role of two blue-green algae in THM and HAA formation

The contribution of two blue-green algae species, Anabaeria flos-aquae and Microcystis aeruginosa, to the formation of trihalomethanes (THMs) and haloacetic acids (HAAs) was investigated. The experiments examined the formation potential of these disinfection by-products (DBPs) from both algae cells and extracellular organic matter (EOM) during four algal growth phases. Algal cells and EOM of Anabaena and Microcystis exhibited a high potential for DBP formation. Yields of total THMs (TTHM) and total HAAs (THAA) were closely related to the growth phase. Reactivity of EOM from Anabaena was slightly higher than corresponding cells, while the opposite result was found for Microcystis. Specific DBP yields (yield/unit C) of Anabaena were in the range of 2-11 mu mol/mmol C for TTHM and 217 mu mol/mmol C for THAA, while those of Microcystis were slightly higher. With regard to the distributions of individual THM and HAA compounds, differences were observed between the algae species and also between cells and EOM. The presence of bromide shifted the dominant compounds from HAAs to THMs. (C) 2009 Elsevier Ltd. All rights reserved.

The impact of fallowing and green manuring on soil conditions and the growth of sugarcane

There are currently concerns within some sugar industries that long-term monoculture has led to soil degradation and consequent yield decline. An investigation was conducted in Swaziland to assess the effects of fallowing and green manuring practices, over a seven-month period, on sugarcane yields and the physical properties of a poorly draining clay soil. In the subsequent first sugarcane crop after planting, yields were improved from 129 t ha(-1) under continuous sugarcane to 141-144 t ha(-1) after fallowing and green manuring, but there were no significant responses in the first and second ratoon crops. Also, in the first crop after planting, root length index increased from 3.5 km m(-2) under continuous sugarcane to 5.2-6.8 km m(-2) after fallowing, and improved rooting was still evident in the first ratoon crop where there had been soil drying during the fallow period. Soil bulk density, total porosity and water-holding capacity were not affected by the fallowing practices. However, air-filled porosity increased from 11% under continuous sugarcane to 16% after fallowing, and steady state ponded infiltration rates were increased from 0.61 mm h(-1) to 1.34 mm h(-1), but these improvements were no longer evident after a year back under sugarcane. Levels of soil organic matter were reduced in all cases, probably as a result of the tillage operations involved. In the plant crop, root length was well correlated with air-filled porosity, indicating the importance of improving belowground air supply for crop production on poorly draining clay soils.

Presubmergence and green manure affect the transformations of nitrogen-15-labeled urea under lowland soil conditions

The effect of presubmergence and green manuring on various processes involved in [N-15]-urea transformations were studied in a growth chamber after [N-15]-urea application to floodwater. Presubmergence for 14 days increased urea hydrolysis rates and floodwater pH, resulting in higher NH3 volatilization as compared to without presubmergence. Presubmergence also increased nitrification and subsequent denitrification but lower N assimilation by floodwater algae caused higher gaseous losses. Addition of green manure maintained higher NH4+-N concentration in floodwater mainly because of lower nitrification rates but resulted in highest NH3 volatilization losses. Although green manure did not affect the KCl extractable NH4+-N from applied fertilizer, it maintained higher NH4+-N content due to its decomposition and increased mineralization of organic N. After 32 days about 36.9% (T-1), 23.9% (T-2), and 36.4% (T-3) of the applied urea N was incorporated in the pool of soil organic N in treatments. It was evident that the presubmergence has effected the recovery of applied urea N.

Empirical Orthogonal Functions: The Medium is the Message

Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality reduction used broadly in meteorology and oceanography. Often in the literature, EOF modes are interpreted individually, independent of other modes. In fact, it can be shown that no such attribution can generally be made. This review demonstrates that in general individual EOF modes (i) will not correspond to individual dynamical modes, (ii) will not correspond to individual kinematic degrees of freedom, (iii) will not be statistically independent of other EOF modes, and (iv) will be strongly influenced by the nonlocal requirement that modes maximize variance over the entire domain. The goal of this review is not to argue against the use of EOF analysis in meteorology and oceanography; rather, it is to demonstrate the care that must be taken in the interpretation of individual modes in order to distinguish the medium from the message.