The counter-propagating Rossby-wave perspective on baroclinic instability. II: Application to the Charney model

The constant-density Charney model describes the simplest unstable basic state with a planetary-vorticity gradient, which is uniform and positive, and baroclinicity that is manifest as a negative contribution to the potential-vorticity (PV) gradient at the ground and positive vertical wind shear. Together, these ingredients satisfy the necessary conditions for baroclinic instability. In Part I it was shown how baroclinic growth on a general zonal basic state can be viewed as the interaction of pairs of ‘counter-propagating Rossby waves’ (CRWs) that can be constructed from a growing normal mode and its decaying complex conjugate. In this paper the normal-mode solutions for the Charney model are studied from the CRW perspective. Clear parallels can be drawn between the most unstable modes of the Charney model and the Eady model, in which the CRWs can be derived independently of the normal modes. However, the dispersion curves for the two models are very different; the Eady model has a short-wave cut-off, while the Charney model is unstable at short wavelengths. Beyond its maximum growth rate the Charney model has a neutral point at finite wavelength (r=1). Thereafter follows a succession of unstable branches, each with weaker growth than the last, separated by neutral points at integer r—the so-called ‘Green branches’. A separate branch of westward-propagating neutral modes also originates from each neutral point. By approximating the lower CRW as a Rossby edge wave and the upper CRW structure as a single PV peak with a spread proportional to the Rossby scale height, the main features of the ‘Charney branch’ (0

Uncertainties in annual riverine phosphorus load estimation: Impact of load estimation methodology, sampling frequency, baseflow index and catchment population density

Models developed to identify the rates and origins of nutrient export from land to stream require an accurate assessment of the nutrient load present in the water body in order to calibrate model parameters and structure. These data are rarely available at a representative scale and in an appropriate chemical form except in research catchments. Observational errors associated with nutrient load estimates based on these data lead to a high degree of uncertainty in modelling and nutrient budgeting studies. Here, daily paired instantaneous P and flow data for 17 UK research catchments covering a total of 39 water years (WY) have been used to explore the nature and extent of the observational error associated with nutrient flux estimates based on partial fractions and infrequent sampling. The daily records were artificially decimated to create 7 stratified sampling records, 7 weekly records, and 30 monthly records from each WY and catchment. These were used to evaluate the impact of sampling frequency on load estimate uncertainty. The analysis underlines the high uncertainty of load estimates based on monthly data and individual P fractions rather than total P. Catchments with a high baseflow index and/or low population density were found to return a lower RMSE on load estimates when sampled infrequently than those with a tow baseflow index and high population density. Catchment size was not shown to be important, though a limitation of this study is that daily records may fail to capture the full range of P export behaviour in smaller catchments with flashy hydrographs, leading to an underestimate of uncertainty in Load estimates for such catchments. Further analysis of sub-daily records is needed to investigate this fully. Here, recommendations are given on load estimation methodologies for different catchment types sampled at different frequencies, and the ways in which this analysis can be used to identify observational error and uncertainty for model calibration and nutrient budgeting studies. (c) 2006 Elsevier B.V. All rights reserved.

Soil fertility management in the mid-hills of Nepal: Practices and perceptions

Sustaining soil fertility is essential to the prosperity of many households in the mid-hills of Nepal, but there are concerns that the breakdown of the traditional linkages between forest, livestock, and cropping systems is adversely affecting fertility. This study used triangulated data from surveys of households, discussion groups, and key informants in 16 wards in eastern and western Nepal to determine the existing practices for soil fertility management, the extent of such practices, and the perception of the direction of changes in soil fertility. The two principal practices for maintaining soil fertility were the application of farmyard manure (FYM) and of chemical fertilizer (mainly urea and diammonium phosphate). Green manuring, in-situ manuring, slicing terrace risers, and burning plant residues are rarely practiced. FYM usage was variable with more generally applied to khet land (average 6053 kg fresh weight manure ha(-1)) than to bari land (average 4185 kg fresh weight manure ha-1) with manure from goats and poultry preferred above that from cows and buffaloes. Almost all households (98%) apply urea to khet land and 87% to bari land, with 45% applying diammonium phosphate to both types of land. Application rates and timings of applications varied considerably both within and between wards suggesting poor knowledge transfer between the research and farming communities. The benefits of chemical fertilizers in terms of ease of application and transportation in comparison with FYM, were perceived to outweigh the widely reported detrimental hardening of soil associated with their continued usage. Among key informants, FYM applied in conjunction with chemical fertilizer was the most popular amendment, with FYM alone preferred more than chemical fertilizer alone - probably because of the latter's long-term detrimental effects. Key informant and householder surveys differed in their perception of fertility changes in the last decade probably because of differences in age and site-specific knowledge. All key informants felt that fertility had declined but among households, only about 40% perceived a decline with the remainder about evenly divided between no change and an increase. Householders with small landholdings (< 0.5 ha) were more likely to perceive increasing soil fertility while those with larger landholdings (> 2 ha) were more likely to perceive declining fertility. Perceived changes in soil fertility were not related to food self-sufficiency. The reasons for the slow spread of new technologies within wards and the poor understanding of optimal use of chemical fertilizers in conjunction with improved quality FYM may repay further investigation in terms of sustaining soil fertility in this region.

Uneven distribution of nutrients in the root zone affects the incidence of blossom end rot and concentration of calcium and potassium in fruits of tomato

Tomato plants ( Lycopersicon esculentum Mill. var. DRK) were grown hydroponically to determine the effect of an uneven distribution of nutrients in the root zone on blossomend rot (BER) and Ca and K concentrations in the fruits. The plants were grown in rockwool with their root system divided into two portions. Each portion was irrigated with nutrient solutions with either the same or the different electrical conductivity (EC) in the range 0 to 6 dS m(-1). Solutions with high EC supplied to both sides of the root system significantly increased the incidence of BER. However, when only water or a solution of low EC was supplied to one portion, BER was reduced by 80%. Fruit yields were significantly higher ( P < 0.01) for plants that received solutions of the uneven EC treatments (6/0 or 4.5/0 EC treatment). Plants supplied with solutions of uneven EC generally had higher leaf and fruit concentrations of Ca but lower concentrations of K than those supplied with solutions of high EC. There was no difference in Ca concentration at the distal end of young fruits of the uneven EC treatment but it was reduced in the high EC treatments. The concentration of K in the mature fruits of the uneven EC treatments was lower than that of the high EC treatments and higher or similar that of the 3/3 or 2.5/2.5 EC treatments ( controls). A clear relationship was found between the incidence of BER and the exudation rate. High rate of xylem exudation was observed in the uneven EC treatments. Reduction of BER in the uneven EC treatments is most likely to be the effect of high exudation rate on Ca status in the young fruits. It was concluded that high EC of solution had positive effects on Ca concentration and incidence of BER provided that nutrient solution with low EC or water is supplied to the one portion of the root system.

Mersenne numbers

These notes have been issued on a small scale in 1983 and 1987 and on request at other times. This issue follows two items of news. First, WaIter Colquitt and Luther Welsh found the 'missed' Mersenne prime M110503 and advanced the frontier of complete Mp-testing to 139,267. In so doing, they terminated Slowinski's significant string of four consecutive Mersenne primes. Secondly, a team of five established a non-Mersenne number as the largest known prime. This result terminated the 1952-89 reign of Mersenne primes. All the original Mersenne numbers with p < 258 were factorised some time ago. The Sandia Laboratories team of Davis, Holdridge & Simmons with some little assistance from a CRAY machine cracked M211 in 1983 and M251 in 1984. They contributed their results to the 'Cunningham Project', care of Sam Wagstaff. That project is now moving apace thanks to developments in technology, factorisation and primality testing. New levels of computer power and new computer architectures motivated by the open-ended promise of parallelism are now available. Once again, the suppliers may be offering free buildings with the computer. However, the Sandia '84 CRAY-l implementation of the quadratic-sieve method is now outpowered by the number-field sieve technique. This is deployed on either purpose-built hardware or large syndicates, even distributed world-wide, of collaborating standard processors. New factorisation techniques of both special and general applicability have been defined and deployed. The elliptic-curve method finds large factors with helpful properties while the number-field sieve approach is breaking down composites with over one hundred digits. The material is updated on an occasional basis to follow the latest developments in primality-testing large Mp and factorising smaller Mp; all dates derive from the published literature or referenced private communications. Minor corrections, additions and changes merely advance the issue number after the decimal point. The reader is invited to report any errors and omissions that have escaped the proof-reading, to answer the unresolved questions noted and to suggest additional material associated with this subject.

Less-is-more effects without the recognition heuristic

Inferences consistent with “recognition-based” decision-making may be drawn for various reasons other than recognition alone. We demonstrate that, for 2-alternative forced-choice decision tasks, less-is-more effects (reduced performance with additional learning) are not restricted to recognition-based inference but can also be seen in circumstances where inference is knowledge-based but item knowledge is limited. One reason why such effects may not be observed more widely is the dependence of the effect on specific values for the validity of recognition and knowledge cues. We show that both recognition and knowledge validity may vary as a function of the number of items recognized. The implications of these findings for the special nature of recognition information, and for the investigation of recognition-based inference, are discussed

Risk and price in the bidding process of contractors

Formal and analytical risk models prescribe how risk should be incorporated in construction bids. However, the actual process of how contractors and their clients negotiate and agree on price is complex, and not clearly articulated in the literature. Using participant observation, the entire tender process was shadowed in two leading UK construction firms. This was compared to propositions in analytical models and significant differences were found. 670 hours of work observed in both firms revealed three stages of the bidding process. Bidding activities were categorized and their extent estimated as deskwork (32%), calculations (19%), meetings (14%), documents (13%), off-days (11%), conversations (7%), correspondence (3%) and travel (1%). Risk allowances of 1-2% were priced in some bids and three tiers of risk apportionment in bids were identified. However, priced risks may sometimes be excluded from the final bidding price to enhance competitiveness. Thus, although risk apportionment affects a contractor’s pricing strategy, other complex, microeconomic factors also affect price. Instead of pricing in contingencies, risk was priced mostly through contractual rather than price mechanisms, to reflect commercial imperatives. The findings explain why some assumptions underpinning analytical models may not be sustainable in practice and why what actually happens in practice is important for those who seek to model the pricing of construction bids.

The relationship between multi-species catch and effort: among fishery comparisons

The control of fishing mortality via fishing effort remains fundamental to most fisheries management strategies even at the local community or co-management level. Decisions to support such strategies require knowledge of the underlying response of the catch to changes in effort. Even under adaptive management strategies, imprecise knowledge of the response is likely to help accelerate the adaptive learning process. Data and institutional capacity requirements to employ multi-species biomass dynamics and age-structured models invariably render their use impractical particularly in less developed regions of the world. Surplus production models fitted to catch and effort data aggregated across all species offer viable alternatives. The current paper seeks models of this type that best describe the multi-species catch–effort responses in floodplain-rivers, lakes and reservoirs and reef-based fisheries based upon among fishery comparisons, building on earlier work. Three alternative surplus production models were fitted to estimates of catch per unit area (CPUA) and fisher density for 258 fisheries in Africa, Asia and South America. In all cases examined, the best or equal best fitting model was the Fox type, explaining up to 90% of the variation in CPUA. For lake and reservoir fisheries in Africa and Asia, the Schaefer and an asymptotic model fitted equally well. The Fox model estimates of fisher density (fishers km−2) at maximum yield (iMY) for floodplain-rivers, African lakes and reservoirs and reef-based fisheries are 13.7 (95% CI [11.8, 16.4]); 27.8 (95% CI [17.5, 66.7]) and 643 (95% CI [459,1075]), respectively and compare well with earlier estimates. Corresponding estimates of maximum yield are also given. The significantly higher value of iMY for reef-based fisheries compared to estimates for rivers and lakes reflects the use of a different measure of fisher density based upon human population size estimates. The models predict that maximum yield is achieved at a higher fishing intensity in Asian lakes compared to those in Africa. This may reflect the common practice in Asia of stocking lakes to augment natural recruitment. Because of the equilibrium assumptions underlying the models, all the estimates of maximum yield and corresponding levels of effort should be treated with caution.