Optimal control of nonlinear differential algebraic equation systems

A novel iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified linear quadratic model based problem with parameter updating in such a manner that the correct solution of the original non-linear problem is achieved. The resulting algorithm has a particular advantage in that the solution is achieved without the need to solve the differential algebraic equations . Convergence aspects are discussed and a simulation example is described which illustrates the performance of the technique. 1. Introduction When modelling industrial processes often the resulting equations consist of coupled differential and algebraic equations (DAEs). In many situations these equations are nonlinear and cannot readily be directly reduced to ordinary differential equations.

Clear-sky biases in satellite infrared estimates of upper tropospheric humidity and its trends

We use microwave retrievals of upper tropospheric humidity (UTH) to estimate the impact of clear-sky-only sampling by infrared instruments on the distribution, variability and trends in UTH. Our method isolates the impact of the clear-sky-only sampling, without convolving errors from other sources. On daily time scales IR-sampled UTH contains large data gaps in convectively active areas, with only about 20-30 % of the tropics (30 S­ 30 N) being sampled. This results in a dry bias of about -9 %RH in the area-weighted tropical daily UTH time series. On monthly scales, maximum clear-sky bias (CSB) is up to -30 %RH over convectively active areas. The magnitude of CSB shows significant correlations with UTH itself (-0.5) and also with the variability in UTH (-0.6). We also show that IR-sampled UTH time series have higher interannual variability and smaller trends compared to microwave sampling. We argue that a significant part of the smaller trend results from the contrasting influence of diurnal drift in the satellite measurements on the wet and dry regions of the tropics.

Semi-dwarfing (Rht-B1b) improves nitrogen-use efficiency in wheat, but not at economically optimal levels of nitrogen availability

A UK field experiment compared a complete factorial combination of three backgrounds (cvs Mercia, Maris Huntsman and Maris Widgeon), three alleles at the Rht-B1 locus as Near Isogenic Lines (NILs: rht-B1a (tall), Rht-B1b (semi-dwarf), Rht-B1c (severe dwarf)) and four nitrogen (N) fertilizer application rates (0, 100, 200 and 350 kg N/ha). Linear+exponential functions were fitted to grain yield (GY) and nitrogen-use efficiency (NUE; GY/available N) responses to N rate. Averaged over N rate and background Rht-B1b conferred significantly (P<0.05) greater GY, NUE, N uptake efficiency (NUpE; N in above ground crop / available N) and N utilization efficiency (NUtEg; GY / N in above ground crop) compared with rht-B1a and Rht-B1c. However the economically optimal N rate (Nopt) for N:grain price ratios of 3.5:1 to 10:1 were also greater for Rht-B1b, and because NUE, NUpE and NUtE all declined with N rate, Rht-Blb failed to increase NUE or its components at Nopt. The adoption of semi-dwarf lines in temperate and humid regions, and the greater N rates that such adoption justifies economically, greatly increases land-use efficiency, but not necessarily, NUE.

Impact of land cover uncertainties on estimates of biospheric carbon fluxes

Large-scale bottom-up estimates of terrestrial carbon fluxes, whether based on models or inventory, are highly dependent on the assumed land cover. Most current land cover and land cover change maps are based on satellite data and are likely to be so for the foreseeable future. However, these maps show large differences, both at the class level and when transformed into Plant Functional Types (PFTs), and these can lead to large differences in terrestrial CO2 fluxes estimated by Dynamic Vegetation Models. In this study the Sheffield Dynamic Global Vegetation Model is used. We compare PFT maps and the resulting fluxes arising from the use of widely available moderate (1 km) resolution satellite-derived land cover maps (the Global Land Cover 2000 and several MODIS classification schemes), with fluxes calculated using a reference high (25 m) resolution land cover map specific to Great Britain (the Land Cover Map 2000). We demonstrate that uncertainty is introduced into carbon flux calculations by (1) incorrect or uncertain assignment of land cover classes to PFTs; (2) information loss at coarser resolutions; (3) difficulty in discriminating some vegetation types from satellite data. When averaged over Great Britain, modeled CO2 fluxes derived using the different 1 km resolution maps differ from estimates made using the reference map. The ranges of these differences are 254 gC m−2 a−1 in Gross Primary Production (GPP); 133 gC m−2 a−1 in Net Primary Production (NPP); and 43 gC m−2 a−1 in Net Ecosystem Production (NEP). In GPP this accounts for differences of −15.8% to 8.8%. Results for living biomass exhibit a range of 1109 gC m−2. The types of uncertainties due to land cover confusion are likely to be representative of many parts of the world, especially heterogeneous landscapes such as those found in western Europe.

Landscape, regional and global estimates of nitrogen flux from land to sea: errors and uncertainties

Regional to global scale modelling of N flux from land to ocean has progressed to date through the development of simple empirical models representing bulk N flux rates from large watersheds, regions, or continents on the basis of a limited selection of model parameters. Watershed scale N flux modelling has developed a range of physically-based approaches ranging from models where N flux rates are predicted through a physical representation of the processes involved, through to catchment scale models which provide a simplified representation of true systems behaviour. Generally, these watershed scale models describe within their structure the dominant process controls on N flux at the catchment or watershed scale, and take into account variations in the extent to which these processes control N flux rates as a function of landscape sensitivity to N cycling and export. This paper addresses the nature of the errors and uncertainties inherent in existing regional to global scale models, and the nature of error propagation associated with upscaling from small catchment to regional scale through a suite of spatial aggregation and conceptual lumping experiments conducted on a validated watershed scale model, the export coefficient model. Results from the analysis support the findings of other researchers developing macroscale models in allied research fields. Conclusions from the study confirm that reliable and accurate regional scale N flux modelling needs to take account of the heterogeneity of landscapes and the impact that this has on N cycling processes within homogenous landscape units.