A singular vector perspective of 4D-Var: Filtering and interpolation

Four-dimensional variational data assimilation (4D-Var) combines the information from a time sequence of observations with the model dynamics and a background state to produce an analysis. In this paper, a new mathematical insight into the behaviour of 4D-Var is gained from an extension of concepts that are used to assess the qualitative information content of observations in satellite retrievals. It is shown that the 4D-Var analysis increments can be written as a linear combination of the singular vectors of a matrix which is a function of both the observational and the forecast model systems. This formulation is used to consider the filtering and interpolating aspects of 4D-Var using idealized case-studies based on a simple model of baroclinic instability. The results of the 4D-Var case-studies exhibit the reconstruction of the state in unobserved regions as a consequence of the interpolation of observations through time. The results also exhibit the filtering of components with small spatial scales that correspond to noise, and the filtering of structures in unobserved regions. The singular vector perspective gives a very clear view of this filtering and interpolating by the 4D-Var algorithm and shows that the appropriate specification of the a priori statistics is vital to extract the largest possible amount of useful information from the observations. Copyright © 2005 Royal Meteorological Society

Can 4D-Var use dynamical information from targeted observations of a baroclinic structure?

Targeted observations are generally taken in regions of high baroclinicity, but often show little impact. One plausible explanation is that important dynamical information, such as upshear tilt, is not extracted from the targeted observations by the data assimilation scheme and used to correct initial condition error. This is investigated by generating pseudo targeted observations which contain a singular vector (SV) structure that is not present in the background field or routine observations, i.e. assuming that the background has an initial condition error with tilted growing structure. Experiments were performed for a single case-study with varying numbers of pseudo targeted observations. These were assimilated by the Met Office four-dimensional variational (4D-Var) data assimilation scheme, which uses a 6 h window for observations and background-error covariances calculated using the National Meteorological Centre (NMC) method. The forecasts were run using the operational Met Office Unified Model on a 24 km grid. The results presented clearly demonstrate that a 6 h window 4D-Var system is capable of extracting baroclinic information from a limited set of observations and using it to correct initial condition error. To capture the SV structure well (projection of 0.72 in total energy), 50 sondes over an area of 1×106 km2 were required. When the SV was represented by only eight sondes along an example targeting flight track covering a smaller area, the projection onto the SV structure was lower; the resulting forecast perturbations showed an SV structure with increased tilt and reduced initial energy. The total energy contained in the perturbations decreased as the SV structure was less well described by the set of observations (i.e. as fewer pseudo observations were assimilated). The assimilated perturbation had lower energy than the SV unless the pseudo observations were assimilated with the dropsonde observation errors halved from operational values. Copyright © 2010 Royal Meteorological Society

The influence of winter oilseed rape (Brassica napus ssp oleifera var. biennis) canopy size on grass weed growth and grass weed seed return

Four experiments conducted over three seasons (2002-05) at the Crops Research Unit, University of Reading, investigated effects of canopy management of autumn sown oilseed rape (Brassica napus L. ssp. oleifera var. biennis (DC.) Metzg.) on competition with grass weeds. Emphasis was placed on the effect of the crop on the weeds. Rape canopy size was manipulated using sowing date, seed rate and the application of autumn fertilizer. Lolium multiflorum Lam., L. x boucheanum Kunth and Alopecurus myosuroides Huds. were sown as indicative grass weeds. The effects of sowing date, seed rate and autumn nitrogen on crop competitive ability were correlated with rape biomass and fractional interception of photosynthetically active radiation (PAR) by the rape floral layer, to the extent that by spring there was good evidence of crop: weed replacement. An increase in seed rate up to the highest plant densities tested increased both rape biomass and competitiveness, e.g. in 2002/3, L. multiflorum head density was reduced from 539 to 245 heads/m(2) and spikelet density from 13 170 to 5960 spikelets/m(2) when rape plant density was increased from 16 to 81 plants/m(2). Spikelets/head of Lolium spp. was little affected by rape seed rate, but the length of heads of A. myosuroides was reduced by 9 % when plant density was increased from 29-51 plants/m(2). Autumn nitrogen increased rape biomass and reduced L. multiflorum head density (415 and 336 heads/m(2) without and with autumn nitrogen, respectively) and spikelet density (9990 and 8220 spikelets/m(2) without and with autumn nitrogen, respectively). The number of spikelets/head was not significantly affected by autumn nitrogen. Early sowing could increase biomass and competitiveness, but poor crop establishment sometimes overrode the effect. Where crop and weed establishment was similar for both sowing dates, a 2-week delay (i.e. early September to mid-September) increased L. multiflorum head density from 226 to 633 heads/m(2) and spikelet density from 5780 to 15 060 spikelets/m(2).

The influence of winter oilseed rape (Brassica napus ssp oleifera var. biennis) cultivar and grass genotype on the competitive balance between crop and grass weeds

Three experiments conducted over two years (2002-04) at the Crops Research Unit, University of Reading, investigated competition between autumn sown oilseed rape cultivars (Brassica napus L. ssp. oleifera var. biennis (DC.) Metzg.) and Lolium multiflorum Lam., L. x boucheanum Kunth and Alopecurus myosuroides Huds., sown as indicative grass weeds. Rape cultivar (cv.) had a substantial effect on grass weed seed return. Over the six cultivars tested, L. multiflorum spikelet production ranged from just under 400 spikelets/m(2) in the presence of cv. Winner to nearly 5800 in competition with cv. Lutin. Cultivar competitiveness was associated with high biomass, large dense floral layers and early stem extension. There was some evidence of differential competitive tolerance between rape cultivars. The results suggested that rape cultivars could be screened for competitiveness by measuring floral layer interception of photosynthetic active radiation. L. x boucheanum cultivars varied in ability to compete with rape. In the absence of inter-specific competition, spikelet density was similar for Aberecho and Polly (circa 31000 spikelets/m(2)) but when grown with rape Polly outyielded Aberecho (i.e. 12 090 and 7990 spikelets/m(2) respectively).

The influence of winter oilseed rape (Brassica napus ssp. oleifera var. biennis) cultivar and grass genotype on the competitive balance between crop and grass weeds

Four experiments conducted over three seasons (2002–05) at the Crops Research Unit, University of Reading, investigated effects of canopy management of autumn sown oilseed rape (Brassica napus L. ssp. oleifera var. biennis (DC.) Metzg.) on competition with grass weeds. Emphasis was placed on the effect of the crop on the weeds. Rape canopy size was manipulated using sowing date, seed rate and the application of autumn fertilizer. Lolium multiflorum Lam., L.rboucheanum Kunth and Alopecurus myosuroides Huds. were sown as indicative grass weeds. The effects of sowing date, seed rate and autumn nitrogen on crop competitive ability were correlated with rape biomass and fractional interception of photosynthetically active radiation (PAR) by the rape floral layer, to the extent that by spring there was good evidence of crop: weed replacement. An increase in seed rate up to the highest plant densities tested increased both rape biomass and competitiveness, e.g. in 2002/3, L. multiflorum head density was reduced from 539 to 245 heads/m2 and spikelet density from 13 170 to 5960 spikelets/m2 when rape plant density was increased from 16 to 81 plants/m2. Spikelets/head of Lolium spp. was little affected by rape seed rate, but the length of heads of A. myosuroides was reduced by 9%when plant density was increased from 29–51 plants/m2. Autumn nitrogen increased rape biomass and reduced L. multiflorum head density (415 and 336 heads/m2 without and with autumn nitrogen, respectively) and spikelet density (9990 and 8220 spikelets/m2 without and with autumn nitrogen, respectively). The number of spikelets/head was not significantly affected by autumn nitrogen. Early sowing could increase biomass and competitiveness, but poor crop establishment sometimes overrode the effect. Where crop and weed establishment was similar for both sowing dates, a 2-week delay (i.e. early September to mid-September) increased L. multiflorum head density from 226 to 633 heads/m2 and spikelet density from 5780 to 15 060 spikelets/m2.

The influence of winter oilseed rape (Brassica napus ssp oleifera var. biennis) canopy size on grass weed growth and grass weed seed return

Four experiments conducted over three seasons (2002-05) at the Crops Research Unit, University of Reading, investigated effects of canopy management of autumn sown oilseed rape (Brassica napus L. ssp. oleifera var. biennis (DC.) Metzg.) on competition with grass weeds. Emphasis was placed on the effect of the crop on the weeds. Rape canopy size was manipulated using sowing date, seed rate and the application of autumn fertilizer. Lolium multiflorum Lam., L. x boucheanum Kunth and Alopecurus myosuroides Huds. were sown as indicative grass weeds. The effects of sowing date, seed rate and autumn nitrogen on crop competitive ability were correlated with rape biomass and fractional interception of photosynthetically active radiation (PAR) by the rape floral layer, to the extent that by spring there was good evidence of crop: weed replacement. An increase in seed rate up to the highest plant densities tested increased both rape biomass and competitiveness, e.g. in 2002/3, L. multiflorum head density was reduced from 539 to 245 heads/m(2) and spikelet density from 13 170 to 5960 spikelets/m(2) when rape plant density was increased from 16 to 81 plants/m(2). Spikelets/head of Lolium spp. was little affected by rape seed rate, but the length of heads of A. myosuroides was reduced by 9 % when plant density was increased from 29-51 plants/m(2). Autumn nitrogen increased rape biomass and reduced L. multiflorum head density (415 and 336 heads/m(2) without and with autumn nitrogen, respectively) and spikelet density (9990 and 8220 spikelets/m(2) without and with autumn nitrogen, respectively). The number of spikelets/head was not significantly affected by autumn nitrogen. Early sowing could increase biomass and competitiveness, but poor crop establishment sometimes overrode the effect. Where crop and weed establishment was similar for both sowing dates, a 2-week delay (i.e. early September to mid-September) increased L. multiflorum head density from 226 to 633 heads/m(2) and spikelet density from 5780 to 15 060 spikelets/m(2).

The influence of winter oilseed rape (Brassica napus ssp oleifera var. biennis) cultivar and grass genotype on the competitive balance between crop and grass weeds

Three experiments conducted over two years (2002-04) at the Crops Research Unit, University of Reading, investigated competition between autumn sown oilseed rape cultivars (Brassica napus L. ssp. oleifera var. biennis (DC.) Metzg.) and Lolium multiflorum Lam., L. x boucheanum Kunth and Alopecurus myosuroides Huds., sown as indicative grass weeds. Rape cultivar (cv.) had a substantial effect on grass weed seed return. Over the six cultivars tested, L. multiflorum spikelet production ranged from just under 400 spikelets/m(2) in the presence of cv. Winner to nearly 5800 in competition with cv. Lutin. Cultivar competitiveness was associated with high biomass, large dense floral layers and early stem extension. There was some evidence of differential competitive tolerance between rape cultivars. The results suggested that rape cultivars could be screened for competitiveness by measuring floral layer interception of photosynthetic active radiation. L. x boucheanum cultivars varied in ability to compete with rape. In the absence of inter-specific competition, spikelet density was similar for Aberecho and Polly (circa 31000 spikelets/m(2)) but when grown with rape Polly outyielded Aberecho (i.e. 12 090 and 7990 spikelets/m(2) respectively).

Quasi-optimal assimilation of satellite retrievals for incremental 4D-Var

An interface between satellite retrievals and the incremental version of the four-dimensional variational assimilation scheme is developed, making full use of the information content of satellite measurements. In this paper, expressions for the function that calculates simulated observations from model states (called “observation operator”), together with its tangent linear version and adjoint, are derived. Results from our work can be used for implementing a quasi-optimal assimilation of satellite retrievals (e.g., of atmospheric trace gases) in operational meteorological centres.

3D-Var assimilation of insect-derived Doppler radar radial winds in convective cases using a high resolution model

The assimilation of Doppler radar radial winds for high resolution NWP may improve short term forecasts of convective weather. Using insects as the radar target, it is possible to provide wind observations during convective development. This study aims to explore the potential of these new observations, with three case studies. Radial winds from insects detected by 4 operational weather radars were assimilated using 3D-Var into a 1.5 km resolution version of the Met Office Unified Model, using a southern UK domain and no convective parameterization. The effect on the analysis wind was small, with changes in direction and speed up to 45° and 2 m s−1 respectively. The forecast precipitation was perturbed in space and time but not substantially modified. Radial wind observations from insects show the potential to provide small corrections to the location and timing of showers but not to completely relocate convergence lines. Overall, quantitative analysis indicated the observation impact in the three case studies was small and neutral. However, the small sample size and possible ground clutter contamination issues preclude unequivocal impact estimation. The study shows the potential positive impact of insect winds; future operational systems using dual polarization radars which are better able to discriminate between insects and clutter returns should provided a much greater impact on forecasts.

Gaussian quadrature 4D-VAR

A new incremental four-dimensional variational (4D-Var) data assimilation algorithm is introduced. The algorithm does not require the computationally expensive integrations with the nonlinear model in the outer loops. Nonlinearity is accounted for by modifying the linearization trajectory of the observation operator based on integrations with the tangent linear (TL) model. This allows us to update the linearization trajectory of the observation operator in the inner loops at negligible computational cost. As a result the distinction between inner and outer loops is no longer necessary. The key idea on which the proposed 4D-Var method is based is that by using Gaussian quadrature it is possible to get an exact correspondence between the nonlinear time evolution of perturbations and the time evolution in the TL model. It is shown that J-point Gaussian quadrature can be used to derive the exact adjoint-based observation impact equations and furthermore that it is straightforward to account for the effect of multiple outer loops in these equations if the proposed 4D-Var method is used. The method is illustrated using a three-level quasi-geostrophic model and the Lorenz (1996) model.

The potential to intensify sulforaphane formation in cooked broccoli (Brassica oleracea var. italica) using mustard seeds (Sinapis alba)

Sulforaphane, a naturally occurring cancer chemopreventive, is the hydrolysis product of glucoraphanin, the main glucosinolate in broccoli. The hydrolysis requires myrosinase isoenzyme to be present in sufficient activity; however processing leads to its denaturation and hence reduced hydrolysis. In this study, the effect of adding mustard seeds, which has a more resilient isoform of myrosinase, to processed broccoli was investigated with a view to intensify the formation of sulforaphane. Thermal inactivation of myrosinase from both broccoli and mustard seeds was studied. Thermal degradation of broccoli glucoraphanin was investigated in addition to the effects of thermal processing on the formation of sulforaphane and sulforaphane nitrile. Limited thermal degradation of glucoraphanin (less than 12 %) was observed when broccoli was placed in vacuum sealed bag (sous vide) and cooked in a water bath at 100 ºC for 8 and 12 min. Boiling broccoli in water prevented the formation of any significant levels of sulforaphane due to inactivated myrosinase. However, addition of powdered mustard seeds to the heat processed broccoli significantly increased the formation of sulforaphane.