Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation

The weak-constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The well-known result that for Gaussian error statistics the minimum of the weak-constraint inverse is equal to the maximum-likelihood estimate is rederived. Then several methods based on ensemble statistics that can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. they also avoid iterative searches in a Hilbert space, and error estimates can be obtained without much additional computational effort. the feasibility of the new methods is illustrated in a two-layer quasigeostrophic model.

The non-conservation of potential vorticity by a dynamical core compared with the effects of parametrized physical processes

Numerical models of the atmosphere combine a dynamical core, which approximates solutions to the adiabatic, frictionless governing equations for fluid dynamics, with tendencies arising from the parametrization of other physical processes. Since potential vorticity (PV) is conserved following fluid flow in adiabatic, frictionless circumstances, it is possible to isolate the effects of non-conservative processes by accumulating PV changes in an air-mass relative framework. This “PV tracer technique” is used to accumulate separately the effects on PV of each of the different non-conservative processes represented in a numerical model of the atmosphere. Dynamical cores are not exactly conservative because they introduce, explicitly or implicitly, some level of dissipation and adjustment of prognostic model variables which acts to modify PV. Here, the PV tracers technique is extended to diagnose the cumulative effect of the non-conservation of PV by a dynamical core and its characteristics relative to the PV modification by parametrized physical processes. Quantification using the Met Office Unified Model reveals that the magnitude of the non-conservation of PV by the dynamical core is comparable to those from physical processes. Moreover, the residual of the PV budget, when tracing the effects of the dynamical core and physical processes, is at least an order of magnitude smaller than the PV tracers associated with the most active physical processes. The implication of this work is that the non-conservation of PV by a dynamical core can be assessed in case studies with a full suite of physics parametrizations and directly compared with the PV modification by parametrized physical processes. The nonconservation of PV by the dynamical core is shown to move the position of the extratropical tropopause while the parametrized physical processes have a lesser effect at the tropopause level.

Formulation of fermentation media from flour-rich waste streams for microbial lipid production by Lipomyces starkeyi

Flour-rich waste (FRW) and by-product streams generated by bakery, confectionery and wheat milling plants could be employed as the sole raw materials for generic fermentation media production, suitable for microbial oil synthesis. Wheat milling by-products were used in solid state fermentations (SSF) of Aspergillus awamori for the production of crude enzymes, mainly glucoamylase and protease. Enzyme-rich SSF solids were subsequently employed for hydrolysis of FRW streams into nutrient-rich fermentation media. Batch hydrolytic experiments using FRW concentrations up to 205 g/L resulted in higher than 90%(w/w) starch to glucose conversion yields and 40% (w/w) total Kjeldahl nitrogen to free amino nitro-gen conversion yields. Starch to glucose conversion yields of 98.2, 86.1 and 73.4% (w/w) were achieved when initial FRW concentrations of 235, 300 and 350 g/L were employed in fed-batch hydrolytic experiments, respectively. Crude hydrolysates were used as fermentation media in shake flask cultures with the oleaginous yeast Lipomyces starkeyi DSM 70296 reaching a total dry weight of 30.5 g/L with a microbial oil content of 40.4% (w/w), higher than that achieved in synthetic media. Fed-batch bioreactor cultures led to a total dry weight of 109.8 g/L with a microbial oil content of 57.8% (w/w) and productivity of 0.4 g/L/h.

A potential vorticity signature for the cold sector of winter extratropical cyclones

The cold sector of a midlatitude storm is characterized by distinctive features such as strong surface heat fluxes, shallow convection, convective precipitation and synoptic subsidence. In order to evaluate the contribution of processes occurring in the cold sector to the mean climate, an appropriate indicator is needed. This study describes the systematic presence of negative potential vorticity (PV) behind the cold front of extratropical storms in winter. The origin of this negative PV is analyzed using ERA-Interim data, and PV tendencies averaged over the depth of the boundary layer are evaluated. It is found that negative PV is generated by diabatic processes in the cold sector and by Ekman pumping at the low centre, whereas positive PV is generated by Ekman advection of potential temperature in the warm sector. We suggest here that negative PV at low levels can be used to identify the cold sector. A PV-based indicator is applied to estimate the respective contributions of the cold sector and the remainder of the storm to upward motion and large-scale and convective precipitation. We compare the PV-based indicator with other distinctive features that could be used as markers of the cold sector and find that potential vorticity is the best criterion when taken alone and the best when combined with any other.

Rossby wave propagation on potential vorticity fronts with finite width

The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here an approximate correction is derived for the case of a finite width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models.