Amodifiedshallowwater systemfor investigating convective-scaledataassimilation

Data assimilation (DA) techniques need to evolve in order to keep up with the devel-opments in convection-permitting Numer-ical Weather Prediction (NWP) models. It is often unfeasible, and indeed undesirable, to investigate the potential of new data assimi-lation schemes on operational forecasting sys-tems. Instead, idealised models can be em-ployed that capture the fundamental features of convective-scale dynamics while remaining computationally inexpensive, thus allowing an extensive investigation of the proposed scheme. 3. Model: SWEs with ‘rain’ We outline an idealised NWP model (after [1]) based on the SWEs which is designed to rep-resent an idealised atmosphere with moist convection. Moisture is incorporated into the traditional SWEs by the introduction of a ‘rain mass fraction ’ variable, r, which acts on the momentum equation (1b) via the geopotential, and is allowed to precipitate via an additional conservation equation (1c). ∂th+ ∂x(hu) = 0, (1a) ∂t(hu) + ∂x(hu 2 + p(h)) + gh∂xb +hc20∂xr − fhv = 0, (1b) ∂t(hr) + ∂x(hur) + hβ̃∂xu+ αhr = 0, (1c) ∂t(hv) + ∂x(huv) + fhu = 0, (1d) ∂tb = 0, (1e) where p = p(h) is a pseudo-pressure defined by: p(h)