Preliminaries: the hydrostatic equation The principle of hydrostatic equilibrium is that the pressure at any point For example, the density of water is 1000 kilograms per cubic meter (in SI
But, even though we can't integrate the hydrostatic equation until some The atmosphere is very close to hydrostatic balance most of the time, except at isolated locations when the vertical profile becomes statically unstable. of a unit-area column of height 10.6 Why do weather maps use pressure surfaces instead of height surfaces? The convection zone. So the pressure 1 m below the surface of water (ignoring The average depth of the ocean is about 4 km, so the pressure on the sea floor is about 400 atmospheres. d. radiation and heat. meters of depth. It is then of interest, and an aim of this article, to determine whether (and to what extent) forecast errors are hydrostatically balanced for a 1.5 km horizontal resolution version of the Met Office Unified Model (UM).To this end, a set of high‐resolution forecasts is generated for a case study on 27 July 2008 using the Met Office ensemble prediction system and the 1.5 km Unified Model over convective and non‐convective regions of the southern UK for a period of up to three hours after the onset of convection. In a recent study, Montmerle and Berre (2010) have developed a new 3D‐Var scheme to assimilate satellite and radar data at mesoscales.
As the convection moves out from the Conv1 column over the next two hours (see Figure Computing the mass‐weighted standard deviation of unbalanced perturbations as in section Mass‐weighted standard deviation of unbalanced perturbations in K over all vertical levels with coarsened resolutions around Conv1 and Non‐Conv columns.To investigate how well hydrostatic balance holds for forecast errors at convective scales, we used an ensemble with 24 members obtained by running the 1.5 km resolution version of the UM, initialized according to the procedure described in section 2.3 and Appendix A. column of the fluid, one unit of area in cross-section. For each of these columns the hydrostatically balanced potential temperature perturbations By constructing the correlation matrices for these columns, it was shown that at 1.5 km resolution hydrostatic balance does not hold in the perturbations in the regions of convection, but does hold in those regions where convection is not present. The assumption that the atmosphere is in hydrostatic equilibrium. strictly incompressible; but very high pressures are required to change Density changes with pressure, and gravity changes with height, so the equation would be: [Remember that hydrostatic equilibrium with the gravitational force throughout the body of the Sun. (The full and balanced ensemble correlation matrices of the perturbations This qualitative comparison between full and balanced correlations of potential temperature indicates that the hydrostatic balance is no longer valid in the perturbations where convection is present.The full ensemble perturbations are close to hydrostatic balance if To evaluate the degree of hydrostatic balance at 1.5 km resolution as a function of time, we plot the ratio Percentage amplitude of unbalanced perturbations relative to full perturbations as a function of time and height at 1.5 km resolution. Department of Mathematics, University of Reading, UKThe work of these authors was supported in part by a NERC CASE award with the Met Office and in part by the NERC National Centre for Earth Observation (NCEO).The contribution of these authors was written in the course of their employment at the Met Office, UK, and is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland.Department of Meteorology, University of Reading, UKThe work of these authors was supported in part by a NERC CASE award with the Met Office and in part by the NERC National Centre for Earth Observation (NCEO).Department of Mathematics, University of Reading, UKThe work of these authors was supported in part by a NERC CASE award with the Met Office and in part by the NERC National Centre for Earth Observation (NCEO).The contribution of these authors was written in the course of their employment at the Met Office, UK, and is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland.Department of Mathematics, University of Reading, UKThe work of these authors was supported in part by a NERC CASE award with the Met Office and in part by the NERC National Centre for Earth Observation (NCEO).The contribution of these authors was written in the course of their employment at the Met Office, UK, and is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland.Department of Meteorology, University of Reading, UKThe work of these authors was supported in part by a NERC CASE award with the Met Office and in part by the NERC National Centre for Earth Observation (NCEO).Department of Mathematics, University of Reading, UKThe work of these authors was supported in part by a NERC CASE award with the Met Office and in part by the NERC National Centre for Earth Observation (NCEO).The contribution of these authors was written in the course of their employment at the Met Office, UK, and is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland.Use the link below to share a full-text version of this article with your friends and colleagues.
The 24 km NAE model has 360 grid points in latitude, 215 in longitude and 38 vertical levels.The current data‐assimilation (DA) system for the 1.5 km model is similar to that used with the operational UK 4 km Met Office model, which is discussed in detail in Dixon To obtain the initial‐condition ensemble at 1.5 km resolution, the following steps are performed (see Figure The full ensemble matrix has dimensions of ${\bf{X}} \in \mathcal{R}^{(360 \times 288 \times 70) \times 24}$In this section we derive the approximation of hydrostatic balance for perturbations by determining, for each of the ensemble members, the hydrostatically balanced potential temperature perturbations Available fields at a given location at a given vertical level are Exner pressure Π, potential temperature potential temperature ensemble )Motions that are predominantly vertical and driven by buoyancy forces arising from static instability, with locally significant deviations from hydrostatic equilibrium.