Predictability of orographic drag for realistic atmospheric profiles Helen Wells and Simon Vosper © Crown copyright Met Office

Contents Introduction to orographic drag parametrization This presentation covers the following areas Introduction to orographic drag parametrization Experimental set-up Results: Show uncertainty in drag due to Use of a simple low-layer depth-averaged UL and NL Differences in profiles between the model and reality Non-linear effects Future Work © Crown copyright Met Office

To Orographic Drag Parametrization Introduction To Orographic Drag Parametrization © Crown copyright Met Office

The current Met Office orographic drag parametrization (total) (GWD) z=0 Sub-grid mountain height, h= 2 = standard deviation of sub-grid orography Depth-averaged low-level L, UL and NL (averaged over z=0 to z=h) Calculate the linear hydrostatic drag (total) = (linear) = LULNLh2 partitioned into (GWD) and (blocked) depending on F=UL/(NLh) A saturation test is then used to determine the height above the orography at which the gravity wave drag is deposited. © Crown copyright Met Office

Orographic Drag Parametrization Work is ongoing to design a new sub-grid scale orographic drag parametrization. Using linear codes and more complex numerical models we have tested several aspects of our current approach including: The calculation of the low-level drag The calculation of the total gravity wave drag The gravity wave drag deposition The characterization of the low-level flow In this talk I will focus on the calculation of the total gravity wave drag and the characterization of the low-level flow. © Crown copyright Met Office

Do we need a stochastic gravity wave drag parametrization? Current gravity wave drag parametrizations are deterministic. This makes sense since it is well known that the drag is predictable for steady flow over small hills (where linear theory is valid). However, even for steady flow over small hills, fine-scale vertical structure in the atmospheric profiles and/or non-linear effects can have a significant effect on the drag. For example, partial internal wave reflection can cause constructive or destructive interference, leading to a high or low drag state respectively. © Crown copyright Met Office

Effect of wave superposition on drag for a simple case Two-layer N (to represent troposphere/stratosphere) Sinusoidal variation in U with height, maximum value (shown on x-axis) at tropopause Drag normalised by linear single layer low-level drag Good agreement between linear and non-linear models Plots of Vertical Velocity © Crown copyright Met Office

Do we need a stochastic gravity wave drag parametrization? Because of the sensitivity of the drag to the details of the profiles it may be appropriate to develop stochastic parametrizations of orographic gravity wave drag. Three possible sources of uncertainty in the drag are to: Use of simple low-layer depth-averaged UL and NL Differences in profiles between the model and reality Sensitivity to fine-scale vertical structure and/or non-linear effects © Crown copyright Met Office

Experimental Set-up For the month of January 2007 take vertical profiles of u, v and θ at 00Z and 12Z from Radiosonde data NWP model (Met Office Unified Model) for a single site (we have used Castor Bay, Ireland). Calculate an average low-level UL and NL Run a 2D linear gravity wave code and a 2D non-linear numerical model for both sets of profiles and compare the gravity wave response and drag. Aim to focus on linear, hydrostatic waves → hill height=10m and half-width=10km © Crown copyright Met Office

Model set-up Run inviscid, free-slip, non-hydrostatic models for a 2D domain with a ridge that is perpendicular to the low-level wind. Smooth U and θ in initial profiles Domain Size: 300km. Horizontal resolution: 1km. Domain Height: 25km. Vertical resolution: 50m (stretched grid in damping layer) Non-linear model: Met Office BLASIUS model For Blasius: Damping columns at lateral edges of domain, where wind and stability are relaxed back to the initial profiles. Damping layer from 15km-25km. Run model for 150,000s © Crown copyright Met Office

Non-hydrostatic effects As a slight aside, we were surprised that ~70% of the profiles gave a significant non-hydrostatic response Near the ground: F=UL/(NLL) ~20/(0.01x10e3) ~0.2 The Non-hydrostatic response is due to the increase of U/N with height. © Crown copyright Met Office

Use of single layer low-level UL and NL Dotted line indicates perfect agreement between single layer calculation and full profile calculation. Actual agreement quite poor, most obvious for high drag cases → representing flow by simple low-level UL and NL is inadequate to correctly predict drag Correlation coefficient=0.48 © Crown copyright Met Office

Are model profiles accurate enough? Dotted line indicates perfect agreement between single layer calculation and full profile calculation. Actual agreement quite poor, again most obvious for high drag cases → model profiles are not currently accurate enough to correctly predict the real drag Correlation coefficient=0.33 © Crown copyright Met Office

Are non-linear effects important? Dotted line indicates perfect agreement between single layer calculation and full profile calculation. Actual agreement quite poor, again most obvious for high drag cases → even for a 10m high hill, non-linear effects (or possibly differences in the model numerics) are significant Correlation coefficient=0.30 © Crown copyright Met Office

Do we need a new approach to gravity wave drag? Dotted line shows a fit to the data. Red line indicates behaviour of our current parametrization Two options: 1. Stochastic Scheme: Most appropriate for ensembles. Multiply parametrized gravity wave drag by this distribution to alter launch stress in a way that reflects uncertainty in the drag parametrization 2. Revised Deterministic Scheme – which is much more sensitive to details in the profiles (e.g. give parametrization some information about reflecting layers) so that on average it exhibits this behaviour. © Crown copyright Met Office

Future Work Analyse the profiles to try and understand what features make the drag predictable / unpredictable. Using any key features identified modify/design profiles to alter the wave response with the aim of understanding the relative importance of non-linearity vs unpredictability. Repeat the whole process for larger hills (where the non-dimensional mountain height exceeds unity) where a fraction of the flow will be blocked by the mountain and the gravity waves are highly non-linear. Feed these results into the design of a new orographic drag scheme © Crown copyright Met Office

Questions and answers © Crown copyright Met Office

Profile Processing For the calculations to work with both our linear code and our non-linear numerical model we had to process the profiles in the following way: Remove the lowest 500m from the profile – i.e. take out the boundary layer which is not represented in our linear code. Rotate the profile so that the low-level wind is aligned along the 2D domain Stabilize any statically unstable/neutral layers in the profiles, to prevent the formation of critical layers. Reduce the vertical wind shear wherever the gradient Richardson number, Ri<0.33 until Ri>0.33. © Crown copyright Met Office