1. Predictability of orographic drag for realistic atmospheric profiles
Helen Wells and Simon Vosper
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2. 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
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3. To Orographic Drag Parametrization
Introduction
To Orographic Drag Parametrization
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4. 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.
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5. 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.
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6. 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.
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7. 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
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8. 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
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9. 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
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10. 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
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11. 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.
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12. 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
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13. 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
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14. 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
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15. 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.
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16. 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
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17. Questions and answers
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18. 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.
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