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Parametrization of the effects of Orography

This article discusses parametrization methods for the effects of orography, with a focus on the drag and effective roughness length parametrizations. It explores recent developments and alternative approaches to improve the representation of orographic effects in numerical weather prediction models. The article also examines the effects of stability, gravity waves, anisotropic topography, and non-linear effects on drag.

markmwright
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Parametrization of the effects of Orography

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  1. Parametrization of the effects of Orography Andy Brown

  2. Effects of small-scale hills on the (area-averaged) boundary layer Drag Effective roughness length parametrizations Recent developments and alternative approaches Other effects Parametrization of the effects of larger-scale hills – and effects on the boundary layer Small scale hills Wavelength less than around 6km – typically to short to excite gravity waves Usually within boundary layer (but not SBL?) Outline

  3. Turbulent form drag and its parametrization

  4. Turbulent form drag • Neutral, inviscid flow over a hill would give perturbations in phase with the hill and hence no drag • BUT stress perturbations close to the surface displace streamline perturbations downstream, and lead to a pressure drag • Linear theory (e.g. Belcher et al., 1993) • Use of enhanced “effective” roughness lengths to represent the effects of turbulent form drag in many NWP models

  5. Experimental support for effective roughness length approach • Grant and Mason (1990) • Llanthony valley, South Wales • Flow normal to approximately 2D ridges • Hignett and Hopwood (1994) • Caersws, Mid-Wales • Flow over approximately isotropic 3D hills • Both experiments suggested that area-averaged wind profile over hills was logarithmic and consistent with • enhanced roughness length • total stress (shear stress plus pressure drag) on surface

  6. Flat case U = (u*/k) ln(z/z0) Hilly case U = (u*eff/k) ln(z/z0eff) (above crests but still within BL) Hignett and Hopwood (1994) : Caersws

  7. Calculation of effective roughness lengths • Total force on surface = turbulent stress + pressure drag ~ undisturbed turbulent stress + pressure drag (1) • Well above hills, have quasi-homogeneous bl and (2) • Assume that at a height hm (which increases with hill wavelength), (2) is valid, wind is unchanged from undisturbed value and is related to undisturbed stress through log-law with vegetative roughness length (3) • From (1) and (3), can calculate z0eff Pressure drag parametrization required

  8. Initial tendency BL budget (pre-z0eff) Dynamics-BL tendency -BL tendency

  9. Momentum Budget Residuals Budget Residual Dec 93 Budget Residual Jan 95 • New Gravity Wave Drag • low level wave-breaking • flow blocking • trapped lee waves • Effective roughness

  10. MSLP Zonal Mean Errors - Day 3 Zonalisation of flow prior to GWD & OR change in Jan95

  11. G32 AIRS G33 4D-Var G27 New Dynamics HadAM4 Physics G34 HadGEM1 Physics G14 4Adv CMT 1D-Var TOVS G15 Resol. 60km 30L G10 New GWD O.Rough G19 3D-Var ATOVS Improvements in Global Model PerformanceDay 1 MSLP RMS errors & model cycles

  12. More recent work on form drag parametrization

  13. Recent work • What about stability effects? • Can effective roughness length parametrizations possibly work in shallow SBLs when the whole concept of hills being immersed within the boundary layer might break down? • Effects of gravity waves in the stable boundary layer? • Are ‘long-tails’ in boundary layer representing some of the effects of orography? • Directional effects in regions of anisotropic topography? • Possible replacements for effective roughness length parametrizations

  14. Stability effects • Effects of low hills • Flow speed-up and surface drag as a function of stability - theory, observations, numerical modelling • Additional effects of larger hills • How do non-linear effects such as separation, drainage currents, pooling of cold air in valleys affect the drag? • Are effective roughness length still a useful concept for parametrization? • Are waves within the stable boundary layer a significant issue?

  15. Linear theory for effects of stability on speed-up and drag • Neutral results for flow speed-up and drag • Effects of stability (Hunt, Richards and Brighton, 1988; Belcher and Wood, 1996) • Consider effects due to changes in undisturbed velocity profile and surface stress, changes in hm, and also dynamic buoyancy effects on perturbations in the outer region. • For moderate levels of stability, dominant effect is increase in shear across middle layer increasing speed up and pressure drag. • For higher stabilities increasing shear effect may be `capped' by middle layer depth reaching boundary layer top. Dynamic effects of buoyancy in outer region then decrease speed up and pressure drag.

  16. Experimental results on speed-up Both Frank et al., 1993 and Coppin et al., 1994 found fractional speed-up increasing above neutral value for moderate stabilties, then appearing to asymptote to a constant value at higher stabilities

  17. Numerical results for effects of stability on speedup and drag Neutral Stable • Consistent with theory and observations • Extend to bigger hills. Large number of numerical simulations performed varying • stability • hill height • hill wavelength • spacing (packed or isolated) • 2D ridges / 3D hills Variation of pressure drag with stability affected by similar considerations (Belcher and Wood, 1996). This variation is not currently well-represented in NWP parametrizations.

  18. Streamfunction from example stable simulation (surface buoyancy flux = -0.001m2s-3) as a function of time Interval = 10 m2s-1 between 0 and 50 m2s-1, 50 m2s-1 thereafter. Regions with streamfunction negative are shaded.

  19. Flow over isolated 2D ridges BLACK: NEUTRAL; BLUE: STABLE Form drag remains significant in stable conditions - absolute values comparable to the neutral values for slopes up to 0.3 For bigger slopes, get some reduction compared to neutral value (more noticeably with packed ridges when get pooling of stagnant air in valleys)

  20. tau13 from simulations of flow over packed 2D ridges of varying height Wavelength = 2000 m Surface buoyancy flux of -0.0005 m2s-3 20m hill 300m hill

  21. Results from simulations of flow over packed 2D ridges of varying height Wavelength = 2000 m Surface buoyancy flux of -0.0005 m2s-3 Boundary layer depth Horizontally averaged stress

  22. For homogeneous boundary layer, expect depth to scale as (u*L/f)1/2 (Zilitinkevich, 1972). Try normalizing hilly boundary layer depths using this scale (where u* and L are calculated using total momentum flux at surface i.e. Pressure drag included). Boundary layer depth is similar to (slightly smaller than) that expected for a homogeneous boundary layer with the same surface temperature and momentum flux. Encouraging for the use of effective roughness length parametrizations

  23. Parametrization of total drag on ridges • BLUE LINE : drag on flat surface (z0=0.1m) as a function of stability • RED LINE : total drag on ridged surface (z0=0.1m) with p-t-h of 200m as a function of stability • GREEN DASHED : drag on flat surface with enhanced roughness (z0eff=1.0m) as a function of stability • Effective roughness length independent of stability would not be too bad an approximation STABLE NEUTRAL

  24. Waves within the stable boundary layer • Repeat of simulations of stable boundary layer flow over a low ridge, but with wind no longer normal to ridge •  = 2 km, Peak to trough height = 20 m, Boundary layer depth = 350 m

  25. Waves within the stable boundary layer • Force on surface follows cosine squared variation (as neutral) except when component of flow across ridge becomes small enough to allow waves • Force is then much bigger

  26. Waves within the stable boundary layer • This case not stable enough for waves • Phase lines of vertical velocity plot vertical • Mean flow momentum flux small through most of boundary layer

  27. Waves within the stable boundary layer • Magnitude of cross-ridge component of flow reduced so that Froude number is now small enough to permit waves • Phase lines of vertical velocity plot slope • Mean flow momentum flux significant throughout boundary layer, and consistent with surface pressure drag (star)

  28. Stability Effects Summary • Fractional speed-up and non-dimensional drag both increase at first with increasing stability due to the increasing shear, then decrease due to dynamical stability effects • The area-averaged boundary layer remains reasonably similar to that over a homogeneous surface, suggesting that an effective roughness length approach to parametrization remains promising • Always likely to excite waves in the SBL from ridges (Fourier modes) aligned closely parallel to the wind. Are these a significant player in the momentum budget? • Are ‘long tails’ commonly used in SBL parametrizations implicitly representing effects of orographically-induced gravity waves and/or of enhanced turbulent mixing due to drainage currents etc.?

  29. Loch Cluanie, Scottish Highlands Deliberately chosen as a region of approximately 2D orography (E-W ridges) Horizontal scale 5-9 km Peak-to-trough height 600 m Experiment in region of anisotropic topography

  30. Composite near neutral sonde profiles for cases with flow within 30 degrees of parallel and normal to ridges Parallel : blue (18 cases) still have logarithmic profile effective roughness of 8 m Normal : red (23 cases) deeper logarithmic layer (>2 km) effective roughness of 47 m Experiment in region of anisotropic topography

  31. Directionally dependent drag • How does the drag on an infinite two-dimensional ridge depend on wind direction? • Is this infinite ridge limit a relevant one in reality? • How elongated does a hill have to become before it acts as an infinite ridge? • Are the Caersws or Loch Cluanie results more typical?

  32. How anisotropic does a hill have to become before it acts like a two-dimensional ridge? Consider ellipsoidal hills and independently vary wind direction aspect ratio of hills (=1 for isotropic hill; infinity for 2D ridge) Drag on anisotropic 3d hills

  33. 1) For isotropic hills the magnitude of the drag is independent of wind direction 3) With an aspect ratio of 2, the results already lie closer to the 2D ridge result than they do to the isotropic hill result 2) For 2D hills, the magnitude of the drag is a strong function of wind direction (approx. cosine squared of angle between wind and normal to ridge)

  34. Directional Effects Summary • Directional dependence rapidly becomes important as an isotropic hill is elongated into a ridge • For low hills, can recover this result by taking 2D FFT of the 3D orography, and summing the 2D drag results • NWP application? • Could make effective roughness length a function of wind direction to capture some of the directional effects • Effects might still be fairly weak, as even if subgrid orography locally looks quite anisotropic, it is likely to look more isotropic again if averaged over a larger area

  35. Why move away from effective roughness lengths? • Rather indirect parametrization (so, for example, difficult to link to gravity wave parametrization) • To leading order, scalar transfer should be unaffected by small-scale hills. However, effective roughness lengths significantly reduce the near-surface winds, and have to use effective scalar roughness lengths to “undo” this effect <Wind> Flat simulation z0=0.1m <Stress> Area-averages from hilly simulation, h=400m, =3000m, z0=0.1m 1d simulation z0eff=25m

  36. Extra orographic stress term added to momentum equations with orographic stress profile specified using surface pressure drag parametrization and exponential decay (on scale related to wavelength) Able to provide required orographic drag without excessive slowing of near-surface winds Currently under test at Met Office Variant of scheme (Beljaars et al., 2004) with further simplifications to allow implicit solving within the boundary layer scheme under test at ECMWF Wood et al. (2001)

  37. Other effects of small scale hills

  38. Orographic effects on heat and moisture • Currently many NWP models have no (explicit) representation of the effects of subgrid orography on heat and moisture transports • Should they have? • Altered large-scale cloud and precipitation in region of significant subgrid orography? • e.g. Leung and Chan (1998), Terra (2004) • Effects of orography on convective triggering (forced ascent; elevated heat source)? • Investigate through simulations across a range of resolutions (climate → O(2km)) • European Alps • Maritime Continent

  39. Parametrization of the effects of larger-scale hills

  40. Gravity waves and flow blocking • In this talk, have deliberately concentrated on the effects of boundary layer scale hills • In principle, gravity wave and flow blocking parametrizations represent the effects of larger scales and different mechanisms • In practice, issues inextricably linked • Lack of knowledge of relative importance in reality of different scales and mechanisms to drag • Implicit tuning of one scheme against another • Did effective roughness lengths look so important in the Met Office model due to the lack at that time of a low-level flow blocking scheme? • Numerical interactions e.g. flow blocking and boundary layer schemes acting in the same place (and solved separately)

  41. Gravity waves and flow blocking Higher level flow passes over mountain and produces propagating gravity waves Low level flow deflected around mountain – flow blocking From Lott and Miller, 1997

  42. Angular momentum budget • January 2001, 31 ECMWF 24 hour forecasts • SSO incorporates parametrized torque due to gravity waves and flow blocking • Significant compared to BL torque, especially at low resolution • Apparently optimum BL torque may depend on how we parametrize SSO torque (and vice versa)

  43. Importance of different scales • Variation of resolved orographic drag on Alps with model resolution (125km to 4km) • Further similar studies planned to provide further information on the relative importance of different scales and mechanisms • e.g. get to high enough resolution to explicitly model effects of boundary layer scale hills and larger scale hills at the same time Smith et al. (2005)

  44. Key questions • What should be the relative importance of different scales and mechanisms (flow blocking, gravity waves, turbulent form drag, boundary layer drag over flat terrain)? • Can the numerical implementation be improved? • Effects of subgrid orography on clouds and moisture – should we be doing more?

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