The Nature of the Wind

Big picture (Why the wind blows) The global circulation Talk Outline Big picture (Why the wind blows) The global circulation Large-scale force balance above the boundary layer The planetary boundary layer (PBL) i. wind ii. friction iii. turbulence (mechanical and thermal) iv. structure and stability E. Wind parameterization Surface characteristics Recent work atmosphere 3 km PBL

How do we identify areas/regions that are favorable for wind energy (commercial)? Are there certain features associated with wind-prone regions (e.g., terrain, water, etc.)? Lecture focuses on why the wind blows and, in particular, why it blows preferentially in some regions or at some times during the diurnal cycle, etc. Regional variablity in the wind will depend on various factors and thus siting can be problematic/challenging.

GLOBAL CIRCULATION Show a current example of flow in GARP (with isotachs). Flow speed is proportional to the spacing of these contours – note regions where there is little flow…

General Circulation: Conceptual Models of the Atmosphere or…. How thermal energy is redistibuted in the atmosphere higher tropopause high isobars ? Low pressure p = rRT sfc winds sfc winds high Hadley Cell Should think of the earth as a thermally driven system that is differentially heated primarily from below (IR) by longwave radiation from the earth’s surface. Consider a highly idealized ‘orb’ with no land mass (this removes the differential heating due to land/ocean contrasts) and assume it is the planetary equinox (sun directly overhead at the equator) and that the orb is not rotating (left fig above). A thermally direct circulation (rising warm air/sinking cold air) in the form of a single “loop” is shown above left with warm air flowing poleward and cold air flowing equatorward. If we add rotation – flow deflects to the right (right/left is w.r.t. fluid motion not any particular direction!!) in the NH. rotating *non-rotating *Uniformly covered with H2O GOOD MODEL? *Sun directly overhead at Eq ok for tropics maybe… *thermally driven

Atmosphere is (in part) thermally driven: e.g. 3 Cell Model polar front sinking (surface trough) (warms) rising Polar easterlies H convergence 60N sinking L sinking L Westerlies divergence H 30N sfc winds Northeast trades convergence low pressure rising (cools) H sfc winds L L One cell model is not a good one! For one, it doesn’t match what we observe! Also numerical simulations indicate that the one cell is unstable (i.e., breaks down). Based on a combination of observations and modeling – a three cell model is a better paradigm. Again – I am showing the orb with and without rotation (and without land). Note that now we have series of “short” segments of rising/sinking representing the latitude bands 0.0-30.0, 30.0-60.0, and 60.0-90.0. There is still rising motion at the equator – however we now have alternating belts of converging and diverging air with attendant vertical motion (rising/sinking). It is this model that better fits what we see from a climate perspective! Non-Rotating Rotating *Uniformly covered with H2O *Studies show 1-cell model unstable *development of mid-lat cyclones *Sun directly overhead at Eq *ITCZ (convergence/rising motion) *Actual airflow more complicated….

Reality… NH winter MSLP (mean sea-level pressure). Notice “trades” (NE flow from high pressure in NH), the alternating belts of L/H pressure. This is consistent with the 3-cell model!

Lower atmosphere is referred to as the troposphere (~ 15 km) 80-90% of the mass of the atmosphere is in the troposphere! Typical atmospheric temperature profile – real ones can vary considerably! Troposphere contains most of the mass of the atmosphere and is < 20 km deep! Think about what 20 km is in terms of horizontal distance  The planetary boundary layer (PBL) is confined to the lower part of the atmosphere (~0-3 km) over which the impact of the earth’s surface can be important.

Looking at the lowest 2 km… increasing friction winds ~ geostrophic planetary boundary layer If we look at the lowest couple of km of the troposphere – we see that friction is increasingly important as one approaches the earth’s surface (makes sense). The height at which the influence of friction is effectively zero is referred to as the “free” Atmosphere. The height where friction becomes constant with depth in the atmosphere is referred to as the surface layer. We’ll talk more about these in a bit. from Doswell wind turbine

Above the top of the boundary layer the atmosphere is close to geostrophic balance… Assume constant PGF 1. parcel begins to accelerate due to pgf pgf 2. Coriolis kicks in (to right of motion) 3. As parcel accelerates, Coriolis increases low 4. As Coriolis increases balances with pgf high (constant wind – no net force) FCoriolis= pgf initial unbalanced flow equilibrium Let’s take a look at a good apx for the flow above the PBL. This balance only applies to ‘straight’ isobars Not quite this simple in reality as geostrophic balance does not describe how we arrive at a balanced flow!

What influences the wind in the PBL? Driven by large-scale horizontal pressure/temperature gradients Impacted by surface roughness characteristics Earth’s rotation (Coriolis) Diurnal temperature cycle at the surface (PBL stratification) Entrainment of air above the PBL Horizontal advection of momentum & heat Large-scale convergence/divergence Clouds and precipitation Topography In the PBL – the following factors are important (some of these are also important above the PBL as well as previously discussed). We’ve talked about the two issues boxed in blue above and I will talk about the red boxed items further below. w

This balance only applies to ‘straight’ isobars geostrophic z Near the sfc (above sfc layer up to 1 km or so) Ekman Spiral Assume constant PGF Ffr FCoriolis= pgf 1. Parcel in geostrophic balance. apply friction 2. Apply friction (disrupt balance). 3. Winds decelerate, Coriolis weakens. 4. PGF causes flow to deflect toward low pressure. high low 5. New force balance established new equilibrium no net force This balance only applies to ‘straight’ isobars OK – so now we are in the “Ekman” layer where friction now enters the force balance. What happens? Well, in addition to Coriolis and the PGF – we now have friction which 1.) slows the wind speed, 2.) decreases the Coriolis deflection which goes as the magnitude of the wind speed, and 3.) deflection toward lower pressure (this is not the only way to get cross isobaric flow in the atmosphere!). geostrophic z x-isobaric toward low pressure x y isobars

DAYTIME BOUNDARY LAYER Things like frictional drag, solar heating, and evapotranspiration generate turbulence of various-sized eddies DAYTIME BOUNDARY LAYER thermally driven high reflection! more absorption An example of the kind of mixing one gets in a boundary layer which includes two effects, thermal mixing and mechanical mixing. The thermal is a daytime phenomenon – resulting from the heating of the surface and the development of buoyant thermals. Another kind of mixing is related to the winds – this is referred to as mechanical and is the only mechanism working at night. shear driven (e.g., nighttime, cloudy/stable daytime conditions) z A good forecast (e.g., wind) is often critically dependent on accurate estimates of surface fluxes

winds are ~ geostrophic Residual layer The residual layer is the part of the atmosphere where mixing still takes place as a result of air flow (mechanical), although heat fluxes from the surface of the Earth are small. The surface layer (~lowest 10% of PBL) is the area most influenced by surface properties like heat fluxes etc..much of what I’ll be talking about coming up is relevant to this layer only. Noon Sunset Sunrise Midnight 1 km 10 km Free Atmosphere surface layer Convective Mixed Layer stable boundary layer Residual Layer winds are ~ geostrophic Note that the residual layer will generally be quite similar to the mixed layer of the prior day…unless there are other large scale things going on (e.g., frontal passage). similar characteristics radiational cooling peak heating

“no-slip lower boundary” The structure of the atmospheric boundary layer wind profile is influenced by the underlying surface and by the stability of the PBL (same stability) “no-slip lower boundary” increasing roughness length  Note wind profiles above (lowest few hundred meters) – slopes differ. Frictional drag increases with increasing surface roughness. Profiles share similar windspeeds ~ 200 m but drop off differently as a function of the surface friction. Note lower boundary condition is “no-slip” which means that friction forces the flow to zero. Surface roughness determines to a certain extent the amount of turbulence production, the surface stress and the shape of the wind profile.

Wind speed increases with height more rapidly in a stable PBL Stability influences the structure of turbulence. In an unstably stratified PBL (e.g. during day-time over land with an upward heat flux from the surface) the turbulence production is enhanced and the exchange is intensified resulting in a more uniform distribution of momentum, potential temperature and specific humidity. In a stably stratified boundary layer (e.g. during night-time over land) the turbulence produced by shear is suppressed by the stratification resulting in a weak exchange and a weak coupling with the surface. Wind speed increases with height more rapidly in a stable PBL OK, we’ve considered the simple case where the roughness length changes while the thermodynamic profile is the same. Now consider identical surface roughness (whatever value) and varying stability. Mixing of any stratified fluid results in a more even distribution of its basic properties such as fluid flow (here wind speed), chemical composition, etc. well-mixed deep mixing shallow/less mixing

Why parameterize the low-level PBL wind? The wind profile can be, to a first order, be represented by simple relationships (combo of empircal and physical!) Using a mean wind value for a site will mask the variation in wind speed. As wind power generated depends upon the cube of the wind speed this may seriously affect the estimate of wind power available over a year. This problem may be overcome by describing the wind speed probability distribution for the year. Use of statistical tools is difficult (e.g., length of sample can impact on the results – ‘representativeness’) Data would be more useful if it could be described by a mathematical expression (e.g., for modeling/parameterizations). Provides estimates of the wind speed (at a level and locale) where none exists Ultimately will help with the ‘siting’ of wind instrumentation

Power Law Profile (Prandtl) NWS winds Power Law Profile (Prandtl) zR = height of uR (~10 m) D typically taken to 0 f(friction) power law should be carefully employed since it is not a physical representation of the surface layer and does not describe the flow nearest to the ground very well Known quantities include Ur and Zr. Estimate alpha based on surface roughness  have an estimate of the wind profile above the canopy. (i.e., should only be used for heights above the roughness elements where the flow is free)

Logarithmic Profile Law (NNBL only) Turbulent mixing in the atmosphere may be considered in a similar way to molecular mixing (this is called K theory) simple laws? The increase of wind speed with height in the lowest 100m can be described by a logarithmic expression (i.e., assumes that the wind variation with height is inversely proportional to the height). u*/k ~ uRln(zR/z0) represents the effect of wind stress on the ground NNBL – Near neutral boundary layer Similar to the power law – we know (measure) Ur at height Zr, k is known, need estimate of the surface roughness (zo) and we can get an estimate of the wind profile with height U(z). (depends on sfc and wind magnitude)

Both the log law and the power law are simplified expressions of the actual wind profile. They are valid in flat homogeneous terrain. They do not include the effects of topography, obstacles or changes in roughness or stability. When either of these 2 simple laws do apply, they are intended for the lower part of boundary layer called the surface layer (i.e. lowest ~50-100 m or so, but above the canopy and in flat homo- geneous terrain). Wind direction is assumed to change little with height Effects of earth rotation are assumed to be minimal Wind structure is determined by surface friction and the vertical temperature gradient.