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Experiment domain

Experiment domain

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Experiment domain

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  1. Experiment domain

  2. Evaporation models Physically based Temperature -based

  3. Physically based models: Radiative parameterization Shortwave radiation balance, Rn Longwave radiation balance, Ln Net available energy, Qn Rin aRin LWin LWout ET H B Ad W t G Ground heat flux

  4. ea = actual vapor pressure Rcs = clear sky SW radiation Rtoa = top-of-atmosphere SW radiation ns = sunshine hours N = daylight hours Physically based models: Radiative parameterization Energy available for evaporation Qn is a function of surface assumptions: for Ep, extensive free water surface for Epan, point-scale, free water surface for ET, prevailing conditions for ETrc, well watered, short grass

  5. Uz = wind speed at height zm av = eddy diffusivity/eddy viscosity (neutral conditions) d = zero-plane displacement height k = von Kármán constant J = day of year Physically based models: Advective parameterizations Model wind functions: • Penman Ep • PenPan Epan • Kimberly Penman ETrc • Penman-Monteith ET • Penman-Monteith Ep • Penman-Monteith ETrc Theoretical vapor transfer function (“wind function”) zm =Uz measurement height zv =ea measurement height z0m = momentum roughness height z0v = water vapor roughness height z0 = aerodynamic roughness height of a free-water surface

  6. Δ = slope of SVP curve with T = desat/dt γ = psychrometric constant esat = saturated vapor pressure Physically based models: Penman Ep • dW/dt negligible at time-step. • unlimited water to surface, so Ep limited only by: • vapor transfer process, or • energy availability. • SVP curve is assumed linear from surface to height of measurement of ea, T. • assumptions for similarity profiles of velocity, specific humidity, and sensible heat apply: • sub-layer is stable, neutrally buoyant, • fluxes do not vary with height, • transport dynamics of water vapor and sensible heat are unaffected by quantities being transported. 24hrs from 12Z 4/25/2010

  7. Physically based models: PenPan Epan • aP adjusts Penman Ep to replicate Epan observations. • accounts for instrumentation effects: • extra SW radiation interception by pan walls, • increased turbulence across water surface. 24hrs from 12Z 4/25/2010

  8. Physically based models: Penman-Monteith ET • models fine-scale diffusion from plants and surface under variable moisture availability: • rs is “stomatal resistance,” a bulk measure of the resistance to the diffusion of water vapor from stomata within the vegetative canopy, reflects moisture availability restrictions, increasing under drier conditions. • ra is “aerodynamic resistance” to the diffusion of both water vapor and H from the canopy to the measurement height, depends on land cover (e.g., crop height) • Penman-MonteithET can then also be used for more specific cases of ETrc and Ep. 24hrs from 12Z 4/25/2010

  9. Physically based models: Penman-Monteith Ep • in Penman-Monteith, Ep is a specific case of ET, with: • unlimited stomatal conductance, or zero rs (i.e., 1/rs = ∞), • ra specified for a free-water surface. 24hrs from 12Z 4/25/2010

  10. Physically based models: Penman-Monteith ETrc • in Penman-Monteith, ETrc is a specific case of ET calculated for specific biological and physical conditions (reference crop): • hypothetical, well-watered crop of height h = 0.12 m, rs = 70 sec/m, a = 0.23, • Uz, T, and ea data from 2-m height, • ra implicitly specified as 208/U2 sec/m. • international standard (FAO-56). • very commonly used in agricultural community. 24hrs from 12Z 4/25/2010

  11. Physically based models: Kimberly Penman ETrc • adjusts Penman Ep to model seasonality in vapor transfer process through aKP and bKP: • seasonal functions of day of year, • calibrated in Kimberly, ID. 24hrs from 12Z 4/25/2010

  12. Tmax = maximum temperature Tmin = minimum temperature Temperature-based models: Hargreaves ETrc • derived for daily ETrc in agricultural regions. • utility where humidity, surface radiation, and Uz data are missing. • aH and bH calibrated on a monthly or yearly basis, with respective default values of 0 W/m2 and 1 for unadjusted Hargreaves ETrc. • (Tmax+Tmin)/2+17.8 term approximates D/(D+g) term in Penman-based combination equations. • DTR term models warming of surface air by radiation. • explicit link to solar radiation, but only in seasonal climatology, through Rtoa. 24hrs from 12Z 4/25/2010

  13. Temperature-based models: Hamon Ep • very simple T-based formulation, • Included for potential comparison to Brekke et al. sensitivity work (USBR), • E[N] = climatological mean daylight hours per day [-] for the month containing the day of interest, • H = max number of daylight hours in day, • in freezing conditions, Ep =0. 24hrs from 12Z 4/25/2010

  14. CBRFC daily Ep 24hrs from 12Z 4/25/2010 PenPan (Epan) Penman Penman-Monteith Hamon (T-based) 0 mm/day 3 6 9 12

  15. Western Region daily Ep 24hrs from 12Z 4/25/2010 Penman Penman-Monteith Hamon

  16. CBRFC daily ETrc 24hrs from 12Z 4/25/2010 Penman-Monteith Kimberly Penman Hargreaves 0 mm/day 3 6 9 12

  17. Western Region daily ETrc 24hrs from 12Z 4/25/2010 Penman-Monteith Hargreaves

  18. Issues with physically based models • Concept: • both radiative and advective drivers explicitly modeled. • Advantages: • sound physical underpinnings, • match observed Ep very well, • wide international, scientific acceptance, • demand from agricultural and municipal users. • Drawbacks: • data requirements: • Uz data are noisy, • Rin data are seldom observed, • Lin data are almost never observed. • In their favor, CBRFC can calibrate parameters (e.g., ra, rs in Penman-Monteith) to close water balances of ~400 basins, accounting for spatial and temporal variations in land cover and vegetation type.

  19. Issues with temperature-based models: Decomposing Ep forcings – the PenPan model dEp/dt = -2.0 mm/yr2 dEp,Advective/dt = -2.6 mm/yr2 dEp,Radiative/dt = +0.6 mm/yr2 dVPD/dt = -0.2 Pa/yr dEp,VPD/dt = 0.0 mm/yr2 dU2/dt = -0.01 m/sec/yr dEp,U2/dt = -2.7 mm/yr2 [Roderick et al. Geophysical Research Letters, 2007]

  20. Issues with temperature-based models • Concept: • T reflects both the advective and radiative drivers, particularly the net radiation balance. • Advantages: • convenience, • low data requirements: • T, Tmax,Tmin, cloud cover data widely available in time and space. • Drawbacks: • lack of rigorous physical underpinning: • Ep not well characterized by T alone, • ignore the advective portion but Uz, specifically shown to drive most of the long-term variability in Epan, • Tdew more influential on temporal variability of VPD than is T. • Shuttleworth [1992] recommends against T-based formulations other than the Blaney-Criddle and Hargreaves equations, and never at sub-monthly resolutions.

  21. Issues with temperature-based models: BuRec study of Runoff under warming • Runoff sensitivity with Hamon Ep adjustment compared to base Ep • Gunnison: ~2 to 2.5x greater • Upper Missouri: ~4x greater [Brekke, Bureau of Reclamation, 2009]

  22. Option: direct estimation of ET by Penman-Monteith: Stomatal resistance, rs rs(t) = f(UZTW(t-1), LZTW(t-1))

  23. Option: direct estimation of ET by Penman-Monteith: Aerodynamic resistance, ra NLCD cover types ra = f(NLCD, season)