Lommel function

Template:Expert-subject Like the Penman equation, the Penman–Monteith equation (after Howard Penman and John Monteith) predicts net evapotranspiration (ET), requiring as input daily mean temperature, wind speed, relative humidity and solar radiation. Other than radiation, these parameter are implicit in the derivation of $\Delta$, $c_{p}$, and $\delta _{q}$, if not conductances below.

The United Nations Food and Agriculture Organization (FAO) standard methods for modeling evapotranspiration use a Penman–Monteith equation. The standard methods of the American Society of Civil Engineers modify that Penman–Monteith equation for use with an hourly time step. The SWAT model is one of many GIS-integrated hydrologic models estimating ET using Penman–Monteith equations.

Evapotranspiration contributions are very significant in a watershed's water balance, yet are often not emphasized in results because the precision of this component is often weak relative to more directly measured phenomena, e.g. rain and stream flow. In addition to weather uncertainties, the Penman–Monteith equation is sensitive to vegetation specific parameters, e.g. stomatal resistance or conductance. Gaps in knowledge of such are filled by educated assumptions, until more specific data accumulates.

Various forms of crop coefficients (K_c) account for differences between specific vegetation modeled and a reference evapotranspiration (RET or ET₀) standard. Stress coefficients (K_s) account for reductions in ET due to environmental stress (e.g. soil saturation reduces root-zone O₂, low soil moisture induces wilt, air pollution effects, and salinity). Models of native vegetation cannot assume crop management to avoid recurring stress.

Equation

${\overset {\text{Energy flux rate}}{\lambda _{v}E={\frac {\Delta (R_{n}-G)+\rho _{a}c_{p}\left(\delta e\right)g_{a}}{\Delta +\gamma \left(1+g_{a}/g_{s}\right)}}}}~\iff ~{\overset {\text{Volume flux rate}}{ET_{o}={\frac {\Delta (R_{n}-G)+\rho _{a}c_{p}\left(\delta e\right)g_{a}}{\left(\Delta +\gamma \left(1+g_{a}/g_{s}\right)\right)L_{v}}}}}$

λ_v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J g⁻¹)

L_v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (L_v = 2453 MJ m⁻³)

E = Mass water evapotranspiration rate (g s⁻¹ m⁻²)

ET_o = Water volume evapotranspired (mm s⁻¹)

Δ = Rate of change of saturation specific humidity with air temperature. (Pa K⁻¹)

R_n = Net irradiance (W m⁻²), the external source of energy flux

G = Ground heat flux (W m⁻²), usually difficult to measure

c_p = Specific heat capacity of air (J kg⁻¹ K⁻¹)

ρ_a = dry air density (kg m⁻³)

δe = vapor pressure deficit, or specific humidity (Pa)

g_a = Conductivity of air, atmospheric conductance (m s⁻¹)

g_s = Conductivity of stoma, surface conductance (m s⁻¹)

γ = Psychrometric constant (γ ≈ 66 Pa K⁻¹)

(Monteith, 1965):

Note: Often resistances are used rather than conductivities.

$g_{a}={\tfrac {1}{r_{a}}}~~\And ~~g_{s}={\tfrac {1}{r_{s}}}={\tfrac {1}{r_{c}}}$

where r_c refers to the resistance to flux from a vegetation canopy to the extent of some defined boundary layer.

Also note that $g_{s}$ varies over each day, and in response to conditions as plants adjust such traits as stoma openings. Being sensitive to this parameter value, the Penman–Monteith equation obviates the need for more rigorous treatment of $g_{s}$ perhaps varying within each day. Penman's equation was derived to estimate daily ET from daily averages.

This also explains relations used to obtain $\delta q$ & $\Delta$ in addition to assumptions key to reaching this simplified equation.

Priestley–Taylor

The Priestley–Taylor was developed as a substitute to the Penman–Monteith equation to remove dependence on observations. For Priestley–Taylor, only radiation (irradiance) observations are required. This is done by removing the aerodynamic terms from the Penman–Monteith equation and adding an empirically derived constant factor, $\alpha$.

The underlying concept behind the Priestley–Taylor model is that an air mass moving above a vegetated area with abundant water would become saturated with water. In these conditions, the actual evapotranspiration would match the Penman rate of potential evapotranspiration. However, observations revealed that actual evaporation was 1.26 times greater than potential evaporation, and therefore the equation for actual evaporation was found by taking potential evapotranspiration and multiplying it by $\alpha$. The assumption here is for vegetation with an abundant water supply (i.e. the plants have low moisture stress). Areas like arid regions with high moisture stress are estimated to have higher $\alpha$ values.

Further reading

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  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

References

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External links

• Derivation of the equation