**4.1 Potential evapotranspiration models**

Penman-Monteith (P-M) equation, taking a full account of energy balance, convection, and canopy resistance while well documented by previous agricultural studies, is widely applied to estimate ET from almost all types of GI such as green roof [6, 57, 74, 83, 93, 96–99], bioretention [64, 80, 100], and permeable pavement [101]. Simpler models, such as Priest-Taylor equation without considering convection [102], or solely temperature-based Thornthwaite Equation [59, 85, 103] and Hargreaves Equation [96, 104], have also applied for GI when fewer inputs and less calibration effort required. Although a simpler method may achieve a better estimate for a unique site, the P-M equation has been framed into the classical protocol [105] to compute reference evapotranspiration (*ETo*), which represents ET from a standard

**117**

*Evapotranspiration from Green Infrastructure: Benefit, Measurement, and Simulation*

land cover with fixed vegetation characteristics (resistance, height, etc.). The concept of *ETo* has been widely accepted and integrated with the adjustments by lists of crop coefficient (*Kc*) and water stress coefficient (*Ks*) [105]. Potential evapotrans-

Although the P-M equation is physically sound, it is problematic to apply it in the urban environment. Originally, the P-M equation was developed to estimate ET from a uniform surface with a homogenous footprint (like open water or wellwatered farmland). Urban environment, however, is composed of heterogeneous surfaces with distinct regimes of reflecting, absorbing, and releasing the incoming radiation, which result in intensive turbulence exchanges within a short period of time. Directly applying the P-M equation in the urban environment essentially breaks its underlying assumption of a homogeneous surface. The P-M equation would need adjustments for such cases after capturing the 3D field of weather variables, especially temperature, wind, and humidity fields. For example, the current practices of implementing the P-M equation only calculate aerodynamic resistance for the neutral stability condition by assuming a logarithmic profile of wind, temperature, and humidity [105, 106]. This assumption is only valid for inertial sublayer well above the building tops but will not hold in the roughness sublayer and urban canopy layer where GI exists [107]. This violation, mostly due to a high degree of vertical mixing (convection) and horizontal transport of air mass (advection), is seldom and hardly addressed during ET estimation for GI. Fundamentally, the P-M equation assumes an equivalent aerodynamic resistance for both sensible heat and momentum transfer under the neutral stability condition and ignores the contribution of advection to the energy supply commonly occurred in an urban environment. Stability correction [108] is cumbersome and may not be influential close to the canopy [109]. The advection tends to be negligible where relatively small differences in surface temperatures exist (like cropland), which is seldom the

A pioneering study proposed two crop coefficients to separately calibrate radiation and convection terms to improve ET estimation for green roofs [84]. This method implicitly assumes that the nightly convection would have the same magnitude as the daytime convection and also removes the moisture restriction on the convection term because of the weak correlation between convection and substrate moisture at nighttime. The two-round correction was able to improve RMSE by 37% for water-limited conditions when ET is generally low but still suffered by underestimating large ET values during wet conditions [84]. This method still does not resolve the inherited problem of the neglect of horizontal advection in P-M equation, which seems to explain why the ratio of observed ET versus *ETo* was much

Another implicit barrier in using the P-M equation for GI application lies in the complexity of the concept of surface resistance. Stomatal conductance, as the backbone of surface resistance, is highly variable and can be a function of instantaneous levels of temperature, vapor pressure deficit, leaf water potential, and ambient carbon dioxide concentration [110]. Stomatal resistance (the reciprocal

[49, 78].

of conductance) of green roof species could vary from 13 to 2500 s m<sup>−</sup><sup>1</sup>

However, in practice, the surface resistance is usually fixed at a constant value in [105, 106]. Therefore, the P-M equation and other common methods tend to struggle to capture both the high and low ET extremes for GI; e.g. for green roofs, the P-M methods often underestimate ET peaks, when moisture supply is adequate to support large ET values (close to PET level) [49, 81, 84, 89, 90]. The average surface resistance adopted by most studies keeps the simulated results approaching the average ET level but missing the higher and lower extremes. Adding a constant crop coefficient will still not improve this situation.

piration of a plant can be achieved by multiplying *ETo* by *Kc*.

*DOI: http://dx.doi.org/10.5772/intechopen.80910*

case in the urban domain [109].

higher during nighttime when no solar radiation exists.
