*Evapotranspiration from Green Infrastructure: Benefit, Measurement, and Simulation DOI: http://dx.doi.org/10.5772/intechopen.80910*

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

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 case in the urban domain [109].

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 higher during nighttime when no solar radiation exists.

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 of conductance) of green roof species could vary from 13 to 2500 s m<sup>−</sup><sup>1</sup> [49, 78]. 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.

*Advanced Evapotranspiration Methods and Applications*

case study using eddy covariance on an 8600 m2

GI unit, which usually only takes a small fraction of a flux footprint and is mixed with other urban land covers with distinct thermal and hydraulic properties. The eddy covariance method can be feasible for a large GI unit that covers the majority of a flux footprint, irrespective of the unsolved energy balance closure issue. A

70% daytime flux footprint matched the green roof surface [82]. A flux tower may become more useful to measure the total change in ET for a neighborhood scale before and after implementing GI, which will provide a critical dataset that is often

The challenges of measuring ET from GI were partly caused by the limitations in the current sensoring technology. To help build a database useful for future research and a wider community, field experimenters should start to record a more complete background information for a GI site, such as detailed species information [78], the surrounding impervious and pervious landscapes, and a broader field of temperature, wind, and humidity conditions that can account for advection and roughness. Meanwhile, the uncertainty information including the accuracy of measurement sensors and the selective ranges of parameters is recommended to be provided [49, 92], especially when the

lacked for calibrating stormwater and urban atmospheric models.

purpose of the observation is to improve the simulation of ET from a GI.

**4. Simulation of evapotranspiration from green infrastructure**

locally-calibrated ET modules but directly use more generic equations.

Simulation of evapotranspiration from green infrastructure is usually a necessary subtask of modeling a larger system such as the building's energy and water budgets, a catchment's drainage network, or a city's land-surface process. Most current efforts regarding ET simulation for GI centered on establishing a wellcalibrated ET model for a single GI unit/type at one site. Such microscale-calibrated models, however, are very difficult to be reused at a different site due to the differences in the configuration of GI, micrometeorological conditions, and data availability. Therefore, most hydrologic and atmospheric models seldom use such

Evapotranspiration simulation usually can be divided into two steps. Potential evapotranspiration (PET) is calculated firstly, which represents the maximum ET amount allowed by the instantaneous meteorological conditions forced by air temperature, solar radiation, wind, air pressure, and humidity [93–95]. Actual evapotranspiration (*ETa*) is then achieved by adjusting PET by further limiting factors such as moisture availability and properties of evapotranspiring media (e.g. physiological characteristics of plant species and hydraulic features of a soil type). Since PET and *ETa* are usually quantified separately, these two terms are discussed

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

green roof found that an average

**116**

separately.

**4.1 Potential evapotranspiration models**

The dilemma is that neither proposing a new framework nor improving the existing one is conceivably easy. Proposing a new PET equation with better representation of convection, advection, and surface resistance will change the *ETo* standard, and then the existing references of crop coefficient and water stress coefficient will need to be recalibrated. On the other hand, existing references of the current practices of using the P-M equation to estimate PET will require additional correction procedures to take account of those misrepresented terms and perhaps other unrepresented background terms.

Advection-Aridity model [111] can be a different method to estimate *ETo* for GI ignoring the restrictions in substrate moisture content and plant responses such as stomatal conductance [102]. Essentially, it merges the Penman equation that captures energy balance and vertical convection with the 'advection-free' Priest-Taylor equation; however, neither of them takes account of horizontal advection, which can be prevalent due to oasis effect in urban canyons. Artificial neural network provides an alternative workaround that establishes a best ET model for a specific GI unit at the microscale [112]. In the new era of big data, it can be envisioned that machine learning can also have a bright future given regional or global training datasets to be established and shared.
