Evaporation from Heterogeneous and Sparse Canopies: On the Formulations Related to Multi-Source Representations

Abstract

Evaporation from heterogeneous and sparse canopies is often represented by multi-source models that take the form of electrical analogues based upon resistance networks. The chosen representation de facto imposes a specific form on the composition of elementary fluxes and resistances. The two-and three-source representations are discussed in relation to previous work where some ambiguities arise. Using the two-layer model (Shuttleworth and Wallace, Q J R Meteorol Soc 111: [839][840][841][842][843][844][845][846][847][848][849][850][851][852][853][854][855] 1985) and the clumped (three-source) model (Brenner and Incoll, Agric For Meteorol 84:187-205, 1997) as a basis, it is shown that the stomatal characteristics of the foliage (amphistomatous or hypostomatous) generate different formulations. New generic and more concise equations, valid in both configurations, are derived. The differences between the patch and layer approaches are outlined and the consequences they have on the composition and formulation of component fluxes are specified. Then, the issue of calculating the effective resistances of the single-layer model from multi-source representations is addressed. Finally, a sensitivity analysis is carried out to illustrate the significance of the new formulations. Keywords Big leaf model · Effective parameters · Evaporation · Heterogeneous and sparse vegetation · Multi-layer models List of SymbolsA Available energy of the whole crop (W m −2 ) A f Available energy of the foliage (W m −2 ) A s Available energy of the substrate (W m −2 ) A vs Available energy of the vegetated soil (W m −2 ) A bs Available energy of the bare soil (W m −2 ) R n Net radiation of the whole crop (W m −2 ) G Soil heat flux (W m −2 ) 123 244 J. P. Lhomme et al. H Sensible heat flux from the complete canopy (W m −2 ) λE Latent heat flux from the complete canopy (W m −2 ) H i Component heat flux (i = f, s, vs, bs) (W m −2 ) λE i Component latent heat flux (i = f, s, vs, bs) (W m −2 ) D a Vapour pressure deficit at reference height (Pa) D m Vapour pressure deficit at canopy source height (Pa) T a Air temperature at reference height ( • C) T m Air temperature at canopy source height ( • C) T i Surface temperature of component i (i = f, s, vs, bs) ( • C) u a Wind speed at reference height (m s −1 ) e a Vapour pressure at reference height (Pa) e m Vapour pressure at canopy source height (Pa) e * (T ) Saturated vapour pressure at temperature T (Pa) c p Specific heat of air at constant pressure (J kg −1 K −1 ) ρ Air density (kg m −3 ) γ Psychrometric constant (Pa K −1 ) Slope of the saturated vapour pressure curve (Pa K −1 ) Canopy Structural Characteristics d Canopy displacement height (m) F Fractional cover of foliage (dimensionless) LAI Leaf area index (m 2 m −2 ) n Parameter with value of 1 for amphistomatous and 2 for hypostomatous foliage z r Reference height (m) z h Mean canopy height (m) z m Mean canopy source height (Canopy aerodynamic roughness length (m) Component Resistances r a Aerodynamic resistance between the source height an...

The SPARSE model for the prediction of water stress and evapotranspiration components from thermal infra-red data and its evaluation over irrigated and rainfed wheat

“…1). This corresponds to (respectively) the "layer" and "patch" approaches described in Lhomme et al (2012). However, the interpretation of the situations for which one or the other approach is valid differs between TSEB and Lhomme et al (2012).…”

“…This corresponds to (respectively) the "layer" and "patch" approaches described in Lhomme et al (2012). However, the interpretation of the situations for which one or the other approach is valid differs between TSEB and Lhomme et al (2012). In TSEB, both soil and vegetation patches share a common surface boundary layer (and therefore the same aerodynamic resistance from the aerodynamic level to the reference level), but the patch representation allows definition of different aerodynamic temperatures at the aerodynamic level over the soil and the vegetation.…”

“…In TSEB, both soil and vegetation patches share a common surface boundary layer (and therefore the same aerodynamic resistance from the aerodynamic level to the reference level), but the patch representation allows definition of different aerodynamic temperatures at the aerodynamic level over the soil and the vegetation. As pointed out by Lhomme et al (2012), the patch representation should in theory only apply to patches large enough to develop different surface boundary layers, e.g. fallow fields amongst wetter and taller vegetated areas rather than bare soil patches even a few metres large.…”

“…The original version of TSEB (Norman et al, 1995) provides two algorithms to describe the soil-vegetationatmosphere interactions, representing, respectively, the "patch" and "layer" approaches following the terminology proposed by Lhomme et al (2012). In the "layer" approach, one assumes that the air is well mixed within the canopy space so that air temperature at the aerodynamic level is rather homogeneous.…”

Generalized combination equations for canopy evaporation under dry and wet conditions

“…The basic principles used in the study are similar to those established by Shuttleworth (1978) in his simplified description of the vegetation-atmosphere interaction: the whole canopy (soil surface included) is assumed to be subject to the same vapour pressure deficit D m at the mean source height z m (d +z 0 ), as in the original Penman-Monteith model and in two-source models (Shuttleworth and Wallace, 1985). Our investigation follows up previous works made on the formulation of evaporation from heterogeneous and sparse canopies (Lhomme et al, 2012(Lhomme et al, , 2013. We show that the generalized formulation derived by Lhomme et al (2013, Eq.…”