Lecture notes: Interception and evapotranspiration I. Vegetation canopy interception (I c ): Portion of incident precipitation (P) physically intercepted, stored and ultimately evaporated from vegetation surface (leaves and stems) Litter interception (I l ) is that amount of direct precipitation, throughfall (T) and stemflow (S) intercepted and stored in litter, then evaporated. Total interception: I t = I c + I l P = I t + T + S (all units LT -1 ) rearranging I t = P - T + S table 7-13 (note different symbols) Rate of interception limited by total precipitation (finite capacity of canopy/litter to hold water or snow), surface area of vegetation (leaf area index (LAI) and stem area index (SAI)), rate of evaporation (more can be intercepted if evaporation is active (breezy day, RH < 100%), and intensity of precipitation. Light rain, long duration, breezy day, can produce substantial amount of interception. table 7-9 (ditto on the symbols) Stemflow is typically small, but is dependent on architecture of trees - branches oriented upward from trunk, can concentrate flow down trunk and deliver to area immediately around roots.
Evapotranspiration: Evaporation + Transpiration evaporation is net phase change of water into vapor - controlled by meteorological factors transpiration is net phase change of water into vapor within leaf interior and flux out of leaf into atmosphere - controlled by combination of meteorological factors and plant physiological factors ET part of water balance and energy balance water balance: dv/dt = p(t) + r si + r gi - r so - r go - et(t) often neglect ground water terms to simplify eq. For one year dv/dt is close to 0, can compute et(t) (for a lake or reservoir) as et(t) = p(t) + r si - r so for a watershed (no stream inflow) et(t) = p(t) - r so Takes 2.45 x 10 6 J to evaporate 1 kg of water - this is the latent heat of vaporization λ = 2.45 x 10 6 J kg -1 Energy budget written in the same way as the water budget, need to balance all inputs (I) and outputs (O) of energy, with et being one of the heat transfer terms: dq/dt = R n - G - H - E l which can be rewritten for E l as E l = R n - G - H - dq/dt where Q is the total storage of heat in a control volume (J), R n is the net radiation (net shortwave - net longwave) in (J m -2 s -1 or W m -2 ), G
is the conductive heat flux (W m -2 ) and E l is the latent heat flux (W m -2 ) - the energy used for evaporation. To get from E l in W m -2 (J m -2 s -1 ) to et in mm s -1 divide by λ (J kg -1 ) to give evaporation rate in kg water m -2 s -1 then divide by density of water (1000 kg m -3 ) which gives evaporate rate in m s -1 and multiply by 1000 mm m -1 giving mm s -1. If this is the average rate of evaporation for a time step (e.g. an hour), multiply out by the number of seconds in the time step (e.g. 3600 sec) to get mm per time step. so, can rewrite eq. as et = (R n - G - H - dq/dt)/(ρλ) if R n = 200 W m -2 and H = 100 W m -2 (G and dq/dt is often small) then et = (200-100)/(1000 * 2.5 x 10 6 ) = 4.0 x 10-8 m s -1 =.144 mm hr -1 Defining the energy transfer terms: R n is the net radiation or the net input of energy resulting from incoming shortwave solar radiation, outgoing reflected shortwave radiation, incoming atmospheric longwave radiation, and outgoing terrestrial longwave radiation: R n = SW down - αsw down + LW atm - LW terrestrial where α is the surface albedo 0<α<1 is the proportion of SW reflected from the surface Sensible heat flux is heat transfer by the flow of a fluid (gas or liquid) towards or away from the surface H = K H v a (T s - T a )
LE (E l in text) = K E v a (e s - e a ) is the heat transfer in the form of vapor flow away or towards the surface G is the conductive heat transfer into (or from) the soil G = K g (T s - T soil ) where K g is the soil conductivity and T soil is the soil temperature and dq/dt is the rate of change of stored energy over time. We can rewrite the ratio of H/LE as the Bowen Ratio, β = H/LE = γ (T s - T a )/(e s - e a ) where γ is known as the psychrometric constant which is about 0.66 mb C o-1 Then the energy budget equation can be simplified, substituting H = βle R n = LE(1 + β) + G + dq/dt which states that the net radiation must be balanced by the disposition of heat by LE, H (written as a function of LE here), G and the change in stored heat. Taking it the next step we get et = (R n - G - dq/dt)/(ρλ(1+β)) in some cases we can neglect G and dq/dt to simplify the expression to et = R n /(ρλ(1+β)) worked example: Suppose net radiation is 500 W m -2, surface temperature is 30 o C, air temperature is 20 o C, surface vapor pressure is 15mb and air vapor pressure is 10mb. What is the rate of evaporation? β = (30-20)/(15-5) = 2.0
et = 500 J s -1 m -2 /(1000 kg m -3 2.5 x 10 6 J kg -1 (1+ 2)) et = 4.17 x 10-7 m s -1 = 4.17 x 10-4 m s -1 = 1.5 mm hr -1 So, all this has been energy budget based, assuming we can measure all the heat transfer and storage terms (or assume they're negligible) or have measurements of temperature and humidity at two levels. Usually we don't have these measurements. We usually only have air temperature, humidity, wind speed, and (hopefully) radiation. In that case there are these other methods that are either empirical or require more assumptions: mass transfer: E = f(v a )(VPD) looks a lot like the equation for latent heat transfer, but needs some function of wind speed which may be empirical or theoretically derived. It assumes that diffusion of vapor away from a wet surface dominates evaporation. Works better with longer time steps, such as a day. Penman combination equation: Combines a simple energy budget with a mass transfer equation. Assumes R n = H + LE and a low, wet, extensive surface (a giant well watered lawn) E = ( R n + γ C p ρ w g a VPD)/ρ w λ(γ+ ) somewhat more complex allows for different types of surfaces, and a range of wetness conditions E = ( R n + γ C p ρ w g a VPD)/ρ w λ( +γ(1 + g a /g c ))