GEO3020/4020 Lecture 3: Evapotranspiration (free water evaporation) Repetition

Flux of water molecules over a surface

Zveg Z0 Zd velocity

Momentum, sensible heat and water vapour (latent heat) transfer by turbulence (z-direction)

Steps in the derivation of LE Fick’s law of diffusion for matter (transport due to differences in the concentration of water vapour); Combined with the equation for vertical transport of water vapour due to turbulence (Fick’s law of diffusion for momentum), gives: DWV/DM (and DH/DM) = 1 under neutral atmospheric conditions vertical transport of water vapor by the turbulent eddies of the wind

Lapse rates (stable, neural, unstable) Actual lapse rate

Latent heat, LE Latent heat exchange by turbulent transfer, LE where ra = density of air; λv = latent heat of vaporization; P = atmospheric pressure k = 0.4; zd = zero plane displacement height z0 = surface-roughness height; za = height above ground surface at which va & ea are measured; va = windspeed, ea = air vapor pressure es = surface vapor pressure (measured at z0 + zd)

Sensible heat, H Sensible-heat exchange by turbulent transfer, H (derived based on the diffusion equation for energy and momentum): where ra = density of air; Ca = heat capacity of air; k = 0.4; zd = zero plane displacement height z0 = surface-roughness height; za = height above ground surface at which va & Ta are measured; va = windspeed, Ta = air temperatures and Ts = surface temperatures.

Selection of estimation method Type of surface Availability of water Stored-energy Water-advected energy Additional elements to consider: Purpose of study Available data Time period of interest

Estimation of free water evaporation Water balance method Mass-transfer methods Energy balance method Combination (energy + mass balance) method Pan evaporation method Defined by not accounting for stored energy

Water balance method Apply the water balance equation to the water body of interest over a time period Dt and solving the equation for evaporation, E W: precipitation on the lake SWin and SWout: inflows and outflows of surface water GWin and GWout: inflows and outflows of ground water DV change in the amount of stored in the lake during Dt But: Difficult to measure the terms Large uncertainty in individual terms gives high uncertainty in E Can however, give a rough estimate, in particular where E and Δt is relative large

Water balance method Apply the water balance equation to the water body of interest over a time period Dt and solving the equation for evaporation, E Data needed Application

Mass-transfer method Physical based equation: Empirical equation: or Empirical equation: Different versions and expressions exist for the empirical constants b0 and b1; mainly depending on wind, va and ea If compared with physical based equation; b0=0 and b1=KLE

Mass-transfer method Data needed Application - va (dependent on measuring height) - es (from Ts) - ea (from Ta and Wa) Application - gives instantaneous rate of evaporation, but averaging is OK for up to daily values - requires data for Ts - KE varies with lake area, atmospheric stability and season Harbeck (1962) proposed the empirical equation: where AL is lake area in [km2], KE in [m km-1 kPa-1]

Eddy-correlation approach The rate of upward movement of water vapor near the surface is proportional to the time average of the product of the instantaneous fluctuations of vertical air movement, , and of absolute humidity, q’, around their respective mean values, Advantages Requires no assumption about parameter values, the shape of the velocity profile, or atmospheric stability Disadvantages Requires stringent instrumentation for accurately recording and integrating high frequency (order of 10 s-1) fluctuations in humidity and vertical velocity For research application only

Energy balance method Substitute the different terms into the following equation, the evaporation can be calculated where LE has units [EL-2T-1] E [LT-1] = LE/ρwλv Latent Heat of Vaporization : lv= 2.495 - (2.36 × 10-3) Ta

Bowen ratio We recognize that the wind profile enters both the expression for LE and H. To eliminate the need of wind data in the energy balance approach, Bowen defined a ratio of sensible heat to latent heat, LE: where is called the psychrometric constant [kPa K-1] Needs measurements at two levels.

Use of Bowen ratio in energy balance approach Original energy balance approach Replace sensible heat, H by Bowen ratio, B Substitute (7-23) into (7-22) The advantage of (7-24) over (7-22) is to eliminate H which needs wind profile data

Energy balance method Data Data demanding, but in some cases less a problem than in the water balance method (regional estimates can be used) Application - gives instantaneous rate of evaporation, but averaging is OK for up to daily values; - change in energy stored only for periods larger than 7 days (energy is calculated daily and summed to use with weekly or monthly summaries of advection and storage); - requires data for Ts (Bowen ratio and L); - most useful in combination with the mass transfer method.

Penman combination method Penman (1948) combined the mass-transfer and energy balance approaches to arrive at an equation that did not require surface temperature data: I. From original energy balance equation: Neglecting ground-heat conduction, G, water-advected energy, Aw, and change in energy storage, DQ/Dt, Equation (7-22) becomes

Penman combination method II. The sensible-heat transfer flux, H, is given by: Introduce the slope of saturation-vapor vs. temperature curve: Derive an expression for H: I. + II. gives the Penman equation:

Penman combination method Note that the essence of the Penman equation can be represented as: The first term and second term of the equation represents energy (net radiation) and the atmospheric contribution (mass transfer) to evaporation, respectively. In many practical application, Ea is simplified as: f(va)(es-ea) and an empirical equations used for f(va).

Penman equation – input data Net radiation (K+L) (measured or alternative cloudiness, C or sunshine hours, n/N can be used); Temperature, Ta (gives ea*) Humidity, e.g. relative humidity, Wa = ea/ea* (gives ea and thus the saturation deficit, (ea* - ea) Wind velocity, va Measurements are only taken at one height interval and data are available at standard weather stations

Penman equation – input data Net radiation (K+L) (measured or alternative cloudiness, C or sunshine hours, n/N can be used); Temperature, Ta (gives ea*) Humidity, e.g. relative humidity, Wa = ea/ea* (gives ea and thus the saturation deficit, (ea* - ea) Wind velocity, va Measurements are only taken at one height interval and data are available at standard weather stations

GEO3020/4020 Lecture 4: Evapotranspiration. - bare soil GEO3020/4020 Lecture 4: Evapotranspiration - bare soil - transpiration - interception Lena M. Tallaksen Chapter 7.4 – 7.8; Dingman

Soil Evaporation Phase 1: Meteorological controlled Phase 2: Soil controlled

Influence of Vegetation Albedo Roughness Stomata Root system LAI GAI

Transpiration

Resistance – Conductance Aerodynamic and surface

The influence of stomatal aperture on transpiration – leaf scale

Modelling transpiration Rearrange to give:

Atmospheric conductance, Cat

Penman equation – 3 versions Orignal Penman (1948) Penman (physical based wind function) Penman (atmospheric conductance)

Estimation of Cleaf The leaf conductance is a function of: Light intensity CO2 level in the atmosphere Vapour pressure difference (leaf – air) Leaf temperature Leaf water content where Cleaf* is the maximum value (all stomata full opening; typical values are given in Table 7-5) and f(x) is a proxy used for each variable above.

Relative leaf conductance [0,1] (ref. Fig. 7-13 and Table 7-6)

Penman-Monteith Penman Penman-Monteith ”Big leaf” concept

Evapotranspiration – measuring and modelling Single leaf or plant Stand Mixed vegetation Regional scale Seasonal variation in LAI (”big leaf”)

Interception Function of: Vegetation type and age (LAI) Precipitation intensity, frequency, duration and type

Interception measurements Direct measurements Measurements of throughfall or net precipitation

Interception measurements Measurements of throughfall or net precipitation Experiemental site in the Huewelerbach catchment, Luxembourg (from TUDelft website)

Interception modelling Regression models (empirical equations) e.g. between interception loss (Ei) and precipitation (R) for a given Δt Conceptual based models e.g. Rutter water balance model which uses the equation for free water evaporation to estimate interception losses. - Requires meteorological data and vegetation characteristics.

Regression model to determine the net precipitation rate

The Rutter model

Regression model to determine S (as the point where the linear line crosses X)

Forest evapotranspiration Example 7- 8 Thetford forest (UK): 16.5 m, vind speed 3.0 m/s Atmospheric conductance: Cat = 23.2 cm/s Transpiration rate Soil moisture deficit = 0 cm ET=1.8 mm/day Soil moisture deficit = 7 cm ET=1.2 mm/day Evaporation of intercepted water ET=54 mm/day (1 mm/0.45 hour) Replacement or addition to transpiration ?

Estimation of potential evapotranspiration Definition: function of vegetation – reference crop Operational definitions (PET) Temperature based methods (daily, monthly) Radiation based methods (daily) Combination method Pan

Actual evapotranspiration Two extreme cases In arid case, P <<PE, water limited AE = P In humid case, P >>PE AE = PE, energy limited

Long-term actual evapotranspiration as presented by Turc-Pike (mid), and Schreiber and Ol’dekop methods.

Estimation of actual evapotranspiration (ET) Potential-evapotranspiration approaches Empirical relationships between P-PET Monthly water balance Soil moisture functions Complementary approach Water balance approaches Lysimeter Water balance for the soil moisture zone, atmosphere, land Turbulent-Transfer/Energy balance approaches Penman-Monteith Bowen ratio Eddy correlation Water quality approaches

Complementary approach Based on heuristic arguments of Bouchet (1963) Simply states that the potential and actual evapotranspiration are not independent, but form a complementary relationship ETw = wet environment evapotr. ETp = potential evapotr. ETa = actual evapotr. evapotranspiration ETa = 2 ETw - ETp Increase of wetness The above figure is identical to Fig 7-25 in the book

Soil moisture functions (hydrological water balance models) Daily or monthly time step General equation qrel is the relative water content in the soil where qfc is the field-capacity, qpwp is the permanent wilting point

Fig 7-24 There are different soil type with different dynamic of drying as evapotranspiration continues From the following slides we see that the linear equation (7-67) or the equation used in HBV model represents only a special case of soil drying dynamics

Drying of soil moisture by evapotranspiration

GEO3020/4020 Evapotranspiration Meteorological Elements Energy Balance Evapotranspiration GEO3020/4020 Evapotranspiration Definition and Controlling factors Measurements Physics of evaporation Estimation of free water evaporation, potential and actual evapotransp. Processes and estimation methods for bare soil, transpiration, interception