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

GEO3020/4020 Lecture 3: Evapotranspiration (free water evaporation). Repetition. Flux of water molecules over a surface. Z veg. Z 0. Z d. velocity. Momentum, sensible heat and water vapour (latent heat) transfer by turbulence (z-direction). Steps in the derivation of LE.

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

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

  2. Flux of water molecules over a surface

  3. Zveg Z0 Zd velocity

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

  5. 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

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

  7. Latent heat, LE • Latent heat exchange by turbulent transfer, LE • where • 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)

  8. Sensible heat, H • Sensible-heat exchange by turbulent transfer, H (derived based on the diffusion equation for energy and momentum): • where • 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.

  9. 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

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

  11. 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

  12. 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

  13. Mass-transfer method Physical based 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

  14. Mass-transfer method Data needed - 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]

  15. 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) fluctuationsin humidity and vertical velocity For research application only

  16. 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

  17. 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.

  18. 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

  19. 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.

  20. 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

  21. 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:

  22. 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, Eais simplified as: f(va)(es-ea) and an empirical equations used for f(va).

  23. 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

  24. 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

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

  26. Soil Evaporation • Phase 1: Meteorological controlled • Phase 2: Soil controlled

  27. Influence of Vegetation • Albedo • Roughness • Stomata • Root system • LAI • GAI

  28. Transpiration

  29. Resistance – ConductanceAerodynamic and surface

  30. The influence of stomatal aperture on transpiration – leaf scale

  31. Modelling transpiration Rearrange to give:

  32. Atmospheric conductance, Cat

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

  34. 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.

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

  36. Penman-Monteith Penman Penman-Monteith ”Big leaf” concept

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

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

  39. Interception measurements • Direct measurements • Measurements of throughfall or net precipitation

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

  41. 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.

  42. Regression model to determine the net precipitation rate

  43. The Rutter model

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

  45. Forest evapotranspirationExample 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 ?

  46. 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

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

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