5-1 GEOG415 Lecture 5: Transpiration Transpiration loss of water from stomatal opening substomatal cavity chloroplasts cuticle epidermis mesophyll cells CO 2 H 2 O guard cell Evaporation + Transpiration = Evapotranspiration (ET) wind Potential evapotranspiration? Largely controlled by meteorological factors.
5-2 Importance of evapotranspiration - plant growth - water supply Runoff Precipitation - Evapotranspiration - climate Measurement of potential ET Class-A pan used as an index of potential ET Need corrections depending on the growing stage. e.g. Potential ET from corn is much smaller than pan evaporation in May. Dunne and Leopold (1978, Fig. 5-1)
5-3 Measurement of actual ET: Lysimeters Dunne and Leopold (1978, Fig. 5-2) IN OUT Precip. + Irrigation - ET - Drainage = Storage change ET = Precip + Irrigation - Drainage - Storage change Drainage lysimeter ignores storage change Limitation? Weighing lysimeter measures storage When a lysimeter is well irrigated, it measures potential ET. Estimation of ET: larger-scale studies Use the water balance. Storage change can be ignored for a long-term study.
5-4 Calculation of ET: Energy balance Q θ = Q n + Q v Q h Q et Storage change Net radiation Advection Sensible heat Latent heat (ET) wind Recall from Lecture 4, Q n = Q s (1 - α) - Q lw Net radiation depends on albedo (α). Typical values (DL, Table 5-1) Surface type Albedo Water 0.05-0.10 Wet soil 0.11 Dry soil 0.18 Pine forest 0.10-0.12 Rye and wheat 0.10-0.25 Alfalfa 0.19-0.25
5-5 The Penman equation can be used to estimate potential ET when Q v is negligible. 100Qn + Eaγ ρl E0 = + γ where γ = 0.66 [mb ºC -1 ], called psychrometric constant. = slope of the e sa - T a curve (see DL, Fig. 4-8) ρ = density of liquid water (1000 kg m -3 ) L = latent heat of vaporization (2.46 10 6 J kg -1 ) E a = aerodynamic evaporation (cm d -1 ), see below. To account for the effects of cover types on the turbulent mass transfer, Van Bavel formula can be used to calculate E a. E a 3.64 ua( esa ea ) = 2 Ta z a ln z0 T a, e a : air temp. (K) and vapor press. (mb) measured at z a e sa : saturation vapor pressure corresponding to T a z 0 : aerodynamic roughness length u a : wind speed (km/d) measured at z a The roughness length reflects the cover type. It is assumed to be about 1/10 of the vegetation height. Compare this to the purely empirical Penman s formula for E a (page 4-14).
5-6 Logarithmic wind profile is commonly observed near the ground surface. 10 10 8 height, z (m) 6 4 height, z (m) 1 0.1 2 z 0 0 0 1 2 3 wind speed, u (m/s) 0.01 0 1 2 3 wind speed, u (m/s) Example of using the Penman-Van Bavel equation T a = 18 C, e a = 12 mb, u a = 1.5 m s -1 all measured at z = 2 m. The height of crop (wheat) is about 0.5 m. z 0 =? E a =? Net radiation Q n = 12 MJ m -2 d -1. E 0 =?
5-7 Table of saturation vapor pressure and the slope of temperature-vapor pressure curve. (Lowe, P.R., 1977. Journal of Applied Meteorology, 16: 100-103) T a e sa T a e sa T a e sa T a e sa (C) (mb) (mb/c) (C) (mb) (mb/c) (C) (mb) (mb/c) (C) (mb) (mb/c) 0 6.1 0.444 10 12.3 0.823 20 23.4 1.456 30 42.6 2.465 1 6.6 0.473 11 13.1 0.873 21 24.9 1.538 31 45.2 2.592 2 7.1 0.504 12 14.0 0.926 22 26.5 1.624 32 47.8 2.724 3 7.6 0.537 13 15.0 0.982 23 28.2 1.713 33 50.6 2.863 4 8.1 0.572 14 16.0 1.040 24 29.9 1.807 34 53.6 3.007 5 8.7 0.608 15 17.1 1.101 25 31.8 1.905 35 56.6 3.156 6 9.3 0.647 16 18.2 1.166 26 33.7 2.007 36 59.9 3.313 7 10.0 0.687 17 19.4 1.233 27 35.8 2.114 37 63.3 3.475 8 10.7 0.730 18 20.7 1.304 28 38.0 2.226 38 66.8 3.644 9 11.5 0.776 19 22.0 1.379 29 40.2 2.343 39 70.6 3.820 The Van Bavel formula for E a is more theoretical, less empirical than the Penman s formula for E a. Are theoretical equations better than empirical ones? What are the limitation of empirical equations?
Temperature-based method for potential ET Assumption: Potential ET is a function of air temperature alone. What is the basis? Limitations? 5-8 Thornthwaite method Originally developed as an index for classifying climate. Assumptions: (1) Air temperature represents the integrated effects of radiation and other controls (wind, humidity, vegetation, soil, etc.) (2) Bowen ratio is fixed. E t = a 10Ta 1.6 (cm month -1 ) c I T a = mean monthly air temperature ( C) I = annual heat index = 12 i= 1 T ai T ai = mean air temperature of the i-th month ( C) a = 0.49 + 0.179I - 7.71 10-5 I 2 + 6.75 10-7 I 3 c = correction factor for monthly sunshine duration (see DL, Table 5-2) 5 1.5
Example The table lists average monthly temperature of a town located at 40 N. I =? a =? For the month of June, E t =? Month T a (C) Jan 0.1 Feb 1.2 Mar 5.1 Apr 6.9 May 15 Jun 18.4 Jul 23.6 Aug 20.3 Sep 15.7 Oct 9.5 Nov 2.8 Dec 0.8 5-9 Correction factor for sunshine duration at 40 N is 1.25 for June (DL, Table 5-2). Potential ET =? Dunne and Leopold (1978, Fig. 5-4)
5-10 Distribution of Thornthwaite potential ET Christopherson (2000, Fig. 9-8)
5-11 Limitation of temperature-based method Temperature-based methods were developed in the mid-latitude continental region (i.e. mid-western USA) as a climatic index, not as a method for calculating ET. Outside such region, the methods may result in significant errors. For example, this diagram shows the comparison of the Thornthwaite and other methods in Kenya, where the climate is strongly affected by the annual shifts of ITCZ. (Dunne and Leopold, 1978, Fig. 5-3) Another note: The Thornthwaite equation does not accept T a < 0 C. What do we do?
5-12 Actual ET: Effects of soil moisture Plants can transpire at the potential rate, limited only by meteorological factors, when the soil is reasonably wet. wind transpiration radiation The ET rate is reduced when the soil water becomes a limiting factor. actual evapotranspiration (AET) Water in drier soil is more strongly bound to the soil particles, resulting in a higher resistance to root uptake. Root uptake Soil water content A block of soil consists of gas, water, and solid particles. Volumetric water content = volume of water / total volume Porosity = void volume / total volume A soil is saturated when water fills up the void space. i.e. water content = porosity total gas water solid particles void
5-13 Field capacity : the amount of water that remains in soil after gravitational drainage. Wilting point: the amount of water that is so tightly held in the soil that plants can not utilize it. Field capacity depends on the type of soil. Sands have lower field capacity than clays. wilting Wilting point is usually considered 15 atm. 1 atm is equivalent to the pressure of 10 m of water. drainage Plant roots can pull the water against the soil s binding force (suction) as large as the force corresponding to the pressure of 150-m water column! Available water (AW) = (water content - wilting point) rooting depth Available water capacity (AWC) = (field capacity - wilting point) rooting depth
5-14 Example A soil sample taken after gravitational drainage has a total volume of 50 cm 3, of which 12 cm 3 is water. Field capacity =? The wilting point of the same soil is known to be 0.11. For a plant with a rooting depth of 60 cm, Available water capacity =? When this soil has a water content of 0.18, Available water =? It is commonly assumed that actual evapotranspiration (AET) is a fraction of the potential evapotranspiration (PET). The relationship between AET and PET is given by: AET = PET f AW AWC Where f ( ) is a function of the ratio AW/AWC. The function depends on many variables, most important of which is the soil type.
5-15 Plants can maintain high rates of ET in sand close to the wilting point. In clay, actual ET decreases gradually as the water content decreases. Why? AET/PET AW/AWC Dunne and Leopold (1978, Fig. 5-6) After a rain or irrigation event, when soil is at near field capacity, plants transpire at a rate close to PET. The rate of ET decreases as available water decreases with time, depending on the rooting depths. Dunne and Leopold (1978, Fig. 5-9)
5-16 Energy balance and global circulation The tropical region receive the highest amount of radiation. highest rate of sensible and latent heat transfer from the ground to atmosphere. This heat is circulate to the higher latitude regions. Upward transport of energy results in converging of air masses inter-tropical convergence zone (ITCZ) characterized by high precipitation Descending air masses create a dry climate (subtropical high). e.g. Sahara Desert. Christopherson (2000, Fig. 6-13)
The global atmospheric circulation is the one of the key factors controlling the distribution of climatic regions. Understanding hydrology is important for understanding world s climate and climate change. 5-17 Christopherson (2000, Fig. 10-4)