Watershed Hydrology NREM 691 Week 3 Ali Fares, Ph.D. Evapotranspiration Watershed Hydrology NREM 691 Week 3 Ali Fares, Ph.D. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Objectives of this chapter Explain and differentiate among the processes of evaporation from a water body, evaporation from soil, and transpiration from a plant Understand and be able to solve for evapotranspiration (ET) using a water budget & energy budget method Explain potential ET and actual ET relationships in the field. Under what conditions are they similar? Under what conditions are they different? Understand and explain how changes in vegetative cover affect ET. Describe methods used in estimating potential and actual ET 11/19/2018 Watershed Hydrology Lab. Fall 2006

Conservation of Energy The conservation equation as applied to energy, or conservation of energy, is known as the energy balance. How precipitation is partitioned into infiltration, runoff, evapo-transpiration, etc., similarly, we can look at how incoming radiation from the sun and from the atmosphere is partitioned into different energy fluxes (where the term flux denotes a rate of transfer (e.g. of mass, energy or momentum) per unit area). 11/19/2018 Watershed Hydrology Lab. Fall 2006

Water & Energy relationship There is strong link between the water and energy balance: Partitioning of incoming radiation into the various fluxes of energy ( energy for ET, energy to heat the atmosphere and energy to heat the ground) depends on the water balance and how much water is present in soils and available for evapotranspiration. the partitioning of precipitation into the various water fluxes (e.g. runoff and infiltration) depends on how much energy is available for ET. Just as changes in water balance were reflected in changes in storage in water amounts (soil moisture in a root zone; level of a lake) changes in energy balance are reflected in temperature changes. Just as we wrote water balances for a number of different control volumes, we could write energy balances for the same control volumes. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Evapotranspiration ET = P – Q – ΔS - ΔD ΔS= watershed storage variation (mm): Send–Sbeginning P = Precipitation (mm) Q = Stream flow (mm) ΔD = Seepage out – seepage in (mm) ET = evaporation and transpiration (mm) This equation is telling us that if you know the water content in the soil profile now (St) and after a certain period of time (1 hour, 1 day) and if you also know how much irrigation or rainfall that was added into the system you can determine the losses out of the system D and ET. Thus, this equation has two unknowns: ET and D. If we determine one of them then the equation will be left with only one unknown that can be determined form the equation. ET can be determined from weather data and using mathematical equation such as penman-monteith. It can be determined form lysimeter measurements. For our case we choose to calculate drainage using Darcy’s flow equation. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Energy Budget for an ideal surface An ideal surface is: smooth horizontal homogeneous extensive very thin land/atmosphere interface no mass no heat capacity no horizontal heat exchange 11/19/2018 Watershed Hydrology Lab. Fall 2006

Energy Budget for an ideal surface Energy budget is: Rn = H + LE + G where Rn is net radiation at the surface; H is sensible heat exchanged with the atmosphere; LE is latent heat exchanged with the atmosphere; and G is heat exchanged with the ground. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Net Radiation Net radiation is composed of shortwave radiation, K, from the sun, and longwave radiation, L from the atmosphere and from the ground, so that Rn = K + L The radiation from the sun (solar radiation) is often referred to as shortwave radiation, and the radiation from the atmosphere and the ground (i.e. atmospheric and terrestrial radiation) as longwave radiation, since the wavelength of the electromagnetic emitted by these bodies is inversely proportional to their temperatures. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Shortwave radiation input. What happens to incoming SR as it enters the earths atmosphere on the way to the surface Backscattered by air e.g. when radiation strikes particles in the atmosphere on the same order of magnitude as the radiation wavelength (dust, moisture, aerosols) Reflected in the atmosphere by clouds Absorbed by clouds, dust, water vapor; or Reflected at land surface Chow et al. (1988) 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Net Solar Energy Flux The net flux of solar energy entering the land surface is therefore given as K = Kin - Kout = Kin (1-a) where K in is the incident solar energy on the surface, and it includes direct solar radiation (i.e. that which makes it through the atmosphere unscathed) and diffuse (due to scattering by aerosols and gases); Kout is the reflected flux; a is the albedo Solar radiation is measured in specialized meteorological stations with radiometers. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Longwave radiation input Longwave radiation input. All matter at a temperature above absolute zero radiates energy in the form of electromagnetic radiation which travels at the speed of light. The rate at which this energy is emitted is given by the Stefan-Boltzman law Qr = esT4 where Qr is the rate of energy emission per L2 T-1, T is the absolute temperature of the surface, s is a universal constant called the Stefan-Boltzman constant, e is a dimensionless quantity called the emissivity 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 The emissivity ranges from 0 to 1, depending on the material and surface texture. A surface with e equal to 1 is called a blackbody. Most earth materials have emissivities near 1. LW radiation is emitted by bodies at near earth surface temperatures (the land surface and the lower atmosphere). The net input of LW radiation, L, is the difference between the incident flux, Lin, which is emitted by the atmosphere, clouds and overlying vegetation canopy, and the outgoing radiation emitted from the land surface: L = Lin - Lout LW radiation is measured using radiometers. As in the case of shortwave, the instruments are rare except at intense research sites. So, it is usually estimated from more readily available meteorological information. These estimates are based on the following physics. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 The flux or radiation emitted by the atmosphere is Lin = eatsTat4 and at denotes atmosphere . Outgoing radiation is the sum of the radiation emitted by the surface and that fraction of the incoming longwave that is reflected Lout = essTs4+(1-es)Lin The subscript s denotes land surface. For the case of gray bodies (e<1) reflectivity equals 1 - emissivity. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Sensible heat Sensible Heat H = cara/rah (Ta-Ts) Note that this equation is essentially a conductivity times a gradient, corrected for the properties of the fluid. ca is the heat capacity of air ra is the density of air rah is the aerodynamic resistance to heat transport and is given by   rah = 1 / k2 u (z(m)) {ln{zm/zo}}2 k is von Karmann's constant (0.4) u (z(m)) is wind speed at measurement height zm zo is known as the roughness height of the surface and depends of the irregularity of the surface 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Latent Heat Latent Heat LE = cara/ grav (es-ea) where L is the latent heat of vaporization E is the rate of evaporation rav = rah g is the psychrometric constant, and is a function of atmospheric pressure, density of air, etc. es,ea are the vapor pressures measured at the surface and in the lower atmosphere   11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Ground heat Flux Ground Heat Flux G = kG dT/dz where kG is the thermal conductivity of the soil dT/dz is the vertical temperature gradient Thermal conductivities of soils depend on soil texture, soil density, and moisture content, and vary widely in space. Owing to this variability, and the fact that dT/dz is tough to measure, G is often neglected or estimated in energy balance computations 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Evapotranspiration For humid climates, vegetative cover affects the magnitude of ET and thus, Q (stream flow). In Dry climate, effect of vegetative cover on ET is limited. ET affects water yield by affecting antecedent water status of a watershed  high ET result in large storage to store part of precipitation More than 95% of 300mm in Arizona > 70% annual precipitation in the US In General: ET/P is ~ 1 for dry conditions ET/P < 1 for humid climates & ET is governed by available energy rather than availability of water 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Evapotranspiration evapotranspiration summarizes all processes that return liquid water back into water vapor - evaporation (E): direct transfer of water from open water bodies or soil surfaces - transpiration (T): indirect transfer of water from root-stomatal system of the water taken up by plants, ~95% is returned to the atmosphere through their stomata (only 5% is turned into biomass!) Before E and T can occur there must be: A flow of energy to the evaporating or transpiring surfaces A flow of liquid water to these surfaces, and A flow of vapor away from these surfaces. Total ET is change as a result of any changes That happens to any of these 3. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Three main factors affect E or T from evaporating & transpiring surfaces: Supply of energy to provide the latent heat of evaporation Ability to transport the vapor away from the evaporative surface Supply of water at the evaporative surface Source of energy? Is solar radiation What take vapors away from evaporating surface? Wind and humidity gradient Evaporation includes: Soil -- vegetation surface – transpiration => Evapotranspiration, ET 11/19/2018 Watershed Hydrology Lab. Fall 2006

The linkage between water and energy budgets Is direct; the net energy available at the earth’s surface is apportioned largely in response to the presence or absence of water. Reasons for studying it are: To develop a better understanding of Hydrological cycle Be able to quantify or estimate E and ET (soil, water or snowmelt) 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Radiation Diffuse skylight is about 15% of total sol radiation Total amount of SW radiation absorbed by objects depends on albedo. The net SW radiation at a surface is: (1-α)(Ws + ws) Light colored surfaces have a higher albedo than dark-colored surfaces. New snow 80-95% Dry sand 35-60% Mixed forest 18% Bare soil 11 Atmosphere & terrestrial objects emit long wave radiation. Soil and plant surfaces reflect only a small portion of total downward long wave radiation (Ia). The net longwave radiation at is a surface is difference between incoming (Ia) & emitted (Ig) long water radiation: Ia – Ig Net radiation available at a surface: Rn = (1-α)(Ws + ws) + Ia – Ig All substances with T > 0 0K (0C + 273) emit EM radiation as: W = εσT4 Eq. 3.2 Radiation amount is temp. dependent. Short- and long- wave are T depended Shortwave radiation: the hotter the sub the shorter the wavelength Absorbed shortwave radiation depends on Albedo. Albedo is the portion of shortwave reflected by an object. Sun @ 6000oK emits 105 cal cm-2 min-1 vs. soil 300oK (27oC) emits 0.66 cal cm-2 min-1 Shortwave radiation comprises direct solar radiation (Ws) & diffuse radiation (ws) ws scattered and reflected radiation Caused by air molecules; reflection from cloud, dust & other particules 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Energy Budget L is latent heat of vaporization, E evaporation, H energy flux that heats the air or sensible heat, G is heat of conduction to ground and Ps is energy of photosynthesis. LE represents energy available for evaporating water Rn is the primary source for ET & snow melt. Net radiation: Rn=(Ws+ws)(1- α)+Ia-Ig Rn is determined by measuring incoming & outgoing short- & long-wave rad. over a surface. Rn can – or + If Rn > 0 then can be allocated at a surface as follows: Rn = (L)(E) + H + G + Ps 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 An island of tall forest vegetation presents more surface area than an low-growing vegetation does (e.g. grass). The total latent heat flux is determined by: LE = Rn + H Advection is movement of warm air to cooler plant-soil-water surfaces. Convection is the vertical component of sensible-heat transfer. In a watershed Rn, (LE) latent heat and sensible heat (H) are of interest. Sensible heat can be substantial in a watershed, Oasis effect were a well-watered plant community can receive large amounts of sensible heat from the surrounding dry, hot desert. See Table 3.2 comparison See box 3.1 illustrates the energy budget calculations for an oasis condition. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Water movement in plants Illustration of the energy differentials which drive the water movement from the soil, into the roots, up the stalk, into the leaves and out into the atmosphere. The water moves from a less negative soil moisture tension to a more negative tension in the atmosphere. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Yw~ -1.3 MPa Yw~ -1.0 MPa Yw~ -0.8 MPa Yw~ -0.75 MPa Yw~ -0.15 MPa Ys~ -0.025 MPa 11/19/2018 Watershed Hydrology Lab. Fall 2006

Soil Water Mass Balance There are different ways to estimate drainage. The direct method is the use of lysimeters. Lysimeters have a weighing device and a drainage system, which permit continuous measurement of excess water and draining below the root zone and plant water use, evapotranspiration. Lysimeters have high cost and may not provide a reliable measurement of the field water balance. 11/19/2018 Watershed Hydrology Lab. Fall 2006

Water Mass balance Equation S =(I + R + U) - (D + RO + ET) ET = Evapotranspiration R, I = Rain & Irrigation D = Drainage Below Rootzone RO = Runoff S = Soil Water Storage variation U = upward capillary flow 11/19/2018 Watershed Hydrology Lab. Fall 2006

Watershed Hydrology Lab. Fall 2006 Rain Transpiration Evapo-transpiration Irrigation Evaporation Runoff Root Zone Water Storage Below Root Zone Drainage 11/19/2018 Watershed Hydrology Lab. Fall 2006

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Effects of Vegetative Cover 11/19/2018 Watershed Hydrology Lab. Fall 2006

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Watershed Hydrology Lab. Fall 2006 ET / Potential ET 11/19/2018 Watershed Hydrology Lab. Fall 2006

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Available Water Content 11/19/2018 Watershed Hydrology Lab. Fall 2006

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Watershed Hydrology Lab. Fall 2006 Available Soil Water 11/19/2018 Watershed Hydrology Lab. Fall 2006

ET & Available Soil Water 11/19/2018 Watershed Hydrology Lab. Fall 2006

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