1Lecture 31, Canopy Evaporation and Transpiration, part 1, Theory November 15, 2010 Instructor: Dennis Baldocchi Professor of Biometeorology Ecosystem Science Division Department of Environmental Science, Policy and Management 345 Hilgard Hall University of California, Berkeley Berkeley, CA 94720 Topics Concepts, 1 1. Evaporation 2. Potential Evaporation 3. Equilibrium Evaporation 4. Transpiration 5. Dew, Condensation, Distillation Modeling Approaches A. Bowen Ratio B. Thornthwaite Equation C. Penman’s Combination Equation D. Penman Monteith Equation E. Isothermal Energy Balance F. Equilibrium Evaporation G. Priestly-Taylor Equation Concepts, 2 1. Canopy conductance 2. Coupling Theory, Canopy Scale 3. Sensitivity and Feedbacks Others Concepts Drought Indices Water Balance L31.1. Introduction2Evaporation is the “physical process by which a liquid or solid is converted to a gaseous state” (Glossary of Meteorology). Plant canopies introduce water vapor into the atmosphere via transpiration and the evaporation of water from the soil and free water on the leaves and stems. Some scientists call the summed rate evapotranspiration. This field has a long and rich history with over 7000 peer-reviewed articles identified on the web of science, circa 2008. Different and opposing views have been used historically to define evaporation (Jarvis and McNaughton 1986). Meteorologists argue from the thermodynamic viewpoint that energy is required to drive the latent heat of vaporization. Evaporation also causes the surface and surrounding air to cool, which condensation releases heat. Physiologists counter that evaporation is driven by a potential difference between the humidity of the surface and the free atmosphere. The problem these opposing arguments is that they are valid for the scale at which they were defined and applied. We will see later how to derive a more general equation for evaporation. Potential Evaporation Potential Evaporation is: “the evaporation from an extended surface of a short grass that is supplied with water and the canopy covers the ground completely.” The original assumption is that potential evaporation cannot exceed evaporation from a free water surface. Several problems arise with this definition. In Davis, Potential evaporation may be only 80% of pan evaporation. In Nebraska, PET can exceed pan evaporation. Hence, free water evaporation may not represent the maximal rate in a region. The surface area of transpiring leaf area exceeds the surface area of a water body, as an evaporation pan. Water is partially transparent to sunlight and stores heat energy. So the energy available to evaporate water will be different than that used to evaporate water from the land surface. Evaporation pans are also subject to error due to the oasis effect and from animals drinking from it. Actual Evaporation Over the years numerous environmental factors have been correlated with evaporation. They include the vapor pressure of the air, which is a function of temperature, wind speed, solar radiation. Plant factors affecting evaporation include stomatal conductance and leaf area index . Surveys on modeling evaporation have been produced by Brutsaert (Brutsaert 1982), Shuttleworth (Shuttleworth 2007), Monteith (Monteith 1981),3Rosenberg et al (1968), Rana and Katerji (Rana and Katerji 2000) Raupach (Raupach 2001), among others. 1. Aerodynamic Approach Theories on evaporation go as far back as Aristotle, who recognized the power that sun and wind have on evaporating water from puddles and ponds. Dalton’s (1801) experiments demonstrated that evaporation from warm water was a function of the vapor pressure of the liquid and that of the air, as determined from the dew point temperature. He derived an empirical equation for evaporation Eeefus()() (1 f(u) is an empirical wind speed function. If we express Eq.1 using an electrical analog, where the aerodynamic resistance Ra is used to evaluate the wind speed function and the vapor pressure deficits are expressed in terms of vapor concentration then: EepeepeRccRasswaws ww ()()() (2 2. Energy Balance Approach The surface energy balance contains a term for latent heat exchange. From the view point of simple algebra one can arrive at a simple equation for evaporation from the net radiation budget. REHSGn (3 nER HSG (4 We can also examine the energy balance between available energy (A) and how it is partitioned into H and E. nEHR SGA Dividing both sides of the equation by E produces 1nHRSGEE4If the partitioning of energy is conserved, we defined by the Bowen ratio, HE We can re-express the equation for latent heat exchange 1nRGSE Similarly, one can use the same logic to define an equation for H. HRGn1() When this relation was first derived by Bowen, it was assumed that  was constant. Today we know this is not true, but we can still utilize this relationship by measuring the Bowen ratio with temperature and humidity gradients. 21212121()()()()vapMMCT TTTeeeeP Where the psychrometeric constant is defined as: pavCPmm But this relation assumes that the sources and sinks of heat and water vapor are identical, as when vapor may originate from vegetation and heat from the hot soil underneath an open and sparse canopy. A second example is when there is advection of heat or moisture, such as at the transition between desert and an irrigated crop or a lake and rough forest. Under many circumstances, like tall forests or open canopies, the eddy exchange coefficients for momentum, heat and water vapor transfer differ (Thom et al. 1975), as can be shown with the correlation between q and T fluctuations differ from one. Hence the Bowen ratio version of the equation for latent heat exchange should be modified5ERGKKnTq1 HKKKKRGTqTqn1() If the sources and sinks of heat and vapor are co-located the ratio of the eddy exchange coefficients will approach unity and fluctuations in temperature and humidity will be highly correlated. We see this to be true over a transpiring wheat crop. Many workers, however, show cases where KT > Kq. Others, including Verma et al at Mead, NE found Kq > Kt for numerous studies using independent measurement methods.