CAPÍTULO 3: RESULTADOS Y DISCUSIÓN
3.1 Procedimiento computacional para la identificación de latidos normales en el
The amount of evapotranspiration from soil covered by vegetation is difficult to evaluate. There are many different methods for measuring evapotranspiration.
Depending on the study objectives, some methods can be more appropriate than others due to their accuracy, their cost, or their adaptability to a particular temporal or spatial scale. Determining evapotranspiration is often an essential step in many applications, and is usually accomplished by modeling.
For practical reasons, we will discuss measurement-based methods and modeling methods separately. There are also different approaches within these two categories.
Among the methods that “measure3” evapotranspiration, there are three approach-es that were developed to meet specific objectivapproach-es:
• Hydrological approaches: hydrological balance assessed on a test plot or a watershed; water budget based on a lysimeter (based on drainage and rainfall measurements, soil moisture profile in a natural environment).
• Micrometeorological approaches: correlational method: the “eddy correlation” method (which provides continuous direct and independent measurements of the mass and energy fluxes on a seasonal or annual time scale), methods based on the Bowen ratio, methods using optical properties of the air (scintillometry), etc.
• Approaches based on plant physiology: measurements of sap flow, measurement of gas emission in a pressure chamber.
Among the modeling methods for estimating evapotranspiration, there are two main approaches:
• Empirical approaches: methods based on the crop coefficient and an estimate of evapotranspiration of a reference crop (mathematical formulation based on empirical or semi-empirical relationship a physical basis); methods based on the water budget of the soil.
• Analytical or physical approaches: combined models based on the energy balance and the transfer of mass, such as the Penman-Monteith equation.
In this section, we are interested particularly in the methods for estimating evapotranspiration, some of which are more complex than others.
Empirical Estimation of Evapotranspiration
To facilitate the estimation of evaporation and to try to standardize the models used, researchers have agreed to determine the water requirements of crops, ETM, by correcting the reference evapotranspiration (ET0) of a reference crop (usually grass) by a coefficient called a crop coefficient kcusing the following formula (Figure 5.9):
(5.22) The time scale for which the water requirements are calculated can be in terms of hours, days, months, decades, or the growth stage of the plant, depending on the study objectives and the availability of data. The value of the kc coefficient is affected mostly
3. Conventionally, if the value of a given parameter is quantified using a single instrument, this is a direct measurement; when this value is the result of a relation between several parameters, it is considered an indirect measurement.
crop grass
by the type of crop, its height, the duration of its cycle and rate of growth, as well as on the frequency of rainfall or irrigation at the beginning of the crop cycle. The coeffi-cient kcis always established experimentally for a given crop and region; tables of these crop coefficients can be used for the same region or a similar one. The possible values of kc are in theory between 0 and 1, depending on the growth stage of the crop.
The precision of this method will depend in part on the choice of the reference crop (grass or a specific amount of water in a standardized pan), and partly on the method for evaluating the kc coefficient. The choice of the method used for evaluating the reference evapotranspiration, ET0, will obviously influence the quality of the results.
The reference evapotranspiration can, like evapotranspiration, be determined using different approaches (e.g. measurements, lysimeters, estimation).
Many authors propose simple methods for estimating ET0 based on statistical-empirical equations (an extensive list of these various methods can be obtained from the FAO (FAO, 1998). From a practical point of view, these methods are easy to use, but most of the equations were established and tested for a particular climatic zone or a given crop. Thus, extrapolating them to other climatic conditions requires a control and sometimes adjustments to adapt them for the local conditions. For example, the equation suggested by Blaney and Criddle in 1970, which provides for the correct estimation of evapotranspiration for arid and semi-arid regions, tends to produce over-estimates for temperate climates.
On the other hand, Turc’s equation (1961) can be used to estimate the reference evapotranspiration for temperate regions. The equation can be expressed for a month or a decade, as follows:
(monthly time step) [mm] (5.23)
radiation temperature wind velocity humidity
+
climate grass reference crop
well-watered grass
=
ET0
+
kc factor
optimal conditions
=
ETM
ET0
Fig. 5.9 : Water requirements of crops (ETM) and reference evapotranspiration (ET0) (modified from FAO 1998).
(decadal time step) [mm] (5.24) Turc’s equation requires the average values of climatic parameters such as temperature T in °C and total solar radiation RG in cal/cm2/day. When the total solar radiation is expressed in W/m2, the equations below are expressed by multiplying the RG value by 2.065. This equation is very easy to apply, but does not take into account the effect of wind. In addition, it is not applicable to small time scales (hourly or daily time steps), which are exactly the ones of interest to an engineer for irrigation projects.
In cases where the relative humidity is lower than 50%, Equation 5.23 must be corrected as follows:
(5.25) There are other empirical equations for estimating the physical evaporation from a reservoir, such as the Primault or Rohwer equations discussed earlier.
Finally, we should mention the Thornthwaite equation (1944), which is based on a long series of lysimetric observations4. This equation calculates a monthly thermal index as follows:
(5.26)
Then, the index is calculated for each month of the year, to produce the total sum I:
(5.27)
Finally, the reference evaporation is calculated by the following:
(5.28)
Today, the analytical methods are the most widely recommended and used for estimating reference evapotranspiration. Of the methods with a physical basis, it would be the Penman-Monteith model, as discussed below.
Estimating Evapotranspiration – Physically-based Model
Penman (1948) was the first to propose a model combining aerodynamic theory
4. A lysimeter is a device used for the continued measurement of surface exchanges, whether infiltration or evapotranspiration, by means of weighing or gravitational measurements (Musy and Soutter, 1991).
and the energy balances to calculate evapotranspiration. These models, known as combined models, have a well-defined physical basis because they take into account both the properties of the canopy and the meteorological conditions. Here, we will discuss the Penman-Monteith model (1981). This equation is derived from the original Penman equation and is the most complete approach for describing the evapotranspi-ration process because it takes into account the physiology of the plant by considering its surface resistance.
The general form of the Penman equation to estimate reference evapotranspiration ET0 is written as:
(5.29)
where ET0 is the reference evapotranspiration [mm/s], Rn is the net solar radiation [W/m2],' is the slope of the vapor pressure curve at mean average air temperature [kPa/C°],
U
is the air density at constant pressure [kg/m3], cp is the heat capacity of humid air [kJ/kg/C°],G
e is the difference between the saturation vapor pressure es [kPa] and the effective vapor pressure in the air ea [kPa] (G
E = ES – Ehas), ra is the aerodynamic resistance [s/m] (a meteorological descriptor expressing the role of atmospheric turbulences in the evaporation process),O
is the latent heat of vaporization of water [MJ/kg] and J is the psychrometric constant [kPa/C°].For practical reasons, some of the climatic variables defined above are regarded as constants and some are calculated based on the available weather data (generally temperature, wind velocity, pressure, total solar radiation, moisture content, and albedo). The values of the various weather constants cited above can be found in the FAO tables (1998).
When these values have been specified, we can determine the aerodynamic resistance rausing equation 5.21, the saturation vapor pressure es using equation 5.3, and the effective vapor pressure of the air ea (in kPa with the temperature in degrees Celsius), etc. Then we proceed as follows:
(5.30) where ea is the effective vapor pressure [kPa], Hr is the relative humidity of the air [%].
This gives us:
(5.31) and finally:
(5.32)
Introducing the concept of surface resistance (rs) into the Penman equation gives us the Penman-Monteith equation:
(5.33)
The success of this method will depend on the precision obtained when estimating the term expressing canopy resistance (or resistance of the surface rs) using the relationship between the resistance of the stomata (a function of the morphological and anatomic characteristics of the stomata, the solar radiation and the water potential) and the Leaf Area Index (LAI).
In conclusion, it is possible to estimate evaporation as well as the reference evapotranspiration by applying relatively complex equations that require complete knowledge of a number of climatic and crop-related parameters. Ultimately, the availability of meteorological data will determine the choice of one equation over another, along with the possibilities for applying a particular method in the region being studied. The UN’s Food and Agriculture Organization (FAO, 1998) published an exhaustive list of the different methods for calculating evapotranspiration for a vegetal cover5. There are several methods and approaches for better estimating the different climatic parameters that are often unknown or measured non-directly: the relative humidity (based on measured temperature), atmospheric pressure (based on the altitude), or the total solar radiation based on the geographic coordinates of the study area and tabulated solar data.
In order to compare the precision of the various equations presented above, Figure 5.10 shows the monthly evapotranspiration determined by using the Penman-Monteith method (Equation 5.33), Turc’s Equation (5.23), and Thornthwaite’s (Equation 5.26).
The crop used for these calculations was grassland with a height of 20 cm, an albedo of 0.25, and surface resistance rc fixed at 200 s/m. The meteorological data are for pressure, wind speed, temperature and relative humidity (provided by an automated station for an hourly time step).
For the purpose of illustration, Figure 5.10 also shows the evapotranspiration values measured in situ at two different locations: an agricultural research station in Changins where the measurements are collected under nearly optimal conditions (the reference crop) and the other in Payerne (where measurements were done under standard conditions). The results are for the year 1991.
5. This material is also available online via the Internet at the following webpage: http://
www.fao.org/docrep/ X0490E/X0490E00.htm s