**2. Material and methods**

## **2.1. Study site**

and timing of water saturation in soils [4]. Therefore, accurate estimation of ET is needed to predict stream flow emanating from forestland, to investigate hydrological processes, and to manage water resources [4, 5]. Forest ET is known to be hard to quantify [6]. It is a complex hydrological process [7, 8], which is influenced by interactions between the atmosphere, soil,

ET can be directly measured by lysimeters, water balance methods, and eddy covariance systems [6, 11–13]. Direct measurement of ET is difficult and requires large amounts of time, labor, and funding [14, 15]. The eddy covariance method is considered the most reliable, but frequently is deficient from a lack of surface energy balance closure [16]. In the absence of direct measurements, ET can be modeled using climatic and ecosystem data [17–20]. Depending on the model used, estimating ET requires input data such as net radiation, air temperature, vapor pressure deficit, wind speed, and soil moisture. Net radiation is the difference between incoming and outgoing radiation [21], and a key variable for calculating potential ET. Air temperature, wind speed, and vapor pressure deficit control atmospheric conditions that impact ET [22]. Vapor pressure deficit also regulates stomatal resistance, which directly affects ET [23]. Soil moisture controls the availability of water for ET and is especially important in arid and semi-arid ecosystems, where ET is primarily water limited [24, 25]. The use of ET equations with fewer input variables is recommended when complete climatological data cannot be obtained [26]. Meteorological models that use onsite input data can produce estimates of

ET similar to measurements by eddy covariance and are less expensive [27].

tial ET from air temperature and solar radiation.

Installing equipment to measure onsite climatological and soil moisture data may still require more resources than are available to forest and water managers. Publicly available climatological data from weather stations may provide a reasonable substitute. Not all weather stations include the full set of measurements necessary to model ET. The U.S. Surface Climate Reference Network provides data from 114 stations in the USA that record all necessary meteorological data. Other networks, such as Ameriflux (ameriflux.ornl.gov), provide additional coverage. Soil moisture data needed to convert potential ET to actual ET are more limited, distributed across a range of government and academic networks, and summarized in the Texas A&M University North American Soil Moisture Database (http://soilmoisture.tamu.edu/).

In the absence of a nearby weather station with a complete suite of measurements, certain inputs, such as net radiation and vapor pressure deficit, can be calculated using empirical models based on basic weather data [26, 28]. For example, Irmak et al. [28] developed equations to calculate net radiation from input variables such as minimum and maximum air temperatures, measured or predicted solar radiation, inverse relative distance from earth to sun, and mean relative humidity. Tabari et al. [26] derived regression equations to estimate poten-

The impact on ET estimation of using offsite meteorological data rather than onsite data is unknown for most forest regions. In this study, we estimated ET for a ponderosa pine (*Pinus ponderosa*) forest from three meteorological models (Priestly-Taylor (P-T), Shuttleworth-Wallace (S-W), and Penman-Monteith with dynamic stomatal resistance (P-M-d)) using onsite and offsite data for net radiation, air temperature, vapor pressure deficit, wind speed, and soil moisture content (θ or SMC in this chapter), and compared these estimates to measurements

and plant canopy [9, 10].

48 Current Perspective to Predict Actual Evapotranspiration

The study site is a ponderosa pine forest located near Flagstaff, Arizona (Northern Arizona University Centennial Forest: 35°5′20.5″ N, 111°45′43.33″ W, elevation 2180 m a.s.l.). Previously, this site was one of the three sites used to measure carbon and water fluxes in ponderosa pine forests of northern Arizona with the eddy covariance (EC) approach [3]. Thinning, harvesting, and fire did not occur at this site over the last century. The control site had an average leaf area index of 2.3 m2 m−2, basal area of 30 m2 ha−1, and tree density of 853 trees ha−1 [3, 27, 29]. Location of study site is shown in **Figure 1**.

### **2.2. ET model selection**

We selected the three best performing ET models from Ha et al. [27] based on the model performance statistics of root mean square error (RMSE) and coefficient of determination (*R*<sup>2</sup> ) in comparisons with ET measured by the eddy covariance approach (**Table 1**). These three models were the Penman-Monteith dynamic (P-M-d), Priestley-Taylor (P-T), and Shuttleworth-Wallace (S-W) models. The P-M-d model updates the Penman-Monteith ET model by modeling canopy resistance as a function of environmental variables [30]. The P-T model is a simplification of the Penman-Monteith model that only requires inputs of net radiation, air temperature, and the Priestly-Taylor coefficient [31]. The S-W model was developed to estimate ET in sparse canopies and calculates soil evaporation and plant canopy transpiration separately [32]. Each of these models calculates potential ET, which we adjusted to actual ET using a relationship with soil moisture [27, 33]. ET calculations were made at the monthly scale because monthly data were available from weather stations and generally provided more accurate ET estimates for the study site than daily data when compared with ET measured with eddy covariance [27]. Detailed explanation of each model and its use in simulating ET at our study site can be found in Ref. [27].

### **2.3. Offsite weather station data**

Daily offsite meteorological data were obtained from the Western Regional Climate Center (WRCC) available at http://www.wrcc.dri.edu/. Weather data were collected from a weather

**Figure 1.** A ponderosa pine forest study site (a star) near the city of Flagstaff (a circle) in northern Arizona with an inset of coterminous United States of America (Basemap sources: www.esri.com, US National Park Service).

station near the Flagstaff Pulliam Airport (Flagstaff 4 SW, AZ; site number: 023009; latitude: 35°8′ N, longitude: 111°40′ W, ground elevation: 2135 m; distance to the study site: 12.2 km). Because net radiation (Rn) data were not available from this station, they were calculated using an empirical equation from the FAO's Irrigation and Drainage paper 56 compiled by Ref. [34]. Inputs were daily offsite maximum and minimum absolute air temperature, actual vapor pressure, dew point temperature, relative humidity, station elevation, solar declination, Sensitivity of Evapotranspiration Models to Onsite and Offsite Meteorological Data for a Ponderosa Pine Forest http://dx.doi.org/10.5772/intechopen.68435 51


**Table 1.** Comparisons of root mean square error (RMSE) and coefficient of determination (*R*<sup>2</sup> ) among three ET models. Numbers in bold indicate the best model for each dataset.

sunset hour angle, inverse relative distance from Earth to sun, sunset hour angle, latitude, and day of the year. Vapor pressure deficit (kPa) was calculated using dew point temperature and relative humidity (%) measured at the station.

Soil moisture data were obtained from the SNOTEL data collection network operated by the Natural Resources Conservation Service (NRCS) of the U.S. Department of Agriculture. Snowpack and climatic data (air and soil temperature and precipitation for all locations and soil moisture data for selected locations) are collected at sites across the Western U.S. Two SNOTEL sites were used, Happy Jack (site number: 969; latitude: 34°45′ N, longitude: 111°25′ W, elevation: 2326 m; distance to study site: 60 km) and Mormon Mountain Summit (site number: 1125; latitude: 34°58′ N, longitude: 111°31′ W, elevation: 2591 m; distance to study site: 32 km). These SNOTEL sites were selected because they were the closest to our study site and they had data available for our period of study (2007–2010). The Mormon Mountain Summit data are available only from June 2008.

station near the Flagstaff Pulliam Airport (Flagstaff 4 SW, AZ; site number: 023009; latitude: 35°8′ N, longitude: 111°40′ W, ground elevation: 2135 m; distance to the study site: 12.2 km). Because net radiation (Rn) data were not available from this station, they were calculated using an empirical equation from the FAO's Irrigation and Drainage paper 56 compiled by Ref. [34]. Inputs were daily offsite maximum and minimum absolute air temperature, actual vapor pressure, dew point temperature, relative humidity, station elevation, solar declination,

**Figure 1.** A ponderosa pine forest study site (a star) near the city of Flagstaff (a circle) in northern Arizona with an inset

of coterminous United States of America (Basemap sources: www.esri.com, US National Park Service).

50 Current Perspective to Predict Actual Evapotranspiration

### **2.4. Analysis of error propagation**

The error introduced in meteorological models of ET by using offsite station data likely can be reduced if some variables are measured onsite. To aid managers in prioritizing the installation of monitoring equipment with limited resources, an analysis was performed to determine how error in different input data combines to overall model error.

Each model was run at the monthly scale over 4 years (2007–2010) with all onsite input data to establish a baseline result. Then, model runs were performed using offsite data for each input variable and onsite data for the remaining input variables. The percent difference between the single offsite input model and the baseline was calculated. This procedure was repeated with each of the major offsite input variables (net radiation: Rn, air temperature: ta, wind speed: u, vapor pressure deficit: vpd, and soil moisture) to evaluate the error introduced by the use of offsite data.

For each model, the three variables to which the model was most sensitive were selected. Error was introduced to each of the three selected variables in increments of 1% to a maximum of 15% for variables positively related to ET or percent decrease for variables negatively related to ET. Thus, compounding errors acted in the same direction providing a worst case scenario estimate of overall model error. The models were run over ranges of percent error for the variables to determine all combinations of percent error in the three variables that produced 15% model error when averaged overall 4 years of simulation. These results show how variation in the accuracy of input variables affects model results.
