**3. Results**

#### **3.1. Sensitivity of annual ET to offsite data**

**Figure 2** shows the sensitivity of annual ET predicted by each model to the use of all offsite input data. When compared to eddy ET measurements at the annual scale, the S-W model performed well, but was sensitive to the use of offsite vpd data. The P-M-d model consistently underestimated eddy ET regardless of data sources. The P-T model consistently overestimated ET, and was sensitive to the use of offsite Rn. The use of offsite soil moisture data generally led to underestimation of ET for all models, especially for data from the Happy Jack site. When compared to modeled ET using all onsite data inputs, the use of offsite data inputs only led to significantly increased error in certain cases. For example, accuracy of the S-W and P-T models was reduced by the use of offsite vpd and Rn data, respectively.

#### **3.2. Sensitivity of monthly ET to offsite data**

ET simulated by the P-T model was sensitive to the use of offsite weather data used to calculate Rn (**Figure 3(a)**). The difference in ET predicted by the P-T model using all offsite data except for Rn was greater than a 15% threshold of acceptability, especially during summer (data not shown). In contrast, using offsite Rn data produced acceptable predictions of ET by the P-M-d and S-W models (**Figure 3(a)**).

Sensitivity of Evapotranspiration Models to Onsite and Offsite Meteorological Data for a Ponderosa Pine Forest http://dx.doi.org/10.5772/intechopen.68435 53

**2.4. Analysis of error propagation**

52 Current Perspective to Predict Actual Evapotranspiration

**3. Results**

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 deter-

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

**Figure 2** shows the sensitivity of annual ET predicted by each model to the use of all offsite input data. When compared to eddy ET measurements at the annual scale, the S-W model performed well, but was sensitive to the use of offsite vpd data. The P-M-d model consistently underestimated eddy ET regardless of data sources. The P-T model consistently overestimated ET, and was sensitive to the use of offsite Rn. The use of offsite soil moisture data generally led to underestimation of ET for all models, especially for data from the Happy Jack site. When compared to modeled ET using all onsite data inputs, the use of offsite data inputs only led to significantly increased error in certain cases. For example, accuracy of the S-W and

ET simulated by the P-T model was sensitive to the use of offsite weather data used to calculate Rn (**Figure 3(a)**). The difference in ET predicted by the P-T model using all offsite data except for Rn was greater than a 15% threshold of acceptability, especially during summer (data not shown). In contrast, using offsite Rn data produced acceptable predictions of ET by

P-T models was reduced by the use of offsite vpd and Rn data, respectively.

mine how error in different input data combines to overall model error.

variation in the accuracy of input variables affects model results.

**3.1. Sensitivity of annual ET to offsite data**

**3.2. Sensitivity of monthly ET to offsite data**

the P-M-d and S-W models (**Figure 3(a)**).

**Figure 2.** Effect of source of meteorological data for variables, wind speed (u), air temperature (ta), vapor pressure deficit (vpd), and net radiation (Rn), and soil moisture content (*θ*), on modeled ET as compared to (a) eddy covariance ET measurements and (b) modeled ET with all onsite inputs. Percent difference is calculated at the annual scale for three models, Penman-Monteith with dynamic canopy resistance (P-M-d), Priestly-Taylor (P-T), and Shuttleworth-Wallace (S-W), with all onsite meteorological inputs, a single offsite meteorological input, all offsite meteorological inputs, and offsite soil moisture from two SNOTEL sites, Happy Jack and Mormon Mountain Summit.

The P-M-d and P-T models were sensitive to the use of offsite ta data, whereas the S-W was not (**Figure 3(b)**). Inaccuracy in predicted ET from the P-M-d model was largest during winter when total ET is close to zero.

The P-M-d and S-W models were highly sensitive to the use of offsite vpd data, whereas the P-T model was not because it does not use vpd as an input parameter (**Figure 3(c)**). Inaccuracy

**Figure 3.** Percent difference in ET from models using all offsite input data and substitution of each input variable with onsite data (subscripted; Rn: net radiation, ta: air temperature, vpd: vapor pressure deficit) for the Penman-Monteith with dynamic canopy resistance (P-M-d), Priestly-Taylor (P-T), and Shuttleworth-Wallace (S-W) models (a–c); and percent difference in seasonal variation between offsite and SNOTEL sites Rn, ta, vpd (d). Dashed horizontal lines indicate ±15% difference lines.

caused by the use of offsite vpd data was greater for the S-W model than the P-M-d model. Sensitivity to the use of offsite u was low for all models (data not shown).

Modeled Rn based on offsite weather data was consistently higher than based onsite Rn (**Figure 3(d)**), with the highest percent difference in summer. The percent difference between offsite and onsite vpd peaked during summer (**Figure 3(d)**). As opposed to Rn, offsite vpd was always lower than onsite vpd (**Figure 3(d)**). Offsite ta data generally provided a good substitute for onsite data, differing by less than 2.5°C throughout the study period. During winter, when temperatures were close to 0°C, the percent difference between offsite and onsite temperatures could be quite large despite small absolute differences. Thus, these values are excluded from **Figure 3(d)**.

The P-T and S-W models were most sensitive to the source of soil moisture content (SMC) data (**Figure 4(a)** and **(c)**). The P-T model was more sensitive than the S-W model, because SMC is

Sensitivity of Evapotranspiration Models to Onsite and Offsite Meteorological Data for a Ponderosa Pine Forest http://dx.doi.org/10.5772/intechopen.68435 55

**Figure 4.** Percent difference in ET from models using all offsite input data and substitution of each input variable with onsite data (subscripted; SMC-HJ: soil moisture content from Happy Jack SNOTEL site, SMC-MMS: soil moisture content from Mormon Mountain Summit SNOTEL site) for the Penman-Monteith with dynamic canopy resistance (P-Md), Priestly-Taylor (P-T), and Shuttleworth-Wallace (S-W) models (a and b); and percent difference in seasonal variations of soil moisture contents (SMC) between two SNOTEL sites (c). Dashed horizontal lines indicate ±15% difference lines.

included in the calculation of the scaling coefficient α in the P-T model. The Happy Jack (HJ) SMC data produced a larger difference in **Δ**ET than Mormon Mountain Summit (MMS) SMC data, which resulted from consistently lower SMC at the HJ site than onsite (**Figure 4(c)**). The SMC at the MMS site was higher than onsite SMC during summer, but lower during winter. SMC data from the MMS site were unavailable between January 2007 and May 2008, so no percent change was calculated during this time (**Figure 4(b)** and **(c)**).

caused by the use of offsite vpd data was greater for the S-W model than the P-M-d model.

**Figure 3.** Percent difference in ET from models using all offsite input data and substitution of each input variable with onsite data (subscripted; Rn: net radiation, ta: air temperature, vpd: vapor pressure deficit) for the Penman-Monteith with dynamic canopy resistance (P-M-d), Priestly-Taylor (P-T), and Shuttleworth-Wallace (S-W) models (a–c); and percent difference in seasonal variation between offsite and SNOTEL sites Rn, ta, vpd (d). Dashed horizontal lines

Modeled Rn based on offsite weather data was consistently higher than based onsite Rn (**Figure 3(d)**), with the highest percent difference in summer. The percent difference between offsite and onsite vpd peaked during summer (**Figure 3(d)**). As opposed to Rn, offsite vpd was always lower than onsite vpd (**Figure 3(d)**). Offsite ta data generally provided a good substitute for onsite data, differing by less than 2.5°C throughout the study period. During winter, when temperatures were close to 0°C, the percent difference between offsite and onsite temperatures could be quite large despite small absolute differences. Thus, these val-

The P-T and S-W models were most sensitive to the source of soil moisture content (SMC) data (**Figure 4(a)** and **(c)**). The P-T model was more sensitive than the S-W model, because SMC is

Sensitivity to the use of offsite u was low for all models (data not shown).

ues are excluded from **Figure 3(d)**.

indicate ±15% difference lines.

54 Current Perspective to Predict Actual Evapotranspiration

The difference between ET modeled with offsite and onsite input data with the P-M-d model led to overprediction of ET during summer (**Figure 5**) due to the error introduced by vpd (**Figure 3(c)**), and underestimated ET during winter due both to error from vpd and ta (**Figure 3(b)**). The P-T model had a bigger difference than P-M-d between offsite and onsite modeled ET during summer due to error introduced by offsite Rn (**Figure 3(a)**). ET stimulated by the S-W model using offsite data was always lower than using onsite data except for June 2007 (**Figure 5**), a pattern driven by error introduced by offsite vpd.

**Figure 5.** Difference in ET between modeled using offsite weather station input data and modeled with onsite data for the Penman-Monteith with dynamic canopy resistance (P-M-d), Priestly-Taylor (P-T), and Shuttleworth-Wallace (S-W) models.

#### **3.3. Sensitivity of annual ET to input errors**

Error in prediction of annual ET by the P-T model was most strongly influenced by error in Rn and, to a lesser extent, SMC (**Figure 6(a)**). Less than 15% error in overall modeled ET was possible with large errors in ta (>15%) and soil SMC (>20%) if onsite Rn (i.e., 0% error in net radiation) is used. Error in the S-W model was most strongly influenced by error in vpd (**Figure 6(b)**). Large errors in soil moisture and temperature were acceptable if vpd is accurate. Because of the threshold responses and complex internal dynamics of the P-M-d model, we conclude that it is not a good choice for this type of error analysis. Therefore, we only considered the S-W and P-T models in this analysis.

#### **3.4. Relationships between onsite and offsite weather data**

A strong linear relationship occurred between onsite data and offsite weather- or SNOTELstation data with *R*<sup>2</sup> 0.72 or higher for all variables, except for u where the *R*<sup>2</sup> was 0.59 (**Figure 7**).

**3.3. Sensitivity of annual ET to input errors**

56 Current Perspective to Predict Actual Evapotranspiration

considered the S-W and P-T models in this analysis.

station data with *R*<sup>2</sup>

models.

**3.4. Relationships between onsite and offsite weather data**

Error in prediction of annual ET by the P-T model was most strongly influenced by error in Rn and, to a lesser extent, SMC (**Figure 6(a)**). Less than 15% error in overall modeled ET was possible with large errors in ta (>15%) and soil SMC (>20%) if onsite Rn (i.e., 0% error in net radiation) is used. Error in the S-W model was most strongly influenced by error in vpd (**Figure 6(b)**). Large errors in soil moisture and temperature were acceptable if vpd is accurate. Because of the threshold responses and complex internal dynamics of the P-M-d model, we conclude that it is not a good choice for this type of error analysis. Therefore, we only

**Figure 5.** Difference in ET between modeled using offsite weather station input data and modeled with onsite data for the Penman-Monteith with dynamic canopy resistance (P-M-d), Priestly-Taylor (P-T), and Shuttleworth-Wallace (S-W)

A strong linear relationship occurred between onsite data and offsite weather- or SNOTEL-

0.72 or higher for all variables, except for u where the *R*<sup>2</sup>

was 0.59 (**Figure 7**).

**Figure 6.** Combination of error in net radiation, air temperature, and soil moisture content that will produce 15% error in the Priestly-Taylor model (a), and vapor pressure deficit, air temperature, and soil moisture that will produce 15% error in the Shuttleworth-Wallace model (b). Model error is calculated at the annual scale over four years (2007–2010). Other model inputs were measured onsite.

**Figure 7.** 1:1 relationship between onsite eddy tower versus offsite weather station input variables for (a) net radiation (W m−2), (b) air temperature (°C), (c) vapor pressure deficit (kPa), and (d) wind speed (m s−1). Soil moisture content data from eddy tower versus Happy Jack (HJ) station (e) and Mormon Mountain Summit (MMS) (f) are also shown. The solid line indicates a 1:1 line and the dashed line is a regression line.

#### **4. Discussion**

The performance of three meteorological ET models (P-M-d, P-T, and S-W) in predicting ET measured by eddy covariance for the ponderosa pine forest in our study was affected by the source of input data. The P-M-d model performed well with offsite Rn data. In most cases, the P-T model performed well when offsite soil moisture content (SMC) data obtained from local SNOTEL sites replaced onsite SMC data. Likewise, the S-W model performed well when onsite Rn, ta, and u data were replaced by offsite data from a nearby weather station. A previous study [27] reported that when using all onsite data, the ET predictions from the S-W model were the closest to ET measured by eddy covariance among five meteorological models, likely because our study site contains a mixture of surface layers (pine canopy, grass, bare soil), which the S-W model was designed to simulate [35–37].

Sensitivity to offsite meteorological data varied among models. The P-T model was sensitive to the use of offsite weather data used to predict Rn (**Figure 2(a)**). The P-M-d model was sensitive to the use of offsite ta and vpd data (**Figure 2(b)** and **(c)**). The S-W model was sensitive to the use of offsite vpd data (**Figure 2(c)**). From this result, we conclude that accurate measurement of vpd is important to properly estimate ET using S-W and P-M-d models. Models using Rn predicted from offsite weather data calculated consistently higher ET than models using onsite Rn data (**Figure 2(d)**), resulting in overestimation of ET by the P-T model, especially in summer (**Figure 2(a)**), when ET is highest and is the most important seasonal component to annual ET.

The suitability of offsite data as inputs into meteorological ET models depended on the variable and model. Offsite weather station data provided suitable estimates of onsite air temperature (**Figure 2(d)**) and therefore, air temperature was not a major source of error in all models for this study site. The sensitivity analysis (**Figure 5**) illustrates that errors in air temperature up to 15% are not likely to lead to large errors in ET estimates. Overestimation of winter ET occurs in the P-M-d model when onsite ta is used (**Figure 2(b)**), but winter ET is a small component of total annual ET. The dynamic model of stomatal conductance in the P-M-d model goes to zero when air temperature is below zero, and the overestimation by this model is the result of a threshold response when onsite air temperature is below zero and offsite air temperature is not. The vpd was consistently lower in the offsite data than the onsite data leading to overestimation of ET by the S-W model without a seasonal pattern. The effect of vpd on the P-M-d model is more complex because increases in vpd increase ET by increasing evaporative demand and decrease ET by reducing stomatal conductance. Thus, overestimation or underestimation of ET is possible when onsite vpd data are replaced with offsite data.
