**4. Results and discussion**

#### **4.1. Net radiation**

Net radiation (*R*net) is the main input in the energy balance equation driving evapotranspiration process. Giving this importance, a comparison between the net radiation observed (*R*net obs) and modeled (*R*net mod) was performed. **Figure 4a** shows simulated and measured hourly data of net radiation as a function of time for the dry period (26 July–3 August 2013). Results show a good agreement between modeled and observed *R*net with the correlation coefficient (*R*<sup>2</sup> ) of 0.92 and root mean square error (RMSE) of 45 W m−2 (**Figure 5a**) during the dry period. There are about 6 days out of nine total days that the model performed remarkably well to simulate the *R*net and the maximum difference did not exceeded 157 W m−2 on 27 July (Julian day 208).

Overall, *R*net mod overestimated *R*net obs by about 16%. Similar results have been reported by Ortega-Farias et al. [36] in a commercial vineyard where the *R*net simulation shows a good agreement with the measured *R*net (*R*<sup>2</sup> = 0.92) with the RMSE less than 48 W m−2. On the other hand, a lower correlation between *R*net obs and *R*net mod was found during the wet period with the *R*<sup>2</sup> of 0.72 and RMSE of 67 W m−2 (**Figure 5b**). However, there were two days from 25 to 26 August that the model simulated very well compared with the measured *R*net, while it was underestimated in the following 2 days (27–28 August) and overestimated in the last 2 days during the wet period (**Figure 4b**). The maximum underestimation for the entire time series was about 85 W m−2, and the maximum overestimate was 199 W m−2.

The high and low correlation between measured and modeled *R*net in different periods can be related to the cloudiness variability in high latitudes. This may be explained based on the variability of incoming solar radiation between those periods as we can see in **Figure 6**. An average of solar radiation of 215 W m−2 with the maximum and minimum of 680, 150 W m−2 respectively were reported in the dry period, while a lower mean and maximum *R*net were found in the wet period (**Table 3**). Ortega-Farias et al. [37] indicated that errors in the calculation of *R*net over a well-irrigated festuca grass were associated with the estimation of atmospheric radiation under cloudy sky conditions. Therefore, to summarize this point, *R*net mod was able to estimate net radiation with a good degree of precision during the dry period than during the wet period.

Evapotranspiration in Northern Agro-Ecosystems: Numerical Simulation and Experimental Comparison http://dx.doi.org/10.5772/intechopen.68347 73

**Figure 4.** Simulated and measured hourly data of net radiation during the dry and wet period as a function of time. (Top panel) Dry period from 26 July to 3 August 2013 (Julian day 207–216) (bottom panel) wet period from 25 to 30 August 2013 (Julian day 237–242).

#### **4.2. Latent heat**

**3.2. Wet period**

period for the simulation in this study.

72 Current Perspective to Predict Actual Evapotranspiration

agreement with the measured *R*net (*R*<sup>2</sup>

than during the wet period.

**4. Results and discussion**

**4.1. Net radiation**

ficient (*R*<sup>2</sup>

the *R*<sup>2</sup>

(Julian day 208).

The meteorological conditions during the wet period 18–30 August 2013 (Julian 230–242) was cooler than the dry period in terms of an average hourly air temperature and soil temperature (**Figure 3b**), while there was a slight difference in solar radiation compared to the dry period (see **Table 3**). The RH was approximately 77% with low level of VPD (0.36 kPa) on average during the wet period (**Table 3**). A total precipitation of 37.60 mm was also reported in this period. However, only data during 25–30 August 2013 (Julian 237–242) are used as the wet

Net radiation (*R*net) is the main input in the energy balance equation driving evapotranspiration process. Giving this importance, a comparison between the net radiation observed (*R*net obs) and modeled (*R*net mod) was performed. **Figure 4a** shows simulated and measured hourly data of net radiation as a function of time for the dry period (26 July–3 August 2013). Results show a good agreement between modeled and observed *R*net with the correlation coef-

period. There are about 6 days out of nine total days that the model performed remarkably well to simulate the *R*net and the maximum difference did not exceeded 157 W m−2 on 27 July

Overall, *R*net mod overestimated *R*net obs by about 16%. Similar results have been reported by Ortega-Farias et al. [36] in a commercial vineyard where the *R*net simulation shows a good

hand, a lower correlation between *R*net obs and *R*net mod was found during the wet period with

The high and low correlation between measured and modeled *R*net in different periods can be related to the cloudiness variability in high latitudes. This may be explained based on the variability of incoming solar radiation between those periods as we can see in **Figure 6**. An average of solar radiation of 215 W m−2 with the maximum and minimum of 680, 150 W m−2 respectively were reported in the dry period, while a lower mean and maximum *R*net were found in the wet period (**Table 3**). Ortega-Farias et al. [37] indicated that errors in the calculation of *R*net over a well-irrigated festuca grass were associated with the estimation of atmospheric radiation under cloudy sky conditions. Therefore, to summarize this point, *R*net mod was able to estimate net radiation with a good degree of precision during the dry period

was about 85 W m−2, and the maximum overestimate was 199 W m−2.

 of 0.72 and RMSE of 67 W m−2 (**Figure 5b**). However, there were two days from 25 to 26 August that the model simulated very well compared with the measured *R*net, while it was underestimated in the following 2 days (27–28 August) and overestimated in the last 2 days during the wet period (**Figure 4b**). The maximum underestimation for the entire time series

) of 0.92 and root mean square error (RMSE) of 45 W m−2 (**Figure 5a**) during the dry

= 0.92) with the RMSE less than 48 W m−2. On the other

**Figure 7** shows simulated and observed latent heat flux (LE) as a function of time during dry and wet periods. High rates of solar radiation heating the soil surface caused the soil to lose water vapor to evaporation from the surface. During nighttime, there was negative conduction to cool the soil surface, and LE became negative due to condensation. The LE was better predicted by the numerical model during the dry period, with an *R*<sup>2</sup> of 0.70 and RMSE of 53 W m−2 than the wet period (*R*<sup>2</sup> = 63 and RMSE = 58 W m−2). There were 2 days that the model overestimated LE, but the time series followed each other, while 1 day obtained similar values and 3 days of modeled LE did not correlate with the observed LE. The maximum difference between observed and simulated LE was about 200 W m−2. Cumulative ET from the observed quantities reached 22 mm with an average of 2.44 mm d−1, while cumulative ET

**Figure 5.** Comparison between the hourly observation of net radiation (*R*net obs) and the simulation of net radiation (*R*net mod) during the dry and wet period. (Top panel) Dry period from 31 July to 3 August 2013 (Julian day 210–215) and during the wet period (bottom panel) from 25 to 30 August 2013 (Julian day 237–242).

from the vsimulation was 15 mm with the mean of 1.67 mm d−1 for the dry period. In contrast, during the wet period, the cumulative ET from the observed was about 6 mm over 6 days, whereas only about 2 mm was found from the simulation of ET cycles. An average precipitation observed was 1.0 mm d−1, while only 0.3 mm d−1 was found for the simulation during the wet period.

#### **4.3. Ground heat fluxes**

The average daytime ground heat flux (*G*) contribution to vapor flux was in the order of 26 W m−2 (ranging from 1 to 79 W m−2), while the value output from the simulation was on average 25 W m−2 (ranging from 0.8 to 49 W m−2; **Figure 8**). In **Figure 8a**, modeled *G* resulted as overestimated for the first two days, and then closely approached the *G* observed at day 3, and underestimated the observations during the last 2 days of the dry period. The maximum reported difference was

Evapotranspiration in Northern Agro-Ecosystems: Numerical Simulation and Experimental Comparison http://dx.doi.org/10.5772/intechopen.68347 75

**Figure 6.** Solar radiation as a function of time during dry and wet periods. (Top panel) Dry period from 26 July to 3 August 2013 (Julian day 207–215) and (bottom panel) wet period from 25 to 30 August 2013 (Julian day 237–242).

44 W m−2 during the overestimating period, whereas the same values were 32 W m−2 found during the underestimating period. On the contrary, the simulation of *G* during the wet period was overestimated for the entire period (**Figure 8b**) with the maximum difference of more than 100 W m−2 during daytime.

#### **4.4. Sensible heat**

from the vsimulation was 15 mm with the mean of 1.67 mm d−1 for the dry period. In contrast, during the wet period, the cumulative ET from the observed was about 6 mm over 6 days, whereas only about 2 mm was found from the simulation of ET cycles. An average precipitation observed was 1.0 mm d−1, while only 0.3 mm d−1 was found for the simulation during the

**Figure 5.** Comparison between the hourly observation of net radiation (*R*net obs) and the simulation of net radiation (*R*net mod) during the dry and wet period. (Top panel) Dry period from 31 July to 3 August 2013 (Julian day 210–215) and

during the wet period (bottom panel) from 25 to 30 August 2013 (Julian day 237–242).

The average daytime ground heat flux (*G*) contribution to vapor flux was in the order of 26 W m−2 (ranging from 1 to 79 W m−2), while the value output from the simulation was on average 25 W m−2 (ranging from 0.8 to 49 W m−2; **Figure 8**). In **Figure 8a**, modeled *G* resulted as overestimated for the first two days, and then closely approached the *G* observed at day 3, and underestimated the observations during the last 2 days of the dry period. The maximum reported difference was

wet period.

**4.3. Ground heat fluxes**

74 Current Perspective to Predict Actual Evapotranspiration

The sensible heat (*H*) fluxes obtained from measurements and from the simulation for agricultural field were compared during the dry and wet period. The time series composite of hourly diurnal variation during dry and wet was illustrated in **Figure 9**. In the dry period, results showed a good correlation between *H* measured by EC and simulated from models with *R*<sup>2</sup> = 0.63 and RMSE = 32 W m−2, whereas a lower correlation was found in *H* observed by LAS (*R*<sup>2</sup> of 0.52 and RMSE of 40 W m−2) (**Figure 9a**). Nevertheless, LAS measurements represent a larger fluxing footprint area than EC-derived fluxes, and the simulations output converge well between these two scale-dependent observations. Overall simulated outputs overestimated *H* from EC except

**Figure 7.** Evapotranspiration time series observed and modeled. (Top panel) Dry period from 26 July to 3 August 2013 (Julian day 207–216) (bottom panel) wet period from 25 to 30 August 2013 (Julian day 237–242).

in the morning where they were closer in value. The ratio of *H* by EC and simulated was about 0.47, while ratio of *H* modeled versus *H* by LAS was 0.82. The maximum of *H* from model, EC, and LAS were 139, 110 and 169 W m−2, respectively, during midday.

Concerning the wet period, very poor correlation was found between *H* measured by LAS and simulated outputs for *H* (*R*<sup>2</sup> = 0.15, RMSE =13 W m−2). It should be noted that *H* by EC was not illustrated during this period because of insufficient data for the analysis. The time-series composite of hourly diurnal variation of *H* from both methods are illustrated in **Figure 9b**. Mean hourly *H* observed was 30 W m−2, while only 15 W m−2 was reported from modeled *H*. In general, *H* showed higher values than *H* simulated by about 51% with the maximum difference of 36 W m−2 during the wet period.

#### **4.5. Soil temperature and soil moisture**

Soil temperature was measured at the same depth as soil moisture. **Figure 10** shows simulated and observed soil temperature as a function of time during dry and wet periods. During the dry period, the value of soil temperature from experiment reached 17°C and was higher than Evapotranspiration in Northern Agro-Ecosystems: Numerical Simulation and Experimental Comparison http://dx.doi.org/10.5772/intechopen.68347 77

**Figure 8.** Time series of simulated and estimated ground heat flux. (Top panel) Dry period from 29 July to 2 August 2013 (Julian day 210–214) (bottom panel) wet period from 26 to 30 August 2013 (Julian day 238–242).

in the morning where they were closer in value. The ratio of *H* by EC and simulated was about 0.47, while ratio of *H* modeled versus *H* by LAS was 0.82. The maximum of *H* from model, EC,

**Figure 7.** Evapotranspiration time series observed and modeled. (Top panel) Dry period from 26 July to 3 August 2013

Concerning the wet period, very poor correlation was found between *H* measured by LAS

not illustrated during this period because of insufficient data for the analysis. The time-series composite of hourly diurnal variation of *H* from both methods are illustrated in **Figure 9b**. Mean hourly *H* observed was 30 W m−2, while only 15 W m−2 was reported from modeled *H*. In general, *H* showed higher values than *H* simulated by about 51% with the maximum dif-

Soil temperature was measured at the same depth as soil moisture. **Figure 10** shows simulated and observed soil temperature as a function of time during dry and wet periods. During the dry period, the value of soil temperature from experiment reached 17°C and was higher than

= 0.15, RMSE =13 W m−2). It should be noted that *H* by EC was

and LAS were 139, 110 and 169 W m−2, respectively, during midday.

(Julian day 207–216) (bottom panel) wet period from 25 to 30 August 2013 (Julian day 237–242).

and simulated outputs for *H* (*R*<sup>2</sup>

76 Current Perspective to Predict Actual Evapotranspiration

ference of 36 W m−2 during the wet period.

**4.5. Soil temperature and soil moisture**

the simulated 11°C for the same depth at the beginning of the simulation period. However, after midday in the first day, the simulated value was higher than observed soil temperature over entire dry period (**Figure 10a**). The soil temperature was better predicted by the numerical model during the wet period, with an *R*<sup>2</sup> of 0.59 and RMSE of 1.82°C than the dry period (*R*<sup>2</sup> = 0.47 and RMSE = 3.27°C). The maximum difference between observed and simulated soil temperature was about 8°C during mid of the day in dry period and the times series followed each other. There was only a day that the model underestimated in a wet period, while most of the time, simulated values overestimated the observed data (**Figure 10b**). A large difference of the soil temperature can cause differences in the land-atmosphere temperature gradient that affect the ground heat flux as described in the previous sections. However, in this case, we found the model in good agreement in predicting soil temperatures for this environment.

The soil moisture was measured in the plot at three depths. From the measurements, we found that the high moisture content was in the lower depth than in the surface layer. The initial soil moisture during the dry period above the soil surface was about 0.28 m3 m−3 (5 cm depth). The numerical model gave a lower level soil moisture around the same depth with a large difference of 0.21 m3 m−3 when compared to the observed data. Some disagreement

**Figure 9.** Time-series composite of hourly diurnal variation of sensible heat flux during (top panel) dry and (bottom panel) wet period.

between modeled and observed data was also found during the wet period where the measurement of soil moisture from the plot was 0.30 m3 m−3 for the first day; however, the simulation gave a lower value of soil moisture with a difference larger than 0.13 m3 m−3. In addition, an underestimation of simulated soil moisture potential is also reported in this study during both periods. This could be due to the lack of representation on the hydraulic properties of the soils especially for the subarctic soil. This is important because the hydraulic conductivity versus the soil moisture potential curve is highly nonlinear and, therefore, the flow of soil moisture from the upper layer to the lower layer in a wet period leads to a large decrease in hydraulic conductivity and liquid water distribution [26, 31], while during the dry period, Evapotranspiration in Northern Agro-Ecosystems: Numerical Simulation and Experimental Comparison http://dx.doi.org/10.5772/intechopen.68347 79

**Figure 10.** Soil temperature time series observed and modeled. (Top panel) Dry period from 26 July to 3 August 2013 (Julian day 207–216), (bottom panel) wet period from 25 to 30 August 2013 (Julian day 237–242).

the soil moisture was more constant along the depths with less dependence on the liquid fraction. The soil moisture content fluctuated through the day according to the vapor flux as reported previously [38–40]. As such, improvements in the model's representation of both soil moisture and soil moisture potential in order to have an optimal simulation output. There is also a need to further study the vertical soil properties along the soil depth under agricultural land in subarctic region. Evaluation of simulation performance for subarctic soil and weather seems that more parameters might be needed to improve model simulation because of influence of the permafrost, soil properties across landscape and weather variability.

### **5. Conclusions**

between modeled and observed data was also found during the wet period where the mea-

**Figure 9.** Time-series composite of hourly diurnal variation of sensible heat flux during (top panel) dry and (bottom

an underestimation of simulated soil moisture potential is also reported in this study during both periods. This could be due to the lack of representation on the hydraulic properties of the soils especially for the subarctic soil. This is important because the hydraulic conductivity versus the soil moisture potential curve is highly nonlinear and, therefore, the flow of soil moisture from the upper layer to the lower layer in a wet period leads to a large decrease in hydraulic conductivity and liquid water distribution [26, 31], while during the dry period,

tion gave a lower value of soil moisture with a difference larger than 0.13 m3

m−3 for the first day; however, the simula-

m−3. In addition,

surement of soil moisture from the plot was 0.30 m3

78 Current Perspective to Predict Actual Evapotranspiration

panel) wet period.

An effort was undertaken to simulate fluxes from surface-atmosphere exchanges based on numerically solving the coupled vapor and liquid water differential equations prescribing soil properties and turbulent exchange parameters. Numerical simulation was forced by meteorological data, radiation, and precipitation from a high-latitude agricultural farm. Similarly, dynamic boundary conditions were introduced throughout the simulation including soil temperature, soil moisture, and soil hydraulic properties.

After examining simulation outputs and comparing them to collocated micrometeorological data, it can be concluded that time series of fluxes during the dry period seemed to be reproduced fairly better than those obtained during the wet period. In general, *R*net has a good agreement between modeled and observed data for both periods with RMSE of 45 W m−2 in a dry period and 48 W m−2 during a wet period. The LE also was well predicted by the model with RMSE not exceeding 53 W m−2. This difference in turbulent fluxes agrees well with other studies in the same area over highly heterogeneous terrain with further canopy complexity [41, 42]. On the other hand, *G* was overestimated with the maximum difference of more than 100 W m−2 in a wet period and 44 W m−2 in a dry period. In addition, the measured *H* by EC and LAS instruments correlated well with the model in terms of the RMSE being in the range of 32–40 W m−2 which falls within the interval of fluxing difference across landscapes observed on the same area for heterogeneous surfaces [41, 42]. However, only the soil temperature correlated better during a wet period than a dry period, while the soil moisture and soil moisture potential was underestimated compared to the observed values. The low correlation in the wet period was due to significant influences of the synoptic variability introducing large changes in cloud coverage and precipitation that are difficult to reproduce by a single point one-dimensional model formulation. Nevertheless, dry conditions that are by far the most stringent conditions for agriculture sustainability reproduces well.

There are still several parameters such as the presence of vegetation above the soil, the swell, and shrink of soil that need to be investigated more in depth and the most important factor is the hydraulic properties of soil and its variability across landscape. This variable is more complicated, and there are many steps to reach an approximately correct value. In the current study, existing values were applied from previous work done around the same study site, while some other values were obtained from field and laboratory experiments. However, it is known that soils in agro-ecosystems tend to experience large changes in some of these properties and, therefore, are difficult to capture. This factor needs to be taken into account when implementing this model over unnatural setting systems.

Finally, based on current numerical model outputs and field experimental observations allowed identification new challenges in northern agro-ecosystems. Improved representation of soil dynamics is necessary to improve fidelity in the simulations, and also there is a need to establish better strategies to compare single-point numerical modeling to scale-dependent micrometeorological observations. In addition, a large deviation in simulated soil profiles and heat exchanges reveals the highly heterogeneous nature of an aerodynamically simple terrain considered in terms of atmospheric observations.
