**2.1. Field experiment**

**1. Introduction**

66 Current Perspective to Predict Actual Evapotranspiration

Northern latitudes have been identified as a region where global climate change will have earlier and stronger impacts than in other regions of the world [1–4]. Most of the region is underlain by discontinuous permafrost or perennially frozen ground in which temperatures remain below 0°C for at least two consecutive years. An active layer on top of the permafrost experiences seasonal thaws and is the primary dominant subsurface component of the land-atmosphere system [5]. Under climate warming scenario, much of this terrain would be vulnerable to subsidence, particularly in ice-rich areas of relatively warm, discontinuous permafrost, and shrinking ponds and lakes [3, 6–10]. All these changes will potentially alter the exchange of surface energy, water, and carbon cycles in high-latitude ecosystems [11] and

Soil moisture plays a critical role in the surface energy balance and water cycle in these regions [1, 12, 13]. It is widely recognized that the soil moisture confined in a thin layer underneath the land surface influences the partitioning of the surface energy fluxes simultaneously modifying surface thermal conductance and rates of evaporation [14]. An example of such an important role is the control of precipitation transfer into the soil and the partitioning of incoming solar radiation into latent, sensible, and ground heat fluxes [15, 16]. In addition, soil moisture and temperature status affect biological processes such as soil microbial activity, seed germination, and plant growth. These variables in turn also affect water and nutrition absorption and solute transport in soil. In a climate change scenario, high-latitudes soils will experience increased summer dryness as climate warming progresses, changing therefore atmospheric vapor pressure conditions and thereby enhancing evapotranspiration (ET) rate. In terms of seasonal effects, inadequate snowmelt infiltration or rainfall during spring and early summer often causes crop water stress and reduction in yield of small grains [17, 18] in agricultural activities of subarctic regions. Therefore, understanding the variation of evapotranspiration (ET) and its impact on crop growth becomes of absolute importance because it mainly controls the available soil water and, therefore, is a limiting factor in agriculture productivity and sustainability. As a result, continuous monitoring of soil water content and soil temperature

Several modeling studies have focused on soil carbon reservoirs (e.g. [20–22]) and permafrost degradation in natural ecosystems across the circumpolar region [21, 23]; nevertheless, agroecosystem has not been taken into consideration until a recent study by Ruairuen et al. [24]. Despite the mentioned complexities in the soil medium, similarities between high latitude and mid-latitude agricultural soils exist mainly during the growing season. This allows for making use of models that are currently in use for mid-latitude agricultural settings. In this case, a fully coupled differential equation system considering both soil temperature and vertical soil moisture distribution, and their interactions are utilized to bring emphasis on the sub-medium transport in contrast to most large-scale ecosystem models where one or two soil

layers are used to simulate soil moisture dynamics in ecosystem models (e.g. [25]).

In this study, we use the numerical model developed by Bittelli et al. [26], which fully couples heat and water transport to deduce the coupled water and heat transport across the soil

consequently, the response at regional level to the atmosphere system.

is a priority in the fields of agronomy and hydrology [19].

The field study was conducted at the Fairbanks Experiment Farm (FEF) of the University of Alaska Fairbanks (UAF) Agricultural and Forestry Experiment Station (AFES) Fairbanks Alaska (**Figure 1**), USA (64°51′16.6″ N, 147°51′36.4″ W, 150 m above sea level) during summer 2013. The soil within the lysimeter plots, established in a previous study, was used for this study because large amounts of data (i.e., soil moisture, soil temperature, and soil moisture

**Figure 1.** Geographic location of the Northern Latitude Study Site (panel left on the top) and Fairbanks Experiment Farm (FEF) at the UAF-AFES within the University of Alaska Fairbanks Campus (panel top right). Bottom panel is the detail on the location of the instrumentation in the study site. The farm dimensions are more than 1 km on East to West direction and about 600 m North to South. Eddy-Covariance (EC) tower (A), lysimeter plot (B), meteorological station (C), large aperture scintillometer (LAS) Scintec BLS900 (D). Airborne survey photo was provided by the UAF Department of Design and Construction obtained by AeroMap Inc. summer of 2003.

potential) were available. The soil composition was sandy loam with 66 sand, 29 silt, and 5% clay, and with the available water holding capacity of about 0.18–0.36 m3 m−3 that was determined from a soil moisture characteristic curve [24]. Parameters for soil hydraulic properties to be introduced in the numerical simulation are listed in **Table 1**. Volumetric soil moisture content was measured *in situ* using three soil moisture sensor (10HS; Decagon Devices Inc., Pullman, WA, USA) at 5, 10, and 20 cm. The sensor has 14.5 cm long prongs, 3.3 cm wide, so the 5-cm sensor spanned the depth 3.3–6.7 cm, the 10-cm sensor spanned the depth 8.3–11.3 cm, and the 20-cm sensor spanned the depth 18.3–21.3 cm. Gravimetric samples were also taken to calibrate the 10HS sensor [24]. Soil moisture was continuously measured with an interval of 30 min. The bulk density was measured in the tested site (**Table 1**). The soil temperature (S-TMB-M006, Onset HOBO Corporation, Bourne, MA, USA) was measured at depths of 5, 10, and 20 cm below the soil surface and used to obtain the ground heat flux in this study.

The observation-based meteorological parameters included air temperature (Tair), relative humidity (RH), air pressure, wind speed (u), and direction, and precipitation at 2 m height above the ground were obtained at 1-min intervals at the experimental station. One-min recordings of these data were averaged to obtain hourly data for input to the simulation.

An independent measure of evapotranspiration was determined using Penman-Monteith method and the more continuous series of data available on this period. Sensible heat flux was measured locally (i.e., ecosystem scale) by means of and eddy-covariance (EC) instrument and processed considering signal distortions under all weather conditions [27] and, at landscape scale, based on a large aperture scintillometer (LAS) [28–30].

#### **2.2. Model implementation**

#### *2.2.1. Model description (PSP\_coupled)*

The numerical model was coded in Python and is set in a time-evolving one-dimensional simulation of coupled flow of liquid water, heat, and water vapor. The model description can be found in Bittelli et al. [26, 31]. **Figure 2** shows the models' conceptual scheme indicating the coupled layers and driving boundary conditions, i.e., soil temperature, liquid water


**Table 1.** Soil properties within lysimeter.

**Figure 2.** Scheme of the computational grid with the driving force terms (temperature, soil water potential, and soil vapor concentration), the soil conductivities and the resistances involved at the soil-atmosphere interface (adapted from Bittelli et al. [26]). The black dot is the mass balance for heat flow and water flux at a given node.

volumetric concentration, and soil resistive and conductive terms. The model computes the soil energy budget. The PSP-coupled model is composed of ten modules with two input data files and one main program file. One data file contains the soil data, and the other one contains the weather data. Model modules include main.py, PSP\_boundary.py, PSP\_public.py, PSP\_ soil.py, PSP\_coupled1D.py, PSP\_readDataFile.py, PSP\_longWaveRadiation.py, PSP\_grid.py, PSP\_plot.py, PSP\_plotEnergy.py, PSP\_ThomasAlgoritmh.py, soil.txt, and Weather.txt.

The main file is main.py, which contains the calls to other embedded subroutines listed. The module PSP\_boundary defines the initial and boundary conditions. The PSP\_public contains all variables that are read by all modules such as latitude, longitude, altitude, albedo, atmospheric pressure and clay content, initial soil temperature, and soil matric potential. The PSP\_soil is written to define the soil properties. The PSP\_couple1D is the module that implements the solver for the different flux equations. The PSP\_longWaveRadiation is for computing the long wave radiation component of the radiation balance at the soil surface. The PSP\_grid module is for building the computational grid and PSP\_ThomasAlgorithm for solving the system of equations. The PSP\_plot and PSP\_plotEnergy are modules for visualizing the data input and output from the model.

### *2.2.2. Initial setting for model simulation*

potential) were available. The soil composition was sandy loam with 66 sand, 29 silt, and 5%

mined from a soil moisture characteristic curve [24]. Parameters for soil hydraulic properties to be introduced in the numerical simulation are listed in **Table 1**. Volumetric soil moisture content was measured *in situ* using three soil moisture sensor (10HS; Decagon Devices Inc., Pullman, WA, USA) at 5, 10, and 20 cm. The sensor has 14.5 cm long prongs, 3.3 cm wide, so the 5-cm sensor spanned the depth 3.3–6.7 cm, the 10-cm sensor spanned the depth 8.3–11.3 cm, and the 20-cm sensor spanned the depth 18.3–21.3 cm. Gravimetric samples were also taken to calibrate the 10HS sensor [24]. Soil moisture was continuously measured with an interval of 30 min. The bulk density was measured in the tested site (**Table 1**). The soil temperature (S-TMB-M006, Onset HOBO Corporation, Bourne, MA, USA) was measured at depths of 5, 10, and 20 cm below the soil surface and used to obtain the ground heat flux in this study. The observation-based meteorological parameters included air temperature (Tair), relative humidity (RH), air pressure, wind speed (u), and direction, and precipitation at 2 m height above the ground were obtained at 1-min intervals at the experimental station. One-min recordings of these data were averaged to obtain hourly data for input to the simulation.

An independent measure of evapotranspiration was determined using Penman-Monteith method and the more continuous series of data available on this period. Sensible heat flux was measured locally (i.e., ecosystem scale) by means of and eddy-covariance (EC) instrument and processed considering signal distortions under all weather conditions [27] and, at

The numerical model was coded in Python and is set in a time-evolving one-dimensional simulation of coupled flow of liquid water, heat, and water vapor. The model description can be found in Bittelli et al. [26, 31]. **Figure 2** shows the models' conceptual scheme indicating the coupled layers and driving boundary conditions, i.e., soil temperature, liquid water

m−3 that was deter-

clay, and with the available water holding capacity of about 0.18–0.36 m3

landscape scale, based on a large aperture scintillometer (LAS) [28–30].

**2.2. Model implementation**

Saturated moisture content; *θ*<sup>s</sup>

**Table 1.** Soil properties within lysimeter.

*K*s

*2.2.1. Model description (PSP\_coupled)*

68 Current Perspective to Predict Actual Evapotranspiration

**Soil property Value** Bulk density (g cm−3) 0.7 Air entry potential (J kg−1) −1.5 Mass sand (kg kg−1) 0.66 Mass silt (kg kg−1) 0.29 Mass clay (kg kg−1) 0.05

(m<sup>3</sup>

*b* value (−) −3.1

(kg s m−3) 7.2 × 10−4

m−3) 0.56

The initial conditions for dry and wet periods were calculated using *in situ* data. To implement the simulation scenarios, two data files need to be created "soil.txt" and "weather.dat." The soil.txt file is required for data input of soil properties such as soil depth (the model set up from 0 to 1.5 m), the saturated soil moisture, residual water content, soil hydraulic properties, and soil matric potential (**Table 1**). The soil file can be used to simulate the two periods; however, additional settings indicating initial conditions should be modified in the PSP\_public module. The weather file is required at hourly weather parameters such as solar radiation, air temperature, precipitation, relative humidity, and wind speed as an input to calculate related parameters. Time step is set to 300 s and input data of 1-h resolution.

The mass of sand, silt, clay, and bulk density was obtained from *in situ* measurements. The parameter for the hydraulic properties was obtained from Cambell and Shiozawa [32], *K*<sup>s</sup> is saturated hydraulic conductivity, *θ*<sup>s</sup> is the saturated soil moisture content, and *b* is constant value.

The PSP\_public is the file that needs to be adapted in all parameters that are read by all modules for the given area in which the simulation is carried out. In this case, the FEF site-specific information was input including latitude, longitude, and altitude. Moreover, the soil initial conditions such as soil water potential, soil temperature, and albedo for dry and wet scenarios needed to be applied into this module (**Table 2**).

In this study, the value of albedo was set as 0.2 for the dry period [33], while a value of 0.15 was applied for the wet period in agriculture land in subarctic region according to previous studies in the same agricultural setting [34].


**Table 2.** Initial setting for model simulation.
