**1. Introduction**

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

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

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 medium forced by radiation and meteorological conditions. As demonstrated in mid-latitudes studies by Bittelli et al. [26], this approach enables numerically stable, energy and mass conservation equation solution in terms of the external forcing and boundary conditions. Such an approach requires a modeling framework that incorporates the interactions among meteorological variables (e.g., air temperature, relative humidity, precipitation, and solar radiation) and soil properties (e.g., soil temperature, soil moisture, and soil water potential) into the coupled numerical model. We also conducted a field experiment to measure net radiation, sensible heat flux, soil moisture, and soil temperature, and use those measured parameters to calculate evapotranspiration in order to compare with simulated results.
