Catchment Hydrological Modeling with Soil Thermal Dynamics During Seasonal Freeze-Thaw Cycles

water

Article Catchment Hydrological Modeling with Soil Thermal Dynamics during Seasonal Freeze-Thaw Cycles

Nawa Raj Pradhan 1,*, Charles W. Downer 1 and Sergei Marchenko 2 1 Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180-6199, USA; [email protected] 2 Geophysical Institute, University of Alaska Fairbanks, Fairbanks, AK 99775, USA; [email protected] * Correspondence: [email protected]

Received: 16 November 2018; Accepted: 2 January 2019; Published: 10 January 2019

Abstract: To account for the seasonal changes in the soil thermal and hydrological dynamics, the soil moisture state physical process defined by the Richards Equation is integrated with the soil thermal state defined by the numerical model of phase change based on the quasi-linear heat conductive equation. The numerical model of phase change is used to compute a vertical soil temperature profile using the soil moisture information from the Richards solver; the soil moisture numerical model, in turn, uses this temperature and phase, information to update hydraulic conductivities in the vertical soil moisture profile. Long-term simulation results from the test case, a head water sub-catchment at the peak of the Caribou Poker Creek Research Watershed, representing the Alaskan permafrost active region, indicated that freezing temperatures decreases infiltration, increases overland flow and peak discharges by increasing the soil ice content and decaying the soil hydraulic conductivity exponentially. Available observed and the simulated soil temperature comparison analysis showed that the root mean square error for the daily maximum soil temperature at 10-cm depth was 4.7 ◦C, and that for the hourly soil temperature at 90-cm and 300-cm was 0.17 ◦C and 0.14 ◦C, respectively.

Keywords: soil thermodynamics; soil hydrodynamics; freezing and thawing; hydraulic conductivity; seasonal change; Caribou Poker Creek Research Watershed

1. Introduction Both the Intergovernmental Panel on Climate Change latest full assessment [1] and the U.S. National Climate Assessment [2] unequivocally state that climate change is occurring due to anthropogenic factors, that signiﬁcant warming has already occurred, and that both data trends and climate modeling indicate that climate change and the problems associated with climate change will only worsen in the future. Of the many issues related to climate change, climate change directly affects soil temperature and trends in soil temperature. After analyzing 50 years of soil temperature proﬁle data at 5, 10, 20, 50, 100, and 150 cm depths across Canada, Qian et al. [3] found a soil temperature warming trend of +0.30 ◦C/decade. Warming was especially prevalent during spring. Qian et al. [3] also found that the increasing trend of soil temperature was directly associated with the increasing trends in air temperature. A change in soil temperature has a determinative role on the response of biochemical processes that control the soil biological cycle of plant nutrient and carbon use and production [4]. A positive trend in the soil temperature has a determinative role on the emission of greenhouse gases in Alaska and other arctic and sub-arctic ecosystems [5,6]. Melvin et al. [7] showed widespread damages to Alaska public infrastructure from increased soil temperature due to climate change. Seasonal changes in air temperature lead to analogous changes in the soil thermal regime, thereby affecting the hydrological response [8,9]. Plot-scale studies by Dunne and Black [9], and Stähli

Water 2019, 11, 116; doi:10.3390/w11010116 www.mdpi.com/journal/water Water 2019, 11, 116 2 of 20 et al. [10] showed that storm runoff generation processes of a watershed are altered as the soil water phase transitions from a non-frozen state to a freezing state with reduced infiltration and enhanced runoff. Without physical processes that explicitly simulate such seasonal changes in hydrological regime, calibrated/effective parameter values alone may not be sufficient to simulate the rainfall-runoff response, especially in a long-term numerical simulation of projected future global warming scenarios in higher latitude regions [8]. It is also significant to note that the freezing condition is highly variable in space and time [11], which a simple conceptual model, or even a physics-based numerical model lacking the required process, may fail to account for. In order to fully analyze the effects of climate change on soil thermal dynamics, and associated hydrologic response for the future climate change scenarios on the response of watersheds with permafrost and/or a seasonally frozen soil regime, understanding and application of soil thermal dynamics interaction with soil hydrological dynamics are required. The purpose of this paper is to describe the development of a distributed, numerical model that accounts for both physics of soil thermodynamics and hydrodynamics including the physical linkage between thermodynamics and hydrodynamics of soil horizons/layers and the atmosphere. This numerical model could then be employed to explicitly simulate the soil thermal state and its effects on hydrological dynamics during changing seasons. The architecture of the numerical models’ linkage development is achieved by two way coupling of the soil moisture physical state accounting of Richards mathematical formulation in the US Army’s physics-based distributed hydrology model, Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model [12,13] and soil thermal regime simulation capability of the Geophysical Institute Permafrost Laboratory (GIPL) numerical model [14,15] of the 1D quasi-linear heat equation with phase change between liquid water and ice. The coupled numerical schemes provide a clear insight of the temporal and spatial variability of the soil thermal state during changing seasons and the effects on hydrological processes that are significant for long-term simulation, such as infiltration and evapotranspiration. The coupled model was deployed in the headwater sub-catchment, 0.2 km2, of the Caribou Poker Creek Research Watershed which included the soil properties and hydro-meteorological measurement site at the peak of the Caribou Poker Creek Research Watershed called CPEAK. The temperature calibration and verification and the coupled model induced thermodynamic and hydrodynamic interaction results’ analysis were done in this 0.2 km2 headwater sub-catchment. Finally, the 0.2 km2 headwater sub-catchment thermodynamic and hydrodynamic interaction results and analysis were employed to explain contrasting spatial and temporal variation in the observed discharge in bigger watershed scales of CPCRW during 2002 summer and fall seasons.

2. Study Area and Data The test case selected in this study illustrates modeling permafrost active area with GIPL coupled in GSSHA.

2.1. Description of the Study Site Figure1 shows the test case, study area, location encompassing watershed and elevations, and model domain and grid. Water 2019, 11, 116 3 of 20 Water 2019, 11, x FOR PEER REVIEW 3 of 20

Figure 1. The test case, study area, location encompassing watershed and elevations, and model Figuredomain 1. and The grid. test case, study area, location encompassing watershed and elevations, and model domain and grid. The study area is contained in the in the Caribou Poker Creek Research (CPCRW), located 48 km northThe of study Fairbanks area 65is contained◦100 N, 147 in◦ 30the0 Win the Alaska. Caribou The Poker CPCRW Creek site Research is part of(CPCRW), the LTER located (Long-Term 48 km northEcological of Fairbanks Research) 65° network.10′ N, 147 Parts°30′ W of Alaska. this watershed The CPCRW are underlainsite is part by of permafrost,the LTER (Long where-Term the Ecologicalmaximum seasonal Research) thaw network. depth thickness Parts of isthis about watershed 0.52 m at are a low underlain elevation by point permafrost, near the conﬂuencewhere the maximumof Poker and seasonal Caribou thaw Creeks depth [16 thickness]. The CPCRW is about watershed 0.52 m at a encompasses low elevation an point area near of 101.5 the kmconﬂuence2 and is oflocated Poker within and Caribou the boreal Creeks forest [16 area.]. The CPCRW watershed encompasses an area of 101.5 km2 and is locatedAs within shown the in boreal Figure forest1, the area. site includes a weather station on the summit of Caribou Peak, CPEAK,As shown which in is Figure at an elevation 1, the site of includes 773 m. Thea weather CPEAK station station on consiststhe summit of a of 10-m Caribou tower Peak, with CPEAK, various whichatmospheric is at an sensors elevation and ground of 773 m. temperature The CPEAK thermistors station consists at several of depths a 10-m ( http://www.lter.uaf. tower with various atmosphericedu/data/metadata/id/442/inline/1 sensors and ground). The site temperature is located on the thermistors broad summit at area several of Caribou depths Peak, (http://www.lter.uaf.edu/data/metadata/id/442/inline/1).right at the tree-line elevation. There are no higher peaks The nearby site tois located limit the on exposure the broad of summit this site. area of CaribouA 10 × Peak,10 GSSHA/GIPL right at the model tree-line grid elevation. was developed There forare simulations no higher peaks in the nearbytest case. to The limit study the exposurearea model of domain,this site. Figure1, includes the CPEAK station so that the observations from the station couldA be 10 used × 10 inGSSHA/GIPL model development model grid and was validation. developed for simulations in the test case. The study area model domain, Figure 1, includes the CPEAK station so that the observations from the station could2.2. Data be used Acquisition in model development and validation. The Institute of Arctic Biology at the University of Alaska, Fairbanks maintains a Long-Term 2.2.Ecological Data Acquisition Research (LTER) site (funded by NSF) called the Bonanza Creek LTER. The Caribou-Poker CreeksThe Research Institute Watershed of Arctic Biology (CPCRW) at isthe one University of the study of Alaska, sites for Fairbanks this LTER projectmaintains where a Long long-term-Term Ecologicalmonitoring Research data are (LTER) collected site and (funded made availableby NSF) called online the (http://www.lter.uaf.edu/data Bonanza Creek LTER. The Caribou). Clicking-Poke onr Creeks Research Watershed (CPCRW) is one of the study sites for this LTER project where long-term monitoring data are collected and made available online (http://www.lter.uaf.edu/data). Clicking on WaterWater 20192019, ,1111, ,x 116 FOR PEER REVIEW 44 of of 20 20

Access Data, Study Sites Catalog in the Data menu of this website brings up a search ﬁlter page for theAccess Study Data, Sites Study Catalog. Sites In Catalog this study in the the Data data menufrom CPEAK of this website were employed brings up as a the search initial ﬁlter condition, page for andthe forcings Study Sites used Catalog. to run and In this validate study the the test data case from model. CPEAK were employed as the initial condition, and forcings used to run and validate the test case model. 2.2.1. Topography 2.2.1. Topography The study area model shown in Figure 1 was developed from a 50 m digital elevation model (DEM)The obtained study area from model the National shown in Elevation Figure1 was Datase developedt (NED), from the a primary 50 m digital elevation elevation data model product (DEM) of theobtained USGS. from theThe National data Elevationwere Datasetdownloaded (NED), thethrough primary elevationthe National data product Map of theViewer USGS. http://nationalmap.gov/viewer.html.The data were downloaded through the National Map Viewer http://nationalmap.gov/viewer.html.

2.2.2.2.2.2. Soil Soil and and Land Land Use Use FigureFigure 22aa showsshows the the soils soils of of the the study study area. area. A description A description of the of soil the properties, soil properties, according according to Rieger to Riegeret al. [ 17et ],al. is [17], shown is shown in Table in1 Table. In Table 1. In1 ,Table literature-deﬁned 1, literature-defined soil thermal soil th properties’ermal properties’ value [ value18–20 ][18– and 20]the and soil the hydraulic soil hydraulic conductivity conductivity value [21 value] are also[21] listed.are also Figure listed.2b Figure shows 2b the shows vegetation the vegetation in the study in thearea study based area on based a uniﬁed on statewidea unified statewide system for system classifying for classifyin vegetationg vegetation in Alaska in [22 Alaska]. [22].

Coniferous open Fairplay silt loam Coniferous Olnes silt loam Deciduousdl d closed Stream Shrub tall Stream (a) Soil type (b) Land use type

Figure 2. Land use and soil map of the study area: (a) soil type and (b) land use type. Figure 2. Land use and soil map of the study area: (a) soil type and (b) land use type. Table 1. Soil textural property of the study area. Table 1. Soil textural property of the study area. Soil Heat Soil Volumetric Saturated Hydraulic Soil Series USDA Texture Drainage SoilConductivity Heat Heat Capacity SaturatedConductivity Hydraulic Soil Soil Volumetric Heat USDA Texture Drainage Conductivity(W/mK) (J/m3K) Conductivity(cm/hour) Series Capacity (J/m3K) Silt loam and (W/mK) (cm/hour) Moderately Fairplay gravelly silt 0.1–2.8 1,600,000–2,800,000 0.6 Silt loam and well drained loam Moderately Fairplay gravelly silt 0.1–2.8 1,600,000–2,800,000 0.6 Silt loam andwell drained Olnes loamvery gravelly Well drained 0.1–2.8 1,600,000–2,800,000 0.6 Silt loamsilt and loam Olnes very gravelly Well drained 0.1–2.8 1,600,000–2,800,000 0.6 2.2.3. Climatesilt of loam the Study Area

2.2.3. TheClimate study of area the liesStudy in theArea interior climatic division of Alaska, a region that is characterized by large diurnal and annual temperature variations, low annual precipitation, low cloudiness and low humidity. In theThe study study region, area lies the 30-yearin the interior normals climatic [23] show division that January of Alaska, is typically a region the that coldest is characterized month, with by a large diurnal and annual temperature variations, low annual precipitation, low cloudiness and low Water 2019, 11, 116 5 of 20 mean temperature of −24.4 ◦C, while July, the warmest month, has a mean of 17.1 ◦C. The annual Water 2019, 11, x FOR PEER REVIEW 5 of 20 precipitation in this region averages 285 mm, over half of which occurs in the months of June, July and August [24humidity.] and with In the 30% study falling region, asthe snow 30-year from normals October [23] show until that mid-April January is typically [23]. Figure the coldest3 shows the month, with a mean temperature of −24.4 °C, while July, the warmest month, has a mean of 17.1 °C. monthly accumulatedThe annual precipitation precipitation in this where region Figureaverages3 a285 is mm, the monthlyover half of accumulated which occurs in precipitation the months of from the year 2001 toJune, 2010 July and and FigureAugust 3[2b4] is and the with 10-year 30% falling average as snow of monthlyfrom October accumulated until mid-April precipitation [23]. Figure 3 shown in Figure3a. Theshows monthly the monthly accumulated accumulated precipitation precipitation is where derived Figure from 3a isthe the available monthly hourly accumulated precipitation data from aprecipitation tipping bucket from the sensor year 2001 at theto 2010 CPEAK and Figure station. 3b is the Figure 10-year3c average is the monthlyof monthly average accumulated temperature precipitation shown in Figure 3a. The monthly accumulated precipitation is derived from the from the yearavailable 2001 hourly to 2010 precipitation and Figure data3d from is the a tipping 10-year bucket average sensor of at monthly the CPEAK average station. temperatureFigure 3c is shown in Figure3thec. Themonthly monthly average averagetemperature temperature from the year 2001 is derived to 2010 and from Figure the 3d available is the 10-year hourly average temperature of data at themonthly CPEAK average station. temperature Figure3 shown shows in Figure that January 3c. The monthly is typically average the temperature coldest is month derived and from July is the warmest monththe available with hourly the maximum temperature amount data at the of CPEAK precipitation. station. Figure 3 shows that January is typically the coldest month and July is the warmest month with the maximum amount of precipitation.

200 (a) Monthly precipitation n 150 h)

100 (mm/mont Precipitatio 50

0 Jul-03 Jul-08 Jan-01 Jan-06 Jun-01 Jun-06 Oct-04 Oct-09 Sep-02 Feb-03 Sep-07 Feb-08 Apr-02 Apr-07 Dec-03 Dec-08 Mar-05 Mar-10 Nov-01 Aug-05 Nov-06 Aug-10 May-04 May-09 100 (b) 10-year average monthly precipitation 80 60 40 (mm/month) Precipitation 20 0 1 2 3 4 5 6 7 8 9 10 11 12 Month of a year 20 (c) Monthly average temperature

˚C ) ˚C 0

-20 Temperature ( Temperature Jul-05 Jan-01 Jan-03 Jan-08 Jan-10 Jun-01 Jun-03 Jun-08 Jun-10 Oct-06 Oct-08 Sep-02 Sep-04 Feb-05 Apr-02 Apr-04 Dec-05 Mar-07 Mar-09 Nov-01 Nov-03 Aug-07 Aug-09 Nov-10 -40 May-06 20 (d) 10-year average of average monthly temperature re 10

(˚C) 0 1 2 3 4 5 6 7 8 9 10 11 12 Temperatu -10 Month of a year

-20 Figure 3.FigureGraphical 3. Graphical information information of of the the monthlymonthly precipitation precipitation and temperature and temperature..

The model employed CPEAK hydro meteorological data (http://www.lter.uaf.edu/data) for the month of May of the year 2002 including: relative humidity (%) from 1993 to 2016, air temperature (◦C) from 1993 to 2016, soil temperature (◦C) from 1998 to 2016, solar radiation (W h m−2) from 1999 to 2016, wind Speed (kts) from 1998 to 2005, barometric pressure (in Hg) from 2000 to 2005, and tipping bucket rainfall rates (mm/hour) from 1993 to 2016. The contact information for the data is at http://www.lter.uaf.edu/contact. Water 2019, 11, 116 6 of 20

3. Methodology

3.1. Process Model Development of the Seasonal Change of the Soil Moisture Phase To take account of the seasonal change of the soil moisture phase, water and ice phase, the GIPL, soil thermal regime simulation model, is employed to calculate a soil temperature profile in every lateral two-dimensional GSSHA computational element employing the soil moisture information from GSSHA hydrologic simulations; GSSHA, in turn, employs the temperature and water/ice phase change information from GIPL to adjust hydraulic conductivities for both the unsaturated soil flow and saturated groundwater flow [13]. This two-way coupling increases computational accuracy in both models by providing additional information and required processes which were not previously included in either model. GSSHA takes account of important hydrological/processes such as evapotranspiration, infiltration, snow accumulation and melting, overland flow, saturated groundwater flow etc. based on physics and distributed in two-dimensional grids [25–29]. GIPL solves the one-dimensional (1D) non-linear heat equation with phase change employing an implicit, finite-difference, numerical scheme. GIPL treats the process of soil freezing and thawing in accordance with relationships between the soil unfrozen water content and temperature. The soil thermal state provided by GIPL is a point process, and is solved for each cell in the 2D grid.

3.2. Numerical Model of Soil Heat Transfer The Stefan problem [30,31] with phase change is the problem of thawing or freezing via conduction of heat. GIPL solves the Stefan problem employing the enthalpy formulation. The 1D, vertical, quasi-linear heat conductive equation [32] is the basis of the GIPL numerical model:

∂H(x, t) = ∇ · (k(x, t)∇t(x, τ)) (1) ∂τ where x is a vertical spatial variable which ranges between xu, upper depth of the computational unit, and xL, lower depth of the computational unit. τ is time and t is temperature. k(x,t) is a thermal conductivity (Wm−1K−1). H(x,t) is an enthalpy function deﬁned as:

Z t H(x, t) = C(x, s)ds + Lθ(x, t) (2) 0 where L is the volumetric latent heat of freeze/thaw (MJm−3), C(x,s) is volumetric heat capacity (MJm−3K−1) where s is the temperature integral term and θ(x,t) is volumetric unfrozen water content (fraction of the total water content). Boundary and initial conditions are required in solving Equation (1). The boundary condition on the upper extent of the domain corresponds to the near land surface air layer. Embedding a seasonal snow layer into the air layer is allowed by the ﬁctitious domain formulation [33]. The upper boundary condition is deﬁned as the Dirichlet type boundary condition.

t(xu, τ) = tair (3) where tair is a daily averaged air temperature. The lower boundary is set as the geothermal gradient as:

∂t(x , τ) l = g (4) ∂x where g is geothermal gradient, a small constant (Km−1) usually within the range of 0.01–0.04 (Km−1) across areas with no geothermal anomalies [34]. For the initial temperature distribution, an appropriate ground temperature proﬁle based on the point location is used.

t(x, τ) = t0(x) (5) Water 2019, 11, 116 7 of 20

The unfrozen water content θ(x,t) is deﬁned as: ( 1, t ≥ t∗ ( ) = ( ) θ x, t η x −b (6) a|c − t| , t < t∗

η(x) is a volumetric soil moisture content. a and b are dimensionless positive constants [35]. The constant t∗ is a freezing point depression, the temperature at which ice begins to form in the soil. For simpliﬁcation, we assumed the freezing point as zero degrees Celsius. The depth and time variation of the unfrozen water content θ(x, t) depend on hydrologic forcing and soil type. A detailed mathematical description of the model and numerical solution methods of Equation (1) can be found in Marchenko et al. [15], Nicolsky et al. [20], and Sergueev et al. [32]. GIPL input data include soil thermal properties, lithological data and vegetative cover, climate data and snow cover. The boundary conditions of the climate data are deﬁned by Equations (3) and (4).

3.3. Numerical Model of Soil Moisture The unsaturated, or vadose, zone controls the flux of water from the land surface to the saturated groundwater zone, and determines the partitioning of water into runoff, infiltration, ET, and groundwater recharge. The Richards Equation [36] is considered the most physically correct mathematical representation of the vadose zone. While flow in the vadose zone is in three dimensions, the predominant direction of flow is vertical. In GSSHA, the 1D, vertical, head based form of the Richards Equation is solved [37,38]:

∂ψ ∂ ∂ψ C (ψ) − K (ψ) − 1 − W = 0 (7) m ∂τ ∂z soil ∂z where Cm, the specific moisture capacity, is the slope of the soil water characteristic curve defined as rate of change of volumetric moisture content with respect to the matric head, ψ is the soil capillary head (cm), z is the vertical coordinate (cm) (downward positive), τ is time (h), Ksoil(ψ) (cm) is the effective hydraulic conductivity and W is a flux term added for sources and sinks (cm h−1), such as ET and infiltration. The head-based form is valid for both saturated and unsaturated conditions [39]. Heads for each cell are first computed using an implicit central-difference in space and forward difference solution and then flux updating is performed to ensure mass balance. The variables Ksoil and Cm from Equation (7) are non-linear parameters and depend on the water content of each cell. Ksoil and Cm are calculated employing Brooks and Corey [40] equations, as extended by Huston and Cass [41]. As infiltration, runoff and ET are dependent on the soil moisture state of the soil column, they are computed as part of the overall solution of Richards Equation, as described in Downer [37] and Downer and Ogden [38]. The proper application of the Richards Equation in GSSHA was described in Downer and Ogden [42]. Actual evapotranspiration is computed from the potential evapotranspiration by adjusting the potential evapotranspiration for the soil moisture in each cell (GSSHAWIKI, 2011, http://www.gsshawiki.com, accessed on 30 November 2018). Actual evapotranspiration depends on the soil moisture, hydraulic properties of the soil and plant characteristics.

3.4. Linking Soil Temperature and Soil Water Computational Nodes The solution domain of GIPL soil temperature model overlaps in a somewhat complex manner with both the saturated and unsaturated soil water movement domains in GSSHA. If there is no-flux lower GIPL boundary condition, the GIPL domain must extend very deep into the soil/permafrost, as much as 1000 m, or more. In GSSHA, only the surficial aquifer is simulated, so the saturated groundwater domain is down to the first confining layer in the subsurface. This is typically on the order of a few to hundreds of meters deep. The unsaturated zone domain is any soil above the saturated zone. The unsaturated domain is Water 2019, 11, 116 8 of 20 dynamic in both space and time and can vary from no domain (groundwater table is at or above the soil Water 2019, 11, x FOR PEER REVIEW 8 of 20 surface) to the depth of the surficial aquifer, depending on groundwater conditions. The unsaturated zone is furthermeters divideddeep. The intounsaturated soil horizons, zone domain as is well any soil as theabove deeper the saturated groundwater zone. The unsaturated media as shown in domain is dynamic in both space and time and can vary from no domain (groundwater table is at or Figure4. Aabove soil the horizon soil surface) is a to layer the depth having of the different surficial aquifer, physical, depending chemical on groundwater or biological conditions. characteristics from the layersThe unsaturated above and zone beneath. is further divided In Figure into4 soil, soil horizons, horizons as well for as thermodynamic the deeper groundwater and hydrodynamicmedia process mayas shown be the in same Figure or 4. differentA soil horizon as per is a the layer significance having different of the physical, physical, chemical chemical or biological and biological characteristicscharacteristics for individual from the layers process. above and beneath. In Figure 4, soil horizons for thermodynamic and hydrodynamic process may be the same or different as per the significance of the physical, chemical Becauseand ofbiological the differences characteristics in domains,for individual and process. requirements for solution, in the coupled framework, the GIPL domainBecause and of the discretization differences in domains, are independent and requirements of the for solution, saturated in the and coupled unsaturated framework, soil water domains andthe GIPL discretizations. domain and discretization The linkage are of computationalindependent of the nodal saturated discretized and unsaturated information soil water from GIPL to GSSHA anddomai vice-versans and discretizations. is shown in The Figure linkage4. Inof computational the soil thermal nodal profile discretized of Figure information4, we from set GIPL 56.7 ◦C as the to GSSHA and vice-versa is shown in Figure 4. In the soil thermal profile of Figure 4, we set 56.7 °C highest landas surfacethe highest temperature land surface as temperatureper: https://wmo.asu.edu/content/world-highest-temperature as per: https://wmo.asu.edu/content/world-highest- , ◦ retrieved 27temperature December, retrieved 2018. In27 Dec theember soil thermal 2018. In the profile soil thermal of Figure profile4, weof Figure set − 4,93.2 we setC −93.2 as the °C as lowest land surface temperaturethe lowest land as per: surface https://www.nasa.gov/content/goddard/nasa-usgs-landsat-8-satellite- temperature as per: https://www.nasa.gov/content/goddard/nasa-usgs- pinpoints-coldest-spots-on-earthlandsat-8-satellite-pinpoints-,coldest retrieved-spots- 27on- Decemberearth, retrieved 2018. 27 December 2018.

−93.2°C 56.7°C

Dynamic Ground Water Table

(a) Soil temperature (b) Soil moisture profile profile Legend Soil temperature profile Soil water content profile Soil layer discretization (soil horizon) Discretization for numerical computation Computational node information exchange and linkage of coupled GSSHA and GIPL

FigureFigure 4. Thermodynamics 4. Thermodynamics couplingcoupling into into the thehydrodynamics hydrodynamics..

3.5. Linking Soil Thermodynamics with Soil Moisture Hydrodynamics The linkage of the soil thermal and water movement solutions in GSSHA facilitates the temperature domain solution adjusting the soil thermal properties based on the varying soil moisture and the soil water movement domain solutions adjusting for the varying soil temperature condition. Water 2019, 11, 116 9 of 20

3.6. Linking Soil Temperature and Hydraulic Conductivity The primary effect of soil temperature on the soil water domain is that freezing soils result in much lower hydraulic conductivities of the soil. In the unsaturated zone, the vertical soil hydraulic conductivity is computed from the relative saturation (SE), a non-dimensional parameter that varies between 0 and 1. The relative fraction of liquid water of the total soil moisture, SE, can be computed from the soil temperature as [43]: m 1 ◦ SE = f or T ≤ 0 C (8) 1 + (∝ |1.22t|)n where n, m and α are the Van-Genuchten-Parameters (derived from literature [44]); t is soil temperature ◦ ◦ ◦ in C. SE is always 1 for temperatures above 0 C. For temperatures below −10 C the value of SE is assumed to be 0. As soil freezes, pathways through the soil, pores, close, reducing the ability of the soil to transmit water. This results in a reduction of the soil hydraulic conductivity. In the unfrozen portion of the soil, an exponential response in effective hydraulic conductivity has been measured for freezing/thawing mineral and organic soils [43]. The temperature adjusted relative saturation, SE, can be used to compute the soil temperature adjusted hydraulic conductivity as the sum of the hydraulic conductivity of the unfrozen pores and the hydraulic conductivity of the frozen pores:

SEln(Kt)+(1−SE)K f Ksoil(t) = e (9)

−1 where Ksoil(t) is the effective hydraulic conductivity in m s ; Kt is the hydraulic conductivity for SE = 1 and Kf is the frozen hydraulic conductivity for SE = 0. In practice, the contribution from the frozen portion of the soil, (1 − SE)Kf is quite small and is often neglected.

4. Model Development of the Study Area A 10 × 10 grid was developed to cover the study area, including the CPEAK station. The model includes precipitation, overland ﬂow, unsaturated zone computations using the 1D Richards Equation, ET using the Penman-Monteith equation [45,46], and 1D soil thermal computations using GIPL. The grid with elevations, soils, and vegetation are shown in Figures1 and2a,b respectively.

4.1. Initial Condition The coupled model included the numerical solution of the soil moisture using Richards Equation in the unsaturated vadose zone, Equation (7), and the numerical solution of the soil thermal state using quasi-linear heat conductive equation, Equation (1). Both of those numerical solutions, Equations (1) and (7), require the initial condition. For this study, initial conditions for soil temperature were obtained from observations from CPEAK ground temperature thermistors at several depths on 2002-5-1, 1 AM, Figure5a. Initial soil moistures were derived from observations at the Caribou-Poker Creeks Research Watershed for 2002-5-1, 1 AM [47], Figure5b. In lieu of soil temperature and moisture measurements, the model itself can be used to establish the proper initial conditions given a sufficient prior period of observed hydro-meteorological forcing input. Downer and Ogden [38] and Senarath et al. [48] showed how the GSSHA model could not only estimate soil moistures with depth, but could actually be used to nullify the effects of assuming an incorrect initial soil moisture state by allowing the model to run through at least one saturating precipitation event and some subsequent drying period before using model results. Without either type of observation, the effect of the initial condition on model results would have to be assessed utilizing sensitivity analysis. To ensure that the initial temperature conditions did not influence the results, the maximum difference of soil temperatures at all depth levels between two successive annual cycles needs to be less than 0.01 ◦C[14]. In this Water 2019, 11, x FOR PEER REVIEW 10 of 20 Water 2019, 11, 116 10 of 20 analysis. To ensure that the initial temperature conditions did not influence the results, the maximum difference of soil temperatures at all depth levels between two successive annual cycles needs to be lessstudy, than we 0.01 employed °C [14]. observed In this study, soil temperature we employed as the observed initial condition soil temperature and did notas the conduct initial a long-termcondition andequilibrium did not conduct temperature a long-term profile assessment.equilibrium temperature profile assessment.

(a) (b)

Figure 5. InitialInitial conditions: conditions: ( (aa)) Initial Initial soil soil temperature temperature profile proﬁle for the thermodynamic numerical simulation and ( b) Initial Initial soil soil moisture moisture content content profile proﬁle for the the unsaturated unsaturated zone zone numerical numerical simulation. simulation.

4.2. Overall Overall Model Processes and Parameter Values 4.2.1. Thermodynamic Process 4.2.1. Thermodynamic Process The soil thermal parametric values represent Alaskan woodland and tundra ecosystem sites in The soil thermal parametric values represent Alaskan woodland and tundra ecosystem sites in the permafrost active region. Table2 shows the parameters and values employed in this test case the permafrost active region. Table 2 shows the parameters and values employed in this test case model where the dominant soil type is silt loam as shown in Figure2a. These parameter values are as model where the dominant soil type is silt loam as shown in Figure 2a. These parameter values are per the literature [17–19]. as per the literature [17–19]. Table 2. Soil thermal parameter values. Table 2. Soil thermal parameter values. Soil Heat Conductivity (W/mK) Soil Volumetric Heat Capacity (J/m3K) Soil Heat Conductivity (W/mK) Soil Volumetric Heat Capacity (J/m3K) 3.0 2,800,000 3.0 2,800,000

As Equation (8) is deployed in the thermodynamic process, the Van-Genuchten-Parameters’ As Equation (8) is deployed in the thermodynamic process, the Van-Genuchten-Parameters’ values were employed as per [44] were n, m and α are 2, 0.5 and 1, respectively, for the silt dominant values were employed as per [44] were n, m and α are 2, 0.5 and 1, respectively, for the silt dominant soil texture. soil texture. 4.2.2. Routing Process 4.2.2. Routing Process Diffusive wave approach was deployed to route the flow. The Manning’s roughness parameter valuesDiff forusive the wave routing approach model was as shown deployed in the to route Table the3 were flow. employed The Manning’s from theroughness literature parameter [ 48,49]. valuesThe land for use the types routing defined model in as Table shown3 are in from the Table Figure 32 wereb. employed from the literature [48,49]. The land use types defined in Table 3 are from Figure 2b. Table 3. Manning’s roughness values. Table 3. Manning’s roughness values. Land Use Type Manning’s Roughness Values Land Use Type Manning’s Roughness Values Coniferous open 0.17 ConiferousConiferous woodland open 0.17 0.19 ConiferousDeciduous woodland closed 0.19 0.2 Shrub tall 0.25 Deciduous closed 0.2 Shrub tall 0.25 4.2.3. Infiltration Process

The soil moisture and infiltration process is defined by the Richards Equation defined by Equation (7). The soil parameter values for the infiltration model as shown in the Table4 were Water 2019, 11, 116 11 of 20 employed from published values for silt loam soil [21]. Brooks and Corey [40] equations, as extended by Huston and Cass [41] were employed as the soil water retention model in the infiltration process.

Table 4. Soil parameter values for the Richards inﬁltration scheme.

Soil Layer Inﬁltration Parameter Top Middle Lower Soil thickness (m) 0.20 0.50 - Saturated hydraulic conductivity (m/s) 0.00008 0.00008 0.00008 Pore size distribution index 0.60 0.694 0.694 Bubbling Pressure head (m) 0.08 0.06 0.06 Porosity (m3/m3) 0.42 0.40 0.40 Residual soil moisture content (m3/m3) 0.04 0.045 0.045

4.2.4. Evapotranspirational Process for the Long-Term Simulation Hydrological modeling of seasonal change requires the model to be set in the long-term simulation mode. To take account of the depletion of the soil moisture after/before rainfall events in the long-term simulation, the evapotranspirational process deﬁned by the Penman-Monteith equation was deployed. ET parameters were estimated based on land cover. For the Penman-Monteith method, values of land surface albedo, vegetation height (for aerodynamic resistance term), vegetation canopy resistance (for stomatal control of the loss of water), and vegetation transmission coefﬁcient (light penetration through canopy) are needed. Table5 shows those parameter values.

Table 5. Evapotranspiration parameter values.

Land Use Type Albedo Vegetation Height (m) Canopy Resistance (s/m) Transmission Coefﬁcient Coniferous open 0.15 10 120 0.18 Coniferous woodland 0.15 10 120 0.18 Deciduous closed 0.2 12 200 0.18 Shrub tall 0.2 1.3 150 0.5

All the parameter values defined in Table5 were taken from the GSSHA wiki https:// www.gsshawiki.com. Table5 albedo and vegetation height values are defined in Eagleson [ 50]; canopy resistance values are defined in Monteith [46]; and the transmission coefficient values are defined in Sutton [51].

5. Result and Discussion

5.1. Observed and Simulated Soil Profile Temperature Figure6 shows the comparison of the observed and simulated soil temperature at various depths over the simulation period, 1–31 May 2002. May is a transition between spring and summer in the study area when the temperatures are increasing above freezing. As shown in Figure6, the air temperature has the most significant influence in the near surface soil layer as shown by the simulated and the observed soil temperature at 10-cm depth time series trend line, in Figure6a. This is because the upper boundary condition for the surface of the soil is the air temperature, as shown by Equation (3), not the actual surface of the soil. This results in the model being overly sensitive to the value of air temperature very near the surface boundary. The effect of this error dissipates as the simulation computation moves deeper into the soil. As the soil layer depth increased, air temperature influence on soil thermo-dynamics diminished along with the increase in the time lag influence as shown in Figure6b. It was also found that the soil thermal conductivity, the dominant thermo-dynamic, parameter value was most sensitive and effective for the near surface simulated temperature to capture the frequency of the observed soil temperature and the air temperature. In Figure6a, the top 10-cm Water 2019, 11, x FOR PEER REVIEW 12 of 20 computation moves deeper into the soil. As the soil layer depth increased, air temperature influence on soil thermo-dynamics diminished along with the increase in the time lag influence as shown in WaterFigure2019 6b., 11 ,It 116 was also found that the soil thermal conductivity, the dominant thermo-dynamic,12 of 20 parameter value was most sensitive and effective for the near surface simulated temperature to capture the frequency of the observed soil temperature and the air temperature. In Figure 6a, the top depth10-cm temperaturedepth temperature time series time showsseries shows that the that maximum the maximum amplitude amplitude of the of daily the daily temperature temperature was betterwas better simulated simulated than than the minimumthe minimum amplitude. amplitude. The The observed observed and and simulated simulated maximum maximum daily daily soilsoil ◦ temperaturetemperature atat 10-cm10-cm depthdepth isis comparedcompared inin FigureFigure6 6c.c. The The root root mean mean errors errors in in Figure Figure6 b6b are are 0.17 0.17 °CC ◦ ◦ andand 0.140.14 °CC forfor 90-cm90-cm andand 300-cm,300-cm, respectively,respectively, andand inin FigureFigure6 c,6c, 4.6 4.6 °C.C. WhileWhile thethe modelmodel tendstends toto capturecapture thethe long-termlong-term evolutionevolution ofof soilsoil temperature,temperature, thethe modelmodel underestimatedunderestimated dailydaily temperaturetemperature fluctuationsfluctuations inin thethe toptop soilsoil layer.layer.

40 (a) at 10-cm depth 30 Air temperature 20 Observed Simulated 10 0

Temperature (˚C) Temperature -10 Time (hours, starting at 1 AM, 1 May 2002) -20 (b) at 90-cm and 300-cm depth 0.00

Observe at 90-cm depth Simulated at 90-cm depth -2.00 Observed at 300-cm depth Simulated at 300-cm depth Temperature (˚C) Temperature Time (hours, starting at 1 AM, 1 May 2002) -4.00 30 (c) at 10-cm depth 20 Observed Simulated 10 Maximum daily Maximum

temperature (˚C) temperature 0 0102030 Time (day, starting at 1 May 2002) -10 3.00

2.00 (d) Precipitation 1.00

Precipitation (mm/hour) Precipitation 0.00

Time (hours, starting at 1 AM, 1 May 2002)

FigureFigure 6.6.Time-series Time-series of of observed observed and and simulated simulated temperature temperature at: at: (a )( 10-cma) 10-cm depth, depth, (b) ( 90-cmb) 90-cm and and 300-cm 300- depthscm depths and and (c) maximum (c) maximum values values at 10-cm at 10-cm depth, depth, (d) corresponding (d) corresponding hourly hourly precipitation precipitation rate. rate. Water 2019, 11, 116 13 of 20 Water 2019, 11, x FOR PEER REVIEW 13 of 20

5.2. Catchment Hydrological Dynamics under Freezing and Thawing

5.2.1. Effective Effective Hydraulic Conductivity with and without Thermodynamics Figure 77 showsshows thethe comparison,comparison, withwith andand withoutwithout thermodynamics,thermodynamics, simulationsimulation evolutionevolution ofof thethe effective hydraulic conductivity at 10 cm depth starting on 1 May 2002. The initial condition for the soil profile,profile, shownshown in in Figure Figure5a, is5a, below is below freezing freezing for the for entire the profile.entire profile. So, for theSo, case for ofthe soil case hydraulic of soil hydraulicconductivity conductivity with thermal with adjustments, thermal adjustments, the hydraulic the conductivityhydraulic conductivity is reduced is from reduced the beginning, from the beginning,corresponding corresponding to the initial to condition, the initial whichcondition, was belowwhich freezing.was below freezing. Figure7 7 also also showshow the the corresponding corresponding air air temperature temperature with with is is continuously continuously below below zero zero degrees degrees C Cfor for the firstthe 107first h. 107 That h. is theThat reason is the the reason simulated the effectivesimulated hydraulic effective conductivity hydraulic with conductivity thermodynamic with thermodynamicprocess in that continuous process in negativethat continuous air temperature negative period air temperature is almost impermeable.period is almost More impermeable. specifically, Morethis impermeability specifically, this is impermeability the result of reduced is the result effective of reduced saturation effective in the saturation soil due in to the the soil soil due being to thecompletely soil being frozen completely as shown frozen in Figure as shown6. Figure in Figure7 shows 6. Figure that the 7 shows effective that hydraulic the effective conductivity hydraulic conductivitywithout thermodynamic without thermodynamic process maintained process its maintained value well its above value zero. well above zero. As the air and soil temperatures rise, the soil begins to thaw, with a resulting increase in hydraulic conductivity. The The expone exponentialntial rise rise of of hydraulic hydraulic conducti conductivityvity is is consistent with other observations of freezing and thawing of mineralmineral andand organicorganic soilssoils [[32].32]. The simulated effective hydraulic conductivityconductivity in in Figure Figure7 is from7 is Equationfrom Eq (9),uation where (9), the where effective the soil effective hydraulic soil conductivity hydraulic conductivityKsoil at a given Ksoil temperature at a given temperature (t) is a function (t) is a of function hydraulic of hydraulic conductivity conductivity of the unfrozen of the unfrozen soil and soil the andeffective the effective saturation saturationSE. SE.

(˚C) 0 0 50 100 150 200 250

Air temperature temperature Air -10

-20 0.03

0.02 With thermodynamics Without thermodynamics 0.01 Effective hydraulic Effective

conductivity (cm/hour) 0.00 0 50 100 150 200 250 Time (hours, starting at 1 AM, 1 May 2002) FigureFigure 7. 7. HydraulicHydraulic conductivity conductivity under under freezing freezing and thawing soil active layer.

5.2.2. Hydrologic Hydrologic Runoff Response Figure 88 showsshows the comparison of of GSSHA GSSHA simulated simulated infiltration infiltration and and discharge, discharge, at at the the outlet outlet of 2 theofthe case case study study watershed watershed of 0.2 of km 0.22 (headwater km (headwater sub-catchment) sub-catchment) shown shownin Figure in 1, Figure with 1and, with without and takingwithout account taking accountof freezing of freezing and thawing and thawing soil pr soiloperties properties in the in thestudy study area. area. While While there there are are no measurements of runoff from the site, the results are consistent with the results presented for air and soil temperature and resulting hydraulic conductivity shown above. The freezing soil temperature, Water 2019, 11, 116 14 of 20 measurements of runoff from the site, the results are consistent with the results presented for air and Water 2019, 11, x FOR PEER REVIEW 14 of 20 soil temperature and resulting hydraulic conductivity shown above. The freezing soil temperature, FigureFigure6 ,6, leads leads to to increased increased coverage coverage of of frozen frozen soil soil which which in in turn turn leads leads to to less less soil soil pore pore water water storage. storage. TheThe reducedreduced soilsoil porepore waterwater storagestorage capacitycapacity leadsleads totodecrease decreasehydraulic hydraulic conductivityconductivity asas shownshown inin FigureFigure7 ,7, which which results results in in decreased decreased infiltration infiltration and and increased increased runoff runoff in in response response to to the the precipitation precipitation event,event, asas shownshown inin FigureFigure8 8graph, graph, with with thermodynamics. thermodynamics. On On the the other other hand, hand, loss loss of of frozen frozen soil soil and and permafrostpermafrost or or without without taking taking account account of of thermodynamicsthermodynamics will will lead lead toto enhancedenhanced connectivityconnectivity betweenbetween thethe surfacesurface andand groundground waterwater storagestorage regimesregimes andand decreaseddecreased overlandoverland flowflow asas shownshown byby thethe graphgraph withoutwithout thermodynamics thermodynamics in in Figure Figure8 .8.

0 1020304050 0

2.5 (a) Precipitation (mm/hour)

Precipitation Precipitation 5 0.012 (b) Infiltration With thermodynamics 0.008 Without thermodynamics

0.004 Cumulative infiltration (m) infiltration 0 0 1020304050 0.010 0.008 (c) Discharge /s) 3 0.006 With thermodynamics 0.004 Without thermodynamics 0.002

Discharge (m Discharge 0.000 0 1020304050 Time (Hour, Starting at 6 AM of 6 May 2002) FigureFigure 8.8. HydrologicHydrologic response, response, with with and and without without thermodynamics, thermodynamics, to toprecipitation precipitation events: events: (a) (aprecipitation) precipitation events events (b) ( binfiltration) inﬁltration comparison comparison (c) ( cdischarge) discharge comparison. comparison.

5.3.5.3. DiscussionDiscussion InIn thisthis thermo-hydrodynamicthermo-hydrodynamic numericalnumerical modellingmodelling effort,effort, thethe analysisanalysis waswas limitedlimited toto thethe immediateimmediate effects effects of of the the soil soil temperaturetemperature on on the the soilsoil hydraulichydraulic conductivityconductivity around around thethe measuredmeasured soilsoil location.location. WeWe diddid notnot attemptattempt toto analyzeanalyze thethe watershed watershed widewide effectseffects duedue to to the the many many complications complications relatedrelated toto doingdoing so.so. TheThe CPCRWCPCRW watershedwatershed hashas veryvery complexcomplex hydrologyhydrology withwith manymany hydrologichydrologic processes,processes, relatedrelated toto mossmoss covered covered peatland peatland and and wetlands wetlands surface/water surface/water groundwatergroundwater interaction,interaction, etc.etc. EvenEven forfor a a summer summer event event when when and and where where thermodynamic thermodynamic effects effects are are null, null, CPCRW CPCRW hydrology hydrology is observedis observed tobe to abe complex a complex process process due due to significant to significant presence presence of moss of moss covered covered peatland peatland andwetland and wetland [52]. Moss-covered[52]. Moss-covered peatlands peatlands and wetlands and wetlands significantly significantly influence theinfluence hydraulic the conductivity,hydraulic conductivity, infiltration, infiltration, evapotranspiration and discharge [53]. In an active permafrost area there is also a seasonal patterns of freezing and thawing of the peat [53]. Teasing out the effects of frozen soil on the hydrology with these complicating factors is a very difficult process and this study has not met this level of validation, which would be a follow-on study. To isolate the immediate effects of the soil Water 2019, 11, 116 15 of 20 evapotranspiration and discharge [53]. In an active permafrost area there is also a seasonal patterns ofWater freezing 2019, 11 and, x FOR thawing PEER REVIEW of the peat [53]. Teasing out the effects of frozen soil on the hydrology15 of 20 with these complicating factors is a very difficult process and this study has not met this level of validation,temperature which on soil would hydraulic be a follow-on conductivity, study. Toin isolatethis work the immediatewe limited effects our analysis of the soil to temperaturea small sub- onwatershed soil hydraulic of the conductivity,scale of 0.2 km in2, this located work at we the limited CPCRW our peak analysis as shown to a small in Figure sub-watershed 1. Moss, peatland of the scaleand ofwetland 0.2 km 2are, located absent at in the this CPCRW 0.2 km peak2 sub-watershed as shown in Figure at the1. Moss,peak. peatlandThe study and site wetland includes are a absenttemperature in this and 0.2 kmhydro2 sub-watershed meteorological at data the peak. measurement The study station, site includes called CPEAK. a temperature There is and no hydrorunoff meteorologicalinformation at dataCPCRW measurement at this scale. station, However, called we CPEAK. can use There the isrunoff no runoff from informationour small watershed at CPCRW to atassess this scale.the impact However, that wethe can change use the in runoffsoil temperature from our small and soil watershed water state to assess have the on impact the hydrology. that the changeSimulation in soil results temperature indicate and that soil the water numerical state haverunoff on and the infiltration hydrology. results Simulation at this results 0.2 km indicate2 scale thatdirectly the numerical correspond runoff to potential and infiltration seasonal resultsvariation at thisof discharge 0.2 km2 scale at larger directly watershed correspond scales to of potential CPCRW seasonalthat have variation measured of discharge atdata. larger The watershed following scalesparagraphs of CPCRW in this that section have demonstrate measured discharge how this data.0.2 km The2 numerical following paragraphsrunoff result in thishelp section explain demonstrate the measured how thisvariation, 0.2 km 2temporalnumerical and runoff spatial, result of helpdischarge explain at the larger measured scales within variation, CPCRW. temporal and spatial, of discharge at larger scales within CPCRW. FigureFigure9 a9a shows shows the the hourly hourly air air temperature temperature at at CPEAK CPEAK from from July July 2002 2002 through through October October 2002. 2002.

20.0 (a) Air temperature

10.0

0.0 Air temperature (˚C) temperature Air

-10.0 0.5 (b) observed discharge 0.4 C3 catchment /s) 3 0.3 C2 catchment 0.2 0.1 0 Discharge (m Discharge

FigureFigure 9.9. CaribouCaribou PokerPoker CreekCreek ResearchResearch WatershedWatershed (CPCRW)(CPCRW) (a(a)) ObservedObserved dischargedischarge ObservedObserved dischargedischarge of of C2 C2 and and C3 C3 catchments, catchments, sub-catchments sub-catchments of of CPCRW CPCRW shown shown in in Figure Figure1 (1 b(b)) air air temperature temperature fromfrom Cpeak Cpeak station station shown shown in in Figure Figure1 .1.

FigureFigure9 b shows9b shows the corresponding the corresponding hourly observed hour dischargely observed (available discharge at http://www.lter.uaf. (available at edu/datahttp://www.lter.uaf.edu/data)) for C2 and C3 watersheds for C2 whichand C3 are wate thersheds sub-watersheds which are of the CPCRW sub-watersheds [54,55]. Two of distinctCPCRW differences[54,55]. Two in distinct discharges differences from C2 in and disc C3harges can be from observed: C2 and C3 can be observed:

1. Although C2 and C3 are the watersheds of similar size, 5.2 km2 and 5.7 km2, respectively, 1. Although C2 and C3 are the watersheds of similar size, 5.2 km2 and 5.7 km2, respectively, C3 C3 discharge is signiﬁcantly higher than C2 discharge. discharge is significantly higher than C2 discharge. 2.2. FromFrom 1919 September September 2002, 2002, C2 dischargeC2 discharge rapidly rapidl increasesy increases to a value to a roughly value equalroughly to C3equal discharge. to C3 discharge.

While the C2 catchment has negligible permafrost, 3.5%, the C3 basin has 53.2% permafrost coverage. Permafrost is a permanently frozen soil. The soil thermal/hydrodynamic relations explained hereWater could 2019, 11 help, x FOR explain PEER theREVIEW response in both basins. In an attempt to explain the above distinct behavior16 of 20 2 ofSeptember C2 and C3 2002. basin Figure discharge, 10 shows we the simulated simulated the hydr CPEAK,ological 0.2 and km thermalwatershed, variables for September for the event 2002. of Figure19–20 September10 shows the 2002. simulated Figure hydrological10a shows the and verifica thermaltion variablesof the simulated for the event soil temperature of 19–20 September at 10 cm 2002.depth Figure with the 10 aobserved shows the temperature verification at of10 thecm simulateddepth with soil the temperatureroot mean error at 10 of cm 0.2. depth Figures with 9a theand observed10a show temperature a significant atdrop 10 cm in depthsoil temperature with the root reaching mean to error −3.8 of °C 0.2. during Figures 19–209a and September 10a show 2002, a ◦ significantfreezing the drop soil in water soil temperature content. Because reaching of tothe− fr3.8ozenC duringsoil water 19–20 content, September the thermo-hydrodynamic 2002, freezing the soil watermodel content. simulated Because effective of the hydraulic frozen soilconducti watervity content, dropped the thermo-hydrodynamicto a value of 0.00003 cm model h−1 at the simulated peak of −1 effectivethe precipitation hydraulic event conductivity in Figure dropped 10b. The to simulated a value of effective 0.00003 cm hydraulic h at the conductivity peak of the value precipitation without eventtaking in into Figure account 10b. The of thermodynamics, simulated effective was hydraulic 0.02 cm conductivity h−1 at the peak value of without the precipitation taking into accountevent in −1 ofFigure thermodynamics, 10b, a difference was of 0.02 4 orders cm h ofat magnitude. the peak of Be thecause precipitation of this drop event in hydraulic in Figure 10 conductivityb, a difference value of 4the orders thermo-hydrodynamic of magnitude. Because model of this simu droplation inhydraulic resulted in conductivity decreased infiltration value the thermo-hydrodynamic and increased runoff, modelas shown simulation in Figure resulted 10c,d respectively. in decreased This infiltration numerical and model’s increased increased runoff, runoff as shown response in Figure in freezing 10c,d respectively.soil conditions This is the numerical representation model’s of increasedthe physical runoff process response that influence in freezing discharge soil conditions at the C3 is basin the representationunder freezing of condition. the physical process that influence discharge at the C3 basin under freezing condition.

0 0102030 -2

-4 Air temperature Temperature (˚C) Temperature Observed at 10-cm depth Simulated at 10-cm depth (a) Temperature -6

0 102030 0

0.4 (b) Precipitation 0.8 (mm/hour) Precipitation 1.2

1.6

0.003 (c) Infiltration 0.002

0.001

Cumulative With thermodynamics infiltration (m)infiltration Without thermodynamics 0 0102030

Figure 10. Cont. Water 2019, 11, 116 17 of 20 Water 2019, 11, x FOR PEER REVIEW 17 of 20

0.03 (d) Discharge

0.02 With thermodynamics 0.01 Without thermodynamics Discharge (m3/s) Discharge 0 0102030 Time (Hour starting at 8 AM of 19 September 2002) FigureFigure 10. 10. CatchmentCatchment hydrological hydrological modeling modeling with with and and without without soil soil thermal thermal dynamics dynamics during during SeptemberSeptember 2002; (a(a)) simulated simulated and and observed observed soil temperaturesoil temperature (b) precipitation (b) precipitation (c) simulated (c) simulated infiltration infiltrationwith and withoutwith and soil with thermodynamicsout soil thermodynamics (d) simulated discharge(d) simulated with anddischarg withoute with thermodynamics. and without thermodynamics. 6. Conclusions 6. ConclusionsSeasonal changes lead to changes in the soil thermal regime. The seasonal change in the thermal regime,Seasonal freezing changes and thawing,lead to changes of soil hasin the a direct soil th impactermal regime. on the hydrological The seasonal response change in of the a watershed thermal regime,due to changesfreezing inand the thawing, void space of soil in thehas soila direct pore-space. impact on Therefore, the hydrological to represent response the watershed of a watershed rainfall duerunoff to changes partitioning in the mechanism void space in in the this soil freezing pore-space. and thawing Therefore, scenario, to represent a hydrological the watershed model rainfall should runoffcapture partitioning the seasonal mechanism rise of soil in temperatures this freezing and and thaw thawing of frozen scenario, soils; thereby, a hydrological intuitively model representing should capturethe transitioning the seasonal of effective rise of soil soil hydraulic temperatures conductivity. and thaw of frozen soils; thereby, intuitively representingThis study the transitioning demonstrates of aeffective coupled soil architecture hydraulic conductivity. for simulating the interaction between soil thermodynamicsThis study demonstrates and hydrodynamics. a coupled The architecture coupling architecturefor simulating linked the theinteraction thermo-dynamic between GIPLsoil thermodynamicsmodel into GSSHA’s and hydro-dynamichydrodynamics. modeling The coupling framework. architecture The water linked and the ice thermo-dynamic phase change condition GIPL modeland its into subsequent GSSHA’s influence hydro-dynamic in the vedose modeling zone hydrology framework. is numerically The water described and ice and phase experimentally change conditiondemonstrated/deployed and its subsequent and influence verified in in the the headwater vedose zone region hydrology at the peak is nu ofmerically the Caribou described Poker Creekand experimentallyResearch Watershed. demonstrated/deployed and verified in the headwater region at the peak of the CaribouIn thisPoker study, Creek the Research months ofWatershed. May and September of the year 2002 were employed in the long-term simulationIn this study, as May the is amonths transition of May between and springSeptember and summerof the year when 2002 the were temperatures employed are in increasingthe long- termabove simulation freezing andas May September is a transition is a transition between between springautumn and summer and winter whenwhen the temperatures the temperatures are increasingare decreasing above below freezing freezing. and September The coupled is a numericaltransition between schemes autumn provided and a clear winter insight when of the the temperaturestemporal and are spatial decreasing variability below of freezing. soil thermal The coupled state during numerical these schemes changing provided seasons a and clear the insight effects ofon the hydrological temporal and processes spatial variability that are significant of soil thermal for long-term state during simulation, these changing such as seasons infiltration and the and effectsrunoff. on A hydrological comparative processes analysis, that under are the significant freezing for condition, long-term showed simulation, decreased such effectiveas infiltration hydraulic and runoff.conductivity, A comparative decreased analysis, infiltration under and the increased freezing runoff. condition, The simulatedshowed decreased results, agreeing effective the hydraulic observed conductivity,ones, showed decreased that the air infiltration temperature and has increase the mostd significantrunoff. The influence simulated in the results, near surface agreeing soil layerthe observedand the effectones, diminishedshowed that along the air with temperature the increase has in the the most soil significant profile depth. influence It was in also the found near surface that the soilsoil layer thermal and the conductivity, effect diminished the dominant along with thermo-dynamic the increase in parameter the soil profile value, depth. was most It was sensitive also found and thateffective the soil for thethermal near-surface conductivity, simulated the temperaturedominant thermo-dynamic to capture the frequencyparameter of value, the observed was most soil sensitivetemperature and andeffective the air for temperature. the near-surface simulated temperature to capture the frequency of the observedAuthor Contributions: soil temperatureSoftware and the development, air temperature. research conceptualization, methodology, analysis, writing, reviewing and editing: N.R.P., C.W.D. and S.M. Author Contributions: Software development, research conceptualization, methodology, analysis, writing, Funding: Article Processing Charges (APCs) for the publication were supported by the Flood and Coastal Systems reviewingResearch Program,and editing: US ArmyN.R.P., Engineer C.W.D. Researchand S.M. and Development Center. Funding:Acknowledgments: Article ProcessingThe Bonanza Charges Creek (APCs) Long-Term for the Ecological publication Research were supported program (BNZ by the LTER) Flood at theand University Coastal Systemsof Alaska Research Fairbanks Program, is thanked US Army for making Engineer and Research sharing theand hydrology Development and climateCenter. data set of the Caribou-Poker Creeks Research Watershed (CPCRW) in Alaska. Constructive comments from two anonymous reviewers are Acknowledgments:greatly appreciated. The Bonanza Creek Long-Term Ecological Research program (BNZ LTER) at the University of Alaska Fairbanks is thanked for making and sharing the hydrology and climate data set of the Caribou-Poker Conflicts of Interest: The authors declare no conflict of interest. Creeks Research Watershed (CPCRW) in Alaska. Constructive comments from two anonymous reviewers are greatly appreciated.

Conflicts of Interest: The authors declare no conflict of interest. Water 2019, 11, 116 18 of 20

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