Soil properties within lysimeter.
Evapotranspiration and near-surface soil moisture dynamics are key-entangled variables regulating flux at the surface-atmosphere interface. Both are central in improving mass and energy balances in agro ecosystems. However, under the extreme conditions of high-latitude soils and weather pattern variability, the implementation of such coupled liquid and vapor phase numerical simulation remain to be tested. We consider the nonisothermal solution of the vapor flux equation that accounts for the thermally driven water vapor transport and phase changes. Fully coupled flux model outputs are compared and contrasted against field measurements of soil temperature, heat flux, water content, and evaporation in a subarctic agroecosystem in Alaska. Two well-defined hydro-meteorological situations were selected: dry and wet periods. Numerical simulation was forced by time series of incoming global solar radiation and atmospheric surface layer thermodynamic parameters: surface wind speed, ambient temperature, relative humidity, precipitation, and soil temperature and soil moisture. In this simulation, soil parameters changing in depth and time are considered as dynamically adjusted boundary conditions for solving the set of coupled differential equations. Results from this evaluation give good correlation of modeled and observed data in net radiation (Rnet) (R2 of 0.92, root mean square error (RMSE) of 45 W m−2), latent heat (0.70, RMSE of 53 W m−2), and sensible heat (R2 = 0.63, RMSE = 32 W m−2) during the dry period. On the other hand, a poor agreement was obtained in the radiative fluxes and turbulent fluxes during the wet period due to the lack of representation in the radiation field and differences in soil dynamics across the landscape.
- coupled fluxes
- soil dynamics
- vapor transport
- numerical simulation
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 . 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  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 . 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 .
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, agro-ecosystem has not been taken into consideration until a recent study by Ruairuen et al. . 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. ).
In this study, we use the numerical model developed by Bittelli et al. , 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. , 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.
2. Materials and methods
2.1. Field experiment
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 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 . Parameters for soil hydraulic properties to be introduced in the numerical simulation are listed in Table 1. Volumetric soil moisture content was measured
|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|
|Saturated moisture content; ||0.56|
|7.2 × 10−4|
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  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 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
The initial conditions for dry and wet periods were calculated using
The mass of sand, silt, clay, and bulk density was obtained from
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).
|Parameters||Dry period||Wet period|
|Number of days||9||6|
|Soil temperature (°C)||17.2||15.0|
|Soil water potential (J kg−1)||−30||−6|
|Initial soil moisture (m3 m−3)||0.28||0.30|
In this study, the value of albedo was set as 0.2 for the dry period , 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 .
3. Simulation scenarios
As mentioned previously, the model was applied to two selected periods (dry and wet) in an agricultural land described in Section 2 during the summer 2013, and its performance was evaluated. In addition and based on local meteorological information, it was verified that the atmospheric boundary layer developed forced by surface and near surface flow conditions without presence of multilayered thermal inversions . However, this condition is difficult to maintain when precipitation arises. The dry period (no precipitation event) spun from 26 July to August 3 (Julian day 207–216) and wet period from 25 to 30 August (Julian day 237–242).
3.1. Dry period
The experimental data were taken from the plots that monitored soil moisture and soil temperature. The meteorological parameters measured about 10 m away from the plot for the dry period are given in Table 3 and Figure 3a. The hourly average vapor pressure deficit (VPD) was 1.18 kPa. Mean-hourly global radiation was 215 W m−2. The average air temperature was 21°C with maximum of 30.7°C and minimum of 9.8°C also reported in this period. The average RH was approximately 58% and wind speed of 2.36 m s−1.
|Mean ||20.66 ± 5.32||11.78 ± 3.41|
|Mean ||18.96 ± 3.2||16.64 ± 1.51|
|Mean RH (%)||57.74 ± 17.26||76.72 ± 16.76|
|Mean VPD (kPa)||1.18 ± 0.76||0.36 ± 0.32|
|Mean u (m s−1)||2.36 ± 1.07||1.68 ± 0.82|
|Mean solar radiation (W m−2)||215.23 ± 221.69||131.31 ± 172.42|
|Mean soil moisture (m3 m−3)||0.2098 ± 0.0015a||0.2097 ± 0.0035a|
3.2. Wet period
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 period for the simulation in this study.
4. Results and discussion
4.1. Net radiation
Net radiation (
The high and low correlation between measured and modeled
4.2. Latent heat
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
4.3. Ground heat fluxes
The average daytime ground heat flux (
4.4. Sensible heat
The sensible heat (
Concerning the wet period, very poor correlation was found between
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 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
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 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, 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.
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,
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.
The authors thank the support of the Agricultural and Forestry Experiment Station (AFES) School of Natural Resources and Extension at the University of Alaska Fairbanks and the support of the Department of Agricultural Sciences at the University of Bologna, Italy. Ms. Watcharee Ruairuen was funded by Suratthani Rajabhat University, Thailand. GJ Fochesatto was supported by the Geophysical Institute, University of Alaska Fairbanks. Elena B. Sparrow was supported by the International Arctic Research Center and Alaska EPSCOR, also at the University of Alaska Fairbanks. Mingchu Zhang was supported by USDA NIFA Multi state NC-1179 funding through the Department of Agriculture and Horticulture, School of Natural Resources and Extension, University of Alaska Fairbanks
Chapin FS III, McGuire AD, Randerson J, Pielke R, Baldocchi D, Hobbie SE, Roulet N, Eugster W, Kasischke E, Rastetter EB, Zimov SA, Running SW. Arctic and boreal ecosystems of western North America as components of the climate system. Global Change Biology. 2000; 6(Suppl. 1):211–223
Serreze MC, Walsh JE, Chapin FS, Osterkamp T, Dyurgerov M, Romanovsky V, Oechel WC, Morison J, Zhang T, Barry RG. Observational evidence of recent change in the northern high-latitude environment. Climatic Change. 2000; 46:159–207
Hinzman LD, Bettez ND, Bolton WR, Chapin FS, Dyurgerov MB, Fastie CL, Griffith B, Hollister RD, Hope A, Huntington HP, Jensen AM, Jia GJ, Jorgenson T, Kane DL, Klein DR, Kofinas G, Lynch AH, Lloyd AH, McGuire AD, Nelson FE, Oechel WC, Osterkamp TE, Racine CH, Romanovsky VE, Stone RS, Stow DA, Sturm M, Tweedie CE, Vourlitis GL, Walker MD, Walker DA, Webber PJ, Welker JM, Winker KS, Yoshikawa K. Evidence and implications of recent climate change in northern Alaska and other arctic regions. Climatic Change. 2005; 72(3):251–298
Intergovernmental Panel on Climate Change. Climate change 2007: The physical science basis. Contribution of working group I to the fourth assessment report of the intergovernmental panel on climate change. iN: Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M, and Miller HL, editors. New York: Cambridge University Press; 2007. p. 996
Molders N, Romanovsky VE. Long-term evaluation of the hydro-thermodynamic soil-vegetation scheme’s frozen ground/permafrost component using observations at Barrow, Alaska. Journal of Geophysical Research. 2006; 11:D04105
Romanovsky V, Burgess M, Smith S, Yoshikawa K, Brown J. Permafrost temperature records: Indicators of climate change. EOS Transactions. 2002; 80:589–594
Yoshikawa K, Hinzman LD. Shrinking thermokarst ponds and groundwater dynamics in discontinuous permafrost near Council, Alaska. Permafrost and Periglacial Processes. 2003; 14:151–160. doi: 10.1002/ppp.451
Smith LC, Sheng Y, MacDonal GM, Hinzman LD. Disappearing Arctic lakes. Science. 2005; 308:1427
Osterkamp TE. Characteristics of the recent warming of permafrost in Alaska. Journal of Geophysical Research. 2007; 112:F02S02
Jorgenson MT, Romanovsky V, Harden J, Shur Y, O’Donnell J, Schuur EAG, Kanevskiy M, Marchenko S. Resilience and vulnerability of permafrost to climate change. Canadian Journal of Forest Research. 2010; 40:1219–1236
Mack MC, Shuur EAG, Bret-Harte MS, Shaver GR, Chapin FS III. Ecosystem carbon storage in Arctic tundra reduced by long-term nutrient fertilization. Nature. 2004; 431:440-443
Clein JS, Kwiatkowski BL, McGuire AD, Hobbie JE, Rastetter EB, Melillo JM, Kicklighter DW. Modelling carbon responses of tundra ecosystems to historical and projected climate: A comparison of a plot- and global-scale ecosystem model to identify process-based uncertainties. Global Change Biology. 2000; 6:141–159
McGuire AD, Clein JS, Melillo JM, Kicklighter DW, Meier RA, Vorosmarty CJ, Serreze MC. Modelling carbon responses of tundra ecosystems to historical and projected climate: Sensitivity of pan-Arctic carbon storage to temporal and spatial variation in climate. Global Change Biology. 2000; 6(Suppl. 1):141–159
McFadden JP, Dugster W, Chapin FS III. A regional study of the controls on water vapor and CO2 exchange in Arctic tundra. Ecology. 2003; 84:2762–2776
Hinzman LD, Kane DL. Potential response of an Arctic watershed during a period of global warming. Journal of Geophysical Research. 1992; 97(D3):2811–2820
McFadden JP, Chapin FS III, Hollinger DY. Subgrid-scale variability in the surface energy balance of arctic tundra. Journal of Geophysical Research. 1998; 103(D22):28947–28961
Sharratt BS. Observations and modeling of interactions between barley yield and evapotranspiration in the Subarctic. Agricultural Water Management. 1994; 25:109–119
Sharratt BS. Barley yield and evapotranspiration governed by tillage practices in interior Alaska. Soil Tillage Research. 1998; 46:225–229
Banimahd SA, Zand-Parsa S. Simulation of evaporation, coupled liquid water, water vapor and heat transport through the soil medium. Agricultural Water Management. 2013; 130:168–177
Zhuang Q, McGuire AD, Mellilo JM, Clein JS, Dargaville RJ, Kicklighter DW, Myneni RB, Dong J, Romanovsky VE, Harden J, Hobbie JE. Carbon cycling in extratropical terrestrial ecosystems of the northern hemisphere during the 20th century: A modeling analysis of the influences of soil thermal dynamics. Tellus. 2003; 55B:751–776
Euskirchen ES, McGuire AD, Kicklighter DW, Zhuang Q, Clein JS, Dargaville R, Dye DG, Kimball JS, McDonald KC, Mellilo JM, Romanovsky VE, Smith NV. Importance of recent shifts in soil thermal dynamics on growing season length, productivity, and carbon sequestration in terrestrial high-latitude ecosystems. Global Change Biology. 2006; 12:731–750
Balshi MS, McGuire AD, Zhuang Q, Mellio J, Kicklighter DW, Kasichke E, Wirth C, Flannigan M, Harden J, Clein JS, Burnside TJ, McAllister J, Kurz WA, Apps M, Shvidenko A. The role of historical fire disturbance in the carbon dynamics of the pan-boreal region: A process-based analysis. Journal of Geophysical Research. 2007; 112:G02029
Lawrence DM, Slater AG, Romanovsky VE, Nicolsky DJ. Sensitivity of a model projection of near-surface permafrost degradation to soil column depth and representation of soil organic matter. Journal of Geophysical Research. 2008; 113:F02011
Ruairuen W, Fochesatto GJ, Sparrow EB, Schnabel W, Zhang M, Kim Y. Evapotranspiration cycles in a high latitude agroecosystem: Potential warming role. PLoS ONE. 2015; 10(9):e0137209. doi:10.1371/journal.pone.0137209
Sitch S, McGuire AD, Kimball JS, Gedney N, Gamon J, Engstrom RN, Wolf A, Zhuang Q, Clein JS, McDonald KC. Assessing the carbon balance of circumpolar Arctic tundra with remote sensing and process based modeling approaches. Ecological Applications. 2007; 17:213–234
Bittelli M, Ventura F, Campbell GS, Snyder RL, Gallegati F, Pisa PR. Coupling of heat, water vapor, and liquid water fluxes to compute evaporation in bare soils. Journal of Hydrology. 2008; 362(3):191–205
Starkenburg D, Metzger S, Fochesatto GJ, Alfieri J, Gens R, Prakash A, Cristobal J, Kane D. Assessment of de-spiking methods for turbulent flux computations in high latitude forest canopies using sonic anemometers. Journal of Atmospheric and Oceanic Technology. 2016; 33:2001–2013. doi: 10.1175/JTECH-D-15-0154.1
Gruber M, Fochesatto GJ. A new sensitivity analysis and solution method for scintillometer measurements of area-averaged turbulent fluxes. Boundary-Layer Meteorology. 2013; 149(1):65–83
Fochesatto GJ, Mayfield JA, Starkenburg DP, Gruber MA, Conner J. Occurrence of shallow cold flows in the winter atmospheric boundary layer of interior of Alaska. Meteorology and Atmospheric Physics. 2013;127(4):369–382. doi: 10.1007/s00703-013-0274-4
Gruber MA, Fochesatto GJ, Hartogensis OK, Lysy M. Functional derivatives applied to error propagation of uncertainties in topography to large-aperture scintillometer-derived heat fluxes. Atmospheric Measurement Techniques. 2014; 7:2361–2371. doi:10.5194/amt-7-2361-2014
Bittelli M, Campbell GS, Tomei F. Soil Physics with Python, Transport in the Soil-Plant-Atmosphere System. Oxford, UK: Oxford University Press. 2015, 464 pages. ISBN: 978-0-19-968309-3
Campbell GS, Norman, JM. An Introduction to Environmental Biophysics, second ed., Springer, New York, USA, 1998.
Davin EL, Seneviratne SI, Ciais P, Olioso A, Wang T. Preferential cooling of hot extremes from cropland albedo management. Proceedings of the National Academy of Sciences. 2014; 111(27):9757–9761
Sharratt BS. Water use, intercepted radiation and soil temperature of skip-row and equidistant-row barley. Agronomy Journal. 1993; 85:686–691
Mayfield JA, Fochesatto GJ. The layered structure of the winter atmospheric boundary layer in the interior of Alaska. Journal of Applied Meteorology and Climatology. 2013; 52:953–973
Ortega-Farias S, Carrasco M, Olioso A, Poblete C. Latent heat flux over Cabernet Sauvignon vineyard using the Shuttle worth and Wallace model. Irrigation Science. 2007; 25:161–170
Ortega-Farias S, Antonioletti R, Olioso A. Net radiation model evaluation at an hourly time step for Mediterranean conditions. Agronomie. 2000; 20:157–164
Jackson RD. Diurnal changes in soil water content during drying, in field soil water regime. 1973. In: Bruce RR (Ed.). Field Soil Water Regime. 5. SSSA Special Publication. pp. 37–55
Cahill AT, Parlange MB. On water vapor transport in field soils. Water Resources Research. 1998; 43:731–739
Parlange MB, Cahill AT, Nielsen DR, Hopmans JW, Wendroth O. Review of heat and water movement in field soils. Soil & Tillage Research. 1998; 47:5–10
Starkenburg D, Fochesatto GJ, Prakash A, Cristóbal J, Gens R, Kane DL. The role of coherent flow structures in the sensible heat fluxes of an Alaskan boreal forest. Journal of Geophysical Research. Atmospheres. 2013; 118:8140-8155. doi:10.1002/jgrd.50625
Starkenburg DP, Fochesatto GJ, Cristóbal J, Prakash A, Gens R, Alfieri JG, Nagano H, Harazono Y, Iwata H, Kane DL. Temperature regimes and turbulent heat fluxes across a heterogeneous canopy in an Alaskan boreal forest. Journal of Geophysical Research Atmospheres. 2015; 120:1348–1360. doi: 10.1002/2014JD02233