A physically based analytical model is formulated to simulate the thaw depth of active layer under changing boundary condition of soil heat flux. The energy conservation statement leads to a nonlinear integral equation of the thaw depth using an approximate temperature profile as an analytical solution of the diffusion equation describing the heat transfer in the active layer. The time-varying soil surface heat flux is estimated using non-gradient models when field observations are not available. The proposed model was validated against field observations at three Arctic forest and tundra sites. The simulated thaw depth and soil temperature profiles are in good agreement with observations hinting the potential for model application at larger spatial scales.

A new dynamic model of snow surface temperature known as force-restore model (FRM) is formulated for one-dimensional heat transfer taking into account of the absorption of solar radiation within snowpack. The FRM formula explicitly includes net solar radiation at snow surface and its time derivative compared to the classical FRM of soil surface temperature. When snow surface heat flux is parameterized in terms of snow surface temperature and radiation fluxes, the FRM only uses surface radiation fluxes as the model input. The proposed FRM not only simulates snow surface temperature but also latent (sublimation), sensible and (conductive) snow surface heat flux. The proposed FRM has been validated using in-situ observations for seasonal and perennial snow in the Arctic and Antarctica.

A novel non-gradient model is formulated for estimating gas fluxes using single-level time-series data of near-surface gas concentration over land surfaces. When the vertical turbulent transport process in the atmospheric surface layer is described by a one-dimensional diffusion equation, a gas flux is expressed as a weighted integral of the time-history of single-level gas concentration. The eddy-diffusivity may be parameterized as a function of sensible heat flux based on the Monin-Obukhov similarity theory without explicit dependence on wind speed and surface roughness. Sensible heat flux may be estimated from net radiation and surface temperature using the maximum entropy production model. Case studies at six sites with diverse vegetation covers, geographic and climatic conditions at sub-daily scale demonstrate the model’s ability to simulate diurnal variations of water vapor and CO2 fluxes using fewer inputs than other models. Good performance of the model at seasonal scale suggests that the proposed model is a promising tool for the assessment of annual water and carbon budgets over vegetated land surfaces.

A physically based model is formulated for the active layer depth of permafrost under changing boundary condition instead of constant boundary condition considered in the traditional Stefan problem. Time varying ground heat flux is obtained from net radiation and surface temperature using the Maximum Entropy Production (MEP) model as the driver of the active layer melting process. Conductive heat flux at the melting front is approximated in terms of an analytical function of ground heat flux. The simulated active layer depth is in good agreement with the field observations.

The Calhoun Critical Zone Observatory (CCZO) has been collecting above and below canopy water, energy and carbon fluxes and other hydro-meteorological processes since 2016. The observations provide a unique opportunity to investigate the coupling between aboveground environmental conditions and belowground fluxes of mass and energy in general and the fate of fixed carbon in forested ecosystems in particular. The simultaneous measurements of soil-canopy-atmosphere states and fluxes reveal the role of pine forest in diurnal and seasonal dynamics of the CCZ ecosystem.