Current Winter Processes Modeling Approaches - WEPP Dennis Flanagan Agricultural Engineer USDA-ARS NSERL West Lafayette, Indiana

WEPP Winter Hydrology Developed by Reza Savabi, Bob Young, George Benoit, John Witte, Dennis Flanagan, Jeanine Ferris Computations on an hourly basis Determines whether precipitation is rain or snow. Adjusts snow depth and density, and determines amount of snow melt. Determines soil frost depth and thaw depth. Determines water movement through frozen/unfrozen soil layers.

Winter Routines are active when: A snowpack already exists, or A soil frost layer already exists, or Average daily temperature is less than 0 o C

Hourly calculations For non-winter periods, daily water balance is only updated once a day. For winter periods, a separate water balance is tracked, and all calculations for water and heat transfer are on an hourly basis. Input values of maximum and minimum air temperatures are used to create hourly temperature values. An hourly radiation value is also calculated.

Hourly temperature calculations Between sunrise and 2:00 p.m. All other times Hourly adjusted surface temperature at top of residue-snow-frozen-layer system

Hourly radiation calculations R slp – solar radiation on sloping surface (Ly min -1 ) alb – albedo of soil or snow atem – atmospheric emissivity suem – surface emissivity SBC – Stephan-Boltzman constant (8.1247x10-11 Ly min -1 o K -4 ) T avek – hourly air temperature ( o K) SOLO – solar constant (0.082 MJ m -2 min -1 ) RELD – relative distance of earth from sun (rad) latrad – latitude (rad) SUND – sun declination (rad) HASR – position of sun at sunrise (rad) HAST – position of sun at sunset (rad) Net daily radiation Adjustment factor to hourly radiation

Snow Melt Assumptions Any precipitation occurring in an hour when temperature is <0 o C is assumed to be snowfall No snowmelt will occur if maximum daily temperature is < -3 o C The snowpack will not melt until the density of the snowpack exceeds 350 kg m -3 The surface soil temperature equals 0 o C during a melt period. The temperature of the cloud base is approximately that of the surface air temperature. The albedo of melting snow is 0.5

Snow Melt Calculations hrmelt = (amelt – bmelt + cmelt + dmelt)

Soil Frost/Thaw Assumptions Heat flow in a frozen or unfrozen soil or snow system is uni-directional. Average 24 hour temperature of the system surface-air interface is approximated by average daily air temperature. Snow and soil thermal conductivity and water flow components assumed constant. Heat lost through frozen zone is first balanced by heat flow in the unfrozen soil as a result of the soil’s temperature gradient and thermal conductivity. Additional heat loss is balanced by the heat of fusion released by freezing water. Further heat loss is balanced by changes in soil heat content of the unfrozen soil, the magnitude calculated by difference.

Soil Frost/Thaw Calculations Uni-directional Heat Flow through the soil or soil-residue-snow system is calculated with: Average Thermal Conductivity ▲T srf – temperature difference across snow-residue-frozen soil system thickness ( o C) Z srf – thickness of system (m) K snow – thermal conductivity of snow (W m -1 o C -1 ) K res – thermal conductivity of residue (W m - 1 o C -1 ) K ftill – thermal conductivity of frozen tilled soil (W m -1 o C -1 ) K futil – thermal conductivity of frozen untilled soil (W m -1 o C -1 ) S nowd, R esd, T illd, U tilld – thicknesses of each layer (m)

Soil Frost/Thaw Calculations Q srf must be balanced by heat flow from the unfrozen soil below the frozen layer (Q uf ). K uf – thermal conductivity of unfrozen soil (W m -1 o C -1 ) T uf – change in temperature from 0 o isotherm to the depth of stable temperature ( o C) Z uf – depth of unfrozen soil (m) L – latent heat of fusion (W s m -3 ) K w – unsaturated hydraulic conductivity of the soil (m s -1 ) P – change in total water potential (m) C uf - heat capacity of unfrozen soil (W m -3 o C -1 ) Z c – depth of unfrozen soil that supplies heat (1.0 m)

Snow Drifting WEPP has a considerable amount of code related to snow accumulation and loss due to drifting, however… This code is not currently active, due to questions about it performance and lack of sufficient data for validation at the time of model release.

Erodibility Adjustments Winter conditions can cause changes in the soil erodibility. A soil that is completely frozen to the surface is assumed to be non-erodible, and adjusted K i and K r are set to zero for that day. A soil that has gone through a number of freeze and thaw cycles is considered to be more erodible while still in a thawing and wet state, and erodibility adjustments are made to the soil on those days of simulation.

Interrill Erodibility Adjustment acyc – freeze thaw cycle factor - matric potential of surface soil (KPa) cycles - number of freeze-thaw cycles (max of 10) Adjustments made until soil dries to less than 1/3 bar water content

Rill Erodibility and Critical Shear Stress Adjustments Adjustments only active until soil dries to field capacity, then not active again until after a new freeze-thaw occurs.