Current Winter Processes Modeling Approaches - WEPP

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

2. 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.

3. Winter Routines are active when: • A snowpack already exists, or • A soil frost layer already exists, or • Average daily temperature is less than 0oC

4. 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.

5. 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

6. Hourly radiation calculations Net daily radiation Adjustment factor to hourly radiation Rslp – 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 oK-4) Tavek – hourly air temperature (oK) 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)

7. Snow Melt Assumptions • Any precipitation occurring in an hour when temperature is <0oC is assumed to be snowfall • No snowmelt will occur if maximum daily temperature is < -3oC • The snowpack will not melt until the density of the snowpack exceeds 350 kg m-3 • The surface soil temperature equals 0oC 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

8. Snow Melt Calculations hrmelt = 0.0254 (amelt – bmelt + cmelt + dmelt)

9. 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.

10. Soil Frost/Thaw Calculations Uni-directional Heat Flow through the soil or soil-residue-snow system is calculated with: ▲Tsrf – temperature difference across snow-residue-frozen soil system thickness (oC) Zsrf – thickness of system (m) Average Thermal Conductivity Ksnow – thermal conductivity of snow (W m-1oC-1) Kres – thermal conductivity of residue (W m-1 oC-1) Kftill – thermal conductivity of frozen tilled soil (W m-1oC-1) Kfutil – thermal conductivity of frozen untilled soil (W m-1 oC-1) Snowd, Resd, Tilld, Utilld – thicknesses of each layer (m)

11. Soil Frost/Thaw Calculations Qsrf must be balanced by heat flow from the unfrozen soil below the frozen layer (Quf). Kuf – thermal conductivity of unfrozen soil (W m-1oC-1) Tuf – change in temperature from 0o isotherm to the depth of stable temperature (oC) Zuf – depth of unfrozen soil (m) L – latent heat of fusion (W s m-3) Kw – unsaturated hydraulic conductivity of the soil (m s-1) P – change in total water potential (m) Cuf - heat capacity of unfrozen soil (W m-3oC-1) Zc – depth of unfrozen soil that supplies heat (1.0 m)

12. 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.

13. 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 Ki and Kr 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.

14. 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

15. 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.