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Frozen Ground Processes: 

Frozen Ground Processes Effects on Hydrological Processes Frozen Ground Physics/Specific Frozen Ground Parameterization Conceptualization of Heat-Water Fluxes Modeling of Frozen Ground Effects on Runoff Test Results

Effects on Hydrological Processes: 

Effects on Hydrological Processes

Effects on Hydrological Processes: 

Effects on Hydrological Processes Figure on the left displays differences in runoff for warm- and cold-season flood events on the Root river, MN where frozen depth can be as much as 2m. The soil moisture only can not explain significant differences in the amount of runoff generated by precipitation events of similar size. Precipitation-Runoff relationship during warm and Cold seasons. Soil moisture is at the points. Figure on the right displays differences in soil and air temperature relationship during warm and cold periods. After strong correlation during warm season there was no correlation at all when soil freezing and snow cover was occurred. Soil vs. Air temperature relationship.

Effects on Hydrological Processes: 

Effects on Hydrological Processes Diurnal cycles of (a) skin temperature, (b) ice content change, (positive when freezing, and negative when thawing), and (c) the first layer soil temperature during snow free surface.

Effects on Hydrological Processes: 

Effects on Hydrological Processes

Frozen Ground Physics/Specific: 

Frozen Ground Physics/Specific Specific Features of Soil Freezing-Thawing Processes are Soil profile is Divided into two or more Parts Separated by a Phase Change Interface Thermal-Hydraulic Properties of the Frozen and Unfrozen Sections are Different, and they are not Strong Functions of Temperature Heat Source/Sink Effects Significantly on the Energy-Water Balance Freezing of Infiltrated Melt/Rain Water Reduces Significantly Losses, and it can Lead to Practically Impermeable Soil Layers

Frozen Ground Physics/Specific: 

Frozen Ground Physics/Specific

Frozen Ground Physics/Specific: 

Frozen Ground Physics/Specific Melt water losses, P, as a function of soil saturation index, W, and freezing depth, L, at the beginning of snowmelt. Snow water equivalent is assumed to be 120 mm.

Frozen Ground Physics/Specific: 

Frozen Ground Physics/Specific Change of the infiltration rate, I, and ice content, Wf, during snowmelt period.

Frozen Ground Parameterization: 

Frozen Ground Parameterization Parameterization has two Parts Calculation of Heat-Water Fluxes and Frost Index Modification of the Water Balance Using Frost Index Requirements Simple Enough Procedure to run with Limited Noisy Data Procedure need to be Compatible with the Sacramento Model Complexity Limited Number of ‘Ill-defined’ Parameters

Calculation of Heat-Water Fluxes: 

Calculation of Heat-Water Fluxes Assumptions N-layer soil column The layer-Integrated diffusion equation Soil moisture & heat fluxes are simulated separately at each time step Surface temperature is equal to air temperature Lower boundary is set at the climate annual air temperature Unfrozen water content is estimated as a function of soil temperature, saturation rate, and ice content Soil column Schematic

Linking of Soil Moisture and Heat States: 

Linking of Soil Moisture and Heat States

Soil Profile Definition and Model Parameter Estimation: 

Soil Profile Definition and Model Parameter Estimation LZFPM LZFSM UZFWM UZTWM LZTWM Soil Texture to Soil Properties (θmax, θfld, θwlt) based on Cosby’s relationships.

Sacramento model parameter grids for the Arkansas river : 

Sacramento model parameter grids for the Arkansas river

Test Results: 

Test Results Soil moisture and temperature results for two experimental sites: Rosemount, MN (2 years) and Valdai, Russia (18 years) Soil temperature only for 15 operational sites, USA (3-5 years)

Test Results: 

Test Results Observed (white) and simulated (red) soil temperature at 20, 40, & 80 cm depth. Valdai, Russia, 1981 – 1982.

Test Results: 

Test Results Observed (white) and simulated (red) soil moisture and temperature at 20, 40, & 80cm depth. Valdai, Russia, 1971 – 1978.

Test Results: 

Test Results Observed (white) and simulated (red) soil temperature at 5, 10, 20, 50, & 100cm depth. Atlantic Site, IA, USA, 1997 – 2000.

Test Results: 

Test Results Observed (white) and simulated (red) soil temperature at 5, 10, 20, 50, & 100cm depth. Waubay Site, SD, USA, 1997 – 2000.

Test Results: 

Test Results Accuracy statistics for soil temperature simulated over Northern part of the US

Test Results: 

Test Results Observed and simulated frost depth and frost index. Root river basin, MN.

Test Results: 

Test Results Water balance component changes due to ice content

Modeling of Frozen Ground Effects on Runoff: 

Modeling of Frozen Ground Effects on Runoff CDF of the freezing depth as a function Of an area average freezing depth (values at the lines). Coefficient of variation of freezing depth Vs. area average freezing depth. 1) Freezing depth surveys; 2) Empirical equation; 3) Based on typical CDF.

Modeling of Frozen Ground Effects on Runoff: 

Modeling of Frozen Ground Effects on Runoff Areas where Θice > Θcr Surface runoff for Θice > Θcr YSAC (1 – Fc) Surface runoff for Θice < Θcr P Fc Total surface runoff is Y = YSAC (1 - Fc) + P Fc YSAC is runoff estimated without frozen ground effect, P is Rainfall + Snowmelt Surface runoff adjustment Impermeable area fraction, Fc Θcr is an ice content threshold above which percolation is close to zero, α is a parameter of a gamma distribution of the ice content, 1/CV2

Modeling of Frozen Ground Effects on Runoff: 

Modeling of Frozen Ground Effects on Runoff Snow water equivalent is assumed to be 120 mm. The parameterization mimics empirical relationship between losses, P, soil saturation, W, and freezing depth, L.

Slide26: 

Observed and simulated hydrographs, frost index, and water balance components. Hydrograph simulated with (red) & w/o (yellow) use of the frost index. Root river, MN.

Frost Index Replacement: 

Frost Index Replacement Basic heat flux equation integrated over selected soil layers Unfrozen soil moisture content is estimated as a function of soil temperature, T, and total moisture, Θ, and ice, Θice, contents Appendix 1

REFERENCES: 

REFERENCES Koren, V., J. Schaake, K. Mitchell, Q.-Y. Duan, F. Chen, J. M. Baker, A parameterization of snowpack and frozen ground intended for NCEP weather and climate models. JGR, Vol. 104, No. D16, 1999. Farouki, Omar T., Thermal properties of soils. Series of Rock and Soil Machanics, Vol. 11 (1986), Trans. Tech. Publications, 1986. Flerchinger, G. N., and K. E. Saxton, Simultaneous heat and water balance model of a freezing snow-residue-soil system, 1. Theory and development. Trans. ASAE, 33(2), 1989. Fukuda, M., and T. Ishizaki, General report on heat and mass transfer. Proc. Symp. Ground Freezing, 2, 1992. Kalyuzhnyy, I. L., N. S. Morozova, and K. K. Pavlova, Experimental Investigations of the Water Conduction of Soils. Soviet Hydrology, Vol. 17, No. 4, 1978. Komarov, V. D., and T. T. Makarova, Effect of the ice content, temperature, cementation, and freezing depth of the soil on meltwater infiltration in a basin. Soviet Hydrology, 3, 1973. O’Neil K., The physics of mathematical frost heave models: A review, Cold Reg. Sci. Technol, 6, 1983. Sheng, D., K. Axelsson, and S. Knutsson, Frost Heave due to Ice Lens Formation in Freezing Soils. 1. Theory and Verification. Nordic Hydrology, 26, 1995. Spaans, E. J. A., and J. M. Baker, The soil freezing characteristic: Its measurement and similarity to the soil moisture characteristic, Soil Sci. Soc. Am. J., 60, 1996. Appendix 2