Embed Size (px)
Citation preview
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
0
10
20
30
40
20 40 60 80 100 120 140 160 180 Precipitation, mm
277
250
214
247
281 283
239
309
341 239
310
479
483
476
281
303
337
374
282
Warm Cold
-10
-5
0
5
10
15
20
25
-40 -30 -20 -10 0 10 20 30 Air temperature
Warm Cold
Figure on the left displays differences inrunoff for warm- and cold-season floodevents on the Root river, MN where frozendepth can be as much as 2m. The soil moisture only can not explain significantdifferences in the amount of runoff generated by precipitation events of similar size.
Precipitation-Runoff relationship during warm andCold seasons. Soil moisture is at the points.
Figure on the right displays differencesin soil and air temperature relationshipduring warm and cold periods. Afterstrong correlation during warm seasonthere was no correlation at all whensoil freezing and snow cover was occurred.
Soil vs. Air temperature relationship.
Effects on Hydrological Processes
-4
-2
0
2
4
6
Skin
te
mp
era
tu
re
, C
elsiu
s11/16/9511/17/9511/18/9511/19/9511/20/95
a)
-4
-2
0
2
4
Ice
co
nte
nt ch
an
ge
, m
m
11/16/9511/17/9511/18/9511/19/9511/20/95
b)
-4
-2
0
2
4
6
Soil tem
perature, C
els
ius
11/16/95 11/17/95 11/18/95 11/19/95 11/20/95
Date, Month/Day/Year
Frozen ground versionOriginal Eta version Observed
c)
Diurnal cycles of (a) skin temperature, (b) ice content change, (positive when freezing, and negative when thawing), and (c) the first layer soiltemperature during snow free surface.
Effects on Hydrological Processes
-125
-75
-25
25
75 R
ain
+M
elt,
Sn
ow
wa
ter
eq
uiv
ale
nt,
T
0
5
10
15
20
25
Ru
no
ff,
mm
10 11 12 1 2 3 4 5 6 7 8 9
Month
Rain+Melt Runoff
Air Temperature (T) Snow water equivalent
Root basin time series, 1966-1967
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
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
Change of the infiltration rate, I, and ice content, Wf,during snowmelt period.
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
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
Surface Temp.
Fixed Annual Temp.
1
2
3
4
Phase transitionlayers
Boundaries of soillayers
Soil column Schematic
Linking of Soil Moisture and Heat States
SAC-SMA storages SOIL layers SAC-SMA storages
SMC1
SMC2
SMC3
SMC4
Soil Profile Definition and Model Parameter Estimation
LZFPMLZFSM
UZFWM
UZTWM
LZTWM
Soil Texture to Soil Properties (θmax, θfld, θwlt) based on Cosby’s relationships.
Sacramento model parameter grids for the Arkansas river
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 ResultsObserved (white) and simulated (red) soil temperature at 20, 40, & 80 cm depth.
Valdai, Russia, 1981 – 1982.
Test ResultsObserved (white) and simulated (red) soil moisture and temperature at 20, 40, & 80cm depth.
Valdai, Russia, 1971 – 1978.
Test ResultsObserved (white) and simulated (red) soil temperature at 5, 10, 20, 50, & 100cm depth.
Atlantic Site, IA, USA, 1997 – 2000.
Test ResultsObserved (white) and simulated (red) soil temperature at 5, 10, 20, 50, & 100cm depth.
Waubay Site, SD, USA, 1997 – 2000.
Test ResultsAccuracy statistics for soil temperature simulated over
Northern part of the US
Site ID 5 cm layer 20 cm layer 50 cm layer
RMS %RMS R RMS %RMS R RMS %RMS R
134585 3.0 23.1 0.96 2.9 19.0 0.99 2.9 20.4 0.99
130364 5.0 33.0 0.96 3.3 23.7 0.99 2.9 22.1 0.98
131060 3.3 23.8 0.96 2.5 19.0 0.97 3.0 21.1 0.97
132209 3.7 27.4 0.97 1.9 15.2 0.99 1.6 13.4 0.99
132724 4.5 38.8 0.96 2.0 21.9 0.98 2.6 25.8 0.98
138296 3.2 25.3 0.97 3.2 26.3 0.98 2.3 19.2 0.99
216654 3.9 44.0 0.97 2.4 31.2 0.98 2.4 25.2 0.99
398980 3.3 31.2 0.96 1.5 16.9 0.99 1.3 15.1 0.99
137844 8.1 51.1 0.95 5.1 36.7 0.98 3.6 29.4 0.99
203099 3.1 27.3 0.98 2.8 25.8 0.99
218692 3.3 30.9 0.99
Average 4.2 33.1 0.96 2.8 23.7 0.98 2.6 22.6 0.99
Test Results
0
20
40
60
80
100
120
140
Fro
st
de
pth
, cm
-70
-60
-50
-40
-30
-20
-10
0
Fro
st
ind
ex,
(C)
112
1012
1912
281
61
151
241
22
112
202
293
93
183
273
54
144
234
Day & Month, 1966
0
20
40
60
80
100
120
140
Fro
st
de
pth
, cm
-70
-60
-50
-40
-30
-20
-10
0F
rost
ind
ex,
(C)
112
1012
1912
281
61
151
241
22
112
202
293
93
183
273
54
144
234
Day & Month, 1967
Estimated Frost depthSimulated Frost Index
OBSmin OBSmax
0
20
40
60
80
100
120
140
Fro
st
de
pth
, cm
-70
-60
-50
-40
-30
-20
-10
0
Fro
st
ind
ex,
(C)
112
1012
1912
281
61
151
241
22
112
202
293
93
183
273
54
144
234
Day & Month, 1968
0
20
40
60
80
100
120
140
Fro
st
de
pth
, cm
-70
-60
-50
-40
-30
-20
-10
0
Fro
st
ind
ex,
(C)
112
1012
1912
281
61
151
241
22
112
202
293
93
183
273
54
144
234
Day & Month, 1969
Estimated Frost depthSimulated Frost Index
OBSmin OBSmax
Observed and simulated frost depth and frost index. Root river basin, MN.
Test ResultsWater balance component changes due to ice content
0
10
20
30
40
50
Ice
co
nte
nt, m
m1 51 101151201251301351401451501551601651701
Time (6-hr) from 11/01/93
-0.1
0
0.1
0.2
0.3
0.4
Percolation change, m
m
-2
0
2
4
6
8
Cum
ulative percolation change, m
m
1 51101151201251301351401451501551601651701Time (6-hr) from 11/01/93
-0.1
0
0.1
0.2
0.3
0.4
Total runoff change, m
m
-1
0
1
2
3
4
Cum
ulative runoff change, m
m
1 51101151201251301351401451501551601651701Time (6-hr) from 11/01/93
-0.1
0
0.1
0.2
0.3
0.4
Evaporation change, m
m
-2
0
2
4
6
8
Cum
ulative evaporation change, m
m
1 51 101151201251301351401451501551601651701Time (6-hr) from 11/01/93
Modeling of Frozen Ground Effects on Runoff
CDF of the freezing depth as a functionOf an area average freezing depth(values at the lines).
Coefficient of variation of freezing depthVs. area average freezing depth.1) Freezing depth surveys; 2) Empirical equation; 3) Based on typical CDF.
Modeling of Frozen Ground Effects on Runoff
2
4
6
8
10
12
0 0.2 0.4 0.6 0.8 1 Impermeable area portion
Impermeable area portion vs.ice content Areas where Θice > Θcr
Surface runoff for Θice > Θcr
YSAC (1 – Fc) Surface runoff for Θice < Θcr
P Fc
Total surface runoff isY = YSAC (1 - Fc) + P Fc
YSAC is runoff estimated without frozen ground effect,P is Rainfall + Snowmelt
Surface runoff adjustmentImpermeable area fraction, Fc
Θcr is an ice content threshold above which percolation is closeto zero,α is a parameter of a gamma distribution of the ice content, 1/CV
2
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.
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
• 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
• 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
