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Frozen Ground Modeling

  Hydrology Laboratory
Office of Hydrologic Development

(Last modified: 6/13/2011)

new iconNOAA Technical Report NWS 52
Physically-Based Modifications to the Sacramento Soil Moisture Accounting Model:  Modeling the Effects of Frozen Ground on the Rainfall-Runoff Process


Seasonally frozen ground can have a very significant effect on the amount of runoff produced during the winter and spring.  Lack of vegetation during the winter, shallow snow cover, and very cold temperatures produce optimal conditions for deep frost penetration.  The Sacramento Soil Moisture Accounting model  (SAC-SMA), widely used by NOAA/NWS, has a frozen ground component.  It is based on an empirical frost index.  There are two main parts to this frozen ground component.  The first, the computation of a frost index and the second, the modification of the rainfall-runoff model based on the frost index.  As stated by Anderson and Neuman[1984], further improvements should include more physically based approaches, e.g. a simple heat transfer procedure for computing the energy flux into or out of the ground, as well as the frost and thaw depths.  This would also reduce a large number of a recent model parameters. HL has begun the development of a new physically-based frozen ground parameterization.  The first part, conceptualization of heat transfer processes, is finished and some tests  performed.

Conceptualization of heat transfer processes

Most common conceptual hydrological models do not have an explicit definition of soil layers.  This complicates the implementation of physically based heat/moisture transfer models that require numerical integration over a soil profile.  A heat transfer procedure should be simple enough to be implemented in operational work when input data are limited and running time can be critical.  Another requirement is that the procedure should also be compatible with the SAC-SMA complexity in calculating soil moisture redistribution during freezing/thawing periods.  HL started development of a physically based frozen ground component for the storage-type Sacramento Soil Moisture Accounting model  (SAC-SMA).  The first step was to define a procedure  to transform layer-structured heat/moisture states into storage-type states, and vice verse.  The SAC-SMA model was used to estimate soil moisture states and runoff components, and a layer integrated form of the heat transfer equation adopted by the NOAH LSM [Koren et al., 1999a] is used to  estimate soil temperature and unfrozen water states.

The SAC-SMA model consists of upper and lower tension and free water storages that interact to generate soil moisture states and five runoff components.  A variable number of soil layers can be used in the heat transfer model, simplifying the coupling to the SAC-SMA.  The SAC-SMA storages, represented as  totals of tension and free water,  plus a water content below wilting point, are  recalculated into a number of soil layers using soil texture data.  Three or four layers are usually used with much higher resolution in the upper zone. At each time step, SAC-SMA liquid water storage changes due to rainfall/snowmelt are estimated, and then they are transformed into soil moisture states of the heat transfer model.  The heat transfer model splits the  total water content into frozen and liquid water portions based on simulated soil temperature profile.  Estimated new soil moisture states are then converted back  into SAC-SMA model storages, see Figure 1.  The time step of the frozen ground component may be a fraction of the SAC-SMA time step.



Figure 1.  Schematic of recalculation of SAC-SMA states (UZTWC, UZFWC, LZTWC, LZFSC, LZFPC) into heat transfer model states (SMC1, SMC2, SMC3, SMC4), and vice verse.
During snow cover periods the SNOW-17 operation, which is a temperature index-based parameterization, is used to calculate a snowpack dynamics.  Because SNOW-17 and SAC-SMA operations use only rainfall and air temperature time series, some modifications were introduced into an original heat transfer parameterization: 1) a soil/snow surface heat balance calculation was replaced by applying air temperature; 2)  snow-soil heat interface was replaced by a predefined constant heat exchange rate.  Tests suggested that these modifications did not lead to significant reduction in the accuracy of parameterization.

Test results

Two experimental data sets were used in tests [Koren et al., 1999b]: 1) From the Rosemount site of the University of Minnesota Agricultural Experiment Station where field measurements were performed during a cold season; 2) Long-term measurements of water balance components from the water balance station Valdai (Russia).  The first data set is a profile type measurement of soil temperature and unfrozen soil moisture content at 8 depths from 2.5 cm to 1 m.  The time interval of measured raw data varies from 10 min to 1 hour.   The second data set represents spatial averages over a small river basin Usadievskiy (watershed of 0.36 km2).  Soil temperature was measured at 20 cm, 40 cm, and 80 cm depths.  Measurements of total soil moisture were taken at the end of each month using gravimetric technique for three soil layers to a depth of 1 m.  Snow water equivalent measurements were also available in non-regular time intervals during snow accumulation and ablation periods.  There are continuous measurements of all variables for 18 years.

Hourly air temperature and precipitation were used as an input data.  There was no calibration. All parameters were defined using soil texture information and recommendations in a literature.  Simulations were performed continuously during available periods of observations (1995-1996 for the Rosemount site, and 1966-1983 for the Valdai station).  The SNOW-17 operation and the SAC-SMA with a new frozen ground component operation were run in both cases.  Observed and simulated soil temperature for a few soil layers agreed well in both cases.  It means that this heat transfer parameterization can be used as a physically-based replacement of an empirical SAC-SMA parameterization to estimate a frost index or a frost depth.  Simulated and observed soil temperatures for the Valdai station are displayed in Figures 2-4 for the period 1971-1974, and in Figures 5-7 for the period 1979-1982.  Results for the Rosemount site during the 1995-1996 cold season are shown in Figure 8.


Anderson, E. A., and P. J. Neuman, 1984.  Inclusion of frozen ground effects in a flood forecasting model, The 5th North. Res. Basin Symp. and Workshop, March 19-23, Vierumaki, Finland, 14pp.

Koren, V., J. Schaake, K. Mitchell, Q.-Y. Duan, F. Chen, and J. M. Baker, 1999a.  A parameterization of snowpack and frozen ground intended for NCEP weather and climate models, JGR, Vol. 104, No. D16, pp. 19,569-19,585.

Koren, V., Q.-Y. Duan, J. Schaake, and K. Mitchell, 1999b. Validation of a snow-frozen ground parameterization of the ETA model, 14th Conference on Hydrology, 10-15 January 1999, Dallas, TX, by the AMS, Boston MA, pp. 410-413.

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