CONCEPTUALIZATION OF HEAT TRANSFER
PROCESSES FOR STORAGE-TYPE HYDROLOGICAL MODELS
(Last modified: 6/13/2011)
NOAA 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, 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
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.
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.