IPW User Command
Category - Physical Modeling: Spatial
isnobal - energy-balance snowmelt model with 2 snow layers
isnobal -t data-tstep[,norm-tstep[,med-tstep[,sm-tstep]]]
[ -r restart-index ] [ -n #steps ]
[ -I init-image ] [ -i input-prefix ] [ -p prfile ]
[ -m mask ] [ -O output-frequency ]
[ -e em_prefix ] [ -s snow_prefix ] [ -U ] [ -K ]
[ -M max-h2o ] [ -C [compress_cmd] ]
[ -T norm-threshold[,med-threshold[,sm-threshold]] ]
DEM grid-based model using the energy balance to calculate snowmelt, and to predict runoff, from input data on snow properties, terrain and region characteristics, precipitation, and climate. Similar to the approach used by Anderson (1976), and Morris (1982), but designed to run on simpler, more generalizable inputs. The model was first presented by Marks (1988), described conceptually by Marks, et. al (1992) and Marks and Dozier (1992), and then described in great detail by Marks, et. al (1997).
The model approximates the snow cover as being composed of two layers, a surface fixed-thickness active layer and a lower layer, solving for the temperature (C) and specific mass (kg/m^2) which is the mass per unit area (from density * depth (kg/m^3 * m)) for each layer, and then computing the temperature and specific mass for the snowcover.
Melt is computed in either layer when the accumulated energy exceeds the "cold content" or when the "cold content" is > 0.0. Cold content is the energy required to bring the snow cover temperature up to freezing (0 C). Runoff is estimated when the accumulated melt and liquid H2O content exceeds a user-defined threshold.
This version of the model is a simplification of the point version, snobal, designed to run over a DEM grid or image of 10^4 to 10^6 cells. It has been successfully tested over the Emerald Lake basin in the Sierra Nevada (5m DEM, 5x10^4 grid cells), the Boise River basin in Idaho (250m DEM, 3.5x10^4 grid cells), and the Park City drainage in the Wasatch Mts. of Utah (75m DEM, 8.2x10^4 grid cells) on runs of 2 weeks to 6 months. The only constraint on the size of the grid is available disk storage, memory, and CPU speed. (A 6 month run over the Park City grid required 500Mb of input files, generated 1500Mb of output, and took 6.5 hours on a SUN Ultra 170E with 256Mb of real memory.)
Constants, assumed over the grid:
max_z_s_0 = 0.25 m Thickness of the active layer
z_u = 5.0 m Height above the ground of the wind
speed measurement
z_T = 5.0 m Height above the ground of the air
temperature and vapor pressure
measurements
Inputs:
Input image data are required for initial snowcover and surface conditions, for input climate data at each time-step, and for precipitation events. Initial condition data are specified only at the beginning of the run. Precipitation data include an ASCII file specifying the time since the run start for the event and the name of the precipitation file, which contains precipitation mass, % snow, snow density, and precipitation temperature.
Initial conditions image (7-band):
z = elevation (m)
z_0 = roughness length (m)
z_s = total snowcover depth (m)
rho = average snowcover density (kg/m^3)
T_s_0 = active snow layer temperature (C)
T_s = average snowcover temperature (C)
h2o_sat = % of liquid H2O saturation (relative
water content, i.e., ratio of water in
snowcover to water that snowcover could
hold at saturation)
If the -r option (restart), the image has an additional band for the lower snow layer's temperature, T_s_l, (8-bands):
z = elevation (m)
z_0 = roughness length (m)
z_s = total snowcover depth (m)
rho = average snowcover density (kg/m^3)
T_s_0 = active snow layer temperature (C)
T_s_l = temperature of the snowpack's lower
layer (C)
T_s = average snowcover temperature (C)
h2o_sat = % of liquid H2O saturation (relative
water content, i.e., ratio of water in
snowcover to water that snowcover could
hold at saturation)
Precipitation data is defined by an ASCII description file that includes one line per precipitation event, where each line has the format:
time_since_run_start (decimal hrs.) name_of_precip_image
where the first entry must be >= start time.
Precipitation image (4-band):
m_pp = total precipitation mass (kg/m^2)
%_snow = % of precipitation mass that was snow (0 to 1.0)
rho_snow = density of snowfall (kg/m^3)
T_pp = average precip. temperature (C) (from dew point
temperature if available, or can be estimated
from air temperature during storm, or minimum
daily temperature)
Like the point model, the DEM-based model will parse mixed rain/snow events. It is designed to accept inputs that could be derived from typical NRCS Snotel data such as total precipitation, snow mass increase, and temperature. The user must estimate average density and percent snow if depth data are unavailable. The model makes the following assumptions about the snow temperature, rain temperature, and liquid water saturation of the snow:
when 0.0 < %_snow < 1.0, (a mixed rain/snow event)
snow temperature = 0.0
rain temperature = T_pp
liquid H2O sat. = 100%
when %_snow = 1.0 and T_pp => 0.0, (a warm snow-only event)
snow temperature = 0.0
liquid H2O sat. = 100%
when %_snow = 1.0 and T_pp < 0.0, (a cold snow event)
snow temperature = T_pp
liquid H2O sat. = 0%
Input images with climate parameters are required for each time-step to drive the model. These 5- or 6-band images must have a common prefix, and a suffix that indicates the relative order of the inputs numerically (e.g., "input_prefix.N", where "N" is the time-step index). The first value of "N" should always be zero (0), and the last should always be (1 - #_inputs). "N" should be padded with zeros so that every value of "N" has the same number of digits as the last value of "N". For example, if there are 1200 input files, then "N" will always have 4 digits (e.g., input_prefix.0000, input_prefix.0001, ..., input_prefix.1199).
Input image (6-band):
I_lw = incoming thermal (long-wave) radiation (W/m^2)
T_a = air temperature (C)
e_a = vapor pressure (Pa)
u = wind speed (m/sec)
T_g = soil temperature at 0.5 m depth (C)
S_n = net solar radiation (W/m^2)
If there is no solar radiation (the sun is "down"), the last band may be omitted.
Time-steps (data time-step and run time-steps):
The "data time-step" is the time interval, in minutes, between the input images. The model assumes that this interval is constant. Because the snowcover energy balance is very sensitive to diurnal variations in climate (radiation, temperature, etc.), the "data time-step" must be 360 minutes (6 hours) or less. Best results are achieved with a data time-step of 180 minutes (3 hours) or less. Data time-steps greater than 60 minutes must be multiples of whole hours (e.g., 120 minutes, or 180 minutes).
A "run time-step" is the internal time-step that the model actually solves the energy balance over. Because input values are assumed to be averages over a run time-step, it is always 60 minutes (1 hour) or less to insure a stable model solution. Solution instabilities occur when the run time-step is too long to account for rapid changes in the energy balance (e.g., at sun rise or sunset), or when a layer's mass is too small to accommodate the assumption of an average flux over the run time-step.
There are 3 lengths of run time-steps: "normal, medium, and small". By default, the model uses the normal run time-step which is the longest of the three run time-steps. The normal time-step must divide evenly into the data time-step (i.e., the data time-step is an integer multiple of the normal run time-step). The input data for a normal run time- step (climate data and some precipitation values) are computed from the input records by linear interpolation.
The shorter run time-steps (medium and small) are to insure solution stability, and are only used as a layer's mass diminishes to the user defined threshold. When either layer's mass drops below the specified threshold, the model divides a larger run time-step into shorter run time-steps (e.g., divides a normal run time-step into medium run time-steps). There are three mass thresholds; one for each run time-step: normal, medium, and small. When a layer's mass falls below the threshold for the the small run time-step, the model removes the layer.
Just as the normal run time-step divides evenly into the data time-step, each of the two shorter run time-steps must divide evenly into the next larger run time-step (medium into normal, small into medium). And like the normal time- steps, the input data for medium and small time-steps are linearly interpolated from the input records.
Because the mass thresholds will be reached at different times over the DEM grid, the model solution of the energy balance at a given time-step may require different run time-steps over the grid. This improves model efficiency, requiring additional iterations only for those grid cells where the mass is below a critical threshold.
Outputs:
The model writes a pair of output images at the end of the model run, unless the output frequency option (-O) is specified. Output images are a 10-band energy and mass flux image, and a 9-band snow condition image. If the "-O" option is specified, a pair of output images can be generated at a frequency up to one per input image. Typically, however, output is generated at a lower frequency than input. For example if input data time-step is 3 hrs (180 min), and a daily output is required, then the output frequency is set at "8" (1 pair of output images for every 8 input images).
Energy & mass flux image (10-band):
R_n = average net all-wave rad (W/m^2)
H = average sensible heat transfer (W/m^2)
L_v_E = average latent heat exchange (W/m^2)
G = average snow/soil heat exchange (W/m^2)
M = average advected heat from precip. (W/m^2)
delta_Q = average sum of e.b. terms for snowcover (W/m^2)
E_s = total evaporation (kg, or mm/m^2)
melt = total melt (kg, or mm/m^2)
ro_predict = total predicted runoff (kg, or mm/m^2)
cc_s = snowcover cold content (energy required to
bring snowpack's temperature to 273.16K)
(J/m^2)
Note: The averages are mean values since the last energy & mass output image; totals are since the last energy & mass output image; If the "-O" option is not set, averages and totals are for the entire run.
Snow conditions image (9-band):
z_s = predicted depth of snowcover (m)
rho = predicted average snow density (kg/m^3)
m_s = predicted specific mass of snowcover (kg/m^2)
h2o = predicted liquid H2O in snowcover (kg/m^2)
T_s_0 = predicted temperature of surface layer (C)
T_s_l = predicted temperature of lower layer (C)
T_s = predicted average temp of snowcover (C)
z_s_l = predicted lower layer depth (m)
h2o_sat = predicted % liquid h2o saturation
norm-tstep is the normal run time-step. It must divide the data time-step evenly (default: 60 min or the data time-step, whichever is smaller).
med-tstep is the medium run time-step. It must divide the normal run time-step evenly (default: 15 min or the normal time-step, whichever is smaller).
sm-tstep is the small run time-step. It must divide the medium run time-step evenly (default: 1 min).
If a layers mass is below med-threshold, the model divides each medium run time-step into small run time- steps (default 10 kg/m^2).
If a layers mass is below sm-threshold, the model considers the layer non-existent, i.e., it removes the layer (default 1 kg/m^2).
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Anderson, E.A., 1976. A point energy and mass balance model of a snow cover. NWS Technical Report 19, National Oceanic and Atmospheric Administration, Washington, DC, 150p.
Morris, E.M., 1982. Sensitivity of the European Hydrological System snow models. In: Hydrological Aspects of Alpine and High-Mountain Areas, J.W. Glen, ed., International Association of Hydrological Sciences, Wallingford, UK, IAHS-AIHS Publication 138, pp 221-231.
Marks, D., 1988. Climate, Energy Exchange, and Snowmelt in Emerald Lake Watershed, Sierra Nevada. PhD Thesis, Departments of Geography and Mechanical Engineering, University of California Santa Barbara, CA, 158p.
Marks, D., J. Dozier, and R.E. Davis, 1992. Climate and energy exchange at the snow surface in the alpine region of the Sierra Nevada: 1. Meteorological measurements and monitoring. Water Resources Research, vol. 28, no. 11, pp. 3029-3042.
Marks, D., and J. Dozier, 1992. Climate and energy exchange at the snow surface in the alpine region of the Sierra Nevada: 2. Snow cover energy balance. Water Resources Research, vol. 28, no. 11, pp. 3043-3054.
Garen, D.C., and D. Marks, 1996. Spatially distributed snow modelling in mountainous regions: Boise River application. In: HydroGIS `96: Application of Geographic Information Systems in Hydrology and Water Resources Management, IAHS Publication No. 235, pp. 421-428.
Van Heeswijk, M., J. Kimball, and D. Marks, 1996. Simulation of water available for runoff in clearcut forest openings during rain-on-snow events in the western Cascase Range of Oregon and Washington. USGS Water- Resources Investigations Report 95-4219, Tacoma, Washington, 67pp.
Marks, D., J. Kimball, and D. Tingey, 1997. The sensitivity of snowmelt processes to climate conditions and forest cover during rain-n-snow: A study of the 1996 Pacific Northwest flood. Submitted to Hydrological Processes).
Marks, D., J. Domingo, D. Susong, and D. Garen, 1997, A topographically distributed energy balance snowmelt model. (submitted to Water Resources Research).
Susong, D., D. Marks, D. Garen, and J. Mason, 1997. Application of an energy-balance snowmelt model to estimate ground-water recharge in a mountain basin under varying climate conditions. (submitted to Hydrological Processes).