Difference between revisions of "Continuous:Snowfall Accumulation and Melting"

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When GSSHA is run in the '''LONG_TERM''' simulation mode, snowfall accumulation and melting is simulated.  Because the CASC2D model has no explicit way to account for the seasonal variability in hydrologic response of watersheds its appropriate use has been limited to periods where seasonal effects can largely be ignored, and has most typically been applied during the summer growing season (Senarath et al., 2000; Downer et al., 2002a).  An energy balance method of estimating snowfall accumulation and melting has been added to the GSSHA model to increase its utility in regions with significant snowfall.  This method is admittedly simple and other factors, soil freezing, change in overland roughness, etc, are not yet considered.  This is an area of active research and model development at ERDC.
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[[Image:MyCoolSnowJPG.jpg]]<br>
  
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Snowfall has a large impact on hydrologic fluxes because snowfall is normally stored for a significant period of time in the snowpack and is later released as melt water.  In many parts of the world melt of the snow cover is the single most important event of the water year (Gray and Prowse, 1993).  Because snowfall accumulation and subsequent melting can have such a large influence in hydrologic response of a watershed, it is important to simulate these processes.  The purpose of the snowfall accumulation and melting routine is to allow an accounting of these processes with the intent to differentiate between precipitation that is rainfall that will immediately infiltrate, pond and runoff or evaporate, and snow and ice that accumulates and significantly alters the timing of hydrologic fluxes.  Precipitation freezing and snowpack melting can be modeled during long-term simulations when hourly hydrometeorological data values of air temperature (''T<sub>a</sub>''), relative humidity (''r<sub>h</sub>''), wind speed (''U'') barometric pressure (''P<sub>a</sub>'') and cloud cover, are required inputs.
+
Snow melt is the single most important event of the water year in many parts of the world (Gray and Prowse, 1993).  Snow accumulation and melt are both spatially heterogeneous, thus distributed domains often give more potential for addressing a variety of real world problems (Kirnbauer, Bloeschl et al. 1994). When GSSHA is run in the '''LONG_TERM''' simulation mode, snowfall accumulation and melt are automatically simulated, with the hydrologic response being a combination of the multiple other processes (infiltration, overland flow, groundwater, etc.) utilized within GSSHA.  GSSHA employs multiple snow model options to use depending on available data and the objective of the study.  These models will be discussed below.
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Because of the distributed domain, the model can also account for '''[[Orographic Effects]]'''.
  
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Anytime the air temperature is below 0&deg; C during precipitation, the precipitation is assumed to be snow or ice that will accumulate on the land surface.  At air temperatures below 0&deg; C, precipitation is nearly always snowfall (Gray and Prowse, 1993). If snow is already present in a cell, the new snow accumulation is added to the existing accumulated snow.  While precipitation in the GSSHA model is distributed over the land surface, the effects of vegetation, elevation, and wind on the spatial distribution of snowfall are ignored.
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Within GSSHA, the snow pack consists of a single layer in each cell.  While multi-layer models have certain advantages - such as time variations of liquid water content (Bloschl & Kirnbauer 1991), interflow within the snow pack layers due to ice sheets, and avalanche modeling (Colbeck 1991) - the required data to populate model such models on a watershed level is currently unrealistic in most basins. Multi-layer snow models are typically deployed at the site-scale, where spatially-close data is available.  The methods used in GSSHA require only the standard precipitation, Chapter 6, and hydrometeorological data, Chapter 9.5, required for any long term continuous simulation in GSSHA, and are readily available from a variety of sources.  While optional inputs are possible, the model can produce accurate results with no additional inputs other than standard precipitation and hydrometeorological inputs. The methods currently used in GSSHA to simulate snow accumulation and melt can be found here [[media:Snow_TN.pdf|Follum and Downer 2013]]  <br>
  
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Snowmelt models use either an energy balance or a temperature-index method.  Physically-based systems are recommended for short term forecasts (Gray and Prowse, 1993), which are needed for hydrologic modeling.  In the energy budget model the amount of heat available is applied to the snowpack and the amount of meltwater is calculated.  The simplest representation of the snowpack is used; each 80 calories of heat added to the snowpack results in the release of 1 cm<sup>3</sup> of meltwater (Linsley et al., 1982, Gray and Prowse, 1993).  This method ignores complex snowpack behavior, such as ripening of the snowpack and refreezing of meltwater.  Hourly values of hydrometeorological variables allow both seasonal and diurnal variations in climatic conditions to be included in the heat balance.
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<br><br>
  
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The amount of heat, Q (cal cm<sup>-2</sup> hr<sup>-1</sup>) available is computed from the components of the energy balance.  In GSSHA the following components are accounted for:
 
  
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''Q<sup>*</sup> - net radiation (in - out),
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'''Snow Related Cards for the GSSHA Project File'''<br>
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''Q<sub>v</sub>'' - heat in precipitation,  
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No additional input cards are required to simulate snow accumulation, melt, and meltwater routing.  The default is for precipitation to be added to the snowpack anytime the air temperature, as specified by the hourly input values, is below 0 C.  Melt occurs according to the hybrid energy balance method, as described below.  Flow through the snow pack and to the overland occurs in waves.  Overland routing will ignore the snow pack.  All of these defaults can be altered as described below.<br><br>
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''Q<sub>e</sub>'' - heat transferred by sublimation and evaporation, and 
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'''[[Snow Card Inputs - Optional]]'''<br>
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''Q<sub>h</sub>'' - sensible heat transfer due to turbulence.
 
  
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For non-precipitation periods the net radiation is typically the dominant source of energy for melting of the snowpack (Gray and Prowse, 1993).  The net radiation is computed using Stephan-Boltzman’s law, with the assumptions that incoming radiation can be computed from the ambient temperature, ''T<sub>a</sub>''  (C), and outgoing radiation is computed assuming the snowpack is at 0&deg; C (Bras, 1990):
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 +
'''GSSHA Snow Accumulation'''<br>
 +
Precipitation accumulates as snow when Air Temperature is less than PXTEMP, where PXTEMP is the temperature (&deg;C) at which precipitation is considered snow (Default of 0&deg;C).  PXTEMP was omitted from Follum & Downer (2013) in error, but included in Follum et al. (2015). <br>
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Because gaging systems often underestimate the amount of precipitation fallen in the form of snow, two multiplication factors are applied to the gage measurement of precipitation (P<sub>x</sub>) to correct the precipitation of newly fallen snow (P<sub>n</sub>), Equation 6.  The snow adjustment factor (SCF) is considered a calibration parameter while the fraction of precipitation in the form of snow (f<sub>s</sub>) is considered constant at 1.0 when temperature are at or below 0&deg; C, and 0.0 when above 0&deg; C.<br>
  
 
{|  
 
{|  
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|  
 
:  
 
:  
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| width=550 | ''Q<sup>*</sup> = 49.56 x 10-10(''T<sub>a</sub>'' + 273)4 – 27 || (92)
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| width=550 | ''P<sub>n</sub> = P<sub>x</sub> * f<sub>s</sub> * SCF || (6)
 
|}
 
|}
  
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Precipitation falling on the snowpack at temperatures above 0&deg; transmits the difference in heat between the raindrop and the snowpack.  Assuming the snowpack is at 0&deg; C and the rainfall is a ambient temperature the difference in heat energy is:
 
  
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{|
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If snowfall occurs, a warning will be printed to the screen and to the Summary file.  When snow accumulation occurs the amount of snow in the watershed is reported at the beginning and end of each event summary in the Summary file.
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|-
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<br><br>
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|
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:
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| width=550 | ''Q<sub>v</sub>'' = ''IT<sub>a</sub>'' || (93)
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'''GSSHA Melt Algorithms'''<br>
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|}
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  '''[[Energy Balance]]''' (EB)<br>
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  '''[[Temperature Index]]''' (TI)<br>
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  '''[[Hybrid Energy Balance]]''' (HY) Default <br>
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  '''[[Radiation-derived Temperature Index]]''' (RTI) <br>
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<br><br>
 +
 
 +
 
 +
'''Adjustment of Atmospheric Radiation Fluxes within the Snow Model'''<br>
 +
GSSHA currently employs methods to account for both longwave and shortwave radiation in each cell.  Longwave radiation is mainly a function of temperature, clouds, and atmospheric emissivity, while the shortwave radiation calculations take into consideration albedo, topographic shading, aspect of the terrain in relation to the sun, albedo of snow as it ages, atmospheric absorption and reflection, clouds, and vegetation.  The calculated longwave and shortwave radiation values are then used within the EB and HY models to simulate the melting of snow.
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In order to account for the '''[[Effects of Shading and Aspect]]''' on the available energy to melt snow, GSSHA employs a method that reduces the amount of energy available to melt snow when the '''[[Energy Balance]]''' or '''[[Hybrid Energy Balance]]''' snow melt algorithms are used.  The '''[[Effects of Shading and Aspect]]''' are set as a default within GSSHA and are only used for snow fall, but are currently being examined in the Evapo-Transpiration methods as well.  Shading and Aspect angles are not accounted for when raster-based HMET data is input into the model (http://www.gsshawiki.com/Distributed_HMET_Data).
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<br><br>
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'''GSSHA Melt-Water Transport Algorithms'''<br>
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Once melt occurs within the snow pack the subsequent melt-water is routed through the snow pack and then to other hydrologic processes within GSSHA (i.e. runoff, infiltration, evaporation, etc.) using melt-water transport (MWT) algorithms.  GSSHA currently employs both a '''[[Vertical MWT]]''' and '''[[Lateral MWT]]''' algorithm.<br>
  
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where:  ''I'' is the precipitation intensity (cm/hr).  Heats transferred from evaporation, sublimation, and turbulent energy are usually much smaller parts of the heat balance and are ignored in many computations (Gray and Prowse, 1993).  However, convective exchange can be significant (Linsley et al., 1982).  If the dew point is below the temperature of the snowpack, assumed to be 0&deg; C, then condensation occurs and heat is transferred (Linsley et al., 1982; Gray and Prowse, 1993).  Estimates of turbulent and latent heat exchange are usually based on measurements of air temperature, humidity, and wind speed (Gray and Prowse, 1993).  During periods of melt, the temperature of the snowpack is 0&deg; C and the saturated vapor pressure (es) is 6.11 mb (Linsley et al., 1982). The latent heat exchange is computed assuming the latent heat of evaporation/condensation is 600 cal g<sup>-1</sup> (Anderson, 1968) and a water density of 1 g cm<sup>-3</sup> as:
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Within a grid cell, a homogeneous snow pack assumption is utilized in GSSHA to alleviate computational and data limitation concerns associated with a heterogeneous assumption (which would include flow fingers).  Equivalent properties for the homogeneous snow pack are often assumed (Colbeck 1979).  In GSSHA, each cell has its own snow pack properties - namely depth, density, hydraulic conductivity, saturation, and effective porosity - derived using the SNAP model (Albert & Krajeski 1998).<br>
  
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{|
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Flow is considered a porous medium, therefore a form of Darcy's Equation
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|-
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(http://en.wikipedia.org/wiki/Darcy%27s_law) is used to determine flux rates through the snow pack.  '''[[Vertical MWT]]''' through the snow pack is considered unsaturated flow, while '''[[Lateral MWT]]''' between the ground surface and the bottom of the snow pack is considered saturated flow.  To simulate the flow within the snow pack, accurately capturing the saturation within the pack is vital because the saturation affects both the hydraulic conductivity and effective porosity of the snow pack.  GSSHA currently uses the SNAP model to determine the saturation, saturated / unsaturated hydraulic conductivity, and effective porosity of the snow pack in each grid cell.  Water is routed to the overland through the snow pack in a series of waves calculated from these parameters.
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|
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<br><br>
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:  
 
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| width=550 | [[Image:Equation094.gif]] || (94)
 
−
|}
 
  
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where:  ''r<sub>h</sub>'' is the relative humidity (%), &fnof;(V) = 0.0002 ''U'' (km/hr) (Anderson 1978), where ''U''U is the wind speed (m s<sup>-1</sup>).  Employing the Bowen ratio (Bowen, 1926) the sensible heat transfer is computed assuming the snow pack temperature is at 0&deg; C, latent heat of evaporation is 600 cal g<sup>-1</sup>, density of water is 1 g cm<sup>-3</sup>, and the Bowen ratio coefficient is 0.61 x 10-3 C<sup>-1</sup> (Bras, 1990) as:
 
  
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{|
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'''GSSHA Snow Depth and Density'''<br>
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|-
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Snow depth and density are simulated in GSSHA independent of what melting algorithm is used. The depth and density of snow is calculated hourly by incorporating the SNAP model (Albert and Krajeski 1998) code into GSSHA.  Information related to SWE, snow depth, density, snow saturation, effective porosity, and hydraulic conductivity are exchanged between the two models.  The SNAP model algorithms are used to calculate all the parameters except SWE.<br>
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|
 
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:
 
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| width=550 | [[Image:Equation095.gif]] || (95)  
 
−
|}
 
  
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where: ''P<sub>a</sub>'' is the atmospheric pressure (mb).
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According to the SNAP formulation, the snow density changes in response to snow accumulation, settlement, and melt, and is computed either with the snow depth predictions, or as updated by the user (Albert and Krajeski 1998). GSSHA currently does not allow the user to update the snow density as a calibration parameter, leaving the snow density to be calculated based on the snow depth predictions of the SNAP alorithms with no calibrated parameters.  For more information on the SNAP model the interested reader is encouraged to review Albert & Krajeski (1998).  For more information on the depth prediction equations used within the SNAP model the interested reader is encouraged to review Anderson (1973), Jordan (1991), and Jordan (1998).<br>
  
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For non-precipitation periods, the energy budget is calculated at an hourly time step (same as the standard hydrometeorological data), so diurnal changes in energy inputs are included in the model formulation.   During precipitation periods the energy budget is updated each overland flow routing time step (generally less than 5 minutes).
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The snow depth simulations from Follum & Downer (2012) show that when the SWE is simulated accurately the SNAP model reasonably simulates the snow depth.  The results show that the SNAP model may slightly overestimate snow depth when compared to observed data [[media:Snow_TN.pdf|Follum and Downer 2013]].
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<br><br>
  
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The described snowfall accumulation and melting calculations proceed anytime the LONG_TERM simulation option is chosen and hourly air temperatures are provided.  If snowfall occurs, a warning will be printed to the screen and to the Summary file.  When snow accumulation occurs the amount of snow in the watershed is reported at the beginning and end of each event summary in the Summary file.
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'''Overland Routing with Snow'''<br>
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During overland flow routing, as described in Section 5.2, GSSHA ignores snow in an overland flow cell unless the user specfies to route the flow through the snow using Darcy's law with the project card '''ROUTE_LAT_SNOW'''.  Routing through the snow as free surface flow may cause simulated flows to be higher and arrive earlier than measured flows strongly influenced by the snowpack.  When this card is specifed, the flow in cells with a snowpack will be computed using Darcy's law.  The default is to use the SNAP calculated vertical hydrualic conductivity (K) for computation of flow through the snow in the lateral flow computations.  The alternative is to specify the lateral hydraulic conductivity with the '''SNOW_DARCY''' card, which is followed with a value of hydraulic conductivity (m/s).  References report hydraulic conductivities of snow on the order of 1 cm/s (0.01 m/s) (Colbeck and Anderson, 1982 for example).  The current implementation of the SNAP model produces simliar values but as of v6.2 the implementation of SNAP in GSSHA is considered experimental and is not currently reccomended and it is reccomended that the user specify the lateral hydrualic conductivity of the snow using the '''SNOW_DARCY''' card.
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<br><br>
  
 
<noinclude>
 
<noinclude>
 
{{Nav|Nav9}}
 
{{Nav|Nav9}}
 
</noinclude>
 
</noinclude>

Latest revision as of 19:30, 3 April 2017

MyCoolSnowJPG.jpg

Snow melt is the single most important event of the water year in many parts of the world (Gray and Prowse, 1993). Snow accumulation and melt are both spatially heterogeneous, thus distributed domains often give more potential for addressing a variety of real world problems (Kirnbauer, Bloeschl et al. 1994). When GSSHA is run in the LONG_TERM simulation mode, snowfall accumulation and melt are automatically simulated, with the hydrologic response being a combination of the multiple other processes (infiltration, overland flow, groundwater, etc.) utilized within GSSHA. GSSHA employs multiple snow model options to use depending on available data and the objective of the study. These models will be discussed below.

Because of the distributed domain, the model can also account for Orographic Effects.

Within GSSHA, the snow pack consists of a single layer in each cell. While multi-layer models have certain advantages - such as time variations of liquid water content (Bloschl & Kirnbauer 1991), interflow within the snow pack layers due to ice sheets, and avalanche modeling (Colbeck 1991) - the required data to populate model such models on a watershed level is currently unrealistic in most basins. Multi-layer snow models are typically deployed at the site-scale, where spatially-close data is available. The methods used in GSSHA require only the standard precipitation, Chapter 6, and hydrometeorological data, Chapter 9.5, required for any long term continuous simulation in GSSHA, and are readily available from a variety of sources. While optional inputs are possible, the model can produce accurate results with no additional inputs other than standard precipitation and hydrometeorological inputs. The methods currently used in GSSHA to simulate snow accumulation and melt can be found here Follum and Downer 2013




Snow Related Cards for the GSSHA Project File
No additional input cards are required to simulate snow accumulation, melt, and meltwater routing. The default is for precipitation to be added to the snowpack anytime the air temperature, as specified by the hourly input values, is below 0 C. Melt occurs according to the hybrid energy balance method, as described below. Flow through the snow pack and to the overland occurs in waves. Overland routing will ignore the snow pack. All of these defaults can be altered as described below.

Snow Card Inputs - Optional


GSSHA Snow Accumulation
Precipitation accumulates as snow when Air Temperature is less than PXTEMP, where PXTEMP is the temperature (°C) at which precipitation is considered snow (Default of 0°C). PXTEMP was omitted from Follum & Downer (2013) in error, but included in Follum et al. (2015).

Because gaging systems often underestimate the amount of precipitation fallen in the form of snow, two multiplication factors are applied to the gage measurement of precipitation (Px) to correct the precipitation of newly fallen snow (Pn), Equation 6. The snow adjustment factor (SCF) is considered a calibration parameter while the fraction of precipitation in the form of snow (fs) is considered constant at 1.0 when temperature are at or below 0° C, and 0.0 when above 0° C.

 Pn = Px * fs * SCF (6)


If snowfall occurs, a warning will be printed to the screen and to the Summary file. When snow accumulation occurs the amount of snow in the watershed is reported at the beginning and end of each event summary in the Summary file.


GSSHA Melt Algorithms

 Energy Balance (EB)

 Temperature Index (TI)

 Hybrid Energy Balance (HY) Default 

 Radiation-derived Temperature Index (RTI)




Adjustment of Atmospheric Radiation Fluxes within the Snow Model
GSSHA currently employs methods to account for both longwave and shortwave radiation in each cell. Longwave radiation is mainly a function of temperature, clouds, and atmospheric emissivity, while the shortwave radiation calculations take into consideration albedo, topographic shading, aspect of the terrain in relation to the sun, albedo of snow as it ages, atmospheric absorption and reflection, clouds, and vegetation. The calculated longwave and shortwave radiation values are then used within the EB and HY models to simulate the melting of snow.

In order to account for the Effects of Shading and Aspect on the available energy to melt snow, GSSHA employs a method that reduces the amount of energy available to melt snow when the Energy Balance or Hybrid Energy Balance snow melt algorithms are used. The Effects of Shading and Aspect are set as a default within GSSHA and are only used for snow fall, but are currently being examined in the Evapo-Transpiration methods as well. Shading and Aspect angles are not accounted for when raster-based HMET data is input into the model (http://www.gsshawiki.com/Distributed_HMET_Data).



GSSHA Melt-Water Transport Algorithms
Once melt occurs within the snow pack the subsequent melt-water is routed through the snow pack and then to other hydrologic processes within GSSHA (i.e. runoff, infiltration, evaporation, etc.) using melt-water transport (MWT) algorithms. GSSHA currently employs both a Vertical MWT and Lateral MWT algorithm.

Within a grid cell, a homogeneous snow pack assumption is utilized in GSSHA to alleviate computational and data limitation concerns associated with a heterogeneous assumption (which would include flow fingers). Equivalent properties for the homogeneous snow pack are often assumed (Colbeck 1979). In GSSHA, each cell has its own snow pack properties - namely depth, density, hydraulic conductivity, saturation, and effective porosity - derived using the SNAP model (Albert & Krajeski 1998).

Flow is considered a porous medium, therefore a form of Darcy's Equation (http://en.wikipedia.org/wiki/Darcy%27s_law) is used to determine flux rates through the snow pack. Vertical MWT through the snow pack is considered unsaturated flow, while Lateral MWT between the ground surface and the bottom of the snow pack is considered saturated flow. To simulate the flow within the snow pack, accurately capturing the saturation within the pack is vital because the saturation affects both the hydraulic conductivity and effective porosity of the snow pack. GSSHA currently uses the SNAP model to determine the saturation, saturated / unsaturated hydraulic conductivity, and effective porosity of the snow pack in each grid cell. Water is routed to the overland through the snow pack in a series of waves calculated from these parameters.


GSSHA Snow Depth and Density
Snow depth and density are simulated in GSSHA independent of what melting algorithm is used. The depth and density of snow is calculated hourly by incorporating the SNAP model (Albert and Krajeski 1998) code into GSSHA. Information related to SWE, snow depth, density, snow saturation, effective porosity, and hydraulic conductivity are exchanged between the two models. The SNAP model algorithms are used to calculate all the parameters except SWE.

According to the SNAP formulation, the snow density changes in response to snow accumulation, settlement, and melt, and is computed either with the snow depth predictions, or as updated by the user (Albert and Krajeski 1998). GSSHA currently does not allow the user to update the snow density as a calibration parameter, leaving the snow density to be calculated based on the snow depth predictions of the SNAP alorithms with no calibrated parameters. For more information on the SNAP model the interested reader is encouraged to review Albert & Krajeski (1998). For more information on the depth prediction equations used within the SNAP model the interested reader is encouraged to review Anderson (1973), Jordan (1991), and Jordan (1998).

The snow depth simulations from Follum & Downer (2012) show that when the SWE is simulated accurately the SNAP model reasonably simulates the snow depth. The results show that the SNAP model may slightly overestimate snow depth when compared to observed data Follum and Downer 2013.

Overland Routing with Snow
During overland flow routing, as described in Section 5.2, GSSHA ignores snow in an overland flow cell unless the user specfies to route the flow through the snow using Darcy's law with the project card ROUTE_LAT_SNOW. Routing through the snow as free surface flow may cause simulated flows to be higher and arrive earlier than measured flows strongly influenced by the snowpack. When this card is specifed, the flow in cells with a snowpack will be computed using Darcy's law. The default is to use the SNAP calculated vertical hydrualic conductivity (K) for computation of flow through the snow in the lateral flow computations. The alternative is to specify the lateral hydraulic conductivity with the SNOW_DARCY card, which is followed with a value of hydraulic conductivity (m/s). References report hydraulic conductivities of snow on the order of 1 cm/s (0.01 m/s) (Colbeck and Anderson, 1982 for example). The current implementation of the SNAP model produces simliar values but as of v6.2 the implementation of SNAP in GSSHA is considered experimental and is not currently reccomended and it is reccomended that the user specify the lateral hydrualic conductivity of the snow using the SNOW_DARCY card.


GSSHA User's Manual

9 Continuous
9.1     Computation of Evaporation and Evapo-transpiration
9.2     Computation of Soil Moisture
9.3     Hydrometeorological Data
9.4     Snowfall Accumulation and Melting
9.5     Sequence of Events During Long-Term Simulations


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