Snow Melt Model

The Snow Melt Model operates by affecting rainfall before it reaches the runoff surfaces. When temperature falls below the dividing temperature between snow and rain (defined in the applicable snow parameters property sheet), the rainfall profile is treated as snow.

The Snow Melt Model used in InfoWorks ICM is based on the SWMM5 continuous simulation model. This topic summarises the equations used in InfoWorks ICM to model snow melt. For a detailed description, see the SWMM5 Users Manual.

The parameters affecting the modelling of snowmelt are defined in the following places:

• Snow Parameters Property Sheet: global snow parameters are defined on the property sheets for InfoWorks Snow Parameters and SWMM Snow Parameters
• Subcatchments Grid: snow pack parameters are defined on the Snow Pack Grid Window or property sheet. A snow pack is associated with a subcatchment on the Subcatchment Grid Window or property sheet.
• Rainfall Event Editor: rainfall profile, temperature profile and wind profile, and for InfoWorks networks only, initial snow conditions, are defined in the Rainfall Event Editor.

Melt rate, snow depth and free water depth results are available for subcatchments containing snow packs.

Note that all snow depths are defined as depth of water equivalent.

Runoff Surfaces InfoWorks networks

When modelling snow melt the subcatchment runoff surfaces are categorised into three types:

• Impervious
• Impervious (ploughable)
• Pervious

Subcatchment runoff surfaces of type impervious may be divided into Impervious and Impervious (ploughable). The proportion of each impervious surface that is ploughable is defined by the Fraction of impervious area ploughable field in the applicable Snow Pack object.

Subcatchment runoff surfaces of type pervious or unknown are categorised as pervious for the snow melt  model.

Melt coefficients, base temperature (above which melt will occur), and free water capacity for each type of snow surface are specified in the Snow Pack object.

The fraction of snow redistributed within the subcatchment and out of the subcatchment is also defined in the Snow Pack object. Redistribution (ploughing) of snow takes place once the snow depth on the ploughable surface reaches the Depth at which snow removal begins.

Calculation of Snow Melt

The Snow Melt Model operates by affecting rainfall before it reaches the runoff surfaces. When temperature falls below the dividing temperature between snow and rain (defined in the applicable snow parameters), the rainfall profile is treated as snow.

A melt rate is calculated for each surface type. For impervious surfaces, the melt rate is the area weighted average of the melt rates from the ploughable and non-ploughable impervious areas.

During periods when the temperature is below the base temperature of the snow pack surfaces, melt does not occur. Snowfall builds up snow depth.

When the snow depth is greater than zero and the temperature is above the base temperature of the snow pack surfaces, melt will only occur when the cold content of the snow pack is greater than or equal to zero (see Equation 7). Runoff can only occur when the free water holding capacity of the snow pack has been filled (see Equation 10).

Rainfall, Wind and Temperature Profiles

The time varying profiles affecting snow melt are defined in the Rainfall Event Editor.

• Rainfall: When temperature falls below the Dividing temperature between snow and rain (defined n the appropriate network's Snow Parameters Property Sheet), the rainfall profile is treated as snow. (A snow catch factor can be defined in the Rainfall properties to account for snowfall that may not be captured by rain gauges.)
• Wind: The wind profile affects the rate of snow melt in wet periods (see Equation 3). If a wind profile is not is not defined, a wind speed of 0 km/h is assumed.
• Temperature: The temperature profile affects the rate of snow melt (see Equations 1 and 3) and the change in cold content of the snow pack (see Equation 8). If a temperature profile is not defined a temperature of 21 °C is assumed.

Defining Seasonal Variation in Melt Rate

A seasonal variation in melt rate can be defined by setting different minimum and maximum melt coefficients in the Snow Pack object.

Minimum melt coefficients are assumed to occur on December 21st and maximum melt coefficients on June 21st.

Sinusoidal interpolation is used to determine a melt rate coefficient for the current day (see Equation 2).

Areal Depletion Curves

Snow does not melt uniformly over the surface of the subcatchment; as melt occurs, the area of the subcatchment covered by snow is reduced.

The Areal Depletion Curves (set up in the appropriate network's snow parameters property sheet) define the relation between the area of the subcatchment that remains snow covered and snow pack depth. The curves are defined by 10 equal increments of relative depth ratio between 0 and 0.9. (Relative depth ratio is the ratio of the current depth of snow to the depth at which there is 100% areal coverage). A value for the fraction of area that remains snow covered is entered for each relative depth ratio.

The fraction of area that remains snow covered is used to adjust the calculation of snow depth (see Equation 7), cold content of the snow pack (see Equation 8 ) and net runoff (see Equation 11).

Equations

Snow Melt

There are two equations for snow melt. One for dry periods (i.e. no rainfall) and one for wet periods.

Snow Melt (in./hr) when there is no rainfall:

SMELT = DHM x (TA-TBase) (1) where: TA= Air Temperature (°F) defined as Temperature profile in Rainfall Event Editor TBase= Base Melt Temperature (°F) defined in Snow Pack object DHM = melt factor (in./hr per °F)   DHM is calculated as: DHM = (DHMAX + DHMIN)/2 + (DHMAX-DHMIN)/2 x[pi/182(D-81)] (2) where: DHMAX= Maximum melt coefficient (in./hr per °F) defined in Snow Pack object DHMIN= Minimum melt coefficient (in./hr per °F) defined in Snow Pack object D = number of the day of the year where 1 = 1st January (when using relative times 00/00/00 00:00 is taken to be day 1)

Snow Melt (in./hr) when there is rainfall:

SMELT = (TA- 32)x(0.001167 + SGAMMA x UADJ + 0.007 x PREC) + 8.5 x UADJ x (EA - 0.18) (3) where: TA = Air Temperature (°F) defined as Temperature profile in Rainfall Event Editor. (If a temperature profile is not defined, a temperature of 21 °C is assumed.) SGAMMA = 7.5 x GAMMA (in. Hg per °F) GAMMA = 0.000359 x PA where PA = atmospheric pressure (in. Hg) UADJ = wind speed function (in. / in. Hg per hr) PREC = rainfall intensity (in./hr) EA = saturation vapor pressure at air temperature (in. Hg)   PA is calculated as: PA = 29.9 - 1.02 (z/1000) + 0.0032 x (z/1000)2.4 (4) where: z = Catchment Elevation (ft) defined in the applicable InfoWorks Snow Parameters or SWMM Snow Parameters property sheet   UADJ is calculated as: UADJ = 0.006 x u (5) where: u = Wind Speed defined as Wind profile in Rainfall Event Editor. (If a wind profile is not defined, a wind speed of 0 km/h is assumed.)   EA is calculated as: 8.1175 x 106 exp [-7701.544/(TA+ 405.0265)] (6)

Snow Depth

Once a melt rate has been calculated, the depth of snow is adjusted by multiplying the melt rate by the fraction of area that is snow covered:

When melt occurs, snow depth of the snow pack at time, t, is calculated as: WSNOW(t) = WSNOW(t-1) - SMELT x ASC (7) Where: WSNOW(t-1) = snow depth at previous timestep SMELT= Melt rate (ft/sec) See Equations 1 and 3. ASC = Fraction of area that is snow covered, determined from Areal Depletion Curves

Cold Content of the Snow Pack

Melt can only occur when the cold content of the snow pack is greater than or equal to zero.

The cold content of the snow pack at time, t, is calculated as:

COLDC(t) = COLDC(t-1) + RNM x DHM x (ATI - TA) X Dt x ASC (8) where: COLDC(t-1)= Cold content at previous timestep RNM = Negative melt ratio defined in the applicable InfoWorks Snow Parameters or SWMM Snow Parameters property sheet DHM = Melt coefficient (ft/sec per °F) see Equation 2 TA= Air Temperature (°F) ATI = Antecedent Temperature Index (°F) Dt= Timestep (sec) ASC = Fraction of area that is snow covered, determined from Areal Depletion Curves   During snow fall ATI is reset to air temperature. When air temperature < Base Temperature ATI is calculated as: ATI(t) = ATI(t-dt) +TIW x (TA(t) - ATI(t-dt)) (9)   where: TIW = Antecedent Temperature Index Weight defined in the applicable InfoWorks Snow Parameters or SWMM Snow Parameters property sheet   When air temperature >= base temperature, ATI is reset to Base Temperature defined in Snow Pack object.

Free Water Capacity

Runoff can only occur when the free water holding capacity of the snow pack has been filled.

The Free water holding capacity of the snow pack is calculated as:

FW = FWFRAC x WSNOW (10) where: FWFRAC= Fraction of free water capacity WSNOW= snow depth (see Equation 7)

Net runoff

The Net runoff onto the surface of the subcatchment is calculated as:

RI = ASC X SMELT + (1.0 - ASC) x RINE + fraction converted to immediate melt (11)   where: ASC = Fraction of area that is snow covered, determined from Areal Depletion Curves SMELT= Melt rate (ft/sec) See Equations 1 and 3. RINE = Rainfall intensity (ft/sec) defined in Rainfall Event Editor