This Hybrid snow method is based on the Radiation-derived Temperature Index (RTI) snow model (Follum et al., 2015; Follum et al., 2019). The Hybrid method improves upon the temperature index method by using estimates of air temperature, shortwave radiation, and longwave radiation at a grid cell to derive a radiation temperature which may better represent the energy fluxes into/out of the snow pack than air temperature alone. The HEC-HMS Hybrid snow method is inherently gridded (there is no banded implementation). Differences between the original RTI snow model and the Hybrid method in HEC-HMS are noted on this page.

Basic Concepts and Equations

Downwelling shortwave radiation ( $\begin{array}{l}SW \downarrow\end{array}$ ) is computed as:

1)	$\begin{array}{l}\displaystyle SW \downarrow = S_0 K_r K_a_t_m K_c K_v K_s K_t\end{array}$

where S₀ is the incident shortwave radiation and K_r, K_atm, K_c, K_v, K_s, and K_t are reduction factors for the distance from the earth to the sun, atmospheric scattering, slope and aspect of the terrain, and topographic shading, respectively. In the original RTI model, the incident shortwave radiation for each grid cell is adjusted by reduction factors for the distance from the earth to the sun, atmospheric scattering, absorption by clouds, vegetation, slope/aspect of the terrain, and topographic shading.

The current implementation of the Hybrid method within HEC-HMS does not include reduction factors for absorption by clouds or vegetation (i.e., K_c, Kv = 1).

The reduction in shortwave radiation due to atmospheric thickness, aerosols, and moisture is computed for each cell based on its elevation (Allen et al., 2005):

2)	$\begin{array}{l}\displaystyle K_a_t_m = 0.75 + 2*10^{-5} Elev_c\end{array}$

where Elev_c is the grid cell elevation.

Solar radiation can be blocked by nearby topography, such as when mountains shade valleys. The solar azimuth and zenith angles are used in combination with the terrain information to determine if a cell within the modeling domain blocks the line between the sun's location and another cell location.

The amount of downwelling shortwave radiation ( $\begin{array}{l}SW \downarrow _,_n_e_t\end{array}$ ) that is absorbed by the snow surface is:

3)	$\begin{array}{l}\displaystyle SW \downarrow _,_n_e_t = (1 - \alpha)SW \downarrow\end{array}$

where $\begin{array}{l}\alpha\end{array}$ is the surface albedo.

Radiation components included in the proxy temperatures Ta and Trad (Follum et al., 2015)

The snow surface temperature is computed using the Stefan-Boltzmann Law to relate radiated energy to temperature:

4)	$\begin{array}{l}\displaystyle T_r_a_d = \left[ \frac {LW _\downarrow + SW _\downarrow _n_e_t}{\epsilon_s_n_o_w \sigma} \right] ^ \frac{1}{4} - 273.15\end{array}$

where $\begin{array}{l}\epsilon_s_n_o_w\end{array}$ is the emissivity of snow (assumed to be 0.99) and $\begin{array}{l}\sigma\end{array}$ is the Stefan-Boltzmann Constant (5.6703728287 × 10^-8 kg s^-3 K^-4).

Precipitation is partitioned into rain and snow using the Rain Threshold Air Temperature and the Snow Threshold Air Temperature. When the air temperature is greater than or equal to the Rain Threshold Air Temperature, any precipitation is assumed to be rain. When the air temperature is less than or equal to the Snow Threshold Air Temperature, any precipitation is assumed to be snow. When the air temperature is between the two threshold temperatures, the amount of precipitation is partitioned between snowfall and rainfall based on the air temperature. The fractions of precipitation in the form of rain and snow are computed as:

5)	$\begin{array}{l}\displaystyle f_R = \frac {Rain Threshold Air Temperature - Air Temperature} {Rain Threshold Air Temperature - Snow Threshold Air Temperature}\end{array}$

6)	$\begin{array}{l}\displaystyle f_S = 1 - f_R\end{array}$

Melt occurs when the energy input into the snowpack overcomes the heat deficit. The change in heat deficit ( $\begin{array}{l}\Delta D_t\end{array}$ ) within the snowpack due to differences between the air and snow surface temperatures is calculated as:

7)	$\begin{array}{l}\displaystyle \Delta D_t = NMF (ATI - T_s_u_r)\end{array}$

where NMF is the negative melt factor, ATI is the Antecedent Temperature Index coefficient as calculated in Anderson (2006), and T_sur is the snowpack surface temperature, which is the lesser of T_a and freezing temperature (0°C).

8)	$\begin{array}{l}\displaystyle NMF = NMF_m_a_x \frac {dt}{6} \frac {M_f}{M_f_,_m_a_x}\end{array}$

where NMF_max is the Maximum Negative Melt Factor, M_f is the Melt Factor, and M_f,max is the maximum melt factor.

The original RTI snow model does not include a precipitation intensity condition (i.e., the algorithm only checks if precipitation has exceeded 1.5 mm in 6 hours).

When at least 1.5 mm of precipitation occurs during the previous 6 hours and the average hourly precipitation exceeds 0.25 mm/hr, an energy balance is used to calculate the amount of snow melt (M) with the assumption that snow surface temperature is 0°C, incoming solar radiation is negligible, and incoming longwave radiation is equal to black body radiation:

9)	$\begin{array}{l}\displaystyle M = \sigma * dt [(T_r_a_d + 273)^4 - 273^4] + 0.0125 * P * f_r * T_r + 8.5 f_u \frac{dt}{6} [(rh * e_s_a_t - 6.11) + 0.00057 P_a * T_a]\end{array}$

where f_u is the Wind Function, rh is the relative humidity, P_a is atmospheric pressure, and e_sat is the saturated vapor pressure.

When the precipitation accumulation and intensity conditions are not met, potential snow melt is computed as:

10)	$\begin{array}{l}\displaystyle M = \frac{MF}{6} (T_r_a_d - T_b_a_s_e) dt + 0.0125 * P * f_r * T_r\end{array}$

In the original RTI model, the melt factor is computed from a minimum and maximum melt factor and parameters that account for seasonal melt variation. In the HEC-HMS implementation, the melt factor is a user-specified parameter.

The snowpack heat deficit is updated and actual snow melt are calculated based on one of three conditions:

Condition	Actual melt	Heat deficit
$\begin{array}{l}M + LW - LWCSWE_t_-_1 - D_t - LWCD_t >= 0\end{array}$	$\begin{array}{l}M + LW - LWCSWE_t_-_1 - D_t - LWCD_t\end{array}$	0
$\begin{array}{l}LW + M - D_t > 0\end{array}$	0	0
Otherwise	0	$\begin{array}{l}D_t - M\end{array}$

where LW is the liquid water held by the snow, LWC is the Water Capacity, and SWE_t-1 is the snow water equivalent from the previous time step.

If the computed snow melt exceeds the available SWE, the melt is reduced to the available SWE.

Required Parameters

The Rain and Snow Threshold Air Temperatures are used to differentiate between precipitation falling as rain and snow, respectively. In particular, precipitation that falls at an air temperature above the Rain Threshold Temperature will occur purely as rain while precipitation that falls at an air temperature below the Snow Threshold Temperature will occur purely as snow. The Rain Threshold Air Temperature must always be greater than or equal to the Snow Threshold Air Temperature. Decreasing the Rain Threshold Air Temperature will cause more precipitation to fall purely as rain while increasing the Rain Threshold Air Temperature will cause less precipitation to fall purely as rain. Conversely, decreasing the Snow Threshold Air Temperature will cause less precipitation to fall purely as snow while increasing the Snow Threshold Air Temperature will cause more precipitation to fall purely as snow. These two parameters can be equivalent or differ by up to a few degrees.

The Base Temperature is the temperature above which snow begins to melt. This parameter typically has a value around the freezing temperature, but can vary by a few degrees. Decreasing the Base Temperature will cause snow melt to occur at colder temperatures while increasing the Base Temperature will require higher temperatures to cause snow melt.

Hybrid Snow Temperature Parameters

The Melt Factor is a coefficient used to calculate snow melt. As a result, it impacts the rate of snow melt. Increasing the Melt Factor will increase the rate of snow melt while decreasing the Melt Factor will decrease the rate of snow melt.

The Maximum Negative Melt Factor is a coefficient used to calculate the heat deficit. This parameter has a positive value despite its name. In order for snow melt to occur, the amount of energy in the snowpack has overcome the heat deficit. Therefore, increasing the Maximum Negative Melt Factor will increase the heat deficit and delay the initiation of snow melt. Decreasing the Maximum Negative Melt Factor will decrease the heat deficit and cause snow melt to initiate sooner.

As in the Temperature Index method, the ATI Coefficient is used to weight the previous time step's ATI in the computation of the current time step's ATI. Increasing the ATI will apply more weight to the previous time step's ATI.

The Wind Function is used to calculate the impediment of flow of vapor when the air temperature is warmer than the snowpack surface temperature. Increasing the Wind Function will increase snow melt and decreasing the Wind Function will decrease snow melt.

The Water Capacity defines the liquid water content above which water leaves the snowpack. Increasing the Water Capacity will delay the time at which water leaves the snowpack while decreasing the Water Capacity will delay the time at which water leaves the snowpack.

The following table presents units, a summary description, allowable values within HEC-HMS, and a recommended range for each of the aforementioned parameters.

Parameter Name	Units	Description	Allowable Range (min - max)	Recommended Range (min - max)
Rain Threshold Air Temperature	deg F deg C	Temperature above which precipitation falls as rain	-58.0 to 113.0 deg F -50.0 to 45.0 deg C	32.0 to 40.0 deg F 0.0 to 4.4 deg C
Snow Threshold Air Temperature	deg F deg C	Temperature above which precipitation falls as snow	-58.0 to 113.0 deg F -50.0 to 45.0 deg C	30.0 to 35.0 deg F -1.1 to 1.7 deg C
Base Temperature	deg F deg C	Temperature above which snow begins to melt	-148.0 to 113 deg F -100.0 to 45.0 deg C	30.0 to 35.0 deg F -1.1 to 1.7 deg C
Melt Factor	in/deg F-6 hr mm/deg C-6 hr	Coefficient used to calculate snow melt	2.19E-5 to 0.052 in/deg F-6 hr 0.001 to 2.4 mm/deg C-6 hr	0.001 to 0.01 in/deg F-6 hr 0.046 to 0.46 mm/deg C-6 hr
Maximum Negative Melt Factor	in/deg F-6 hr mm/deg C-6 hr	Coefficient used to calculate heat deficit	2.19E-5 to 0.052 in/deg F-6 hr 0.001 to 2.4 mm/deg C-6 hr	0.001 to 0.05 in/deg F-6 hr 0.046 to 2.28 mm/deg C-6 hr
ATI Coefficient	unitless	Controls how much weight is put on temperatures from previous time intervals when computing ATI	0.001 to 1.0	0.5 to 0.99
Wind Function	in/in Hg-6 hr mm/mb-6 hr	Used to calculate wind scour from snowpack	0.0013 to 1.33 in/in Hg-6 hr 0.001 to 1.0 mm/mb-6 hr	0.5 to 0.75 in/in Hg-6 hr 0.37 to 0.56 mm/mb-6 hr
Water Capacity	%	Liquid water content above which water leaves the snowpack	0.001 to 10 %	3.0 to 5.0 %

A Note on Parameter Estimation

Regardless of the source of information used to estimate initial parameter values, including the table presented above, all Hybrid snow parameters must be calibrated and validated.

Required Boundary Conditions

In addition to parameters, the Hybrid snow method requires the following meteorologic boundary conditions:

Tutorials describing example applications of this snowmelt method, including parameter estimation and calibration, can be found here: Calibrating Gridded Snowmelt: Upper Truckee River, California and Calibrating Point Snowmelt: Swamp Angel Study Plot, Colorado.

A tutorial illustrating how to use the Uncertainty Analysis to evaluate Hybrid Snow parameter sensitivity can be found here: Evaluating Gridded Hybrid/RTI Snowmelt Parameter Sensitivity.

Descriptions of the user interface features pertaining to this method can be found here: Hybrid Snow section of the User's Manual.