# Presentation: 700143

## Rain-on-SnowSnowmelt Modeling

- Pete Fickenscher
- -----
- Hydrologist
- California-Nevada River Forecast Center
- National Weather Service
- -----
- San Joaquin River Flood Control Association
- Feb. 16, 2006

## Snowmelt Due to Rain-on-Snow

## Mr = Cw*Px  * (Tw-273.16)

Mr = Melt Rate (mm)
Cw = Specific heat of water
Px = Precipitation (mm)
Lf = Latent heat of fusion
Tw = Wet-bulb Temp. (K)

- Mr = Melt Rate (mm)
- Cw = Specific heat of water
- Px = Precipitation (mm)
- Lf = Latent heat of fusion
- Tw = Wet-bulb Temp. (K)

**Snowmelt Due to Rain-on-Snow**

**Lf**

- _  __Tw        Melt (% of Px)_
- 50 °F	12.5 %
- 68 °F	25.0 %

-  Simple Energy Balance

## M  = (0.0125 * Px * Ta)                             		{ rainmelt}
     + 3.67 * 10-9  *  Δt/6 *(Ta+273)4 – 20.4  		{ longwave exchange}
     + 8.5 * UADJ * Δt/6*[(0.9 * esat – 6.11) + 0.00057 * Pa * Ta
						{turbulent transfer}

**     ****+ 3.67 * 10****-9****  *  ****Δ****t/6 *(Ta+273)****4**** – 20.4  ****	****	****{ longwave exchange}**
**     ****+ 8.5 * ****UADJ**** * ****Δ****t/6*[(0.9 * e****sat**** – 6.11) + 0.00057 * Pa * Ta**
**	****	****	****	****	****	****{turbulent transfer}**

**Rain-on-Snow**

- Snow-17  -  Operational Equation

- M = Melt (mm)
- Ta = Air Temperature (°C)
- Px = water equivalent of precipitation (mm)
- UADJ = average wind function during rain-on-snow
- esat = saturation vapor pressure at the air
- Pa = mean sea level atmospheric pressure

## M  = (0.0125 * Px * Ta)                             	{ rainmelt}
     + 6.12 * 10-10  *  Δt [(Ta+273)4 – 2734]  	{ longwave exchange}
     + 8.5 * UADJ * Δt/6*[(0.9 * esat – 6.11) + 0.00057 * Pa * Ta
					{turbulent transfer}

**     ****+ 6.12 * 10****-10****  *  ****Δ****t [(Ta+273)****4**** – 273****4****]  ****	****{ longwave exchange}**
**     ****+ 8.5 * ****UADJ**** * ****Δ****t/6*[(0.9 * e****sat**** – 6.11) + 0.00057 * Pa * Ta**
**	****	****	****	****	****{turbulent transfer}**

**Rain-on-Snow**

- Snow-17  -  Operational Equation

- _Assumptions:_
-  no solar radiation
-  relative humidity = 90%
-  atmospheric radiation = black body at Ta
-  wet bulb temperature (rainwater ) = Ta
-  UADJ is the **average** wind function during rain-on-snow events
-  The snowmelt occurs at the **surface** of the snowpack

## Rain-on-Snow

- Snow-17  -  Rainmelt

- Assume a 6 hour event with constant Ta = 45 °F**  **and
- 2 inches of rain

## Rain-on-Snow

- Snow-17   -   Longwave Radiation

- Note: This melt is independent of rainfall amount**      **

- Assume a 6 hour event with constant Ta = 45 °F**      **

## Rain-on-Snow

- Snow-17  -  Turbulent Transfer

- Note: This melt is independent of rainfall amount.
- UADJ set to 0.09 (12 mph wind)

- Assume a 6 hour event with constant Ta = 45 °F**      **

## Rain-on-Snow

- Snow-17  -  Component Comparison

- Assume 2 inches of rain  during a 6 hour event with constant Ta

- _  __Ta        Total Melt (inches)_
- 45 °F	0.50 (25%)
- 40 °F   	0.30 (15%)
- 35 °F	0.11 ( 6%)

- Note: 41 °F  0.34 (17%)

## Example – 1997 Event

## Example – 1997 Event

- _Blue Canyon (5300’)_
- Average Temp (42.5 °F):
-   Rainfall = 19.8 inches
-   SWE loss**  **= 5.3 inches**    **
**Ratio = 27 %**

- _Greek Store (5600’):_
-   Rainfall = 13.8 inches
-   SWE loss**  **= 0.80 inches**    **
**Ratio =  6 %**

- Dec. 30, 1996 – Jan. 2, 1997

- Greek Store snowpack was deeper and less “ripe”, more sheltered.
- Rain-on-snow melt is highly dependent on pack conditions

## Example – 1997 Event

- _Huysink (6600’)_
- Average Temp (42.5 °F)
-   Rainfall = 16.55 inches
-   SWE loss**  **= 2.0 inches**    **
**Ratio = 12 %**

- _Central Sierra Snow Lab:    CSSL (6900’):_
-  Rainfall = ??
-  SWE loss**  **= 0.0 inches
**Ratio = 0 %**

- Dec. 30, 1996 – Jan. 2, 1997

- At 6900’ the rain passed through the deep CSSL snowpack with no melt.

## Example – 1997 Event

- Dec. 30, 1996 – Jan. 2, 1997

- NFDC1UP is represents the basin average rain-on-snow snowmelt

- _SNOW – 17 (NFDC1UP):_
-   Average Temp (41 °F)
-   Rainfall = 18.0 inches
-   SWE loss**  **= 3.28 inches**    **
**Ratio = 18 %**

## Snowmelt Due to Rain-on-Snow

- Summary

-  Rain-on-Snow is a complex phenomena.
-  Many variables need to be considered.  (Temperature, humidity, wind speed, snowpack conditions, forests,...)
-  The strongest component is usually turbulent transfer.
-  All components together may reach 25% (or more) snowmelt-to-rain ratios in very warm events, especially at lower elevations.
-  When snowpack is deep and still cold, little additional snowmelt occurs during rain-on-snow events.