Snow Water Equivalentil modello di accumulo e

scioglimento nevoso operativo in Praga

Fausto Tomei, Andrea Spisni, Cesare GovoniARPA SIMC, Bologna

SAM - simple distributed snow accumulation

and melt (Brooks, 2003)

Bacino sperimentale (2 ha) situato a 8 km nord da Troy - ID, USA

SAM (1)

• The SAM model is similar to the simple approach of Anderson (1968) and

not require any iterative solutions.

• Snowmelt in the SAM model is simulated by applying an hourly mass and

energy balance to a single layered snow pack (plus a thin soil layer).

• The energy content U (kJ m-2) is defined relative to a reference state of

water at 0 °C. If U <0, the snowpack is composed solely of ice, if U= 0, then

ice and liquid phase can both be present and if, finally, U > 0 no snow cover

is present and the energy content is related to the layer of soil below.

• The total mass of the snowpack W (expressed in water equivalent depth, m)

includes both an ice phase Wice (m) and a liquid phase Wliq (m)

SAM (2)Energy and mass balance equations:

rT QQdt

dU +=

rrrr M E S P +++=dt

dW

Where:

QT energy flux crossing the upper and lower boundaries of the snow pack

Qr exchange of latent heat due to thawing or refreezing

Pr is the rainfall rate

Sr is the snowfall rate

Er is the sublimation rate from the snow pack

Mr is the meltwater rate

These equations are solved using a quasi-steady state assumption where U

and W for the current time can be determined from their quantities in the

previous time step.

SAM (3)The net energy flux QT (kJ m-2 hr-1) is defined as:

Where:

Qs is the net shortwave radiation

Qlw is the net longwave radiation

Qh is the sensible heat flux

Ql is the latent heat flux due to sublimation / condensation

Qp is the advected heat transfer from precipitation

Qg is the ground heat flux

The shortwave radiation, crucial variable for the energy balance, is

calculated in Praga using algorithms derived from r.sun, an open source

package included in the GRASS GIS, starting from hourly measured values

of global radiation.

gplhlwsT Q Q Q Q Q Q Q +++++=

SAM (4)

Air temperature T is used to distinguish whether the precipitation falls

as rain or snow following the simple approach of the U.S. Army

Corps of Engineers (1956) and Tarboton and Luce (1996):

Pr = P for T ≥ Tmax

Pr = P(T - Tmin)/(Tmax-Tmin) for Tmin < T < Tmax

Pr = 0 for T ≤ Tmin

The method uses a minimum (Tmin) and maximum (Tmax) threshold

temperature to define a temperature range where precipitation is

composed of a mixture of rain and snow. Between these thresholds

the total rainfall is determined using T.

Variabili di input (orarie)Temperatura media a 2 m (°C) Irradianza globale (W m-2)

Umidità relativa (%) Precipitazione (mm)

Confronto tra SWE osservata e simulata a Troy – Idaho, USA (1999-2002)

Validazione (1)

Confronto tra spessore del manto nevoso osservato e simulato

a Doccia di Fiumalbo, inverno 2005-2006

Validazione (2)

y = 0.9986x

R2 = 0.8223

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0.000 0.200 0.400 0.600 0.800 1.000 1.200

Validazione (3)

Confronto tra spessore del manto nevoso osservato e simulato a Doccia di Fiumalbo, inverno 2005-2006

Validazione (4)

Confronto tra % innevamento da satellite e % innevamento da modello (2001-2007)

Modifiche apportate al modello

• Passo di grid ridotto (da 1000 m a 450 m)

• Inserita mappa di uso del suolo (per gestire i corpi d’acqua)

• Utilizzo come input di precipitazione dei soli pluviometri riscaldati e controllati

• Soglia di temperatura massima e selezione delle stazioni di misura della temperatura rese variabili per i singoli eventi nevosi

• Inserita possibilità di caricare mappe di SWE corrette da satellite come variabile di stato sostitutiva

Precipitazionigggggg

TMedgggggg

Radiazionegggggg

2009.0

1.0

1

08

16

2009.0

1.0

2

08

16

2009.0

1.0

3

08

16

2009.0

1.0

4

08

16

2009.0

1.0

5

08

16

2009.0

1.0

6

08

16

2009.0

1.0

7

08

16

2009.0

1.0

8

08

16

2009.0

1.0

9

08

16

2009.0

1.1

0

08

16

Te

mp

era

tura

[°C

]

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

Pre

cip

itazio

ni [m

m]

5

4

3

2

1

0

Precipitazionigggggg

TMedgggggg

Radiazionegggggg

2009

.01

.01

08

16

20

09.0

1.0

2

08

16

2009.0

1.0

3

08

16

2009

.01.0

4

08

16

2009.0

1.0

5

08

16

2009.0

1.0

6

08

16

200

9.0

1.0

7

08

16

2009.0

1.0

8

08

16

2009.0

1.0

9

08

16

2009.0

1.1

0

08

16

Te

mp

era

tura

[°C

]

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

Pre

cip

itazio

ni [m

m]

5

4

3

2

1

0

Pluviometri riscaldati

snowmelt

Sassostornosnow

Sestola

Precipitazioni registrate dai pluviometri di Sestola (riscaldato) e Sassostorno (non riscaldato) situati a 6 km di distanza

22 dicembre 2009

23 dicembre 2009

24 dicembre 2009

PRAGA e SATELLITE: 7 gennaio 2010 ore 12.00

PRAGA e SATELLITE: 7 febbraio 2010 ore 9.30

PRAGA e SATELLITE: 13 febbraio 2010 ore 12

PRAGA e SATELLITE: 21 febbraio 2010 ore 12

PRAGA e SATELLITE: 21 febbraio 2010 ore 12 correzione

SWE e COSMOI2: 01 febbraio 2010 ore 12

25

120

63134

115

50

74

SWE e COSMOI2: 01 febbraio 2010 ore 12

Previsione criticità idrologica

Bibliografia

• Anderson, E.A. 1968. Development and testing of snow pack energy balance equations. Water Resour. Res. 4:19-37.

• Bittelli M., Tomei F., Pistocchi A., Flury M., Boll J., Brooks E.S. , Antolini G., Development and testing of a physically based, three-dimensional model of surface and subsurface hydrology, Advances in Water Resources, vol.33, Issue 1, January 2010, 106-122.

• Brooks, E.S. 2003. Distributed hydrologic modeling of the eastern Palouse. Ph.D. dissertation, University of Idaho, Moscow.

• Brooks, E.A. and J. Boll. 2005. A simple GIS-based snow accumulation and melt model, Proceedings of the 2005 Western Snow Conference, April 11-14, 2005, Great Falls, MT, 6 pp.

• Koivusalo, H., M. Heikinheimo, and T. Karvonen., 2001. Test of a simple two-layer parameterisation to simulate the energy balance and temperature of a snow pack. Theor. Appl. Climatol. 70:65-79.

• Marks, D., J. Domingo, D. Susong, T. Link, and D. Garen., 1999. A spatially distributed energy balance snowmelt model for application in mountain basins. Hydrol. Process. 13:1935-1959.

• Page, J., 1986. Prediction of solar radiation on inclined surfaces. Solar energy R&D in the European Community, series F – Solar radiation data, Dordrecht (D. Reidel), 3, 71, 81-83.

• Rigollier, Ch., Bauer, O., Wald, L. 2000. On the clear sky model of the ESRA - European Solar radiation Atlas - with respect to the Heliosat method. Solar energy, 68, 33-48.

• Tarboton, D.G. and Luce, C.H. 1996. Utah Energy Balance Snow Accumulation and Melt Model (UEB); Computer model technical description and users guide. Utah Water Research Laboratory and USDA Forest Service Intermountain Research Station.

• Unsworth, M.H. and L.J. Monteith, 1975. Long-wave radiation at the ground. Angular distribution of incoming radiation. Quarterly Journal of the Royal Meteorological Society 101(427):13-24.

• U.S. Army Corps of Engineers. 1956. Snow Hydrology, Summary Report of the Snow Investigations, North Pacific Division, Portland, OR, 437 pp.