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.