Snow and the energy budget

In many parts of the world snow forms an important part of the hydrological cycle. Where it is the major input of water in the annual water balance, it can be critical in water resources assessment, while the snowmelt period can be the most critical periodfor flooding in some areas. In California, for example, up to 80 per cent of the annual discharge of some rivers is generated by snowmelt. Thus the build-up and

(a) Soil moisture in top metre of soil (fraction of saturation)

(b) Rainfall and surface runoff (mm day 1)

(a) Soil moisture in top metre of soil (fraction of saturation)

rainfall accumulation surface runoff iukAL

01 Feb 01 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct 01 Feb 01 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct

(c) Gridsquare Mean potential and actual Evaporation (mm day-1) (d) Median soil moisture deficit (mm) 6.00

01 Feb 01 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct 01 Feb 01 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct

(c) Gridsquare Mean potential and actual Evaporation (mm day-1) (d) Median soil moisture deficit (mm) 6.00

01 Feb 01 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct 01 Feb 01 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct

Fig. 10.14 Predictions with the MOSES-PDM model for a grid square in southern England, March to September in the dry summer of 2003 (after Smith et al, 2004, © Crown copyright 1994, the Met Office).

01 Feb 01 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct 01 Feb 01 Mar 01 Apr 01 May 01 Jun 01 Jul 01 Aug 01 Sep 01 Oct

Fig. 10.14 Predictions with the MOSES-PDM model for a grid square in southern England, March to September in the dry summer of 2003 (after Smith et al, 2004, © Crown copyright 1994, the Met Office).

melting of the snowpack is then an important hydrological problem. It depends on both the amounts of input precipitation but once a snowpack has developed, also on the energy budget of the surface. Rapid snowpack melting can be an important cause of flooding in some parts of the world. Warm air masses and heavy rainfalls on to a snowpack can cause such rapid melting. A good example was the Red River Flood in April and May of 1997 on the US-Canada border. This flood was the result of a heavy winter snowfalls followed by a period of extremely warm temperatures in the melt season. The Red River reached flood levels of 16.6m at Grand Forks, North Dakota, and caused the evacuation of 50 000 people and $3.5bn damages.

10.9.1 Estimating snowmelt by the energy budget method

The principles are much the same as for evapotranspiration. In this case, a simplified surface energy budget at a point can be expressed as

where 1M is the latent heat of melting (334 kJ kg-1), M is the melt rate in water depth per unit area per unit time (mms-1), RN is net radiation, C is sensible heat flux from the atmosphere, V is energy storage in the snowpack, Gis heat exchange with the underlying soil, I is the precipitation input rate as a depth of water equivalent per unit

Fig. 10.15 Soil moisture deficit predictions with the MOSES-PDM model over western Europe for 20 September 2003. White: 0 mm; dark blue: 0-20 mm; green: 60-80 mm; yellow: 80-100 mm; orange: 100-140 mm (after Smith et a/., 2004, © Crown copyright 1994, the Met Office).

time, Cp is the specific heat of water, Tp is the temperature of the precipitation and Ts is the temperature of the snow. Under some circumstances, water can also be lost from a cold snowpack directly to the atmosphere as vapour, a process called sublimation. There may also be additional small transfers of water from a humid atmosphere to a cold snowpack as condensation.

The energy storage term, V, is important in snowmelt, since melt will not occur until the snowpack is 'ripe', i.e. at or close to 0°C (273.2 K). Thus in following the accumulation and melt of a snowpack over time it is necessary to keep track not only of the water equivalent of the pack but also of its temperature. While the pack is still at temperatures below freezing, the change in temperature over time will depend on the inputs of energy from net radiation, and exchanges with the atmosphere and the soil. Losses and gains of heat in the pack will also depend on the thermal characteristics of the snow, which can change as the pack ripens and the structure of the snow grains changes due to compaction and diurnal freeze/thaw processes. The evolution of the temperature of the pack will also depend on the temperature at which new precipitation is added to the pack. Snow can fall and add to the pack at temperatures well below zero degrees, but this is particularly important when warm rain falls on to a ripe snowpack. Under these conditions, often found, for example, during spring melt periods on the west coast mountains of the USA, the additional input of energy from the rain and turbulent transfers of sensible heat in (relatively) warm air moving over the snow surface can lead to periods of rapid melting and consequent snowmelt floods. Northern California is also particularly susceptible to such events (locally called a 'pineapple express') when warm tropical air masses move inland from the Pacific during winter. One such period occurred in the early January 1997 in California, when torrential rains on to a deep snowpack produced some of the highest discharges recorded in some Californian rivers and filled reservoirs close to overtopping. It is worth noting that a number of such floods have been recorded, with that in January 1862 producing the highest recorded river levels.

In the various terms of (10.29), net radiation and sensible heat flux can be either measured or estimated as before, given the surface temperature of the pack and the air, together with information about the albedo and aerodynamic roughness of the pack and wind speed (using equations 10.15, 10.16, 10.17, 10.20). The storage term and ground heat flux term can be estimated by knowing the surface temperature of the pack and the thermal properties of the snow and ground. The input of energy from precipitation can be estimated from knowing the temperature and intensity of the input water equivalent.

The difficulty of implementing a full energy budget for a snowpack in this way comes from the fact that where snow accumulation and melt is most important, which is in mountain areas, it can be very difficult to estimate many of the different quantities required. The net radiation varies with slope and aspect. The temperature of incoming precipitation (and whether it is rain or snow) can depend on elevation. Air temperature will also vary with elevation, but with lapse rates that vary with the prevailing weather system. The accumulation of snow in different parts of a catchment can depend on drifting due to changing wind patterns so that there can be a wide distribution of snow depths in a given range of elevation. The albedo of snow will normally decrease over time as the snowpack ages and ripens, unless there is a fall of fresh snow. All of these factors can make it difficult to predict spatial patterns of snow accumulation and quantify rates of melt. An example of this is given in Section 9.1.5 where the pattern of rain and snow in different parts of a catchment in Switzerland proved to be so important in the magnitude of a flood peak.

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