Small-scale heterogeneity of the

The surface temperature forms as a result of the partitioning of energy at the surface, so that it is related to all components of the surface energy budget. As the exposition does not vary strongly within the study area, we do not expect considerable variations of the incoming short-wave radiation. An exception is the escarpment, which is also shaded during part of the time, so that we do not consider it any further in our analysis. The surface albedo is most likely lower in the wet areas compared to the dry areas (compare Fig. 3.5), so that they receive a higher net short-wave radiation, although they feature a colder surface temperature. The measurements of sensible and latent heat fluxes with the eddy covariance method reveal a dependence of the Bowen ratio on the surface soil moisture conditions (Fig. 4.5). Therefore, the differences in the surface temperature between wet and dry areas can most likely be explained by increased evapotranspiration over the wet areas, which cools the surface and efficiently reduces the difference between surface and air temperature. In contrast, the dry areas heat up and release energy via sensible heat fluxes and increased long-wave radiation. In the time directly after snow melt, when the thaw front is close to the surface, a significant ground heat flux cools the surface and constitutes an important term in the surface energy budget (Sect. 4.2, Fig. 4.4). As the the sum of sensible, latent and ground heat fluxes is equal to the net radiation, this interpretation is supported by the observed dependence of the spatial variability of the surface temperatures on Qnet (Fig. 4.17). In

case of high net radiation, strong sensible, latent and ground heat fluxes, which differ throughout the study area, lead to a large spatial variability of the surface temperature. In case of low net radiation, they necessarily feature low values, so that spatially different fluxes and thus differences of the surface temperature cannot develop.

We support this reasoning by applying the energy balance model described in Sect. 2.4.7 to model the spatial differences of the surface temperature with a common set of forcing data. The forcing data are

• soil temperature at 0.15 m depth measured in a dry and a wet area within the scene monitored by the thermal imaging system,

• air temperature, relative humidty and wind speed at 2 m height measured at the Bayelva station, approximately 400 m from the thermal imaging system,

• incoming short-wave and longwave radiation measured at the BSRN sta- tion, approximately 1.5 km from the thermal imaging system.

For simplicity, we use a constant albedo α=0.15 and emissivity ε=0.97. Fur- thermore, a constant soil thermal conductivity Kh=1.3 Wm−2is assumed, which

most certainly does not reflect the true soil conditions with spatially variable thermal conductivities. However, the impact on the surface temperature is rather limited, as the ground heat flux is a relatively small contribution to the surface energy budget (see Sect. 4.2). Therefore, the two parameters varied are the roughness length z0 and the surface resistance rs. Fig. 4.18 displays surface

temperatures from a wet and a dry area (depicted in Fig. 3.5) measured by the thermal imaging system and model results for two different surface resis- tances for a period in summer 2009. A satisfactory agreement between measured and modeled surface temperatures can be achieved with a roughness length of z0=1 mm common to both areas, but strongly different surface resistances rs.

Accordingly, the average Bowen ratio obtained from the surface energy budget equation is highly different between the two sites, which confirms the above interpretation: while the latent heat flux is dominant at the wet area with a Bowen ratio of less than 0.5, it is more than ten times smaller than the average sensible heat flux at the dry area. The Bowen ratio of the wet area is well in the range determined with eddy covariance in case of a high surface soil moisture (Sect. 4.2, Fig. 4.5), while the Bowen ratio determined for the dry area is much higher than all Bowen ratios in the eddy covariance measurements. However, the dry area recorded by the thermal imaging system most likely features a much smaller surface moisture content compared to the footprint of the eddy covariance system, which even under dry conditions maintains a volumetric soil water content of around 0.2 at the surface (Fig. 4.4). Particularly in case of the dry area, a few systematic deviations between measured and modeled surface temperature are obvious. On the first few days after 11 July and after 31 July, the modeled temperatures are too high, which is most likely explained by wet- ter soil conditions after snow melt and after precipitation events, respectively. Accordingly, a smaller surface resistance rs would be appropriate during these

times, which illustrates the difficulties when modeling surface temperatures in case of changing surface soil moisture. The selected roughness length z0=1 mm

0 5 10 15 20

11-Jul 21-Jul 31-Jul 10-Aug 2009

Tsurf / °C

thermal imaging system, wet surface energy budget model, rs = 30 sm-1, z0 = 1mm

11-Jul 21-Jul 31-Jul 10-Aug 2009

0 10 20

30 Tsurf / °C

thermal imaging system, dry surface energy budget model, rs = 3000 sm-1, z0 = 1mm

Figure 4.18: Surface temperature of a wet and a dry area (depicted in Fig. 3.5) measured by the thermal imaging system and modeled from atmospheric pa- rameters by the surface energy budget equation. See text.

is smaller than the roughness length of 7 mm, that has been determined by measurements of the eddy covariance system (see Sect. 4.1.2). However, the wider area around the eddy covariance system (Fig. 4.1), that is characterized by mudboils and scattered rocks, may indeed feature a higher roughness length compared to the area recorded by the thermal imaging system.

The example illustrates the potential of process-oriented models based on the surface energy budget equation to model the spatial variability of the surface temperature. They basically allow to describe a large part of the recorded spa- tial variability by one parameter, the surface resistance rs. Similarly, variations

of the surface temperature due to different albedo or exposition can be naturally accounted for in terms of the surface energy budget equation.

Table 4.3: Maximum uncertainty associated with the weekly average tempera- ture of each pixel according to the error calculation (see Sect. 2.7). High values indicate frequent clear-sky conditions, where the incoming thermal radiation is small. max. error/ K 2008 2009 04/07-10/07 1.0 11/07-17/07 1.3 18/07-24/07 1.3 25/07-31/07 1.0 0.4 01/08-07/08 0.7 0.7 08/08-14/08 0.4 0.6 15/08-21/08 0.6 22/08-28/08 0.4 29/08-04/09 0.9 08/09-14/09 0.3