The determination of area-averaged turbulent surface fluxes from low-level flights using inverse modelling: Verification, benefit, and comparison

The determination of the area-averaged turbulent fluxes at the earth's surface during a field experiment is desirable for several reasons. This can be the closure of the energy balance. Or the initialization or validation of a numerical atmospheric model, for instance a LES (Large Eddy Simulation). It should be kept in mind, that ground-station and tower measurments as well as remote sensings like wind profilers, SODAR, and LIDAR remain point measurements. Even with the application of Taylor's hypothesis these ground-based measurements cannot represent a whole area. For this reason it is useful to have at least one system involved with a field experiment that measures real area-averaged turbulent fluxes. The area-representative fluxes may then be used to develop averaging strategies for data measured at ground-based stations in a heterogeneous terrain.

Generally aircraft are the most suitable instrument to measure area-averaged turbulent fluxes. For the determination of the mean surface fluxes, a typical method is to fly square-shaped flight patterns at several altitudes (3D pattern) within the atmospheric boundary layer (ABL). Assuming a linear flux profile in the ABL the area-averaged fluxes are then extrapolated to the ground. The drawbacks of this method are obvious: First, flights at minimum three different altitudes are necessary, which consumes time and money. Second, for the time of flights stationarity or at least a linear time behavior must be assumed. And third, a linear flux profile through the entire ABL must be assumed, which is not problematic for heat fluxes in a convective ABL, but unlikely for momentum and latent heat and for other types of thermal stratification.

Grunwald et al. (1998) introduced the low-level flight (LLF) method to determine the surface fluxes from flights at only one low flight level by solving the budget equation. To do so, the method required additional measurements with e.g. ground-based systems to receive the horizontal gradients and the temporal development of temperature, humidity, and wind. Therefore the LLF method could not be used autonomously.

To obtain a stand-alone procedure we combined LLF with the inverse theory (well-known in geology) to calculate the missing parameters in the budget equations. We named this strategy then LLF+IM. This method allows the determination of the area-averaged turbulent surface fluxes performing only one low-level flight (e.g. at 100 m or less) of square shape without any supporting data from other systems.

The independence from other systems enabled us to verify our method in the framework of large joint field campaigns like LITFASS: In LITFASS 1998 two airborne measurement systems (Helipod and Do 128) performed 3D flight patterns and LLF as well. At the surface a tower, wind profiler, LIDAR, SODAR, and ground stations operated simultaneously. Additionally our method was inspected using large eddy simulations (LES) of the ABL over both homogeneous and heterogeneous surfaces.

The results of the data analysis are convincing. Even in a strongly convective ABL (i.e. with large eddies that worsen the statistical certainties) the surface fluxes were calculated with small statistical errors compared to the ground-based measurements. Both airborne systems delivered nearly exactly the same fluxes (see the attached Figure). The simulation of our strategy in LES models showed no systematic discrepancy but identical statistics above both homogeneous and heterogeneous surfaces.

After the quality control of data and method the area-averaged fluxes measured by the Helipod are now used in several field campaigns for initialization and verification of numerical models, for cross-validation of remote sensing data, as well as for the development of an averaging strategy for ground-based measurements.

The results encouraged us to analyze the surface fluxes of homogeneous sections in an otherwise heterogeneous terrain. During the LITFASS field experiments in 1997, 1998, 2002, and 2003 the helicopter-borne turbulence probe Helipod performed LLF above a terrain that consists of forest, grassland, agriculture, and lakes. For each surface type the fluxes were calculated from airborne measurements at different days and times of day. As expected, the turbulent fluxes vary a lot. But above a certain height (like the 'blending height') there is only one vertical flux profile representing the entire ABL over the heterogeneous surface. Therefore the vertical gradients of the fluxes have to alter with height, which can be shown using Helipod measurements and the inverse theory.

Finally, the comparison with results from ground-based micro-meteorological measurements on various surface types demonstrate the benefit of the LLF+IM. The extrapolated surface fluxes were consistent and their statistical errors were reasonable small.