Separating the corn from the beans: conditional sampling from airborne turbulence measurements to assess the contribution of individual components to the bulk flux

Atmospheric exchange with a heterogeneous surface becomes horizontally blended aloft into a bulk flux representing some sort of weighted average of the exchange at the surface. Bottom-up estimates aggregating a bulk flux estimate for landscape scale from fluxes estimated for the patch scale need to understand the weighting function and how it varies with observable conditions. Though airborne flux measurements are an effective tool, small-scale heterogeneity is challenging. Horizontal resolution of airborne flux estimates is limited, and the blending height decreases with the scale of the heterogeneity requiring low-altitude flight to discern a signal. Our airborne campaign of June 2005 in east-central Illinois provides an opportunity to examine the blending under particularly favorable circumstances. Two crops, corn and soybeans, dominate the landscape in rectangular fields of 500 m scale. Corn grows rapidly in June, vastly outrunning soybeans in taking up CO2. This striking heterogeneity is regularly observed from towers in a landscape otherwise quite uniform. Several flux towers deployed in the area during June 2005 sampled this heterogeneity on the surface. Airborne measurements sampled varying degrees of horizontal blending, depending on the horizontal scale of individual fields, the measurement altitude, and the mixing conditions. Towers and airplane measured fluxes of heat, momentum, water, and CO2 by eddy-covariance. Flights, nominally at 30 m, included some passes within 3 m of the ground and some above 50 m. Current understanding of the blending height predicts significant attenuation of horizontal heterogeneity by 30 m above this terrain.

We cast the airplane's measured quantities' departure from a base state into noncentral covariances over 1-s blocks (about 40 m). The base state is a trend over an entire transect, about 30 km. These blocks are not Reynolds averages, rather the departure quantities' mean over each block represents the larger scales of turbulence from which the block came. We call such blocks "flux fragments." If we combine sufficient fragments that the full sample approximates a Reynolds average, we can hope to have captured the larger scales of turbulence. Mesoscale features, a complication in general, are minimized in central Illinois's uniform terrain.

Each fragment is associated with a surface type (corn, beans, both, neither) by fuzzy logic. The membership function is derived by correlating a footprint estimate with the surface on which it lies using a geographical information system. By this framework we can determine an optimum tradeoff between sufficient sample size in each category and sufficient confidence that a given fragment represents the surface associated with it. The primary measure of sufficient sample size will be compliance with Reyonlds averaging. Other issues of sufficiency in sample size can be tested by statistical techniques, but not at this preliminary stage.

Results from the flights in Illinois from June 2005 will demonstrate the technique and its effectiveness. This approach promises to facilitate studies of the mechanism of the atmosphere's horizontal blending of surface heterogeneity, especially where the heterogeneity includes patchwork on a scale of hundreds of meters, characteristic of many landscapes. Understanding the horizontal blending and the factors that control it will greatly aid design of meaningful airborne flux missions, especially where low-altitude flight is neither safe nor legal. Using different footprint models can explore why heat fluxes' footprints have been sometimes found to differ from those for moisture or CO2. The technique can extend to more complex situations of terrain and mesoscale structure if modeling, mesonet, or other available means can suitably characterize the additional structure.