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# Flux footprint

Environmental Monitoring:

# Flux footprint

This article has been reviewed by the following Topic Editor: Catherine Gautier

## Introduction

Flux footprint (also known as atmospheric flux footprint) is an upwind zone where the atmospheric flux measured by a scientific  instrument is generated. Specifically, the term flux footprint describes an upwind zone observed by the instruments measuring vertical turbulent fluxes, such that heat, water, gas and momentum transport generated in this area is registered by the instruments. Another frequently used term, fetch, typically refers to the distance of the instrumentation from the tower when describing the footprint.

## Visualization of the concept

Figure 1. General concept of the flux footprint. The darker the red color – the more contribution that is coming from the surface area certain distance away for the instrument.

As a practical example, consider an instrument measuring a flux of water (evapotranspiration) few meters above the surface in the situation with no wind. In such a case, the instrument would measure evapotranspiration generated immediately beneath the instrument location and brought upwards by mostly non-turbulent exchange. Now lets consider situation with a strong wind: it would blow air located under the instrument away, would bring in air generated somewhere upwind and brought upwards to a considerable degree due to turbulent exchange. So, the water flux footprint was just under the instrument in the first case, and was somewhere upwind in the second case.

In Figure 1, the general concept of the flux footprint is visualized: the darker the red color – the greater the contribution that is coming from the surface area a certain distance away for the instrument. So, the majority of the contribution usually derives, not from underneath the instrument or from kilometers away, but rather from a locus in between. Size and shape of the footprint are also  dynamic variables that change over time.

## Mathematical foundation

Figure 2. Mathematical representation of footprint.

Atmospheric transport can be viewed as a Lagrangian transport model. In such a case, the footprint is the zone of cumulative contribution to flux measurement computed from analytical solutions of the diffusion equation. For example, for near-neutral conditions, following Schuepp et al (1990) and Gash (1986), the mathematical representation of footprint would be that seen in Figure 2.

## Main factors affecting flux footprint

Three main factors affecting the size and shape of flux footprint are: (1) measurement height, (2) surface roughness, and (3) atmospheric thermal stability.

Increase in measurement height, decrease in surface roughness, and change in atmospheric stability from unstable to stable would lead to an increase in size of the footprint and move peak contribution away from the instrument. The opposite is also true. Decrease in measurement height, increase in surface roughness, and change in atmospheric stability from stable to unstable would lead to a decrease in size of the footprint and move peak contribution closer to the instrument.

## Examples of real-field flux footprint distribution

Figure 3. Relative contribution of the land surface area to the flux for two different measurement heights at near-neutral stability.

Degree to which flux footprint is affected by these factors is illustrated for the all three respective cases below on the example of actual evapotranspiration flux (ET) measured over prairie in summer time (Figures 3 through 5).

Relative contribution of the land surface area to the flux for two different measurement heights at near-neutral stability is shown in Figure 3. Please note that not only distance to the peak contributing was affected by a measurement height, but magnitude of the peak and overall distribution of the footprint was affected significantly as well.

Below is an example of relative contribution of the land surface area to the flux for two different surface roughnesses at near-neutral stability (Figure 4). Area under the curves on the plot above and on the two plots below sums up to nearly one hundred percent of the flux contribution. The remaining few percent of flux are coming from an area beyond 500 metres.

Example of the relative contribution of the land surface area to the flux for two different cases of thermal stability is shown below (Figure 5). This example is adopted from Leclerc, M.Y., and G.W. Thurtell (1990).

Figure 4. Relative contribution of the land surface area to the flux for two different surface roughnesses at near-neutral stability.
Figure 5. Relative contribution of the land surface area to the flux for two different cases of thermal stability.

• Burba, G.G. 2001. Illustration of Flux Footprint Estimates Affected by Measurement Height, Surface Roughness and Thermal Stability. In K.G. Hubbard and M.V.K. Sivakumar (Eds.) Automated Weather Stations for Applications in Agriculture and Water Resources Management: Current Use and Future Perspectives. World Meteorological Organization publication No.1074.HPCS Lincoln, Nebraska – WMO Geneva, Switzerland, 77-87.
• Finn, D., Lamb, B., Leclerc, M.Y., and T.W. Horst: 1996, Experimental evaluation of analytical and Lagrangian surface layer flux footprint models, Boundary-Layer Meteorology 80: 283-308.Gash, J.H.C.: 1986, A note on estimating the effect of limited fetch on micrometeorological evaporation measurements, Boundary-Layer Meteorology 35: 409-413
• Horst, T.W.: 1979, Lagrangian similarity modeling of vertical diffusion from a ground level source, Journal of Applied Meteorology 18: 733-740.
• Leclerc, M.Y., and G.W. Thurtell: 1990, Footprint prediction of scalar fluxes using a Markovian analysis, Boundary-Layer Meteorology 52: 247-258.

## Citation

George Burba (Lead Author);Catherine Gautier (Topic Editor) "Flux footprint". In: Encyclopedia of Earth. Eds. Cutler J. Cleveland (Washington, D.C.: Environmental Information Coalition, National Council for Science and the Environment). [First published in the Encyclopedia of Earth October 3, 2007; Last revised Date June 15, 2012; Retrieved May 24, 2013 <http://www.eoearth.org/article/Flux_footprint?topic=49501>

## The Author

George Burba is a Principal Scientist in Advanced Research and Development Division of LI-COR Biosciences, and a Graduate Adjunct Faculty with the School of Natural Resources at the University of Nebraska-Lincoln. He received an M.S. in Geoecology from Lomonosov Moscow State University (Russia), an M.S. in Micrometeorology, and a Ph.D. in Bio-Atmospheric Sciences from School of Natural Resources of the University of Nebraska-Lincoln (USA). His research interests are bio-atm ... (Full Bio)