## 5 Applications
This is achieved by combining a limited number of transmitters with a network of receivers located around the perimeter of the desired area or a limited number of transmitter/receiver modules and reflectors distributed around the perimeter of the area with a field model to construct two-dimensional estimates of GHG distributions and time-varying fluxes. The latter concept is illustrated in the idealized field shown in the left-hand panel of Figure 11. This figure shows a two-transmitter configuration with 58 receivers/reflectors located around an idealized 1 km \(\times\) 1 km field. While the field illustrated in this example is highly regular in nature, the same concept can be applied to fields with irregular boundaries as long as an unobstructed line-of-sight exists between each transmitter and receiver/reflector pair. The figure also shows a representative set of synthetic plumes defined by a complex set of two-dimensional Gaussian distributions, and the red lines represent the possible transmitter/receiver measurement paths. The resulting along-path measurements alone can provide an estimate of localized field DAMF and could be used to detect and estimate time-varying changes in local GHG DAMF. They also can be combined with a two-dimensional estimation technique to model the time-varying distribution of GHGs in the field itself. An example is shown in the right-hand panel of Figure 11. This technique, which is based on prior work and has been demonstrated in a number of previous efforts using laser absorption spectroscopy and microwave attenuation to construct two-dimensional fields of CO\({}_{2}\) concentrations [33] and rain rate [34, 35, 36] over defined areas of interest, models the field of interest as a limited set of base functions whose integrated intensities along the sampling paths best matches the observed values for a given set of best-fit criteria, e.g., mean-squared error. The resulting estimate from a prototype implementation of this approach is illustrated in the right-hand panel of Figure 11.  
Figure 11: Simulated two-dimensional retrieval of CO\({}_{2}\) field concentrations. Left-hand panel illustrates example synthetic field, and right-hand panel demonstrates retrieved field distribution based on simulated integrated CO\({}_{2}\) column measurements and least-squared fit algorithm. The red rays depict the LAnTeRN transmitter/receiver line-of-sight sample integration paths. In this example the two transmitters are locate in the lower corners of the simulated field. The fidelity of the resulting field distribution estimate and its location accuracy depends in part on how well the chosen analytical model matches the true field distribution, the placement of the transmitters and receivers, and the number of intersecting samples. While this approach is not designed to provide absolute measurements at discrete locations with sub-meter accuracy, it does capture the general shape and location of GHG plumes, which are normally diffuse in nature, and provides a robust method for tracking time-varying aspects of their distributions. The reflector configuration depicted reduces the cost of this type of mapping operation and is well suited for some applications like carbon sequestration sites, but would be impacted by large aerosol concentrations in applications like volcano monitoring, due to partial path returns. However, several similar implementations are possible, for example using transmitter/receiver pairs in all four corners can enable direct transmission measurements over several transects in order to determine and correct for potential bias from intermediate scatter sources under those circumstances.