## 5 Research gaps in C and Water Flux Estimates and Scaling Approaches  
A variety of methods are being used in the C and water cycles studies. As shown in Figure 3, different approaches have different temporal and spatial scales. The most direct measurements of the terrestrial C flux are made either at the plot scale (10\({}^{-2}\)-10\({}^{1}\) m\({}^{2}\)), e.g., using biometric methods and various forms of chamber, or at the ecosystem (patch) scale (10\({}^{4}\)-10\({}^{6}\) m\({}^{2}\)), using the EC technique. Ecohydrological / ecosystem modeling and remote sensing estimations are generally available across variable spatiotemporal scales. These estimates are normally available within a nested framework that permits a progressive comparison of measurements made by surface instrumentation (scale: 1 to 10 m), surface flux equipment (10 m to 1 km), airborne remote sensing equipment (100 m to several km), satellite remote sensing (30 m to global scale) and EC tower (1-3 km). The atmosphere integrates surface fluxes over many temporal and spatial scales and links scalar sources and sinks with concentrations and fluxes. This principle has been successfully used to develop inverse models to estimate annual C budgets [225-230]. However, due to model limitations and paucity of continental CO\({}_{2}\) observations these studies have yielded C fluxes only at coarse resolution, over large spatial regions [231-233]. Progress in C balance studies has been achieved at both ends of the spatial scale spectrum, either large continents (larger than 10\({}^{6}\) km\({}^{2}\), e.g., global inverse modeling) or small vegetation stands (less than 1-3 km\({}^{2}\), e.g., EC-measurements). Methods to estimate CO\({}_{2}\) sources and sinks at the intermediate scale (i.e., landscape to regional scales) between continental and local scales are less well advanced. Moreover, the C cycle in different regions can vary markedly in response to changing climate [5]. Reliable estimates of terrestrial C sources and sinks at landscape to regional spatial scales (finer than those used in global inversions and larger than local EC flux measurements and roughly defined as the range between 10\({}^{2}\) and 10\({}^{6}\) km\({}^{2}\)) are required to quantitatively account for the large spatial variability in sources and sinks in the near-field of a measurement location [234], as well as fundamental to improving our understanding of the C cycle [235]. It is generally considered unreliable to upscale stand-level fluxes (i.e., EC measurements) to a region by simple spatial extrapolation and interpolation because of the heterogeneity of the land surface and the nonlinearity inherent in ecophysiological processes [236]. It is also challenging to apply atmospheric inversion technique to regional scales for quantifying annual C budgets because at such intermediate scales the atmosphere is often poorly constrained [86,237]. Moreover, aggregation errors and errors in atmospheric transport, both within the PBL and between the PBL and free troposphere, can also be obstacles to using these approaches to obtain quantitative estimates of regional C fluxes [76]. Hence, there is a strong motivation to develop methods to quantify and validate estimates of the C balance at these intermediate scales [76-77,79,86]. Observations of CO\({}_{2}\) over the continent within the PBL reflect exchange processes occurring at the surface at a regional scale (10\({}^{2}\)-10\({}^{5}\) km\({}^{2}\)). The flux information contained in CO\({}_{2}\) concentration data represents footprints of up to  
Figure 3: Temporal and spatial scales of different approaches. \(10^{5}\) km\({}^{2}\)[75, 76], which are several orders of magnitude larger than the direct EC-flux footprint. This information is therefore needed in our effort to upscale from site to region. Moreover, the number of CO\({}_{2}\) mixing ratio measurements above the land surface, made by either tower or aircraft, is steadily increasing.