## 4 Combining ground data and VIs to scale biophysical processes over large areas
### What Flux Towers Measure and Sources of Error in Flux Towers  
Flux towers measure, among other things, the individual components of the Surface Energy Balance:\[\mathrm{R_{n}}\ \mathrm{-}\ \mathrm{G}\ \mathrm{-}\ \mathrm{H}\ \mathrm{-}\ \lambda\mathrm{ET}=0 \tag{5}\]  
where \(\lambda\) is the latent heat of evaporation of water; \(\mathrm{R_{n}}\) is net radiation flux (\(\mathrm{R_{s}}\) minus outgoing short wave and long wave radiation); \(\mathrm{G}\) is soil heat flux; and \(\mathrm{H}\) is sensible heat flux to the atmosphere (units are \(\mathrm{W}\ \mathrm{m}^{\text{-}2}\))(flux tower methods are reviewed in [51, 52]). Flux towers also measure fluxes of carbon dioxide and other gasses in an out of canopies. Two types of towers have been widely employed: Bowen Ratio Energy Balance (BREB) and eddy covariance (EC) towers. BREB towers measure gradients of temperature, moisture and carbon dioxide at two points in the turbulent boundary layer over a canopy at (typically) 2 second intervals and data are averaged over 20 minute intervals. Gradients measured over the canopy cannot be used to directly compute fluxes because the transfer coefficients are not known. However, if transfer coefficients for sensible heat and moisture are assumed to be equal their ratio can be calculated (the Bowen ratio) [53]:  
\[\beta=\gamma\mathrm{[T_{1}\ \mathrm{-}\ \mathrm{T_{u}}]/[e_{1}\ \mathrm{-}\ e_{u}]}= \mathrm{H}/\lambda\mathrm{ET} \tag{6}\]  
where \(\gamma\) is the psychrometric constant, \(\mathrm{T_{1}}\) and \(\mathrm{T_{u}}\) are upper and lower temperatures and \(\mathrm{e_{l}}\) and \(\mathrm{e_{u}}\) are lower and upper moisture contents. Then Equations (5) and (6) can be combined to solve for \(\lambda\mathrm{ET}\):  
\[\lambda\mathrm{ET}=(\mathrm{R_{n}}\ \mathrm{-}\ \mathrm{G})/(\beta+1) \tag{7}\]  
BREB towers have net radiometers and soil heat flux plates to measure \(\mathrm{R_{n}}\) and \(\mathrm{G}\); they can also be used to measure gradients in carbon dioxide and other gasses to determine their fluxes in and out of canopies, assuming their transport coefficients are the same as for moisture and sensible heat. EC towers are instrumentally more sophisticated than BREB towers [52]. They contain sensitive instruments that measure carbon dioxide, moisture, air temperature and the vertical components of wind speed at a single point over the canopy. Data are collected 20 times per second and are averaged every 30 minutes. Over the longer time scale, the vertical component of wind speed is expected to be zero over a level surface, but at the shorter time scale eddies of air can have a net upward or downward velocity. If, on average, upward eddies have higher moisture content than downward eddies, then a net flux of water out of the canopy is measured over integrated 30 minute data intervals; on the other hand, if downward eddies have higher carbon dioxide content than upward eddies, a net flux of carbon into the canopy is measured. EC towers provide direct measurements of fluxes. Additional instruments measure wind speed, net radiation, soil heat flux and other parameters required in detailed SVAT models and to solve Equation (5). Flux measurements are subject to several sources of error. They are point measurements, but they require a uniform fetch of vegetation of several thousand square meters (e.g., 50 m x 50 m) around the towers to produce results that are representative of a particular ecosystem, and these conditions are often not perfectly met in natural landscapes. Instrument error and data drop-out introduce errors of about 20% when different towers are intercalibrated at the same site [52]. Furthermore, when EC results are compared to BREB results, EC moisture flux estimates are often 10-30% lower than energy closure (BREB) results. EC results are often increased to account for this \"closure error\" [54], but the best way to achieve closure, and the cause of the closure error, are still unclear [51, 52]. Flux towers measure net ecosystem rates of carbon dioxide and moisture fluxes in and out of canopies.