# Presentation: 576269

## Uncertainty in tower-based measurements of carbon and energy fluxes: A multi-site analysisAndrew D. Richardson1, David Y. Hollinger2, George G. Burba3, Kenneth J. Davis4, Lawrence B. Flanagan5, Gabriel G. Katul6, J. William Munger7, Daniel M. Ricciuto8, Paul C. Stoy6, Andrew E. Suyker8, Shashi B. Verma8, and Steven C. Wofsy7.1University of New Hampshire, Complex Systems Research Center, Durham NH 03824. E-mail: andrew.richardson@unh.edu; 2USDA Forest Service, NE Research Station; 3Li-Cor Biosciences, Inc.; 4Penn State University; 5University of Lethbridge; 6Duke University; 7Harvard University; 8University of Nebraska-Lincoln. 

- Uncertainty in H is relatively constant (≈20 W m-2) throughout the year, whereas LE uncertainty is generally < 5 W m-2 during the winter months, and > 15 W m-2 from May-September (panel A, data represent means across all sites). FCO2 uncertainty (panel B) also follows a strong seasonal pattern. Lethbridge data for unproductive drought years (99-01) and more productive non-drought years (02-04) illustrate how the flux uncertainty is larger when the flux itself is larger (i.e., June-September).

- Flux magnitude effects
- For all three fluxes, the uncertainty scales with the magnitude of the flux, although the relationship differs for |F| > 0 and |F| < 0. The flux uncertainty does not → 0  as F → 0, so there is underlying base uncertainty that is always present. The patterns are very similar across these four forested sites, suggesting that these results could be used as a general model of uncertainty at other forested sites.

- Statistical properties of the inferred uncertainty
- The daily-differenced data have a mean close to zero. The standard deviation of the differences varies among H, LE, and FCO2, and in relation to environmental factors, e.g. time of year or time of day. The distribution of the differences is, for the most part, symmetric, because the skewness is close to zero. However, the distribution is more strongly peaked than a normal distribution, because the kurtosis > 3. Results from the other towers were similar.

- Distribution of the uncertainty
- At all sites, and for each of H, LE, and FCO2,  the distribution of the flux uncertainty was more closely approximated by a double exponential, or Laplace, distribution (red line) than a normal, or Gaussian, distribution (black line). A double exponential distribution is leptokurtic in that it has a tighter central peak. The distribution of the uncertainty is strikingly similar at Howland and Harvard. The uncertainty appears to be smaller (at least for LE and FCO2) at Lethbridge, a grassland site. At the tall tower site (Argyle, located near Howland and measuring similar forest vegetation), the distribution of the uncertainty has heavier tails than any of the other sites.

- Wind speed effect
- For FCO2, flux uncertainty decreases with increasing wind speed. Although theory predicts that this should also be the case for H and LE, energy flux uncertainties appear not to exhibit this behavior.

**Uncertainty in tower-based measurements of carbon and energy fluxes: A multi-site analysis**Andrew D. Richardson1, David Y. Hollinger2, George G. Burba3, Kenneth J. Davis4, Lawrence B. Flanagan5, Gabriel G. Katul6, J. William Munger7, Daniel M. Ricciuto8, Paul C. Stoy6, Andrew E. Suyker8, Shashi B. Verma8, and Steven C. Wofsy7.1University of New Hampshire, Complex Systems Research Center, Durham NH 03824. E-mail: andrew.richardson@unh.edu; 2USDA Forest Service, NE Research Station; 3Li-Cor Biosciences, Inc.; 4Penn State University; 5University of Lethbridge; 6Duke University; 7Harvard University; 8University of Nebraska-Lincoln.

- Overview
- ● Measured flux data, *X*, represent the true flux, *F*, plus or minus some random measurement error, , plus or minus any systematic errors, : *X* = *F* + . The random measurement error (“flux uncertainty”) is distinct from potential systematic errors due to incomplete spectral response or lack of nocturnal mixing (*u**). It is necessary to know the characteristics of the flux uncertainty  for model-data syntheses (i.e., properly conduct maximum-likelihood estimation when assimilating models and data), to make valid statistical comparisons between measured and modeled data, or to estimate confidence intervals on annual flux sums.
- ● Data from seven sites (five forested sites, one grassland, and one agricultural site) are used to show that the uncertainty in measured fluxes (H, LE, and FCO2) follows a double-exponential, rather than a normal, distribution, and increases as a linear function of the magnitude of the flux.
- ● Variation in the flux uncertainty follows similar patterns at the different sites. The flux uncertainty decreases with increasing wind speed for FCO2 but not for H or LE.
- ● These results provide a foundation for incorporating flux data uncertainty information in model-data assimilation problems.

- Determining the flux uncertainty
- Our objective is to determine the statistical properties of the random measurement error, . We are most interested in calculating the standard deviation of , (). We will also attempt to identify an appropriate probability distribution function for .
- In a recent paper (Hollinger and Richardson, 2005) we proposed that simultaneous measurements (*X*1, *X*2) from two towers separated by ≈ 775 m at the Howland Forest AmeriFlux site (35 miles north of Bangor, ME, USA, 45° 15' N, 68° 44' W, 60 m asl), give us a means by which  can be estimated, provided that the iat each tower are independent and identically distributed:
- However, at most flux tower sites around the world, continuous paired measurements like this are not being made. We therefore developed an alternative method, in which time substitutes for space, and flux measurements made on two successive days, exactly 24 hours apart, under similar environmental conditions (PPFD within 75 mol m-2 s-1, air temperature within 3 oC, and wind speed within one speed bin), are used as analogues of the simultaneous two-tower paired measurements *X*1, *X*2.
- Results using this “daily differencing approach” have been shown (Hollinger and Richardson, 2005) to be quite comparable to the uncertainty estimates calculated with the two-tower method. Comparison of the Rn- relationships indicates that the daily differencing approach leads to an overestimation of (H) by about 20 W m-2, and an overestimation of (LE) by about 20-25%; the wind speed- relationship indicates that (FCO2) is also overestimated by about 20-25% with the daily differencing approach.

- Conclusions
- ● The flux measurement uncertainty in H, LE and FCO2 is distributed as a double-exponential distribution. The distribution is much more peaked than a normal distribution. The standard deviation of the uncertainty is not constant, but rather varies with the magnitude of the flux, and in relation to other environmental parameters. As a result, there are definite seasonal patterns in the LE and FCO2 uncertainties, but H uncertainty is more or less constant throughout the year.
- ● The relationship between (FCO2) and wind speed is probably due to enhanced mixing and suggests that windier sites are preferable. But increasing measurement height to increase *u* has drawbacks: at the Argyle (tall tower) site, the FCO2 uncertainty was very high at low wind speeds.
- ● Because the uncertainty is non-normal and heteroscedastic, two of the assumptions underlying least squares optimization are violated. Maximum likelihood estimation techniques, which make use of the flux uncertainty information, have been developed for the double-exponential case with non-constant i, and are preferable to least-squares optimization.

- 

- Characterizing the distribution

- Acknowledgements
- The Howland flux research was supported by the USDA Forest Service Northern Global Change Program, the Office of Science (BER), U.S. Department of Energy, through the Northeast Regional Center of the National Institute for Global Environmental Change under Cooperative Agreement No. DE-FC03-90ER61010, and by the Office of Science (BER), U.S. Department of Energy, Interagency Agreement No. DE-AI02-00ER63028.  The data used here for Howland, as well as the other tower sites, are available at http://public.ornl.gov/ameriflux/ subject to AmeriFlux “Fair-use” rules.

- Study sites

- A double exponential distribution with mean zero has the following probability distribution function:
- The double exponential distribution is character-ized by the scale parameter , and has a standard deviation of  = √2 . An estimator for  is:
- This table shows that magnitude of the uncertainty ( = √2 ) is relatively similar across all sites for H.
- For LE and FCO2, the uncertainty is considerably smaller at Lethbridge than the other sites. The pattern of variation in relation to environmental conditions is, however, similar across sites.

*This poster, and related papers, can be downloaded from: *http://www.forest.sr.unh.edu/richardson