1. Towards a robust, generalizable non-linear regression gap filling algorithm (NLR_EM) Ankur R Desai – National Center for Atmospheric Research (NCAR) Boulder, Colorado, USA University of Wisconsin, Atmospheric & Oceanic Sciences, Madison, Wisconsin, USA Pennsylvania State University, Meteorology, University Park, Pennsylvania, USA Bruce D Cook – University of Minnesota, Forest Resources St. Paul, Minnesota, USA Kenneth J Davis – Pennsylvania State University, Meteorology University Park, Pennsylvania, USA Gap Filling Workshop 18 Sept 2006 Max-Planck BGC, Jena, Germany

2. Goals Simple, fast, general GPP/RE and gap-filling estimation for eddy flux NEE Simple, fast, general GPP/RE and gap-filling estimation for eddy flux NEE Theoretically meaningful parameters Theoretically meaningful parameters Statistically valid regression Statistically valid regression Flexible moving window regression Flexible moving window regression Temperature / PAR forcing only Temperature / PAR forcing only Used at ChEAS Ameriflux sites Used at ChEAS Ameriflux sites Code written in IDL, available to all Code written in IDL, available to all

3. Primary references Desai, A. R., P. Bolstad, B. D. Cook, K. J. Davis, and E. V. Carey, 2005: Comparing net ecosystem exchange of carbon dioxide between an old-growth and mature forest in the upper Midwest, USA. Agric.For.Meteorol., 128, 33-55 (doi: 10.1016/j.agrformet.2004.09.005). Desai, A. R., P. Bolstad, B. D. Cook, K. J. Davis, and E. V. Carey, 2005: Comparing net ecosystem exchange of carbon dioxide between an old-growth and mature forest in the upper Midwest, USA. Agric.For.Meteorol., 128, 33-55 (doi: 10.1016/j.agrformet.2004.09.005). Cook, B. D., K. J. Davis, W. Wang, A. R. Desai, B. W. Berger, R. M. Teclaw, J. M. Martin, P. Bolstad, P. Bakwin, C. Yi, and W. Heilman, 2004: Carbon exchange and venting anomalies in an upland deciduous forest in northern Wisconsin, USA. Agric.For.Meteorol., 126, 271-295 (doi:10.1016/j.agrformet.2004.06.008). Cook, B. D., K. J. Davis, W. Wang, A. R. Desai, B. W. Berger, R. M. Teclaw, J. M. Martin, P. Bolstad, P. Bakwin, C. Yi, and W. Heilman, 2004: Carbon exchange and venting anomalies in an upland deciduous forest in northern Wisconsin, USA. Agric.For.Meteorol., 126, 271-295 (doi:10.1016/j.agrformet.2004.06.008). Eyring, H., 1935: The activated complex in chemical reactions. J.Chem.Phys., 3, 107-115. Eyring, H., 1935: The activated complex in chemical reactions. J.Chem.Phys., 3, 107-115.

4. Sites that use NLR_EM http://cheas.psu.edu http://cheas.psu.edu http://cheas.psu.edu Sites that use it: Sylvania Old-growth, Lost Creek wetland, WLEF 447-m tall tower (3 levels), Willow Creek upland. Others only site-to-site comp. Sites that use it: Sylvania Old-growth, Lost Creek wetland, WLEF 447-m tall tower (3 levels), Willow Creek upland. Others only site-to-site comp.

5. Algorithm highlights 1 parameter set per day for ER and GPP 1 parameter set per day for ER and GPP 30-60 day moving window: size increases until 200 good half-hourly points – all user definable 30-60 day moving window: size increases until 200 good half-hourly points – all user definable One-tailed t-test for parameter fit One-tailed t-test for parameter fit if confidence < 0.90, replace ER/GPP with daily mean ER/GPP over window if confidence < 0.90, replace ER/GPP with daily mean ER/GPP over window mostly occurs in winter mostly occurs in winter Monte-Carlo random gap generator to compute sensitivity of filling to gaps - reported for sites Monte-Carlo random gap generator to compute sensitivity of filling to gaps - reported for sites

6. Respiration Use nighttime u*-screened NEE and 5 cm soil temperature (can use air temp instead) Use nighttime u*-screened NEE and 5 cm soil temperature (can use air temp instead) Regress against Eyring equation: Regress against Eyring equation: similar to Arrhenius but more accurate description of reaction activation energies by including entropy similar to Arrhenius but more accurate description of reaction activation energies by including entropy For regression, total carbon content not needed For regression, total carbon content not needed

7. Respiration Gibbs free energy: Gibbs free energy: Regress with linear form of equation: Regress with linear form of equation:

8. Example of ΔG++ From Cook et al (2004) From Cook et al (2004)

9. GPP Simple 2 or 3 parameter equation: Simple 2 or 3 parameter equation: Can relate b1/b2 to Amax and quantum yield Can relate b1/b2 to Amax and quantum yield b3 can be included as an intercept b3 can be included as an intercept T-test failure replaces b1 with mean GPP T-test failure replaces b1 with mean GPP Levenberg-Marquardt non-linear regression Levenberg-Marquardt non-linear regression

10. Example of b1/b2 From Cook et al (2004) From Cook et al (2004)

11. Error estimation Simple Monte Carlo estimate of error induced by gap-filling Simple Monte Carlo estimate of error induced by gap-filling 100 sets of random 10-40 artificial gaps of lengths 30 minutes – 5 days 100 sets of random 10-40 artificial gaps of lengths 30 minutes – 5 days Error reported as standard deviation and range of NEE across 100 sets (e.g., Desai et al., 2005; Desai et al., in press, Ag. For Met.) Error reported as standard deviation and range of NEE across 100 sets (e.g., Desai et al., 2005; Desai et al., in press, Ag. For Met.)

12. Other notes Can use filled or non-filled met data Can use filled or non-filled met data ChEAS filled met relies on cluster of met sites ChEAS filled met relies on cluster of met sites Without filled met data, mean diurnal values and interpolation used to fill either met or flux Without filled met data, mean diurnal values and interpolation used to fill either met or flux Can use other ER/GPP equations Can use other ER/GPP equations Day/night determined by sunrise/set at lat/lon and by a low PAR criterion Day/night determined by sunrise/set at lat/lon and by a low PAR criterion Algorithm has been used across Ameriflux in a Modis GPP – flux tower evaluation project Algorithm has been used across Ameriflux in a Modis GPP – flux tower evaluation project Filling NEE = ER - GPP Filling NEE = ER - GPP

13. Next steps Harder to use well in non-temperate sites Harder to use well in non-temperate sites Exploration of phenologically controlled windows Exploration of phenologically controlled windows Not good for moisture-limited sites Not good for moisture-limited sites Cross-site Gibbs free energy comparisons require total carbon content, but has promising use for examining ER parameter spatial var. Cross-site Gibbs free energy comparisons require total carbon content, but has promising use for examining ER parameter spatial var. Interested in understanding model bias in gap filling and exploring energy activation across sites used in this study Interested in understanding model bias in gap filling and exploring energy activation across sites used in this study

14. Advertisement GPP/ER intercomparison GPP/ER intercomparison Tuesday, 13:00 Tuesday, 13:00 Most gap-filling methods can produce GPP/ER Most gap-filling methods can produce GPP/ER How variable are they? How variable are they? Across methods / sites Across methods / sites Due to gaps in NEE Due to gaps in NEE Can we infer ecosystem parameters? Can we infer ecosystem parameters? I have most of these data, but not all I have most of these data, but not all Send them in to me Send them in to me or else or else