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Campbell, Quantifying uncertainty in ecology: Examples from small watershed studies.
- 1. Quantifying Uncertainty in Ecology: Examples from Small Watershed Studies John Campbell – US Forest Service Ruth Yanai – SUNY-ESF Mark Green – Plymouth State Univ. Ecological Society of America Meeting Minneapolis, MN - August 2013
- 2. LTER Workshop Participants Sites Fernow - WV Biscuit Brook - NY HJ Andrews - OR Luquillo - PR Niwot Ridge – CO Marcell - MN Sleepers River – VT Coweeta – NC Campbell, J.L., Yanai, R.D., Green, M.B., Levine, C. R, Adams, M.B., Burns, D.A., Buso, D.C., Harmon, M.E., LaDeau, S.L., McDowell, W.H., Parman, J.N., Sebestyen, S.D., Shanley, J.B., Vose, J.M.
- 3. QUEST is a NSF funded Research Coordination Network (PI: Ruth Yanai) The goal is to improve understanding and facilitate use of uncertainty analyses in ecosystem studies.
- 4. Become a part of QUEST! •Visit our website (www.quantifyinguncertainty.org) •Download papers and presentations •Get sample code •Stay updated with QUEST News •Join our mailing list (quantifyinguncertainty@gmail.com) •Meet us for dinner tonight (7pm - Hell’s Kitchen)
- 5. Paired watershed studies • Watersheds are unreplicated • It’s difficult to find suitable replicate watersheds and expensive to treat them • Uncertainty analysis can be used to report statistical confidence Andréassian 2004 Journal of Hydrology 29:1-27
- 6. Easier said than done… • Difficult to identify sources of uncertainty • Difficult to quantify sources • Multiple approaches to uncertainty analysis • No single answer
- 7. Uncertainty in the flux of Ca W6 W5 • Net hydrologic flux = precipitation inputs minus stream outputs • W5 - whole tree harvest during winter of 1983-1984 • All trees >5 cm dbh were removed (boles and branches) • Purpose: evaluate impact of this more intensive management practice on nutrient removals and site productivity
- 8. Net hydrologic flux (kg ha-1 yr-1) Ca response to harvesting 0 Harvest -3 -6 -9 -12 -15 -18 W6 (reference) W5 (harvested) -21 -24 1960 1970 1980 1990 2000 Water year (June 1) Calcium data courtesy G.E. Likens 2010
- 9. Sources of uncertainty Precipitation Stream water • Interpolation model • Watershed area • Collector undercatch • Rating curve • Chemical analysis • Gaps in discharge • Gaps in chemistry • Chemical analysis • Streamwater interpolation model
- 10. Precipitation interpolation method W3 Thiessen polygon W3 Kriging W2 W6 W5 W4 W1 W2 W6 W5 W4 W1 W8 W7 W8 W7 W9 W9 W3 W3 Inverse distance weighting Spline W2 W6 W5 W4 W1 W2 W6 W5 W4 W1 W8 W8 W7 W7 W9 W9 W3 Regression W2 W6 W5 W4 W1 W8 W7 W9 Precip. gage Watershed 1000 Precip. 0 1000 m 1600 mm
- 11. Precipitation interpolation method 1520 Annual precip. (mm) 1500 1480 1460 Thiessen Kriging IDW Spline Regression 1440 1420 1400 1380 1360 1340 W1 W2 W3 W4 W5 W6 W7 W8 W9 Uncertainty = 0.6%
- 12. Chemical analyses • Precision describes the variation in replicate analysis of the same sample • At Hubbard Brook, one sample of every 40 is analyzed four times Uncertainty = 1.0%
- 13. Watershed area
- 14. Watershed area W6 Uncertainty = 2.3%
- 15. Gaps in streamflow • • 7% of streamflow record is gaps 65% due to the chart recorder (53% clock)
- 16. Gaps in streamflow • Randomly generate fake gaps • Fill the gaps based on regression from the reference watershed • Calculate the different between the predicted and actual value • Repeat thousands of times • More detail to follow Uncertainty = 3.3%
- 17. What is Monte Carlo analysis? Monte Carlo simulations use repeated, random sampling to compute results. 1) Select a distribution to describe possible values (not necessary to assume a normal distribution) 2) Generate data from this distribution 3) Use the generated data as possible values in the calculation to produce output
- 18. Monte Carlo approach Watershed Area Streamflow Etc. Net Hydrologic Flux Calculation
- 19. Net hydrologic flux (kg ha-1 yr-1) Ca response to harvesting 0 -3 Harvest Harvest -6 -9 -12 -15 -18 W6 (reference) W5 (harvested) -21 -24 1960 1970 1980 1990 Water year (June 1) 2000 2010
- 20. W5 Ca net hydrologic flux (kg/ha./yr) Ca response to harvesting 0 -5 -10 -15 -20 -25 -25 -20 -15 -10 -5 W6 Ca Net hydrologic flux (kg/ha/yr) 0
- 22. Conclusions • Uncertainty analysis can be used in cases where replication is not possible • Monte Carlo is just one of many possible approaches • There’s no such thing as a perfect uncertainty analysis • It’s important to report how the uncertainty was calculated
- 23. Acknowledgments LTER Workshop Participants Craig See Brannon Barr Gene Likens Amey Bailey Ian Halm Nick Grant Tammy Wooster Brenda Minicucci Funding was provided by the NSF and LTER Network Office. Calcium data were obtained through funding from the A.W. Mellon Foundation and the NSF, including LTER and LTREB.