This document discusses quantifying uncertainty in ecosystem budgets. It provides examples of different types of uncertainty commonly encountered in ecosystem studies, including natural variability, measurement error, and model error. The document also examines specific studies that have quantified uncertainty in components of the nitrogen budget at the Hubbard Brook Experimental Forest, including precipitation inputs, streamflow outputs, forest biomass nitrogen, soil nitrogen pools, and nitrogen accumulation rates. Monte Carlo simulations were used to analyze how uncertainty in inputs propagates to uncertainty in overall budget calculations. The studies aim to improve estimates of uncertainty and identify areas where reducing uncertainty could have the most impact.

1. Uncertainty in Forest Carbon
and Nutrient Budgets
Ruth D. Yanai
State University of New York
College of Environmental Science and Forestry
Syracuse NY 13210, USA

2. Quantifying uncertainty in ecosystem budgets
Precipitation (evaluating monitoring intensity)
Streamflow (filling gaps with minimal uncertainty)
Forest biomass (identifying the greatest sources of uncertainty)
Soil stores (detectable differences)
QUANTIFYING UNCERTAINTY
IN ECOSYSTEM STUDIES

3. UNCERTAINTY
Natural Variability
Spatial Variability
Temporal Variability
Knowledge Uncertainty
Measurement Error
Model Error
Types of uncertainty commonly
encountered in ecosystem studies
Adapted from Harmon et al. (2007)

4. Bormann et al. (1977) Science
How can we assign confidence in ecosystem
nutrient fluxes?

5. Bormann et al. (1977) Science
The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr

6. Net N gas exchange = sinks – sources =
- precipitation N input
+ hydrologic export
+ N accretion in living biomass
+ N accretion in the forest floor
± gain or loss in soil N stores
- weathering N input
The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± ?? kg/ha/yr

7. The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± ?? kg/ha/yr

8. Measurement Uncertainty Sampling Uncertainty
Spatial and Temporal Variability
Model Uncertainty
Error within models Error between models
Volume = f(elevation, aspect): 3.4 mm
Undercatch: 3.5%
Chemical analysis: 0-3%
Model selection: <1%
Across
catchments:
3%
Across years:
14%

10. We tested the effect of sampling intensity by sequentially omitting
individual precipitation gauges.
Estimates of annual precipitation volume varied little until five or more
of the eleven precipitation gauges were ignored.

11. The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± ?? kg/ha/yr

12. The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± ?? kg/ha/yr

13. Yanai, Levine, Green, and Campbell (2012) Journal of Forestry

14. Don Buso HBES

15. Gaps in the discharge record are filled by
comparison to other streams at the site,
using linear regression.
S5
S12
S16
S17
S20
0
100
200
0 100 200
0
100
200
300
0 100 200 300
0
50
100
150
0 50 100 150
0
50
100
150
0 50 100 150
0
50
100
0 50 100

16. Cross-validation: Create fake gaps and
compare observed and predicted discharge
Yanai et al. (2014)
Hydrological Processes

17. Net N gas exchange = sinks – sources =
- precipitation N input (± 1.3)
+ hydrologic export (± 0.5)
+ N accretion in living biomass
+ N accretion in the forest floor
± gain or loss in soil N stores
The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± ?? kg/ha/yr

18. Net N gas exchange = sinks – sources =
- precipitation N input (± 1.3)
+ hydrologic export (± 0.5)
+ N accretion in living biomass
+ N accretion in the forest floor
± gain or loss in soil N stores
The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± ?? kg/ha/yr

19. Tree Inventory
log(Height) = a + b*log(Diameter) ± error
log (Mass) = a + b*log(1/2 r2
*Height) ± error
Nutrient content = Mass * (Concentration ± error)
Sum all trees and all tissue types
Allometric Equations
and Nutrient Concentrations

20. Monte Carlo
Simulation
Yanai, Battles, Richardson, Rastetter,
Wood, and Blodgett (2010) Ecosystems
Monte Carlo simulations use
random sampling of the
distribution of the inputs to a
calculation. After many
iterations, the distribution of the
output is analyzed.

21. Repeated Calculations of N in Biomass
Hubbard Brook Watershed 6

22. 611 ± 54 kg N/ha
Nitrogen Content of Biomass
with Uncertainty

23. ***IMPORTANT***
Random selection of parameter
values applies across all the
trees and all the time periods in
each iteration.
The uncertainty between two
measurements can be less than
in a single measurement!

24. 100 Simultaneous Calculations
of N in Biomass in 1997 and 2002

25. 100 Simultaneous Calculations
of N in Biomass in 1997 and 2002

26. Accumulation Rate of N in Biomass
Distribution of Estimates
18 ± 5 kg N/ha over 5 yr

27. C1 C2 C3 C4 C5 C6 HB-Mid JB-Mid C7 C8 C9 HB- Old JB-Old
Young Mid-Age Old
Biomass of thirteen stands
of different ages

28. C1 C2 C3 C4 C5 C6 HB-Mid JB-Mid C7 C8 C9 HB- Old JB-Old
3% 7% 3%
4% 4% 3% 3% 3%
3% 2% 4% 4% 5%
Coefficient of variation (standard deviation / mean)
of error in allometric equations
Young Mid-Age Old

29. C1 C2 C3 C4 C5 C6 HB-Mid JB-Mid C7 C8 C9 HB- Old JB-Old
Young Mid-Age Old
3% 7% 3%
4% 4% 3% 3% 3%
3% 2% 4% 4% 5%
CV across plots within stands (spatial variation)
Is greater than the uncertainty in the equatsions
6% 15% 11%
12% 12% 18% 13% 14%
16% 10% 19% 3% 11%

30. Yanai, Levine, Green, and Campbell (2012) Journal of Forestry

31. Net N gas exchange = sinks – sources =
- precipitation N input (± 1.3)
+ hydrologic export (± 0.5)
+ N accretion in living biomass (± 1)
+ N accretion in the forest floor
± gain or loss in soil N stores
The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± ?? kg/ha/yr

32. Net N gas exchange = sinks – sources =
- precipitation N input (± 1.3)
+ hydrologic export (± 0.5)
+ N accretion in living biomass (± 1)
+ N accretion in the forest floor
± gain or loss in soil N stores
The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± ?? kg/ha/yr

33. Oi
Oe
Oa
E
Bh
Bs
Forest
Floor
Mineral
Soil
}
}

34. Nitrogen in the Forest Floor
Hubbard Brook Experimental Forest
y = 0 .0 0 0 2 x - 0 . 1 6 1 9
R 2
= 0 . 0 1 0 9
0
0 . 0 5
0 .1
0 . 1 5
0 .2
0 . 2 5
1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 1 9 9 5 2 0 0 0 2 0 0 5
ForestFloorN(kg/m2)

35. Nitrogen in the Forest Floor
Hubbard Brook Experimental Forest
y = 0 .0 0 0 2 x - 0 . 1 6 1 9
R 2
= 0 . 0 1 0 9
0
0 . 0 5
0 .1
0 . 1 5
0 .2
0 . 2 5
1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 1 9 9 5 2 0 0 0 2 0 0 5
ForestFloorN(kg/m2)
The change is insignificant (P = 0.84).
The uncertainty in the slope is ± 22 kg/ha/yr.

36. Net N gas exchange = sinks – sources =
- precipitation N input (± 1.3)
+ hydrologic export (± 0.5)
+ N accretion in living biomass (± 1)
+ N accretion in the forest floor (± 22)
± gain or loss in soil N stores
The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± ?? kg/ha/yr

37. Studies of soil change over time often fail to detect a difference.
We should always report how large a difference is detectable.
Yanai et al. (2003) SSSAJ

38. Power analysis can be used to determine the
difference detectable with known confidence
Yanai et al. (2003) SSSAJ

39. Sampling the same experimental units over time
permits detection of smaller changes
Yanai et al. (2003) SSSAJ

40. In this analysis of forest floor studies,
few could detect small changes
Yanai et al. (2003) SSSAJ

41. Net N gas exchange = sinks – sources =
- precipitation N input (± 1.3)
+ hydrologic export (± 0.5)
+ N accretion in living biomass (± 1)
+ N accretion in the forest floor (± 22)
± gain or loss in soil N stores
The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± ?? kg/ha/yr

42. Nitrogen Pools (kg/ha)
Hubbard Brook Experimental Forest
1796
29
10
1260
750
3080
Forest Floor
Live Vegetation
Coarse Woody Debris
Mineral Soil
10 cm-C
Dead Vegetation
Mineral Soil
0-10 cm
Yanai et al. (2013) ES&T

43. Quantitative Soil Pits
0.5 m2
frame

44. Excavate Forest Floor by horizon
Mineral Soil by depth increment

45. Sieve and weigh in the field
Subsample for laboratory analysis

46. In some studies, we excavate in the
C horizon!

47. We can’t detect a difference of 730 kg N/ha in the mineral soil.
From 1983 to 1998, 15 years post-harvest, there was an
insignificant decline of 54 ± 53 kg N ha-1
y-1
Huntington et al. (1988)
Yanai et al. (2013) ES&T

48. Net N gas exchange = sinks – sources =
- precipitation N input (± 1.3)
+ hydrologic export (± 0.5)
+ N accretion in living biomass (± 1)
+ N accretion in the forest floor (± 22)
± gain or loss in soil N stores (± 53)
The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± ?? kg/ha/yr

49. Net N gas exchange = sinks – sources =
- precipitation N input (± 1.3)
+ hydrologic export (± 0.5)
+ N accretion in living biomass (± 1)
+ N accretion in the forest floor (± 22)
± gain or loss in soil N stores (± 53)
The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± 57 kg/ha/yr

50. Net N gas exchange = sinks – sources =
- precipitation N input (± 1.3)
+ hydrologic export (± 0.5)
+ N accretion in living biomass (± 1)
The N budget for Hubbard Brook published
in 1977 was “missing” 14.2 kg/ha/yr
14.2 ± 2.6 kg/ha/yr
Draw your budget boundaries to ask questions
that can be answered with confidence!

51. The Value of Uncertainty Analysis
Quantify uncertainty in our results
Uncertainty in regression
Monte Carlo sampling
Detectable differences
Identify ways to reduce uncertainty
Devote effort to the greatest unknowns
Improve efficiency of monitoring efforts

52. Be a part of QUEST!
• Find more information at: www.quantifyinguncertainty.org
• Read papers, share sample code, stay updated with QUEST News
• Email us at quantifyinguncertainty@gmail.com
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QUANTIFYING UNCERTAINTY
IN ECOSYSTEM STUDIES

53. References
Yanai, R.D., N. Tokuchi, J.L. Campbell, M.B. Green, E. Matsuzaki, S.N. Laseter, C.L.
Brown, A.S. Bailey, P. Lyons, C.R. Levine, D.C. Buso, G.E. Likens, J. Knoepp, K.
Fukushima. 2014. Sources of uncertainty in estimating stream solute export from
headwater catchments at three sites. Hydrological Processes. DOI: 10.1002/hyp.10265
Yanai, R.D., M.A. Vadeboncoeur, S.P. Hamburg, M.A. Arthur, M.A. Fuss, P.M.Groffman,
T.G. Siccama, and C.T. Driscoll. 2013. From Missing Source to Missing Sink: Long-
Term Changes in a Forest Nitrogen Budget. Environmental Science & Technology.
47(20):11440-11448.
Yanai, R.D., C.R. Levine, M.B. Green, and J.L. Campbell. 2012. Quantifying uncertainty
in forest nutrient budgets, J. For. 110: 448-456
Yanai, R.D., J.J. Battles, A.D. Richardson, E.B. Rastetter, D.M. Wood, and C. Blodgett.
2010. Estimating uncertainty in ecosystem budget calculations. Ecosystems 13: 239-248
Wielopolski, L, R.D. Yanai, C.R. Levine, S. Mitra, and M.A Vadeboncoeur. 2010.
Rapid, non-destructive carbon analysis of forest soils using neutron-induced gamma-ray
spectroscopy. For. Ecol. Manag. 260: 1132-1137
Yanai, R.D., S.V. Stehman, M.A. Arthur, C.E. Prescott, A.J. Friedland, T.G. Siccama, and
D. Binkley. 2003. Detecting change in forest floor carbon. Soil Sci. Soc. Am. J. 67:1583-
1593
My web site: www.esf.edu/faculty/yanai (Download any papers)

54. Alternative spatial models for precipitation in the Hubbard Brook Valley

55. Alternative spatial models for precipitation in the Hubbard Brook Valley
0.36%
0.58%
0.24%
0.77% 0.83%