1. Bayesian Deconvolution of Belowground Ecosystem Processes Kiona Ogle University of Wyoming Departments of Botany & Statistics

2. Ecosystem Processes Emphasis on aboveground What about belowground?

3. N H20H20H20H20 H20H20H20H20 H20H20H20H20 C C N P Biogeochemical Cycles

4. N H20H20H20H20 H20H20H20H20 H20H20H20H20C C N P Belowground system is critical to understanding and forecasting whole-ecosystem behavior

5. Deconvolution of Belowground Processes The water cycle Partitioning plant water sources The carbon cycle Partitioning soil respiration Data-model assimilation Diverse data sources Stable isotopes Bayesian deconvolution framework Today’s example

6. Challenges Patitioning sources of CO 2 fluxes Patitioning sources of CO 2 fluxes Systems: soils & ecosystems Sources: autotrophs vs. heterotrophs Source contributions wrt soils: Source contributions wrt soils: By soil depth (including litter) By species or functional group (autotrophs) Spatial variability Temporal dynamics Environmental drivers

7. CO 2 Partitioning Soil Respiration How does pulse precipitation affect sources of respired CO 2 ? From where in the soil is CO 2 coming from??? Relative contributions of C3 roots (shrub), C4 roots (grass), and heterotrophs (soil & litter)? CO 2 ?? ?? ??

8. Bayesian Deconvolution Approach Integrate multiple sources of information Integrate multiple sources of information Diverse data sources Different temporal & spatial scales Literature information Lab & field studies Detailed flux models Detailed flux models Respiration rates by source type & soil depth Dynamic models Mechanistic isotope mixing models Mechanistic isotope mixing models Multiple sources

9. The Deconvolution Problem Isotope mixing model (multiple sources & depths) Relative contributions (by source & depth) Total flux (at soil surface) Flux model (source- & depth- specific) Mass profiles (substrate, microbes, roots) (Q 10 Function, Energy of Activation) ?? Contributions by source ( i ) and depth ( z )? Temporal variability? Source-specific respiration? Spatial & temporal variability? ?? ?? Theory & Process Models

10. What is  i ? (source-specific parameters) The Deconvolution Problem Objectives Flux model (source- & depth- specific) Covariate data  Total soil flux  Contributions How to estimate  i, r i, and p i ?

11. posterior  likelihood  process model  prior Bayesian Deconvolution The Bayesian Model Statistical model (Bayesian probability model) Likelihood of data (isotopes & soil flux) From isotope mixing model & flux models Functions of  i The Likelihood Goal: find values of  i that result in “best” agreement b/w models & data From Keeling plots From automated chambers

12. Bayesian Deconvolution Prior Information Example: Example: Lloyd & Taylor (1994) model E o T o Informative priors for E o and T o : Statistical model (Bayesian probability model) posterior  likelihood  process model  prior

13. stochastic dataLiterature data Data Source Examples Soil Isotopes ( δ 13 C Tot ) (automated chambers & Keeling plots) Soil CO 2 flux (manual chambers) Pool Isotopes ( δ 13 C i ) (roots, soil, litter; Keeling plots) Soil CO 2 flux (automated chambers) Root respiration (in situ gas exchange) Root distributions (arid systems, different functional types) Soil carbon (arid systems; total C) Root respiration (arid systems, different functional types) Microbial mass (arid systems; total mass) Root mass (arid systems; total mass) Litter (arid systems; total mass, carbon, microbes) Soil temp & water (automated, multiple locations, many depths) covariate data Soil samples (carbon content, C:N, root mass) Soil incubations (root-free, carbon substrate, microbial mass, heterotrophic activity)

14. Implementation Markov chain Monte Carlo (MCMC) Markov chain Monte Carlo (MCMC) Sample parameters ( θ i ) from posterior Posteriors for: θ i ’s, r i ( z,t ) ’s, p i ( z,t ) ’s, etc. Means, medians, uncertainty WinBUGS WinBUGS Free software BUGS: Bayesians Using Gibbs Sampling

15. Example Deconvolution Results Date Total root respiration (umol m -2 s -1 ) Soil water (v/v) Rain (mm) Mesquite (C3 shrub) Sacaton (C4 grass) Soil water

16. Example Deconvolution Results Date Total root respiration (umol m -2 s -1 ) Soil water (v/v) Day 210Day 213Day 216 0-5 5-10 10-15 15-20 20-25 25-30 30-40 40-50 Depth (cm) 0-5 5-10 10-15 15-20 20-25 25-30 30-40 40-50 0-5 5-10 10-15 15-20 20-25 25-30 30-40 40-50 Relative contributions by depth

17. Some Issues Work-in-Progress Uncertainty in Isotope data Uncertainty in Isotope data Keeling plot intercepts Limited amount of data Indistiguishable source signatures Flux models Flux models Alternative models Acclimation & temporally-varying parameters Interactions & feedbacks (e.g., soil water, temp) Spatial variability

19. The Inverse Problem Plant water uptakeSoil respiration Isotope mixing model Fractional contributions Total flux Flux model Substrate or root profiles (Q 10 Function, Energy of Activation) ?? ??

20. The Inverse Problem Isotope mixing model (multiple sources & depths) Relative contributions (by source & depth) Total flux (at soil surface) Flux model (source- & depth- specific) Mass profiles (substrate, microbes, roots) (Q 10 Function, Energy of Activation) ?? Contributions by source ( i ) and depth ( z )? Temporal variability? ?? Source-specific respiration? Spatial & temporal variability?

21. What is  i ? (source-specific parameters) Likelihood of data (isotopes & soil flux) From isotope mixing model & flux models The Deconvolution Problem Data-Model Integration Flux model (source- & depth- specific) Covariate data  Total soil flux  Contributions Depend on  i

22. Isotopes: Tools for Partitioning Isotopes Isotopes δ 13 C of soil respired CO 2 ( ) δ 13 C of potential sources ( ) Simple-linear mixing (SLM) model Simple-linear mixing (SLM) model Consider three potential sources By simple mass-balance: p i = relative contribution of source i

23. Limitations of SLM Models Nonidentifiability of ’s Nonidentifiability of p i ’s Estimate limited number of sources Range of potential values (e.g., Phillips & Gregg) Not constrained by mechanisms Lack mechanistic insight Lack mechanistic insight Controls on relative contributions Threshold responses Lack predictive capability Lack predictive capability Temporal reconstructions Spatial patterns Plant species or functional types

24. Limitations of SLM Models Don’t integrate other sources of information Don’t integrate other sources of information Flux data Environmental drivers Source or pool characteristics Existing studies Complimentary lab studies