## Ecosystem Metabolism

## 2015 Short Course: Methods and models for estimating aquatic ecosystem metabolism

Umeå University, Umeå, Sweden

Spring 2015

## Contact Erin Hotchkiss (ehotchkiss[at]gmail.com) for Methods in Stream Ecology chapter that emerged from these lessons and other collaboraitons

Part 1 - Introduction to aquatic ecosystem metabolism: History and methods

Staehr, P. A., et al. 2010. Lake metabolism and the diel oxygen technique: State of the science. Limnol. Oceanogr.: Methods 8: 628-644.

Staehr, P. A., et al. 2012. The metabolism of aquatic ecosystems: history, applications, and future challenges. Aquat. Sci. 74: 15-29.

Additional references:

Odum, H. T. 1956. Primary production in flowing waters. Limnol. Oceanogr. 1: 102-117.

Grace, M. R. & S. J. Imberger. 2006. Stream Metabolism: Performing & Interpreting Measurements. Water Studies Centre Monash University, Murray Darling Basin Commission and New South Wales Department of Environment and Climate Change. Accessed online.

Hall, R. O. & J. L. Tank. 2009. Correcting whole-stream estimates of metabolism for groundwater input. Limnol. Oceanogr.: Methods 3: 222-229.

Part 2 - Introduction to Likelihood and Bayesian

Clark, M. 2014. Bayesian Basics: A conceptual introduction with application in R and Stan. Accessed online.

Additional references:

Hilborn, R. & M. Mengel. 1997. The Ecological Detective: Confronting Models with Data. Princeton University Press.

Ellison, A. M. 2004. Bayesian inference in ecology. Ecology Letters 7: 509-520.

Hobbs, N. T. & R. Hilborn. 2006. Alternatives to statistical hypothesis testing in ecology: A guide to self teaching. Ecological Applications 16: 5-19.

Arhonditsis, G. B., et al. 2008. Addressing equifinality and uncertainty in eutrophication models. Water Resour. Res. 44: doi:10.1029/2007WR005862.

Johnson, V. E. 2013. Revised standards for statistical evidence. Proc. Natl. Acad. Sci. USA 110: 19313-19317.

Ellison, A. M., et al. 2014. FORUM: P values, hypothesis testing, and model selection. Ecology 95: 609-653.

Part 3 - Aquatic ecosystem metabolism models: Structure, complexity, and parameter estimation

Hotchkiss, E. R. & R. O. Hall. Methods Summary: Inverse modeling of whole-ecosystem metabolism in streams and rivers.

Hanson, P. C. et al. 2008. Evaluation of metabolism models for free-water dissolved oxygen methods in lakes. Limnol. Oceanogr.: Methods 6: 454-465.

Grace, M. R., et al. 2015. Fast processing of diel oxygen curves: Estimating stream metabolism with BASE (BAyesian Single-station Estimation). Limnol. Oceanogr.: Methods 13: 103-114.

Additional references:

Van de Bogert, M. C., et al. 2007. Assessing pelagic and benthic metabolism using free water measurements. Limnol. Oceanogr.: Methods 5: 145-155.

Reichert, P. et al. 2009. Estimating stream metabolism from oxygen concentrations: Effect of spatial heterogeneity. J. Geophys. Res. 114: doi:10.1029/2008JG000917.

Holtgrieve, G. W., et al. 2010. Simultaneous quantification of aquatic ecosystem metabolism and reaeration using a Bayesian statistical model of oxygen dynamics. Limnol. Oceanogr. 55: 1047-1063.

Cremona, F. et al. 2014. High-frequency data within a modeling framework: On the benefits of assessing uncertainties of lake metabolism. Ecological Modelling 294: 27-35.

Hotchkiss, E. R. & R. O. Hall. 2014. High rates of daytime respiration in three streams: Use of δ18O2 and O2 to model diel ecosystem metabolism. Limnol. Oceanogr. 59: 798-810.

Hall, R. O. et al. 2015. Turbidity, light, temperature, and hydropeaking control primary productivity in the Colorado River, Grand Canyon. Limnol. Oceanogr. 60: 512-526.

Part 4 - Review R code for Likelihood and Bayesian 1-station metabolism models

On your own: run original code for 1 day of metabolism estimates using (1) Likelihood and (2) Bayesian parameter estimation. Update the R code to run for several days of O2 data from three different streams using "guidelines" handout. Reflect on the additional questions provided.

Part 5 - Review, quality check, and compare output from Likelihood and Bayesian metabolism models

## 2010 Workshop: Inverse Modeling Methods for Estimating Aquatic Ecosystem Metabolism

American Society of Limnology & Oceanography

North American Benthological Society

Date: 06 June 2010

Time: 13:00 - 17:00

Location: Peralta/Lamy, Santa Fe Conference Center

RSVP to: Bob Hall (bhall[at]uwyo.edu) & Erin Hotchkiss (ehotchki[at]uwyo.edu)

Workshop Description:

There is a current increase in interest in calculating aquatic whole-ecosystem metabolism using inverse modeling approaches. In some cases it is possible to solve for more than just metabolism; reaeration can be estimated, which allows broad application of the method, but at a possible cost of higher uncertainty in metabolism estimates.

This workshop will discuss methods, models, and assumptions behind inverse approaches to estimating aquatic ecosystem metabolism. Questions will include how to both calculate and minimize uncertainty on parameter estimates (i.e. photosynthesis, respiration, reaeration) and how many parameters can be estimated with low uncertainty given variation in diel oxygen or oxygen isotope data. We envision a session with a few short presentations addressing modeling of metabolism, followed by small or large group discussions on specific questions.

The overall goal of the workshop will be to develop recommendations for modeling metabolism, including parameter estimation and uncertainty.

Specific questions:

How do we calculate and minimize parameter uncertainty?

Given oxygen data, how many parameters (e.g. K) can we solve for besides metabolism?

What are options for model structure and model validation?

Schedule:

12:40 - Load presentations onto computer

Part 1. Methods used to estimate aquatic metabolism

13:00 - Workshop introduction: Goals, questions, and a little data (Bob Hall)

13:17 - Estimating metabolic parameters from one- and two-station diel dissolved oxygen curves: Successes and challenges (Mike Grace)

13:34 - Estimating metabolism parameters and uncertainty: maximum likelihood approach with bootstrapping (Christopher Solomon, Matthew Van de Bogert, & Paul Hanson)

13:51 - Bayesian methods for aquatic ecosystem metabolism parameter estimation: current models and future directions (Gordon W. Holtgrieve & Daniel E. Schindler)

14:08 -Sampling more places less frequently: What increase in error are we to accept for better spatial coverage? (Jason Venkiteswaran)

14:25 - Revised techniques for estimating stream metabolism from oxygen concentrations: The effect of spatial heterogeneity (Peter Reichert, Urs Uehlinger, & Vicenç Acuña)

14:42 - Estimates of stream metabolism by modeling dissolved oxygen fate and transport in unsteady flow (Robert Payn)

15:00 - 15 minute break

Part 2. Small group discussion and recommendations

15:15 - Break out into small groups for more focused discussions:

1. Measuring versus modeling K

2. Parameter uncertainty

3. Model structure and model validation

4. Others?

16:15 - Groups report recommendations; large group discussion

16:40 - Workshop summary: Recommendations and future directions (Erin Hotchkiss)