Lake metabolism modeling from sensor network data Pan-American Sensors for Environmental Observatories (PASEO), 2009, Bahia Blanca, Argentina Paul Hanson, Tim Kratz, and Luke Winslow University of Wisconsin, Center for Limnology Support provided by Mellon Foundation Gordon & Betty Moore Foundation

“A skilled limnologist can probably learn more about the nature of a lake from a series of oxygen determinations than from any other kind of chemical data.” G. Evelyn Hutchinson (1957)

Dissolved gases, through their observable changes through time, allow us to understand what cannot be seen – the way lakes work.

Observable veneer In ecosystems, the connections are not obvious or even observable, and they are physical, chemical, and biological in nature. C B P C B P C B P S The way things work P = physical process C = chemical process B = biological process S = state variable

Theory Observations Models What can be observed? What spatio-temporal scale? Do we intervene or control? Is it a population to be sampled? Dynamic through space and time? Are relationships empirical or mechanistic? What are the process rates? What’s the importance to the larger story?

Dissolved gas basics The simple approach to calculating lake metabolism In truth, it’s complicated Outline

Lake Taihu, China Trout Bog, U.S.A. Ormajarvi, Finland Sparkling L., U.S.A. Rotorua L., New Zealand Dissolved oxygen (mg L -1 ) Day 1 Day 2

Lake Taihu, China Trout Bog, U.S.A. Ormajarvi, Finland Sparkling L., U.S.A. Rotorua L., New Zealand Dissolved oxygen (mg L -1 ) Day 1 Day 2 GPP +R R R

Examples of dissolved oxygen saturation over 10 days (obtained from GLEON, using VaDER) Lake Mendota Sparkling Lake Crystal Bog Lake Date in 2008 Dissolved Oxygen (% sat)

atmosphere water 210,000 µatm x 1.26 x µatm x 3.39 x10 -2 = 265 µmol L -1 (~8.5 mg L -1 ) = 13 µmol L -1 (~0.6 mg L- 1 ) O 2 CO 2 partial pressure Henry’s* constant (25°C) concentration in water x = GasPartial Pressure (atm) Nitrogen0.78 Oxygen0.21 Argon0.01 Carbon dioxide *Henry’s constant (  mol  atm -1 ) is a function of temperature and salinity Dissolved Gases in Fresh Water 3.2 Solubility

Common units of O 2 and CO 2 common gas pressure units: 1 atmosphere = 1013 millibars = 101 kilopascals common dissolved gas units (concentration): O 2 (DO): 1 mg L -1 x (32 mg mmol -1 ) -1 x 1000 µmol mmol -1 = 31.3 µmol L -1 CO 2 : 1 mg L -1 x (44 mg mmol -1 ) -1 x 1000 µmol mmol -1 = 22.7 µmol L -1 common dissolved gas units (areal): g m Units of measure

Temperature (°C) CO 2 (mg L -1 ) DO saturation CO 2 saturation Saturation Gas Concentrations (in equilibrium with the atmosphere) supersaturation undersaturation supersaturation undersaturation DO (mg L -1 ) 12.8

Photosynthesis Photosynthesis and Respiration 6CO 2 + 6H 2 O  C 6 H 12 O 6 + 6O 2 O2O2 CO 2 Respiration: all the time Photosynthesis: in the presence of light Carbs

atmosphere water DO < 100% saturated GPP < R (i.e., -NEP)

atmosphere water DO > 100% saturated GPP < R (i.e., -NEP)

Modeling metabolism: the simple approach A free-water approach Mass balance equation Many simplifying assumptions Minimal data requirements

dO2/dt = GPP – R + F + A Odum, H. T Primary production in flowing waters. Limnol. Oceanogr. 1: Gross primary production Ecosystem respiration Atmospheric exchange All other fluxes, e.g., loads, exports, transfer between thermal strata Observed oxygen data from sensors

dO2/dt = GPP – R + F + A (Odum 1956) R = – dO2/dt + F + GPP + A GPP = dO2/dt + R – F + A NEP = GPP– R Nighttime Daytime From night time Odum, H. T Primary production in flowing waters. Limnol. Oceanogr. 1:

R = – dO2/dt + F + GPP + A

Why add F? Imagine placing a barrier over the lake to prevent atmospheric exchange. The change in oxygen, driven exclusively by R, would look more like the red line.

GPP = dO2/dt + R – F + A

Why subtract F? Imagine the barrier again… F artificially increases GPP by driving DO toward saturation Why subtract F? Imagine the barrier again… F artificially increases GPP by driving DO toward saturation Why add R? If R were somehow turned off, the increase in DO would have been greater. Why add R? If R were somehow turned off, the increase in DO would have been greater.

atmosphere water F (mg/L/d) = k(m/d) * ( DO sat (mg/L) – DO obs (mg/L)) / z (m) epilimnion z = mixed layer depth (e.g., 2 m) k = piston velocity, or the depth equilibrated per day (e.g., 0.5 m/d) k = f(wind speed, water temperature)

atmosphere water epilimnion 3. Mixed layer depth (atmospheric exchange) Data requirements for the simple model (sampled at least hourly) 1. Dissolved oxygen 2. Water temperature (gas solubility) 5. Barometric pressure or altitude (gas solubility) 4. Wind speed or 0.45 (atmospheric exchange)

Hanson, P.C., Bade, D. L., Carpenter, S. R., and T. K. Kratz Lake metabolism: Relationships with dissolved organic carbon and phosphorus. Limnol. Oceanogr. 48: Examples of surface water metabolism rates from 25 lakes in northern Wisconsin 80  1 mg L -1 d -1

Metabolism Recipe (simple) 1.R TS for each time step (TS) at night… 1.Calculate F TS using difference equation and Cole and Coraco (1998) 2.R TS is the (-) change in DO plus (+) the F 2.GPP TS for each time step during day light… 1.Calculate F TS using difference equation and Cole and Coraco (1998) 2.GPP TS is the (+) change in DO plus (+) R 24 minus (-) F TS 3.R 24 = some integration of R TS over 24 hours 4.GPP24 = some integration of GPP TS during daylight hours 5.F24 = some integration of F TS over 24 hours Cole, J. J., and N. F. Caraco Atmospheric exchange of carbon dioxide in a low-wind oligotrophic lake measured by the addition of SF6. Limnol. Oceanogr. 43:

Issues and Assumptions 1.Model 1.Atmospheric exchange (F) model 2.Buoy measurements representative of the ecosystem 3.Biological model underlying GPP and R 4.A, or everything that’s not F, GPP, or R 2.Calculation of the simple model 1.Integration from GPP TS and R TS to GPP 24 and R 24 2.Availability of wind speed, barometric pressure, mixed layer depth 3.Daytime R = Nighttime R

(From: Cole and Caraco 1998) Issue Below wind speeds of about 3 ms -1, there is high uncertainty in the estimate of k. This is a problem for most small lakes. Issue Below wind speeds of about 3 ms -1, there is high uncertainty in the estimate of k. This is a problem for most small lakes. Cole, J. J., and N. F. Caraco Atmospheric exchange of carbon dioxide in a low-wind oligotrophic lake measured by the addition of SF6. Limnol. Oceanogr. 43:

Dis solv ed Oxy gen (mg L DayNight Day (a)(a) (b)(b) Elapsed time (hours) Dissolved oxygen (mg L -1 ) High macrophyte density Low macrophyte density littoral pelagic Lauster, G. H., P. C. Hanson, and T.K. Kratz Gross primary production and respiration differences among littoral and pelagic habitats in North Temperate lakes. Canadian Journal of Fisheries and Aquatic Sciences. 63(5): Issue Different habitats within the lake have different metabolic rates, and sometimes this can be very important. Issue Different habitats within the lake have different metabolic rates, and sometimes this can be very important.

anaerobic respiration PP R photo-oxidation Internal waves strata/sediment exchange littoral-pelagic exchange ground water loads surface water loads Atm exchange deposition temperature irradiance factors affecting DO measurements Figure 2

dO2/dt = GPP – R + F + A+ E Issue If we eliminate A and E from the equation and we assume we know F, then all real processes in A and E are subsumed by GPP and R. f 0+0+ Stylized frequency distribution of R estimates from one week of DO data Negative R not biologically possible Some modes clearly represent non-biological processes

How complicated does the biological model need to be? Examples of added complexity: 1.GPP could be a linear or non-linear function of irradiance 2.R daytime could be a function of irradiance 3.Photo history of algae could affect their GPP or R

Hanson, P.C., S.R. Carpenter, N. Kimura, C. Wu, S.P. Cornelius, and T.K. Kratz Evaluation of metabolism models for free-water dissolved oxygen methods in lakes. Limnol. Oceanagr. Methods. 6:

Irradiance Gross Primary Productivity, Respiration 0 0 R0R0 P0P0 IP Pmax IR Simple model Complicated model(s) Figure X. Responses for ecosystem GPP and R as a function of irradiance. Parameters are per Table X. (From Hanson et al. 2008) Hanson, P.C., S.R. Carpenter, N. Kimura, C. Wu, S.P. Cornelius, and T.K. Kratz Evaluation of metabolism models for free-water dissolved oxygen methods in lakes. Limnol. Oceanagr. Methods. 6:

I original Beta = 4 Beta = 6 Beta = 8 Day of year PAR (µmol m -2 s -1 ) Hanson et al. 2008

Table 3 From the Word documentHanson et al. 2008

GraphResults.m Dissolved oxygen (mg L -1 ) Day of year A) Crystal Bog B) Trout Lake Observation M 1 M 2 M 3 M 4 M 5 Hanson et al With metabolism model prediction, much variance remains unexplained

x x Depth (m) A) Crystal Bog Lake B) Trout Lake Stability (m -1 ) DO (mg L -1 ) T (°C) T DO Crystal Bog Lake Day of year Hanson et al. 2008

What are the other controls over DO at short (minutes-days) time scales?

Sparkling Lake (2004) Buoyancy frequency Z I Wind Temp. DO Day of year (total of 50 days)

Time scale Time Signal per scaleDetails per scale Sparkling Lake Dissolved Oxygen

DOBuoyancy Frequency Time Wavelet transforms Neural networks

For 20 lakes, DO correspondence with… Irradiance Langman, O.C., P.C. Hanson, S.R. Carpenter, K. Chiu, and Y.H. Hu. In review. Control of dissolved oxygen in northern temperate lakes over scales ranging from minutes to days. Aquatic Biology.

For 20 lakes, DO correspondence with… Temperature Langman et al. in review

For 20 lakes, DO correspondence with… Wind Speed Langman et al. in review

So environmental data are noisy! How often and for how long do you need to measure DO to be confident in the metabolism estimate?

DO (mg L -1 ) Required duration (days) Day of year Sampling period (hours) A BC D EF GPP R NEP F atm Figure X. Dissolved oxygen time series (A-C, note differing y axis scales), metabolism (D-F, note differing y axis scales), and required sample duration (G-I) in three study lakes (columns). Metabolism values are means calculated at different sampling periods. Required sample duration is the number of days required to sample at the specified sampling period to detect metabolism within 20% of the mean with a power of 80%. Day of year GPP, R, NEP (mg L -1 d -1 ) Sampling period (hours) Little Arbor Vitae Lake Sparkling LakeTrout Bog Lake GHI observed saturation Staehr et al. In process

Summary Environmental data are noisy A simple metabolism model can work Data requirements are minimal Metabolism field is changing rapidly