Problems estimating GPP and ER in artifical, non-mixing containers

Dear Allison and Bob,

last year I asked you for some help regarding estimating metabolism in replicated cattle tank [1000l] ecosystems (https://github.com/USGS-R/streamMetabolizer/issues/367). With your help I was able to resolve most of the problems I had with these short timeseries.

However, I have just started to work on data from bigger [ponds [15000l]](https://www.eawag.ch/en/aboutus/working/researchenvironment/experimental-ponds/), where the timeseries are considerably longer (150-200 days), but with similar data structure (15 min resolution, measurements of O2 concentration and saturation, temperature and light).

As last time, I have smoothed my data (temp, O2, and light with a loess smoother, 1 day window size), but I am running similar issues as last time: positive ER estimates and "chopped off peaks" in the DO predictions (see plots below). Looking at the DO predictions, the results are not terrible, but I really don't get the positive ER estimates. So, there are some specific questions I have:

- how much does the time window size (=number of consecutive days) affect the estimates?
- and related, over a longer timestretch, `day_start` and `day_end` I specify will differ for a lot of my days. why is this parameter so important (has a big effect on the model estimates), and, is there a way to specify it dynamically (or chop up the timeseries)?
- regarding positive ER estimates you mentioned last time that :

> If the nighttime oversaturation is real, you may simply need to interpret the ER values as being ER minus the rate of O2 pushing its way into the water from bubbles.

do you think there is a way to calculate this gas transfer from my data?
- can I still interpret my GPP estimates meaningfully even if ER is positive / not meaningful, i.e. just use GPP and ignore ER? I was thinking of this because of Bob's comment:

> ER >> GPP is weird unless you are adding external C or the tanks have high ER from productivity that occurred before you measure metabolism. But ER is difficult to measure.

Below is my model output, and the plotted metabolism estimates. I realize that this is a pretty specific problem, and not a bug or generalizeable issue and you probably cannot spend a lot of time on it. Any thoughts are highly appreciated - thanks for your help!

[mod.data.1.txt](https://github.com/USGS-R/streamMetabolizer/files/2804849/mod.data.1.txt)


```
metab_model of type metab_bayes
streamMetabolizer version 0.10.9
Specifications:
model_name b_Kn_oipi_tr_plrckm.stan
engine stan
split_dates FALSE
keep_mcmcs TRUE
keep_mcmc_data TRUE
day_start 4
day_end 28
day_tests full_day, even_timesteps, complete_data, pos_discharge
required_timestep NA
GPP_daily_mu 3.1
GPP_daily_lower -Inf
GPP_daily_sigma 6
ER_daily_mu -7.1
ER_daily_upper Inf
ER_daily_sigma 7.1
K600_daily_meanlog_meanlog 0
K600_daily_meanlog_sdlog 1
K600_daily_sdlog_sigma 0.05
err_obs_iid_sigma_scale 0.03
err_proc_iid_sigma_scale 5
params_in GPP_daily_mu, GPP_daily_lower, GPP_daily_sigma, ER_daily_mu, ER_daily_upper, ER_daily_sigma, K600_daily_meanlog_mean...
params_out GPP, ER, GPP_daily, ER_daily, K600_daily, K600_daily_predlog, K600_daily_sdlog, err_obs_iid_sigma, err_obs_iid, err_...
n_chains 4
n_cores 8
burnin_steps 500
saved_steps 500
thin_steps 1
verbose FALSE
model_path C:/R/library/streamMetabolizer/models/b_Kn_oipi_tr_plrckm.stan
Fitting time: 198.8 secs elapsed
Parameters (23 dates):
date GPP.daily GPP.daily.lower GPP.daily.upper ER.daily ER.daily.lower ER.daily.upper K600.daily K600.daily.lower
1 2016-06-25 1.9235106940 1.5546260028 2.1068155693 -1.78593622468 -2.837732608558 -1.0475971979 0.5172439444 0.2322636465
2 2016-06-26 2.0194641199 1.8447006955 2.1919723116 0.44287583521 -0.076361921056 1.0134568470 0.7380909758 0.5514256920
3 2016-06-27 2.4101872500 2.1472031022 2.5957082538 0.05336073694 -0.607526741711 0.6696580081 0.5065047291 0.3700766107
4 2016-06-28 2.6924826183 2.4266813080 2.9042982917 1.57862336017 0.801652646936 2.5567539834 0.8355450635 0.6919972033
5 2016-06-29 3.6138749359 3.4647739204 3.8439259025 -0.85835427863 -1.549463219613 -0.2913297211 0.4488613663 0.3298092030
6 2016-06-30 3.4723441818 3.2452894163 3.6482994156 4.07405399552 3.166775146038 6.3090806256 1.5998213051 1.3896263063
7 2016-07-01 2.6771336529 2.4864780740 2.8529340979 3.83484149751 3.145690219061 4.9406817883 1.0173423554 0.8997480120
8 2016-07-02 1.4480214638 1.2474434705 1.6642115617 -1.24495195958 -1.834716672553 -0.3954006420 0.3561904395 0.2347237976
9 2016-07-03 1.9599520363 1.8022373147 2.1294993926 0.62327563856 0.001476605237 1.1489087127 0.3082071348 0.1816466209
10 2016-07-04 4.7817022873 4.6294262743 4.9473200151 0.08300143154 -0.700073669186 0.8252816594 0.5873964411 0.4657374708
K600.daily.upper msgs.fit
1 0.7162728375 w
2 0.9517103198 w
3 0.6543058953 w
4 1.0289028763 w
5 0.5682756388 w
6 2.0399464124 w
7 1.2513357040 w
8 0.5309216874 w
9 0.4426556606 w
10 0.6887456752 w
...
Fitting warnings:
There were 31 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
http://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
There were 4 chains where the estimated Bayesian Fraction of Missing Information was low. See
http://mc-stan.org/misc/warnings.html#bfmi-low
Examine the pairs() plot to diagnose sampling problems
23 dates: overall warnings
Fitting errors:
1 date: data don't end when expected
Predictions (23 dates):
# A tibble: 10 x 9
date GPP GPP.lower GPP.upper ER ER.lower ER.upper msgs.fit msgs.pred

1 2016-06-25 1.92 1.55 2.11 -1.79 -2.84 -1.05 "w " " "
2 2016-06-26 2.02 1.84 2.19 0.443 -0.0764 1.01 "w " " "
3 2016-06-27 2.41 2.15 2.60 0.0534 -0.608 0.670 "w " " "
4 2016-06-28 2.69 2.43 2.90 1.58 0.802 2.56 "w " " "
5 2016-06-29 3.61 3.46 3.84 -0.858 -1.55 -0.291 "w " " "
6 2016-06-30 3.47 3.25 3.65 4.07 3.17 6.31 "w " " "
7 2016-07-01 2.68 2.49 2.85 3.83 3.15 4.94 "w " " "
8 2016-07-02 1.45 1.25 1.66 -1.24 -1.83 -0.395 "w " " "
9 2016-07-03 1.96 1.80 2.13 0.623 0.00148 1.15 "w " " "
10 2016-07-04 4.78 4.63 4.95 0.0830 -0.700 0.825 "w " " "
...

```