Process Based Models
Bayesian Methods for Ecological and Environmental Modelling
What is a process based model? (PBM)
Model structure based on mechanistic process understanding
Often deterministic
Good for extrapolation (eg forecasting) and “what if” type questions
Examples:
- General Circulation Models GCMs (Climate modelling)
- Numerical Weather Prediction Models (Weather forcasting)
- Even Newton’s Laws of Motion
PBM inputs and outputs
Model Tuning Approach
Aim to understand/predict something in nature
Build a model representing our current best understanding of the processes involved
- Model includes uncertain “tunable” parameters
Collect evidence/data to test/validate model against
Model does not agree with data/evidence
- Try to improve model performance against data by “tuning” parameters
Storm of 1987
“…earlier on today apparently a woman rang the BBC and said she’d heard there was a hurricane on the way. Well if you are watching don’t worry, there isn’t…”
18 died in Britain, four in France
Devastation costs more than one billion pounds
An estimated 15 million trees were lost
Worst storm since 1703, one in 200 year storm for southern Britain
A public enquiry was held and an internal enquiry was conducted by the Met Office
“…unlike 1987, we now run multiple forecasts (called ensembles) that help us to understand the probabilities involved in a forecast and give a better estimate of the risk of high impact weather events.”
Climate Uncertainty
Model predictions without uncertainty could miss less likely but high impact events
Uncertainty in PBMs
Run VSEM
| best | lower | upper | |
|---|---|---|---|
| KEXT | 0.500 | 2e-01 | 1e+00 |
| LAR | 1.500 | 2e-01 | 3e+00 |
| LUE | 0.002 | 5e-04 | 4e-03 |
| GAMMA | 0.400 | 2e-01 | 6e-01 |
| tauV | 1440.000 | 5e+02 | 3e+03 |
| tauS | 27370.000 | 4e+03 | 5e+04 |
| tauR | 1440.000 | 5e+02 | 3e+03 |
| Av | 0.500 | 2e-01 | 1e+00 |
| Cv | 3.000 | 0e+00 | 4e+02 |
| Cs | 15.000 | 0e+00 | 1e+03 |
| Cr | 3.000 | 0e+00 | 2e+02 |
Prior
Should reflect prior thinking about uncertainty in parameters
Check for convergence
# # # # # # # # # # # # # # # # # # # # # # # # #
## MCMC chain summary ##
# # # # # # # # # # # # # # # # # # # # # # # # #
# MCMC sampler: DEzs
# Nr. Chains: 6
# Iterations per chain: 3334
# Rejection rate: 0.979
# Effective sample size: 104
# Runtime: 4.45 sec.
# Parameters
psf MAP 2.5% median 97.5%
KEXT 2.134 0.999 0.500 0.963 1.000
LUE 19.336 0.002 0.001 0.003 0.004
tauV 10.565 942.569 773.456 966.040 2307.896
tauS 1.216 49264.635 6595.068 41146.995 49927.328
Av 6.697 0.663 0.213 0.607 0.906
Cv 6.278 2.924 0.101 3.498 63.329
Cs 3.924 14.362 0.984 11.336 450.243
Cr 2.504 3.781 0.748 3.665 59.356
error-sd 2.362 0.122 0.122 0.402 0.626
## DIC: 1285829
## Convergence
Gelman Rubin multivariate psrf: 159.98
## Correlations
KEXT LUE tauV tauS Av Cv Cs Cr error-sd
KEXT 1.000 -0.565 -0.707 -0.134 0.520 -0.155 -0.283 -0.239 -0.436
LUE -0.565 1.000 0.751 -0.405 -0.864 0.017 -0.095 0.004 0.495
tauV -0.707 0.751 1.000 0.103 -0.680 0.004 0.071 -0.164 0.249
tauS -0.134 -0.405 0.103 1.000 0.339 -0.339 -0.073 -0.336 -0.575
Av 0.520 -0.864 -0.680 0.339 1.000 0.014 0.140 0.041 -0.308
Cv -0.155 0.017 0.004 -0.339 0.014 1.000 0.589 0.448 0.349
Cs -0.283 -0.095 0.071 -0.073 0.140 0.589 1.000 0.642 0.243
Cr -0.239 0.004 -0.164 -0.336 0.041 0.448 0.642 1.000 0.323
error-sd -0.436 0.495 0.249 -0.575 -0.308 0.349 0.243 0.323 1.000Check for convergence longer chain (150k)
# # # # # # # # # # # # # # # # # # # # # # # # #
## MCMC chain summary ##
# # # # # # # # # # # # # # # # # # # # # # # # #
# MCMC sampler: DEzs
# Nr. Chains: 6
# Iterations per chain: 50000
# Rejection rate: 0.943
# Effective sample size: 719
# Runtime: 229.801 sec.
# Parameters
psf MAP 2.5% median 97.5%
KEXT 1.001 0.529 0.254 0.538 0.820
LUE 1.001 0.002 0.002 0.002 0.002
tauV 1.005 1394.867 1171.209 1425.719 2844.404
tauS 1.002 25672.714 21957.750 26787.986 49039.340
Av 1.008 0.508 0.355 0.503 0.578
Cv 1.002 3.020 2.849 3.008 3.460
Cs 1.007 14.915 14.503 14.952 16.571
Cr 1.009 3.037 2.648 3.025 3.371
error-sd 1.003 0.100 0.098 0.101 0.413
## DIC: 65862.58
## Convergence
Gelman Rubin multivariate psrf: 1.012
## Correlations
KEXT LUE tauV tauS Av Cv Cs Cr error-sd
KEXT 1.000 -0.386 -0.621 0.035 0.588 -0.035 -0.040 -0.019 -0.271
LUE -0.386 1.000 0.251 -0.112 -0.174 -0.079 -0.008 0.020 -0.248
tauV -0.621 0.251 1.000 0.507 -0.821 0.072 0.089 -0.002 0.367
tauS 0.035 -0.112 0.507 1.000 -0.371 0.014 0.045 -0.004 0.109
Av 0.588 -0.174 -0.821 -0.371 1.000 0.109 0.072 0.151 -0.263
Cv -0.035 -0.079 0.072 0.014 0.109 1.000 0.789 0.688 0.420
Cs -0.040 -0.008 0.089 0.045 0.072 0.789 1.000 0.711 0.484
Cr -0.019 0.020 -0.002 -0.004 0.151 0.688 0.711 1.000 0.444
error-sd -0.271 -0.248 0.367 0.109 -0.263 0.420 0.484 0.444 1.000Remove burn-in and take sample
| best | lower | upper | |
|---|---|---|---|
| KEXT | 0.500 | 2e-01 | 1e+00 |
| LAR | 1.500 | 2e-01 | 3e+00 |
| LUE | 0.002 | 5e-04 | 4e-03 |
| GAMMA | 0.400 | 2e-01 | 6e-01 |
| tauV | 1440.000 | 5e+02 | 3e+03 |
| tauS | 27370.000 | 4e+03 | 5e+04 |
| tauR | 1440.000 | 5e+02 | 3e+03 |
| Av | 0.500 | 2e-01 | 1e+00 |
| Cv | 3.000 | 0e+00 | 4e+02 |
| Cs | 15.000 | 0e+00 | 1e+03 |
| Cr | 3.000 | 0e+00 | 2e+02 |
| error-sd | 0.100 | 1e-02 | 7e-01 |
Model predictions
