Upload
dionne
View
51
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Using the Model to Evaluate Observation Locations and Parameter Information in the Context of Predictions. Data Worth and Predictions. Predictions: Most models are developed with the intention of making predictions about future system behavior - PowerPoint PPT Presentation
Citation preview
Using the Model to Evaluate Observation Locations and
Parameter Information in the Context of Predictions
Data Worth and PredictionsPredictions:• Most models are developed with the intention of making predictions
about future system behavior• Predictions can also be posed as some unknown occurrence at some
location in the model domain that can be simulated by the model – such as flow in an unmonitored stream reach
Approach :• The best possible model is developed and calibrated under the
assumption that a model that reproduces past system response and system properties makes reliable predictions
• But does the best fitting model always produces the best predictions?
Evaluations (questions we should ask!):• How much uncertainty accompanies simulated predictions?• Which observations and parameters most influence the value of this
predictive uncertainty?
Predictions – Death Valley
Model:• Hydrogeology described
by many parameters• Large number of head
and flow observations to calibrate the model
Prediction:• Groundwater flow
directions and velocities in the Yucca Flats area
Predictions – Death Valley
Prediction• Advection is often the
dominant aspect of groundwater transport
• Advection can be simulated using particle tracking or path lines
• This is available within MODFLOW using the Advection (ADV) package
• MODFLOW can also provide sensitivities pertaining to the pathway
Predictions – AdvectionPrediction• Specifically – MODFLOW
calculates the travel path in three directions:• X - East-West• Y - North-South• Z - Up-Down
• Using calculations described later, the variance of these predictions can be easily determined
Parameters – Predictions (PPR)
1. Parameter Information
• Which parameters are most important to predictions
• What information might be cost-effectively collected to further reduce predictive uncertainty?
Observations – Predictions (OPR)
2. Observation Locations
• Existing observationsExisting observations: Which existing observation locations are most influential?
• New observationsNew observations:: Where could new measurements be made to reduce predictive uncertainty?
Data Worth and PredictionsEvaluations:• How much uncertainty accompanies simulated
predictions?• Evaluate deterministically – trial and error sensitivity.• Evaluate using multiple models and Monte-Carlo methods• Evaluate using statistics – variance, standard deviation
• Which parameters and observations are most influential in the calculation of this predictive uncertainty?• Statistical methods enable rapid evaluation of the
contribution of (a) parameters and / or (b) observations to the uncertainty (standard deviation) of one or more predictions
• First order second moment (FOSM) methods• First order – linear sensitivities• Second moment – variances and standard deviations
Predictions – Uncertainty
Standard Deviation• Measure of spread of values
for a variable• Has a stochastic basis• Involves assumptions• Regardless – a means for
comparing relative predictive uncertainty
Normal distribution
Data Worth and PredictionsApproach:• Define the prediction:
• How can we simulate the predicted quantity?• How can we summarize the ‘value’ of the prediction
numerically?
• Gather information obtained through calibration:• Observation sensitivities and weights• Prior information on parameters
• Calculate prediction sensitivities:• Using methods similar to when calculating observation
sensitivities• Include all parameters if possible
• calibrated parameter values • measured parameter values
Data Worth and PredictionsApproach:• Calculate the current prediction variance• Calculate a hypothetical prediction variance assuming changes
to (a) information about parameters or (b) available observations
• The Parameter-PRediction (PPR) Statistic:• Evaluate worth of potential knowledge about parameters, posed in
the form of prior information - add this to calculations
• The Observation-PRediction (OPR) Statistic:• Evaluate existing observation locations by omitting them from the
calculations • Evaluate potential new observation locations by adding them to the
calculations
Note: PPR was called Value of Improved Information (VOII) in one journal article
[1- (sznew / sz)] x 100
Data Worth and Predictions
Determine Predictive Uncertainty
EVALUATE CURRENT CONDITIONS
EVALUATE POTENTIAL
OBSERVATIONS
EVALUATE EXISTING
OBSERVATIONS
CALCULATE & REPORT PREDICTION
STATISTICS
EVALUATE POTENTIAL
PARAMETER DATA
Determine Predictive Uncertainty
EVALUATE CURRENT CONDITIONS
EVALUATE POTENTIAL
OBSERVATIONS
EVALUATE EXISTING
OBSERVATIONS
CALCULATE & REPORT PREDICTION
STATISTICS
EVALUATE POTENTIAL
PARAMETER DATA
Data Worth and Predictions
Approach:• Recently encapsulated in a program:
• OPR-PPR Program• In review
• Class Exercise will use the OPR and PPR methods with a synthetic model that is described both in the OPR-PPR documentation, and in Hill and Tiedeman (2007)
Relevant ReferencesTiedeman, C.R., Hill, M.C., D’Agnese, F.A., and Faunt, C.C., 2003, Methods
for using groundwater model predictions to guide hydrogeologic data collection, with application to the Death Valley regional ground-water flow system: Water Resources Research, 39(1): 5-1 to 5-17, 10.1029/2001WR001255. (The PPR statistic is the same as what is called the VOII statistic in this paper)
Tiedeman, C.R., D.M. Ely, M.C. Hill, and G.M. O'Brien, 2004, A method for evaluating the importance of system state observations to model predictions, with application to the Death Valley regional groundwater flow system, Water Resources Res., 40, W12411, doi:10.1029/2004WR003313.
Tonkin, M.J., Tiedeman C.R., Ely, D.M., and Hill M.C., (in press), Documentation of OPR-PPR, a Computer Program for Assessing Data Importance to Model Predictions Using Linear Statistics, Constructed using the JUPITER API, JUPITER: Joint Universal Parameter IdenTification and Evaluation of Reliability API: Application Programming Interface, U.S. Geological Survey Techniques and Methods Report TM6-E2.