PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Calibration & Sensitivity Analysis• Head measured in an observation well is known as a target. Baseflow measurements or other fluxes (e.g., ET)are also used as targets during calibration.Targets in Model Calibration• The simulated head at a node representing an observation well is compared with the measured head in the well. (Similarly for flux targets…) Residual error = observed - simulated• During model calibration, parameter values (e.g., R and K) are adjusted until the simulated head matches the observed value within some acceptable range of error. Hence, model calibration solves the inverse problem.Calibration Targetscalibration valueassociated error20.24 m0.80 mTarget with relativelylarge associated error.Target with smaller associated error.Examples of Sources of Error• Surveying errors • Errors in measuring water levels• Interpolation error• Transient effects• Scaling effects• Unmodeled heterogeneitiesLeave this box unchecked sothat gwv will compare simulatedheads at the node with the targetvalues.• Head measured in an observation well is known as a target. Baseflow measurements or other fluxes are also used as targets during calibration.Targets in Model Calibration• The simulated head at a node representing an observation well is compared with the measured head in the well. (Similarly for flux targets…) Residual error = observed - simulated• During model calibration, parameter values (e.g., R and T) are adjusted until the simulated head matches the observed value within some acceptable range of error. Hence, model calibration solves the inverse problem.Basecase simulation for the 2006 Final ProjectPerfect fitAll heads aretoo low.Residual = observed - simulated2006 valuesCalibration parameters are parameters whose valuesare uncertain. Values for these parametersare adjusted during model calibration.Typical calibration parameters include hydraulic conductivity and recharge rate.Parameter values can be adjusted manually by trial and error.This requires the user to do multiple runs of the model.…or parameter adjustment can be done with the helpof an inverse code. The inverse code will automatically finda set of parameters that matches the observed head values.Automated calibration using inverse modelingCodesMODFLOWP – used in MODFLOW2000GV CalibrationPESTUCODEAvailable in GWV for usewith MODFLOW 88/96xyoceanocean2LLIsland Recharge Problem- Forward ProblemwellParameters known with certainty:R= 0.003375 ft/dK= 100 ft/dayKRyhxh 2222222Solve for headh =120.014xy oceanIsland Recharge Problem – Inverse ProblemHead in well = 120.014 feet(target)wellUncertain parametersInitial guessesR= 0.001 ft/dK= 50 ft/dayKRyhxh 2222222Add a flux targetto estimate bothR and KF= -57120 ft3/day2 parametersand 2 targets;Ideally shouldhave at least1 more target.Targetsh = 120.014 ftF = -57120 ft3/dayWe are trying to estimate R and K.Correct answers:K = 100 ft/dayR = 0.003375 ft/day2 parametersand 2 targets;Ideally shouldhave at least1 more target.Sensitivity analysis is used:• During calibration (Sensitivity coefficients = sum of squared residuals/parameter value or h/parameter value)• As an uncertainty analysis after calibrationThe Problem of ZonationMost inverse codes estimate parameters inpre-determined, fixed zones.Yet, the boundaries/existence of such zonesis usually uncertain.Pilot points can be used instead.Parameters are estimated at arbitrarily selectedpoints known as pilot points. Then parametervalues are interpolated between pilot