Procedure to Compare Numerical Simulation of Geophysical Flow

with Field Data

Laércio M. NamikawaGeo559 - Spring2004

Objective

• Develop a quantitative procedure to compare output of a numerical simulation of geophysical flow with fieldwork data.

• Geophysical flow challenges for comparison:– Large scale phenomena:

• Knowledge of variables is limited.– Low recurrence

• Small number of real cases.– Dynamic nature:

• Requires analysis of a series of data, each from different time

Volcán de Colima

• Compare simulation with real event of a block and ash flow– April of 1991

http://www.gomanzanillo.com/old_articles/volcano/volfire.htm

Titan2D Simulation• DEM, Internal Friction, Bed Friction• Starting Location, Shape, Volume

Model Performance Measure• Constraints:

– Data from real event is a footprint of flow path;

– Simulation results are available in a series of adapted grids with flow pile height at every time of the simulation.

Proposed Measurement Procedure

• Create a summary of simulation results;

• Define a map with distances to real event flow footprint;

• Apply quantitative analysis using statistics and spatial database approach.

Summary of Simulation ResultsProblems

• Huge amount of data:– 200 files, one for each simulation time step.– 400 Mbytes total.

• Complex structure: Adaptative grid.

Summary of Simulation ResultsSolution

Create GRID with cells equal to zero;For each file: Build irregular mesh; For each mesh element: If rectangular element: For each cell inside element:

Calculate pile height using linear interpolation;Cell value is the highest between calculated and previous.

If triangular element: For each cell inside element:

Calculate pile height using linear interpolation;Cell value is the highest between calculated and previous.

Create Map with Distances to Real Event Flow

• Scan and georeference flow map;

• Digitize flow polygons;• Create skeleton lines

using Delaunay triangulation;

• Create distance to flow center, to flow polygon outline, and composed (center+outline) distance.

Quantitative AnalysisTest Cases

• Best – generated from real flow.

• Second best – “shorter” version of Best.

• Third – simulation.

• Worst – simulation with a very large volume.

Quantitative Analysis Using Statistics and Spatial Database

Approach

• Divide area in analysis units;• For each unit, acquire attributes:

– Mean:• Pile height;• Distance to flow center;• Distance to flow outline;• Composed distance (center+outline).

• Find correlation among attributes;• Select correlation which better fits test

cases.

Analysis UnitsUnit:100 by 100 meters

Find Correlation

Normal Distribution of ResidualsPile height Natural Log

Pile height

Distance Natural LogDistance

Convert distances and pile height to natural log of distances and pile height.

Find Correlation Linear Regression

Assumption: Small pile height at great distances indicates good model performance.

Dependent variable:Pile height

Best predictor:Combined distance center+edge

Problem: Regression line slope increases from Third Best to Worst case.

Diagnosis: Regression is representing only total pile height in the whole area, with no relationship with morphology of the flow.

Logistic Regression

• Assumption: Small pile height outside flow path indicates good model performance.

– Dependent variable: InFlow (1: Inside; 0: Outside)– Predictor: Pile height.

• Problem: Pile height for probability equal to 0.5 Third Best is lower than for Best and Second best cases.

• Diagnosis: Regression is representing only the total pile height in the whole area, with no relationship with morphology of the flow.

• Solution: Include distance in regression.– Regression significance test: Only combined distance is

significant in all cases.

Logistic RegressionDependent variable: InFlow

1: Inside real event flow footprint;0: Otherwise.

Predictors: Pile height;Combined distance: center+outline

Probability of Being Inside Flowat 200 meters from center

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

PileHeig

ht1.8 3.8 5.8 7.8 9.8 11

.813

.815

.817

.8

Pile Height (m)

Prob

abiit

y p(sim1)

p(sim2)

p(feb22)

p(feb10)

Probability of a Pile 5 Meter High Being Inside Flow

0

0.2

0.4

0.6

0.8

1

Distanc

e 50 100

150

200

250

300

350

400

450

Distance from Flow Center (m)

Prob

abiit

y p(sim1)

p(sim2)

p(feb22)

p(feb10)

sim1 sim2

feb22 feb10

Conclusion• Quantitative performance measure:

– Logistic Regression with InFlow depending on pile height and combined distance.

• Combination of distances center+outline captures the morphology of flow footprint.

• Performance measures should consider unique characteristics of the phenomena, available data, and model.