1

Brent E. Huntsman, CPGDaniel J. Wagel

Terran Corporation

Development and Application of an Artificial Neural Network Model to

Forecast Ground-water Flooding Events

MT-6

MT-3

GagingStation

2

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The Great Flood of 1913The Great Flood of 1913

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Needs StatementNeeds Statement

How can ground water levels in the downtown area of Dayton be accurately predicted to control subsurface dewatering systems ?

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Modeling ApproachesModeling Approaches

• Analytical ModelsExample: Rorabaugh

• Numerical Models Example: MODFLOW

• Artificial Neural Networks Example: Your Brain

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ANN ModelsANN Models

An information processing paradigm composed of many highly interconnected processing elements (neurons), configured for a specific application, working in unison to solve specific problems.ANN models are trained, they learn and

become experts for a specific problem.

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3

Why Use ANN Models for Water Why Use ANN Models for Water Level Predictions ?Level Predictions ?

• Can use large, complex data sets• Generalized decisions from imprecise data• Learn by example, iteratively trained and

retrained• Complete hydrogeologic characterization of a

site is not necessary

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ANN Models ANN Models –– Basic NetworksBasic Networks

Hierarchical Layers• Input Layer

Long-term data records

• Hidden Layer (s)Processing & weight adjustments

• Output LayerResults from learned association

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ANN Model SoftwareANN Model Software

EasyNNEasyNN--plusplus Version 7.0Version 7.0

• Backpropagation learning algorithm• Training, validating & querying data sets• CPU intensive

http://easynn.com

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ODNRODNRGroundwater LevelsGroundwater Levels

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NOAA NCDCNOAA NCDCWeather Weather

ConditionsConditions

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USGS USGS –– Stream FlowStream Flow

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4

River Discharge and Precipitation River Discharge and Precipitation for 1985for 1985--20052005

River Discharge and Precipitation

10

100

1,000

10,000

100,000

1/1/85 9/28/87 6/24/90 3/20/93 12/15/95 9/10/98 6/6/01 3/2/04

Date

Dis

char

ge (

CFS

)

0

1

2

3

4

Pre

cip

itatio

n (

in)

DischargePrecipitation

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MTMT--6 Water Level and Average 6 Water Level and Average Temperature for 1985Temperature for 1985--20052005

MT-6 Water Level and Average Temperature

700

705

710

715

720

725

730

735

740

1/1/85 2/9/89 3/20/93 4/28/97 6/6/01

Date

Wat

er L

evel

(ft

)

-20

0

20

40

60

80

100

Tem

pera

ture

(°F)

MT-6 Water LevelAverage Temperature

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Groundwater Flooding in DaytonGroundwater Flooding in Dayton

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Annual Groundwater LevelsAnnual Groundwater Levelsin Well MTin Well MT--6 6

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200419991994198919841979197419691964195919541949670675680685690695700

705710715720

Ele

vati

on

(ft

. m

sl)

Year

Minimum

Mean

Maximum

Begin Design &Construction ofAdministration Bldg.

Flood Event SequenceFlood Event Sequence

MT-3, MT-6, Precipitation and Discharge

714

715

716

717

718

719

12/25/03 12/30/03 1/4/04 1/9/04 1/14/04 1/19/04 1/24/04

Date

Wat

er L

evel

(ft

)

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Pre

cipi

tatio

n an

d D

isch

arge

MT-3MT-6

Precipitation

Discharge

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Graphical Graphical Representation of Representation of

ANN ModelANN Model

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EasyNNEasyNN PredictionsPredictions

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Results of Early MTResults of Early MT--6 Models6 Models

MT-6 Compared to Results of Two Early Models

714

715

716

717

718

12/25/03 12/30/03 1/4/04 1/9/04 1/14/04 1/19/04 1/24/04Date

Wat

er L

evel

(ft)

MT-6

MT-6 Model (Prec, Temp)

MT-6 Model (CFS, Temp)

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Construction of Precipitation FunctionConstruction of Precipitation Function

40Prec Function

714

715

716

717

718

12/25/03 12/30/03 1/4/04 1/9/04 1/14/04 1/19/04 1/24/04

Date

Wat

er L

evel

(ft)

0

50

100

150

200

250

300

350

Pre

cip

itat

ion

(in

x 1

00)

MT-6

40Prec Function

Precipitation

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Distributes each precipitation event over a 40-day period.

Construction of Discharge FunctionConstruction of Discharge Function40CFS Function

714

715

716

717

718

12/25/03 12/30/03 1/4/04 1/9/04 1/14/04 1/19/04 1/24/04

Date

Wat

er L

evel

(ft

)

0

50

100

150

200

250

300

350

400

450

Dis

char

ge

(CF

S/1

00)

MT-640CFS Function

Discharge

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Distributes discharge over a 40-day period.

Model Results for Entire PeriodModel Results for Entire Period

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MT-6 Model Using Rainfall, Temperature, River Dischargeand Previous MT-6 Reading as Inputs

711

712

713

714

715

716

717

718

1/1/1985 2/9/1989 3/20/1993 4/28/1997 6/6/2001

Date

Wat

er L

evel

(ft

)

MT-6

MT-6 Model

Detail of 1990Detail of 1990--1991 Flood Event1991 Flood Event

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MT-6 Model Using Rainfall, Temperature, River Dischargeand Previous MT-6 Reading as Inputs

714

715

716

717

718

12/25/1990 12/30/1990 1/4/1991 1/9/1991 1/14/1991 1/19/1991 1/24/1991

Date

Wat

er L

evel

(ft)

MT-6MT-6 Model

6

Detail of 1990Detail of 1990--1991 Flood Event1991 Flood Event

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MT-6 Model Using Rainfall, Temperature, River Dischargeand Previous MT-6 Reading as Inputs

714

715

716

717

718

12/25/1990 12/29/1990 1/2/1991 1/6/1991 1/10/1991

Date

Wat

er L

evel

(ft)

MT-6MT-6 Model

MT-6 Input

Detail of 2003Detail of 2003--2004 Flood Event2004 Flood Event

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MT-6 Model Using Rainfall, Temperature, River Dischargeand Previous MT-6 Reading as Inputs

714

715

716

717

718

12/25/2003 12/30/2003 1/4/2004 1/9/2004 1/14/2004 1/19/2004 1/24/2004

Date

Wat

er L

evel

(ft)

MT-6MT-6 Model

Comparison of Water Levels Comparison of Water Levels In MTIn MT--6 and MT6 and MT--33

MT-6 and MT-3

y = 0.6611x + 240.97R2 = 0.7277

698

700

702

704

706

708

710

712

714

716

718

720

690 695 700 705 710 715 720 725MT-3 Water Level (ft)

MT-

6 W

ater

Lev

el (

ft)

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Diagram of MTDiagram of MT--6 ANN Model 6 ANN Model Using MTUsing MT--3 as an Input3 as an Input

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MTMT--6 Model Using MT6 Model Using MT--3 as Input 3 as Input 20032003--2004 Flood Event2004 Flood Event

MT-6 Model Using MT-3 and Previous MT-6 Reading as Inputs

714

715

716

717

718

12/25/03 12/30/03 1/4/04 1/9/04 1/14/04 1/19/04 1/24/04

Date

Wat

er L

evel

(ft)

MT-6MT-6 Model

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ANN Model ANN Model Calculations can be Calculations can be

Performed in a Performed in a SpreadsheetSpreadsheet

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4 Input Nodes

8 Nodes in One Hidden Layer

1 Output Node

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MTMT--6 Model Implemented 6 Model Implemented In an Excel SpreadsheetIn an Excel Spreadsheet

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Calculate and export a Weight for each Connection and a Bias for each Node using the EasyNN software.

Enter the Value and Min/Max range for the four input parameters.

Use the Value and Min/Max range to calculate the Net Input for the four Input Nodes.

MTMT--6 Model Implemented 6 Model Implemented In an Excel SpreadsheetIn an Excel Spreadsheet

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Use the Value and Min/Max range to calculate the Net Input for the four Input Nodes.

Calculate the Net Input for Hidden Node 4 by summing the products of the Net Inputs and incoming Connection Weights and adding the Bias.

Perform the same calculation for each hidden layer node.

Calculate the Activation using the formula:

InputNeteActivation −+

=1

1

Sum the products of the Activations and Weights for each connection from the hidden layer to Output 12.

Calculate the Activation for Output 12 and use the Output Range to calculate the predicted value for MT-6.

ConclusionsConclusions

• Ground water levels in a BVA during flood events were successfully predicted using ANN modeling techniques.

• ANN model predictive results were comparable using either hydrologic & climatological parameters or near-river ground water levels.

• By integrating numerical and ANN modeling techniques, a robust ground water level forecasting system and better aquifer characterization is achievable.

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Neural networks do not perform miracles.But if used sensibly, they can produce some amazing results.

C. Stergiou and D. Siganos, Imperial College, London