Grey-box modeling: systems approach to water management

Md Moudud Hasanr0435449IUPWAREDate 25.01.2017

Report on Systems Approach to Water Management

•Background •Objectives•Study area•Data collection and evaluation•Model setup and calibration•Model performance evaluation•Model uncertainty quantification •Climate change scenario•Control on a reservoir

Contents

•Background •Objectives•Study area•Data collection and evaluation •Model setup and calibration•Model performance evaluation•Model uncertainty quantification •Climate change scenario•Control on a reservoir

Contents

•Models are often used to predict the behavior of a natural system▫(i) Detailed physically-based models (white box), ▫(ii) Conceptual models (grey -box) ▫(iii) Empirical models

•White-box model: ▫accurate and reliable,▫requires powerful computing system and much time

•Black-box models:▫relation between input and output▫ inaccurate results for extrapolation

•Grey-box model: ▫balance between the detailed physically-based model and empirical model.

Background


Contents

•To build precipitation runoff grey-box model using the system approach

concept

•To compare Grey-box model’s performance with the performance of the

white box model (semi-distributed SWAT model).

Objectives


Contents

Study area• Spring creek watershed ,Center County,

Pennsylvania, USA

• 370 km2 area

• Average elevation: 370m

▫ elevation varies from 675 m to 280 m.

• Groundwater basin: 22 percent larger

• land use:

▫ 34% agriculture

▫ 23% developed

▫ 43% forest


Contents

Data• Observed data:▫ daily discharge ▫precipitation▫maximum daily temperature ▫minimum daily temperature

• SWAT model simulated ▫ daily evapotranspiration▫ daily discharge

• 12 years (01-01-2002 to 31-12-2013) • Collected from M.G. Mostofa Amin the author of (Amin et al. 2017)

• Daily discharge data: http://waterdata.usgs.gov/pa/nwis/rt• Weather data: http://ches.communitymodeling.org/ and http://climate.psu.edu/

http://waterdata.usgs.gov/pa/nwis/rt

http://ches.communitymodeling.org/

http://climate.psu.edu/

Data manipulation

1/1/02 5/16/03 9/27/04 2/9/06 6/24/07 11/5/08 3/20/10 8/2/11 12/14/120.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00 0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

Runoff (m3/s) Precipitation (mm)

Time (day)

Disc

harg

e (m

3/s)

Prec

ipita

tion

(mm

)

Daily discharge Daily precipitation

Water balance

0.001000000000.002000000000.003000000000.004000000000.005000000000.006000000000.00

Cumulative Runoff Cumulative Pcipitation

Loss Cumulative Evapotranspiration

Time (day)

Cum

ulati

ve v

olum

e (m

3)


Contents

•Model-1:

Grey-box model construction Precipitation

Input flow

Baseflow Overland flow Interflow

Runoff

Net Input

Loss

Rainfall

WBF WOF WIF

KBFKOF KIF

𝑃𝑛𝑒𝑡=𝐷𝑎𝑖𝑙𝑦 𝑝𝑟𝑒𝑐𝑖𝑝𝑖𝑡𝑎𝑖𝑜𝑛∗ 𝐿𝑜𝑠𝑠 𝑓𝑎𝑐𝑡𝑜𝑟

𝑞𝑜𝑢𝑡 (𝑡 )=𝑒𝑥𝑝(− 1𝑘 )𝑞𝑜𝑢𝑡 (𝑡−1 )+(1−𝑒𝑥𝑝(− 1𝑘 ))𝑞𝑖𝑛 (𝑡))

•Model-2:

Grey-box model construction

Precipitation

Input flow


Runoff

Net Input

Loss

Rainfall

WBF WOF WIF

KBFKOF KIF

𝐿=¿𝑃𝑛𝑒𝑡 _ 𝑇𝑎𝑣𝑔=𝐷𝑎𝑖𝑙𝑦 𝑝𝑟𝑒𝑐𝑖𝑝𝑖𝑡𝑎𝑖𝑜𝑛−𝐿

•Model-3:

Grey-box model construction Precipitation

Temperature <

Tc snow

Input flow

Snow pack

Snow melt


Runoff

Net Input

Loss

No

Rainfall

YesSnowfall

WBF WOF WIF

KBFKOF KIF

𝑀=¿

𝑆𝑝𝑎𝑐 𝑘𝑡=𝑆𝑝𝑎𝑐𝑘𝑡 −1−𝑀𝑎𝑡 −1+𝑃𝑠𝑛𝑜 𝑤𝑡

𝑀𝑎𝑡={ 𝑀 𝑡 𝑖𝑓 𝑆𝑝𝑎𝑐 𝑘𝑡>𝑀𝑡

𝑆𝑝𝑎𝑐𝑘𝑡 𝑖𝑓 𝑆𝑝𝑎𝑐 𝑘𝑡<𝑀𝑡

0 𝑖𝑓 𝑆𝑝𝑎𝑐𝑘𝑡 ≤0}

• Input calibrated based on water balance. •Excel solver was used to optimize the parameter: ▫objective function (Nash Sutcliff Efficiency (NSE)) or error.

•Fine tuning was done manually

Model calibration

Parameter name Unit Model-1 Model-2 Model-3

1 Loss factor, Lf - 0.55

2 Slope parameter of loss, S - 0.6 0.56

3 The critical temperature for snow fall, Tc snow °C 1

4 Base temperature, Tbase °C 0

5 Melting factor, C mm day-1 °C-1 0.6

6 Critical net precipitation, Pc net m3/s 360 360 360

7 Overland flow portion, WBF - 0.08 0.08 0.08

8 Overland flow recession constant, kOF days 1 1 1

9 Interflow Portion, WBF - 0.22 0.35 0.35

10 Interflow recession constant, kIF days 20 30 30

11 Base flow portion, WBF - 0.7 0.57 0.57

12 Base flow recession constant, kBF days 170 170 170 Total number of parameters 8 8 11

Model parameter

Water balance check

4/19/2001 1/14/2004 10/10/2006 7/6/2009 4/1/2012 12/27/20140

500000000

1000000000

1500000000

2000000000

2500000000

3000000000 Cumulative Observed flowModel-1 Cumulative InputModel-2 Cumulative InputModel-3 Cumulative Input

Time (day

Cum

ulati

ve V

olum

e (m

3)

Simulated outflow and observed outflow

11/1/2007 2/9/2008 5/19/2008 8/27/20080

10

20

30

40

50

60

Observed flowModel-1 Simulated FlowModel-2 Simulated FlowModel-3 Simulated Flow

Time (day)

Flow

(m3/

s)

Model-1 Model-2 Model-3

Coefficient of efficiency (EF) [-] 0.36 0.65 0.71

Model selection

Black box Model

• Transfer function was also used with 5 poles and 4 zeros

• Mean squared error of transfer function was 9.25

0 500 1000 1500 2000 2500 3000 3500 4000 4500Time

0

20

40

60

80

100

120

140

Flow

(m3/

s)

Measured and simulated model output

•Performance of black-box was less accurate than Grey-box model

•Performance of selected model (Model-3) was acceptable

•Performance can be increased by including a soil storage process

Findings


Contents

•To evaluate the performance of grey-box model by both graphical and

statistical goodness-of-fit methods

•To compare with white-box model (SWAT model)

•To determine the application field of the model

Objectives

•Statistical goodness-of-fit:

▫Mean error (ME)

▫Mean squared error (MSE)

▫Model residual variance (S²EQ)

▫Coefficient of efficiency (EF)

•Graphically evaluate model performance

▫ WETSPRO: Sub-flow filtering and POT selection.

▫Model validation

Methodology

Grey-box model (Model-3) White box model (SWAT)

Mean error (ME) [m3/s] -0.19 -0.47

Mean squared error (MSE) [m3/s] 4.49 3.94

Model residual variance (S²EQ) [m3/s] 4.52 3.71

Coefficient of efficiency (EF) [-] 0.71 0.75

Statistical goodness-of-fit methods

Parameters QUICK FLOW periods SLOW FLOW periods

Max. ratio difference with subflow [-]:0.4 0.3

Independency period [day]:30 130

min peak height [m3/s]:1 1

Sub flow filtering

0 500 1000 1500 2000 2500 3000 3500 4000 45000

20

40

60

80

100

120

140Time seriesPOT values indep. quick flow periodsHydrograph separation quick flow

Number of time steps

Flow

(m3/

s)

Independent of base flow method

Validation Extremes High

0.1 1 10 1000

20

40

60

80

100

120

140observedWhite-box (SWAT)Grey-box

Return period [years]

Flow

(m3/

s)

Validation Extremes Low

0.1 1 10 1000

0.1

0.2

0.3

0.4

0.5

0.6 observedWhite-box (SWAT)Grey-box


1 /fl

ow (m

3/s)

Validation Maxima

2 3 4 5 6 7 8 9 100

2

4

6

8

10

12White-box (SWAT)Grey-boxbisectormean deviation

BC( Observed maxima )

BC

( Sim

ulat

ed m

axim

a )

Validation Minima

1 1.2 1.4 1.6 1.8 2 2.20

0.5

1

1.5

2

2.5White-box (SWAT)Grey-boxbisectormean deviation

BC( Observed minima )

BC

( Sim

ulat

ed m

inim

a )

Cumulative Flow

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

5000

10000

15000

20000

25000

30000

35000observedWhite-box (SWAT)Grey-box

Time

Cum

ulat

ive

Flow

(m3/

s)

•According to overall goodness-of-fit, both models were acceptable.

•White-box can simulate peak flow better

•Grey-box model simulates low flow more efficiently

•Grey-box model can be used for low flow analysis

Findings


Contents

•To determine the total uncertainty of the grey-box model using nearly independent low flow values

Objectives

Box-Cox transformation

0 2 4 6 8 10 12 14 16 18

-2-1.5

-1-0.5

00.5

11.5

2 Before Box-Cox transformation After Box-Cox transformation

Mod

el re

sidua

l (m

3/s)

=0.25𝐵𝐶 (𝑄 )=𝑄𝜆−1𝜆

Box-Cox (Minimum flow)

Mean error (ME) -0.16

Model residual variance (S²EQ) 0.08

Model residual standard deviation (SEQ) 0.28

Model uncertainty

After Box-Cox transformation

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5

4BisectorMean DeviationStandard Deviation

BC(Observed discharge (m3/s)

BC (S

imul

ated

dis

char

ge (m

3/s)


Contents

•To simulate a “high” climate change scenario in grey-box model.

•To determine the impact of climate change on flood frequency

Objectives

•Climate Perturbation Tool – Precipitation & Temperature

•Target year 2080

•High winter (wet winter)

•Grey-box model to simulate the outflow

•WETSPRO to extract POT values

•Extreme value analysis tool (ECQ)

•General Pareto Distribution (GDP)

Methodology

Simulation of grey-box model

4/19/2001 1/14/2004 10/10/2006 7/6/2009 4/1/2012 12/27/20140

20

40

60

80

100

120

140

160

180Future scenario simulation Current scenario simulation

Time (day)

Flow

(m

3/s)

•Generalized Pareto distribution: heavy tail

Extreme value analysis

Calibrated GPD Parameter Value

Parameter name

Current scenario Future scenario (2080)

Gamma 0.30 0.44

Beta 5.15 6.57

Threshold flow xt 16.77 14.84

Threshold rank t 46 61

Flood frequency analysis

0.1 1 10 100 10000.0020.0040.0060.0080.00

100.00120.00140.00160.00180.00 Empirical 2080

Theoritical 2080Emperical Current Theoritical Current


Peak

flow

[m3/

s]

•Flood frequency will be higher in future

•Climate change scenario of Belgium was used for this study area.

•Climate change scenario of respected area should be used

Findings


Contents

• to understand the functioning of feedback and feedforward control on a

reservoir

• to get familiar with the simulation package Matlab/Simulink.

Objective

No Feed Control

0 500 1000 1500 2000 2500 3000 3500 4000Time (sec)

5

5.2

5.4

5.6

5.8

6

6.2

Wat

er le

vel (

m)

Reservoir surface area, 𝐴=∆𝑉∆h =

𝑄𝑡∆ h=

3×36006.1015−5=9804.81𝑚

2

Feed-forward control

0 500 1000 1500 2000 2500 3000 3500 4000Time (sec)

4.995

5

5.005

5.01

5.015

5.02

5.025

Wat

er le

vel (

m)

Feedback control

0 500 1000 1500 2000 2500 3000 3500 4000Time (sec)

4.99

4.995

5

5.005

5.01

5.015

5.02

5.025

5.03

5.035

5.04

Wat

er le

vel (

m)

Feed-Back Control

Feedback control : integral gain (Ki) =0

0 500 1000 1500 2000 2500 3000 3500 4000Time (sec)

5

5.01

5.02

5.03

5.04

5.05

5.06

5.07

Wat

er le

vel (

m)

Effect of the proportional gain (Kp)

0 500 1000 1500 2000 2500 3000 3500 4000Time (sec)

5

5.005

5.01

5.015

5.02

5.025

5.03

Wat

er le

vel (

m)

Ki=0, Kp=155

0 500 1000 1500 2000 2500 3000 3500 4000Time (sec)

5

5.005

5.01

5.015

5.02

5.025

wat

er le

vel (

m)

Ki=0, Kp=255

0 500 1000 1500 2000 2500 3000 3500 4000Time (sec)

-15

-10

-5

0

5

10

15

20

25

Wat

er le

vel (

m)

Ki=0,Kp=355

Combine Feedback and Feedforward control

0 500 1000 1500 2000 2500 3000 3500 4000time (sec)

4.992

4.994

4.996

4.998

5

5.002

5.004

5.006

5.008

Wat

er le

vel (

m)

Feedforward and Feedback

Reference level at 4m

0 500 1000 1500 2000 2500 3000 3500 4000Time (sec)

3.6

3.8

4

4.2

4.4

4.6

4.8

5

Wat

er le

vel (

m)

Reference level 4m

1250 sec

•The feedforward can control water level with fast response but error in

measurement may cause problem.

•The feedback control system can stabilize water level effectively but

delay response is issue.

•For complicated and important system both control system should be

used for better control.

Findings

• Amin, M.G. Mostofa et al. 2017. “Simulating Hydrological and Nonpoint Source Pollution Processes in a Karst Watershed: A Variable Source Area Hydrology Model Evaluation.” Agricultural Water Management 180: 212–23.

• Van Uytven, E., and P. Willems. 2016. “Climate Perturbation Tool: A Climate Change Tool for Generating Perturbed Time Series - Manual Version January 2016.” KU Leuven - Hydraulics Section (January).

• Willems, Patrick. 2004. “Parsimonious Model for Combined Sewer Overflow Pollution.” In 4th International Conference on Sewer Processes & Networks (4th SPN), Funchal, Madeira, Portugal, 22-24 November, 10p.

• Willems, Patrick. 2008. “Modelling Guidelines for Water Engineering - 4. Model Calibration and Validation.” Hydraulics Laboratory, Kasteelpark Arenberg 40, B-3001 Leuven: 1–33.

• Willems, Patrick. 2009. “A Time Series Tool to Support the Multi-Criteria Performance Evaluation of Rainfall-Runoff Models.” Environmental Modelling and Software 24(3): 311–21

References

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Grey-box modeling: systems approach to water management

Engineering

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