This document summarizes a study that developed and evaluated a grey-box precipitation-runoff model for the Spring Creek watershed in Pennsylvania. It describes: 1) Developing three variations of a grey-box model using different approaches to account for factors like temperature, snowmelt, and evapotranspiration. 2) Calibrating the models and evaluating their performance against observed flow data using statistical metrics. 3) Comparing the best-performing grey-box model (Model 3) to a white-box SWAT model, finding they both performed acceptably with some differences. 4) Analyzing the uncertainty of the grey-box model using low flow values.

1. Md Moudud Hasan
r0435449
IUPWARE
Date 25.01.2017
Report on Systems Approach to Water
Management

2. • 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

3. • 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

4. • 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

5. • 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

6. • 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

7. • 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

8. 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

9. • 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

10. 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/

11. Data manipulation
0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.000.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
1/1/02 5/16/03 9/27/04 2/9/06 6/24/07 11/5/08 3/20/10 8/2/11 12/14/12
Precipitation(mm)
Discharge(m3/s)
Time (day)
Runoff (m3/s) Precipitation (mm)

12. Daily discharge Daily precipitation

13. • 𝑃𝑟𝑒𝑐𝑖𝑝𝑖𝑡𝑎𝑖𝑜𝑛 = 𝑅𝑢𝑛𝑜𝑓𝑓 + 𝐸𝑣𝑎𝑝𝑜𝑟𝑎𝑡𝑖𝑜𝑛 + 𝐺𝑜𝑢𝑛𝑑𝑤𝑎𝑡𝑒𝑟 𝑜𝑢𝑡𝑓𝑙𝑜𝑤 − 𝐺𝑟𝑜𝑢𝑛𝑑𝑤𝑎𝑡𝑒𝑟 𝑖𝑛𝑓𝑙𝑜𝑤
• 𝐿𝑜𝑠𝑠 = 𝑃𝑟𝑒𝑐𝑖𝑝𝑖𝑡𝑎𝑖𝑜𝑛 − 𝑅𝑢𝑛𝑜𝑓𝑓
 𝐿𝑜𝑠𝑠 = 𝐸𝑣𝑎𝑝𝑜𝑟𝑎𝑡𝑖𝑜𝑛 + 𝐺𝑜𝑢𝑛𝑑𝑤𝑎𝑡𝑒𝑟 𝑜𝑢𝑡𝑓𝑙𝑜𝑤 − 𝐺𝑟𝑜𝑢𝑛𝑑𝑤𝑎𝑡𝑒𝑟 𝑖𝑛𝑓𝑙𝑜𝑤
Water balance
0.00
1000.00
2000.00
3000.00
4000.00
5000.00
6000.00
Cumulativevolume(m3)
Millions
Time (day)
Cumulative Runoff
Cumulative Pcipitation
Loss
Cumulative Evapotranspiration

14. • 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

15. • Model-1:
Grey-box model construction
Precipitation
Input flow
Baseflow Overland flow Interflow
Runoff
Net Input
Loss
Rainfall
WBF WOF WIF
KBF
KOF KIF
𝑃𝑛𝑒𝑡 = 𝐷𝑎𝑖𝑙𝑦 𝑝𝑟𝑒𝑐𝑖𝑝𝑖𝑡𝑎𝑖𝑜𝑛 ∗ 𝐿𝑜𝑠𝑠 𝑓𝑎𝑐𝑡𝑜𝑟
𝑞 𝑜𝑢𝑡 𝑡 = 𝑒𝑥𝑝 −
1
𝑘
𝑞 𝑜𝑢𝑡 𝑡 − 1 + 1 − 𝑒𝑥𝑝 −
1
𝑘
𝑞𝑖𝑛(𝑡)

16. • Model-2:
Grey-box model construction
Precipitation
Input flow
Baseflow Overland flow Interflow
Runoff
Net Input
Loss
Rainfall
WBF WOF WIF
KBF
KOF KIF
𝐿 =
𝑠𝑇𝑎𝑣𝑔 𝑖𝑓 𝑇𝑎𝑣𝑔 > 0
0
𝑃𝑛𝑒𝑡_𝑇𝑎𝑣𝑔 = 𝐷𝑎𝑖𝑙𝑦 𝑝𝑟𝑒𝑐𝑖𝑝𝑖𝑡𝑎𝑖𝑜𝑛 − 𝐿

17. • Model-3:
Grey-box model construction
Precipitation
Temperature
< Tc snow
Input flow
Snow pack
Snow melt
Baseflow Overland flow Interflow
Runoff
Net Input
Loss
No
Rainfall
Yes
Snowfall
WBF WOF WIF
KBF
KOF KIF
𝑀 =
)𝐶(𝑇∗
𝑚𝑎𝑥 − 𝑇𝑏𝑎𝑠𝑒 if 𝑇∗
𝑚𝑎𝑥 > 𝑇𝑏𝑎𝑠𝑒
0 if 𝑇∗
𝑚𝑎𝑥 < 𝑇𝑏𝑎𝑠𝑒
𝑆 𝑝𝑎𝑐𝑘 𝑡
= 𝑆 𝑝𝑎𝑐𝑘 𝑡−1
− 𝑀 𝑎 𝑡−1
+ 𝑃𝑠𝑛𝑜𝑤 𝑡
𝑀 𝑎 𝑡
=
𝑀𝑡 𝑖𝑓 𝑆 𝑝𝑎𝑐𝑘 𝑡
> 𝑀𝑡
𝑆 𝑝𝑎𝑐𝑘 𝑡
𝑖𝑓 𝑆 𝑝𝑎𝑐𝑘 𝑡
< 𝑀𝑡
0 𝑖𝑓 𝑆 𝑝𝑎𝑐𝑘 𝑡
≤ 0

18. • 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

19. 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

20. Water balance check
0
50000
100000
150000
200000
250000
300000
4/19/2001 1/14/2004 10/10/2006 7/6/2009 4/1/2012 12/27/2014
CumulativeVolume(m3)
x10000
Time (day
Cumulative Observed flow
Model-1 Cumulative Input
Model-2 Cumulative Input
Model-3 Cumulative Input

21. Simulated outflow and observed outflow
0
10
20
30
40
50
60
11/1/2007 12/21/2007 2/9/2008 3/30/2008 5/19/2008 7/8/2008 8/27/2008 10/16/2008
Flow(m3/s)
Time (day)
Observed flow
Model-1 Simulated Flow
Model-2 Simulated Flow
Model-3 Simulated Flow

22. Model-1 Model-2 Model-3
Coefficient of efficiency (EF) [-] 0.36 0.65 0.71
Model selection

23. Black box Model
• Transfer function was also used with 5
poles and 4 zeros
• Mean squared error of transfer
function was 9.25

24. • 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

25. • 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

26. • 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

27. • 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

28. 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

29. 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
20
40
60
80
100
120
140
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Flow(m3/s)
Number of time steps
Time series
POT values indep. quick flow periods
Hydrograph separation quick flow
POT values indep. slow flow periods
Independent of base flow method

30. Validation Extremes High
0
20
40
60
80
100
120
140
0.1 1 10 100
Flow(m3/s)
Return period [years]
observed
White-box (SWAT)
Grey-box

31. Validation Extremes Low
0
0.1
0.2
0.3
0.4
0.5
0.6
0.1 1 10 100
1/flow(m3/s)
Return period [years]
observed
White-box (SWAT)
Grey-box

32. Validation Maxima
0
2
4
6
8
10
12
0 2 4 6 8 10
BC(Simulatedmaxima)
BC( Observed maxima )
White-box (SWAT)
Grey-box
bisector
mean deviation
standard deviation

33. Validation Minima
0
0.5
1
1.5
2
2.5
0 0.5 1 1.5 2 2.5
BC(Simulatedminima)
BC( Observed minima )
White-box (SWAT)
Grey-box
bisector
mean deviation
standard deviation

34. Cumulative Flow
0
5000
10000
15000
20000
25000
30000
35000
0 1000 2000 3000 4000 5000
CumulativeFlow(m3/s)
Time
observed
White-box (SWAT)
Grey-box

35. • 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

36. • 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

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

38. Box-Cox transformation
-2
-1
0
1
2
0 5 10 15 20
Modelresidual(m3/s)
Before Box-Cox transformation After Box-Cox transformation
𝜆 =0.25𝐵𝐶 𝑄 =
𝑄 𝜆
− 1
𝜆

39. Box-Cox (Minimum flow)
Mean error (ME) -0.16
Model residual variance (S²EQ) 0.08
Model residual standard deviation (SEQ) 0.28
Model uncertainty

40. After Box-Cox transformation
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.5 1 1.5 2 2.5 3 3.5 4
BC(Simulateddischarge(m3/s)
BC(Observed discharge (m3/s)
Bisector
Mean Deviation
Standard Deviation

41. • 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

42. • To simulate a “high” climate change scenario in grey-box model.
• To determine the impact of climate change on flood frequency
Objectives

43. • 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

44. Simulation of grey-box model
0
20
40
60
80
100
120
140
160
180
4/19/2001 1/14/2004 10/10/2006 7/6/2009 4/1/2012 12/27/2014
Flow(m3/s)
Time (day)
Future scenario simulation Current scenario simulation

45. • 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

46. Flood frequency analysis
0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
160.00
180.00
0.1 1 10 100 1000
Peakflow[m3/s]
Return period [years]
Empirical 2080
Theoritical 2080
Emperical Current
Theoritical Current

47. • 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

48. • 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

49. • to understand the functioning of feedback and feedforward control on a
reservoir
• to get familiar with the simulation package Matlab/Simulink.
Objective

50. No Feed Control
Reservoir surface area, 𝐴 =
∆𝑉
∆ℎ
=
𝑄𝑡
∆ℎ
=
3 × 3600
6.1015 − 5
= 9804.81 𝑚2

51. Feed-forward control Feedback control

52. Feedback control : integral gain (Ki) =0

53. Effect of the proportional gain (Kp)

54. Combine Feedback and Feedforward control

55. Reference level at 4m
1250 sec

56. • 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

57. • 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

58. mdmoudud.hasan@student.kuleuven.be