Watershed Hydrology Modeling: What is Considered Calibrated?
Presented by:
Jeremy Wyss, HITTetra Tech
27th Annual Alabama Water Resources ConferenceOrange Beach, Alabama
Watershed Models Play an important role in linking sources of pollutants to receiving
waterbodies as point and nonpoint source loads. Are driven by precipitation, land use, impervious area, slope, soil
type and drainage area. Are simplified mathematical representations of complex real
world systems which make use of known interrelationships to predict change in response to perturbation of independent variable or forcing function from its current state.
To be considered credible, the ability of the model to represent real world conditions should be demonstrated through calibration/corroboration.
LSPC, HSPF, SWAT, WAM, SWMM, WARMF, etc…
Model Calibration/Corroboration Calibration – parameter adjustment to achieve the best fit
between model prediction and field observations. Explicit focus on available stream gages at multiple locations in
the watershed (each has it’s own uniqueness to capture). Calibration is for a specific period of time.
Corroboration – utilizes the calibrated model for a different period of time at multiple locations in the watershed.
Investigates whether a models predictive capability is similar to that achieved over the calibration period.
Statistical and Graphical comparison of observed and simulated.
Hydrology Graphical Comparison
Daily Average Flow (normal scale)Daily Average Flow (log scale)Daily Average Water BalanceMonthly Average Regression Monthly Average Flow BalanceMonthly Average Flow
y = 0.7394x + 97.379R2 = 0.8785
0
200
400
600
800
0 200 400 600 800
Average Observed Flow (cfs)
Ave
rage
Mod
eled
Flo
w (
cfs)
Avg Flow (1/1/1998 to 12/31/2009)Line of Equal ValueBest-Fit Line
J F M A M J J A S O N D
0
200
400
600
800
1 2 3 4 5 6 7 8 9 10 11 12
Month
Flow
(cfs
)
0
1
2
3
4
5
6
Mon
thly
Rai
nfal
l (in
.)
Avg Monthly Rainfall (in.)Avg Observed Flow (1/1/1998 to 12/31/2009)Avg Modeled Flow (Same Period)
Average by Month Regression Average by Month Distribution
J F M A M J J A S O N D
0
100
200
300
400
500
600
700
1 2 3 4 5 6 7 8 9 10 11 12
Month
Flow
(cfs
)
0
1
2
3
4
5
6
Mon
thly
Rai
nfal
l (in
.)
Average Monthly Rainfall (in) Observed (25th, 75th)Median Observed Flow (1/1/1998 to 12/31/2009) Modeled (Median, 25th, 75th)
Monthly Distribution Box Plot10
100
1000
10000
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Percent of Time that Flow is Equaled or Exceeded
Dai
ly A
vera
ge F
low
(cfs
)
Observed Flow Duration (1/1/1998 to 12/31/2009 )
Modeled Flow Duration (1/1/1998 to 12/31/2009 )
Daily Average Flow Duration
0%
20%
40%
60%
80%
100%
120%
Jan-98 Jul-99 Jan-01 Jul-02 Jan-04 Jul-05 Jan-07 Jul-08
Nor
mal
ized
Flo
w V
olum
e (O
bser
ved
as 1
00%
)
Observed Flow Volume (1/1/1998 to 12/31/2009 )
Modeled Flow Volume (1/1/1998 to 12/31/2009 )
Daily Average Flow Accumulation
0
500
1000
1500
J-98 J-99 J-01 J-02 J-04 J-05 J-07 J-08
Month
Flow
(cfs
)
0
2
4
6
8
10
12
14
Mon
thly
Rai
nfal
l (in
.)
Avg Monthly Rainfall (in.)Avg Observed Flow (1/1/1998 to 12/31/2009 )Avg Modeled Flow (Same Period)
Hydrology Statistical ComparisonE = Nash-Sutcliffe Coefficient of Efficiency
E’ = Garrick Baseline Adjusted Coefficient of Efficiency
Used to assess the predictive power of hydrological modelsRange from -∞ to 1 -infinity < E < 0: The observed mean is a better predictor than the modelEqual to 0: The long-term average of the observed data is just as good a predictor as the modelBetween 0 and 1: The closer the model efficiency is to 1, the more accurate the model isObtaining a value of 0.7 or better is a reasonable indicator of adequate fit.
Hydrology Calibration Pitfalls
10
100
1000
10000
100000
1/1/2001 7/1/2001 1/1/2002 7/1/2002 1/1/2003 7/1/2003 1/1/2004 7/1/2004 1/1/2005 7/1/2005 1/1/2006 7/1/2006 1/1/2007 7/1/2007
Date
Flow
(cfs)
0
1
2
3
4
5
6
7
8
9
10
Daily R
ainfall (in.)
Avg Daily Rainfall (in.) Avg Observed Flow (1/1/2001 to 12/31/2007 ) Avg Modeled Flow (Same Period)
10
100
1000
10000
100000
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Percent of Time that Flow is Equaled or Exceeded
Dai
ly A
vera
ge F
low
(cfs
)
Observed Flow Duration (1/1/2001 to 12/31/2007 )
Modeled Flow Duration (1/1/2001 to 12/31/2007 )
0.1
1
10
100
1000
10000
1/1/2002 10/1/2002 7/1/2003 4/1/2004 1/1/2005 10/1/2005 7/1/2006 4/1/2007 1/1/2008 10/1/2008 7/1/2009 4/1/2010 1/1/2011 10/1/2011 7/1/2012
Date
Flow
(cfs)
0
12
34
5
67
89
10
Daily R
ainfall (in.)
Avg Daily Rainfall (in.) Avg Observed Flow (1/1/2002 to 9/30/2012 ) Avg Modeled Flow (Same Period)
Hydrology Acceptance CriteriaModel Component Very Good Good Fair Poor
Error in total volume ≤ 5% 5 - 10% 10 - 15% > 15%
Error in 50% lowest flow volumes ≤ 10% 10 - 15% 15 - 25% > 25%
Error in 10% highest flow volumes ≤ 10% 10 - 15% 15 - 25% > 25%
Error in storm volume ≤ 10% 10 - 15% 15 - 25% > 25%
Winter volume error ≤ 15% 15 - 30% 30 - 50% > 50%
Spring volume error ≤ 15% 15 - 30% 30 - 50% > 50%
Summer volume error ≤ 15% 15 - 30% 30 - 50% > 50%
Fall volume error ≤ 15% 15 - 30% 30 - 50% > 50%
R2 daily values > 0.80 > 0.70 > 0.60 ≤ 0.60
R2 monthly values > 0.85 > 0.75 > 0.65 ≤ 0.65
Nash-Sutcliffe > 0.75 > 0.65 > 0.50 ≤ 0.50
• How accurate is the model?
• Is the model good enough for this evaluation?
Our “Rating” Approach• Assign weight to each statistical measure
• Assign value to “Very Good”, “Good”, “Fair” and “Poor” ranges
• Multiply weight by value and sum results to obtain quantitative score
• Compare quantitative score to range to produce qualitative grade
• Produce a summary of statistical bias (all +, all -, or mixed)
• Process completed for Calibration/Validation on Period of Record and for each individual year
Floyds Fork Watershed: Hydrology Calibration Maps produced by M.Akasapu, 02-04-2013
NAD_1983_UTM_Zone_17N0 3 61.5
Miles
0 3 61.5Kilometers
Jefferson
Bullitt
Spencer
Shelby
Henry
Oldham
Salt River
Floy
ds F
ork
Ced
ar C
reek
Long
Run
USGS ID: 03297900
USGS ID: 03298000
USGS ID: 03298135
USGS ID: 03298150
USGS ID: 03298200
Floyds Fork
Che
now
eth
Run
Penn
sylv
ania
Run
Cur
rys
Fork
USGS ID: 03298300
USGS ID: 03298250
LegendFlow Calibration
VG (80-75)
G (74-55)
F (54-35)
P (34-20)
Waterways
Watershed Boundary
County
Next Steps
0%10%20%30%40%50%60%70%80%90%
100%
1/1/1998 10/1/1998 7/1/1999 4/1/2000 1/1/2001 10/1/2001 7/1/2002 4/1/2003 1/1/2004 10/1/2004 7/1/2005 4/1/2006 1/1/2007 10/1/2007 7/1/2008 4/1/2009
Date
Water B
alan
ce (O
bs + M
od)
Avg Modeled Flow (1/1/1998 to 12/31/2009 ) Avg Observed Flow (1/1/1998 to 12/31/2009 ) Line of Equal Value
0%10%20%30%40%50%60%70%80%90%
100%
1/1/1998 10/1/1998 7/1/1999 4/1/2000 1/1/2001 10/1/2001 7/1/2002 4/1/2003 1/1/2004 10/1/2004 7/1/2005 4/1/2006 1/1/2007 10/1/2007 7/1/2008 4/1/2009
Date
Water B
alan
ce (O
bs + M
od)
Avg Modeled Flow (1/1/1998 to 12/31/2009 ) Avg Observed Flow (1/1/1998 to 12/31/2009 ) Line of Equal Value• Add/Incorporate/Create and Standard Operation Procedure for visual
component
• Determine how to incorporate Modeling Efficiencies into Rating
Comments/Questions?
Watershed Hydrology Modeling: What is Considered Calibrated?