Uncertainty due to gap-filling in
long-term hydrologic datasets
Craig See1, Jeremy Hayward1, Ruth
Yanai1, Mark Green2, Doug Moore3
Amey Bailey4
1. SUNY College of Environmental Science and Forestry, Syracuse, NY
2. Plymouth State University, Plymouth, NH
3. University of New Mexico, Albuquerque, NM
4. USDAForest Service, Northern Research Station
All long term datasets contain gaps
Credit: Don Buso
Why Gap Filling?
Sometimes we need a continuous record
(calculating fluxes)
(Kiang et. al 2013)
Gap filling methods
•
•
•
•
Use of historical averages
Bayesian Bootstrapping
Expectation-maximization algorithm
Use neighboring values
– Direct substitution
– Regression
All gap filling methods introduce
new error into the final total!
Stream flow Gap Causes
Coweeta
Hubbard Brook
1%
1%
6%
10%
13%
8%
25%
Equipment failure
Maintenance
6%
Operator error
12%
Ice in v-notch
Debris in v-notch
68%
Misc.
50%
Precipitation Volume Gaps at
Hubbard Brook
Precipitation Chemistry Gaps at
Sevilletta NWR
5%
2%
8%
Contaminated Sample
Technician Error
Overflow
Missing in Field
85%
Credit: Odonfiction.wordpress.com
Credit: Doug Moore
Streamflow gaps at Gomadansan
Experimental Forest
0
50
100
150
0
50
100
300
200
weir
12
100
0
150
100
weir
16
50
0
150
100
weir
17
50
0
100
weir
20
50
0
0
100
200
300
0
50
100
150
(Yanai et al. 2013, in review)
Example: Stream Flow at Hubbard Brook
• Long term record from 2
watersheds
• Model predicting one from
the other
• Record of actual gaps
occurring
– Gap length
– Flow rate at start of gap
Credit: HBRF
Watershed 6 stream flow (ft3/s)
Stream flow at Hubbard Brook
1962-2001
Watershed 5 stream flow (ft3/s)
Absolute difference (ft3)
Flow rate during gap impacts uncertainty in
total volume (half hour gap)
Initial stream flow (ft3/s)
Methods-flow distribution
Frequency
Randomly sample 100,000 “fake gaps” from the
data to create a distribution of change in flow
during a gap.
Change in stream flow (ft3/s)
Creating a sampling pool
For each “real gap” in the record:
• Randomly create a “fake gap” of same length
from the master dataset
• Randomly select a flow-change value from the
flow distribution
• Does the max. flow rate inside the fake gap
exceed the max. flow rate of the real gap ± the
flow change value?
– If yes, reject and pick another fake gap
– If no, include this fake gap in sampling pool
Sampling Pools
• Create a sampling pool of 1000 possible
uncertainties for each real gap in the record
• To calculate uncertainty for a year, sum
random values pulled from sampling pools for
each real gap in that year.
• Do this for 100,0000 iterations.
Frequency
1996 (wet year)
-6.7%
6.7%
Anualstream flow uncertainty (mm)
Frequency
2001 (dry year)
-14.5%
14.5%
Annualstream flow uncertainty (mm)
Dry Year (2001)
Frequency
Wet Year (1996)
-6.7%
6.7%
Annual stream flow uncertainty (mm)
14.5%
14.5%
Annual stream flow uncertainty (mm)
Precipitation gaps at Sevilleta
(1989-1996)
How do we incorporate “gap uncertainty” into annual
nitrate deposition estimates?
Precipitation gaps at Sevilleta
How do we incorporate “gap uncertainty” into annual
nitrate deposition estimates?
Methods-Wet Deposition Gaps
• Construct a variogram based on observations
that include all gauges (84 observations)
• Use basic kriging interpolation to estimate
deposition for all observations
• Re-run analysis separately for all combinations
of funnels.
• Create distribution of observed-expected for
each combination
Gauge 8 removed
Frequency
Frequency
Gauge 3 removed
-1.5%
1.5%
Observed – Expected NO3 (mg/m2)
-2.6%
2.6%
Observed – Expected NO3 (mg/m2)
Precipitation gaps at Sevilleta
How do we incorporate “gap uncertainty” into annual
nitrate deposition estimates?
Removing multiple gauges rarely changes the range of
possible errors, but increases the chance of higher
error within that range for a given event.
Gauge 3&8 removed
Frequency
Frequency
Gauge 8 removed
-2.6%
Observed – Expected NO3
2.6%
(mg/m2)
-2.6%
2.6%
Observed – Expected NO3 (mg/m2)
There is no correlation between amount of deposition
from a collection, and the percent error in gap filling
with kriging.
Gauge 8
120
Percent error
100
80
60
40
20
0
0
5
10
15
20
25
Observed NO3 (mg/m2)
Its OK to express your sampling pool as a percentage.
Frequency
To account for differences in collection, express the
distribution as a percent of N deposition during a
given event
Gauge 8
Percent of observed value
Use these percentages and the deposition estimate
for a real gap to create a sampling pool!
Summary
• Data gaps can contribute significant
uncertainty to estimates of ecosystem
nutrient inputs and outputs.
• With long term datasets, this uncertainty can
be estimated empirically
Advantages:
Disadvantages:
• Doesn’t rely on parametric
estimates
• Can use any model
• Easy to understand
• Requires data
• Computationally intensive
• The past doesn’t always
predict the future!
Thank you!
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Co-authors
John Campbell
Franklin Diggs
Becka Walling