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Hydrologic trend analysis
Dennis P. LettenmaierDepartment of Civil and Environmental Engineering
University of Washington
GKSS School on Statistical Analysis in Climate Research
Lecce, Italy
October 15, 2009
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Outline of this talk
1. Water cycle observations
2. Long-term trend analysis of hydrologic variables1. Nonparametric approach (seasonal Man n Kendall)
2. Examples
3. Some pitfalls in trend analysis
3. Analysis and trends in hydrologic extremes
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1. Water cycle observations
• Land surface water balance
• Atmospheric water balance
• Land surface and atmospheric water and energy balances both contain evapotranspiration (with a multiplier)
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Precipitation measurement (dominant hydrological forcing)
• In situ methods use gauges (essentially points)– Issues with representativeness, changes of instrumentation in time, biases
(see Phil Jones lecture)– Wind catch deficiency is critical problem for solid precipitation, of
somewhat lesser (but not necessarily negligible) magnitude– Small scale spatial variability (tends to average out with time)
• Surface radars– Provides near spatially continuous coverage– Terrain blockage issues, also tilt angle, other issues– Complications in producing climate quality records
• Remote sensing– Indirect (aside from TRMM radar)– Sampling issues aside from geostationary– Solid precipitation issues
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Stream discharge (streamflow) measurement
Stage (water height), not discharge is measured. Discharge is derived via a (usually power law) rating curve derived from discrete stage and discharge measurements, applied to time-continuous stage measurements
Visuals courtesy USGS
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Snow Water Equivalent (SWE) measurement – manual snow courses
Visuals courtesy NRCS
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SWE measurement – automated snow pillows
Typical SnoTEL installation Enhanced SnoTEL installation
Visuals courtesy NRCS
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Other hydrological variables• Soil moisture
– few climate quality observations with consistent observation methods– In situ methods are complicated by short scale (as small as 1 m) spatial variability
• Evapotranspiration– Most common long-term measurement is pan evaporation, which can be considered a rough
index to potential (not actual) evapotranspiration– Flux towers (AmeriFlux, EuroFlux, FluxNet) provide estimates of latent heat flux (essentially
actual evapotranspiration) via either eddy correlation or Bowen ratio methods. However, record lengths are short from a climatological perspective, and generally not of trend quality
• Groundwater– Relatively few well observations of long length that are not affected by management
(withdrawals)– Satellite (GRACE) data provide an alternative over large areas, but record is short (less than a
decade), and measurement is effectively all changes in moisture content (atmospheric, soil moisture, lakes, etc)
• Lakes and wetlands– Very few records suitable for trend analysis– Some work on high latitude lakes (surface area) from remote sensing
• Glaciers– Relatively small number of glaciers have detailed mass balance records, but many changes are
not subtle– Changes in area are generally easier to detect than storage (and are amenable to visible satellite
imagery with record lengths exceeding 30 years– Satellite altimetry (e.g. ICESAT) provides basis for storage estimates, but record lengths are
short
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Hydrologic data characteristics• Precipitation: usually measured as accumulations over time, statistics are
characterized by intermittency and high Cv and skewness for accumulation intervals < multiple days. Correlation lengths increase with accumulation intervals, generally greater for winter (synoptic scales events) than summer (convective); skewness and Cv decrease with accumulation intervals (and intemittency vanishes)
• Streamflow: Most variable of land surface fluxes; can be intermittent for short accumulation intervals in arid areas and in some cases small drainage areas. Controls include precipitation and evaporative demand, but also land surface characteristics and drainage areas. It is an areal integrator. Spatial correlation lengths usually longer than for precipitation.
• Evapotranspiration: Least variable of three major land surface hydrologic fluxes. Near-direct measurement difficult, and mostly applicable to points, large area estimates from remote sensing (essentially indirect/model), or by difference
• Soil moisture: Few long-term observations available, most viable approach (not without shortcomings) is model reconstruction
• Groundwater: Few long-term observations available that are not dominated by management effects; large area estimates (which include other storage terms) now possible via satellite microgravity (GRACE)
• Snow water equivalent: Point measurements from snow courses (now increasingly replaced with automated snow pillows)
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2.1 Hydrologic trend analysis – nonparametric approaches
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Testing for Trends
Ho: Distribution (F) of R.V. Xt is same for all t
H1: F changes systematically with time
We may also want to describe the amount or rate of change, in property (e.g. central tendency) of the distribution
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Parametric vs Nonparametric statistics
Parametric: Assume the distribution of Xt (often Gaussian)
Nonparametric: Form of distribution not assumed (but often are some assumptions, e.g. common distribution aside from change in central tendency)
Nonparametric tests are usually more robust to violation of assumptions that must be made for parametric tests, however when parametric tests are appropriate, the range of quantitative inferences that can be made is usually greater
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Monotonic Trend: Continuing (and not reversing) with time
Parametric test example: linear regression (with time)
Nonparametric test examples: Kendall’s tau; spearman’s rho (essentially rank correlation with time)
Step Trend: One-time change, of fixed amountParametric test example: t-testNon-parametric test example: Mann
Whitney
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Kendall’s Tau ()• Tau () measures the strength of the monotonic
relationship between X and Y. Tau is a rank-based procedure and is therefore resistant to the effect of a small number of unusual values.
• Because depends only on the ranks of the data and not the values themselves, there are adjustments for missing or censored data (essentially treated as ties) – tests work with a “limited amount of” such data
• In general, for linear associations, < r. Strong linear correlations of r > 0.9 corresponds to > 0.7.
• For trend test, Y can be time
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• The test statistic S measures the monotonic dependence of X on t:
– S = P - M
– where : P = # of (+), the # of times the X’s increase with t, or the # of Xi < Xj for all ti < tj (“concordant pairs”).
– M = # of (-), the # of times the X’s decrease with t, or the number of Xi > Xj for all ti <tj (“discordant pairs”).
– i = 1, 2, … (n-1); and j = (i+1), …, n.
• There are n(n-1)/2 possible comparisons to be made among the n data pairs. If all y values increased along the x values, S = n(n-1)/2. In this situation, = +1, and vice versa. Therefore dividing S by n(n-1)/2 will give a -1 < < +1.
• Adjustment can be made for ties (missing or censored data)
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is defined as :
• Critical value of S can be determined by enumerating the discrete distribution of S, when the data are randomly ranked with time
• For n > about 10, there is a large sample approximation to the test statistic; for smaller values, tables of the exact distribution are available
2/)1(
nnS
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Key assumptions for Kendall’s tau (or Mann-Kendall test)
• Common distribution of Xt (most importantly homoscedastic)
• Independence (no temporal correlation)
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Large sample approximation• The large sample approximation Zs is given by:
• And, Zs = 0, if S = 0, and where:
• The null hypothesis is rejected at significance level if Zs > Zcrit where Zcrit is the critical value of the standard normal distribution with probability of exceedance of /2 (i.e., S is approximately normally distributed with mean 0).
0if1 S
SZ
ss
0if1 S
SZ
ss
)52)(1)(18/( nnns
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Kendall slope estimator
Med {(Xj-Xi)/(tj-ti)} for all j>I
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Seasonality effects
Usually result in violation of key assumption, as
distributions of most hydrologic (and climatic)
variables change with season
One approach is to “homogenize” time series e.g.
by seasonal transformation (can be left with issues
as to seasonally varying correlation)
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where ti is number of ties in season i
From Hirsch et al (1982)
Seasonal Kendall Test (per Hirsch et al, 1982)
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Absent missing data (note that g is season index, p is number of seasons):
Where rgh is Spearman’s rho (rank correlation) between seasons g and h
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From Hirsch et al (1982)
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2.2 Examples
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Minimum flowIncreaseNo changeDecrease
Mann Kendall analysis -- annual minimum flow from 1941-70 to 1971-99
Visual courtesy Bob Hirsch, figure from McCabe & Wolock, GRL, 2002
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About 50% of the 400 sites show an increase in annual median flow from 1941-71 to 1971-99
Median flowIncreaseNo changeDecrease
Visual courtesy Bob Hirsch, figure from McCabe & Wolock, GRL, 2002
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About 10% of the 400 sites show an increase in annual maximum flow from 1941-71 to 1971-99
Maximum flowIncreaseNo changeDecrease
Visual courtesy Bob Hirsch, figure from McCabe & Wolock, GRL, 2002
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USGS streamgage annual flood peak records used in study (all >=100 years)
Visual courtesy Bob Hirsch
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Number of statistically significant increasing and decreasing trends in U.S. streamflow (of 395 stations) by quantile (from Lins and Slack, 1999)
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Annual hydroclimatic trends over the continental U.S., 1948-88
from Lettenmaier et al, 1994
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Monthly streamflow trends over the continental U.S., 1948-88
from Lettenmaier et al, 1994
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Estimated spatial correlation functions (anisotropic)
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Field significance levels (from Lettenmaier et al, 1994)
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Model Runoff Annual Trends
• 1925-2003 period selected to account for model initialization effects
• Positive trends dominate (~28% of model domain vs ~1% negative trends)
Positive +
Negative
Drought trends in the continental U.S. – from Andreadis and Lettenmaier (GRL, 2006)
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HCN Streamflow Trends• Trend direction and significance in streamflow data from HCN
have general agreement with model-based trends
Subset of stations was used (period 1925-2003)
Positive (Negative) trend at 109 (19) stations
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Soil Moisture Annual Trends
• Positive trends for ~45% of CONUS (1482 grid cells)
• Negative trends for ~3% of model domain (99 grid cells)
Positive +
Negative
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2.3 Pitfalls in trend analysis
1) Spurious trends (e.g., changes in instruments; site-specific effects). Solution: understand the data and adjust as necessary; evaluate spatial consistency of trends (site specific effects should not have a spatial signature)
2) Multiple comparison problem (“fishing expeditions”). Solution: test field significance; pre-specify the tests, time periods, etc to be tested.
3) Strong conclusions from short record lengths (e.g. satellite data)
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References
Fowler, H.J., and C.G. Kilsby, 2003. A regional frequency analysis of United Kingdom extreme rainfall from 1961 to 2000, International Journal of Climatology 23, 1313-1334.
Hirsch, R.M., J.R. Slack, and R.A. Smith, 1982. Techniques of trend analysis for monthly water quality data, Water Resources Research 18, 107-121.
Hirsch, R.M., and J.R. Slack, 1984. A nonparametric trend test for seasonal data with serial dependence, Water Resources Research 20, 727-732.
Lettenmaier, D.P., E.F. Wood, and J.R. Wallis, 1994. Hydro-climatological trends in the continental U.S., 1948-88, Journal of Climate 7, 586-607.
Livezey, R.E., and W.E. Chen, 1983. Statistical field significance and its determination by Monte Carlo techniques, Monthly Weather Review 111, 46-59.
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3. Analysis and trends in hydrological extremes
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Probability weighted moments and L-moments
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Clearwater River flood frequency distribution (from Linsley et al 1975)
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Fitted flood frequency distribution, Potomac River at Pt of Rocks, MD
Visual courtesy Tim Cohn, USGS
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Problems with traditional fitting methods –mixed distributions
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Pecos River flood frequency distribution (from Kochel et al, 1988)
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Inferred elasticity (“sensitivity”) of extreme floods with respect to MAP as a function of return period (from regional flood frequency equations)
QT = K Ab1 * Pb2
dQ/Q)/dP/P = dln[Qp]/dln[P] = b2
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JANUARY FLOODS
JANUARY 12, 2009
When disaster becomes routineCrisis repeats as nature’s buffers disappear
Disaster Declarations
Federal Emergency Management Agency disaster declarations in King County in
connection with flooding:
January 1990
November 1990
December 1990
November 1995
February 1996
December 1996
March 1997
November 2003
December 2006
December 2007Mapes 2009
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Urban Stormwater InfrastructureUrban Stormwater Infrastructure
Urbonas and Roesner 1993
Minor Infrastructure
Roadside swales, gutters, and sewers typically designed to convey runoff events of 2- or 5-year return periods.
Major Infrastructure
Larger flood control structures designed to manage 50- or 100-year events.
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ObjectivesObjectives
1. What are the historical trends in precipitation extremes across Washington State?
2. What are the projected trends in precipitation extremes over the next 50 years in the state’s urban areas?
3. What are the likely consequences of future changes in precipitation extremes on urban stormwater infrastructure?
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Literature ReviewLiterature Review
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Literature ReviewLiterature Review
Karl and Knight 1998
• 10% increase in total precip (nationally) since 1910
• Mostly due to trends in highest 10% of daily events
Kunkel et al. 1999, 2003
• 16% increase in frequency of 7-day extremes (nationally) from 1931-96
• Some frequencies nearly as high at beginning of 20th century as at end of 20th century
• No significant trend found for Pacific Northwest
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Literature ReviewLiterature Review
Madsen and Figdor 2007
• Statistically significant increase of 30% in frequency of extreme precipitation in Washington from 1948-2006
• Statistically significant increase of 45% in Seattle
• Statistically significant decrease of 14% in Oregon
• Non-significant increase of 1% in Idaho
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Literature ReviewLiterature Review
Two main drawbacks with prior research:
• Not focused on sub-daily extremes most critical to urban stormwater infrastructure
• Not focused on changes in event intensity most critical to urban stormwater infrastructure
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Literature ReviewLiterature Review
Fowler and Kilsby 2003
• Used “regional frequency analysis” to determine changes in design storm magnitudes from 1960
to 2000 in the United Kingdom
• Employed framework that we adapted for our study
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Historical Precipitation Historical Precipitation AnalysisAnalysis
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Study LocationsStudy Locations
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Visual InspectionVisual Inspection
• Divided precipitation records into two 25-year time periods (1956-1980 and 1981-2005).
• Compared annual maxima between two periods at storm durations ranging from 1 hour to 10 days.
• Time series of 1-hour and 24-hour annual maxima on following six slides for SeaTac, Spokane, and
Portland Airports (shown in color, with other stations in each region shown in gray).
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1-Hour Annual Maxima at SeaTac1-Hour Annual Maxima at SeaTac
Avg at airport = 0.34” Avg at airport = 0.36”
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1-Hour Annual Maxima at Spokane1-Hour Annual Maxima at Spokane
Avg at airport = 0.36” Avg at airport = 0.36”
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1-Hour Annual Maxima at Portland1-Hour Annual Maxima at Portland
Avg at airport = 0.39” Avg at airport = 0.40”
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24-Hour Annual Maxima at SeaTac24-Hour Annual Maxima at SeaTac
Avg at airport = 2.00”
Avg at airport = 2.48”
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24-Hour Annual Maxima at Spokane24-Hour Annual Maxima at Spokane
Avg at airport = 1.04” Avg at airport = 1.12”
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24-Hour Annual Maxima at Portland24-Hour Annual Maxima at Portland
Avg at airport = 1.95” Avg at airport = 1.97”
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Regional Frequency AnalysisRegional Frequency Analysis
Principle:
• Annual precipitation maxima from all sites in a region can be described by common probability distribution after site data are divided by their at-site means.
• Larger pool of data results in more robust estimates of design storm magnitudes, particularly for longer return periods.
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Regional Frequency AnalysisRegional Frequency Analysis
Methods:
• Annual maxima divided by at-site means.
• Regional growth curves fit to standardized data using method of L-moments.
• Site-specific GEV distributions obtained by multiplying growth curves by at-site means.
• Design storm changes calculated for various return periods.
• Sample procedure shown on following slides.
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1. Annual maxima calculated for each station in region.1. Annual maxima calculated for each station in region.
Average = 2.00”Average = 2.48”
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2. Each station’s time series divided by at site mean.2. Each station’s time series divided by at site mean.
Average = 1 Average = 1
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3.3. Standardized annual maxima pooled and plotted using Standardized annual maxima pooled and plotted using Weibull plotting position.Weibull plotting position.
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4.4. Regional growth curves fitted using method of L-moments. Regional growth curves fitted using method of L-moments.
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5.5. Site-specific GEV distributions obtained by multiplying Site-specific GEV distributions obtained by multiplying regional growth curves by at-site means. regional growth curves by at-site means.
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6.6. Probability distributions checked against original at-site Probability distributions checked against original at-site annual maximaannual maxima
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7.7. Changes in design storms calculated for various return Changes in design storms calculated for various return periods.periods.
+37%
+30%
Change in Average Annual Maximum = +25%
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Statistical SignificanceStatistical Significance
• General indication of how likely a sample statistic is to have occurred by chance.
• We tested for:
→ differences in means (Wilcoxon rank-sum)
→ differences in distributions (Kolmogorov-Smirnov)
→ non-zero temporal trends (Mann-Kendall)• Tests performed at a 5% significance level.
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Results of Historical AnalysisResults of Historical Analysis
Changes in average annual maxima between 1956–1980 and 1981–2005:
SeaTac Spokane Portland
1-hour +7% -1% +4%
3-hour +14% +1% -7%
6-hour +13% +1% -8%
24-hour +25% +7% +2%
5-day +13% -10% -5%
10-day +7% -4% -10%
*
* Statistically significant for difference in means
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Decadal changes in regional growth curves, UK 1961-2000
from Fowler and Kilsby, 2003
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Future PrecipitationFuture PrecipitationProjectionsProjections
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Global Climate ModelsGlobal Climate Models
ECHAM5
• Developed at Max Planck Institute for Meteorology (Hamburg, Germany)
• Used to simulate the A1B scenario in our study
CCSM3
• Developed at National Center for AtmosphericResearch (NCAR; Boulder, Colorado)
• Used to simulate the A2 scenario in our study
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Global Climate ModelsGlobal Climate Models
Mote et al 2005
ECHAM5
CCSM3
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Dynamical DownscalingDynamical Downscaling
Courtesy Eric Salathé
Global ModelGlobal Model Regional ModelRegional Model
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Results of Future AnalysisResults of Future Analysis
SeaTac Spokane Portland
1-hour +16% +10% +11%
24-hour +19% +4% +5%
1-hour -5% -7% +2%
24-hour +15% +22% +2%
* Statistically significant for difference in means and distributions, and non-zero temporal trends
EC
HA
M5
CC
SM
3
* *
* *
Changes in average annual maximum precipitation
between 1970–2000 and 2020–2050:
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Future Runoff Future Runoff SimulationsSimulations
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Overview: Bias CorrectionBias Correction and Statistical DownscalingBias Correction and Statistical Downscaling
• Performed at the grid point from each simulation that was closest to SeaTac
• Bias corrected data used to drive hydrologic model
Area (ac)
Imp Area
Thornton 7140 29%
Juanita 4352 34%
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Overview: Bias CorrectionBias Correction and Statistical Downscaling Bias Correction and Statistical Downscaling of hourly precipitationof hourly precipitation
• Raw RCM output differs from observed record in both frequency of events and amounts of precipitation.
• For example, from 1970 to 2000 for SeaTac Airport:
- CCSM3/A2 simulation resulted in 11,734 hours of nonzero precipitation for a total of 225 inches during the month of January,
- Observations recorded 4144 hours of nonzero precipitation for a total of 162 inches during the months of January.
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Overview: Bias CorrectionBias Correction and Statistical DownscalingBias Correction and Statistical Downscaling
• Despite biases in modeled data, projections may still prove useful if interpreted relative to the modeled
climatology rather than the observed climatology.
• Performed separately for each calendar month.
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Overview: Bias CorrectionBias Correction and Statistical DownscalingBias Correction and Statistical Downscaling
• Procedure based on probability mapping as described by Wilkes (2006) and Wood et al. (2002):
1. Simulated 1970–2000 data truncated so that each month had the same number of nonzero hourly values as the corresponding observed record.
2. Simulated 2020–2050 data truncated with same thresholds.
3. Monthly totals recalculated, and Weibull plotting position used to map those totals from the modeled empirical cumulative distribution function (eCDF) to those from the observed eCDF.
4. Modeled hourly values rescaled to add up to new monthly totals.
5. New hourly values mapped from their eCDF to the hourly values from the observed eCDF, and once again rescaled to add up to the monthly totals derived in the first mapping step.
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Overview: Bias CorrectionBias Correction and Statistical DownscalingBias Correction and Statistical Downscaling
• Raw RCM output differs from observed record in both frequency of events and amounts of precipitation.
• Despite these biases, projections may still prove useful if interpreted relative to the simulated climatology rather than the observed climatology.
![Page 87: Hydrologic trend analysis Dennis P. Lettenmaier Department of Civil and Environmental Engineering University of Washington GKSS School on Statistical Analysis.](https://reader030.fdocuments.net/reader030/viewer/2022033105/56649d425503460f94a1ce67/html5/thumbnails/87.jpg)
Overview: Bias CorrectionBias Correction and Statistical DownscalingBias Correction and Statistical Downscaling
• Procedure based on probability mapping as described by Wilks (2006) and Wood et al. (2002)
• Performed at the grid point from each simulation that is closest to SeaTac
• Bias corrected data used to drive hydrologic model in Thornton and Juanita Creek watersheds.
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• 7590 (11,734 - 4144) hours w/ smallest amounts of nonzero precip eliminated from 1970–2000 simulated record, coinciding w/ a truncation threshold of 0.012”.
• Any hour during the 2020–2050 simulated record w/ a nonzero precip of less than 0.012” also eliminated (6824 out of 10,322, for a remainder of 3498 hours).
Overview: Bias CorrectionStep 1: Truncate simulated data so that each month has the same Step 1: Truncate simulated data so that each month has the same number of nonzero hourly values from 1970 to 2000 as the observed data. number of nonzero hourly values from 1970 to 2000 as the observed data.
Observed
1970-2000
4144
11,734
Hours of Nonzero Precipitation in January
10,322
CCSM3
1970-2000
CCSM3
2020-2050
Observed
1970-2000
4144
CCSM3
1970-2000
CCSM3
2020-2050
41443498
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• Corresponding precipitation total reduced from 5724 mm to 5272 mm from 1970 to 2000, and from 4960 mm to 4573 mm from 2020 to 2050.
Overview: Bias CorrectionStep 1: ContinuedStep 1: Continued
Observed
1970-2000
4118 mm
5724 mm
Total Precipitation in January
4960 mm
CCSM3
1970-2000
CCSM3
2020-2050
Observed
1970-2000
5272 mm4573 mm
CCSM3
1970-2000
CCSM3
2020-2050
4118 mm
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Step 2: Recalculate simulated monthly totals, and map those totals from Step 2: Recalculate simulated monthly totals, and map those totals from the simulated eCDF of 1970-2000 to the observed eCDF of 1970-2000.the simulated eCDF of 1970-2000 to the observed eCDF of 1970-2000.
• Simulated monthly totals replaced with values having the same nonexceedance probabilities, with respect to the observed climatology, that they have with respect to the simulated climatology. Simulated hourly values rescaled to add up to new monthly totals.
0.01 0.1 0.3 0.5 0.7 0.9 0.99 0
50
100
150
200
250
300
350
400
450
500
Nonexceedance Probability
Tot
al M
onth
ly P
reci
pita
tion
(mm
)
Monthly Empirical CDF for January
obs (1970-2000)
simraw (1970-2000)simraw (2020-2050)
0.01 0.1 0.3 0.5 0.7 0.9 0.99 0
50
100
150
200
250
300
350
400
450
500
Nonexceedance Probability
Tot
al M
onth
ly P
reci
pita
tion
(mm
)
Monthly Empirical CDF for January
obs (1970-2000)
simcor (1970-2000)simcor (2020-2050)
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Step 3: Map new hourly values from simulated eCDF of 1970-2000 to Step 3: Map new hourly values from simulated eCDF of 1970-2000 to the observed eCDF of 1970-2000.the observed eCDF of 1970-2000.
• Simulated hourly values replaced with values having the same nonexceedence probabilities, with respect to the observed climatology, that they have with respect to the simulated climatology. Hourly values again rescaled to add up to monthly totals derived in the first mapping step.
0.001 0.01 0.1 0.3 0.5 0.7 0.9 0.99 0.99910
-1
100
101
102
Nonexceedance Probability
Hou
rly P
reci
pita
tion
(mm
)
Hourly Empirical CDF for January
obs (1970-2000)
simcor (1970-2000)simcor (2020-2050)
0.001 0.01 0.1 0.3 0.5 0.7 0.9 0.99 0.99910
-1
100
101
102
Nonexceedance Probability
Hou
rly P
reci
pita
tion
(mm
)
Hourly Empirical CDF for January
obs (1970-2000)
simraw (1970-2000)simraw (2020-2050)
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Step 4: Recalculate annual maxima at durations ranging from 1-hr to Step 4: Recalculate annual maxima at durations ranging from 1-hr to 10-days10-days
• New simulated annual maxima roughly match observed annual maxima from 1970 to 2000
1.01 1.1 1.5 2 5 10 20 30 40 50 100 20
30
40
50
60
70
80
90
100
110
Return Interval (years)
Pre
cip
ita
tio
n (
mm
)
Generalized Extreme Value Distributions of 12-Hour Annual Maxima
obs fit (1970-2000)simraw fit (1970-2000)simraw fit (2020-2050)
0.01 0.1 0.3 0.5 0.7 0.9 0.99
Nonexceedance Probability
1.01 1.1 1.5 2 5 10 20 30 40 50 100 20
30
40
50
60
70
80
90
100
110
Return Interval (years)
Pre
cip
ita
tio
n (
mm
)
Generalized Extreme Value Distributions of 12-Hour Annual Maxima
obs fit (1970-2000)simcor fit (1970-2000)simcor fit (2020-2050)
0.01 0.1 0.3 0.5 0.7 0.9 0.99
Nonexceedance Probability
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Results of Bias CorrectionResults of Bias Correction
Raw Bias Corrected Bias
1-hour -19% -7%
24-hour +11% -2%
1-hour -33% -13%
24-hour -22% +3%
EC
HA
M5
CC
SM
3
Improvements to bias of average annual maximum:
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Results of Bias CorrectionResults of Bias Correction
Raw Change Corrected Change
1-hour +16% +14%
24-hour +19% +28%
1-hour -5% -6%
24-hour +15% +14%
EC
HA
M5
CC
SM
3
Comparison of changes in average annual maximum between 1970–2000 and 2020–2050:
*
* Statistically significant for difference in means and distributions, and non-zero temporal trends
*
* *
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Results of Bias-Correction (CCSM3/A2Results of Bias-Correction (CCSM3/A2))
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Results of Bias-Correction (ECHAM5/A1BResults of Bias-Correction (ECHAM5/A1B))
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Hydrologic ModelHydrologic Model
• Used HSPF (Hydrologic Simulation Program – Fortran), a continuous rainfall-runoff model that has been regionally validated and endorsed by EPA, USGS, FEMA, and WA-DOE for several decades.
• Primary inputs are hourly precipitation, daily potential evapotranspiration.
• Typically accurate given calibration with good contemporaneous precipitation and flow data.
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Thornton CreekThornton Creek
Bypass PipeBypass Pipe
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Thornton CreekThornton Creek
Historical to Future Change in Peak Flow
-10%
0%
10%
20%
30%
40%
50%
60%
Av
g. C
ha
ng
e 2
-yr
to 5
0-y
r
CCSM3-WRF
ECHAM5-WRF
Kramer Ck135 ac
South Branch 2294 ac
North Branch4143 ac
Thornton Ck7140 ac
Changes in Average Streamflow Annual Maxima (1970-2000 to 2020-2050)
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Results of Hydrologic ModelingResults of Hydrologic Modeling
Changes in average streamflow annual maxima at outlet of watershed between 1970-2000 and 2020-2050:
Juanita Creek Thornton Creek
CCSM3 +25% +55%
ECHAM5 +11% +28%
* Statistically significant for difference in means
**
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The November SurpriseThe November Surprise
JAN FEB MAR APR
MAY JUN JUL AUG
SEP OCT NOV DEC
Courtesy Eric Salathé
NOV
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INCREASE?
25-yr 24-hr Design Storms at SeaTac25-yr 24-hr Design Storms at SeaTac
VARIABILITY?ECHAM5?
CCSM3?
![Page 103: Hydrologic trend analysis Dennis P. Lettenmaier Department of Civil and Environmental Engineering University of Washington GKSS School on Statistical Analysis.](https://reader030.fdocuments.net/reader030/viewer/2022033105/56649d425503460f94a1ce67/html5/thumbnails/103.jpg)
Concluding thoughts on hydrologic extremes
• Much of the work in the climate literature on “extremes” doesn’t really deal with events that are extreme enough to be relevant to risk analysis (typically estimated from the annual maximum series)
• Regional frequency analysis methods help to filter the natural variability in station data
• Decadal scale differences in flood risk are detectable in the historical record, to what extent are these manifestations of decadal (vs long-term) climate variability?
• RCMs help to make extremes information more regionally specific, but nonetheless contain information that may be “smoother” than observations
• Extent to which RCM-derived changes in projections of extremes are controlled by GCM-level extremes is unclear
• Use of ensemble approaches is badly needed, however RCM computational requirements presently precludes this