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Tree-ring reconstructions of streamflow and climate and their application to water management Jeff Lukas Western Water Assessment, University of Colorado.

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Part 4: Generating the streamflow or climate reconstruction Reconstruction: estimate of past hydrology or climate, based on the relationship between tree-ring data and an observed record Annotated Core Presentation Parts 4-6

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Overview of reconstruction methodology Adapted from graphic by David Meko Tree Rings (predictors) Statistical Calibration Reconstruction Model Streamflow/climate reconstruction Observed Flow/Climate (predictand) Model validation

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Moisture sensitive species Location – From a region that is climatically linked to the gage of interest –Because weather systems cross watershed divides, chronologies do not have to be in same basin as gage Length –Last year close to present for the longest calibration period possible –First year as early as possible (>300 years) but in common with a number of chronologies Significant correlation with observed record Requirements: Tree-ring chronologies

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Length – minimum 40 years in common with tree-ring data for robust calibration Natural/undepleted record – flows must be corrected for depletions, diversions, evaporation, etc. Homogeneous (climate record) – inspected for station moves, changes in instrumentation Fraser River at Winter Park Undepleted Flow (from Denver Water) USGS Gaged Flow The reconstruction quality relies on the quality of the observed record. Requirements: Observed streamflow/climate record

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Tree-ring data are calibrated with an observed streamflow record to generate a statistical model –Individual chronologies are used as predictors (dependent variables) in a statistical model, or –A set of chronologies is reduced through averaging or Principal Components Analysis (PCA), and the average or principal components (representing modes of variability) are used as predictors in a statistical model –Most common statistical method: Linear Regression –Other approaches: neural networks Alternative: Non-Parametric method uses the relationships within the tree-ring data set to resample years from the observed record Reconstruction modeling strategies Tree Rings (predictors) Statistical Calibration Observed Flow/Climate (predictand)

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Are regression assumptions satisfied? How does the model validate on data not used to calibrate the model? How does the reconstruction compare to the gage record? Model validation and skill assessment

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How does the model validate on data not used to calibrate the model? CalibrationValidation Split-sample with independent calibration and validation periods Cross-validation: leave-one- out method, iterative process Calibration/validation

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Two statistics for model assessment Gage R2R2 RE Boulder Creek at Orodell Rio Grande at Del Norte Colorado R at Lees Ferry Gila R. near Solomon Sacramento R CalibrationValidation What are desirable values? Of course, higher R 2 s are best, and positive value of RE indicates some skill (the closer to R 2 the better) Calibration: Explained variance: R 2 Validation: Reduction of Error (RE): model skill compared to no knowledge (e.g., the calibration period mean)

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How does the reconstruction compare to the gage record? The means are the same, as expected from the the linear regression Also as expected, the standard deviation (variance) in the reconstruction is lower than in the gage record Observed vs. reconstructed flows - Lees Ferry

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Subjective assessment of model quality Are severe drought years replicated well, or at least correctly classified as drought years? Wet years?

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Subjective assessment of model quality Are the lengths and total deficits of multi-year droughts replicated reasonably well?

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From model to full reconstruction When the regression model has been fully evaluated, the model is applied to the full period of tree-ring data to generate the reconstruction Tree Rings (predictors) Statistical Calibration Reconstruction Model Observed Streamflow (predictand) Model validation

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Part 5: Uncertainty in the reconstructions

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Sources of uncertainty in reconstructions Observed streamflow and climate records contain errors Trees are imperfect recorders of climate and streamflow, and the reconstruction model will never explain all of the variance in the observed record (model error) A number of decisions are made in the modeling process, all of which can have an effect on the final reconstruction (model sensitivity)

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Using the model error to generate confidence intervals for the reconstruction Colorado R. at Lees Ferry Gray band = 95% confidence interval around reconstruction (derived from mean squared error, RMSE) Indicates 95% probability that the observed flow falls within the gray band

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Lees Ferry Reconstruction, Year Running Mean Assessing the drought in a multi-century context Data analysis: Dave Meko Application of model error: using RMSE-derived confidence interval in drought analysis

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An alternative approach to generate confidence intervals on the reconstruction Noise-added reconstruction approach A large number of plausible realizations of true flow from derived from the reconstructed values and their uncertainty allow for probabilistic analysis. Meko et al. (2001) One of 1000 plausible ensemble of true flows, which together, can be analyzed probabilistically for streamflow statistics

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Sensitivity of the reconstruction to choices made in the reconstruction modeling process the calibration record used the span of years used for the calibration the selection of tree-ring data the treatment of tree-ring data the statistical modeling approach used There is usually no clear best model

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Sensitivity to calibration period Calibration data ––– Standard Model ––– Ensemble Mean ––– Ensemble Members ––– Each of the 60 traces is a model based on a different calibration period All members have similar sets of predictors South Platte at South Platte, CO Annual Flow (MAF)

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Sensitivity to available predictors How sensitive is the reconstruction to the specific predictor chronologies in the pool and in the model? Best stepwise model R 2 = 0.82 Alternate stepwise model - predictors from best model excluded from pool R 2 = 0.79 Animas River at Durango, CO – two independent models

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Sensitivity to available predictors The two models correlate at r = 0.89 over their overlap period, Completely independent sets of tree-ring data resulted in very similar reconstructions Animas River at Durango, CO - two independent reconstructions 0 200, , , ,000 1,000,000 1,200, Alternate Best-fit

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Analysis from David Meko Sensitivity to other choices made in modeling process Lees Ferry reconstructions from 9 different models that vary according to chronology persistence, pool of predictors, modeling strategy Lees Ferry Reconstructions, 20-yr moving averages

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Lees Ferry reconstructions, generated between 1976 and 2007 Differences due to combinations of all of the factors mentioned 20-year running means calibration Stockton-Jacoby (1976), Michaelson (1990), Hidalgo (2001), Woodhouse (2006), Meko (2007)

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Colorado at Lees Ferry, Reconstructed and Gaged Flows Extremes of reconstructed flow beyond the gaged record often reflect tree- ring data outside the calibration space of the model Uncertainty related to extreme values

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Uncertainty summary We can measure the statistical uncertainty due to the errors in the reconstruction model, but this does not fully reflect uncertainty resulting from sensitivity to model choices There are other ways to estimate reconstruction uncertainty or confidence intervals (i.e. Meko et al. noise added approach) For a given gage, there may be no one reconstruction that is the right one or the final answer Some reconstructions may be more reliable than others (model validation assessment, length of longer calibration period, better match of statistical characteristics of the gage record) A reconstruction is a plausible estimate of past streamflow

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Part 6: What reconstructions can tell us about droughts of the past

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Colorado River: The 20 th century contains only a sample of the interannual variability of the last 500 years

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Rio Grande: The extreme low flows of the past 100 years (like 2002) were exceeded prior to 1900 Gage record in blue, reconstruction in green 5 reconstructed annual flows before 1900 were likely to have been lower than 2002 gaged flow (1685, 1729, 1748, 1773, 1861) 2002

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Rio Grande: Multi-year droughts were clustered in time, with fewer droughts in the 20 th century Reconstructed Rio Grande Streamflow, Periods of below-average flow, of 2 years or more (length of bar shows acre-feet below average)

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Rio Grande: The longest observed droughts are exceeded in length by pre-1900 droughts LONGEST OBSERVED (5) (11) (6) (7) (6) (6) (7 years) Reconstructed Rio Grande Streamflow, Periods of below-average flow, of 2 years or more (length of bar shows acre-feet below average)

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Colorado River: At decadal time scales, the 20 th century is notable for wet periods, but not dry periods

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626, , , , , , , , , , , s1600s1700s1800s1900s Annual flow, acre-feet Rio Grande: On century time scales, the 20 th century was overall wetter than the previous four centuries Mean annual flow, by century Reconstructed Rio Grande Streamflow,

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25-yr running means of reconstructed and observed annual flow of the Colorado River at Lees Ferry, expressed as percentage of the observed mean (Meko et al. 2007). Reconstructed flow of Colorado River at Lees Ferry, Medieval period Colorado River: The Medieval Period (~ ) had multi-decade dry periods with no analog since

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