1. Generating the streamflow or climate reconstruction
Annotated Core Presentation Parts 4-6
Part 4:
Generating the streamflow or climate reconstruction
In Part 4, we describe the statistical methods used to generate tree-ring reconstructions and to validate the results.
Reconstruction: estimate of past hydrology or climate, based on the relationship between tree-ring data and an observed record

2. Overview of reconstruction methodology
Tree Rings
(predictors)
Observed Flow/Climate
(predictand)
Statistical Calibration
Reconstruction Model
Model validation
A reconstruction is an estimate of past hydrology or climate, based on the relationship between tree-ring data and an observed record.
This schematic chart shows the generalized methodology for nearly all published climate and streamflow reconstructions. All of these steps will be discussed in greater detail in the following slides. First, a selected observed hydrology or climate record is statistically calibrated against a set of tree-ring data which overlaps it in time, typically using a linear regression procedure. This creates an equation or reconstruction model that describes the relationship between the two datasets.
This model is then subjected to validation tests, and the model will be re-calibrated if the tests are failed (or to evaluate multiple models). Once the model is validated, then the full length of the tree-ring data (i.e., before the start of the overlap or calibration period) is input into the model to generate the full-length ( year) reconstruction.
Streamflow/climate reconstruction
Adapted from graphic by David Meko

3. Requirements: Tree-ring chronologies
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
To increase the likelihood of producing a robust and useful reconstruction, the tree-ring chronologies that are used in the modeling process need to be screened according to several of criteria. The first is obvious: they should come from species known to be moisture-sensitive.
The second, location, is more flexible than one might think. Because of regional coherence in climate variability, trees do not need to be in the same basin as the gage of interest in order to capture a relevant signal. For example, reconstructions of streamflow for the Colorado Front Range (east of the Continental Divide) are improved when chronologies from west of the Continental Divide are included in the modeling. This is because most of the runoff in Front Range streams comes from precipitation carried by westerly storms which also influence tree growth west of the Divide.
Chronology length is a critical consideration on both “ends”, because with the typical methods, the reconstruction length is limited by the shortest chronology contributing to the reconstruction. Using only the most recent tree-ring data will maximize the calibration period and increase the robustness of the model, but one must usually compromise since the number of available chronologies decreases as the last year approaches the current year. Likewise, using the longest chronologies back in time will lead to a longer reconstruction (which is usually inherently more useful), but the number of chronologies available inevitably drops off as one goes further back in time. There are alternative reconstruction approaches, such as time-varying subsets and non-parametric techniques, which alleviate the compromise between length and availability and can make use of all available tree-ring data in each time period.
Finally, it is necessary to screen the chronologies for significant (p<0.05) relationships with the observed hydrology, especially in regions like the upper Colorado River basin where chronologies are numerous. This prevents the inclusion of spurious predictors in the model.

4. Requirements: Observed streamflow/climate record
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
Any observed streamflow or climate record selected as a target for reconstruction must meet two key criteria. The first is length: the record must be long enough that the overlap or calibration period with the tree-ring data is at least 40 years (this will depend on the tree-ring data as well). The longer the calibration period, the greater the range of variability that the model will be “trained” on, leading to more reliable estimates of past variability. With less than 40 years of overlap, it is likely that this training will be inadequate (think about the sub-periods of the Lees Ferry observed record).
Just as critically, an observed hydrology used in modeling must represent the natural or undepleted streamflow, since the trees don’t “know” about diversions, reservoir evaporation, etc. While in some basins these effects are small enough that the USGS gaged record can be used as-is, in most basins, a concerted effort must be made to compute and back out human influences on the hydrology. Many water management agencies have developed natural/undepeleted flow records for their gages of interest, but others have not.
The analogous criterion for instrumental climate records is that those records not have abrupt changes, or inhomogeneities, related to station moves, changes in instrumentation, or changes in observing standards.
The graph shows a typical difference between gaged flow and undepleted flow, here on the Fraser River in Colorado which starting around 1936 was subjected to transbasin diversion. Clearly, the gaged record is an inappropriate target for reconstruction, since it contains abrupt changes unrelated to climate.
The final message here is that a reconstruction can only be as good as the observed record on which it is based, and even a carefully calculated undepleted flow record is less reliable than the underlying gage record—which itself has uncertainties.
The reconstruction quality relies on the quality of the observed record.

5. Reconstruction modeling strategies
Tree Rings
(predictors)
Statistical Calibration
Observed Flow/Climate
(predictand)
Reconstruction modeling strategies
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
Many specific reconstruction modeling strategies have been used over time, but they all follow the basic scheme of tree-ring data being used as predictors and calibrated with an observed record (predictand) to generate a statistical model. The tree-ring chronologies can be used directly as predictors, or averaging or Principal Components Analysis can be used to reduce the chronologies into a smaller set of predictors. Some type of linear regression is usually employed to generate the statistical model, with stepwise multiple linear regression or Principle Component regression being the most common types.
Regardless of the method used in modeling, the goal is to identify the subset of tree-ring data that best explains the variability in the observed record, under the assumption that the subset of tree-ring data so identified will also provide the best estimates of hydrology prior to the observed period.
Recently, an alternative to this basic regression-modeling scheme has been proposed: a non-parametric method that examines the relationships within the tree-ring data set to identify similar tree-ring patterns among years in the “observed” and “paleo” periods, and then use that information to resample the flows in the observed hydrology to populate the reconstructed hydrology (Gangopadhyay et al 2009). In principle, this method is more directly data-driven since it doesn’t rely on a single model to estimate all past streamflows. The results of the non-parametric method, for the Colorado River at Lees Ferry, were very similar to those for regression-based methods, giving confidence that both methods effectively translate the underlying tree-ring data. This methodology has yet to be tested in other basins.
Reference:
Gangopadhyay, S., B. L. Harding, B. Rajagopalan, J. J. Lukas, and T. J. Fulp (2009), A nonparametric approach for paleohydrologic reconstruction of annual streamflow ensembles, Water Resour. Res., 45, W06417

6. Model validation and skill assessment
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?
Once we have used some method of linear regression to generate a model, then we must first make sure that the standard assumptions of regression modeling are satisfied. These mainly pertain to the residuals, or model errors.
The residuals must be normally distributed
The residuals must not be significantly autocorrelated
The residuals must not be correlated with individual predictors
The residuals must not have a significant trend over time
If these assumptions are violated, then the model may be unreliable, and should be re-calibrated.
If the model meets the assumptions, we then examine how the model validates: how well does it estimate data not used to calibrate the model. And also how well the model represents the important features of the observed record. Both of these are detailed in the following slides.

7. Calibration/validation
How does the model validate on data not used to calibrate the model?
Calibration
Validation
Split-sample with independent calibration and validation periods
There are two strategies for validating the model. The first is to withhold a portion (30-50%) of the observed record from the calibration and use it only for validation. The model calibrated on one portion of the data is then used to estimate the withheld observations, creating a set of validation data. The observed record must be at least years long for this strategy to be used. The advantage here is that the validation data is completely independent of the calibration dataset, with the tradeoff that the reconstruction is not trained on all of the available observed data.
An alternative method is the cross-validation or “leave-one-out” procedure. First, the reconstruction model is calibrated using the full available overlap period. Then using the tree-ring predictors obtained in that calibration, additional models are sequentially calibrated by leaving one observation out of the observed record, with each model used to estimate the withheld observation. For example, if the calibration period is , a model would be calibrated on and used to estimate 1916, then a second calibrated on 1916 and and used to estimate 1917, and so on, until estimates of every flow year from are generated, to use as the validation data set. The main advantage here is that the reconstruction is trained on all of the available data, but that exact model is not being tested on independent data. Instead, the predictors in that model are tested in their ability to estimate pseudo-independent data.
Note: Cross-validation can also be performed by leaving out periods of more than one year.
Cross-validation: “leave-one-out” method, iterative process
Calibration/validation

8. Two statistics for model assessment
Calibration: Explained variance: R2
Validation: Reduction of Error (RE): model skill compared to no knowledge (e.g., the calibration period mean)
Gage R2 RE
Boulder Creek at Orodell
0.65
0.60
Rio Grande at Del Norte
0.76
0.72
Colorado R at Lees Ferry
0.81
Gila R. near Solomon
0.59
0.56
Sacramento R.
0.73
Calibration
Validation
Of the two key statistics for reconstruction model assessment, R2 (R-squared), or the explained variance, is usually seen as indicating the quality of the model. However, R2 by itself can be misleading, since it only measures the goodness-of-fit during the calibration period. To be useful, a reconstruction must be good at estimating values outside of the calibration period, and R2 suggests this ability, but does not measure it. An “overfitted” reconstruction model can have a high R2, but do relatively poorly at estimating past streamflows.
So we also need to look at the validation equivalent of R2, which is called the Reduction of Error (RE) statistic. What RE measures is the how skillfully a model estimates flows during the validation period compared to a “no-knowledge” model, in which every value is the mean streamflow during the calibration period. If RE is greater than zero, than the model is said to have some skill. In practice, the RE value should be similar to the R2 value. If the explained variance is quite high, and the RE is not comparable, then it’s likely that the model is overfitted.
Generally, the higher the R2 and RE values, the better—but how high do they need to be? This will vary by region, and there is no firm cutoff for a “useful” reconstruction. In general, in the Southwest US and California, the trees have a very strong moisture signal, and R2 and RE values tend to be from 0.60 to 0.80, as in the examples in the table. In the Northern Rockies and the Pacific Northwest, the moisture signal is generally weaker, and so the statistics are somewhat lower, from 0.45 to 0.65.
What are desirable values?
Of course, higher R2s are best, and positive value of RE indicates some skill (the closer to R2 the better)

9. How does the reconstruction compare to the gage record?
Observed vs. reconstructed flows - Lees Ferry
In addition to examining the validation statistics, we also plot the reconstructed streamflows with the observed streamflows, and calculate some basic statistics capturing important characteristics of both records. Shown here is the reconstruction of the Colorado River at Lees Ferry, AZ, by Woodhouse et al. (2006), specifically the “Lees-A” model, plotted with the observed “natural flow” record for that gage. Note that the fit is very good over the combined calibration/validation period ( ), with an R2 of 0.81, and an RE (calculated from a cross-validation procedure) of
In the table in the lower left, we see that the observed and reconstructed mean flow from are exactly the same (15.22 MAF), since a linear regression will by design replicate the mean. Note that the standard deviation (“StDev”) is lower in the reconstruction (3.88 MAF vs MAF), which is another byproduct of linear regression: the variance in the observed record is “compressed”, with the degree of compression being inversely related to the explained variance. If the R2 were lower, the difference in the standard deviation would be greater. The practical effect of this compression of variance is that the high extreme flows tend to be underestimated in the reconstruction (as can be seen in the plot), and to a lesser extent, the low extreme flows tend to be overestimated. In other words, a reconstruction based on linear regression will tend to be conservatively estimate past extremes.
Reference:
Woodhouse, C.A., S.T. Gray, and D.M. Meko Updated streamflow reconstructions for the Upper Colorado River basin. Water Resources Research 42(5): W05415.
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

10. Subjective assessment of model quality
Beyond the calibration and validation statistics, anyone who plans to use a reconstruction for planning will want to know, “Does it get the droughts right?” In the Lees-A reconstruction of Lees Ferry, the lowest 11 observed annual flows (red arrows) are all reconstructed as being below-average, and in most cases the severity of the low flow is captured well.
The magnitude of wet years may not be estimated as well as the dry years. This is because trees will grow progressively wider rings with more moisture, to an extent. Then something other than moisture limits growth. Also, tree-ring widths do not reflect well precipitation that comes in intense events (e.g., summer thunderstorms) when much of the moisture runs off rather than soaking into the soil.
Are severe drought years replicated well, or at least correctly classified as drought years?
Wet years?

11. Subjective assessment of model quality
Another aspect of getting the droughts “right” is replicating the length and total deficit of multi-year droughts, which are critical metrics for water systems with multiyear storage. Here, the Lees-A model does represent fairly well the four droughts of 3+ years which occurred between 1906 and 1995.
Are the lengths and total deficits of multi-year droughts replicated reasonably well?

12. 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)
Observed Streamflow
(predictand)
Statistical Calibration
Reconstruction Model
Model validation
Once the reconstruction model has been fully evaluated, we can then enter the full-length tree-ring predictors into the model (the regression equation) to generate the full reconstruction. In the case of the “Lees-A” model, the shortest predictor chronology extends back to 1490, so the full reconstruction also goes back to 1490.

13. Uncertainty in the reconstructions
Part 5:
Uncertainty in the reconstructions
In Part 5, we explore the sources of uncertainty in the reconstructions, and how the uncertainty can be measured and represented (e.g., as confidence intervals around the reconstructed annual flows).

14. 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”)
The first source of uncertainty in reconstructions was alluded to in Part 4: any observed streamflow or climate record used to calibrate the reconstructions has its own uncertainty (especially if it has been “naturalized” using other records), and this uncertainty will propagate into the reconstruction.
The second source of uncertainty—model error—is well-understood and appreciated, and can be quantified. Because trees are imperfect recorders of streamflow and climate, the reconstruction model will never exactly fit the observed record, and so there will be model error. (Errors in the observed record can also contribute to mis-fitting and to model error.) We can use these differences between observed and reconstructed flows, or residuals, to estimate confidence intervals for the reconstruction, as will be shown a little later on.
The third source of uncertainty—model sensitivity—is not as well-appreciated as the first two. In developing a reconstruction model, we make a number of decisions, and the final output can be different depending on what we choose. Model sensitivity can’t be quantified, although we can perform sensitivity analyses, as shown in the next several slides, to at least get a better sense of the magnitude of the sensitivity.

15. Colorado R. at Lees Ferry
Using the model error to generate confidence intervals for the reconstruction
Colorado R. at Lees Ferry
The most widely recognized source of uncertainty is model error. The root mean square error (RMSE) is equivalent to 1-sigma (1 standard deviation) uncertainty and can be used to generate confidence intervals that encompass varying proportions of the observed flows. Here we show in gray the 95% confidence intervals, generated by multiplying the RMSE by 2 (actually, 1.96) and “padding” that value on both sides of each year’s reconstructed flow (shown in gray). The 95% confidence interval indicates that 95% of the observed values should fall within the gray band.
In applying these confidence intervals to the full reconstruction, we assume that the errors in the calibration/validation period are representative of those in the full reconstruction.
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

16. Application of model error: using RMSE-derived confidence interval in drought analysis
Lees Ferry Reconstruction, Year Running Mean Assessing the drought in a multi-century context
Confidence intervals derived from the RMSE can be readily used in probabilistic drought analyses. Here we see the 80% confidence band around the reconstruction of Lees Ferry flow (gray), compared to the observed record (black). Both records have 5-year running means applied to them. The level of the lowest observed 5–year mean flow ( ; 65% of normal observed flow) is shown as a red line extended to the left.
Any period in which the gray band intersects the red line indicates at least a 10% probability that the reconstructed 5-year mean flow—considering the uncertainty expressed by model error—exceeded the lowest observed flow. The greater the overlap of the gray band, the higher the probability of exceedance. For the late 1840s drought ( ), there is greater than a 50% probability that the reconstructed flow was in fact lower than the observed worst-case.
Data analysis: Dave Meko

17. 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.
A somewhat different way to generate confidence intervals is to first consider the model errors as noise. Then one generates multiple time series of random noise of the same length as the reconstruction, based on the distribution of values from the model errors. Each random noise series is then added to the initial reconstruction to generate multiple noise-added reconstructions (in this case, 1000). The spread of these realizations represents the uncertainty. Each realization (such as the one shown here) is just as plausible as the initial reconstruction. With 1000 traces, probabilistic analyses are likely to be more robust than analyses based on a single set of model errors.
Reference:
Meko, D.M., M. D. Therrell, C. H. Baisan, and M. K. Hughes Sacramento River flow reconstructed to A.D. 869 from tree rings. Journal of the American Water Resources Association 37(4):
One of 1000 plausible ensemble of “true” flows, which together, can be analyzed probabilistically for streamflow statistics
Meko et al. (2001)

18. 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
Here are the major choices that one must make in model development that have some effect on the final reconstruction. Many of these choices are subjective and as a result, there is usually no “best” or optimal model. Instead, there are tradeoffs involved in each choice.
There is usually no clear “best” model

19. Sensitivity to calibration period
South Platte at South Platte, CO
Annual Flow (MAF)
The observed flow records used for calibration may range from 40 to over 100 years long, and may have inhomogeneities (like changes in how depletions are estimated) which might argue for the exclusion of some of the data. How sensitive is the reconstruction to differences in the calibration period?
Here, an ensemble reconstruction approach was used for the South Platte River, in which 60 models were separately fitted from the same pool of tree-ring chronologies, but with different calibration periods (e.g., half of the available observed data, two-thirds of the data, all data but 10 years, etc.). The spread of the green lines shows the sensitivity (and uncertainty) in the reconstruction resulting from this one choice. The ensemble mean (red line), is almost identical to the “standard model” based on the full observed record.
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

20. Sensitivity to available predictors
How sensitive is the reconstruction to the specific predictor chronologies in the pool and in the model?
Animas River at Durango, CO – two independent models
Even in a region like western Colorado where many tree-ring chronologies have been developed, the tree-ring data set is a small sample of all possible chronologies that could be collected from the entire population of old moisture-sensitive trees. Here we calibrated two models for the Animas River in Colorado on independent sets of tree-ring chronologies to test the sensitivity of the reconstruction to the specific set of chronologies that is available. Both models have excellent statistics. How similar are the reconstructions?
Best stepwise model
R2 = 0.82
Alternate stepwise model - predictors from best model excluded from pool
R2 = 0.79

21. Sensitivity to available predictors
Animas River at Durango, CO - two independent reconstructions
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1500
1550
1600
1650
1700
1750
1800
1850
1900
1950
2000
Alternate
Best-fit
The two models correlate at r = 0.89 over their overlap period,
Completely independent sets of tree-ring data resulted in very similar reconstructions
The plot of the full “best-fit” and “alternate” reconstructions for the Animas River show very high agreement between the two reconstructions, suggesting that at least in this region, the overall results are fairly robust to the specific set of chronologies available for modeling. Note, though, that there can be substantial differences in estimated flow in individual years.

22. 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
Here, David Meko performed a sensitivity analysis for the reconstruction of the Colorado River at Lees Ferry, AZ (Woodhouse et al. 2006), in which he varied three modeling choices:
Using chronologies in which the low-order persistence (autocorrelation) has been either (a) retained or (b) removed
Either (a) lagging the chronologies (+/- 1 year) to generate additional predictors, or (b) not lagging them
Using the chronologies (a) directly as predictors, or (b) reducing the chronologies using principal components analysis and using the PC’s as predictors
All possible combinations of these three choices resulted in 9 different models, whose results are shown in the graph. While the timing of wet and dry periods is consistent between the nine reconstructions, the magnitude of these flow anomalies can vary substantially, indicating the level of sensitivity to these modeling choices.
This sensitivity analysis was repeated using a shorter calibration period (~50 years vs. 90 years), emulating the Stockton and Jacoby (1976) reconstruction of Lees Ferry. This second analysis showed a much greater spread among the nine reconstructions, indicating that a longer calibration period is likely to result in a reconstruction that is less sensitive to modeling choices.
Reference:
Woodhouse, C.A., S.T. Gray, and D.M. Meko Updated streamflow reconstructions for the Upper Colorado River basin. Water Resources Research 42(5): W05415.
Analysis from David Meko

23. Lees Ferry reconstructions, generated between 1976 and 2007
Differences due to combinations of all of the factors mentioned
Over the past 30 years, different investigators have developed at least 7 different reconstructions for the Colorado at Lees Ferry. Here we show 5 of them, and the differences between them are caused by different choices in all of the areas previously mentioned:
- the calibration record used
- the span of years used for the calibration
- the selection of tree-ring data (and major expansion of the pool of available chronologies since ~2001)
- the treatment of tree-ring data
- the statistical modeling approach used
Note that while there are large differences in magnitudes among the reconstructions, there is very good agreement in the sign (positive, negative) and timing of large departures in flow from average conditions. In other words, the “system state” (wet or dry) captured by the tree rings is more robust to modeling choices than is the specific flow magnitudes.
References:
Hidalgo H.G., T.C. Piechota, and J.A. Dracup Alternative principal components regression procedures for dendrohydrologic reconstructions. Water Resources Research 36(11):
Meko, D.M., Woodhouse, C.A., Baisan, C.A., Knight, T., Lukas, J.J., Hughes, M.K., and Salzer, M.W Medieval Drought in the Upper Colorado River Basin. Geophysical Research Letters 34, L10705.
Michaelsen, J., H.A. Loaiciga, L. Haston, and S. Garver Estimating drought probabilities in California using tree rings. California Department of Water Resources Report B Santa Barbara, CA: University of California.
Stockton, C. W. and G. C. Jacoby Long-term surface-water supply and streamflow trends in the Upper Colorado River basin based on tree-ring analyses. Lake Powell Research Project Bulletin 18: 1-70.
Woodhouse, C. A. S. T. Gray, and D. M. Meko Updated streamflow reconstructions for the Upper Colorado River basin. Water Resources Research 42, W05415, doi: /2005WR
calibration
20-year running means
Stockton-Jacoby (1976), Michaelson (1990), Hidalgo (2001), Woodhouse (2006), Meko (2007)

24. Uncertainty related to extreme values
Colorado at Lees Ferry, Reconstructed and Gaged Flows
An additional source of uncertainty is related to extreme reconstructed values. We show here the reconstruction of Colorado at Lees Ferry from Woodhouse et al. (2006). The blue lines show the range of the observed flows on which the reconstruction was calibrated. The reconstructed flows which are outside these bounds probably were derived from tree-ring values that are outside the “calibration space” of the model—in other words, they are extrapolated flow estimates, rather than interpolated flow estimates, as is typical. Extrapolated flow estimates may have greater uncertainty than is indicated by the validation statistics, because those statistics don’t strictly apply to them.
Accordingly, the very lowest reconstructed flows (e.g., 1685: ~2 MAF) are probably less reliable than the less-extreme reconstructed low flows that are based on tree-ring data within the range of tree-ring values to which the model was fitted.
Also, in regression modeling, the reconstructed flow is not constrained by zero, so negative flows may be estimated in the very driest years. While a negative reconstructed flow on major rivers is physically implausible and may be seen as “unreliable”, the confidence intervals around that negative value will always extend into the positive flow range.
Extremes of reconstructed flow beyond the gaged record often reflect tree-ring data outside the calibration space of the model

25. 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
To summarize this Uncertainty Summary: A reconstruction is a plausible estimate of past streamflow, there is no one “right” or “final” reconstruction, and every reconstruction contains uncertainty from multiple sources.

26. What reconstructions can tell us about droughts of the past
Part 6:
What reconstructions can tell us about droughts of the past
In Part 6, we show selected graphs and analyses from recently developed streamflow reconstructions from two basins in the western US—the upper Colorado River and the Rio Grande--which illustrate the information and general “lessons” that can be gleaned from the reconstructions of past flow.
NOTE: While not all reconstructions in the western U.S. depict every “lesson” shown in these examples, these are the types of evaluations all reconstructions can provide. Note also that the longer the reconstruction, the greater the chance that events in the gage period (i.e. severity of low flows, runs of below average flows) have been exceeded in the past.

27. Colorado River: The 20th century contains only a sample of the interannual variability of the last 500 years
If we categorize reconstructed annual flows (here for the Colorado River at Lees Ferry) by flow percentile, and then plot the resulting flow sequences, it is easier to see how the 20th century contains only a small sample of the interannual variability shown over the full, 500+ year reconstruction. For example, there is no analog since the 1900 for the three straight years in the 1840s below the 10th percentile. Note also that the number of years below the 10th percentile has varied from century to century, with the 1900 having the fewest, almost 2/3 fewer than in the 1500s or 1800s.

28. Rio Grande: The extreme low flows of the past 100 years (like 2002) were exceeded prior to 1900
For many gages in the Intermountain West, 2002 was the lowest annual flow in the observed record. But reconstructions generally show that one or more years prior to 1900 probably had lower flows than 2002 (or 1977 or 1954). Here, the reconstruction for the Rio Grande at Del Norte, CO ( ), indicates that 5 years between 1536 and 1900 were likely to have had lower flows than 2002.
So while 2002, 1977, and 1954 were extreme drought years across the region, they are unlikely to represent the worst potential drought.
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)

29. Rio Grande: Multi-year droughts were clustered in time, with fewer droughts in the 20th century
Reconstructed Rio Grande Streamflow,
Periods of below-average flow, of 2 years or more
(length of bar shows acre-feet below average)
Looking at multi-year droughts (2 or more consecutive years of below-average flow) reconstructed for the Rio Grande, we see two features: First, the droughts are not evenly distributed in time, and there are multidecadal periods free of multi-year drought. One of those periods was in the early 1900s, and overall the 1900s had somewhat fewer droughts, and less severe droughts (annual deficit on the vertical axis) than in previous centuries.

30. Rio Grande: The longest observed droughts are exceeded in length by pre-1900 droughts
(6)
LONGEST OBSERVED (5)
(7 years)
(6)
(7)
(11)
(6)
Here, again on the Rio Grande, several multi-year droughts prior to 1900 were longer than the longest observed drought (5 years). One of these was 11 years long ( ), and while the average severity of this drought was not particularly high, there were no wet years for over a decade to helped refill reservoirs being depleted by consistent, moderate drought.
Reconstructed Rio Grande Streamflow,
Periods of below-average flow, of 2 years or more
(length of bar shows acre-feet below average)

31. Colorado River: At decadal time scales, the 20th century is notable for wet periods, but not dry periods
When we look at hydrologic variability over longer time scales, such as 20-year moving averages, we see that the 20th century is unrepresentative of the longer record. Here the reconstruction for the Colorado River at Lees Ferry shows that the 1900s contained two of the five wettest 20-year periods of the past 500 years (2nd and 4th), while the driest period of the 1900s ( ) only ranks 8th overall.

32. Reconstructed Rio Grande Streamflow, 1536-1999
Rio Grande: On century time scales, the 20th century was overall wetter than the previous four centuries
626,000
641,000
632,000
625,000
661,000
600,000
620,000
640,000
660,000
680,000
700,000
1500s
1600s
1700s
1800s
1900s
Annual flow, acre-feet
Reconstructed Rio Grande Streamflow,
Mean annual flow, by century
Here, again on the Rio Grande, if we look at century time scales, we find that the 20th century had a mean annual flow 3% to 6% greater than the previous four centuries. In a river basin where depletions are nearly equal to supply, that 3 to 6% could make a big difference.

33. Reconstructed flow of Colorado River at Lees Ferry, 762 - 2005
Colorado River: The Medieval Period (~ ) had multi-decade dry periods with no analog since
Reconstructed flow of Colorado River at Lees Ferry,
Medieval period
There are a few reconstructions of flow in the western US that extend back into the Medieval Period (~ ), which is known from other climate proxy data to be a generally drier period than average in the western US. Here, the reconstruction of the Colorado River at Lees Ferry (Meko et al. 2007) shows that during the Medieval Period, there were at least two multi-decadal dry episodes, in the 800s and in the 1100s, that were more severe, or longer, than later dry periods. The mid-1100s dry period lasted for about 60 years, during which 4 out of 5 years had below-average flow.
Reference:
Meko, D.M., Woodhouse, C.A., Baisan, C.A., Knight, T., Lukas, J.J., Hughes, M.K., and Salzer, M.W Medieval Drought in the Upper Colorado River Basin. Geophysical Research Letters 34, L10705.
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).