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What Does the DWR Tree Ring Study Tell Us About Sacramento River Hydrology?

How will future hydrologic conditions compare to current ones?  This question has been asked throughout western water.  There are two strands of thought suggesting a challenging future: (i) the 20th century was an unusually wet period, and (ii) climate change will confront water managers with more severe drought conditions.

For the Sacramento River watershed in California, there is unexpectedly good news.  While California must confront variability in hydrologic conditions in the Sacramento River watershed, recently released tree-ring data suggest that the current severe drought conditions do not a signal that California will be facing more severe hydrologic challenges in the future.

The California Department of Water Resources (“DWR”) recently released a draft Final Report Klamath/San Joaquin/Sacramento Hydroclimatic Reconstructions from Tree Rings,   I cracked open the study expecting to find data at least supporting the first proposition above—the 20th century was an unusually wet period.  This expectation was based on my experience with the Colorado River.

Colorado River Remembrances

In 1995, I examined the Bureau of Reclamation data on the Annual Natural Flow of the Colorado River (Water Strategist “Meeting the Challenge”, Fall 1995, p. 7).  The average annual Natural Flow of the Colorado River for the 1906-1994 period (available data in 1995) was 15.0 million acre-feet.  Tree-Ring studies suggested that the long-term average annual flow was 13.5 million acre-feet.  In fact, the 20th Century record of the Bureau data supported the view that river flows were returning to long-term hydrologic conditions measured by Tree-Ring studies (see table).

Average Annual Natural Flow of Colorado River


Million Acre-Feet


















Consistent with the view that the 1922 Colorado River Compact was negotiated during a period of abnormally high-flow years, average annual flows for the latter half of the period (1951-94) were 13.9 million acre-feet, or 2.1 million acre-feet less than the 16.0 million acre-feet of average annual flows experienced in the earlier half of the period (1906-1950).  And, for all but the 1981-94 period, average annual flows for consecutive periods since 1906 were steadily declining towards the 13.5 million acre-foot average.  Yet, the hydrology for the 1981-94 period is itself interesting.  For the 1983-86 period of extensive flooding, the annual natural flow of the Colorado River averaged 22.2 million acre-feet.  During the other years in that period, the annual natural flow averaged 11.8 million acre-feet.

The last 20 years of data supports the conclusion of the earlier analysis.  The 10-year moving average of annual natural flow of the Colorado River has been steadily declining.  By 2008, the ten-year moving average was at 12.2 million acre-feet—below the long-term average of Tree-Ring studies.  See “Increasing Hydrologic Risk in the Colorado River Basin”, is a “new normal” on the Colorado River relative to 20th century hydrologic conditions. 

Sacramento River Tree Ring Study

The annual unimpaired runoff of the Sacramento River Four River Index averaged 18.3 million acre-feet from the year 900 through 2012 (the period that the DWR study reconstructed unimpaired runoff from tree rings)—see figure.  Reflecting the fickleness of Mother Nature, there is a wide variability in annual flows.  What surprised me was that the 100-year moving average has been stable for almost the seven plus centuries of data.  It is difficult to find any footprint of climate change in this chart.

Tree Ring History

To examine the likelihood of consecutive years (or “runs”) of above and below average annual unimpaired runoff, I divide each of the 1,113 years of data into three categories:

  • Above Threshold: annual unimpaired runoff  greater than 105% of 18.3 million acre-feet
  • Below Threshold: annual unimpaired runoff below 95% of 18.3 million acre-feet
  • Inside Threshold: annual unimpaired runoff between 95% and 105% of 18.3 million acre-feet

Forty-one percent of the years were either years above and below the threshold and the seventeen percent were years inside the threshold (see chart).

Composition of Runs

About two-thirds of the time the annual unimpaired runoff of the Sacramento River is in a one-time, non-consecutive year of above, below or inside the threshold.  The frequency (probability) of consecutive runs of more than four years is remote (less than 1%, or once a century).  The likelihood of a consecutive runs of given lengths (2, 3, or 4 years) of either above or below the threshold is about the same.

Frequency of Runs

Once a consecutive run starts, how long will it last?  I focus on below threshold years (see table—the second through fourth columns, respectively, are for the second, third and fourth year of a run and the percentages show the probability that the run ends in the year shown in the first column).  Generally speaking, there is about a 50% chance that the current year of any run of below threshold years is the last year of the run.  Therefore, the probability that the current year of a two-year consecutive run of below threshold years ends is 52.5%; the probability that the current year of a three-year run of below threshold years ends is 46.4%; the probability that the current year of a four-year run of below threshold years ends is 46.7%.  If you are in the second, third or fourth year of a consecutive run of below threshold years, the probability of a consecutive run of 5 years or more of below threshold years is, respectively, 13.6%, 28.6%, and 53.3%.

Probability of Length of Run of Below-Threshold Years by Year of Run

Year of Run

Length of Run









































5 years of more





Tree Rings versus DWR Estimates

How do the estimates of unimpaired runoff from DWR compare with tree ring studies?  Very well (see chart).  The correlation (measure of the tendency of the two series to move together) is 0.86—in other words, annual variations in the unimpaired runoff estimated by the DWR Tree Ring study explains 75% of the annual variation in the unimpaired runoff estimated by DWR (and vice versa).  While the series move together closely, they are not identical.  Interestingly, the DWR Tree Ring study estimated unimpaired runoff for the Sacramento River at 23.5 million acre-feet in 2012 (last year estimated by study), while DWR’s estimate was only 11.8 million acre-feet.

Sacramento River Index Chart

What This All Means for California’s Water Supplies?

Tree-ring studies provide valuable information about hydrologic conditions from a longer-term perspective than other sources of hydrologic data.  The tree ring data correlates well with DWR data on the unimpaired runoff of the Sacrament River Four River Index.  The longer-term perspective and data from tree-rings provides valuable insights about the nature of hydrologic risk confronting California:

  • Long-term trends in unimpaired runoff of the Sacramento River Four River Index is stable—there is no obvious footprint from climate change
  • There is about a one-third chance that, in any year, the unimpaired runoff will be part of a run of consecutive years either above, below or inside a threshold defined as 5% +/- of the long-term average
  • The likelihood of consecutive above-threshold and below-threshold runs are about the same
  • While consecutive runs of more than 4 years are remote, if there has been a consecutive run of three or four years of below-threshold years, then there is a significant risk that hydrologic conditions are signaling a few more years of below-threshold conditions.

California is in the third consecutive year of below normal years.  Based on tree-ring data, there is a significant risk that there may be a few more years of severe hydrologic conditions ahead.  The implications for management of water storage are straight-forward.  Taking water from storage today to avoid shortages now may become a source of regret in a couple of years.

The DWR tree ring study provides information on more than the Sacramento River Four River Index.  The tree ring data for different watersheds, of course, must be analyzed separately.

Written by Rodney T. Smith, Ph.D.