Decadal prediction of Colorado River streamflow anomalies using ocean-atmosphere teleconnections



[1] The Atlantic Multidecadal Oscillation (AMO) and Pacific Decadal Oscillation (PDO) time series are used to forecast a decade ahead streamflow anomalies in the upper Colorado River at Lee's Ferry. In the instrumental record, we obtain unusually high decadal forecast skill that is statistically significant at the 95% confidence level, suggesting strong ocean-atmosphere-land teleconnection. In order to test whether such teleconnection existed in the past, we compare the retrospective forecast skill to the skills obtained using the available ocean-atmosphere teleconnection and streamflow reconstructions derived from tree rings. We find much lower skill in the reconstructed record. Using frequency analysis, we show that the streamflow and sea surface temperature oscillations in the instrumental records all have dominant low frequency periodicities (>35 years) that explain much of the total variance. However, such dominant periodicities do not appear in the power spectra of the reconstructed records of AMO, PDO and streamflow. Given that these dominant low periodicities are likely responsible for the high prediction skill in the instrumental record, it remains uncertain whether reliable decadal streamflow predictions in the upper Colorado River basin will be possible in the years ahead.

1. Introduction

[2] Despite recent progress in seasonal to annual hydroclimate predictions based on ocean-atmosphere teleconnections induced by phenomena such as ENSO and PDO [Bracken et al., 2010; Sankarasubramanian et al., 2008; Switanek et al., 2009], little is known about how such teleconnections affect weather and water availability at longer time scales. Long-term anomalies in water availability, such as multi-year droughts, can significantly affect societal and environmental health. Given the natural variability of climate, regions that have faced droughts in the past will undoubtedly experience future events of similar magnitude and duration [Cook et al., 2004; Meko et al., 2007]. Being able to forecast the magnitude and timing of decadal-length droughts allows for better water management and subsequently improved municipal and agricultural planning.

[3] Sea surface temperature (SST) anomalies in both the Atlantic and the Pacific oceans have been proposed as drivers of low frequency ocean-atmosphere-land teleconnections that could modulate or influence regional hydro-climates [Barlow et al., 2001; Ellis et al., 2010; McCabe and Palecki, 2006; Nigam et al., 1999, 2011; Tootle and Piechota, 2006]. The AMO (Atlantic Multidecadal Oscillation) is defined as the average SST over the north Atlantic (between the equator and 70 N [Guan and Nigam, 2009]), while the PDO (Pacific Decadal Oscillation) is defined as the leading principal component of SSTs in the Pacific northward of 20 N. Hidalgo [2004] and McCabe et al. [2007]have shown that there have been below/above average decadal flows in the Upper Colorado River basin at Lee's Ferry (river flow gauging station near Lake Powell that receives runoff from the Upper Colorado) when AMO is positive/negative and PDO is negative/positive. Therefore, in this study we address the following question: can the AMO and PDO time series, as expressions of ocean-climate processes and their associated teleconnections, be used to provide statistically significant skillful decadal forecasts of hydro-climate in the upper Colorado River basin?

[4] This study first develops a statistical method that uses prior decadal averages of AMO and PDO to forecast next decade streamflow anomalies. Additionally, we test these forecasts for statistical significance. Second, we use tree ring reconstructions of streamflow, AMO and PDO to see whether there is forecasting skill in the period preceding the instrumental record. We then compare the forecast skills of the instrumental and reconstructed records.

2. Data and Analysis

[5] Observed naturalized flows for the Colorado River, at Lee's Ferry, were produced by the Bureau of Reclamation [Prairie and Callejo, 2005], while the tree-ring reconstruction of streamflow at the same location was performed byMeko et al. [2007] (all data used are provided as auxiliary material). The observed naturalized flows currently exist for the years 1906–2007, while the reconstructions range between 762-2005. Additionally, the observed time series of the AMO [Enfield et al., 2001] and PDO [Mantua et al., 1997] indices can be obtained from NOAA at The AMO and PDO have observed records that cover the years 1856–2009 and 1900–2009, respectively. Reconstructions of AMO and PDO were obtained from NOAA's Paleoclimatology website The reconstruction of AMO [Gray et al., 2004] is for the time period 1567–1990, while the reconstructions of PDO [D'Arrigo et al., 2001; Biondi et al., 2001; MacDonald and Case, 2005; Shen et al., 2006] are for the time periods 1700–1979, 1661–1991, 993–1996 and 1470–1998, respectively.

[6] The observed and reconstructed streamflow and AMO/PDO data are subjected to smoothing using a ten-year running mean (from now on referred to as 10yrRM) [Hurkmans et al., 2009; Mauget, 2004; O'Lenic et al., 2008]. The resulting time series are expressed as values corresponding to the last year of the 10yrRM. For example, the last 10yrRM value is 2007 and corresponds to the years 1998–2007.

[7] We first tested the hypothesis that the previous decades' observed 10yrRM AMO and PDO values could be used to make relevant and statistically significant predictions of next decade streamflow anomalies at Lee's Ferry. In this effort, retrospective forecasts were made for the last forty 10yrRMs (1968–2007). Figure 1ashows 10yrRMs of AMO and PDO with the 10yrRMs of Lee's Ferry streamflow lagged by 10 years. The 10yrRMs of AMO and PDO have a correlation coefficient of .02, and are therefore treated as independent time series. The 10yrRMs are expressed as z-scores, or standard deviations from the mean. The + and x symbols correspond to above and below average streamflow, respectively, while the magnitudes of the departures are reflected by the size of the symbols. For reference we provide the size of the symbols when 1-σand 2-σ variability would occur.

Figure 1.

(a) Standardized departures of Lee's Ferry streamflow lagged 10 years behind departures of AMO and PDO. All values are 10-year running means. The AMO and PDO values are the 10yrRMs between 1915–1997, while the streamflows at Lee's Ferry are between 1925–2007. The + and x symbols correspond to above and below average streamflow, respectively, while the magnitudes of the departures are reflected by the size of the symbols. (b) The initial 54 values (10yrRMs between 1915–1968) of AMO and PDO with Lee's Ferry streamflows lagged by 10 years. The black circle shows an example of the average AMO/PDO over the previous ten years (1978 10yrRM) that is used to predict streamflow for the following decade (1988 10yrRM). The gray circle surrounds the values that are used to make the forecast.

[8] Using smoothed 10yrRMs of streamflow requires that we consider how the forecasts might be influenced by autocorrelation. However, it is only the lag-10 autocorrelation (e.g., pairing a streamflow value corresponding to the decade 1971–1980 with a value from 1981–1990) that necessitates attention. This is because even though our window moves a single year and, subsequently, overlap exists in the forecasts, there is not any overlap between the information used to derive the forecast and the forecasted value itself.

[9] Even though no streamflow data from the time we are forecasting is used, there still could be persistence that could affect the decadal forecasts. To observe if this persistence affects the independence of the smoothed data from one distinct decade to the next, we forecast decadal values of streamflow using the last decadal streamflow value and the lag-10 autocorrelation. We find that making forecasts using persistence in conjunction with the climatology would give skill that is worse than using the climatology alone. Therefore, we assume that the forecasted decadal streamflow is independent of the prior decade's value, and we compare our forecast skills to the climatology alone. This is explained in more detail in the Results section.

[10] Figure 1b is used to illustrate our methodology. Figure 1b shows the values of AMO and PDO from the year 1915 (referring again to the years 1906–1915) through the year 1968, paired with Lee's Ferry streamflow values that are between 1925 and 1978. We use the statistical relationships from this time period to retrospectively forecast Lee's Ferry streamflow for the years 1979–1988, using SST information only up through 1978. The forecasts are made as standard deviations from the mean (using the data that was available prior to the forecast). The black circle in Figure 1b shows the AMO/PDO value for 1969–1978. A Euclidean distance measure (the spatial distance between the points in the scatter plot) is used to make all of the forecasts of decadal streamflow. We obtained the best retrospective forecast skill by averaging the streamflow from the closest seven points with respect to the most recent AMO/PDO value. The closest points, in the current example, are shown within the gray circle in Figure 1b. The skill measure used is defined as skill = 1 − [Σ(XobsXsim)2/Σ(XobsXclm)2], where Xobs and Xsim are the time series of the observations and simulations (or forecasts), respectively, and Xclm is the climatological mean of all the available prior streamflows. Forecasts that perform worse, equal to, or better than the climatology have skill scores that are less than zero, zero, or greater than zero, respectively.

[11] In addition to testing for statistically significant decadal forecast skill of streamflow at Lee's Ferry using the observed record, it is desirable to see if the skill in the reconstructed record is of similar magnitude. Reconstructions of AMO and PDO are therefore used to forecast decadal Lee's Ferry reconstructed values. The reconstructions were subdivided into moving windows of ninety-three 10yrRMs (which is the length of the observed record). Then, similarly to the observed record, the last 40 values of each reconstructed window at Lee's Ferry were retrospectively forecasted using the closest points from a Euclidian distance measure. For example, the last 40 decadal values of the reconstructed Lee's Ferry are forecasted from the time period 1608–1700. This skill value corresponding to the forecasts of the decadal values for 1661–1700 is attributed to the year 1700. The same procedure is then performed using the years 1609–1701 to obtain another skill value for that subset of the reconstructions. With this approach, a time series of skills can be obtained to compare with the skill value of the observed record.

3. Results

[12] The forecasts of decadal streamflow at Lee's Ferry, for the instrumental record, are shown in contrast to the observations in Figure 2. The skill of decadal prediction of Lee's Ferry streamflow is 0.44 and is statistically significant against the climatology at the 97% confidence level. Statistical significance of the skill against the climatology is calculated using a Monte Carlo approach. Random values are smoothed in the same manner as the climate indices and streamflow data. This is done by first selecting 49 random values from a gamma distribution that is fit to the observed annual streamflow data. The values are then smoothed with a 10-value moving window. Next, this smoothed vector has the mean subtracted out and divided by the standard deviation of the observed 10yrRM streamflow data. This randomly generated set of predictions is then used to obtain a corresponding skill. This process is replicated 10,000 times with a skill measure calculated each time. Skill values of .37 and .23 correspond to 95% and 90% statistical significance levels, respectively. Additionally, we found the skill associated with making predictions using both past climatology and persistence of the decadal streamflow data. This was done by first acquiring the lag-10 autocorrelation of the smoothed data preceding the forecast time. Since we are dealing with z-scores of decadal streamflow, the correlation coefficient is the same as the slope of the regression line. A forecast is then made for the next decade by multiplying the z-score of the most recent completed decade by the lag-10 autocorrelation value. Using persistence to make forecasts for the last forty 10yrRMs leads to a skill of −.07. This means that persistence with climatology provides worse forecasts than the climatology alone. Therefore, we are confident in the statistical significance levels obtained with the Monte Carlo approach explained above.

Figure 2.

Observations and predictions of Lee's Ferry streamflow. The x-axis corresponds to the last year of the 10-year period of interest.

[13] Each of the four PDO reconstructions were used together with the sole AMO reconstruction to retrospectively forecast decadal streamflows at Lee's Ferry. The different combinations of reconstructions and their associated skill through time can be seen in Figure 3. It can be seen that the skill obtained in the instrumental record (0.44, shown as the bold gray dashed line) is rarely met or exceeded with any of the combinations of reconstructions over their respective time periods. The set of reconstructed skills matches or exceeds the instrumental record about one percent of the time, and the time-averaged skills using the reconstructions were −.28, −.26, −.35 and −.33 (green, red, blue and black, respectively inFigure 3). It is interesting to note that correlations obtained between concurrent decades do not necessarily translate into skillful forecasts. We observe the largest correlation coefficient for concurrent decades is .62 (using reconstructions of PDO [Biondi et al., 2001] and Lee's ferry streamflow), while it is −.18 when streamflow is lagged by 10 years.

Figure 3.

The change in predictive skill through time when using the different combinations of reconstructions. Each skill value is obtained using the last forty 10yrRMs from a discrete time period equal in length to the observed time series. The thinner gray line (Skill = 0) provides a reference skill equal to the climatology. The thicker gray dashed line (Skill = .44) shows the skill from the instrumental record.

4. Discussion and Conclusions

[14] This study first used the instrumental records to show that there is statistically significant skill in forecasting the next decade of Lee's Ferry streamflow using the previous decadal values of AMO and PDO. This by itself is a remarkable result given the strength of the forecast skill (0.44 at 97% significance level). However, with all available combinations of reconstructed teleconnections, the level of decadal forecast skill of streamflow at Lee's Ferry is drastically less than what is seen in the instrumental record. What could explain this dramatic shift in decadal forecast skill? Figure 4 provides frequency analyses of the instrumental and reconstructed records of AMO, PDO and Lee's Ferry streamflow. The fact that all three time series have a dominant low frequency in the instrumental records can explain why we observe such a high level of forecast skill. All three of the observed time series have dominant periodicities greater than 35 years. Forecasting proves to be quite skillful when all three variables have much of their variance explained by similar low frequency oscillations. However, we do not see such dominant periodicities in the power spectra of the reconstructed records of AMO, PDO and streamflow. Is there an underlying physical mechanism that has caused these variables to align in the instrumental record, or has this happened by chance?

Figure 4.

Frequency analyses of the observed and reconstructed records of streamflow at Lee's Ferry, AMO and PDO (reconstruction of PDO is Biondi et al. [2001]). The x-axes are the periods, while the y-axes are the amplitudes explained by each period. The left column all extend 77 years along the x-axis, which is half of the length of the AMO time series (statistically relevant periodicities require two cycles). There are clear dominant periods in the observed records that are seen at longer than 35 years. The reconstructed records, down the right column, do not have comparable dominant frequencies.

[15] There exists the possibility that there is a physical relationship between the sea surface temperature oscillations (characterized by AMO/PDO) and Colorado streamflow through ocean-atmosphere-land teleconnections, as suggested by several studies [Barlow et al., 2001; Hidalgo, 2004; Nigam et al., 2011; Tootle and Piechota, 2006]. If this is the case, we would expect that the dominant periodicities will continue to be aligned for the three variables, and the skill in forecasting decadal streamflow will persist. Using the reconstructions, however, we do not see alignment in the periodicities of these three variables. This is reflected in the poor forecast skills in the reconstructions. There is a more obvious physical relationship, though, between tree ring growth and the amount of water that has fallen in a basin and ending up as streamflow, than between SSTs and regional hydro-climate (e.g., an El Niño year does not always provide a spatial rainfall pattern like we expect). Given this scenario, we can compare the distributions and periodicities of the instrumental records of AMO and PDO with the Lee's Ferry reconstruction. We observe that the dominant periodicities of AMO and PDO (between 50 and 70 years) are not dominant periodicities in the Lee's Ferry reconstruction.

[16] These results and analyses raise several questions. It remains unclear whether the low frequency variability of climate indices, such as AMO and PDO, are accurately preserved in the tree-ring reconstructions of the different time series. If this is not the case it could explain the loss of decadal forecasting skill in the paleo record. Also, is there a dynamic connection between SSTs (that comprise the AMO/PDO) and precipitation in the regions where tree rings were used, or are the AMO/PDO reconstructions strictly statistical? This is a question concerning causality. ENSO is, at some level, dynamically understood and the most well known of the SST climate teleconnections. However, we still cannot quantify precipitation in regions affected by ENSO with good accuracy. Therefore, even if strong correlations exist between tree rings and the instrumental records of AMO/PDO, these are statistical relationships that are not necessarily indicative of our understanding of any physical mechanisms involved. Due to this fact and the general uncertainty associated with the reconstructed teleconnections, caution should be exercised when interpreting the results derived using these time series.

[17] Enfield and Cid-Serrano [2006] and Gangopadhyay and McCabe [2010] have presented probabilistic methods to project teleconnections or streamflow given the time since the last regime shift. Methods such as these could be used to supplement our decadal streamflow forecasts derived from the AMO and PDO indices. However, these methods would only extend upon the statistical nature of our forecasts. More research is required to define physical links between the SSTs that make up the AMO/PDO and streamflow [Cook et al., 2007; Seager et al., 2005]. When using the methodology herein to forecast future decadal streamflows, two results require consideration: 1) There is a large gap between the forecasting skill in the instrumental and reconstructed records; and 2) The dominant periodicities seen in the instrumental AMO/PDO are not present in the Lee's Ferry streamflow reconstructions. These results appear to foretell a future of less skillful forecasts of Lee's Ferry decadal streamflow than the instrumental record indicates. Time will reveal whether the hydrologic regime in the upper Colorado River basin will continue to shift in phase with AMO and PDO time series.


[18] The authors would like to thank Terry Fulp, Jim Prairie and the entire Bureau of Reclamation, Lower Colorado Regional Office, for funding this study. Also, the editors and reviewers at GRL provided invaluable suggestions that assisted us in shaping the current version of the manuscript.

[19] The Editor thanks three anonymous reviewers for their assistance in evaluating this paper.