Long-Lead Seasonal Prediction of Streamflow over the Upper Colorado River Basin: The Role of the Pacific Sea Surface Temperature and Beyond

Siyu Zhao aDepartment of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, California

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Rong Fu aDepartment of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, California

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Yizhou Zhuang aDepartment of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, California

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Gaoyun Wang aDepartment of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, California
bDepartment of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing, China

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Abstract

We have developed two statistical models for extended seasonal predictions of the upper Colorado River basin (UCRB) natural streamflow during April–July: a stepwise linear regression (reduced to a simple regression with one predictor) and a neural network model. Monthly, basin-averaged soil moisture, snow water equivalent (SWE), precipitation, and the Pacific sea surface temperature (SST) are selected as potential predictors. Pacific SST predictors (PSPs) are derived from a dipole pattern over the Pacific (30°S–65°N) that is correlated with the lagging streamflow. For both models, the correlation between the hindcasted and observed streamflow exceeds 0.60 for lead times less than 4 months using soil moisture, SWE, and precipitation as predictors. This correlation is higher than that of an autoregression model (correlation ~ 0.50). Since these land surface and atmospheric variables have no statistically significant correlations with the streamflow, PSPs are then incorporated into the models. The two models have a correlation of ~0.50 using PSPs alone for lead times from 6 to 9 months, and such skills are probably associated with stronger correlation between SST and streamflow in recent decades. The similar prediction skills between the two models suggest a largely linear system between SST and streamflow. Four predictors together can further improve short-lead prediction skills (correlation ~ 0.80). Therefore, our results confirm the advantage of the Pacific SST information in predicting the UCRB streamflow with a long lead time and can provide useful climate information for water supply planning and decisions.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Siyu Zhao, siyu_zhao@atmos.ucla.edu

Abstract

We have developed two statistical models for extended seasonal predictions of the upper Colorado River basin (UCRB) natural streamflow during April–July: a stepwise linear regression (reduced to a simple regression with one predictor) and a neural network model. Monthly, basin-averaged soil moisture, snow water equivalent (SWE), precipitation, and the Pacific sea surface temperature (SST) are selected as potential predictors. Pacific SST predictors (PSPs) are derived from a dipole pattern over the Pacific (30°S–65°N) that is correlated with the lagging streamflow. For both models, the correlation between the hindcasted and observed streamflow exceeds 0.60 for lead times less than 4 months using soil moisture, SWE, and precipitation as predictors. This correlation is higher than that of an autoregression model (correlation ~ 0.50). Since these land surface and atmospheric variables have no statistically significant correlations with the streamflow, PSPs are then incorporated into the models. The two models have a correlation of ~0.50 using PSPs alone for lead times from 6 to 9 months, and such skills are probably associated with stronger correlation between SST and streamflow in recent decades. The similar prediction skills between the two models suggest a largely linear system between SST and streamflow. Four predictors together can further improve short-lead prediction skills (correlation ~ 0.80). Therefore, our results confirm the advantage of the Pacific SST information in predicting the UCRB streamflow with a long lead time and can provide useful climate information for water supply planning and decisions.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Siyu Zhao, siyu_zhao@atmos.ucla.edu

1. Introduction

The Colorado River provides water for nearly 40 million people in the southwestern United States and northern Mexico. It irrigates ~20 000 km2 of land and generates more than 4200 MW of hydroelectric energy per year (U.S. Bureau of Reclamation 2012). The upper Colorado River basin (UCRB), defined by the river network upstream of the U.S. Geological Survey stream gauge at Lees Ferry, Arizona, provides around 90% of the streamflow for the Colorado River (Jacobs 2011), thus making it a vital part of water supply in the southwestern United States. However, recent studies showed a significant negative trend of the UCRB natural streamflow (Reynolds et al. 2015; Woodhouse et al. 2016; Xiao et al. 2018) associated with sustained drought conditions (e.g., Xiao et al. 2018; Hoerling et al. 2019; Hobbins and Barsugli 2020; Milly and Dunne 2020). This decline in the streamflow strains the Colorado River water supply and therefore necessitates skillful, long-lead predictions of the UCRB streamflow for water resource decisions.

Currently, the Colorado Basin River Forecast Center (CBRFC) provides monthly updates of seasonal (April–July) forecasts of the UCRB streamflow starting in January. They apply the ensemble streamflow prediction approach, which incorporates both the Sacramento Soil Moisture Accounting model and the Snow-17 model (Werner and Yeager 2013). In addition to official CBRFC forecasts, considerable effort has been made to explore ways to improve the streamflow prediction skill. For example, Bracken et al. (2010) developed a multisite seasonal ensemble streamflow forecast technique and showed that their approach is overall comparable to existing operational models and had better skill when predicting wet years. They could also extend forecasts 2 months earlier (in November) than official forecasts by CBRFC with reasonable prediction skills. Other studies focused on improving streamflow predictions in a portion of the UCRB. For example, Switanek et al. (2009) showed good prediction skills for the spring discharge volume of the Gunnison River basin using December sea surface temperature (SST) in Gaussian mixture models. Oubeidillah et al. (2011) showed that a nonparametric forecast model based on exceedance probability forecasts could provide reasonably long lead times (3–9 months) when forecasting the streamflow for three stations over the west boundary of the UCRB.

In addition to developing new forecast techniques, many studies have focused on improving streamflow predictability and predictor quality. Maurer and Lettenmaier (2003) showed that seasonal streamflow (or runoff) is associated with climate signals [e.g., El Niño–Southern Oscillation (ENSO) and Arctic Oscillation (AO)] and land surface and atmospheric variables [e.g., soil moisture, snow water equivalent (SWE), and precipitation]. Water stored in snowpack and soil column can be released months later, making it possible to satisfactorily predict streamflow with short lead times using measured soil moisture and SWE (e.g., Regonda et al. 2006; Bracken et al. 2010). Furthermore, to increase prospects of long-lead hydrologic forecasts, numerous studies have focused on understanding the relationship between large-scale climatic teleconnections and western U.S. hydroclimate systems (e.g., Schubert et al. 2004; Zhang and Mann 2005; Dai 2013; Seager et al. 2015; Zhao et al. 2017). In particular, singular value decomposition analysis has been applied to identify the teleconnection between oceanic–atmospheric variability and regional streamflow. Many studies used SST and geopotential height as predictors in forecast models (e.g., Lamb et al. 2011; Oubeidillah et al. 2011; Sagarika et al. 2015, 2016). Indices derived from the Pacific SST are likely better suited for long-lead forecasts of streamflow while indices obtained from 500 hPa geopotential height improve short-lead forecasts (Oubeidillah et al. 2011).

As indicated by these previous studies, oceanic–atmospheric indices can be used for streamflow forecasts for long lead times. However, some issues remain unaddressed. It is still necessary to further improve skills of long-lead prediction of streamflow by constructing better oceanic indices. Furthermore, it is unclear whether a nonlinear machine learning approach is superior to a linear approach for seasonal predictions of the UCRB streamflow. The goal of our study is to explore the potential for an extended seasonal prediction with lead times up to 1 year for the UCRB streamflow using both a linear and a nonlinear statistical forecast model.

2. Data and methodology

a. Data

The monthly total natural flow data for 20 locations over the UCRB are obtained from the Bureau of Reclamation (BOR) from 1910 to 2018 (Prairie and Callejo 2005). In contrast to the historic flow, the natural flow excludes anthropogenic impacts (i.e., consumptive uses/losses of water and reservoir regulation) to the extent possible and has been widely used (e.g., Meko et al. 2007; Bracken et al. 2010; Harding et al. 2012). Monthly mean lake elevation data are also obtained from the BOR from 1980 to 2018. The observed monthly averaged (or accumulated) land surface and atmospheric variables [snowmelt, precipitation, surface skin temperature, evapotranspiration, soil moisture (0–100 cm), and SWE] were generated by the VIC land surface model from the phase 2 of the North American Land Data Assimilation System (NLDAS-2) with a resolution of 0.25° for the period of 1979–2018 (Xia et al. 2012). Outputs from other two models of the NLDAS-2, the Noah and Mosaic land surface models, are compared with those from the VIC model. These land surface and atmospheric variables from the NLDAS-2 datasets have been widely applied in previous studies for climate predictions (e.g., Hao et al. 2016, 2018; Getirana et al. 2020).

This study also uses monthly mean geopotential height and vertically integrated water vapor flux from the European Centre for Medium-Range Weather Forecasts (ECMWF) fifth-generation reanalysis (ERA5) with a resolution of 2.5° from 1979 to 2018 (Copernicus Climate Change Service 2017). Monthly mean SST comes from the Hadley Centre Sea Ice and Sea Surface Temperature (HadISST) with a resolution of 1.0° from 1909 to 2018 (Rayner et al. 2003). Both the ERA5 and HadISST data are widely used for climate predictions (O’Reilly et al. 2017; Albergel et al. 2018). The Atlantic multidecadal oscillation (AMO), Pacific decadal oscillation (PDO), and Southern Oscillation index (SOI) indices are obtained from the National Oceanic and Atmospheric Administration (NOAA) (Trenberth 1984; Mantua et al. 1997; Enfield et al. 2001).

In this study, the hindcast of streamflow covers boreal spring and summer (April–July) for the period of 1980–2018. To further examine the robustness of the result, the period of 1950–2018 is applied for the prediction, in which SST is the only predictor. Specifically, 0-month lead (LD0) predictions are initialized using observations averaged (or accumulated) over March, 1-month lead (LD1) predictions are initialized using observations in February, …, and 12-month lead (LD12) predictions are initialized using observations in March of the previous year.

b. Creating predictors with cross validations

We identify predictors for the streamflow based on correlations between the April–July UCRB streamflow and a suite of climate variables that affect streamflow. Since climate variables within the UCRB, such as SWE, soil moisture, and precipitation, are important to the UCRB streamflow for short lead times, we design statistical forecast models for the period of 1980–2018 using these basinwide variables. Due to the limited record length of these variables in the NLDAS-2, we apply the leave-three-out cross-validated approach for the period of 1980–2018 to train the model: for the prediction of 1 year, we drop data in that year and its previous and following years. Specifically, to predict the first year 1980 and last year 2018, we drop years 1980–82 and 2016–18 and use data of 1983–2018 and 1980–2015 for training, respectively.

In addition to land surface and atmospheric variables, we also use SST data (available for more than 100 years) to predict the UCRB streamflow. To avoid artificial skills due to predictor screening (e.g., DelSole and Shukla 2009), we apply the retrospective cross-validated approach in which data during and after the time when the forecast is initialized are not used for training (e.g., Ionita et al. 2008). The leave-three-out approach is also applied, and its skills are compared to those of the retrospective approach. As artificial skills decrease with an increase of sampling sizes, we compare the two cross-validated approaches for two periods, 1980–2018 and 1950–2018, to assess potential artificial skills induced by sampling sizes.

For the retrospective cross validation, we use data spanning 40 years to train the statistical model. To predict streamflow in a given year (year T) of 1980–2018, we calculate the correlation coefficient between the April–July streamflow and SST for each lead time of LD0–LD12. For example, for LD12 of 1980, the SST predictor used for training spans March 1939–March 1978, and the predictand (i.e., streamflow) is from the period of April–July 1940–79. For LD0 of 1980, the SST predictor used for training spans March 1940–March 1979, and the predictand is from the period of April–July 1940–79. For the longer predicted period (1950–2018), for example, for LD0 of 1950, the SST predictor used for training spans March 1910–March 1949, and the predictand is from the period of 1910–49.

For the leave-three-out cross-validated approach, DelSole and Shukla (2009) have suggested that predictors identified based on high correlations with the predictand may lead to artificial prediction skills if data are not fully cross validated (i.e., all data are used to evaluate correlations for selecting predictors). To address this issue, we leave out the 3 years centered as the year of hindcast when training the statistical model. For example, for LD0 of 2010, we only use data during the periods of 1980–2008 and 2012–18 to calculate the correlation between SST and streamflow. Note that the three years 2009, 2010, and 2011 are also excluded from the calculation of the climatological mean.

c. Pacific SST predictors

Based on correlation maps obtained for year T for all lead times (LD0–LD12), we derive a Pacific SST predictor (PSP) for each predicted year T at each lead time τ. Specifically, we 1) divide the gridded SST (located within 30°S–65°N, 120°E–70°W) at the lead time τ into two groups, one for positive and the other for negative correlations (significant at the 0.05 level; we assume the samples are independent and do not take into account autocorrelation), 2) compute the average of SST for each group, and 3) calculate the difference between the two groups. The PSP can be shown as follows:
PSP(T,τ)=iPosSSTi/PosjNegSSTj/Neg,
where “Pos” and “Neg” are the total number of grid points over the selected domain with positive and negative correlations (significant at the 0.05 level), respectively. For the retrospective cross validation, for each predicted year T at each lead time τ, the PSP contains 41 values, including 40 values for training and 1 value for prediction. For example, the PSP for 1980 at LD0 includes 40 values for training (from March 1940 to March 1979) and 1 value for prediction (March 1980). For the leave-three-out cross validation, for example, the PSP for 2010 at LD0 includes 36 values for training (from March 1980 to March 2008, and from March 2012 to March 2018) and 1 value for prediction (March 2010).

d. Statistical forecast models

Three statistical forecast models, an autoregression model, a stepwise linear regression model (reduced to a simple regression with one predictor), and a neural network model, are applied to predict the UCRB streamflow. The autoregression model uses the streamflow at Lees Ferry during LD0–LD12 to predict the April–July UCRB streamflow. Linear regression coefficients are computed between the April–July and leading streamflow. The stepwise linear regression adopts a sequential forward selection approach, which selects contributing factors (i.e., predictors) in a sequential order by maximizing the total variance explained at each step (e.g., Liu et al. 2016; Wang and Moon 2017; Moon et al. 2018). At the first step, the predictor that is statistically significant at the 0.05 level and has the highest correlation with the predictand (i.e., highest explained variance) is selected. In the next step, we select the predictor (statistically significant; the significance is based on difference from zero correlation coefficient) yielding the highest correlation coefficient together with the predictor selected in the previous step. The same procedure is then sequentially repeated until no statistically significant factor can be selected.

The third model uses a neural network approach to fit inputs (predictors) and target (predictand) and then to perform predictions. The neural network has been widely used to identify nonlinear relationships among geophysical fields (e.g., Hsieh and Tang 1998; Hsieh 2000, 2001). This method supplements traditional linear statistical methods in forecasting meteorological and oceanographical fields (e.g., Tangang et al. 1997; Sahai et al. 2000; Acharya et al. 2014; Gaitan et al. 2014; Ramseyer and Mote 2016).

We solve the input-output fitting problem applying a two-layer feed-forward neural network, with a tan-sigmoid (also known as hyperbolic tangent) transfer function in the hidden layer and a linear transfer function in the output layer, consistent with previous studies (e.g., Tangang et al. 1997, 1998; Hsieh and Tang 1998; Tang et al. 2000; Gaitan et al. 2014). In the hidden layer, the transfer function is
y(t)=tansig[W(x)x(t)+b(x)],
where x is the input (predictor) vector (k × 1) at a specific time t; W(x) is the weight matrix (m × k); b(x) is the bias parameter vector (m × 1); y is the “medium” vector (m × 1) of the hidden layer at time t; k is the number of elements in input vector; and m is the number of neurons in the hidden layer. Here, 5 neurons are used in the hidden layer (similar results are obtained for neuron number varying from 3 to 20; small number reduces computational expense). Note that the nonlinearity of the neural network is controlled by weights in the tan-sigmoid transfer function (e.g., Hsieh 2001). Similarly, the transfer function of the output layer can be expressed as
z(t)=linear[W(y)y(t)+b(y)].
In (3), y is the medium vector (m × 1) obtained in (2); W(y) is the weight matrix (n × m); b(y) is the bias parameter vector (n × 1); and z is the output (predictand) vector (n × 1) of the output layer at time t, where n is the number of neurons in the output layer (n = 1 here as streamflow is the only predictand).

The neural network is trained using the Bayesian regularization backpropagation algorithm. This algorithm minimizes the combination of weights and squared errors and shows considerably better performance than other training algorithms when input data are limited (e.g., MacKay 1992; Burden and Winkler 2008; Gaitan et al. 2014; Ramseyer and Mote 2016). Moreover, to minimize the effect of overfitting and nonlinear instability in the neural network, we use the output ensemble mean (e.g., Tangang et al. 1997; Hsieh and Tang 1998; Gaitan et al. 2014). Since parameters of the neural network are randomly initiated before training (Hsieh and Tang 1998), we run the model 10 times and thus obtain 10 ensemble members. Other approaches (which are not used in this study) to prevent overfitting include network pruning, penalizing the excessive parameters, stopped training method, and bootstrap aggregation (bagging), which are briefly discussed in Hsieh and Tang (1998).

In this study, we apply several methods to avoid overfitting and hence poor skills in prediction (e.g., Regonda et al. 2006; Adebiyi and Zuidema 2018). These methods include 1) cross validation, 2) selection of contributing factors in a sequential order in the stepwise linear regression, 3) regularization and use of output ensemble in the neural network, and 4) calculation of correlation coefficients among different predictors.

e. Verification

Three verification metrics, the Pearson correlation, mean absolute percent error (MAPE), and Heidke skill score (HSS) are computed to assess prediction skills of the forecast models. The Pearson correlation is expressed as
Pearson correlation=cov(obs,hindcast)/(σobsσhindcast),
where “hindcast” and “obs” are predicted and observed flow, respectively; cov( ) is the covariance between the two variables and σ( ) denotes the standard deviation of a variable. The mean absolute error (MAE) and MAPE are defined as
MAE=iNY|hindcastiobsi|/NY,MAPE(%)=MAE/clm×100.
In (5), “clm” is the climatological mean observed natural flow during April–July, and “NY” is total number of years. The HSS is a widely used statistical verification score to assess probabilistic forecasts (e.g., Doswell et al. 1990; Jury et al. 1999; Yoo et al. 2018) and is shown as
HSS(%)=(HE)/(NYE)×100,
where H and E are the total and expected number, respectively, of correct predictions of the sign of the normalized total natural flow. For a random forecast, E has an expected value of NY/3. The value of HSS varies from −50 to 100. A score of 100 (−50) indicates a perfect (perfectly incorrect) prediction.

3. Results

a. The streamflow over the UCRB

Since land surface and atmospheric variables from the NLDAS-2 are only available from 1979, we mainly focus on natural flow from 1980 to 2018. Figure 1a shows the long-term climatology (averaged over the period of 1980–2018) of the total natural flow during April–July for the 20 locations over the UCRB. The gauge number and name of these locations are listed in Table 1. The total natural flow represents the total flow in the entire basin above a given gauge, while the intervening natural flow represents the flow that originates upstream of a given gauge but below all upstream gauge locations. For example, the total natural flow of the Colorado River at Lees Ferry (site 20) is the summation of the intervening flow at site 20 and the total flow at sites 8, 16, 17, and 19. According to this definition, the total natural flow at Lees Ferry can represent the total flow of the entire UCRB, with an average river volume of ~12 billion m3 during April–July.

Fig. 1.
Fig. 1.

(a) Climatology of the total natural flow (unit: 109 m3) during April–July for the 20 locations over the UCRB. (b) Climatology of the monthly mean total natural flow (red solid line; unit: 109 m3) at Lees Ferry. The black dashed line represents the climatology of annual mean total natural flow. (c) April–July total natural flow at Lees Ferry (red solid line; unit: 109 m3) and April–July mean lake elevation for Lake Powell (blue solid line; unit: m) and Lake Mead (green solid line; unit: m) from 1980 to 2018. Dashed lines are their trends.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

Table 1.

Natural flow gauge number and name over the UCRB.

Table 1.

To understand the seasonal cycle of the total natural flow over the UCRB, we calculate the climatology of both monthly (red solid line) and annual (black dashed line) mean total natural flow at Lees Ferry (Fig. 1b). Result shows that the annual mean total flow is 1.5 billion m3 and the monthly mean flow persistently exceeds this value from April to July, attaining a maximum value of 4.5 billion m3 in June and then rapidly decreasing to 1.1 billion m3 in August. Since the flow volume during April–July has large contribution to the annual total flow, we will focus on this period in this study, consistent with the period chosen by CBRFC and other studies (e.g., Bracken et al. 2010; Werner and Yeager 2013; Xiao et al. 2018). We additionally calculate the April–July total natural flow at Lees Ferry (red solid line) for each year from 1980 to 2018, which shows a significant downward trend (significant at the 0.05 level according to Student’s t test) (Fig. 1c). Previous studies suggested that the declining streamflow could be related to sustained drought conditions in recent years (e.g., Xiao et al. 2018; Hoerling et al. 2019; Hobbins and Barsugli 2020; Milly and Dunne 2020). This downward trend is included when training the model. Moreover, the declining streamflow over the UCRB has directly influenced the water storage of two important reservoirs on the Colorado River (Lakes Powell and Mead), as shown by the fluctuation of the water level of the two reservoirs between 1980 and late 1990s and the sharp drop from 2000 to 2004 (Fig. 1c).

b. Predictor identification

In this section, we select predictors for seasonal predictions and create indices for the monthly, basin-averaged snowmelt, precipitation, surface skin temperature, evapotranspiration, soil moisture, and SWE for LD0–LD12. We calculate the correlation between the leave-three-out cross-validated indices and total natural flow at Lees Ferry. For each predicted year (over the period of 1980–2018) at each lead time, we obtain one correlation coefficient for each variable. Figure 2 shows correlation coefficients for each predicted year (39 gray lines) and the average of all years (red line). Soil moisture and SWE have much higher correlations from LD0 to LD3 (>0.55, significant at the 0.01 level) (Figs. 2e,f) than other variables, indicating that soil moisture and SWE dominate the variation of the total natural flow. This result is consistent with earlier studies that suggested that soil moisture and SWE are good predictors for short-lead predictions of streamflow (e.g., Maurer and Lettenmaier 2003; Regonda et al. 2006; Bracken et al. 2010). For LD4 and longer lead times, the correlation coefficient decreases rapidly to less than 0.30. We also calculate the averaged correlation coefficient between soil moisture and SWE. Results show that their correlation varies from 0.30 to 0.35 for LD0–LD3, indicating that they are not strongly correlated, and varies from 0.10 to 0.60 for longer lead times. The correlation coefficient between precipitation and total natural flow is significant for LD3–LD4 (Fig. 2b). The influence of precipitation on prediction skills will also be explored later.

Fig. 2.
Fig. 2.

(a) Correlation coefficients between the total natural flow during April–July at Lees Ferry and basin-averaged snowmelt from LD0 to LD12. The gray lines represent correlations between the two variables with the leave-three-out approach. There are 39 gray lines in total and each year during 1980–2018 has one line. The red line denotes the average of all the gray lines. (b)–(f) As in (a), but for precipitation, surface temperature, evapotranspiration, soil moisture, and SWE, respectively. The black dashed lines denote correlation coefficients significant at the 0.01 level.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

To further check the robustness of basin-averaged indices, we perform several additional sensitivity experiments. Results from these experiments for soil moisture and SWE for LD0–LD4 are shown in Tables S1 and S2 in the supplemental material. First, we select different regions for areal average by choosing larger areas, varying from the area of 35°–44°N, 105°–113°W to 32°–47°N, 102°–116°W, and smaller areas, varying from the area of 36°–40°N, 109°–113°W over the UCRB only to 35°–43°N, 105°–109°W. Second, we perform an empirical orthogonal function analysis for monthly land surface and atmospheric variables to obtain their leading principal component (PC) acting as indices. We then calculate the correlation coefficient between the first PC and the streamflow. Third, we compute the UCRB averaged variables using data from the Noah and Mosaic land surface models. Finally, we calculate the correlation between basin-averaged variables and total natural flow at three upstream locations, which represent different branches of the flow (sites 8: flow from the Colorado River and Gunnison River, 16: Green River, and 19: San Juan River). The results (Tables S1 and S2 in the online supplemental material) obtained from these sensitivity experiments are all qualitatively similar to those in Fig. 2.

Similar to previous studies (e.g., Regonda et al. 2006; Switanek et al. 2009; Bracken et al. 2010; Oubeidillah et al. 2011), we compute the correlation coefficient between the monthly Pacific SST and total natural flow at Lees Ferry for LD0–LD12 for each year over the period of 1980–2018 using the retrospective approach. Figure 3 shows the averaged correlation coefficients over 1980–2018 for each lead time. The correlation map for individual years will be shown later. This averaged correlation map shows SST–streamflow correlations over a running 40-yr window and exhibits a negative west–positive east correlation pattern (shading) from LD0 to LD12. The negative correlation extends from the western North Pacific and bifurcates around the western equatorial warm pool region, while the positive correlation appears over the west coast of North America and the eastern tropical Pacific. To further examine the robustness of this negative west–positive east correlation dipole pattern, we compute the correlation coefficient between SST and streamflow with the 1) leave-three-out approach for 1980–2018, 2) retrospective approach for 1950–2018, and 3) leave-three-out approach for 1950–2018. The averaged correlation map confirms the dipole correlation pattern, despite of varying magnitudes of the correlation among different cross-validated approaches and periods (Figs. S1–S3).

Fig. 3.
Fig. 3.

(a) Correlation coefficients (shading) between the April–July natural flow and Pacific SST at LD0 with the retrospective approach averaged over the period of 1980–2018. Contours denote correlation coefficients significant at the 0.05 level. (b)–(g) As in (a), but for LD2, LD4, LD6, LD8, LD10, and LD12, respectively.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

As described in the methodology, the correlation maps and the resultant significant (at the 0.05 level) grid points with positive and negative correlations are different for different years and different lead times. Figures 4 and S4 show correlation maps (only values significant at the 0.05 level are shown) for all years during 1980–2018 at LD4 and LD10, respectively, for the retrospective approach. Take LD4 as an example: the early period has two strong (a weak) positive (negative) locations, while the 2000 and beyond have weaker positive locations and a new negative location over the Southern Hemisphere. Such year-to-year variation of correlations are further examined by calculating the trend and variability of these correlations (Fig. S5). The negative trend and large variability over 30°–50°N are likely associated with a lower correlation between the UCRB streamflow and decadal variability of SST that lines up with the PDO epochal shifts in recent decades. Correspondingly, we calculate the correlation coefficient between the streamflow and SST using the leave-three-out approach (e.g., Figs. S6 and S7). Note that at LD10 domains with significant correlations are quite small using the retrospective approach (Fig. S4) before 2000 compared to those for the leave-three-out approach (Fig. S7). This is because longer data records are used in the retrospective approach. The correlation between the SST and streamflow are stronger in recent decades for LD10.

Fig. 4.
Fig. 4.

Correlation coefficients between the April–July natural flow and Pacific SST at LD4 with the retrospective approach for each predicted year of 1980–2018. For example, for year 2010, the data in 1970–2009 are used to calculate the correlation coefficient in that year. Only values significant at the 0.05 level are plotted. The positive and negative values are actually used for deriving the PSP for each year.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

Based on the above results, we create PSPs for predicting the streamflow (see section 2c for details). The year-to-year correlation maps are used to create the PSP(T, τ). Then, the correlation between the PSP, which varies in each year and each lead time, and the streamflow is calculated for LD0–LD12 for each predicted year (gray lines) (Fig. 5). For the shorter predicted period (1980–2018), the averaged correlation coefficients (red lines) are all significant at the 0.01 level and are much higher than those of soil moisture and SWE indices for LD4–LD12 (Figs. 5a,b vs Figs. 2e,f). For the longer period (1950–2018), the averaged correlation coefficients are also significant (Figs. 5c,d).

Fig. 5.
Fig. 5.

(a) Correlation coefficients between the total natural flow during April–July at Lees Ferry and PSPs from LD0 to LD12 for the period of 1980–2018. The gray lines represent correlations between the two variables with the retrospective approach. There are 39 gray lines in total and each year during 1980–2018 has one line. The red line denotes the average of all the gray lines. (b) As in (a), but with the leave-three-out approach. (c),(d) As in (a) and (b), but for the predicted period of 1950–2018. There are 69 gray lines in total and each year during 1950–2018 has one line. The black dashed lines denote correlation coefficients significant at the 0.01 level. Note that in (d) the time length for the training is 66 years, leading to a lower threshold of the significance.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

We also perform sensitivity experiments for 1980–2018 by 1) applying the spatial average approach (“region 2” minus “region 1”; represented by domains of 20°S–10°N, 150°–90°W, and 20°–40°N, 120°E–150°W, respectively), 2) using the leading PC of the Pacific SST, and 3) enlarging the domain and considering the effect of the Atlantic (30°S–65°N, 120°E–10°W). The resultant correlation coefficients in the first two experiments are much lower than those in Fig. 3, while those in the third experiment are similar. Additionally, we compute the correlation between the streamflow and other climatic indices (the PDO, SOI, and AMO). Results show that the streamflow is positively (negatively) correlated with PDO (AMO) index with the highest correlation of 0.41 at LD1 (−0.44 at LD6), while the correlation with SOI index is quite low (the highest correlation of −0.35 at LD12). All these results are summarized in Table S3.

c. Seasonal and extended seasonal predictions

In this section, we perform seasonal predictions for the UCRB streamflow. First, we apply the statistical forecast models in association with the leave-three-out approach to predict the UCRB streamflow (for 1980–2018) using normalized soil moisture and SWE indices only. Figure 6a shows correlation coefficients between the predicted and observed streamflow from LD0 to LD12. For the stepwise linear regression and neural network models, the Pearson correlation is much higher than that of the autoregression (the baseline of the prediction skill), especially for LD0–LD3 (>0.60 vs ~0.50). However, the prediction skill drops rapidly afterward. We also compare the MAPE in Fig. 6b with official forecasts from CBRFC, which predicted the streamflow at Lake Powell (NWS ID: GLDA3) and calculated the MAPE for the period of 1980–2010 from LD0 to LD3. The error in our predictions is generally smaller than theirs (gray line). The HSS of predictions of all years and anomalous years (with magnitude greater than one standard deviation) ranges in 50%–80% and 90%–100%, respectively, for the lead time of LD0–LD3 (Figs. 6c,d). An HSS of 50% (black dashed line) indicates a skillful prediction (e.g., Jury et al. 1999). These results suggest that hydrologic memory provided by soil moisture and snow storage is less than 4 months.

Fig. 6.
Fig. 6.

(a) Correlation coefficients between the predicted and observed natural flow from LD0 to LD12 for the period of 1980–2018. The red and blue lines respectively denote results from the neural network (ensemble mean) and stepwise linear regression using soil moisture and SWE indices as predictors. Shading represents the spread of the minimum and maximum values of 10 ensembles of the neural network. The green dashed line denotes results of the autoregression model. (b)–(d) As in (a), but for MAPE (%), HSS (%), and HSS (%) for anomalous years (magnitude greater than one standard deviation), respectively. The gray solid line in (b) denotes results in CBRFC forecasts. The horizontal black dashed lines in all panels indicate a skillful prediction. Lead times to the left of the vertical black dashed lines show good prediction skills.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

In addition, we examine prediction skills when incorporating a normalized precipitation index into the forecast models. The correlation between precipitation and soil moisture (SWE) varies in 0.15–0.30 (0.10–0.50) for LD0–LD4. Consistent with the correlation in Fig. 2b, there is a slight improvement of prediction skills in LD4 (Fig. S8). Snowmelt is not used as a predictor even though the averaged correlation coefficient between snowmelt and streamflow is statistically significant for LD3 (Fig. 2a). The reason is that snowmelt has a high correlation with precipitation for LD3 (0.72). Surface temperature and evapotranspiration are not selected due to their low correlations with streamflow (the highest value ~0.40) (Figs. 2c,d).

Next, we investigate the potential for longer-lead predictions. We apply the stepwise linear regression (reduced to a simple regression with PSPs alone) and neural network models to predict the streamflow using PSPs only. For the period of 1980–2018, the Pearson correlation is generally between 0.40 and 0.60 for both the retrospective and leave-three-out approaches (Figs. 7a,e), while there is an obvious decrease for the retrospective approach after LD7, consistent with a weaker correlation between the SST and streamflow thereafter (Figs. 3e–g). The Pearson correlation of the autoregression model for the lead time longer than 4 months is below 0.20 (green line in Fig. 6a). Using the retrospective approach, the MAPE is lower than 27% for LD0–LD2 and LD6–LD9. HSS for all years and anomalous years vary in 50%–70% and 60%–90%, respectively, for LD0–LD2 and LD6–LD9 (Figs. 7b–d). Skills for LD4 and LD10–LD12 are quite low (Figs. 7a–d). Thus, PSPs can provide skillful prediction for both seasonal (LD0–LD2) and extended seasonal predictions (LD6–LD9). The prediction skills between the two forecast models are similar, indicating a largely linear system between SST and streamflow.

Fig. 7.
Fig. 7.

(a)–(d) As in Fig. 6, but using PSPs as the predictor with the retrospective approach for the period of 1980–2018. (e)–(h) As in (a)–(d), but with the leave-three-out approach.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

Figure 8 and Fig. S9 show the error of predicted streamflow using the two approaches. The total natural flow with large magnitudes (see Fig. 1c for the magnitude) is underestimated, whereas the flow with small magnitudes is overestimated by the two models. We also calculate the probability distribution function (PDF; %) for the observed and predicted streamflow (Figs. S10 and S11). The two forecast models overestimate the probability of neutral years (with total flow ~9–15 billion m3) by nearly 100% for most lead times. The probability of wet and dry years (with total flow greater and less than 18 and 7 billion m3, respectively) are underestimated, indicating that statistical models tend to make more “central” predictions. For the longer predicted period (1950–2018), both approaches show some skills for long-lead predictions, but skills in the retrospective approach are generally lower than the leave-three-out one (Fig. 9).

Fig. 8.
Fig. 8.

(a) The error (predicted flow minus the observation; unit: 109 m3) of total natural flow during April–July at Lees Ferry for the neural network (red; ensemble mean) and stepwise linear regression (blue) at LD0 from 1980 to 2018 using PSPs as the predictor with the retrospective approach. (b)–(m) As in (a), but for LD1, LD2, …, and LD12, respectively.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

Fig. 9.
Fig. 9.

As in Fig. 7, but for the period of 1950–2018.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

Finally, we apply the two models to predict the streamflow using four predictors (soil moisture, SWE, precipitation, and PSPs). To be consistent with land surface and atmospheric variables, PSPs derived from the leave-three-out approach for 1980–2018 is used here. For predictions from LD0 to LD3, the Pearson correlation is around 0.80, indicating a very high prediction skill (Fig. 10a). The MAPE in our two forecast models is much smaller than that of official CBRFC forecasts for LD1–LD3, especially for the neural network (Fig. 10b). Compared to Fig. 6, the prediction skill is largely improved relative to the prediction using only soil moisture and SWE as predictors for both models, especially for the lead time greater than 3 months. For LD5–LD12, the skills of the neural network are much lower than those of the stepwise linear regression, since the low-correlation indices (i.e., soil moisture, SWE, and precipitation) are used as predictors in the neural network and the sequential forward selection approach is not applied in this model. For LD5–LD12 of the stepwise linear regression, prediction skills with four predictors are similar to those with PSPs only (blues lines in Fig. 10 vs Figs. 7e–h), indicating that such skills are mainly from the Pacific SST. For LD0–LD3, the errors of the predicted streamflow agree with the high skills using the four predictors (Fig. 11) and are smaller than those in Fig. 8.

Fig. 10.
Fig. 10.

As in Fig. 6, but using soil moisture, SWE, precipitation, and PSPs (with the leave-three-out approach) as predictors.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

Fig. 11.
Fig. 11.

As in Fig. 8, but using soil moisture, SWE, precipitation, and PSPs (with the leave-three-out approach) as predictors.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

Overall, our results suggest that using PSPs can improve long-lead prediction skills. For seasonal prediction (LD0–LD3), soil moisture, SWE and precipitation within the UCRB and PSPs show better prediction skills than those using only SWE and soil moisture. For extended seasonal prediction (LD6–LD9), land surface and atmospheric variables do not provide significant predictability and PSPs alone show moderate prediction skills. The comparison of the prediction skills among various combinations of the predictors, including 1) soil moisture and SWE; 2) soil moisture, SWE, precipitation, and PSPs; 3) soil moisture, SWE, precipitation, and PDO; and 4) soil moisture, SWE, precipitation, and SOI using the stepwise linear regression, is provided in Fig. S12. The result suggests that the skills for the long-lead prediction with PSPs are superior to those with standard SST index (e.g., PDO and SOI), highlighting the advantage of PSPs derived in this study.

d. Dynamical patterns associated with the streamflow

Given that the Pacific SST provides long-lead prediction of the streamflow, we further examine dynamical patterns (during the period of 1980–2018) associated with the UCRB streamflow. Figures 12a, 12c, 12e, and 12g show a composite of SST anomalies for LD0–LD3, LD4–LD6, LD7–LD9, and LD10–LD12, respectively, for anomalous years (magnitude of normalized flow greater than one standard deviation; anomalies in positive years minus those in negative years). In general, the composite SST anomaly with a cold west–warm east pattern is consistent with the negative west–positive east pattern of correlation shown in Fig. 3, suggesting that anomalous years of the streamflow largely contribute to such correlation.

Fig. 12.
Fig. 12.

(a) Composite of SST anomaly (unit: °C) during LD0–LD3 for anomalous years (magnitude of normalized flow greater than one standard deviation; anomalies in positive years minus those in negative years). Contours are significant at the 0.05 level. (b) As in (a), but for geopotential height at 250 hPa (shading; unit: m) and vertically integrated water vapor flux (vectors; unit: kg m−1 s−1). Contours are significant at the 0.05 level. (c)–(h) As in (a) and (b), but for composites during LD4–LD6, LD7–LD9, and LD10–LD12, respectively.

Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0824.1

During spring of the preceding year (LD10–LD12), a meridionally oriented tripole in geopotential height is associated with moisture flux originating from the tropical Pacific toward the southwestern United States (Fig. 12h). The moisture transport becomes weak during summer (LD7–LD9), accompanied by a retreat of the positive SST anomaly over the central Pacific toward the west coast of South America (Figs. 12e,g). During fall (LD4–LD6), wave train patterns dominate over the Northern Hemisphere (Fig. 12d) and are responsible for downstream propagation of Rossby wave energy (e.g., Zhao et al. 2018, 2020; Zhao and Deng 2020). The composite SST anomaly displays a zonally extended tripole structure in the midlatitude North Pacific (Fig. 12c), bearing some similarity to a Pacific extreme pattern, which has been used to make skillful statistical predictions of U.S. summer heat waves (McKinnon et al. 2016). Finally, during winter before the runoff season (LD0–LD3), the PDO-like SST anomaly (Fig. 12a) is accompanied by the moisture transport from the western Pacific to the southwestern United States (Fig. 12b). Future studies need to be aware of the role of these large-scale atmospheric circulation patterns in determining whether the apparent predictability suggested by our statistical predictions represents real physical predictability.

4. Summary

This study investigates the UCRB streamflow predictions using multiple predictors and provides a long-lead seasonal prediction using stepwise linear regression and neural network forecast models. Predictors from monthly land surface and atmospheric variables within the UCRB are identified by calculating correlation coefficients between these basin-averaged variables and UCRB streamflow. Soil moisture and SWE indices show the highest correlations than other predictors for forecast lead times from 1 to 4 months. Precipitation index is significant for the lead time of 3 and 4 months. In addition, PSPs are developed, which take advantage of a dipole structure in the correlation map between the Pacific SST and UCRB streamflow, to improve predictions with lead times greater than 4 months.

The normalized soil moisture and SWE indices are first applied to the two forecast models to predict the UCRB streamflow. Prediction skills are generally good with correlation > 0.60 when the forecast is initialized using observations after November, but skills decrease significantly for longer lead times. The introduction of a precipitation index slightly improves prediction skills. To further investigate the potential for longer-lead predictions, PSPs alone are used for prediction. We apply two cross-validated approaches (retrospective and leave-three-out) for two predicted periods (1980–2018 and 1950–2018) to examine the robustness of the results and impacts of artificial skills induced by predictor screening and sampling sizes. The two models show moderate skills when the forecast is initialized using observations in June of the previous year (correlation ~0.50 with retrospective approach for 1980–2018). Similar prediction skills between the two models suggest a largely linear system between SST and streamflow. Finally, four predictors including soil moisture, SWE, precipitation, and PSPs are selected and they show high prediction skills (correlation ~0.80) for lead times less than 4 months.

5. Discussion

Compared to previous studies that predict the UCRB streamflow, this study derives PSPs in a different manner, apply different forecast models, and use high-resolution SST data. For example, in Switanek et al. (2009), SSTs were spatially averaged on 10° latitude × 20° longitude moving windows (in rectangular domains), which include grids with significant correlation with the discharge volume of the Gunnison River basin. In our study, only grid points with correlation coefficients exceeding the 0.05 significant level are used to compute PSPs. This approach ensures that we select all significant grid points, leading to PSPs highly correlated with the streamflow. The skills of the long-lead prediction with PSPs are superior to those with standard SST index (e.g., PDO and SOI). Our study provides a new benchmark for predicting the UCRB streamflow using the Pacific SST information. In conclusion, the results in this study 1) corroborate earlier findings showing that the use of the Pacific SST information can add long-lead predictability to the UCRB streamflow prediction; 2) suggest PSPs provide an advantage over standard oceanic index, such as PDO or ENSO index; and 3) provide useful climate information for water resource managers in time to act within existing fiscal management protocols.

Ongoing and future work includes further improving prediction skills by tuning neural network parameters/functions and incorporating other variables into the model. Furthermore, our results suggest that the correlation between SST and streamflow are stronger in recent decades for long lead times. The long-lead prediction skills shown here are probably associated with the emergence of the stronger correlations in recent decades. It is still an open question to understand whether such correlations will continue or reverse and how the change of the correlations influences long-lead predictions in the future. Finally, the high prediction skills shown by our statistical models emphasize a need to understand mechanisms behind statistical relationships among SSTs, large-scale atmospheric circulation patterns, and streamflow.

Acknowledgments

We thank the three anonymous reviewers for their insightful comments. We also thank Sarah Rose Worden for comments of the revised version of the manuscript. This study is supported by the California Department of Water Resources Grant (4600013129), NOAA Award (NA170AR4310123), and National Aeronautics and Space Administration (NASA) Climate Indicators and Data Products for Future National Climate Assessment (NNX16AN12G).

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