Abstract

Singular value decomposition (SVD) is used to identify the variability common to global sea surface temperatures (SSTs) and water-balance-modeled water-year (WY) runoff in the conterminous United States (CONUS) for the 1900–2012 period. Two modes were identified from the SVD analysis; the two modes explain 25% of the variability in WY runoff and 33% of the variability in WY SSTs. The first SVD mode reflects the variability of the El Niño–Southern Oscillation (ENSO) in the SST data and the hydroclimatic effects of ENSO on WY runoff in the CONUS. The second SVD mode is related to variability of the Atlantic multidecadal oscillation (AMO). An interesting aspect of these results is that both ENSO and AMO appear to have nearly equivalent effects on runoff variability in the CONUS. However, the relatively small amount of variance explained by the SVD analysis indicates that there is little covariation between runoff and SSTs, suggesting that SSTs may not be a viable predictor of runoff variability for most of the conterminous United States.

1. Introduction

It is important to understand the climatic driving forces of water supply variability to improve water management and seasonal water supply forecasts. A number of studies have indicated that sea surface temperatures (SSTs) are an important driver of hydroclimatic variability in the conterminous United States (CONUS) (Redmond and Koch 1991; Mantua et al. 1997; Enfield et al. 2001; Hoerling and Kumar 2003; McCabe et al. 2004; Sutton and Hodson 2005; Schubert et al. 2004; Seager et al. 2005; Cook et al. 2007; Goodrich 2007). Sea surface temperature indices that appear to be strongly related to U.S. hydroclimatic variability are the El Niño–Southern Oscillation (ENSO), the Pacific decadal oscillation (PDO), and the Atlantic multidecadal oscillation (AMO).

ENSO is an important source of interannual hydroclimatic variability (Trenberth 1976, 1984, 1997; Horel and Wallace 1981; Namias and Cayan 1984; Ropelewski and Halpert 1986; Yarnal and Diaz 1986; Redmond and Koch 1991; McCabe and Dettinger 1999). In a widely cited study, Redmond and Koch (1991) identified significant correlations between the average June–November Southern Oscillation index (SOI, an index of ENSO) and winter precipitation in the western United States for the period 1934–85. Their analysis indicates positive correlations between the SOI and winter precipitation in the northwestern United States and negative correlations between the SOI and winter precipitation in the southwestern United States. Where these correlations are statistically significant and reliable, they have been used to make probabilistic forecasts of winter precipitation in the western United States from SOI (Redmond and Koch 1991; Kahya and Dracup 1994; Piechota and Dracup 1996). Persistent ENSO events also may be a source of decadal-to-multidecadal hydroclimatic variability (Seager et al. 2005).

The PDO (Mantua et al. 1997) represents low-frequency changes in the SST patterns of the Pacific Ocean and is computed from SSTs in the Pacific Ocean north of 20°N. The PDO is generally correlated with the ENSO and incorporates subtle multiple-frequency responses to ENSO as well as responses to extratropical ocean circulation dynamics (Gu and Philander 1997; Alexander et al. 1999; Newman et al. 2003). Thus, some argue that the PDO may be nothing more than a low frequency realization of ENSO. However, the PDO index does not always correlate well with ENSO indices (Mantua et al. 1997) and may explain modulations in the strength of ENSO teleconnections to U.S. hydroclimate (Cayan et al. 1998; Cole and Cook 1998; Gershunov and Barnett 1998; McCabe and Dettinger 1999; 2002).

The AMO is an index of SSTs in the North Atlantic Ocean between the equator and 70°N (Enfield et al. 2001). Recent research has indicated that multidecadal variability in North Atlantic climate is dominated by a single mode of SST variability (Sutton and Hodson 2003; Knight et al. 2006). Sutton and Hodson (2005) provide evidence that basinwide changes in the North Atlantic Ocean are an important driver of decadal to multidecadal variations in the summer climate of North America and Europe. In addition, the relations they report between the North Atlantic Ocean and North American climate are consistent with the findings of McCabe et al. (2004) obtained by analyzing observed precipitation.

Runoff, defined herein as total flow per unit area delivered to streams and rivers, integrates the variability of both temperature and precipitation and is a useful indicator of water supply and water supply variability. Previous studies have identified modes of joint variability in global SSTs, global runoff, and global Palmer drought severity index (PDSI) (McCabe and Palecki 2006; McCabe and Wolock 2008; Apipattanavis et al. 2009). These studies, however, have provided only spatially coarse information about the relations between SSTs and runoff in the CONUS. The objective of this paper, in contrast, is to complete a more spatially refined analysis of the climate factors that drive runoff variability in the CONUS and to determine if SSTs are viable for forecasting runoff variability in this geographic region. Additionally, this study will determine if similar, different, or additional SST relations with runoff are identified in an analysis of just CONUS runoff compared to a global runoff analysis.

2. Data and methods

Because there are few long-term (50–100 yr in length) measurements of streamflow (or runoff) in the CONUS, for this analysis we computed runoff using a monthly water balance (WB) model (McCabe and Wolock 1999; Wolock and McCabe 1999). The WB model uses an accounting procedure to compute the allocation of water among various components of the hydrologic system based on monthly time series of precipitation (P), temperature (T), and potential evapotranspiration (PET) (McCabe and Wolock 1999; Wolock and McCabe 1999; McCabe and Markstrom 2007; McCabe and Wolock 2008). The WB model includes the concepts of climatic water supply and demand, seasonality in climatic water supply and demand, snow accumulation and melt, and soil moisture storage (Wolock and McCabe 1999; McCabe and Markstrom 2007; McCabe and Wolock 2008, 2011a,b).

a. Data

Monthly temperature and precipitation data provided on a 4-km × 4-km grid for the period January 1895 through December 2012 were obtained from the Parameter-Elevation Regression on Independent Slopes Model (PRISM) dataset (www.ocs.orst.edu/prism/). Temperature and precipitation data for all grid cells in the CONUS (481 639 PRISM grid cells) were used as input to a monthly time step WB model to estimate monthly runoff, where runoff is defined as the flow per unit area delivered from each grid cell to streams and rivers in units of millimeters per month. In the analysis presented here, runoff estimates for 1895–98 were discarded to avoid effects of initial model conditions.

For computational efficiency in statistical analyses, the runoff estimates from the WB model were aggregated to the U.S. Geological Survey Hydrologic Unit Code 8 (HUC8). This provided 2109 HUC8s for analysis in the CONUS (Fig. 1a). The monthly runoff estimates were aggregated to compute mean water-year (WY) runoff for each HUC8. A water year is the 12-month period 1 October through 30 September, designated by the calendar year in which it ends.

Fig. 1.

Map of (a) center points of USGS HUC8s and (b) SST grid cells.

Fig. 1.

Map of (a) center points of USGS HUC8s and (b) SST grid cells.

Monthly sea surface temperature data were obtained from the Kaplan extended dataset of monthly SSTs (Kaplan et al. 1998; www.esrl.noaa.gov/psd/data/gridded/data.kaplan_sst.html). The SST data are on a 5° resolution grid and span the period 1856 to the present. The monthly SST data were aggregated to compute mean WY SSTs for the 5° resolution grid. The number of grid cells with complete data for the 1900–2012 period on a global basis is 1207 (Fig. 1b).

b. Water balance model

Climate inputs to the WB model are monthly P and T; the latter is used to compute monthly potential evapotranspiration using the Hamon equation (Hamon 1961). The Hamon PET equation has been evaluated and compared with a number of other models and is considered a reliable monthly PET model (Lu et al. 2005; Legates and McCabe 2005; Federer et al. 1996; Vörösmarty et al. 1998). In a study of five PET models for use with global water balance models, Federer et al. (1996) found that estimates of PET from the Hamon model agreed with estimates from other models across a wide range of climates. Vörösmarty et al. (1998) compared 11 different PET models for a wide range of climatic conditions across the CONUS. They found that the Hamon model was comparable to more input-detailed models and concluded that the Hamon model produced satisfactory estimates of PET. They also stated that the Hamon model appeared to have an appropriate empirical response to the interaction of vegetation type and climate.

In the WB model, monthly temperature also is used to determine the proportions of monthly precipitation that are rain and snow. Precipitation that is snow is accumulated in a snowpack; rainfall is used to compute direct runoff, actual evapotranspiration (AET), soil moisture storage recharge, and surplus, which eventually becomes runoff. When rainfall for a month is less than PET, AET is equal to the sum of rainfall, snowmelt, and the amount of moisture that can be removed from the soil. The fraction of soil moisture storage that can be removed through AET linearly declines as soil moisture storage decreases; that is, water becomes more difficult to extract from the soil as the soil becomes drier and less moisture is available for AET. When rainfall (and/or snowmelt) exceeds PET in a given month, AET is equal to PET; water in excess of PET replenishes soil moisture storage. When soil moisture storage reaches capacity during a given month, the excess water becomes surplus and eventually becomes runoff. For additional details of the WB model, see McCabe and Markstrom (2007). Similar WB models have been used successfully in other studies (McCabe and Ayers 1989; Legates and Mather 1992; Wolock and McCabe 1999; Legates and McCabe 2005; McCabe and Wolock 2008, 2011a,b).

The WB model parameters used for this study include 1) a parameter that specifies the fraction of monthly P that becomes direct runoff (Rdirect), 2) temperature thresholds that determine the proportions of monthly P that are rain (Train) and/or snow (Tsnow), 3) a snowmelt factor (a), and 4) a parameter (rfactor) that specifies how much surplus in a month becomes runoff. The parameter values used in all simulations were Rdirect = 0.05, Train = 7.0°C, Tsnow = −4.0°C, a = 0.47, and rfactor = 0.5. These values were taken from a previous application of the model (McCabe and Wolock 2011a,b) and are similar to values reported by others. For example, Tarboton et al. (1991) reported Train = 3.3°C and Tsnow = −1.1°C for use with a monthly time step snow model. Additionally, the snowmelt rate factor (a) value of 0.47 is within the range of values reported by Rango and Martinec (1995). Only soil moisture storage capacity varied spatially, and this parameter was computed using the available water capacity values from the State Soil Geographic Data Base (STATSGO) dataset and by assuming a 1-m vegetation rooting depth (http://websoilsurvey.sc.egov.usda.gov/App/HomePage.htm).

The WB model has been described, evaluated, and verified in several previous studies (McCabe and Wolock 1999; McCabe and Wolock 2008; Hay and McCabe 2010; Gray and McCabe 2010; McCabe and Wolock 2011a,b). Results of these verifications indicate that the WB model is sufficiently accurate to reproduce the considerable year-to-year variability in runoff for locations across the CONUS representing a range of climatic and physiographic regions. For example, McCabe and Wolock (2011b) compared WB model-estimated runoff and measured runoff for 735 basins across the CONUS. For these sites, the period-of-record requirement was at least 30 years of streamflow data during 1951–2008. Comparison of the measured and estimated monthly runoff indicated that the WB model reliably simulated the temporal variability of monthly runoff for most of the stream gauges. The distribution of correlation values between WB estimated and measured monthly runoff for the 735 stream gauges had a median value of 0.78, with a 25th percentile value of 0.61 and a 75th percentile value of 0.87. Additionally, the mean bias for the 735 stream gauges was 1 mm, with a 25th percentile of −3 mm and a 75th percentile of 5 mm. Given that on a WY basis, runoff = P − AET, the ability of the WB model to simulate runoff also suggests that the model reliably estimates WY AET.

Figure 2 illustrates a comparison of measured WY runoff with WB-estimated WY runoff for several basins in the CONUS that occur over a range of physiographic and climatic regions for the period 1940 through 2007 (this period is common to all of the selected basins) (Fig. 2). The evaluation was performed for these basins because 1) these basins are minimally influenced by anthropogenic disturbances, 2) these basins include at least 60 years of complete runoff records, and 3) reliable climate inputs for the WB model (i.e., monthly temperature and precipitation data) and reliable measurements of runoff are available for analysis.

Fig. 2.

Time series of measured and WB model–estimated WY runoff for river basins in the CONUS across a range of physiographic and climatic regions.

Fig. 2.

Time series of measured and WB model–estimated WY runoff for river basins in the CONUS across a range of physiographic and climatic regions.

The comparisons for the selected basins indicate good correlations, ranging from 0.80 to 0.96, all of which are statistically significant at a 99% confidence level (p < 0.01). Three of the basins, however, indicate noticeable bias between measured and WB model-estimated WY runoff (i.e., sites 3, 4, and 5; Fig. 2). Biases in WB model estimates, such as those for sites 3, 4, and 5, are likely due to hydrologic processes not included in the WB model, such as the effect of deep groundwater contributions to runoff and in-stream water losses in channels located in arid areas. Other substantial biases occur in locations where runoff is generated by short-duration high-intensity precipitation events that are not resolved on a monthly time step. Additionally, uncertainties in the P and T data used as inputs to the WB model may contribute to the biases. Although there are some biases in the WB model estimates of WY runoff, the strong temporal correlations between WB model estimated and measured runoff suggest that the WB model reliably simulates the response of runoff to temporal variability in temperature and precipitation. Since the focus of this study is on temporal variability in runoff, the WB model is appropriate for the analyses presented.

For the analyses presented in this study, WY runoff estimates for the years 1900 through 2012 are used. The WY runoff and SST time series were detrended before analysis in order to focus on variability not related to long-term trends. Linear trends accounted for only a small percentage of variance in runoff for most of the HUC8s. The median variance accounted for by long-term linear trends in runoff was 2.2%, with a 25th percentile of 0.06% and a 75th percentile of 5.4%. In contrast, linear trends accounted for a substantial amount of variability in SSTs for a number of sites. The median variance accounted for by linear trends in SSTs was 21.4% with a 25th percentile of 6.6% and a 75th percentile of 38.2%. Additionally, all time series were converted to z scores to facilitate comparison between data types with different units.

c. Singular value decomposition

A singular value decomposition (SVD) of the joint runoff and SST datasets was performed to identify the common modes of variance between the runoff and SST data (Enfield and Alfaro 1999; McCabe and Palecki 2006). Singular value decomposition isolates dominant modes of cross-covariance between datasets (Enfield and Alfaro 1999) and has been used in a number of climatic studies (Enfield and Alfaro 1999; McCabe and Palecki 2006; McCabe and Wolock 2008).

The expansion coefficients (time series) of the dominant SVD modes and the patterns of heterogeneous correlations between the SVD modes and WY runoff and WY SST time series were examined to identify the SST processes related to the variability in runoff.

3. Results and discussion

Two modes were retained from the SVD analysis. The total variability explained by the first two SVD modes is 25% for WY runoff and 33% for WY SSTs. The first SVD mode explains 11% of the variability in WY runoff and 20% of the variability in WY SSTs. The second SVD mode explains 14% of the variability in WY runoff and 13% of the variability in WY SSTs. These two SVD modes were retained because each explain at least 10% of the variability in WY runoff and WY SSTs.

The correlations between the SVD1 expansion coefficients (time series) and time series of WY runoff indicate negative correlations in the northwestern and northeastern United States, and positive correlations in the southwestern United States (Fig. 3a). The correlations of SVD1 expansion coefficients with time series of WY SSTs show positive correlations in the Indian Ocean and the eastern tropical Pacific Ocean and negative correlations in the north-central Pacific Ocean and the central South Pacific Ocean (Fig. 3c). The correlation between the SVD1 expansion coefficients for runoff (Fig. 4a) and SSTs (Fig. 4b) is 0.74 (p < 0.01).

Fig. 3.

Maps of heterogeneous correlations between the expansion coefficients for the first two modes (SVD1 and SVD2) from a singular value decomposition of WY runoff (R) and WY SSTs and time series of WY runoff and WY SSTs.

Fig. 3.

Maps of heterogeneous correlations between the expansion coefficients for the first two modes (SVD1 and SVD2) from a singular value decomposition of WY runoff (R) and WY SSTs and time series of WY runoff and WY SSTs.

The pattern of correlations for WY SSTs (Fig. 3c) is similar to the SST pattern associated with ENSO (and the PDO), and the pattern of runoff correlations (Fig. 3a) is similar to the pattern of the effects of ENSO (and PDO) on U.S. hydroclimate (Redmond and Koch 1991; McCabe and Dettinger 1999). To examine the relations of ENSO (and PDO) with runoff and SSTs further, we computed correlations between an index of ENSO (i.e., Niño-3.4 SSTs, computed as the average of SSTs for the region 5°S–5°N, 170°–120°W) and the PDO index with the SVD1 expansion coefficients for runoff and SSTs (values of the PDO index were obtained from http://jisao.washington.edu/pdo/PDO.latest). Times series of both WY Niño-3.4 SSTs and WY PDO were detrended and converted to z scores for use in the remainder of the analyses. The resultant correlations between WY Niño-3.4 SSTs and the expansion coefficients of SVD1 for runoff and SSTs are 0.68 (p < 0.01) and 0.92 (p < 0.01), respectively (Figs. 4 and 5). The correlations between WY PDO and the expansion coefficients of SVD1 for runoff and SSTs are 0.53 (p < 0.01) and 0.69 (p < 0.01), respectively. These correlations strongly suggest that SVD1 reflects the common variance in runoff in the CONUS related to ENSO and PDO. The correlations also indicate that SVD1 is more highly correlated with Niño-3.4 SSTs than with PDO. Since ENSO and PDO are related, partial correlations between SVD1 for WY runoff and WY Niño-3.4 SSTs and WY PDO were computed to remove the effects of the interrelationships between ENSO and PDO. The partial correlation of WY Niño-3.4 SSTs with SVD1 for WY runoff, controlling for WY PDO, is 0.55 (p < 0.01), whereas the partial correlation between WY PDO and SVD1 for WY runoff, controlling for WY Niño-3.4 SSTs, is 0.26 (p < 0.01). The partial correlations indicate much stronger correlation of SVD1 for WY runoff with WY Niño-3.4 SSTs than with WY PDO. However, the partial correlation with WY PDO is statistically significant at p < 0.01, and thus there appear to be some effects of WY PDO on WY runoff that are not represented by WY Niño-3.4 SSTs.

Fig. 4.

Expansion coefficients for the first two modes (SVD1 and SVD2) from a singular value decomposition of WY runoff and WY SSTs. Also plotted are time series of z scores of WY Niño-3.4 SSTs, PDO, and the AMO.

Fig. 4.

Expansion coefficients for the first two modes (SVD1 and SVD2) from a singular value decomposition of WY runoff and WY SSTs. Also plotted are time series of z scores of WY Niño-3.4 SSTs, PDO, and the AMO.

Fig. 5.

Scatterplots comparing the expansion coefficients for the first two modes (SVD1 and SVD2) from a singular value decomposition of WY runoff and WY SSTs and z scores of WY Niño-3.4 SSTs, PDO, and AMO. Correlation coefficients (r) for each comparison are listed in the lower right-hand corner of each scatterplot. All correlations are significant at the 99% confidence level.

Fig. 5.

Scatterplots comparing the expansion coefficients for the first two modes (SVD1 and SVD2) from a singular value decomposition of WY runoff and WY SSTs and z scores of WY Niño-3.4 SSTs, PDO, and AMO. Correlation coefficients (r) for each comparison are listed in the lower right-hand corner of each scatterplot. All correlations are significant at the 99% confidence level.

The correlations between the SVD2 expansion coefficients and WY runoff time series for the CONUS indicate negative correlations for most of the CONUS (Fig. 3b). The clearest signal indicated by the correlations of SVD2 expansion coefficients with WY global SSTs are positive correlations across the North Atlantic Ocean (Fig. 3d). The correlation between the SVD2 expansion coefficients for runoff (Fig. 4e) and SSTs (Fig. 4f) is 0.45 (p < 0.01).

The positive SST correlations between SVD2 expansion coefficients and SSTs in the North Atlantic Ocean suggest that this SVD mode represents the variability of the AMO (Enfield et al. 2001; McCabe et al. 2004; Sutton and Hodson 2005). Values of mean WY AMO were computed as the average of WY SSTs for the region 0°–70°N, 60°–10°W. As with other datasets used in this study, the time series of WY AMO was detrended and converted to z scores. Correlations between the time series of WY AMO and SVD2 expansion coefficients for runoff and SSTs are 0.35 (p < 0.01) and 0.89 (p < 0.01), respectively. Additionally, the correlations between SVD2 expansion coefficients and runoff (Fig. 3b) indicate that some of the strongest relations between AMO and runoff are for the Mississippi River basin and the northern Rocky Mountains (including the Upper Colorado River basin). The relations between AMO and the hydroclimate of the Mississippi River basin also were reported by Enfield et al. (2001) and Rogers and Coleman (2003), and the relations between AMO and runoff in the Upper Colorado River basin are consistent with those reported by McCabe et al. (2007) and Nowak et al. (2012).

Time series (Fig. 4) and scatterplots (Fig. 5) comparing the SVD expansion coefficients for runoff and SVD and time series of Niño-3.4, PDO, and AMO illustrate the strength of the relations between these variables. Correlations between the SVD1 expansion coefficients and Niño-3.4 SSTs and PDO are all statistically significant at p < 0.01. Similarly, the correlations between the SVD2 expansion coefficients and AMO also are statistically significant at p < 0.01.

To examine the possible relations among ENSO, PDO and SVD1 and between AMO and SVD2, a comparison of the primary spectral frequencies of these time series was performed. An analysis of the dominant spectral frequencies in these time series using Morlet wavelet analysis (Torrence and Compo 1998) provides an additional technique to determine similarity among the time series. The wavelet analyses for the SVD1 expansion coefficients for runoff and SST (Figs. 6a,b) indicate a relatively large amount of variability at about 3–7 yr, which reflects ENSO variability (Fig. 6c). Additionally, the wavelet analyses for SVD1 (Figs. 6a,b) indicate substantial variability at low frequencies at approximately 50 yr. This low frequency variability matches well with the variability of the PDO (Fig. 6d).

Fig. 6.

Wavelet power spectrum of the expansion coefficients for the first mode (SVD1) from a singular value decomposition of WY runoff and WY SSTs and WY Niño-3.4 SSTs and the PDO. Plots show the relative amount of variance (i.e., power) contained in different portions of the frequency domain over time. Relative power increases from blue to red.

Fig. 6.

Wavelet power spectrum of the expansion coefficients for the first mode (SVD1) from a singular value decomposition of WY runoff and WY SSTs and WY Niño-3.4 SSTs and the PDO. Plots show the relative amount of variance (i.e., power) contained in different portions of the frequency domain over time. Relative power increases from blue to red.

The wavelet analyses for the SVD2 expansion coefficients for runoff and SSTs indicate dominant variability common to runoff and SSTs at a period greater than 50 yr (Figs. 7a,b). This low frequency variability appears to be similar to the low frequency variability of the AMO (Fig. 7c). The wavelet analysis for SVD2 for runoff indicates other relatively strong periods of variability that are not found for SVD2 for SSTs or for the AMO. This result suggests that there is additional variability in SVD2 for runoff that is not represented by the variability in SVD2 for SSTs or AMO.

Fig. 7.

Wavelet power spectrum of the expansion coefficients for the second mode (SVD2) from a singular value decomposition of WY runoff and WY SSTs and WY AMO. Plots show the relative amount of variance (i.e., power) contained in different portions of the frequency domain over time. Relative power increases from blue to red.

Fig. 7.

Wavelet power spectrum of the expansion coefficients for the second mode (SVD2) from a singular value decomposition of WY runoff and WY SSTs and WY AMO. Plots show the relative amount of variance (i.e., power) contained in different portions of the frequency domain over time. Relative power increases from blue to red.

The pattern of correlations of SVD1 with time series of WY runoff (Fig. 8a) is similar to the pattern of correlations of WY Niño-3.4 SSTs (and WY PDO) with time series of WY runoff (Figs. 8b,c). The correlation between the pattern of SVD1 correlations and the pattern of WY Niño-3.4 correlations is 0.91 (p < 0.001) and the correlation between the pattern of SVD1 correlations and the pattern of correlations for WY PDO is 0.85 (p < 0.001) (Fig. 8). The similarity in the patterns of correlations further supports the conclusion that SVD1 reflects the influence of ENSO (and PDO) on WY runoff in the CONUS. Similarly, a comparison of a map of correlations between WY runoff and the expansion coefficients for SVD2 and a map of correlations between WY runoff and WY AMO also indicates similar patterns (Figs. 8d,e). The correlation between these two map patterns is 0.49 (p < 0.001). Although the correlations between time series of WY runoff and WY Niño-3.4 (and PDO) and WY AMO indicate patterns that are similar to the patterns of correlations between WY runoff and the expansion coefficients of SVD1 and SVD2, the correlations between WY runoff and Niño-3.4 (and PDO) (Figs. 8b,c) and AMO (Fig. 8e) are weaker than are the correlations between WY runoff and SVD1 and SVD2 expansion coefficients (Figs. 8a,d). Thus, although SVD1 and SVD2 are related to the effects of ENSO (and PDO) and AMO on WY runoff in the CONUS, the relations to these climate indices leave a substantial amount of variability in SVD1 and SVD2 that is not explained by Niño-3.4, PDO, and AMO.

Fig. 8.

Maps of correlations between time series of WY runoff (R) for sites in the CONUS and the expansion coefficients for the first two modes [(a) SVD1 and (d) SVD2] from a singular value decomposition of WY runoff and WY SSTs, and time series of WY (b) Niño-3.4 SSTs, (c) PDO, and (e) AMO.

Fig. 8.

Maps of correlations between time series of WY runoff (R) for sites in the CONUS and the expansion coefficients for the first two modes [(a) SVD1 and (d) SVD2] from a singular value decomposition of WY runoff and WY SSTs, and time series of WY (b) Niño-3.4 SSTs, (c) PDO, and (e) AMO.

The identification of ENSO and AMO as climatic drivers of the variance common to SSTs and runoff in the CONUS is similar to findings from other studies examining hydroclimatic variables (e.g., runoff and PDSI values) and SSTs at global spatial scales (McCabe and Palecki 2006; McCabe and Wolock 2008; Apipattanavis et al. 2009). For example, McCabe and Palecki (2006) found that the primary modes of decadal to multidecadal variability in global PDSI values and global SSTs are related to variability in the PDO, Indian Ocean SSTs, and the AMO. In a similar study of global annual PDSI values and global annual SSTs, Apipattanavis et al. (2009) reported that the dominant modes of joint variability in global PDSI and global SSTs in the twentieth century indicated a secular trend and variability related to ENSO. An additional significant mode of variability (for the Northern Hemisphere only) was related to the AMO. McCabe and Wolock (2008) examined decadal to multidecadal variability in global runoff and global SSTs. Results of their study indicated that the primary modes of variability common to global runoff and global SSTs (on decadal to multidecadal time scales) were a long-term trend, ENSO, and North Atlantic SSTs (i.e., AMO).

Other previous studies have shown that warm North Atlantic SSTs (+AMO) are associated with dry conditions in the CONUS, whereas cool North Atlantic SSTs (−AMO) are associated with wetter-than-average conditions in the CONUS (Enfield et al. 2001; Gray et al. 2003, 2004; Hidalgo 2004; McCabe et al. 2004; Sutton and Hodson 2003, 2005; McCabe and Palecki 2006). Additionally, previous research has indicated that cool Niño-3.4 SSTs (i.e., La Niña conditions) have been a significant, and possibly the primary, driver of drought in the CONUS (Schubert et al. 2004; Seager et al. 2005).

An additional analysis was performed to determine the amount of temporal variance in WY runoff for each HUC8 that is explained by WY Niño-3.4, WY PDO, and WY AMO. The amount of explained variance in WY runoff was determined through a regression analysis with WY runoff as the dependent variable and WY Niño-3.4, PDO, and AMO as the dependent variables. Results of these regressions indicate that the largest amount of variance in WY runoff explained by Niño-3.4 and AMO is found for HUC8s across the southern United States, particularly in New Mexico and Texas (Fig. 9). However, the percent explained variance in WY runoff is low for all HUC8s. The median percent explained variance is only 5%, with a 25th percentile of about 3% and a 75th percentile of 9% (the maximum explained variance for any HUC8 was only 31%).

Fig. 9.

Percent variance in WY runoff explained by WY Niño-3.4 SSTs, PDO, and AMO.

Fig. 9.

Percent variance in WY runoff explained by WY Niño-3.4 SSTs, PDO, and AMO.

Although tropical Pacific Ocean and North Atlantic Ocean SSTs influence the temporal and spatial variability of the hydroclimate of the CONUS, particularly on decadal and multidecadal time scales (Enfield et al. 2001; Gray et al. 2003; McCabe et al. 2004; Hidalgo 2004; Schubert et al. 2004; Seager et al. 2005; McCabe and Palecki 2006), the total variability in runoff explained by ENSO, PDO, and AMO on WY time scales is small. Thus, a substantial portion of the variability in WY runoff is not explained by WY SSTs.

4. Conclusions

The common variance in WY runoff simulated by a water balance model for the CONUS and WY global SSTs for the 1900–2012 period is identified by using SVD. Results indicated that there are two primary modes of common variance in these two datasets. The first mode is associated with ENSO and PDO variability and the second SVD mode is related to the variability of the AMO. From the perspective of explained variance, SST variability of the North Pacific Ocean, represented by ENSO and PDO variability, and of the North Atlantic Ocean, represented by AMO variability, appear to explain nearly the same amount of variance in WY runoff. These results for the CONUS are similar to those from previous studies of global runoff and indicate that for both the CONUS and the world as a whole the North Pacific and Atlantic Oceans are drivers of hydroclimate. However, on a WY time scale, SSTs have a relatively small amount of variance in common with WY runoff in the CONUS, which suggests that runoff, at least from the perspective of SSTs as the driving force, may be unpredictable on a WY time scale. A possible exception is runoff for the southern United States. In this region, the explained variance in WY runoff by ENSO, PDO, and AMO is larger than for any other region of the CONUS. Because these SST indices explain at least 20% of the variability in WY runoff in the southern United States and because SSTs change relatively slowly, these SST indices may be useful to provide forecasts of the tendency (greater than or less than average) of WY runoff for this region.

Acknowledgments

The authors thank Dr. David McGinnis (Montana State University) and three anonymous reviewers for helpful comments and suggestions.

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