Spatiotemporal Variation in the Continental US Streamflow in Association with Large-Scale Climate Signals Across Multiple Spectral Bands

Abstract

The study attempts to investigate the significant spatiotemporal variations in the continental United States’ streamflow as a response to large-scale climate signals across multiple spectral bands (SBs). Using non-parametric (long-term) trend and (abrupt) shift detection tests, coupled with discrete wavelet transform, 237 unimpaired streamflow stations were analyzed over a study period of 62 years (1951 to 2012), looking at the water year and seasonal data, along with three discrete SBs of two, four, and eight years. Wavelet coherence analysis, derived from continuous wavelet transform, determined the association between the regional streamflow patterns and three large-scale climate signals, i.e., El Niño Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), and Atlantic Multi-decadal Oscillation (AMO), across continuous SBs ranging from two to 16 years. The results indicated significant positive (negative) trends and shifts in the northeastern and north-central (northwestern) regions with an increase in the number of stations as the SBs increased. The spatiotemporal association between regional streamflow and the climate signals varied significantly (from no correlation, R_n²~ 0, to perfect correlation, R_n²~ 1.0) even amongst adjacent regions. Among the climate signals, ENSO showed the highest association (R_n²~ 1.0), having a consistent phase relationship with the regional streamflow patterns, especially in the higher SBs. PDO (with the least influence among the three signals) and AMO showed stronger associations, mostly in the lower SBs. These results may help explain the teleconnections between the climate signals and the US streamflow variations across multiple SBs, which may lead to improved regional flow regulations.

Appendices

Appendix A

The original water-year and seasonal data were decomposed into a set of relatively simpler subseries known as approximation coefficients (AC) and detail coefficients (DC) by passing a low pass and high pass filter, respectively. The resulting subseries corresponded to the lower frequencies and higher frequencies of the original time series. At each decomposition level, the resulting DC corresponded to the lower DS, while the resulting AC was further decomposed to obtain a new set of DC and AC. This process was continued until the ACs produced a sufficient resolution (certainty). Three DSs, named as DS2, DS4, and DS8 represented the time-series data at the SBs of two, four, and eight years, respectively. Based on the literature cited in the main text, the SBs were obtained at every 2ⁿ scale, where n is the decomposition level with an initial value of n = 1.0. Hence, two, four, and eight years corresponded to the first three decomposition levels for this study. Fig. 1 (right) shows that after three decompositions, the time series associated with the third AC hardly showed any presence of periodic behavior. In other words, the resolution or the amount of certainty in the wavelet time-frequency spectrum diminished as the decomposition levels (DSs) went higher.

Appendix B

Table 1 Number of stations with significant positive (Pos.) and negative (Neg.) trends under the Mann-Kendall (MK) test in water-year and seasonal data along with their decompositions

Table 2 Number of stations with significant positive (Pos.) and negative (Neg.) shifts under the Pettitt’s test in water year and seasonal data along with their decompositions

Appendix C

The spatial pattern of trends was more irregular with the seasons when compared to the water year trends. Nevertheless, seasons showed the presence of spatial coherence or region-specific trends (Fig. 5). In fall and its DSs, positive trends were mostly observed in the northeastern regions, whereas negative trends were prevalent in the northwestern regions (Fig. 5). Trends located on the extreme east and west regions, i.e., NE, MA, and PN, showed a higher rate of increase in the number of stations with trends compared to the central regions as the DSs went higher. Consequently, regions with field significance also increased as the DSs went higher. During winter and its DSs, besides the northwestern regions, negative trends were also observed in some of the mid-eastern regions, while positive trends mostly were located in the northeastern and central regions (Fig. 5). The increase in the number of stations with trends was observed to be higher in the western regions, i.e., PN and CA, compared to the eastern and central regions as the DSs went higher. At DS4 and DS8, all the regions showed field significance.

In spring and its DSs, stations with trends showed quite a different pattern when compared to the other seasons. Stations with negative trends were found in the eastern regions; such trends were almost absent during the other seasons (except for a few stations during winter) (Fig. 5). With the increase in DSs, NE, MA, SAG, PN, and CA showed a higher increase in negative trends compared to the other regions, while the central regions showed an increase in stations with positive trends. In summer and its DSs, stations with positive trends mostly were located in the northeastern and north-central regions, while negative trends were prevalent in the northwestern regions (Fig. 5). Eastern regions, e.g., NE, MA, and OH, showed the maximum increase in stations with positive trends, while the increase in negative trends was found to be the highest in PN as the DSs went higher. In both spring and summer, with the increase in DSs, more regions showed field significance.

Figure 5

Location of stations with significant trends under the MK test for the seasonal data and their DSs. Upward (downward) pointing blue (red) triangles represent significant positive (negative) trends. Shaded regions represent field significance

Stations with shifts during the seasons (Fig. 6) followed similar patterns as the trends during the seasons. In fall and its DSs, positive shifts were found in the northeastern regions, while negative shifts were located in the western regions (Fig. 6). The increase in stations with negative shifts was higher in the western regions, e.g., PN; while stations with positive shifts were observed to increase in the eastern regions, e.g., NE and MA. All the regions showed field significance in DS4 and DS8. In winter and its DSs, negative shifts were observed in the southeastern regions, which were not present in fall, while positive shifts were located in the northeastern and central regions (Fig. 6). The rate of increase in the number of stations with negative shifts was higher compared to the rate of increase in stations with positive shifts as the DSs went higher. The majority of the stations with negative shifts were located in SAG and PN, while stations with positive shifts were more spatially dispersed across the regions with a higher concentration in the eastern regions, i.e., NE and MA. Similar to fall, all the regions showed field significance in DS4 and DS8.

In spring and its DSs, negative shifts were observed in the eastern and northwestern regions, while positive shifts were found in the north-central regions (Fig. 6). The results show that similar to fall and winter, with the increase in DSs, stations with significant shifts also increased. A high concentration of stations with negative shifts was observed in NE, SAG, GL, and PN. MA, OH, and UMS showed a high concentration of stations with positive shifts. The number of regions with field significance was fewer compared to fall and winter in the lower DSs. However, all the regions showed field significance in DS8. In summer and its DSs, positive shifts were observed in the northeastern regions, while negative shifts were predominant in the northwestern regions (Fig. 6). The number of stations with negative shifts showed a much higher increase in PN, while positive shifts increased in NE and MA as the DSs increased. Similar to spring, all the regions were found to be field significant in DS8.

Figure 6

Location of the stations with significant shifts under the Pettitt’s test for the seasonal data and their DSs. Upward (downward) pointing blue (red) triangles represent significant positive (negative) trends. Shaded regions represent field significance

Appendix D

The number of stations with significant shifts during the study period in water year and its DSs is shown in Fig. 7. A Higher number of stations with shifts were found from the 1960s to 1980s in all the time series. The results showed that the location in time and direction of the shifts varied across the DSs. DS2 and DS4 showed similarity in their shifts distributions, while DS8 showed an oscillatory alternating reverse pattern – a series of years with positive shifts followed by a series of years with negative shifts. Moreover, in DS2 and DS4, there were instances where both directional shifts occurred in the same year, which was rarely observed in the original water year and DS8.

As seen in Fig. 7, the occurrence of shifts showed an oscillating tendency in the higher SBs, especially in DS8. As a result, the shift years were compared against the years associated with the coupled phases of the climate signals, i.e., ENSO, PDO, and AMO, to detect their concurrency during the study period, since climate signals also show oscillating trends. Both the ENSO (El Niño and La Niña) phases were compared against the PDO (warm or cold) and AMO (positive or negative) phases to observe their coupled effects on the regional streamflow. The majority of the stations with shifts that coincided with the PDO cold years were found to be during the La Niña years (Fig. 8). Both positive and negative shifts were found during the La Niña years, while only positive shifts were found during the El Niño years. During the PDO warm years, both positive and negative shifts were observed during the El Niño and La Niña years, though the number of stations with significant shifts was much less when compared to the PDO cold years. The remaining stations with shifts were spread out across the study area without any visible spatial pattern.

Figure 7

Number of stations with significant shifts in water year and its DSs. Blue (red) bars indicate positive (negative) shifts. Blue (red) lines represent the 2-year-moving-average trend lines for positive (negative) shifts

During the AMO positive (warm) years, positive shifts were more prevalent compared to negative shifts (Fig. 8). Also, the majority of the stations during the AMO warm years coincided with the El Niño years across the continental US, while only one station coincided with a La Niña year. A few stations were found not to coincide neither with the El Niño nor the La Niña years, but no pattern was observed among them. During the AMO negative (cold) years, both positive and negative shifts were observed across the US, with the majority of the stations coinciding with the La Niña years. Similar to the AMO warm years, a few stations were found to coincide neither with the El Niño nor the La Niña years. The comparison of PDO and AMO phases showed similar locations of stations with shifts – the similarity was found to be higher during their cold phases.

Figure 8 shows that NE, MA, GL, OH, UMS, SRR, MO, and PN had a significant number of stations with shifts at one or more of the coupled phases of the climate signals, i.e., El Niño/La Niña phase during PDO warm/cold years, and/or El Niño/La Niña phase during AMO positive/negative years. All these regions also showed field significance during the DSs of the water year (Fig. 2). The concept of CWT was applied to evaluate the variance of these regions’ streamflow and the climate signals across multiple CSs. The first principal component (FPC), obtained from the principal component analysis (PCA) of all the stations in a region, was used to represent the regional streamflow time series. Table 3 lists the percentage of variability explained by the FPC from the PCA analysis for each region. The CWTs explained how these individual time series have varied over time across the CSs (Figs. D3 and D4), where the higher power in the wavelet power spectrum represents higher variability.

Figure 8

(1^st row) Location of stations with significant shifts coinciding with the PDO warm (left) and cold (right) years, in conjunction with the ENSO (El Niño or La Niña) years. (2^nd row) Location of stations with significant shifts coinciding with the AMO warm (left) and cold (right) years, in conjunction with the ENSO (El Niño or La Niña) years. Upward (downward) pointing triangles indicate positive (negative) shifts

Table 3 Percentage of variance explained by the first principal component (FPC) obtained from the principal component analysis (PCA) of the selected regions

The CWTs of the climate signals revealed that each of them experienced higher variance at different CSs during various time intervals. The highest significant variance for ENSO was observed in CS4 to CS8 between 1980 and 1990 (Fig. 9). For PDO, the highest significant variance was observed in CS8 to CS12 from 1995 to 2005. For AMO, there was higher variance after CS16 but it was not found to be statistically significant. The highest significant variance for AMO was found below CS4. The global wavelet spectrums for each of the climate signals also showed similar higher power as was observed in their wavelet power spectrums. The three-to-six-year-scale-average for each of the climate signals showed their periodic nature over the study period (Fig. 9).

Figure 9

Standardized time series, continuous wavelet power spectrum, global wavelet spectrum, and three-to-six-year-scale average time-series of (a) ENSO, (b) PDO, and (c) AMO. Red (blue) represents stronger (weaker) power or variance. 5% significance zones against the red noise are delineated by the thick black contour lines

The results showed that ENSO had a much-defined periodicity, which was less than a decade, compared to PDO and AMO. For PDO, there was no definite periodicity during the study period. Though AMO showed cyclic behavior, the periodicity varied from a decade to more than a decade over the study period.

The CWTs of the regional streamflow showed significant variation among them (Fig. 10). There was a definite presence of higher variance after 1970 for the majority of the regions, though the ranges of CSs varied. From the global wavelet spectrums, it was observed that the majority of the regions experienced higher variance in CS8 to CS16. Higher variance beyond CS16 was also observed for certain regions. All the regions, except for MO, had more than one significant zone of noticeable duration (Fig. 10).

Figure 10

Standardized time series, continuous wavelet power spectrum, global wavelet spectrum, and three-to-six-year-scale average time-series (1^st row, left to right) New England (NE), Mid-Atlantic (MA), Great Lakes (GL), Ohio (OH), (2^nd row, left to right) Upper Mississippi (UMS), Souris-Red-Rainy (SRR), Missouri (MO), and Pacific Northwest (PN). Red (blue) represents stronger (weaker) power or variance. 5% significance zones against the red noise are delineated by the thick black contour lines