1
The Relative Impact of the Pacific Decadal Oscillation Upon 1
the Hydrology of the Upper Rio Grande and Adjacent 2
Watersheds in the Southwestern United States. 3
4
5
Michael G. Wallace, Michael Wallace & Associates (MWA), Albuquerque, New Mexico. 6
7
2
8
Key Points: 9
A number of Southwestern U.S. stream flow histories match the PDO time series. 10
High PDO correlations persist for the Otowi gage under various moving averages 11
The AMO, the ENSO, and GHGs exhibit poor correlations to the stream histories 12
Abstract: 13
Researchers have observed and reported on the apparent connections between the 14
Pacific Decadal Oscillation (PDO) and the hydroclimatology of the U.S. Southwest. Yet for the 15
most part, as a possible causal mechanism for Southwestern U.S. climate, the PDO has shared 16
the stage with other candidate drivers, including the Atlantic Multi-decadal Oscillation (AMO), 17
the El Niño - Southern Oscillation (ENSO), and greenhouse gas emissions (GHGs). Often the 18
large number of potential candidates is reflective of the lack of clear correlations that can be 19
applied to any single potential driver. Yet the Otowi stream flow gage positioned along the Rio 20
Grande in Northern New Mexico, with a monthly time series history going back to 1895, 21
exhibits a striking alignment specifically to the PDO. In this study a simple analysis was 22
undertaken to more fully explore the correlations between the Otowi gage records and the 23
PDO as well as the other commonly cited drivers. The study indicates a consistently high 24
correlation of the Otowi records to the PDO, which improves with increasing magnitude of the 25
moving average applied, reaching as high as 0.84. Other subsets of the Otowi - PDO time series 26
pair were examined, which showed correlations in many cases exceeding 0.9 and reaching 0.94. 27
3
The study also confirmed the consistent lack of correlation between the Otowi gage and the 28
other candidate drivers. 29
Introduction 30
Whether simulation or stochastic methodologies are used in climate forecasting, a 31
comprehensive evaluation of the actual time series data is a critical component to both. This 32
evaluation is challenged by the unbounded nature of the climatic data, necessitating at some 33
point, somewhat arbitrary designations and/or cut offs in both temporal and spatial data. For 34
example, the use of a 30 year climatology, also known as a 30 year climate normal, has been 35
recognized as an arbitrary designation, ever since it was first adopted by nation members of the 36
International Meteorological Organization (IMO) for the initial period of 1901 - 1930. Moreover 37
the value of a climate normal for causal identification and predictive purposes is acknowledged 38
to be low, if only due to perceived non-stationary behavior (Arguez and Vose, 2011). In 39
extending the scope of desired prediction from climatologic to hydroclimatologic causality, the 40
challenges are compounded. In that scale-dependent context, causality must account for both 41
stationary and non-stationary factors, and some of those can often clearly be attributed to 42
human influences, including reservoirs, irrigation activities, levee developments, urban 43
pavement expansion, and numerous other factors. 44
Hydroclimatologists recognize as well as other climatologists that secular trends in a 45
time series may either indicate non-stationarity, or the trend may be a component of a larger 46
scale cycle that is longer than the time series being evaluated. Accordingly, the concept of 47
cyclostationarity can often be employed successfully for time-series evaluations (if not 48
4
predictive purposes) via spectral analysis, when and where such cycles can be appropriately 49
identified (Wei, 2006, also Weedon, 2003). 50
Outside of obvious diurnal and seasonal oscillations, such cycles have long been sought 51
in modern climatic patterns. The most notable candidates are associated with oceanic 52
influences and include the El Niño - Southern Oscillation (ENSO), the Atlantic Multi-decadal 53
Oscillation (AMO) and the Pacific Decadal Oscillation (PDO). Of these oscillations, the PDO not 54
only has an interesting correspondence to the 30 year climate normal, but it also exhibits at the 55
very least, a recognized partial causality with regard to Southwestern U.S. climate as well as 56
other parts of the world, including roughly half of the northern hemisphere as well as locations 57
along every continent in the Southern Hemisphere (Mantua, 2002, also Okumura, 2012). 58
Naturally any improvements to current techniques in climate prediction would be of 59
extreme value at any region of the populated globe. Moreover, the Southwestern U.S., by 60
virtue of its typically arid regime in conjunction with a growing population, is a region that has 61
an acute need for improved climate prediction techniques. Yet any such climate predictive 62
product would require extensive validation prior to its use. Validation exercises of interest 63
include one of the simplest stochastic tools of all, namely correlation coefficients (ρ), and 64
associated lag correlations. 65
This investigation constitutes such an initial first order validation study applied to 66
several candidate oceanic and other drivers as they might relate to a key region within the 67
Southwestern United States, namely the Upper Rio Grande Watershed (URGW). 68
The Upper Rio Grande Watershed 69
5
The headwaters of the Upper Rio Grande Watershed (URGW) (Figure 1) originate at an 70
approximate elevation of 4300 masl (14107 ft) along the Continental Divide within the San Juan 71
Mountains of southwestern Colorado (U.S.). The 'pour point' of this watershed is defined at an 72
elevation of approximately 1670 masl (5479 ft) at the Otowi gage along the main stem of the 73
Rio Grande in north central New Mexico . The sparsely populated watershed covers 74
approximately 37040 km2 (14301 mi2). Approximately half of the watershed is steep 75
mountainous terrain, and roughly half of the remaining lowlands, over 86,000 hectares (212500 76
acres), are devoted to irrigation-based agriculture. Significant portions of the watershed have 77
been under cultivation for over a century (Scurlock, 1998). 78
Following a pattern typical of the surrounding Southern Rocky Mountains and the 79
adjacent Basin and Range environments, the upper elevations are dominated by conifer forests 80
while the lower terrain consists of mixed grasslands, sagebrush and riparian vegetative covers, 81
in addition to the cultivated portions. Significant portions of the watershed are composed of 82
exposed bare rock and sediments, in association with the steep terrain and primary geologic 83
features. That geologic framework covers a diverse range of components; from an extension 84
of the Rio Grande Rift Zone trending from south to north, to the Rocky Mountain orogenic 85
network on either side of the rift zone. Precambrian rocks form the basement of the 86
groundwater regime. Those are overlain in large sections by sequences of Mesozoic and 87
Cenozoic sediments and those are intermingled with Tertiary igneous intrusions including dikes, 88
sills, and ash layers from volcanic activities. This portion of the rift zone is structurally 89
characterized by horst and graben features and accordingly contains numerous long and deep 90
faults trending south to north. (Falk et al., 2013 also Bexfield and Anderholm, 2010) 91
6
The large sediment filled structural depression roughly covering the northern half of the 92
watershed includes a topographically closed basin with an evaporite sump feature near the 93
Great Sand Dunes National Park. That area has been termed the Closed Basin, and the closure 94
only extends to local drainage at the surface. Underlying groundwater resources are significant 95
within that region and it is believed that for the most part, the boundaries of the groundwater 96
basin correspond laterally to the boundaries of the watershed. Regardless of the surface 97
drainage closure at the Closed Basin, there are no physical obstructions to groundwater flow 98
motion from the upper portions of the watershed to the lower southern portions. (Bexfield and 99
Anderholm, 2010, and Simonds, 1994). Within New Mexico, the Rio Grande Rift structure 100
continues as well as the mountainous boundaries defining the western and eastern sides, but 101
the alluvial sediment filled basin is significantly narrowed and in many places disrupted by fault 102
related plateaus. 103
Numerous stream flow gages are located throughout the Upper Rio Grande, its 104
tributaries and adjacent watersheds, including the Otowi gage in north central New Mexico 105
(USGS 2014a). Other gages outside of this watershed have been examined in association with 106
this study, including the Navajo River at Banded Peak Ranch, gage in Southern Colorado (simply 107
termed 'Navajo gage' in the remainder of this text) 144 km (89.5 mi) to the northwest of Otowi 108
(Falk et al., 2013), and the Gila river gage, 381 km (236.7 mi) to the southwest (USGS 2014b), of 109
the Otowi gage as depicted in Figure 1. 110
The Otowi gage has been monitored since 1895 by the U.S. Geological Survey, making 111
this point one of the oldest continuous sources of stream flow data in North America (USGS 112
7
2014a) . Moreover this site is closely monitored with regard to an interstate and international 113
water rights compact involving the states of Colorado, New Mexico, and Texas, as well as the 114
Republic of Mexico (Rio Grande Compact, 1939). Figure 2 is a representation of the recorded 115
stream flows at that gage using three different (centered) moving averages; a 12 month, a 10 116
year, and a 20 year average respectively. 117
The Otowi gage measures both natural flows and captures the impacts of several 118
reservoir operations upstream in addition to a river augmentation project known as the Closed 119
Basin Project (Simonds, 1994) and a trans basin diversion program known as the San Juan 120
Chama Project (U.S. Bureau of Reclamation, 2014), both administered by the U.S. Bureau of 121
Reclamation. The average stream flow rate past the gage is approximately 42.5 cubic meters 122
per second (cms) (1,500 cubic feet per second, cfs) , such that the total volume of water 123
transmitted per year is roughly 1.23 km3 (1 million acre feet). Stream flows have a seasonal 124
component, overlain by related water use for irrigation, with a major peak typically occurring in 125
late Spring and a major low typically occurring in Winter. In this investigation, seasonal and 126
diurnal components have been filtered out through the use of moving averages. 127
As identified in Table 1., the sources of water to the Otowi can be divided into four 128
components. These sources are also represented graphically over time in Figure 3. 129
Table 1. Approximate Relative Source Contributions to the Otowi Stream Flow Gage Record 130
Water Source Approximate Percent
Annual Contribution (%)
8
Note percentages vary from
year to year
1. Colorado Rio Grande Watershed 20
2. Colorado Closed Basin Project Artificial
Contributions
3
3. New Mexico Rio Grande Watershed Excluding
Chama Reach
67
4. San Juan Cross Basin Artificial Contributions 10
131
In addition to the various source contributions, there are of course depletions to flows 132
that might otherwise reach the Otowi gage, such as the annual use of significant quantities of 133
Rio Grande waters, and related aquifer extractions for irrigation in Colorado's San Luis Basin. 134
In addition there are modifications to flow timing and rates that are nominally attributable to 135
reservoir operations upstream, particular within the Chama Reach. As for most watersheds, it 136
is also understood that at various times and locations, there are losses via evapotranspiration 137
and groundwater recharge (losing streams), as well as some gains via groundwater discharge 138
(gaining streams). 139
It is notable that Figure 2, covering the entire period of Otowi recorded flows from 1895 140
to the present, indicates a downward trend in flow rates over the entire time frame, as well as a 141
decrease in overall variability (from low flows to high flows. Also a mild upward trend is 142
apparent since the flow minima which occurred in the mid 1950s. 143
9
Apart from natural variability and/or the fact that several years of data are missing from 144
the early half of the series, the long term downward trend at Otowi might be explained by the 145
history of continual growth in irrigated acreage of the San Luis Valley in the upstream Colorado 146
segment of the watershed study area over the first half of the time series. Irrigation was 147
already widespread via purely surface water diversions in the valley at the beginning of gage 148
recording just prior to 1900. Yet by the time of the Rio Grande Interstate Compact agreement 149
in 1940, irrigation consumption of water via both surface water diversion and groundwater 150
pumping in the San Luis Valley rose to three quarters of a cubic kilometer (600,000 acre ft) per 151
year. Irrigation has held constant in that area since that time, in line with requirements 152
associated with the Compact. The decrease in stream flow variability (as compared to stream 153
flow rate) over the total time frame may be partially explained by a history of upstream 154
reservoir developments along with the other features cited. 155
Although anthropogenic explanations can be proposed for features of an early trend 156
and a contraction in variability, they do not explain the overall major pattern of peak - trough - 157
peak most strongly represented in the 10 and 20 year moving average curves in Figure 2. 158
Moreover, notable secondary patterns are also apparent in other regionally proximal 159
stream gages which are not impacted by irrigation or reservoirs, as represented in Figure 4. 160
That figure includes the Otowi gage as well as the Gila River gage and the Navajo gage time 161
series. Both additional gages are in separate basins and are closer to their respective 162
headwaters. 163
10
For this initial study, given this first order confirmation, and its regional importance to 164
water planning within and interstate compact framework, the Otowi gage is utilized in this 165
paper as the signature time series for evaluation of the candidate climate drivers featured in 166
this report. 167
Candidate Climate Drivers for Stream Flows of the URGW 168
As defined initially by Zhang et al (1997), and extended and summarized by Mantua 169
(2002), the PDO index has been derived through principal component (PC) analyses using 170
empirical orthogonal functions (EOFs) of sea surface temperature patterns associated with the 171
Pacific Ocean north of 20o latitude. Mantua's (2002) summary provides several examples of 172
positive PDO correlations with regional climates at locations ranging from Africa to North 173
America. 174
According to Mantua, a high PDO index is expressed by a persistent cold phase in the 175
north central Pacific Ocean surface and a related warm phase along the margins of the eastern 176
Pacific in the northern hemisphere. This is accompanied by a persistent low sea level pressure 177
at the north central Pacific Ocean. The oscillation between a high PDO index and a low PDO 178
index appears to roughly correspond to a 25 to 30 year periodicity (Lewis and Hathaway, 2001). 179
Given that transition period, a total cyclic period of the PDO is considered to range from 50 to 180
60 years, at least for the few periods measured over the past 100+ years. 181
Mantua summarized the wide ranging correlations of the PDO time series with 182
hydroclimatologic teleconnections that reach around the world. These include precipitation 183
anomalies within the coastal Gulf of Alaska, and the Southwestern United States (SWUS). 184
11
Mantua also cited supporting dendrochronology research by numerous authors, which to a 185
greater or lesser degree, correlate to the PDO over the modern period for which the PDO can 186
be directly estimated (approximately since 1900). By this correlation, researchers such as 187
Biondi (2001) have produced proxy based PDO histories which extend back in time to the 17th 188
Century. 189
Subsequent researchers (Lewis and Hathaway, 2001, 2002) have pointed to such work 190
to propose (but not quantify) a correlation between the PDO (in conjunction with ENSO and 191
GHG patterns) and drought patterns in northern New Mexico, including the stream flows at 192
Otowi gage and other points within and west of the URGW. 193
In spite of the widely observed relations of the PDO to distal climates, researchers have 194
typically been careful to frame PDO influences within a broader background of uncertainty and 195
variability. They have done so in part because the PDO phenomenology remains largely 196
unexplained. Yet as Mantua relates "Even in the absence of a theoretical understanding, PDO 197
climate information improves season-to-season and year-to-year climate forecasts for North 198
America because of its strong tendency for multi-season and multi-year persistence" 199
As already suggested, the PDO typically shares significant attention from researchers 200
with at least three other candidates in relation to causality of SWUS climate; the Atlantic Multi-201
decadal Oscillation (AMO), the El Niño - Southern Oscillation (ENSO), and global changes in 202
atmospheric greenhouse gas concentrations (GHGs). Recent work by Chylek et al. represents 203
an example of that approach (Chylek et al., 2013, 2014). Those papers document the 204
application of multiple linear regression analysis to those factors, as well as to solar forcing and 205
12
dust effects, in order to develop empirical relations which might be useful to forecast future 206
climate over the next several decades. The papers posit the AMO in particular, and also GHGs 207
as important co-drivers of global climate at least with regard to mean near-surface air 208
temperature. Notably the 2013 devotes attention to the climate of the US Southwest and 209
places a somewhat higher focus upon the PDO. 210
The AMO is an index based on sea surface temperature (SST) anomalies across the 211
northern hemisphere portion of the Atlantic Ocean. It has an apparent periodicity of 65 to 80 212
years (Schlesinger and Ramankutty, 1994). Its impact on North American climate has been 213
investigated by numerous researchers, since the pattern was first identified in the 1990s 214
(Schlesinger and Ramkutty, 1994, McCabe et al., 2004), and formally defined in 2000 (Kerr). The 215
work of Enfield et al. (2001) includes a consideration of the correlations between the AMO and 216
stream flow histories associated with the Mississippi and Okeechobee rivers in the US. That 217
analysis indicated in some cases a correlation that slightly exceeded 0.5. The AMO is believed 218
by some researchers to be the primary driver of drought in the conterminous US. Those 219
authors also contend that the PDO sign merely modulates that primary AMO impact feature 220
(McCabe, 2004). 221
The ENSO and its potential impacts on SWUS climate have also been investigated in 222
great detail, including the research by Hidalgo and Dracup (2003), and as already described, 223
Lewis and Hathaway (2001, 2002). The Lewis and Hathaway team asserted that "ENSO drives 224
weather patterns for nearly three quarters of the globe and is one of the most powerful 225
influences on world climate, second only to the changes in weather brought by the seasons". 226
However those authors did not develop correlations of the ENSO to the climate of the SWUS. 227
13
Correlations of the ENSO to SWUS climate were explored in some detail by Hidalgo and Dracup, 228
who compiled selected seasonal precipitation and stream flow data from a relatively large 229
number of stations within the Upper Colorado River Basin (UCRB). From that data set, they 230
developed synoptic correlation maps to the various types of El Niño series identified in the 231
literature. They determined that the correlations were for the most part, greatest for summer 232
and fall and weakest for winter and spring periods. 233
These investigators also explored possible relationships between the robustness of the 234
ENSO - UCRB correlations and the timing of PDO peaks, based on past work by Gershunov and 235
Barnett (1998). It is notable that these studies cover an area immediately adjacent to the 236
Upper Rio Grande Basin, including the southern Rocky Mountain chain which contains some of 237
the headwaters for both the Rio Grande and the Colorado river. Yet, although the authors 238
explored a relationship between the PDO and the ENSO series, and also a relationship between 239
the ENSO series and the UCRB, they did not explore a correlation relationship between the PDO 240
and the UCRB series. 241
The potential impact of GHGs upon climate of the SWUS has also been investigated over 242
many decades. In an early example (Revelle and Waggoner, 1983), researchers employed an 243
empirical relationship (Langbein 1949) between runoff, temperature, and precipitation for arid 244
climates, to suggest that rising global levels of GHGs (presumably leading to increased 245
temperatures) would lead to increased drought in the SWUS. It should be noted that although 246
this paper asserted a strong correlation, no actual correlation statistics were provided. Also that 247
paper had been authored before the enhanced identification of the ocean patterns of PDO, 248
ENSO, and AMO. Subsequently the Lewis and Hathaway studies suggested an opposite relation 249
14
in which a warming SWUS climate, in conjunction with the PDO and the ENSO would lead to 250
more moist conditions. 251
More recent reports have fallen back upon conclusions similar to the assertions made 252
by Revelle and Waggoner. For example the Upper Rio Grande Impact Assessment (Llewellyn et 253
al., 2013) nominally describes ocean drivers, but does not evaluate their potential impacts to 254
the study area. Moreover the report largely disregards approximately 60 years of Otowi gage 255
and related records and concludes that rising GHGs are the primary driver of contemporary 256
amplified drought in the upper Rio Grande watershed. Many additional examples of a narrative 257
in which GHGs first raise temperatures and those temperature increases lead directly to 258
amplifications of drought occurrence and severity in the Southwestern U.S. can be found in the 259
peer reviewed literature including Nohara et al.( 2006), Cook et al. (2010), and Willliams et al. 260
(2014, in press). These conclusions are also featured in UN IPCC publications (Stocker et al., 261
2013), and in popular news media (Chuck, 2014). 262
Although nominal diurnal and seasonal cycles can be seen, it is clear from the 263
instrumental record of the Mauna Loa series that lower frequency oscillatory behavior of CO2 264
emissions over time frames of years is not evident. Rather, the average global atmospheric 265
concentration of CO2 rises essentially monotonically. This puts the CO2 causality question in a 266
somewhat different frame than the other candidate drivers, which all express clear oscillatory 267
behavior over multi-year time scales. 268
As this section documents, a variety of drivers for climate in the URGW have been 269
proposed within peer reviewed publications. Most if not all research to date attributes URGW 270
15
climate to a combination of several drivers. Most relevant reports assign a primary causality of 271
contemporary SWUS and/or URGW drought patterns to GHG-induced global warming. Those 272
sources in some cases indicate that the patterns are modulated to some extent by various 273
candidate ocean oscillations. However, in most cases, correlation metrics are notably lacking. 274
Comparisons between Otowi Flows and Candidate Climatic Drivers 275
In this investigation, the Otowi gage represents the signature hydroclimatologic index 276
for the URGW. Accordingly, the candidate causality components are each independently 277
compared to the time series of the Otowi gage under a low pass filter prior to the development 278
of correlation coefficient evaluations. For each comparison, it was desired to capture the 279
longest available continuous records reaching to the current time. Naturally the correlation 280
development is focused on comparisons of two independently derived time series which at a 281
zero lag, cover the same time spans in those series. 282
For ease of visual comparison, the various time series have been broken out into several 283
individual charts. Figure 5 is a time series comparison of the Otowi gage and the PDO under a 284
four year trailing average. Figure 6 provides a comparison for the Otowi gage versus the AMO, 285
and Figure 7 covers a pattern for the Otowi gage versus ENSO. Although each ocean oscillatory 286
pattern has been characterized in the original literature according to a favored lowest 287
frequency, the actual time series data for each, as well as for the Otowi gage, are available in 288
raw form as monthly values. Figure 8 closes the candidate set by comparing the Otowi gage 289
series and the PDO index to the measured atmospheric CO2 values recorded at Mauna Loa 290
Station in Hawaii. 291
16
Visual examination of each figure is suggestive that the PDO pattern most consistently 292
aligns with the Otowi stream gage history by any reasonable measure. Moreover the PDO 293
pattern typically anticipates or is synchronous with the Otowi gage pattern. It appears that the 294
same case could be made for the PDO versus the Gila and the Navajo gages as well, and that is 295
suggestive of a broad PDO influence beyond the neighborhood of the Otowi gage. 296
However, these two observations of alignment and precedence cannot be asserted for 297
any of the other causal candidates. For example, in Figure 6, the late 1940s downward trend of 298
the Otowi gage anticipates a downward trend in the AMO by approximately 2 decades, yet the 299
beginning of an upward trend in the AMO anticipates the Otowi upward trend by several years. 300
In order to develop a more systematic and quantitative assessment, correlation metrics 301
were obtained from these time series sets and are summarized in Tables 2 and 3, as well as 302
Figure 9. To facilitate development of these correlation metrics in a consistent fashion, the 303
longest time series in each specific comparison case was truncated to match the shortest time 304
series. Moreover, because of a series of missing years in the Otowi gage record prior to 1919, 305
the 1919 date was the earliest Otowi year selected as the starting point. Also the Mauna Loa 306
series and the ENSO series have later starting dates than the other parameters, as detailed in 307
the tables. Moreover the actual starting dates in the correlations vary further, because of the 308
use of trailing averages. Accordingly, for example, because of the employment of a 4 year 309
moving average, the starting date for a CO2 related comparison is 1962. 310
Table 2. Summary of Settings for the Otowi Correlation Coefficient Analyses 311
17
1 year trailing moving average Span
Otowi versus PDO 94 yrs, 1920 to 2013
Otowi versus AMO 94 yrs, 1920 to 2013
Otowi versus ENSO 64 yrs, 1950 to 2013
Otowi versus GHG 55 yrs, 1959 to 2013
4 year trailing moving average
Otowi versus PDO 91 yrs, 1923 to 2013
Otowi versus AMO 91 yrs, 1923 to 2013
Otowi versus ENSO 61 yrs, 1953 to 2013
Otowi versus GHG 52 yrs, 1962 to 2013
10 year trailing moving average
Otowi versus PDO 85 yrs, 1929 to 2013
Otowi versus AMO 85 yrs, 1929 to 2013
Otowi versus ENSO 55 yrs, 1959 to 2013
Otowi versus GHG 46 yrs, 1968 to 2013
312
Table 3. Summary of Correlation Coefficients ƿ, Between Candidate Causal Factors and the 313
Otowi Stream Flow Gage (zero lag) under various trailing moving averages and time spans as 314
tabulated in Table 2. 315
18
Parameter in
comparison to Otowi
Gage Record
1 yr avg 4 yr avg 10 yr avg
PDO 0.34766 0.66535 0.83617
AMO -0.11669 -0.19098 -0.16745
ENSO -0.00974 0.09377 0.28394
GHG 0.02605 0.11991 0.12933
316
Clearly the relation between the PDO and the Otowi gage is the strongest correlation of 317
all of the candidates. That conclusion holds under all moving average approaches and under all 318
subsets of the time series that were evaluated. Moreover the correlation value of 319
approximately 0.84 for the 10 year average case can be considered to qualify as an 320
extraordinarily high value, given the independent origins and modalities of the two data sets. 321
This is a somewhat unexpected result given many of the past assertions in the prior literature, 322
with the nominal exception of Falk et al. (2013). The Falk et al. study in particular took the 323
notable step of evaluating a limited set of Navajo stream flow statistics through the lens of the 324
PDO by virtue of the clear correspondence in the two time series. 325
There are consequences regarding the poor correlations of the Otowi gage to the other 326
parameters. For example, if a principal components regression analysis (PCRA), such as 327
detailed in Garen (1992), were to be implemented to complement existing local forecasting 328
exercises, the low correlations would produce low eigenvector values. Accordingly, those terms 329
19
would logically drop out of such a regression based forecasting equation. However, this paper 330
is primarily focused on understanding the relative degree of correlations between the 331
candidates, and therefore follow up work to develop such a forecasting tool is outside of the 332
scope of this paper. 333
Within the scope of this study, the correlation between the PDO and the Otowi gage 334
invites additional attention with regard to a possible lag correlation. To produce lag outputs, 335
one series must be shifted with respect to the other. In the case of the 10 year moving average 336
series for PDO versus Otowi gage, this lag series was approached in a simple step wise process. 337
First, the Otowi time series was anchored to the late terminus at year 2013, while the PDO 338
series was allowed to shift temporally backward in one - year increments until a maximum 339
correlation was identified. This necessitated reducing the total time span of each series by 4 340
years (from 85 years length to 81 years length) to fit within the total span utilized for this 341
moving average value. Figure 10 is a representation of the time series which encompasses the 342
possible cases. Second, correlation coefficients are calculated for lag cases from zero to three 343
years. Figure 11 is a chart of those results which shows not only a new high correlation for the 344
zero lag case but also indicates the highest correlation so far in this analysis, exceeding 0.88, at 345
a lag of one year. 346
A lag of one year nominally offers the potential for improved predictive value. However, 347
such a lag may be simply due to storage effects within the watershed, both natural (snow 348
accumulation, and plant and soil storage effects) and artificial (reservoir effects). For example, 349
depleted reservoirs along the Chama tributary can contain more than enough capacity in their 350
20
own right to receive over 1 million acre feet, which is roughly the annual flow volume past the 351
Otowi gage over the course of one year. On the other hand, when reservoirs are full, then the 352
artificial storage capacity has a relatively insignificant impact on the flow response. Overall, in 353
this context, a lag of one year to zero years would be consistent with the time series 354
observations but does not add significant predictive value without more detailed evaluations of 355
reservoir and other time series histories. 356
As stated, the truncation of the 10 year trailing average time series case at a zero lag led 357
to a further improved correlation coefficient for the Otowi gage versus the PDO, from 0.84 to 358
0.88. This invites additional exploration of potentially even larger correlations under selected 359
subsets of the time series. A limited manual approach was undertaken to simply see if any such 360
subsets might exist. It was found quickly that many such subsets likely can be found. Figure 12 361
shows an example in which (for a zero lag condition), spans centered around the year 1971 362
(roughly the midpoint of the time series shown in Figure 10) were successively narrowed until 363
an optimal correlation of 0.94 was reached at a total span of 53 years. Notably, the cycle 364
length already estimated in the literature for the PDO and discussed earlier in this report is 365
approximately equivalent to that value. 366
More systematic approaches might lead to the discovery of even higher correlations. 367
However, the further removed in time such span-based correlations are found, the less 368
potentially relevant they are to the current time frame of greatest concern. In any event 369
correlations greater than 0.5 are customarily considered to merit attention, while those less 370
than 0.5 are typically considered to be diagnostic of an uncorrelated pattern. 371
21
Summary and Discussion 372
A literature review, along with simple time series analyses and correlation techniques 373
were applied to evaluate causality of ocean oscillatory and GHG influences upon climate in the 374
Upper Rio Grande Watershed of the Southwestern United States. The analysis adopted the 375
Otowi gage time series record as the performance metric. Through a set of correlation 376
evaluations based on a 1 year, 4 year, and a 10 year moving average, the PDO expressed 377
exceptionally high correlation coefficients, reaching as high as 0.94, while the correlations for 378
the remaining candidates were for all cases significantly below 0.5. 379
ACKNOWLEDGEMENTS 380
All reviewers will be acknowledged in the final product. 381
I also wish to acknowledge my advisor at University of New Mexico, Dr. Harjit Ahluwalia for 382
perspective and guidance on this project. 383
Also in accordance with AGU specifications, the data and calculations are also included in this 384
initial submission as a zip file, MGW_WRR_datafiles.zip. 385
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Sources. Background image from Aster DEM 30 m coverage from GeoBrain system http://geobrain.laits.gmu.edu Boundary of URGW (black outline) adapted from Scurlock, 1998
Navajo Gage
Otowi Gage
Gila Gage
New Mexico
50 km
N
Lat 36 59 56.3 Long 109 02 42.6
Texas Mexico
Figure 1. Map of three stream flow gages in the study area.
Figure 2. Otowi gage time series as represented by three moving averages.
Derived from source USGS 2014a
Figure 3. Otowi gage source components. Time series truncated prior to 1950
Derived from sources USGS 2014a, USGS 2014c, USGS 2014d, and Simonds, 1994
Figure 4. Otowi, Gila, and Navajo time series comparisons, 4 year trailing averages
Derived from sources Otowi: USGS 2014a Gila: USGS 2014b Navajo: CWR 2014
Figure 5. Otowi Gage and PDO Index time series comparisons, 4 year trailing averages
Derived from sources Otowi: USGS 2014a PDO index: Mantua N.J. 2014
Figure 6. Otowi Gage and AMO Index time series comparisons, 4 year trailing averages
Derived from sources AMO: NOAA/ESRL/PSD1 2014 Otowi: USGS 08313000 2014a
Figure 7. Otowi Gage and ENSO Index (ONI) time series comparisons , 4 year trailing averages
Derived from sources ENSO (ONI): National Weather Service. Climate Prediction Center. 2014 Otowi: USGS 08313000 2014a
Figure 8. Comparison of normalized four year trailing moving average time series between normalized Otowi Gage, PDO, and Manua Loa CO2 data sets
Derived from sources MLCO2: Mauna Loa CO2 Data 2014 PDO index: Mantua N.J. 2014 Otowi: USGS 2014a
Figure 9. Correlations of Candidate Causal Parameters to Otowi Stream Flow Gage Record; Graphical Representation of Table 3.
Derived from multiple sources referenced in this paper
Figure 10. Time series overlay of PDO Index and Otowi Gage flows, 10 year trailing averages
Derived from sources PDO index: Mantua N.J. 2014 Otowi: USGS 2014a
Figure 11. Correlation coefficients between Otowi Gage flows and the PDO Index, based on time series of Figure 10, under varied lags, for an 81 year span, with the end of the Otowi series always anchored at year 2013
Derived from sources PDO index: Mantua N.J. 2014 Otowi: USGS 08313000 2014a
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