PROJECTED NORTHERN ROCKY MOUNTAIN ANNUAL STREAMFLOW FOR 2000-2099 UNDER
THE B1, A1B AND A2 SRES EMISSIONS SCENARIOS
.
ABSTRACT
Jeannine-Marie St. Jacques1*, Suzan Lapp1*, Yang Zhao2, Elaine M. Barrow1 and David J. Sauchyn1; 1Prairie Adaptation Research Collaborative (P.A.R.C.),
Room 120, 2 Research Drive, Regina, SK, Canada, S4S 7H9; 2Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan,
Canada, S4S 0A2; *Corresponding authors’ e-mail: stjacqje@uregina.ca, lapp200s@uregina.ca.
The 20th century hydroclimatology of the northern Rocky Mountains is heavily influenced by
recurring large-scale climate patterns: the Pacific Decadal Oscillation (PDO), the El NinoSouthern Oscillation (ENSO), and the Arctic Oscillation/North Atlantic Oscillation
(AO/NAO). Hence, northern Rocky Mountain river discharge variability can be successfully
modeled by regression techniques using these climate indices as predictors. Generalized least
squares (GLS) regression addresses residual autocorrelation and allows reliable significance
testing of any predictor coefficients, and hence, is highly suitable for hydrological modeling.
We developed GLS regression equations which captured a major portion of streamflow
variability for ten centennial-length northern Rocky Mountain annual discharge records. Both
unregulated and paired regulated and naturalized flows were examined. Using archived global
climate model runs from the Coupled Model Intercomparison Project Phase 3 (CMIP3), we
projected the PDO, ENSO and NAO for the 21st century for the B1, A1B and A2 SRES
emission scenarios. These projected climate indices were used as inputs into the GLS
equations, giving projected northern Rocky Mountain river discharges for the 21st century.
These projections showed generally declining trends in surface water availability for 20002099. Researchers have projected increases in summer warmth and typically decreasing
summer precipitation, and increases in winter precipitation and temperature for this region
under greenhouse forcing. Our results suggest that in the competition between these two
opposing effects on surface water availability, the former will dominate.
Figure 1. Map
of the northern
Rocky
Mountains
showing the
seven gauge
locations
Flow record
[HYDAT or USGS code]
Record
period
Flow regime
Significant
linear trend?
Low-pass
variance
Drainage
(km2)
Mean Qt
(m3/s)
1.North Fork Flathead R., MT
[12355500]
1936-2008
natural
none
43.1%
4009.3
83.9
2. Marias R. near Shelby, MT
[06099500]
1912-2007
natural
decreasing
45.3%
3242.0
25.0
3. Waterton R. near Waterton Park,
AB [05AD003]
1912-2007
natural
none
40.6%
612.7
17.6
4. Elk R. at Phillips Bridge, BC
[08NK005]
1933-2008
natural
decreasing
40.7%
4450.0
75.9
5. St. Mary R. at International
Boundary, AB [05AE027]
1903-2007
regulated
decreasing
51.6%
1206.4
20.2
6. St. Mary R. at International
Boundary
1912-2001
naturalized
none
38.9%
1206.4
25.1
1912-2007
1912-2001
regulated
none
38.5%
319.2
8.6
naturalized
none
38.6%
319.2
9.1
regulated
decreasing
52.2%
17,045.6
84.6
naturalized
decreasing
44.1%
17,045.6
109.6
7. Belly R. near Mountain View, AB
[05AD005]
8. Belly R. near Mountain View
9. Oldman R. near Lethbridge, AB
[05AD007]
10. Oldman R. near Lethbridge
1912-2007
1912-2001
Table 1. Details of the ten northern Rocky Mountain discharge records. Significant linear
trend as assessed for record period following the methodology of St. Jacques et al. [2010].
Low-pass variance is the variance in low-frequency filtered streamflow data as a percentage
of the total variability. Mean Qt is mean daily discharge averaged over the year. The
naturalized records are from the same location as the corresponding actual flow gauge.
METHODS
• We developed GLS regression equations [Brockwell and Davis, 2002] which captured at least 50% of the
low frequency streamflow variability (a 5-year binomial smoother was used) for ten centennial-length
northern Rocky Mountain annual discharge records. Both unregulated and paired regulated and naturalized
flows were examined (Figure 1, and Tables 1 and 2).
•
•
Using archived global climate model runs from the Coupled Model Intercomparison Project Phase 3
(CMIP3), we examined the GCMs’ ability to acceptably model the PDO, ENSO and NAO [Lapp et al., in
review]. Ten GCMs were found acceptable (Table 3). We then projected the PDO, ENSO and NAO for the
21st century for the B1, A1B and A2 SRES emission scenarios (Table 4).
These projected climate indices were then used as inputs into the GLS regression equations (Table 2),
giving projected northern Rocky Mountain river discharges for the 21st century (Figure 3).
Flow record
R2*
(regular)
R2**
(innovations)
GLS equation
AICc
1.North Fork
Flathead River
0.53
0.75
464.4
2. Marias River
0.56
0.74
526.2
3. Waterton River
4. Elk R. at Phillips
Bridge
5. Actual St. Mary
River
6. Naturalized St.
Mary River
0.57
0.66
359.4
0.54
0.71
478.8
0.61
0.75
492.6
0.51
0.71
393.5
7. Actual Belly River
8. Naturalized Belly
River
9. Actual Oldman
River
10. Naturalized
Oldman River
0.55
0.64
239.1
0.57
0.67
214.0
0.62
0.73
787.3
0.49
0.65
729.0
Residual
model
Qt = 0.10 – 7.92*PDO – 2.21*NAOP1 – 4.18*PDOP2 –
3.39*SOIP2
Qt = 0.21 – 3.0*trend – 2.07*PDO – 1.06*NAOP1 –
1.21*PDOP1 – 2.06*PDOP2 – 2.44*SOIP2
Qt = 0.06 – 0.58*trend – 1.06*PDO + 0.57*SOIN1 –
1.06*PDOP2 – 0.69*SOIP2
Qt = 0.05 – 1.75*trend – 6.66*PDO –1.68*NAON1 –
1.37*NAOP1 – 3.09*PDOP2 – 3.12*SOIP2
Qt = -0.03 – 3.10*trend –1.52*PDO + 0.80*NAOP2 –
1.31*PDOP2 – 1.50*SOIP2
Qt = -0.03 – 1.55*PDO +0.76*SOI – 0.90*NAON1
+1.09*NAOP2 – 0.98*PDOP2 – 1.04*SOIP2
Qt = 0.01 – 0.32*trend – 0.40*PDO + 0.34*SOIN1 +
0.31*NAOP2 – 0.47*PDOP2 – 0.35*SOIP2
Qt =0.002 – 0.37*PDO + 0.24*SOI + 0.31*SOIN1 +
0.24*NAOP2 – 0.50*PDOP2 – 0.34*SOIP2
Qt = 0.11 – 17.17*trend – 9.25*PDO – 9.52*PDOP2 –
9.75*SOIP2
Qt = -0.24 – 5.16*trend – 8.38*PDO – 10.02*PDOP2 –
10.19*SOIP2
ARMA(2,1)
ARMA(2,3)
ARMA(1,2)
ARMA(2,1)
ARMA(0,3)
ARMA(3,2)
ARMA(1,2)
ARMA(2,1)
ARMA(2,3)
ARMA(2,3)
RP
(p-level)
1.1
(0.29)
30.0
(4.3xe-8)
12.8
(0.0003)
18.2
(2.0xe-5)
22.6
(2.0xe-6)
0.58
(0.45)
15.3
(9.0xe-5)
0.02
(0.89)
19.7
(9.0xe-6)
3.6
(0.06)
* R2 computed without modeled error adjustment, 1 – (sum-of-squares of regression residuals/total-sum-of-squares). **R2 computed with the modeled error adjustment.
Table 2. Identification of the optimum generalized least squares (GLS) equations and residual models for
northern Rocky Mountain streamflow. AICc: corrected Akaike Information Criterion. Predictor variables are
standardized to zero mean and unit standard deviation; discharge Qt is centered to zero mean. 0, 1, +2
year lags of climate indices included in analysis. P1: climate leads streamflow 1 year. P2: climate leads
streamflow 2 years. N1: climate lags streamflow 1 year. RP: Neyman-Pearson statistic testing significance
of trend term in model (results significant at the 10% level in bold).
#
IPCC4
Country
Atmosphere
Model ID
resolution
1
CGCM3.1(T47)
Canada
3.7ox3.7o L31
2
CGCM3.1(T63)
Canada
2.8ox2.8o L31
3 ECHAM5/MPI-OM Germany 1.875ox1.865o L31
4
GDFL-CM2.1
USA
2.5ox2.0o L24
5
MIROC3.2(hires)
Japan
1.125ox1.12o L56
6 MIROC3.2(medres) Japan
2.8ox2.8o L20
7
MRI-CGCM2.3.2
Japan
2.8ox2.8o L31
8
NCAR-CCSM3
USA
1.4ox1.4o L26
9
NCAR-PCM
USA
2.8ox2.8o L18
10 UKMO-HadCM3
UK
3.75ox2.5o L15
Ocean resolution
1.84ox1.85o L29
1.4ox0.9o L29
1.5ox1.5o L40
1.0ox1.0o L50
0.28ox0.188o L47
(0.5-1.4o) x1.4o L43
(0.5-2.5o) x2.0o L23
(0.3-1.0o) x1.0o L40
(0.5-0.7o) x0.7o L32
1.25ox1.25o L20
# 21st century runs
B1 A1B A2
3
3
3
1
1
0
2
2
1
1
1
1
1
1
0
1
1
1
5
5
5
1
0
1
2
2
2
1
1
1
Table 3. List of
chosen GCMs
which
adequately
modeled the
PDO, ENSO and
NAO and the
number of
available 21st
century runs per
scenario.
RESULTS AND DISCUSSION
• More than half of the variance in the low frequency streamflow was explained by the GLS equations
(mean R2regular = 0.56, mean R2 innovations = 0.70) (Table 2). Use of standardized variables means that
the relative importance of each predicator variable can be assessed by comparing their coefficients. The
PDO and its lags are the most important predicators in all cases, and a negative relationship exists
between northern Rocky Mountain streamflow and the PDO (Table 2) [e.g., St. Jacques et al., 2010].
•
•
These projections showed generally declining trends in surface water availability for 2000-2099. For
the A2 scenario, seven records showed declining multi-model mean projections, two of the naturalized
records showed increasing trends in the multi-model means, and one natural record showed no trend
(Figure 3). Results were identical for the B1 and A1B emission scenarios and hence are not shown.
Researchers [IPCC4, 2007, Lapp et al., 2009] have projected increases in summer warmth and
typically decreasing summer precipitation (consistent with the negative trend terms in our GLS
models), and increases in winter precipitation and temperature for this region under greenhouse forcing
(consistent with Lapp et al.’s [in review] negative mean PDO shift). Our results suggest that in the
competition between these two opposing effects on surface water availability, the former will dominate
in this region.
Figure 2. Plots of the ten northern Rocky Mountain flow records, smoothed by 5-point binomial filters (black
lines), together with fitted multiple linear GLS regressions with ARMA modeled error terms (blue), fitted
multiple linear GLS regressions without the error terms (green), and significant trend lines (red). Trend lines
only shown where significant. Mean daily flows (m3/s) averaged over the year are presented.
Winter PDO
B1
A1B
Jun.-Nov. SOI
A2
B1
SRES emission scenario
Observed mean
1900-1999
All-model 1900-1999
simulation mean
-0.109
-0.075
-0.101
0.061
0.066
0.063 -0.059 -0.050 -0.060
All-model 2000-2099 mean
-0.161*
-0.162
-0.321
-0.017
0.052
0.089 -0.040 0.177
0.168
A1B
Winter NAO
-0.098
A2
B1
A1B
A2
0.485
0.161
Table 4. 20th century observed mean climate indices and multi-model mean climate indices for the 20th
century simulations and for the 21st century projections under the B1, A1B and A2 emission scenarios.
Red values identify a future shift to a positive PDO or negative SOI (El Niño-like) or negative NAO mean
state; and blue to the opposite conditions (i.e., negative PDO or positive SOI (La Niña-like) or positive
NAO), relative to the 20th century simulation mean. Bold underscore denotes a significant change in a
multi-model mean index at the p < 0.05 level, relative to the 20th century simulation mean, as assessed by a
Monte Carlo permutation t-test. Bold * denotes significant change at the p < 0.10 level.
Figure 3. Northern Rocky Mountain river projections 2000-2099 under the A2 emissions
scenario, together with observed records (1905-2005), and 20th century river hindcasts
(1900-1999) (daily mean flows (m3/s), averaged over the year). The grey lines are the
individual model runs, the heavy blue lines are all-model means of the GCM runs, and the
heavy red lines are the observed river records.
SELECTED REFERENCES
Brockwell, P.J., and R.A. Davis (2002), Introduction to time series and forecasting, 2nd ed., Springer-Verlag,
New York.
Lapp, S., D.J. Sauchyn and B. Toth. (2009). Constructing scenarios of future climate and water supply for
the SSRB: Use and limitations for vulnerability assessment. Prairie Forum 34: 153-180.
Lapp, S.L., J.M. St. Jacques, E.M. Barrow and D.J. Sauchyn (in review). GCM Projections for the Pacific
Decadal Oscillation under Greenhouse Forcing for the Early 21st Century. Submitted to Intl. J. Clim.
St. Jacques, J.M., D.J. Sauchyn and Y. Zhao (2010), Northern Rocky Mountain streamflow records: global
warming trends, human impacts or natural variability?, Geophys. Res. Let., 2009GL042045.