Evaluating the Approaches and Assumptions
Used to Calculate X2 Using
Field Observations and Numerical Simulations
Michael L. MacWilliams, Ph.D.
Delta Modeling Associates, Inc.
CWEMF Annual Meeting
April 24, 2013
Outline
• What is X2?
• How Is X2 Estimated?
– Longitudinal Salinity Observations, Regression
Relationships, Fixed Surface Salinity, Modeling
• Do Different Methods Yield Different X2?
– Assumptions of Common Calculation Approaches
• Does Stratification Matter?
– What can we Learn about X2 from Observations?
– What can we Learn about X2 from Modeling?
• Conclusions
What is X2?
Jassby et al. (1995)
X2 is defined as the position
of the 2 psu bottom salinity
value, measured along the
axis of the estuary in km from
the Golden Gate.
Why is X2 Relevant?
• The abundance or survival of
several estuarine biological
populations in the San Francisco
Estuary is positively related to
freshwater flow (Jassby et al. 1995).
• The 1994 Bay-Delta agreement
established standards for X2 based
on outflow.
• The Delta Smelt Biological Opinion
established a Fall X2 RPA during
Sept-Nov following above normal or
wet water years.
X2 is defined as the position
of the 2 psu bottom salinity
value, measured along the
• Understanding how specific projects
axis of the estuary in km from
or restoration actions affect X2
provides a metric for both the
the Golden Gate.
potential impact on species and
water operations.
Outline
• What is X2?
• How Is X2 Estimated?
– Longitudinal Salinity Observations, Regression
Relationships, Fixed Surface Salinity, Modeling
• Do Different Methods Yield Different X2?
– Assumptions of Common Calculation Approaches
• Does Stratification Matter?
– What can we Learn about X2 from Observations?
– What can we Learn about X2 from Modeling?
• Conclusions
How is X2 Estimated?
1) Direct Observations
2) Using Flow-X2 Regression Relationships
3) From Observed Surface Salinity (CX2)
4) Using Hydrodynamic Models
How is X2 Estimated?
1) Direct Observations
What Can We Learn from Observations?
What Can We Learn from Observations?
How is X2 Estimated?
2) Using Flow-X2 Regression Relationships*
• Jassby et al. (1995):
– X2(t)= 8 + 0.945*X2(t-1) – 1.5log(QOUT(t))
• Jassby et al. (1995) as cited by Monismith et al. (2002):
– X2(t)= 10.2 + 0.945*X2(t-1) – 2.3log(QOUT(t))
• Monismith et al. (2002):
– X2(t)= 0.919*X2(t-1) + 13.57(QOUT(t)-0141)
• DAYFLOW:
– X2(t)= 10.16 + 0.945*X2(t-1) – 1.487log(QOUT(t))
• Jassby et al. (1995) and Monismith et al. (2002) assumed
that the bed salinity was 2.0 psu when the surface salinity
was equal to 1.76 psu (3.36 mmhos/cm)
– Assumes 0.24 psu stratification
*As summarized by: Anke Mueller-Solger (2012)
How is X2 Estimated?
3) Using Observed Surface Salinity (CX2)
• Operationally X2 (CX2) is calculated from observed surface
EC at Martinez, Port Chicago, Mallard Island and Collinsville
using the equation (Applies only for 56<X2<81):
–
–
–
–
wEC is the daily-average EC in mmhos/cm of the westerly station
eEC is the daily-average EC in mmhos/cm of the easterly station
wkm is the km from the Golden Gate of the westerly station
ekm is the km from the Golden Gate of the easterly station
• Assumes bed salinity is 2 psu (3.80 mmhos/cm) when
surface EC is 2.64 mmhos/cm (1.36 psu).
– Assumes 0.64 psu stratification
How is X2 Estimated?
4) Using Hydrodynamic Models
How is X2 Estimated?
4) Using Hydrodynamic Models
September 27, 1994
January 18, 1995
How is X2 Estimated?
4) Using Hydrodynamic Models
Outline
• What is X2?
• How Is X2 Estimated?
– Longitudinal Salinity Observations, Regression
Relationships, Fixed Surface Salinity, Modeling
• Do Different Methods Yield Different X2?
– Assumptions of Common Calculation Approaches
• Does Stratification Matter?
– What can we Learn about X2 from Observations?
– What can we Learn about X2 from Modeling?
• Conclusions
Do Different Methods Yield Different X2?
From: Gross, MacWilliams and Kimmerer (2010)
Outline
• What is X2?
• How Is X2 Estimated?
– Longitudinal Salinity Observations, Regression
Relationships, Fixed Surface Salinity, Modeling
• Do Different Approaches Yield Different X2?
– Assumptions of Common Calculation Approaches
• Does Stratification Matter?
– What can we Learn about X2 from Observations?
– What can we Learn about X2 from Modeling?
• Conclusions
What Can We Learn from Observations?
September 27, 1994
January 18, 1995
Observed X2: 87.3
Observed X2: 51.6
Observed Surface Salinity at X2: 1.95
Observed Surface Salinity at X2: 0.14 PSU
Observed Stratification at X2: 0.05 PSU
Observed Stratification at X2: 1.86 PSU
X2 From 1.76 PSU Surface Salinity: 88.2
X2 From 1.76 PSU Surface Salinity: 37.0
Bed Salinity at 1.76 PSU Surface: 1.80 PSU
Bed Salinity at 1.76 PSU Surface: 16.0 PSU
Observed Stratification at
1.76 PSU Surface Salinity
More than 0.24 PSU
stratification
Less than 0.24 PSU
Stratification
Observed X2 From
Surface vs. Bed Salinity
Observed Surface EC
Observed & Predicted Surface EC
Surface Salinity vs. Bed Salinity
Surface Salinity vs. Bed Salinity
Surface Salinity vs. Bed Salinity
X2 from Bed Salinity
more than X2 from
Surface Salinity
X2 from Surface
Salinity more than
X2 from Bed Sal
Surface Salinity vs. Bed Salinity
Evaluation of Jassby et al. (1995):
Assumes 0.24 psu stratification
Assumption of 0.24 psu stratification
(3.37 mmhos/cm surface EC)
tends to under predict X2 relative to X2
calculated from OBSERVED bed salinity
Evaluation of CX2:
Assumes 0.64 psu stratification
Assumption of 0.64 psu stratification
(2.64 mmhos/cm surface EC)
tends to over predict X2 relative to X2
calculated from PREDICTED bed salinity
Surface Salinity & Stratification
Observed Surface Salinity at Observed X2
Observed Stratification at Observed X2
X2 and LSZ Area: 1994 - 1997
X2 and LSZ Area: 1994 - 1997
Conclusions
• A variety of approaches are available to estimate X2.
• All estimates of X2 derived from surface salinity make some
assumption about stratification.
• Stratification typically varies as a function of X2, but also shows
significant scatter resulting from both spring-neap variability and
antecedent conditions.
• Flow-X2 Relationships derived from the Jassby et al. (1995) or
Monismith et al. (2002) approaches tend to underestimate
stratification and therefore underestimate X2.
• The current real-time equation used to calculate X2 (CX2)
assumes a relatively high amount of stratification and therefore
tends to overestimate X2, particularly for 70 < X2 < 81.
• Models and extensive data are now available to help improve
approaches for estimating X2.
Acknowlegments
Edward Gross
Wim Kimmerer
Anke Mueller-Solger
Aaron Miller
Bruce Herbold
USACE
DWR
USBR
IEP/POD
Contact info:
[email protected]
www.deltamodeling.com