1 Brainstorming for Presentation of Variability in Current Practices Scenario B. Contor August 2007

2 The first three sections are to describe the pseudo data. These will be followed by several sections of possible presentation formats based upon the pseudo data. Slides colored yellow are for ESHMC review and not proposed as alternatives for presentation.

3 Pseudo Data, Monthly Gains Targets (See spreadsheet “PseudoHistory.xls”) (Purposely constructed to not look like Snake Plain data, so we don’t get bogged down in discussions of the data themselves.)

4

5 7-yr Rand: Ten random numbers spread across the time series, interpolated for intermediate years. 7-yr Sin: Sine wave x 2, 7yrs peak-to-peak 7-yr Var: (7-yr Rand + 7-yr Sin) * (scale factor)

6 (sine wave * scale factor)

7 (sine wave * annual random number * scale factor)

8 (monthly random number * scale factor)

9 (comparison of magnitudes)

10 (sum of components)

11 Pseudo Data, Modeling Results, “Extended Data” (See spreadsheet “PseudoHistory.xls”)

12 (“Pseudo Target” is 13-month moving average of hypothetical gains, “Extended Model Data” is trace of annual stress period results )

13 (“Pseudo Target” is 13-month moving average of hypothetical gains, “Extended Model Data” is trace of annual stress period results )

14 Pseudo Data Modeling Results, “Four Methods” (See spreadsheet “PseudoHistory.xls”)

15 (Four methods are trace into the future of constant stress representing “average” conditions and practices )

16 Current Average Condition Implied Equilibrium Method 1 Implied Equilibrium Method 2 Implied Equilibrium Method 3 Implied Equilibrium Method

17 Presentation of Historical Record, option (a)

18 Figure 1: Historical gains data Proposed narrative: Monthly gains in My Favorite Reach range from a loss of approximately 60 cfs to a reach gain of over 400 cfs, over the period of record. From 1928 to 1960 there was an apparent downward trend in mean gains from 200 cfs to just under 170 cfs, followed by an increasing trend from the 1960s to 2006 to a mean gain of about 215 cfs. This is the most recent period for which gains calculations have been completed. Gains are estimated based on stream gage data, diversions, returns, and tributary contributions. Inherent in these data and resulting estimates is some uncertainty which is not addressed in this report. The Current Practices Scenario does not represent any trends which may occur in the future, because it is an analysis of the implications of today’s practices and conditions. The reader should consider that there may be trends in future practices and/or hydrologic conditions, which are not represented in the scenario.

19 Figure 2: Historical gains data with trend removed, and 13-month moving average representation of possible cyclical behavior Proposed narrative: The “detrended gains” line illustrates the typical historical behavior of monthly gains about the long-term mean value. This time series suggests that for any particular month, the gains could be 220 cfs higher, or 230 cfs lower, than the prevailing long-term mean. The 80 th and 20 th percentile values for detrended monthly gains are about 90 cfs higher, or 70 cfs lower, than the prevailing long-term mean. The 20 th and 80 th percentiles of the 13-month moving average time series indicate that even with annual variability removed, a particular year’s average gains could vary from the long-term trend by plus 50 to minus 30 cfs. Informal inspection of the moving average suggests that there are multi-year cyclical patterns in these data. (more)

20 Proposed narrative for Figure 2 (Continued): In considering the implications of the Current Practices Scenario, the reader should contemplate both the historical variability that has been observed in My Favorite Reach as well as the possibility that future changes could occur in both the cyclical and seasonal variability of gains. (If the reach data did appear to exhibit changes in variability, those would also be pointed out here.)

21 Note: This slide is not proposed to be presented in the report. For the benefit of the ESHMC, it illustrates that the 13-month moving average seems to do a reasonable job of capturing the cyclical behavior that was purposely inserted into the pseudo data. One can experiment with the spreadsheet and see that the departure of the 13-month MA from the actual cyclical behavior depends mostly on the weight of the random noise factor. Surprisingly, even when the 7-year cycle is weighted much higher than the 3-year, the 13-month MA seems to give the most intuitive representation of the combined cyclical behavior.

22 Presentation of Historical Record, option (b)

23 Figure 1: Historical gains data Proposed narrative: Monthly gains in My Favorite Reach range from a loss of approximately 60 cfs to a reach gain of over 400 cfs, over the period of record. From 1928 to 1960 there was an apparent downward trend in mean gains from 200 cfs to just under 170 cfs, followed by an increasing trend from the 1960s to 2006 to a mean gain of about 215 cfs. This is the most recent period for which gains calculations have been completed. Gains are estimated based on stream gage data, diversions, returns, and tributary contributions. Inherent in these data and resulting estimates is some uncertainty which is not addressed in this report. (more)

24 Proposed narrative (continued): The Current Practices Scenario does not represent any trends which may occur in the future, because it is an analysis of the implications of today’s practices and conditions. The reader should consider that there may be trends in future practices and/or hydrologic conditions, which are not represented in the scenario. These data suggest that for any particular month, the gains could be 220 cfs higher, or 230 cfs lower, than the prevailing long-term mean. The 80 th and 20 th percentile range is from 90 cfs higher to 70 cfs lower than the prevailing long-term mean. The 20th and 80th percentiles of the 13-month moving average time series indicate that even with annual variability removed, a particular year’s average gains could vary from the long-term trend by plus 50 to minus 30 cfs or more. Informal inspection of the moving average suggests that there are multi-year cyclical patterns in these data. In considering the implications of the Current Practices Scenario, the reader should contemplate both the historical variability that has been observed in My Favorite Reach as well as the possibility that future changes could occur in both the cyclical and seasonal variability of gains. (If the reach data appeared to exhibit changes in variability, those would also be pointed out here.)

25 Presentation of Historical Record, option (c)

26 Figure 1: Historical gains data Proposed narrative: Monthly gains in My Favorite Reach range from a loss of approximately 60 cfs to a reach gain of over 400 cfs, over the period of record. Gains are estimated based on stream gage data, diversions, returns, and tributary contributions. Inherent in these data and resulting estimates is some uncertainty which is not addressed in this report. (more)

27 Proposed narrative (continued): Inspection of these data suggests that reach gains are subject to annual variability, short- to medium-term cyclical variability, and to longer-term trends. The Current Practices Scenario does not represent any trends or cyclical variability, because the purpose is to estimate the average equilibrium implied by current practices and conditions. In interpreting scenario results, the reader should contemplate the future trends and variability that may be expected to occur. The reader should also consider that a consequence of changing conditions and practices may be that future trends and variability patterns will not be identical to the trends and patterns observed in the past.

28 Presentation of Alternate Scenario Simulations, option (1)

29 Figure 1. Simulated & observed average reach gains for My Favorite Reach

30 Proposed narrative: Simulation vs Target: In Figure 1, the dark blue line represents a 13-month moving average of historical gains estimates based on measured data for My Favorite Reach, through the most recent report date. The heavy yellow line represents the average model simulation using the extended data set. Discrepancies between these two lines may be attributed to: 1) uncertainty in measured data; 2) imprecision in model parameters and setup; 3) imprecision in the extended data set. The four solid traces beyond spring of 2007 indicate the implied timing of adjustment from today’s condition to the hypothetical long-term equilibrium condition associated with four different “best estimate” representations. These are estimates of the hydrologic impact of today’s practices applied to average historical hydrologic conditions. These traces are NOT predictions because they include no representation of any future trends or cyclical behavior. The lowest of the four estimates for My Favorite Reach is about 26 cfs lower than today’s average modeled reach gains (from the extended data) and the largest is about 81 cfs higher. This range of 107 cfs from low to high indicate the uncertainty in our ability to estimate the average recharge. For context, this range may be compared to today’s modeled average gains of 225 cfs, the target gains from 2002 through 2006 (217 to 315cfs), the 2006 observed average gains of 218 cfs, and the historical variability illustrated in Figure 1 with the dashed lines. The upper and lower black dashed lines at approximately -60 and +540 cfs represent the historical maximum and minimum departures of actual monthly gains from the average trend, historically, applied to the largest and smallest of the four long-term equilibrium discharges for My Favorite Reach. The upper and lower red dashed lines similarly apply the 20th and 80th percentile monthly departures from the average historical trend to the four traces. note to ESHMC: In real life the sim. would be smoother than target

31 Presentation of Alternate Scenario Simulations, option (2) (this option would essentially be the format in the slides presented to ESHMC 23 July 2007, which included blue vertical error bars added to the upper and lower traces)

32 Presentation of Alternate Scenario Simulations, option (3)

33 Figure 1. Simulated & observed average reach gains for My Favorite Reach

34 Proposed narrative: Simulation vs Target: In Figure 1, the dark blue line represents a 13-month moving average of historical gains estimates based on measured data for My Favorite Reach, through the most recent report date. The heavy yellow line represents the average model simulation using the extended data set. Discrepancies between these two lines may be attributed to: 1) uncertainty in measured data; 2) imprecision in model parameters and setup; 3) imprecision in the extended data set. Implied Equilibrium: The four solid traces beyond spring of 2007 indicate the implied timing of adjustment from today’s condition to the hypothetical long-term equilibrium condition associated with four different “best estimate” representations. These are estimates of the hydrologic impact of today’s practices applied to average historical hydrologic conditions. The upper and lower black dashed lines represent the final equilibrium discharges of My Favorite Reach associated with the highest and lowest of the four methodsThese traces are NOT predictions because they include no representation of any future trends or cyclical behavior. The lowest of the four estimates for My Favorite Reach is about 26 cfs lower than today’s average modeled reach gains and the largest is about 81 cfs higher. This range of 107 cfs from low to high indicates uncertainty in our ability to estimate the average recharge. For context, this range may be compared to today’s modeled average gains of 225 cfs, the target gains from 2002 through 2006 (217 to 315cfs, and the most recent (2006) average observed gains of 218 cfs. Future Expectations: Future trends and cyclical behavior are not part of this scenario and do not communicate information about the state of balance of today’s practices and today’s recharge conditions. However, actual future gains in My Favorite Reach will be strongly influenced by future trends. In contemplating the results of this scenario, and especially in contemplating future reach gains, the reader should also consider expectations of seasonal and cyclical variability and any expected future trends.

35 Presentation of Alternate Scenario Simulations, option (4)

36 Figure 1. Simulated & observed average reach gains for My Favorite Reach

37 Proposed narrative: Simulation vs Target: In Figure 1, the dark blue line represents a 13-month moving average of historical gains estimates based on measured data for My Favorite Reach, through the most recent report date. The heavy yellow line represents the average model simulation using the extended data set. Discrepancies between these two lines may be attributed to: 1) uncertainty in measured data; 2) imprecision in model parameters and setup; 3) imprecision in the extended data set. Implied Equilibrium: The four horizontal traces represent the implied equilibrium discharges for My Favorite Reach associated with four different “best estimate” representation of the water budget associated with today’s practices and long-term average climate conditions. They are NOT predictions because they do not include any representation of future trends or variability. The timing of the hypothetical adjustment to this equilibrium condition is represented by times of x, y, z, and aa years to achieve 75% of the modeled change from today’s condition, for methods 1, 2, 3 and 4 respectively. The lowest of the four estimates for My Favorite Reach is about 26 cfs lower than today’s average modeled reach gains and the largest is about 81 cfs higher. This range of 107 cfs from low to high indicates uncertainty in our ability to estimate the average recharge. For context, this range may be compared to today’s modeled average gains of 225 cfs, the target gains from 2002 through 2006 (217 to 315 cfs), and the most recent (2006) average observed gains of 218 cfs. Future Expectations: Future trends and cyclical behavior are not part of this scenario and do not communicate information about the state of balance of today’s practices and today’s recharge conditions. However, actual future gains in My Favorite Reach will be strongly influenced by future trends. In contemplating the results of this scenario, and especially in contemplating future reach gains, the reader should also consider expectations of seasonal and cyclical variability and any expected future trends.

38 Presentation of Alternate Scenario Simulations, option (5)

39 Figure 1. Simulated & observed average reach gains for My Favorite Reach. Gray bars: 20 th & 80 th percentile departures from average trend. Black bars: 20 th & 80 th percentile cyclical variation.

40 Proposed narrative: Simulation vs Target: In Figure 1, the yellow bar represents the average reach gains for My Favorite Reach from the most recent data (2006). The first red bar represents the extended-data simulation for the same period. Differences are due to three factors; 1) imprecision in gains data; 2) imprecision in conceptual model and numerical model parameters; 3) imprecision in extended data set. Implied Equilibrium: The blue bars represent the implied equilibrium discharges for My Favorite Reach associated with four different “best estimate” representation of the water budget associated with today’s practices and long-term average climate conditions. They are NOT predictions because they do not include any representation of future trends or variability. The timing of the hypothetical adjustment to this equilibrium condition is represented by times of x, y, z, and aa years to achieve 75% of the modeled change from today’s condition, for methods 1, 2, 3 and 4 respectively. For context, these equilibrium discharges may be compared with the second red bar, the extended-data representation of today’s average gains. The lowest of the four estimates for My Favorite Reach is about 26 cfs lower than today’s average modeled reach gains and the largest is about 81 cfs higher. This range of 107 cfs from low to high indicates uncertainty in our ability to estimate the average recharge. For context, this range may be compared to today’s modeled average gains of 225 cfs, the target gains from 2002 through 2006 (217 to 315 cfs), and the most recent (2006) average observed gains of 218 cfs. (more)

41 Proposed narrative (continued): We expect that the equilibrium condition implied by today’s practices, if the period-of-record hydrologic regime were to continue, would be for average gains in My Favorite Reach to be somewhere between 199 and 306 cfs. About this average we would expect multi-year cyclical variation with 20 th /80 th percentile deviations on the order of cfs. Including cyclical and annual variability, we would expect monthly gain to have a 20 th /80 th percentile range of approximately 80 cfs about these simulated equilibrium gains. The 20 th /80 th percentile expectation for a given year, then, is for annual average gain to be in the range of cfs. A given month may be expected to range between 119 and 385 cfs. Future Expectations: Future trends and cyclical behavior are not part of this scenario and do not communicate information about the state of balance of today’s practices and today’s recharge conditions. However, actual future gains in My Favorite Reach will be strongly influenced by future trends. In contemplating the results of this scenario, and especially in contemplating future reach gains, the reader should also consider expectations of seasonal and cyclical variability and any expected future trends.