Adapting Colorado River Basin Depletions to Available Water to Live within Our Means

The exploratory model is a generic simulation model. The object-oriented programming allows users to build a network in a structured way, the open-source feature provides users the ability to code unique features and model behaviors, and Python libraries provide tools for fast data processing. Building a customized model and running a simulation with the exploratory model mainly involves four steps.

Multidimensional uncertainty analysis can reveal the effects of multiple uncertain factors on the activity or system of interest. It was used by Brown et al. (2012) to help understand how decisions are sensitive to uncertain changing precipitation, temperature, and other factors. The exploratory model provides such a tool to help identify the combinations of future streamflow, user demands, and operating policies that push the system into vulnerable or undesirable states. The insights from sensitivity analysis can help guide when and how to adapt operating policies to avoid system failure. In the exploratory model, to initiate a multidimensional uncertainty analysis, first the inflow ranges and different demand levels are specified in SensitivityAnalysis.py, then user polices are defined in ReleaseFunction.py, and finally the policies are simulated under different combinations of inflows and demands in start.py. Results from this process can help identify (1) under what conditions and how long the system will fail, and (2) policies that reduce failures or more quickly recover the system.

In the exploratory model for the Colorado River Basin, two reservoirs, Lake Powell and Lake Mead, account for approximately 83% of the entire basin storage volume. There are two aggregated users: the Upper Basin, and the Lower Basin and Mexico (Fig. 1). In this example, three upper basin tributaries (Upper Colorado River, Green River, and San Juan River) were aggregated into one tributary to Lake Powell, and three tributaries (Paria River, Little Colorado River, and Virgin River) were aggregated into one tributary to Lake Mead. Lake Mead downstream gains and losses include inflow below Lake Mead, changes to Lake Mohave and Lake Havasu storage, and evaporation losses. All individual Upper Basin users were combined into one Upper Basin user (UB), and all Lower Basin and Mexico users were combined into one Lower Basin user (LB and Mexico). We assumed that the combined Upper Basin user consumes water above Lake Powell, and that the combined Lower Basin user consumes water below Lake Mead and its downstream gain and losses.

The exploratory model simulates reservoirs from upstream to downstream. For each reservoir, the water balance equation—inflows minus releases minus evaporation equals change in storage—is applied to simulate the changes in reservoir storage based on different operating rules. In the exploratory model, all basic param for Lake Powell and Lake Mead were obtained from the August 2020 version of CRSS. In CRSS, evaporation for Lake Powell is calculated using a periodic net evaporation method, and Lake Mead evaporation is the product of reservoir surface area and evaporation rates. To be consistent with CRSS, we used the same method in the exploratory model.

The Direct Natural Flow scenario from 1906 to 2018, which had $18.2\mathrm{bcm}/\mathrm{year}$ ($14.76\mathrm{maf}/\mathrm{year}$) mean natural flows at Lees Ferry, was incorporated into the exploratory model. This scenario includes the mid-20th century drought from 1953 to 1977, with $15.9\mathrm{bcm}/\mathrm{year}$ ($12.89\mathrm{maf}/\mathrm{year}$) mean natural flows at Lees Ferry and the Millennium Drought from 2000 to 2018, with $15.3\mathrm{bcm}/\mathrm{year}$ ($12.44\mathrm{maf}/\mathrm{year}$) mean natural flows at Lees Ferry. In the Direct Natural Flow scenario, the index sequential method (Kendall and Dracup 1991; Ouarda et al. 1997) is applied to generate 113 hydrologic traces. This scenario is provided by the US Bureau of Reclamation and is used in CRSS (August 2020 version). For sensitivity analysis, we used scenarios of Lees Ferry natural flow that ranged from 17.3 to $6.2\mathrm{bcm}/\mathrm{year}$ ($14–5\mathrm{maf}/\mathrm{year}$) each year and were observed in the tree-ring reconstructed flow record from 1416 to 2015 (Salehabadi et al. 2020). This range captures long-term droughts such as the mid-20th century drought and the Millennium Drought, and it also captures short-duration droughts such as the extreme dry year 2002 [$7.3\mathrm{bcm}/\mathrm{year}$ ($5.9\mathrm{maf}/\mathrm{year}$)] and the 2012–2013 drought sequence [$10.7\mathrm{bcm}/\mathrm{year}$ ($8.7\mathrm{maf}/\mathrm{year}$)]. We assumed that average intervening inflow below Lake Powell was $1.1\mathrm{bcm}/\mathrm{year}$ ($0.9\mathrm{maf}/\mathrm{year}$) (Wang and Schmidt 2020), which included tributaries within the Grand Canyon and streamflow from the Virgin River.

We used an increasing UB demand scenario projected by the Upper Colorado River Commission (UCRC 2007) that also is the default demand schedule in CRSS (August 2020 version). In addition to the LB and Mexico demand schedule, Lake Mead also needs to release water to meet LB gains and losses (including inflow below Lake Mead, changes to Lake Mohave and Lake Havasu storage, and evaporation losses). These data used in the exploratory model varied among different streamflow traces, and all were obtained from CRSS (August 2020 version). In sensitivity analysis, average UB demand was assumed to be 6.6 bcm (5.35 maf) per year (UCRC 2007, schedule B), and average LB and Mexico demand was assumed to be 11.8 bcm (9.6 maf) per year (Fleck 2020) (Table 1).

In the current version of the exploratory model, we replicate seven important CRSS Lake Powell operating rules that equalize Lake Powell and Lake Mead storages under different elevation tiers defined in the 2007 Interim Guidelines (USBR 2007). In addition to these rules, the exploratory model also provides a compact version of the equalization rule that uses fewer parameters than the replicated rules. In this rule, Lake Powell releases are iterated to balance Lake Powell and Lake Mead. The 2007 Interim Guidelines, Drought Contingency Plan (USBR 2019), and International Boundary and Water Commission (2012, 2017) determine LB and Mexico contributions (or cutbacks) under different Lake Mead elevations; the lower the elevation, the larger is the cutback. In the exploratory model, a nested if-else statement is used to return increasing cutback values as Lake Mead elevation falls from 332 to 312 m (1,090 to 1,025 ft). A new $\mathrm{DCP}+1.5$ rule returns cutbacks 1.5 bcm (1.2 maf) per year larger than the DCP for the same elevation tier. This $\mathrm{DCP}+1.5$ rule goes further than a December 2021 pledge by the Lower Basin states to conserve an additional 0.6 bcm (0.5 maf) each year for 2 years (USBR et al. 2021).

The adaptive policy in this research was defined as adapting depletion to the average past 10-years of system gain (Fig. 2). Gain is the difference between inflow and reservoir evaporation. The ADP uses the most recent hydrologic information every year to assist with the next year’s decision-making regarding depletions and reservoir storage. The benefits to using hydrologic information from several past years include the following: (1) it allows users to use only the available water coming into the system; (2) it dynamically balances basin depletion and water system gains; (3) it captures recent hydrologic changes; (4) it uses the most recent data; and (5) it prevents severe reservoir drawdown during one or more low inflow years. Water conserved in reservoirs still belongs to users, and can be used when severe drought occurs. Eq. (1) assumes that next-year depletion for the entire basin is equal to the average past gains to the systemwhere $D_y$ = total water depletion in year $y$; $I_t$ = inflow in past year $t$; $E_t$ = evaporation in past year $t$; $N$ = total years to look backward; and $y-N$ to $y-1$ = lookback period.

Water shortages in the coming year are calculated by subtracting the total system depletion determined using Eq. (1) from the original basin demand schedule. Many strategies exist to allocate entire basin shortages to UB or LB and Mexico. We tested different strategies ranging from the UB bearing all shortages to the UB bearing no shortages. In this research, we simulated the ADP strategy along with the equalization policy (to determine where to store water) across all historical streamflow records (1906–2018). The ADP strategy is assumed to start in January 2021 and will be triggered only when Lake Mead elevation is less than 323 m (1,060 ft) and the average system gain over the last 10 years is smaller than the next year’s demand schedule. Selecting 323 m (1,060 ft) creates a buffer before Lake Mead drops below 312 m (1,025 ft). When Lake Mead elevation is above 323 m (1,060 ft), LB and Mexico contributions are calculated by the DCP operation. The 323 m (1,060 ft) trigger is 10.7 m (35 ft) and 3 bcm (2.4 maf) higher than the 312 m (1,025 ft) trigger in the Lower Basin DCP. Managers can trigger the adaptive rule at higher or lower elevations. Triggering at a higher elevation will reduce depletions earlier and leave more water in the reservoir.

To validate the exploratory model, we set the values for Lake Powell inflow and intervening Lake Mead inflow, starting storage, maximum releases, demands, and operating rules in the exploratory model to be the same as the values in the August 2020 version of CRSS (Appendix). Results for one hydrologic trace that repeated a mid-20th century drought show that simulation results for Lake Powell and Lake Mead storage, inflow, and outflow from the exploratory model were very close to those of CRSS (Fig. 3). The average flow at Lees Ferry during this mid-20th century sustained drought (1953–1977) was $15.9\mathrm{bcm}/\mathrm{year}$ (12.89 $\mathrm{maf}/\mathrm{year}$), which was 87% of the long-term average from 1906 to 2018 (Salehabadi et al. 2020). Validation results for other hydrologic traces also were similar (Appendix). The computational time for each hydrologic trace in the exploratory model was about 0.35 s, which is 50 times faster than the CRSS single-trace run time of about 20 s in the same computational environment (single-core testing with Intel Core i7-9850H CPU at 2.60GHz). Minor differences between the exploratory model results and CRSS results were due to the exploratory model replicating many important policies in CRSS, but not all of them (Appendix). These validation results demonstrate the capability of the exploratory model to simulate correctly the two largest reservoirs in the Colorado River system.

We used the sensitivity analysis tool introduced in the section “Sensitivity Analysis” to analyze system performance under different natural flows at Lees Ferry, user demands, and release policies. Under many scenarios in which Lees Ferry natural flow ranged from 6.2 to 15.3 bcm (5–12.4 maf) every year, the existing Lower Basin DCP operations drew down the combined storage of Lake Powell and Lake Mead to 14.8 bcm (12 maf) in less than 5 years (Fig. 4). We selected the combined 14.8 bcm (12 maf) storage threshold because it represented drawdown to 7.4 bcm (6 maf) of storage in each reservoir, which are the elevations to protect the minimum power pool for Lake Powell [1,074 m (3,525 ft)] and the lowest operation tier in the Drought Contingency Plan for Lake Mead [312 m (1,025 ft)]. With natural flow of 15.3 bcm (12.4 maf) at Lees Ferry every year, increasing the largest DCP cutback by 1.5 bcm (1.2 maf) per year over the existing cutback pushes the drawdown time to about 20 years. However, with natural flow of 12.3 bcm (10 maf) or lower at Lees Ferry every year, all versions of the DCP drew down combined reservoir storage to 14.8 bcm (12 maf) in about 3 years or less. The shaded section in Fig. 4 shows the numerous combinations of event duration and natural flow volume at Lees Ferry that occurred in the observed and paleo records (Salehabadi et al. 2020, Fig. 14). These numerous hydrologic scenarios are possible and quickly can draw down reservoir storage to critical levels. The solid and dashed lines in the shaded area indicate that DCP and DCP+ will not get the LB, Mexico, or UB through many hydrologic events from the observed and paleo records.

In contrast, the ADP keeps combined reservoir storage above 14.8 bcm (12 maf) for 40 years or longer for Lees Ferry natural flows above 6.2 bcm (5 maf) per year each year. For Lees Ferry natural flow of about 6.2 bcm (5 maf) per year each year, the ADP does not maintain combined storage above 14.8 bcm (12 maf) because the reservoir storage falls below 14.8 bcm (12 maf) before the ADP rule is triggered. The ADP rule sustains reservoir levels through much longer droughts than do the current DCP operations. The ADP rule sustains reservoir levels because the ADP rule adapts and cuts back depletions to the available gains to the system—the inflow minus evaporation. In contrast, the DCP operations and variants cut back depletions according to a lower fixed lake level schedule that does not consider annual reservoir inflow. In short, the ADP requires users to conserve more water than the DCP. When UB demands are reduced to 5.6 bcm (4.5 maf) per year, it can delay the time at which the combined reservoir storage draws down to 14.8 bcm (12 maf) (Appendix).

Fig. 5 shows trade-offs between combined reservoir storage volume at the end of the simulation and steady-state basin depletion. The larger the end-of-planning horizon combined storage (which is affected by different policies, indicated by different marker shapes), the smaller are the steady state total depletions under the same amount of natural flow at Lees Ferry (indicated by intensity). Among the three tested policies, DCP emptier reservoir storage first; however, steady-state basin depletion is the largest because reservoir evaporation no longer is a factor after Lake Powell and Lake Mead become run-of-river reservoirs. DCP+ preserves more water than DCP, but only avoids emptying reservoir storage when natural flows were not low. ADP kept the combined reservoir storage higher than 14.8 bcm (12 maf) at the expense of having the lowest steady-state depletion among these policies. However, when combined reservoir storage reaches steady state, only minimal additional cutbacks from ADP are required to keep the reservoirs running above 14.8 bcm (12 maf) compared with DCP or DCP+.

Previous analysis showed that inflow is one dominant factor in declining reservoir storage. Therefore, in addition to reservoir elevation and storage, operating rules for the Colorado River also can consider inflow information because the combined effect of inflow and releases contributes to the changes in reservoir storage. Previous analysis also showed that ADP could keep the combined Lake Powell and Lake Mead storage above 14.8 bcm (12 maf) under different natural flow scenarios at Lees Ferry. This indicates that adapting depletions to inflow is a promising strategy to sustain reservoir storages.

Figs. 6(a and b) compare Lake Powell and Lake Mead elevations for the ADP and DCP policies under the Millennium Drought hydrology [average Lees Ferry natural flow of 15.3 bcm (12.4 maf) per year] (Salehabadi et al. 2020). The ADP policy keeps Lake Powell above 1,064 m (3,490 ft) (the Lake Powell minimum power pool) and Lake Mead above 312 m (1,025 ft) for most of the time [Figs. 6(a and b)], but at the sacrifice of experiencing large water shortages [Figs. 6(c and d)]. The additional water saved by ADP in earlier years is not wasted; instead, some of the water is stored in both Lake Powell and Lake Mead, thus leaving more water for future use. These results demonstrate the value of water conservation. Users get through a hydrologic scenario that continues the Millennium Drought by conserving 0 to 1.2 bcm (1.0 maf) per year [Fig. 6(d)] more than the current DCP. Conserving 1.2 bcm (1.0 maf) more than the current DCP means conserving as much as 0.6 bcm (0.5 maf) per year more than the Lower Basin’s December 2021 conservation pledge of 0.6 bcm (0.5 maf) per year (USBR et al. 2021). Results for the mid-20th century drought (Appendix) were similar, and also highlighted the value of water conservation.

In addition to distributing shortages proportionally to UB and LB and Mexico, we also simulated different allocations of new shortages to the UB and LB and Mexico, and found a quasi-linear tradeoff (Fig. 7). In Fig. 7, the circle represents the complete fulfillment of all demands over the next 19 years. Clearly, the entire basin will not have enough water to satisfy all UB and LB and Mexico demand if the Millennium Drought continues. The quasi-linear tradeoff also indicates that both UB and LB and Mexico contributions are important; no plan is superior to all others. The split of the new shortages should be negotiated by all basin users in a more collaborative way. Results for the mid-20th century drought (Appendix) were similar.