DELTA ISB: Water Supply Reliability Estimation: an overview

Water supply reliability. It’s half of the co-equal goals of “providing a more reliable water supply for California and protecting, restoring, and enhancing the Delta ecosystem. The co-equal goals shall be achieved in a manner that protects and enhances the unique cultural, recreational, natural resource, and agricultural values of the Delta as an evolving place.” (Water Code 85054)  But what exactly does it mean? And how do you measure it?

At the October meeting of the Delta Independent Science Board, Dr. Jay Lund gave an overview of water supply reliability.  His presentation discussed water system portfolios, water demands, what factors can make water systems unreliable, the approaches to estimating water supply reliability, and the metrics used.


Dr. Lund began with a cartoon, which he noted summarizes well most of us understand our water supply systems.  It also illustrates how reliable most of our water systems are (at least for human purposes) that most of us feel quite comfortable not knowing all the details about how water gets to us.  He also noted the cartoon illustrates where you have to begin whenever you talk about water to any public group or any group of politicians or leaders.

California has a very elaborate water supply system, resulting from the complexity of the state’s hydrology and water demand.  On the map, the dark blue areas show the 20% of the surface area of California that is responsible for two-thirds of all the runoff in the state; the light blue shows another 20% of the surface area that is responsible for an additional 24% of the state’s runoff. The red area to the south, primarily, is 30% of the state’s surface area is responsible for point 1% (.1%) of all the runoff.

So together, 90% of the surface water comes from 40% of the land area,” Dr. Lund noted.

The human demands include agriculture, mainly in the red and orange parts of the Central Valley; agriculture in the Imperial Valley, which is entirely in the red zone; and important coastal agriculture, very little of which is actually tied to the Delta.  The major cities in the San Francisco Bay Area, Central Valley, Fresno, Sacramento, and Southern California where about two-thirds of the state’s population resides, are also pretty dry.

California has a Mediterranean climate, which means that the water is available in the winter; however, we need it most during the summer and fall.  To manage the system where the water is not to where we want it, we have to move water in space and time by quite a bit, he said.

The map to the right shows all the major infrastructure in California’s water system: a large number of reservoirs, major groundwater basins, particularly in the Central Valley, and large aqueducts.  The map is colorful because all these bits of infrastructure are owned by different layers of government: different federal agencies, different state agencies, and a significant amount by local and regional water agencies.

All of this has to sort of function as one system, and over time, it has somewhat managed to operate in a very challenging water supply environment with a lot of inverse seasonality and a lot of variability,” Dr. Lund said.

The chart on the lower left illustrates how variable California’s precipitation is from year to year. There is a very long dry season and a short wet season.  The water year begins October 1st, and Dr. Lund pointed out that it’s not all that unusual that we haven’t received much precipitation yet this year.  A few large storms make the difference between a wet year and a dry year here in California.  The wet season usually ends in early April and is followed by a long dry season.

The map on the upper right shows the annual coefficient of variation for precipitation from precipitation gauges all across the continental US. In the east, there isn’t much in terms of annual variability and precipitation; as you move west, it gets more variable, and then when you get to California, there is a much greater annual coefficient of variation, even more so in Southern California

We have quite a lot of variation within the year and a tremendous amount of variation relative to other parts of the country,” Dr. Lund said. “We have more floods and droughts per average year than any other part of the country.

The slide is a plot of the unimpaired Delta outflow, which is what outflow would be if there were no projects or water diversions.  The green bar represents an average year, the red bar is the driest year of record, and the blue bar is the wettest year of record up until most recently. 2017 was actually tremendously wet, even wetter than 1983 in California, he noted.

You can see the seasonality and you can see the effect of snowmelt,” he said.  “Essentially, our precipitation ends in April, but we have a snowmelt pulse coming out for a few months after that.”

The map on the right on the slide is the California water system, and for conceptual clarity, the diagram on the left shows the elements of a typical water system. There’s usually a surface water source, and there are often surface water reservoirs and groundwater basins, which typically have more storage capacity than surface water. Then we have movements of water in and out, sometimes imported from or export to other basins. And there are different kinds of human water demands and different kinds of environmental water demands at different locations at different times.

You can sort of imagine how you can reduce the simple one to a system of equations,” he said.  “It’s the same equations you can apply to anything more complex.”

Dr. Lund next presented a slide showing Orange County’s water system.   They have Delta water supplies, water marketing transfers that they make with Metropolitan Water District and others, local reservoirs and groundwater banks, Colorado River supplies, and their own water demands that they manage.  They are also concerned about climate change.

They try to manage all of these sources and all these water demands together, both for planning timescales and certainly in operational timescales,” he said.


The table shows the portfolio elements that a water supply system can have.  There are quite a few different types of water sources, and there are ways of moving that water about in space and in time. Some of it happens naturally, such as the snowpack; some happens artificially, and some of which is both natural and artificial, as with aquifers. 

We have lots of ways of treating water to make water available for different kinds of water uses that they wouldn’t naturally be available for,” said Dr. Lund.  “And there are all kinds of operational strategies, rules, policies, and agreements that one can have to juggle and logistically manage all these sources, sinks, treatments, and facilities infrastructure together.

The top part of the chart is the water supply side of a portfolio; the middle section is all the different water use efficiency and water use reduction activities both for agricultural and urban uses, along with ecosystem uses, recreation, and any other uses.  There are various water use efficiency and water use reduction activities that can be done, all of which come with costs because this water is useful and valued for quite a few different purposes. These water systems involve many different groups of people, agencies, and individual decision-makers, from the water users to the different water managers that often have coordinating agreements for the water market activities among them.

So a third important aspect of a water system portfolio is the incentives so that people work well together, such as prices, markets, learning, shaming, education, subsidies, taxes – the kinds of things that are necessary to keep the social cohesion that keeps these systems working well together,” Dr. Lund said. 

He presented the slide at the lower left showing San Diego County Water Authority’s portfolio, noting that they went from being almost essentially dependent on Metropolitan Water District to developing quite a bit of diversification over time, including potable reuse, some desalination, groundwater, and different ways of conveying water from the Colorado River.

It’s important to emphasize that these portfolios and water management activities happen at lots of different scales,” said Dr. Lund.  “At the local scale, there are a lot of different activities that the local agencies themselves can do. And they can work with other neighboring agencies and distant agencies to implement some of these.  There are other statewide and regional activities that help regions cooperate, as well as things like state plumbing codes, which can affect demand.  So water management activities, including planning, essentially become portfolio planning to try to come up with desirable mixes of all these actions that will work well under the wide variety of hydrologic conditions and long term water demand conditions that we expect for the system.”


Water demands are often a neglected aspect of water supply reliability.  There are many different types of demands. Most of us think of urban water demands for drinking, sanitation, landscaping, and all the things that we do as cities, as well as commercial and industrial uses.

Agriculture itself has quite a diversity of water demands for different kinds of crops, soil management, and leaching of salts, among other things. With orchards of fruit or nut trees, there’s essentially a permanent demand for water for the lifetime of those trees, whereas with vegetables and pasture land, you can decide to fallow for a year without extraordinary economic losses.

There is quite a lot of interest and concern with environmental water demands regarding quantity, quality, the dilution of pollution pollutants, and the importance of those water supplies to sustain different kinds of habitat at different times of the year under wet or dry year conditions.

There are a lot of different ways that water works to support ecosystems where people are still trying to work a lot of these demands out in a more formal way,” he said. 

These demands vary with time. Urban water demands vary by the hour during the day. All of these water demands vary seasonally; they also vary over longer periods and with historical development and economic conditions.

Dr. Lund pointed out that all water demands, uses, and shortages are not equally valued.  Everybody has a different idea of how they should be valued, but there’s probably a lot of consensus that they are valued differently by different people at different times.

There are different views on quantifying water demands. One approach is to have point demand volumes over time, such as shown on the graph on the left.  Environmental water uses might be high sometimes and low at others. Agricultural water use for irrigation systems tends to be seasonal but relatively low at other times a year.  With urban water use, there is a lot of landscape irrigation in one season and relatively low in other seasons, but still quite valuable indoor water uses the rest of the year. This is typically how most water demands are quantified, he said.

Dr. Lund noted that the economic value of those demands also varies.  At any given time, the volume of that water has different incremental values as you move up; typically, there’s a diminishing incremental value of additional water for most uses.

The consequences of shortages are significant when you’re characterizing water demands, said Dr. Lund.  “A couple of great quotes on the subject: ‘There is a shortage of sports cars, I don’t have one.’ So when you hear people complaining about water shortages, this quote comes to mind. People often complain about shortages, meaning they would like to have more for free, please.  The other quote that brings to mind this economic view of water shortages: ‘There’s rarely a shortage of water, but often a shortage of cheap water.’ Just like sports cars. This diminishing value of additional water.”

He presented the chart below showing cumulative jobs and revenues for California agriculture, noting that the chart is ordered from the high valued jobs and crops to the lower value ones.  The chart shows that about half of the irrigated acreage in California is responsible for 85 to 90% of the ag jobs and revenue, as well as the water use, he said.  He also noted that the same kind of general shape also applies for urban water use: About half of our urban water use in California is for landscape irrigation, which has very little economic value, at least in the drought year.


What makes water systems unreliable?  Certainly lack of inflow and drought, he said.  “One of the biggest sources of unreliability in actual municipal water systems nationally is floods; a flood can take out a drinking water treatment plant,” Dr. Lund said.  “Earthquakes wildfires, …  technical and operational failures, such as Flint.  Human failures leading to operational failures.  Increasing water demands; Cape Town, South Africa, had some problems with not preparing for growing water demands.  Regulatory systems for environmental regulations – there’s a lot of concern that they will reduce water availability for other human uses. And sometimes you’ll have agreements to share water, and then agreements fall through. And multiple failures can occur from time to time. So lots of different ways you can have unreliability.”

In terms of representing summary reliability, they will typically look at particular scenarios, such as time series of scenarios happening or not happening, reliability/unreliability events happening or not happening, and digesting those down to the probabilities. Then use historical experiences, scenarios of concern, or synthetic cases as the basis for characterizing the conditions and potential unreliability.


We use a lot of time series in all of this, and then often do some kinds of Monte Carlo analysis to estimate probabilities,” said Dr. Lund.  “Typically, there’ll be a system simulation model that basically takes elaborations of that simple system that we looked at before, where we have inputs and the inflows, the capacities of different elements of the system, the water demands we expect, and the operating rules.  We’ll have a time step based simulation and we march through time with the different inflows and demands. Operating with the rules and things such as capacities and conservation of mass, we get deliveries, shortages, and losses as outputs. and then we can interpret those results probabilistically.”

Simulation modeling is a ‘what if’ approach.  Models are used to represent very complex systems, and there is a legion of simplified details, capacities, and responses. These simulations are run for each case to estimate response using conditions and consequences or to explore different operating strategies, operating rules, and other things.  Probabilities are assigned to these results to assess the overall reliability and consequences and what that should mean for operating, planning, and policy decisions.

The slide shows some example results from a model pulled from the 2015 report from the state on water deliveries with the Delta tunnel and existing conditions.  The results are sorted and ordered by rank, and used to develop probability of exceedance plots for different amounts of water exports.

He pointed out that in the year 2014 and 2015, the actual deliveries during the drought were less than anything that had been predicted, so you always have to take model results and any kind of analysis with a grain of salt.

The analysis of seasonal operational reliabilities is called position analysis.  It is commonly done each season for seasonal operations planning.  Managers will try to game out for several years to figure out how to best manage the system probabilistically over time for droughts.

It’s really important to interpret these probability estimates in context. These are not numbers that have relevance outside of the larger context of what available problems and options are that exist for managers and policymakers. There’s a lot of modeling error in these kinds of processes that are unavoidable.”

A couple of Dr. Lund’s favorite quotes:  “‘ All models are wrong, but some are useful’ by the famous statistician George Box,” he said.  “‘ The purpose of computing is insight, not numbers.” So when I see these kinds of studies done, I’m always interested in what they learned from it. I don’t particularly care about the numbers.  I want to know what you can learn from the numbers and the patterns in the numbers. But all the components of this modeling have different kinds of elements of formulation, calibration, version control, testing, and interpretation that goes into this, so to me, the interpretation and the documentation of this process is quite important.”

The longest-standing regularly performed water supply reliability studies related to the Delta is the State Water Project delivery capabilities report, which is updated every two years.

Local areas tend to do their own analysis.  The slide shows analysis for Orange County’s complex regional system.  They’re looking at different kinds of climate change and other kinds of Delta management activities and how that would affect their delivery reliability and shortage liability their liability results.

The major water users in California, certainly the urban agencies, do a lot of this kind of analysis internally and with others quite often,” Dr. Lund said. “Orange County’s water system lies within the Metropolitan Water District; Metropolitan Water District does the analysis, making assumptions about how Orange County is going to react and vice versa. So this is a pretty integrated system that everybody does their analysis on their own and sometimes together.” 

The slide is an example from the Metropolitan Water District’s integrated water management analyses.  “As a wholesaler, they basically collect every local water user’s unreliability and feel they have to try to manage for it, so they try to keep a fair bit of water in storage just for such occasions,” he said. 

The chart shows a non-exceedance probability plot and annual water delivery. In this plot, the axes are switched from what they usually are in probability distributions.  Dr. Lund said that the plot shows about a 75% chance that you will have less than the straight-line amount of about 750,000 acre-feet per year of water delivery from the primary surface water source and about a 25% chance of having surplus water above this delivery target of about 750,000 acre-feet.

So in 25% of the years, you might think about what you can do with that surplus water. Can I bank it? Can I sell it? Can I exchange it with somebody else?” he said. “And in the drier years, you will think about what to do. When I don’t have enough surface water, which is usually the cheapest? What else can I do? Can I pump groundwater? Can I fallow some of the annual crops? Can I purchase perhaps very expensive water from a neighboring district to water the trees in the system? This is an agricultural illustration for how these portfolios stick within a probabilistic context across many different kinds of water use.”


There are quite a few water supply reliability metrics developed and used for different purposes. One is ‘firm yield,’ which is essentially the largest water demand that you can supply with 100% reliability for an exact repeat of the historical record. Dr. Lund noted that the firm yield is not 100% reliability, but it will be 100% reliability for a repeat of the historical record; if it’s a short record, it might not be very much reliability at all.

Percent reliabilities have been used to achieve a fixed stated delivery target for several years. There are all kinds of quantitative indices for robustness, resilience, and vulnerability with different conceptual and numerical equation manifestations, such as expected annual damages.  And there are probability distributions of performance, such as the probability distribution of deliveries, which can be quite insightful.


Climate change will have some fairly big effects on water supply reliability. “We’re expecting to see more floods and droughts, even as the average precipitation stays about the same,” said Dr. Lund. “Certainly, the loss of snowpack is going to have some impacts on water supply reliability as well, although probably less impact than what most people fear.”

There are many forms of non-stationarity in the system and not just climate change. There are changes in the infrastructure and deterioration in water quality in some of the larger aquifers. The Sacramento San Joaquin Delta itself is a source of non-stationary and unreliability in terms of earthquakes and the potential for salt intrusion into the Delta.

Agricultural water use has non-stationarity in terms of the agricultural water demands, crop commodity prices, population growth, and even water conservation actions in cities. Non-stationarity in ecosystems comes in the form of new invasive species and continued degradation of the ecosystem.  There is non-stationarity in terms of new chemicals affecting water quality and new technologies that give us sensors to more tightly manage water in some positive ways. And there can be non-stationarity in terms of the administration, the regulations, the agreements, the funding, the storage policies, infrastructure capacities – all of these, at least conceptually, should be evaluated and considered in water supply reliability studies as much as is possible, he said.


The process of making reliability estimates forces you to integrate knowledge about the system – the water demands, the water supplies, the operations, the capacities, the things that you expect are going to affect that system for the seasonal operations timeframe and the longer-term planning and policy timeframes you have in mind.

Certainly, there are a lot of uncertainties in that timeframe, but just like retirement planning, we still do retirement planning calculations, even though we don’t believe all the assumptions completely,” said Dr. Lund. “There are some interesting issues of the reliability of components within a water supply system and the reliability of the overall system. You try to have some kinds of redundancy and some kinds of contingency planning so that your overall system reliability exceeds the reliability of individual components. Although you can have a fairly fragile system, where the reliability of the system is much less than the reliability of individual components because you rely upon them in series.” 

The water management portfolio idea is essential for water supply reliability.  The goal is to develop these portfolios of supply and demand management to increase the system’s reliability, even though the components themselves might be individually much less reliable.

It’s both the insights and the errors that come out of modeling and the importance of making interpretations of that, and thinking about the results to get insights and not believe the numbers too much.  And the many forms of non-stationarity that affect the system.”


Then Dr. Lund discussed the ongoing Delta ISB review of water supply reliability estimation.  There is a substantial partial draft that some on the board will continue to work at, albeit at a slower pace as the state has yet to find funding to pay the science board.  They are working on getting the draft completed for an internal review.  After the board is satisfied with the internal draft, it will be circulated for public review.

Often some substantial improvements come with that, as well as further reflections from the science board folks,” he said. “We’ll see those further comments and revisions, then have a final report and then follow up actions to follow up on the report to make sure people understand what we’re saying.”


These are a few thoughts reflecting on that report that we’ve got in draft form,” said Dr. Lund. “Environmental water supply reliability is an important consideration for the system in the future and in the present.  Since our board is mostly environmental water folks, I would really appreciate it if you all would develop thoughts over time so we can integrate into this report on how to consider environmental water supply reliability together with human water supply reliability, which has been well developed over the last century. How do we reconcile estimates of reliability from different model users, different models, different modelers, and different agencies that might even have a different interest in these numbers?”

There’s some interest in the field about having reliability without probability – essentially robustness kinds of measures. I think there are some interesting discussions to be had around that. How should decision-makers consider water supply reliability estimates?  We’re interested in taking science and seeing how we can make it more useful for decision-makers, operators, policymakers, and the like.”

Then to me, one of the underlying difficulties of the whole subject is that it’s important enough that the decimal dot dust in our errors and our calculations are worth about $1,000 an acre-foot during drought,” he said. “So it’s pretty easy to have a few 1000 acre-feet or 10s of 1000s, maybe even 100,000 or so acre-feet of error and these models that would be basically worth $100 million in a drought year. So errors are really important.”


Dr. Diane McKnight said she was interested in the graph showing economic value versus percent used for agriculture. “I was wondering if you were to do a graph like that for environmental water use, could you associate some water use it with the Endangered Species Act? And some with the Clean Water Act or state regulations? Is that a way to attribute the economic value of the water that’s being used for maintaining, say, a population of endangered fish?

We can probably go into the literature on the economic valuation of the existence value of different kinds of fish as there’s a lot of literature that attempts to do that,” said Dr. Lund. “I think there is, in principle, some valuation that society will put on these environmental resources. But I don’t think we’ve gained a lot of consensus as to exactly how to quantify that. We’re kind of fortunate in the agricultural sector, in particular, where most of this agriculture is a business, and so for business, you can use market values as a way of benchmarking the economic value of that water use as an input to commercial agriculture. And you can do fairly similar things for coming up with pretty reasonable economic values of urban water use.”

“I think what Diane might be getting at is the embodied water, if you will, of fish as a way to value it,” said Dr. Lisa Wainger.  “You may be interested to know that there is a legally defined value to assign to salmon for the purposes of water allocation. So while economists may argue about that number, there is a number that California uses but only for the endangered salmon.”

Dr. Diane McKnight asked which of the regulatory frameworks – Endangered Species Act versus the Clean Water Act – has the largest impact in terms of these environmental needs or uses of water.  Is that known?

There’s a couple of really interesting studies for the Delta that have looked at the last 20 years of Delta outflows and traced back looking at why did that water flow out to sea,” said Dr. Lund. “For a lot of it during the flood years, they’re just basically wasn’t enough capacity to capture all of that. But during the low flow years, there has to be some amount of water that would flow out the Delta just to keep saline intrusion from coming in for the water users and the water export facilities in the Delta. And if you take add increments to that, for how much additional water has to go out of the Delta in order to meet Endangered Species Act kind of requirements, it’s actually a fairly small amount of water. Although it tends to be in drought periods, so the economic impacts are felt fairly directly.”

One of the two co-equal goals is improved water supply reliability, but I have no idea what that means,” said Dr. Jim Cloern. “I think your table of the metrics of reliability was really helpful. My question is, what kinds of actions are feasible for improving reliability?  and I know damming more rivers isn’t one of them … “

There’s a large amount of literature that looks at the relative improvements in reliability that you get for each of those kinds of actions that are in that portfolio table, which might include damming more rivers, in principle,” said Dr. Lund. “From the analyses that I have been part of, we see relatively little improvements in water supply reliability for most storage expansions. Far less than I think is the popular understanding.”

Dr. Tanya Heikkila said the robustness issue kind of piqued her interest. Could you talk a little bit more about that and what you mean by that?

I think this is a really interesting issue, and I’m not quite sure exactly what I think about it,” said Dr. Lund. “But probabilities are always slippery creatures.  You get into a lot of controversy about how to estimate probabilities. Maybe some of you have tried to estimate probabilities from data. And so there’s now a school of thought that says, Well, why don’t we just look at the reliability of the system for a very wide range of random scenarios. And we’ll use that as our standard and not calculate probabilities.

I can see some insights that come out of that, in the sense that you should always listen to probabilities, but you shouldn’t always believe them,” continued Dr. Lund. “And you should be prepared for extremes, even though they’re improbable or need to think about preparing for extremes, even though they’re improbable. So I think this sort of robustness philosophy helps people think how they would respond to improbable events that might have large consequences. Even though from a probabilistic perspective, it might be unwise to invest a lot in preparing for them upfront. So you might want to do a combination of probabilistic as well as sort of extreme scenario worst-case modeling.”

One of the potential uses of robustness analysis is to say, based on all the probabilities that we’ve estimated, our best guess is this is what the future looks like. And here’s our optimal solution for that best guess,” said Dr. Wainger.  “But the robustness analysis might say, you know, that is the best if we’re right, but it’s not the best if we’re wrong. And so you that’s what the scenario exploration allows you to see is that maybe you want to back away from that one optimum, if you’re more likely to generate net benefits over a range of outcomes.”

Dr. Lund agreed.  “So a true devotee of the probabilistic school would say, well, you should really be doing a two stage optimization that incorporates the unreliability of your probabilities.”


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