DR. JAY LUND: Water Supply Reliability Estimation: An overview

Water supply reliability.  It’s a term often talked about in the realm of California water, but what does it really mean?  And how can you describe it in quantitative terms?  As the Delta Independent Science Board prepares to tackle the subject, Dr. Jay Lund gave this seminar on water supply reliability and how to estimate it as preparation for a workshop on the subject.

He began by pointing out that we’re supposed to be managing for coequal goals of ecosystem health and water supply reliability, but probably more than 90% of our discussions and our science is spent on the ecosystem health part.  So in this presentation, he will give an overview of water supply reliability so everyone will have a common starting place to approach the subject.


In this presentation, Dr. Lund said he’d be discussing water supply portfolios, noting that we often talk about water supply reliability as if it was just one source of water and that we only need to estimate the reliability of that one source, but that’s not how California works, he said.

Usually we have a mix of supplies and a mix of water demand management activities that we bring together as a portfolio so it’s important to look at the supplies and demands together as a portfolio,” he said.  “We are also managing water not just for one demand, but usually for a whole group of demands – different urban, agricultural, and environmental demands.”

He’ll also discuss different sources of unreliability.  Droughts and climate change are easily thought of as reasons why a water system wouldn’t be reliable, but there are a number of other things that can cause water systems to become unreliable, he noted.  Historically, probably the biggest source of unreliability is floods.

Floods can be the biggest way to lose water supplies because they flood out your drinking water treatment plant, and then you have to spend months until that’s repaired and you’re completely out for that period of time,” he said.

Dr. Lund said he would also discuss estimating reliability in terms of simulation models and different approaches for using simulation models to estimate the reliability of water systems.  “All these models are wrong, but they are still better than our intuitions,” he said.  “It forces us to think about things more precisely.”

He’ll also touch on metrics and summarize and give some lessons learned at the end.


How do we get water into our homes?  Most of the public and most politicians do not have a good understanding of water systems, which Dr. Lund said is actually a positive thing.  “If you go to other parts of the world who have very unreliable water systems, you know exactly how the system works because you have to deal with it every day, so our ignorance is actually a positive sign that we have other things to think about.”

Water in California is complex.  The map on the left is the runoff available in different parts of California; he noted that the runoff is in the locations where the people and agricultural demands are not.  California also has a Mediterranean climate, so water tends to be available in the winter time, but the demand for water is in the summer, so the water is available when and where the people and the water demands aren’t.

To manage this mismatch seasonally and geographically, the state has built a tremendous system of water infrastructure as shown on the map on the right: dams and reservoirs, conveyance infrastructure, reoperation of rivers, and groundwater aquifers.  He also noted that the map is very colorful because there are 3000-4000 different agencies that manage some aspect of water.  Most of them are local, but there are a number state and federal agencies as well as regional agencies that have to get along in order for this system to work, he said.

The chart on the lower left shows the precipitation in the Sacramento Valley over the water year starting from October 1st, which shows the tremendous variability both seasonally and between the years.

The map on the upper right shows how this variability compares to other parts of the nation; he noted that California has more flood years and more drought years on average than any other part of the country, and this variability will increase with climate change.

The bad news is it’s going to get worse, but the good news is we’re actually among the best at managing variability of any state in the country,” he said, illustrating the point by presenting a graph showing unimpaired flow from the Delta between the wettest year on record at the time in 83 and driest year in 77, as well as the average year, which shows the tremendous seasonal and interannual variability for runoff as well as precipitation.


Water systems have a lot of different components.  The graphic on the left shows a simple system that has a river flowing into a reservoir, a groundwater basin that provides supplies as well; at times, they can move water from the surface water into the groundwater, and they can pump from the groundwater to supply urban and farms.  Sometimes they can import and export water from the system, and then there is also fish.

But for the purposes of water supply reliability for the state of California and for most of the water users, Dr. Lund noted that it’s more like the graphic on the right, where there are a lot of interacting interconnected water users and water supplies over the state for different purposes that are governed by different entities.

He then presented a graphic of Orange County Water Agency’s water system which has supplies that come in from the Delta and from the Colorado River through the Metropolitan Water District of Southern California.  There are water transfers that go back and forth between different users and different contractors in the system, and they have regional surface water reservoirs and groundwater banking operations.  They have a variety of water demands including retail demand, so there are a lot of things going on, both on the supply side and the demand side, he noted.

Dr. Lund presented a table showing water supply system portfolio actions, noting that most modern water systems operate with a portfolio of water supplies and water demand management.

There are a lot of different ways that we can gather up water, a lot of ways that we can move water around from where it is to where we’d like it to be, a lot of ways of storing it, essentially making water move through time if you will, and then ways of treating the water so it’s poor water quality can be made higher quality for some uses,” he said.  “There are operational things that we can do to manage all that network of supplies and demands more efficiently.  And then because every water system has thousands if not millions of people involved in it from the users to the managers so the managers of the other neighboring systems and the suppliers, we have to have a set of incentives so everybody gets along well.  Agreements, pricing and markets, education and subsidies are all the things we do to try to get people to work well together.”

He then presented a chart (lower, left) showing how San Diego’s water supply portfolio has evolved over time.  San Diego used to be very dependent on Metropolitan Water District and now they are trying to diversify over time as their population has grown quite a bit, he said.

These portfolios operate at the local level as well as statewide.  “The Delta is central to that statewide part of the portfolio, so when people are operating these water supplies in and out of the Delta, they are often operating so that it matches the portfolios of water users all over the state,” he said.  “I tend to think it’s not very useful to look only at the water supply reliability of exports from the Delta.  What you really want to look at is the delivery reliability or the mix of supply reliability for the users all over the state and the consequences of that reliability or unreliability.”


There are many different types of water demands.  Urban demands include landscaping, sanitation, drinking water, and others; the largest component of urban water use is outside landscaping which is about half of statewide water use for urban users.  There is a mix of agricultural demands such as trees, vegetables, and pasture, and they all have different values, different timings, and different abilities to be curtailed during a drought, he noted.  Environmental water uses are also highly variable in terms of timing, water quality and dilution, habitat, and the ecosystem support services that come from water deliveries for ecosystem purposes or environmental purposes.

These demands all vary with time.  Urban water uses vary over the day with such things as showers or landscape irrigation.  There is tremendous seasonal variability in water use as well, and over time there has been a historical change in water use, as populations grow, as water conservation technologies get implemented, as the commodity prices for different crops change, and the growth or decline of different kinds of crops and different acreages.

The uses and the shortages for all these different uses are not equally valued,” said Dr. Lund.  “Everybody feels that their use is very valuable, but if you look at it economically, or in a larger social sense, I don’t think we could argue that all uses equally valued.  A lot of our disputes are over, ‘you’re valuing it more than I do’.  There’s a little bit of subjectivity here, but certainly in economic terms, they are not all equally valuable.  And that provides ability to have water markets and things like that to decrease the cost of unreliability.”

He presented a slide showing two different views of water demands.  Traditionally, we tend to look at point demands for water, so at each time of the year, we’d look at how much water each of these uses is going to want in a deterministic way.  This can be useful, but it doesn’t give a sense for the relative value, he said.

Another way to look at water demand is with an economic view.  If you ask an economist what water demand looks like, they’ll give you something that looks more like the chart on the right.  “At any particular time in this diagram, it would say, if you give me a little bit of water, I value that at a very steep rate, but once I get plenty of water, a little bit more water doesn’t help me a lot more, or it might even be bad for me, it might flush out pigs or overwater the crops,” he said.

The economic view of water demands is very insightful because it gives you a sense for the consequences of shortages.  “It’s sort of like a tree falls in the forest, but if nobody’s there to hear it, does it make a sound?  If there’s a water shortage but there’s nobody there to suffer any damage, is there really a shortage?,” he said.  “You could argue about that but I think you get the sense.  A quote that I like to use from my colleague Richard Howitt is ‘There’s a shortage of sport cars. I don’t have one.’  We would all like to have more water, more money, more land, more sports cars, things like that, but there’s a way to look at tradeoffs here.”

This is well illustrated by crops in California, he said, presenting a plot of all the crops in California.  There is about 8 million acres of irrigated land, and on the plot, all the crops are ordered by their profitability and the number of jobs; he noted that about half of the irrigated acres are responsible for about 80-85-90% of all the jobs and all the crop revenue in California.

This means if you manage a shortage well, you have relatively little damage,” he said.  “If you’re one of the grain farmers, you will feel it.  But that’s hopefully something a well-managed society can help compensate for.”

He pointed out that the urban sector has the same kind of general shape of impact to shortage in the urban sector.  “During the last drought in 2015, we shorted all the urban areas by about 25% and we did not have 25% unemployment resulting from that, because we just didn’t irrigate the lawns as much.  We had almost no economic impact from that tremendous reduction in water use.”


There are a lot of different ways water systems can fail.   The first one planners and policy people look at is lack of inflow in droughts.  We spend probably a disproportionate amount of time at the policy level looking at droughts, and obviously they are important, but they are not the only way things can go wrong, Dr. Lund said.

Floods are a very common way to have big shortages of water.  A hurricane comes through with a storm surge, or a major river flood which takes out drinking water systems and drinking water treatment plants, and interrupts supplies for months.  Earthquakes and wildfires can disrupt systems, as can mechanical and operational failures as was the case in Flint, Michigan, where it was really a social failure.

Water demands, such as in the case of Cape Town, South Africa where the water demand had grown quite a bit and they hadn’t really built out to prepare for those kinds of demands.  There are environmental regulations and water quality regulations that sometimes will affect the reliability of quantity deliveries.

There can be unreliable rules or agreements.  He noted that water contracts are very common in this system and are needed in order to make all of these hundreds and thousands of institutions work well together in their supply and demand portfolios.  Agreements can be violated, there can be misunderstandings, or an expected delivery doesn’t happen.  And then of course there can be multiple failures or a cascade failures where one little failure causes another failure and so on.

So when we talk about unreliability, we ought to look at the whole gamut,” he said.


How do you represent all these sources of unreliability? He acknowledged these systems are pretty complex.  “How good is our intuition for reliability of these systems?  I would say not very good,” he said.  “Even people who are really experienced with these systems probably have pretty good intuition, but they aren’t going to communicate so well by intuition and they are certainly not going to be able to communicate with other stakeholders and regulators with intuition, so they are going to have to do some numbers on this.  These numbers are going to be terrible.  They are going to have errors, they are going to have problems, but they are still better than our intuition, still better than our rhetoric, and more reliable than our rhetoric or our hopes.”

Unreliability is typically represented as events, such as what if a pump goes out, a dam fails, or an outflow fails?  What happens if the time periods of inflows into the reservoirs are less because of climate change or drought, or really big because of a flood?  We might have probabilities on these events and on these different time series that help us work out the relative frequency of different kinds of failures, and how they are going to work together in a system or in a portfolio of activities, he said.

The probabilities might be based on historical experiences, such as the historic record of inflows into the reservoir, how often pumps tend to go out, or how often an operator makes a foolish mistake; we generally have some historic understanding of what these things are likely to be.  There might be scenarios of concern, such as a worst case scenario for climate change with a new technology that’s not completely tested, what happens if it works well, what happens if it works poorly.

So when we look at reliability and unreliability, we have to make essentially cases that are based on some notion of what we think is going to happen based on historic experience or some other synthetic means,” he said.

Mostly time series and Monte Carlo analyses are used.  The Monte Carlo Analysis came out of World War II and the Manhattan Project.  “In our modeling, Monte Carlo analysis basically relates to gambling where you’re going to try things a bunch of times randomly, so you’re going to draw from the random distributions of all those types of unreliability and all those types of water demands, and then you’re going to see the simulations of what’s the relative frequency of failures after you’ve drawn from all those random distributions, and rerun the model hundreds of thousands of times.”

A simulation model represents a simplification of the whole system; it has all the major components in the system, such as the capacities of all the bits of infrastructure, the inflows, the water available, the water demands, the operating rules including regulations and reservoir operations.  The outputs are the deliveries, the water storages, the water losses, and any economic losses from any shortages that might occur.

Dr. Lund said the way it works is by conservation of mass:  inflow minus outflow is change in storage.  He gave an analogy of conservation of people in the room: People coming in, people going out, and the number of people in the room; the room is storing people, he explained.  There are rules and capacities; only so many people can be accommodated in the room; the doors will only allow people to leave at a certain rate.

These simulation models are pretty universal in that they will take a time series of these inflows and demands and the operating rules and capacities, and it will start at an initial time period with some initial storage, and then for each time step, it will go to the next time step and determine how much storage there is, what are the inflows and the demands, it consults the operating rules and capacities, and figures out how much water is delivered and how much water is kept in storage.  It then goes to the next time step and does it all over again.  It’s really pretty methodical.”

All these simulation models are essentially ‘what if’ models, Dr. Lund said.  What do we think would happen if we had these capacities, if we had these rules, if we had these regulations, if we had these demands?  They really represent legions of details simplified; when you think about all the people, all the pipes, all the users in water demand systems, all of which are behaving a little bit erratically.  The model is trying to simplify that down so that there is some aggregate representation of what’s likely to happen.

We run these simulations for each case, for each of the different inflow scenarios, each of the different demand scenarios, and each of the different reliability scenarios that we have,” he said.  “We estimate the responses and the consequences of that operation, and then we’ll take the results for each case and assign probabilities to each of those cases and their outputs to assess the overall reliability and the overall consequences from that simulation.”

Dr. Lund then gave an example from the 2015 State Water Project Water Supply Delivery Reliability Report for 2015.  “These are run for some particular level of development,” he said.  “So they say by this year or by 2030, we’re going to expect this much water demand, these will be the rules of the game, the operating rules and the regulatory rules, and we’re going to take the historic record and we’re going to run the model for that historic record for that future level of development and we’re going to get a time series of model results.”

He pointed out that on the time series graph (upper), there are two lines, one with the BDCP (now WaterFix) and one for existing conditions as of that time; the results are highly variable.  He explained how that is then translated into reliability.  “So we have to have some probabilities, and we’re going to take all the deliveries here, in this case, these are diversions from the Delta, and we’re going to sort them from the highest to lowest.  The highest has a low probability, and the lowest has a low probability, and that gives the cumulative probability, so the lowest one has a high probability of being exceeded, it is exceeded in almost 100% of all years.  And then we’ll plot these up from lowest to highest with their probabilities, and we can see from this then that the probability of having less than 5 million acre-feet of exports is about 55% for current conditions.”

Dr. Lund noted that when he did this for the 2015 Water Supply Reliability Report, he also plotted what happened in 2014 and 2015, and what those recurrence frequencies would be, and they turned out to be lower.  “This is not bad,” he said.  “This is just an indication that when people give you these curves, they are probably wrong.  They are not totally wrong, they are still insightful, and they still give you some ideas of what’s going on and how reliable things are, but it’s not unusual in one of the worst droughts on record to see results that are worse than what you predicted, and you have to be prepared for that if you’re a responsible person running a water system.  You’ve got to be prepared for all kinds of things to go wrong.”

Another way to look at reliability is in the context of seasonal operations.  One approach is predictive of long-term planning.  In a particular operating season, we know where the water storage is now, but at the start of the winter season, we don’t know how wet the winter is going to be and how much snowpack there’s going to be, he said.

So we could start off with today’s storage in the simulation model, and then run the simulation model with forecast demands and the many future possible inflows,” he said.  “In the chart on the left for the Columbia River system, we ran it for 65 historical years, we run it through the model, and what it tells you is that for the next couple of months, I think that reservoir is going to be pretty high, and there’s almost 100% probability that it’s going to refill by June.  These are good things to know.”

The chart on the lower right is a different approach called the plotting position approach.  “You could plot up a cumulative distribution of what’s the probability distribution of storage in this reservoir or of demand, whatever you like,” he said.  “If you’re the State Water Board and you’re interested in what’s the likelihood of Reclamation running out of water for winter-run salmon before the end of this year, you might be doing this kind of analysis.”

Dr. Lund then gave some overall thoughts on estimating system reliability.  “’All models are wrong but some are useful’ is my favorite quote from George Box,” he said.  “We get these delivery reliability results from models and model results, but we really have to think about these results.  Someone just gives you a pile of numbers, it’s just a pile of numbers. …  So if you hire a consultant or a university person and they give you a pile of numbers, you want the insights.  What does this mean for my operation?  You want that person to learn enough about your operation so that they can tell you what this means for what you should or shouldn’t be doing to prepare for different contingencies.”

There really isn’t a ‘best model’ or a ‘right model’ as models have different components to them, he said.  “It has the software component that includes the mathematical formulation, the calibration of all the little parameters, constants in the model, and whatever version it was, because if you’re really using a model, you’re always changing it.  You have these experts that are using different data, they are updating the data, they are updating the operating rules, they are modifying the model, the calibration, and the person behind the model is really orchestrating all of this, and hopefully interpreting it to give you some insights.”

The model is really just an analytical form of reasoning to give you some insights, not just necessarily numbers.  Hopefully much more than numbers, but the interpretation and the documentation of these models is really fundamental.  It’s not unusual at all to see two very good modelers come out with fairly different, up to +/- 10-20% differences in water supply reliability in some cases.”

Dr. Lund then ran through a few examples, starting with a chart from the State Water Project Delivery Capabilities Report (lower, left).  The report, produced every 2 years, estimates for each of the individual contractors what the probability of distribution of deliveries is on an annual basis for every water contractor with the historical hydrology and present conditions in terms of regulations and other factors.

Orange County has a much more complex local and regional system with a lot of different supplies and abilities to manage demand and groundwater (above, right).  The particular report the chart is pulled from is looking at the effects of climate change as well as WaterFix as they get a lot of water directly or indirectly from the Delta.

They have these nice exceedance probability plots of their water deliveries from the different sources and then the probability of distribution of the shortages that they might get under different conditions with or without WaterFix and different kinds of climate change or other investments,” he said.

Metropolitan Water District does a lot of integrated modeling as their system is even more complex because as a wholesaler, they have to represent their retailers’ water demand and how they are going to respond over time.

They have a very integrated system model and they have a very different way of representing the probabilistic aspect of inflows and droughts, so their demands are really important,” he said.  “The chart is from one of their probability distribution reports that comes from their integrated regional modeling.  They really like to keep an million acre-foot of storage so they get really nervous if they have less that 1 MAF of water in storage, so they are always interested in what’s the probability we’re going to have less than 1 MAF of storage.”

Dr. Lund then returned to a delivery reliability example plot and provided some interpretation.  The example is the delivery reliability for an agricultural water system which has 700,000 acre-feet per year as a delivery target.  On the far right side of the graph, it shows that in 30% of the years, they will have that much or more; that surplus water presents an opportunity for the water to be banked, recharged into an aquifer, or transferred.

When there is less than the target deliveries as shown on the left side of the plot, then it is a struggle.  They might have to pump groundwater or fallow annual crops.  “You might fallow some annual crops with some probability and some amount, and you might be purchasing water from outside to keep your trees going in some fraction of the years,” he said.  “So when you look at these probability curves in the context of the whole portfolio, you can look at what’s the relative frequency that I’m going to have surface water deliveries as well as all of the different major elements of your portfolio being activated.  And what’s that going to cost you, because you have costs for each of these things as well.”

For an urban area, you might have different levels of water conservation that you’re implementing, groundwater pumping, or water contracts that you’re activating with agricultural users to buy water, and then more draconian types of water rationing that you’ll do under very big shortages.”


There’s a lot of different metrics for reliability.  The oldest and the one still in use the most is the ‘firm yield’ which is the amount of water that a reservoir system could theoretically deliver with 100% reliability with the historical unimpaired inflow record.  “So if things weren’t changing in terms of hydrology, in theory you could rely on that firm yield,” Dr. Lund said.  “It’s not really that way entirely because if you have a short record, it’s easy to have a high firm yield; the longer the record, the more likely it is you’re going to have a worse drought.  A firm yield is never completely firm.”

There are a lot of different words for this:  Robustness, resiliency, vulnerability.  Expected annual damage is used in flood damages and flood management, but also has some value in water supply unreliability, he said.  “There are a lot of ways to quantify reliability, but that doesn’t make it less confusing, and sometimes it makes it more confusing.”

Climate change will affect reliability as there will be more variability, both seasonally and interannually in hydrology and surface water supplies; it’s going to make groundwater components much more important, he said.  He noted that the plot is of export reliability from DWR for quite a few conditions, and pointed out that most of them are getting worse or getting more variable at least, even when they have the same average.

People talk about non-stationarity and climate change as if climate change is the only form of nonstationarity that our systems have, but California has always been a nonstationary  system.

We’ve always had nonstationarity in water demands and in the economic structure of the values that we’re using water for,” he said.  “Nonstationarity in terms of the species that are coming in – so lots of different forms of nonstationarity including the rules and regulations that add to the nonstationarity of the system.”


Dr. Lund then wrapped it up with some issues and lessons.  “Reliability estimates really are an integration of the knowledge that we have of the system – the demands, the supplies, and the operations,” he said.  “I think it has a lot of value because it forces us to think in detail about how all these things come together and which ones are important and which ones are less important.”

I think the reliability of the components is less important than the reliability of the system which is the main reason we have these portfolios because they give us a more robust and more reliable system.  When you look at the reliability of the Delta versus the reliability of the ability of providing water at the user level, portfolio reliability and the management are really key.  How do you respond to shortages and what portfolio of options do you have for managing under these different conditions?

Model results and these estimates of unreliability and reliability are all going to be insightful and they are all going to have some errors, so you shouldn’t take them as gospel,” he cautioned.  “They have tremendous importance for insights and the interpretation because that’s what you’re really interested in.  You’re not really interested in the numbers, you’re interested in the insights as to what you should do for management and regulation.  Nonstationarity has many forms and you should all demand interpreted delivery reliability plots.


Question: Ecosystem demand management – could you give us a few examples of what that looks like?

An example out of the drought was what we did for waterfowl,” said Dr. Lund.  “There was an organization, TNC, they were involved with several land managers and refuge managers during the drought.  They saw the birds coming and they said, we think we need this many acres of this type of habitat at these locations.  Let’s go negotiate with different farmers and talk to each other to coordinate the management of supplying those water-supply based resources for the birds as they came through.  There’s quite a lot of things.  I think demand management on the ecosystem side has been relatively unexplored, unformalized, but I think it’s certainly there.”

Question: What about water rights and reliability?

The water rights are just the rules of who gets water first and when you are shorted, so when we talk about operating rules for the system, the water rights are part of that,” he said.

Question:  How would you take into account water markets, in the sense that wholesalers deal with water trading and exchanging and so forth, and yet ratepayers are kind of locked in, it’s really regulated.  How does that influence the reliability of water?

Quite a bit.  Let’s take a simple case.  Say during the drought, you have an agricultural area that has very senior water rights and you’re growing something not as valuable, maybe it’s rice – it’s something they can fallow.  Then you have an urban area or maybe an almond farmer that has something where the economic damages of shorting them, even if there are more senior water rights, are pretty high.  They might want to go to talk to the agricultural water user that’s growing rice and say, how about if I buy some water from you?  So you can increase the unreliability to the farmer, but he’s happier because you paid him, the rice farmer, whereas the almond farmer or the city are happy to have paid someone else, they would rather have had full deliveries of course, but they’d rather pay the farmer then suffer the shortage.  In the model we can represent that.  One of the kinds of modeling I do is optimization modeling which has a lot of that going on.”

Question: DWR produces their delivery reliability report every two years and they have a methodology that they have used for quite a while … Do you have any thoughts about how delivery reliability of export supplies out of the Delta might be provided in a more helpful or more productive way?

I think that could be a really interesting outcome of this review.  There’s a lot of other state policies that are important for this.  We have the environmental flows, we have WaterFix just in the Delta, and even outside of the Delta, we have the Sustainable Groundwater Management Act implementation, so I would imagine that all those farmers in the San Joaquin and Tulare Basins that are in overdraft, they are going to be looking to see how much more water if any they can get out of the Delta, and that’s going to have a tremendous impact on demand south of the Delta for water.  Those in turn, the quantity and the economic value of those deliveries, and that could easily drive some markets, in terms of farmers in Kern County trying to buy water from the north.”


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