Alternative household water affordability metrics using water bill delinquency behavior

Rising water prices threaten affordable access to basic water service in the U.S., especially in low-income communities. Faced with unaffordable water bills, households may use less water than is healthy, forgo other essential services, or fall behind on water bill payments, risking water shutoffs. Affordability ratios (ARs), which express water bills as a fraction of income, are the most common measure of water affordability. However, ARs can underestimate unaffordability due to both spatial aggregation bias and their reliance on indirect proxies for ability to pay. New metrics are needed to identify households at risk of water insecurity due to affordability challenges. Here we investigate alternative water affordability metrics that use water bill late payments and debt to track actual payment behavior at the household level. We define metrics that capture the frequency, duration, and severity of water bill delinquency. We apply these metrics to a case study in Santa Cruz, California, using monthly billing data for approximately 40 000 households from 2009 through 2021. We find large variation in delinquency across households and over time, with higher delinquency linked to proxies for low wealth such as lower assessed home value. Census blocks with similar ARs often have distinct patterns of delinquency behavior, suggesting that block-level median affordability estimates may be masking sub-populations facing affordability challenges. These results highlight the benefits of using multiple, household-level metrics to capture the role affordability plays in household water security.


Introduction
Water unaffordability impacts millions of households across the U.S. [1,2].This problem is growing due to underinvestment in aging water infrastructure [3], increasing utility costs to address emerging contaminants that threaten water quality [4,5], and climate change impacts on water supply [6,7].Water affordability disproportionately burdens low-income communities and communities of color [8,9].Rising water prices can harm health and wellbeing by forcing some low-income households to decrease water use or other essential expenditures like groceries or medical bills [10,11].Accrual of unpaid water bills may lead to water shutoffs [12], with communities of color facing higher shutoff risks than white communities [8,13].
We define water affordability as a household's capacity to cover water costs for essential uses such as drinking, cooking, and sanitation without neglecting other essential expenditures [2,14].The volume of water required to meet these needs varies across households due to differences in household occupancy and plumbing efficiency [15,16].A household's ability to pay for basic water services is affected by income, wealth, and other dimensions of financial burden such as debt or family support obligations [10,17].Water utilities and policymakers need metrics to monitor and address affordability across households and over time [18], but measuring affordability is challenging because of difficulties quantifying essential use and ability to pay, and a lack of sufficiently granular data.
The affordability ratio (AR) is a common measure of household water cost burden and is used by both the U.S. Environmental Protection Agency (EPA) and American Water Works Association [19,20].Typically calculated as the ratio of water bill costs to gross income [10,21,22], ARs often misestimate affordability challenges for several reasons.First, there are conceptual limitations.Quantifying essential use is difficult due to variability in household needs, and thus ARs often rely on total water bill costs rather than costs for essential use [22,23].Additionally, water bills do not capture other waterrelated expenses, such as bottled water [24] or filters [25].Second, ARs often suffer from aggregation bias.They typically capture an average or snapshot in time [10] for a census block [2] or city [10].Recent improvements have focused on low-quantile income estimates, such as 20th percentile or poverty income levels [10,22], and on using disposable rather than gross income [10,23,26].Finally, households with water affordability challenges are typically identified using an AR threshold [27] (e.g.2%-2.5% [1,10,28]) that is somewhat arbitrary.More recent work has analyzed a weighted average or distribution of ARs across an area to avoid picking a threshold [14,29].Furthermore, recent survey-based studies have used expenditure or self-reported income data to measure individual household ARs to avoid aggregation bias [23,[30][31][32].As critiques of ARs grow, alternative metrics such as hours of labor required at minimum wage [10] and combination approaches are emerging, including recent work that combines the AR for the 20th percentile income group and the Poverty Prevalence Indicator [21,26,33].
In contrast to ARs, behavioral metrics use payment patterns as a measure of ability to pay.While they address some of the above limitations, they also face data access challenges and potential disconnects between observed behaviors and affordability [25,34].In the water sector, water shutoffs are the most common behavioral metric [12,35,36].However, shutoffs (like foreclosures [37]) are an extreme measure, implemented after extended non-payment, and therefore capture only the most severe affordability challenges [18].Non-payment, or delinquency, behavior offers an alternative, potentially identifying affordability issues before shutoffs [21,38,39].In other sectors, various metrics have captured the prevalence [40][41][42][43], frequency [44,45], duration [37,40,42], and severity [44] of delinquency.These metrics have the potential to identify households at risk of water insecurity due to affordability challenges both within and across communities.For example, the California State Water Resources Control Board's 2022 affordability analysis assesses the frequency of residential delinquencies across community water systems [46].One study also compares shutoff and delinquency patterns across sociodemographic groups in Durham, North Carolina [47].However, to our knowledge, no previous work has compared alternative water delinquency metrics to assess their potential to measure household affordability.
Here we propose and assess multiple householdlevel water delinquency metrics.Specifically, we define three metrics that have been applied in housing and electric utility spaces but are less common in the water sector: frequency (i.e.how often households make late payments), duration (i.e.how long households are behind on water bill payments), and severity (i.e. the magnitude of household water debt accrual).We apply these metrics to a case study in Santa Cruz, California, a small, coastal city with a wide income distribution, using 13 years of water billing data.We evaluate correlations between the three delinquency metrics and the AR and assess how these metrics vary with demographic and housing characteristics.We find that delinquency frequency and duration are highly correlated with each other and show linkages to proxies for low wealth, such as homes with smaller areas or lower tax values, highlighting their potential to identify household-level water affordability challenges using only utility billing data.

Delinquency metrics
We propose three delinquency metrics (figure 1), calculated using household-level billing data.First, we define penalty frequency as the fraction of months where an account incurs a late penalty.Late penalties occur when the balance is not fully paid by the due date and may compound if successive bills are not paid on time.While we expect many households to occasionally pay bills late (for example, if they forget), high penalty frequency may indicate households that have trouble paying bills.Frequency values can range from zero (no late penalties) to one (every month includes a late penalty).Second, we define debt duration as the average number of months of a set of contiguous cumulative debt occurrences.The minimum duration value, if defined, is one month because water bills are recorded monthly.We hypothesize that penalty frequency is correlated with debt duration values because households with frequent penalties are likely to have more than one penalty in a row.However, a high penalty frequency value but lower debt duration, may indicate chronic payment hardships.Alternatively, a low penalty frequency value but high debt duration may indicate temporary financial hardship (e.g.job loss).Third, we define normalized debt severity as the average monthly debt for months with outstanding debt, normalized by water use.This metric captures the magnitude of the burden on a household from unpaid water bills.We normalize by water use because the volumetric component of water bills is proportional to water use, as Santa Cruz uses a volumetric rate structure (see section 2.2).Therefore, we hypothesize that normalized debt severity may identify households that are conserving water due to financial hardship.This is because when households use less water, the fixed fee makes up a higher proportion of total bill charges.Because late penalties are charged in proportion to total unpaid bill amount, a high normalized severity reflects large penalties and debt proportional to water use.
Additionally, we calculate ARs for comparison with the three delinquency metrics.We define the block-group AR as the ratio of average total monthly water bills across the block group to median household income (MHI) for that block group [2,10].For comparison with household metrics, we additionally disaggregate block-group ARs to the household level by using average household bills in the numerator and keeping block-group MHI in the denominator.

Case study area
We analyze Santa Cruz, California as a case study.As the publicly-owned local utility, the Santa Cruz Water Department (SCWD) oversees water service for approximately 96 000 residents in the city and surrounding areas [48].Santa Cruz has a wide income distribution, with 20% of households below the federal poverty level (compared to 13% statewide [49]) and 20% earning over $200 000 annually (compared to 14% statewide) [48,50].The University of California, Santa Cruz skews the population younger with 27% of residents aged 20-29 (compared to 15% statewide) [48,50].Santa Cruz is also vulnerable to droughts as it relies on highly variable local surface water for water supply, necessitating costly infrastructure investments to maintain reliable supply [48].To finance infrastructure projects, Santa Cruz implemented a new fee in 2016 and applied yearly rate increases thereafter [51], raising tier 1 rates by 350% from 2016 to 2021.The combination of income inequality and high water rates make Santa Cruz an informative case for studying water affordability metrics.
During our study period, 2009-2021, multiple events influenced water use and payment behaviors in Santa Cruz.First, there was a California drought emergency from January 2014 to April 2017 [52].Following statewide voluntary conservation programs [53,54], Santa Cruz implemented mandatory 30% water use reductions from pre-drought levels from May 2014 to November 2015 [48,[55][56][57].To recover revenue lost from curtailment, SCWD implemented fixed monthly drought surcharges [58].Households also received excess water use penalties when they surpassed 10 hundred cubic-feet (ccf) per month [59].Second, in response to the COVID-19 pandemic, California enacted a water shutoff moratorium from April 2020 to December 2021 to prevent water service disconnections due to inability to pay [60,61].The state then established a financial aid program for community water systems, which Santa Cruz participated in, to recover unpaid bills accrued during the pandemic, paying off over half a million delinquent residential and commercial customers [62,63].
Household water bills comprise two main elements.First, there is a flat charge based on meter size to recover costs related to meter reading, bill deliveries, and customer service.Second, there is a volumetric charge for water use with an increasing block rate structure, where high-volume users pay more per unit than low-volume users [64,65].Additionally, when payments are late, users accrue a late penalty equivalent to 10% of the outstanding balance.In 2016, SCWD changed the water billing rate structure to more effectively promote conservation, revenue sufficiency, water affordability, and rate stability [51].Specifically, they decreased the block rate from five to four tiers, decreased fixed fees, and increased volumetric fees, increasing the proportion of revenue generated from high volumetric use [51,66].Volumetric fees were divided into two types to recover utility operational costs and costs supporting capital investments [66].

Data
We obtain SCWD household billing data for every account active between January 2009 and December 2021.The data includes: account open and close dates; billing start and end dates; water quantity consumed by tier; volumetric costs including consumption, infrastructure reinvestment, rate stabilization, and elevation surcharge costs; and all fixed fees including drought cost recovery, standby, sewer, and refuse fees.Additionally, it includes bill payments, late penalties, account balances, and credits.We deidentify account holder names, account numbers, and billing addresses and aggregate service addresses to the census block group level.
We select a subset of accounts for our analysis.We use only single-family dwellings, as the majority of multi-family units (12% of all bills) are not submetered and do not pay their own water bills.We remove outliers in water use including individual bills with zero water use or above 55 ccf (the 99.9th percentile).We remove single-family accounts with bimonthly bills (7% of bills) or bills that do not include sewer and refuse (28% of bills), so that all bills are directly comparable.We also remove bills with less than 12 months of data (3% of bills).Finally, we remove duplicate bills (<2.5% of households after previous pre-processing steps).These data cleaning and filtering steps narrow our dataset to 60% of the original 62 000 accounts, resulting in 1.9 million bills.
We also use demographic and property data to assess how water affordability varies across demographic groups and housing characteristics.We obtain 2019 5 year MHI block group-level data from the U.S. Census Bureau American Community Survey [50].We remove seven block groups that are either outside of the SCWD service area or contain an insufficient number of accounts.In total, our analysis uses 44 block groups.Finally, we obtain householdlevel 2021 property and tax data from the County of Santa Cruz tax assessor's database [67].We use home tax value; house main area and total parcel size; number of rooms, bedrooms, and bathrooms; year built and effective year built (the last year of major renovations); and an indicator for the presence of a pool.

Water use, bill, and payment behavior patterns
We illustrate the distribution of household water use, bills, and late penalty behavior in Santa Cruz in figure 2. We observe a wide range of water use patterns across households and over time.Across the entire study period, we see strong seasonality in water use related to higher outdoor consumption for swimming pools, lawn irrigation, and gardening [68,69].Monthly household water use ranges from 0.9 (5th percentile) to 22.6 ccf (95th percentile) between 2009 and 2014, with a median of 5.9 and interquartile range of 3.5-9.2ccf (figure 2(a)).During the 2014-2017 drought, when SCWD mandated curtailment and applied a $7.37 drought surcharge, water use declines (2.9-6.8 ccf interquartile range).These reductions are followed by a partial rebound from 2017 onwards.Specifically, upper quartile water use increases slightly to 6.9 ccf, whereas bottom quartile water use does not noticeably rebound (2.2 ccf).These patterns may suggest permanent efficiency upgrades [70] or permanent behavioral changes [54,71] for upper quartile users in indoor use, with rebound likely occurring primarily for outdoor uses.
Similar to water use patterns, annual water bill cycles are consistent before 2014 and range from $60 (5th percentile) to $288 (95th percentile) per month (figure 2(b)).During the drought, higher quartile water bills also decrease, while lower quartile water bills stay fairly constant.Unlike water use patterns, both the average and the variability of water bills increase after the drought.This trend may be due to the effects of the November 2016 rate structure change and annual rate increases on upper quartile demand households (table S1).By January 2020, where 25th percentile water bills increase by $14 (14%), the 95th percentile increases by $121 (39%).While increasing bills may be less of a concern for high-income households, even small bill increases may cause financial hardship for low-income households.For example, 14% of households surveyed across the US report that a $12 increase in monthly water bills would lead to cutbacks on other essential goods [72].
In figure 2(c), we illustrate the percentage of households who incur late penalties each month.We find substantial temporal variability in penalties, which is likely driven by multiple utility-level policies.From 2009 through 2013, 6%-9% of households consistently experience late penalties.However, households with a late penalty surge to almost 20% in January 2014 following the removal of a late payment grace period, which also coincides with the beginning of a multi-year drought.Penalties gradually decrease throughout the drought to 12% before dropping temporarily to 2% (with a quick rebound to 14%) after the drought surcharge ends in August 2016.From 2017 through 2019, 10%-12% of households consistently experience late penalties.The contrast between late penalties during and after the drought suggests that high penalty percentages are influenced by the removal of the grace period and the drought surcharge, which may increase bills for some low-income customers [7,65].During the 2020-2021 COVID-19 debt-relief period, penalties drop to zero due to water bill debt forgiveness across the service area.
Next, in figure 3, we move from city-wide trends to household-level patterns.To protect the privacy of individual households, we develop two contrasting synthetic water bill time series.We present a time series that is representative of a low-wateruse, high-delinquency household (figure 3(a)) and another that is representative of a high-water-use, low-delinquency household (figure 3(b)).Methods for developing the synthetic bills are described in section S2.For both synthetic households, the largest bill components are sewer and refuse costs (light gray) and tiered volumetric water use costs (varied shades of blue).Water use decreases during the drought in both households, as shown through the decreased tier 2+ costs in blue, especially in the high-volume household.Additionally, the rate structure change in 2016 decreases the flat fee (pale orange), increases tier 1 costs (light blue), and adds new miscellaneous fees such as infrastructure reinvestment and rate stabilization charges, standby meter costs, and excess water use charges (in the other category) for both households.
The two synthetic households vary in their delinquency behavior.The low-delinquency household exhibits infrequent, one-off missed payments.As a result, the penalty frequency (0.023) is low, the debt duration is one month, and the average debt severity is $122 ($15/ccf).In contrast, the high-delinquency household exhibits recurring penalties and cumulative debt throughout the time series (shown in orange), leading to higher penalty frequency (0.39) and debt duration (2.2 months).The average debt severity is $110 ($26/ccf), which is smaller in absolute terms compared to the low-delinquency household but higher when normalized to water use.In fact, cumulative debt from the late penalties alone (which equal 10% of the value of the unpaid bill) can exceed the base water bill in some months (shown in the black dots).Overall, the high-delinquency household exhibits higher values across all three delinquency metrics than the low-delinquency household.

Household delinquency metric distributions and correlations
Next, we calculate delinquency metrics for each household and present statistics in figure 4. Delinquency metrics and water use vary substantially across the households in our dataset and all exhibit highly skewed distributions.Over the 13 year period, 65% of households incurred at least one late penalty and 88% of these did not pay off the debt before the next bill cycle.Among households that incur a late penalty, 55% have an average penalty frequency of less than once per year, but the 95th percentile is 0.63 (figure 4(a)).Similarly, 55% of households that accumulate debt have a debt duration of one month (the minimum value), and the 95th percentile is 5.5 months (figure 4(c)).Normalized debt severity has a median of $24/ccf and a 95th percentile of $64/ccf (figure 4(f)).Average water use also has a long upper tail with a median of 5.3 ccf and a 95th percentile of 11.7 ccf (figure 4(j)).A correlation analysis shows meaningful differences across the three delinquency metrics and water use (figures 4(b), (d), (e), (g), (h), and (i)).A strong, positive correlation exists between penalty frequency and debt duration (ρ = 0.57), which is expected as households with frequent penalties likely have consecutive penalties.While it is possible to have frequent penalties and a low duration (chronic hardship) or low penalties but high duration (temporary hardship), it is less common.No strong relationship exists between frequency or duration and normalized debt severity (ρ = 0.03 and ρ = −0.09)or water use (ρ = 0.08 and ρ = 0.12).This may be because a household can pay part of their bill each month, and hence have a low debt severity but a high penalty frequency (and debt duration) from late or incomplete payments.Additionally, while frequency and duration focus on the presence or absence of penalties or debt, normalized debt severity accounts for water use, identifying households that cut back on water use to reduce bills.Debt severity also incorporates how much debt the household is able to pay off.We see a negative correlation between normalized severity and average water use (ρ = −0.60),which is explained by the fact that fixed fees make up a larger portion of bills when usage is low.Low correlations across some metrics may suggest that they capture distinct aspects of water use and delinquency and thus provide a more complete picture of water affordability challenges.

Water affordability ratio and delinquency metric comparisons
After calculating household delinquency metrics, we now compare them to block-group-level ARs, the most common existing water affordability metric.Since household-level income data is unavailable, block group ARs reflect the ratio of average water costs across households in a given block group to that group's MHI.ARs range from <1 to 8%, with 23 out of 44 block groups having ARs greater than the EPA-recommended threshold of 2% (figure 5(a)) [10,28].The percentage of individual households with ARs above 2% is likely higher due to spatial aggregation bias, which can obscure effects on households below median income levels.Spatially, ARs are correlated with income distributions (figure S1), reflecting greater wealth in the north of the city, lower-income neighborhoods in the south, and a large student population in the west.
We then examine the relationship between different household delinquency metrics and ARs within and across block groups.Figures 5(b)-(d) illustrate each delinquency metric by block group colored by the AR.Specifically, we plot the 80th percentile (p80) of the metric distribution across households in each block group, capturing the upper quantile of affordability challenges in each block group according to each metric.Full CDFs are plotted in S4.We highlight five block groups (labeled in figure 5(a)) for discussion.Block groups D and E, which have similarly high ARs (5.3% and 7.0%, respectively), also have among the highest penalty frequencies (p80 values of 0.21 and 0.22) (figures 5(b) and (d)).These two block groups may represent more homogeneous lowerincome populations leading both ARs and penalty frequency to indicate high unaffordability.However, block group A, which has a low AR (1.6%), also has a high penalty frequency distribution (p80 = 0.23).Block group A may represent a more heterogeneous population leading to a low aggregated AR, but a high proportion of the population incurring frequency delinquency.
Similar nuances emerge for debt duration and normalized debt severity (figures 5(b)-(d)).For instance, block groups A and B have similarly low ARs (1.6% and 1.9%), but among the highest and lowest normalized debt severity (p80 values of $35.35/ccf and $25.00/ccf).In fact, block group A has among the highest 80th percentile metric values across all three delinquency metrics, further supporting our hypothesis of a heterogeneous population.Conversely, block groups D and E have moderate normalized debt severity distributions despite higher ARs.These differences may be driven by water use behaviors, as high use increases water costs and ARs but decreases normalized debt severity.The inverse relationship between water use and normalized debt severity warrants further consideration as an affordability indicator: it may be useful in identifying households intentionally using less water to reduce bills, but variable water use patterns may confound its direct connection to affordability.

Housing characteristics and delinquency metric relationships
Finally, we compare our delinquency metrics and ARs to lower, middle, and upper decile house main area, tax value, and average monthly water use (figure 6).We use these housing characteristics because we expect they are correlated with wealth and they are available at the household level.We observe higher delinquency in households with smaller house area (figures 6(a)-(c)) and lower tax value (figures 6(e)-(g)).For example, in figure 6(a), while the 80th percentile for penalty frequency in houses with the largest main area (p90 and above) is 0.10 (just over 1 penalty per year), the 80th percentile for houses with the smallest main area (p10 and below) is 0.22 2.5 penalties per year).Interestingly, although tax value is often correlated with income [73], the differences between the distributions of delinquency metrics for each tax value decile group are small.One possible explanation for this result is tax values are only updated to reflect inflation, a change in ownership, or completed new construction, and so may not reflect market property values [74].Even though it is used in the literature [73], tax value may also not be a good proxy for income; for example, in the case of retired households with no income but a large tax value.Tax value also does not consider if the occupants rent or own the house.Alternatively, this result may suggest limitations in our delinquency metrics as indicators of affordability.
When we compare household area and tax values to ARs (using household bills by block-group MHI), we find the opposite trend from our delinquency metrics: less household area and lower tax value correspond to lower ARs (figures 6(d) and (h)).One possible reason for this result could be that larger house main areas use more water and hence pay higher water bills, leading to higher ratio values.Alternatively, this result may be evidence of aggregation bias in the AR results, as the income value used for each household is the MHI for that household's block group.Finally, higher water use leads to greater delinquency and AR values for all metrics except normalized debt severity (figures 6(i)-(l)).This result is consistent with the expectation that higher water use correlates with payment challenges since higher water use directly increases bills.Variation in water use has been correlated with many factors, including housing characteristics [69,75], climate factors [69,76], appliance efficiency [6], household size [69,77,78], and race [76].Drivers of water use may also relate to drivers of delinquency frequency and duration.For example, household size is correlated with higher water use [69] and could also reflect greater essential expenditures, making water more difficult to afford [10].

Discussion and conclusions
This study contributes the first comparison of household-level water delinquency metrics.We propose metrics using the frequency, duration, and severity of late penalties and associated debt, analogous to previous metrics developed in other sectors, and calculate them using 13 years of household billing data in Santa Cruz, California.By comparing these metrics with each other, traditional block-grouplevel ARs, water use, and housing characteristics, we assess the potential utility of delinquency metrics in water affordability assessments.Table 1 summarizes the purposes, drivers, implications, and limitations of our delinquency metrics and ARs.
Our results suggest these metrics capture distinct aspects of water payment behaviors and also differ from aggregated ARs.First, delinquency frequency and duration both show promise as household affordability metrics.We see both higher frequency and duration values with household characteristics indicative of lower wealth.Additionally, frequency and duration are highly correlated but have subtle distinctions.For example, we find differences in the ordering of distributions of frequency and duration metrics for different block groups.These differences may reflect different emphases on temporary payment hardships (with higher duration values) versus chronic hardships (with higher frequency values).
We also find that normalized debt severity is not highly correlated with frequency or duration or ARs.Our goal in normalizing debt severity by average water use is to identify households with a high level of debt relative to their water use, potentially indicating affordability-driven conservation behavior.However, it is possible to conflate high-income and high-wateruse households who miss one water bill with lowincome and low-water-use households accruing debt.(figures S3-5 replicate our results using debt severity without normalization, highlighting its direct link to water use.)Since multiple factors influence water use and payment behavior, including other expenditures [10] and outdoor vs. indoor use [69], it is difficult to directly isolate aspects related to payment hardships.Additionally, a household could pay part of each month's water bill, accruing small amounts of debt, but still facing chronic affordability challenges.Normalized debt severity may need to be paired with other metrics to address possible conflation issues.In one example for energy services, the amount of debt owed is paired with service disconnections to avoid mis-identifying high-income households who miss a single payment [44].
Next, this study highlights the importance of household-level data.For example, while higher ARs also often have higher distributions of penalty frequency and debt duration values (e.g. in block groups D and E in figure 5), we also see block groups with low ARs but high delinquency metrics.This is likely due to greater heterogeneity in water affordability challenges within the block group.For example, in block group A, where we see a low AR but high penalty frequency and debt duration, 33% of households make less than $40 000 per year (the California Poverty Measure poverty line is $39 900 [49]), even though the MHI is $116 518 [50].This wide income distribution highlights how spatially aggregated metrics underestimate household affordability challenges, particularly in areas with high inequity.
While our delinquency metrics highlight new aspects of water affordability, there are limitations.First, our approach requires utility data, which is not publicly available, potentially requiring close collaboration between utilities, researchers, and policymakers.While computing delinquency metrics requires fewer data types compared to ARs, ARs can be computed using publicly-available data.Second, because utilities track delinquencies differently, these metrics may be difficult to analyze across utilities (or across time if a utility changes their billing system).Third, using delinquency metrics as a measure of affordability may be limited in their application to multi-family homes, which often have only one water meter.As water submeters become more commonsuch as in California, which implemented a submeter requirement in 2018 [79]-future work can compare delinquency metrics across multi-family households.Fourth, our use of static income and housing characteristics assumes that these measures are relatively stable over time.Finally, while our metrics may be generally applicable, our results are limited to our dataset in Santa Cruz, and may differ in other cities with different water use patterns, rate designs, utility late payment and shutoff policies, and sociodemographic characteristics.Future research can further assess what aspects of delinquency are most related to water affordability challenges to enhance the utility of these metrics for decision-making-for example, by comparing renters (who may not directly pay for their water) and owners or identifying thresholds that indicate recurrent, severe patterns of delinquency.Importantly, delinquency metrics must be further assessed as reliable measures of water affordability using surveys, interviews, or other methods.Delinquency metrics have possible uses for utilities and policymakers.While ARs enable assessment across communities, delinquency metrics may also identify high-risk households within communities.
At the utility level, they can be used to provide household-level targeted bill relief (e.g.payment plans or rate assistance [80]) before resorting to shutoffs.At the state or federal level, delinquency metrics can help identify if disparities are greatest across or within systems.This may help governments target financial support for both at-risk systems and at-risk households within lower risk systems.This is particularly relevant in California, where the Office of Environmental Health Hazard Assessment recently developed water system-level affordability indicators to support its 2012 Human Right to Water legislation [46,81,82].This approach is likely to miss populations vulnerable to affordability challenges in urban areas with low community-wide ARs.With further cross-community validation, future state-and federal-level affordability metric recommendations could include delinquency metrics to complement ratio metrics [46], to assess water insecurity driven by affordability challenges [83].

Figure 2 .
Figure 2. (a) Distribution of household water use, (b) distribution of household water bills, and (c) fraction of household water bills with late penalties from 2009-2021 in Santa Cruz, California.

3 .
Synthetic time series plots of water billing data and cumulative debt for (a) a low-water-use, high-delinquency household and (b) a high-water-use, low-delinquency household.Water bill categories include: flat fees based on meter size; volumetric costs divided into tiers based on water usage; sewer and refuse charges, which are constant every month; drought surcharges; other fees dependent on water use such as infrastructure reinvestment and rate stabilization; taxes; and late penalties.

Figure 4 .
Figure 4. Delinquency metric distributions and relationships.Histograms of (a) frequency, (c) debt duration, (f) normalized debt severity, and (j) average water use.The percentage of zeros in the distribution, which we omit for visual clarity, are included at the top right of each panel.(b), (d), (e), (g), (h), (i): Bivariate data density plots.Warmer plot colors indicate higher density.Spearman's rank correlation coefficient is included at the top right of each panel.

Figure 5 .
Figure 5.Comparison of block group affordability ratios (AR) and delinquency metrics.(a) Map of ARs by census block group for the City of Santa Cruz using average water bills from 2009 through 2021 and 2019 5-year MHI from the American Community Survey (2015-2019).Scatter plots comparing 80th percentile delinquency metrics for each block group colored by AR: (b) debt duration vs. penalty frequency, (c) normalized debt severity vs. debt duration, and (d) normalized debt severity vs. penalty frequency.The map shows a large range of ARs across the city, and the scatter plots show that block groups with similar ARs do not necessarily exhibit similar delinquency metric distributions, highlighting possible aggregation bias in block group ARs.

Table 1 .
Comparison of delinquency metrics and affordability ratios (ARs).indicate common features across metrics.