Apartments along Brays Bayou

Inherent Bias and Limitations of Flood-Mitigation Benefit Index

In the last few weeks, Michael Bloom, a fellow member of the Harris County Community Flood Resilience Task Force, and I have debated the inherent bias and limitations of a Flood-Mitigation Benefit Index (FMBI) proposed by a majority of the Task Force to Harris County Commissioners Court.

According to Mr. Bloom, the index will:

  • Reveal and document patterns of historical discrimination.
  • Help plan where additional flood-risk reduction investments should be made.

Population-Based, Not Damage-Based Mitigation

The formula is: 

Benefit = Total Cost/(Population X Risk)


  • Cost = total flood-mitigation construction spending (and only construction spending) that benefits a census tract.
  • Population = the number of people who live in census tracts.
  • Risk = the annual chance of flooding (applied to census tract(s)) expressed as a whole number. For instance, a 1% annual chance equals 1. And a 10% annual chance equals 10, etc.

The Task Force hopes to calculate and compare the results for each census tract in the county.

The formula measures the historical per capita flood-mitigation costs 
supposedly associated with the “current” level of risk in a census tract – NOT historical flood damage.

According to proponents, “a high benefit score means no more mitigation spending is needed. And a low score means more spending is needed.”

But consider these two examples: 

  1. 4,000 people live with a 1% annual chance of flooding and have received $200 in prior investment. Their FMBI would be 0.05. That’s extremely low. And scores that low indicate such areas need help “regardless of prior investment.”
  2. 8000 people live in the 10-year flood plain and have received $10 million in prior investment. Their FMBI equals 125. That’s 2,500 times higher. 

According to a spokesperson for the FMBI, “A high FMBI means we don’t need to make more investments in that location.” Yet twice as many people live with ten times the risk in the area with the higher index.

So, who deserves the most help? Residents with the lowest FMBI? The formula SAYS they need help the most. But they actually have the lowest risk.

The Value of Market Testing

None of the hypothetical examples used to “sell” the formula hint at the possibility of such an upside-down result. 

The example above proves several things: 

  • The formula can produce inconsistent and misleading results.
  • It doesn’t always measure what it purports to measure. It has validity problems, as previously discussed.
  • Adjusting for population doesn’t prove historical discrimination. The most densely populated area has 50,000 times more investment.

The formula needs rigorous testing and ground-truthing before going any further. This is a best practice for any new scientific formula – especially one intended to guide future investment. 

In addition to producing unintended results, the formula has several other problems that require discussion. 

No Right-Of-Way Acquisition Costs Included

The FMBI formula includes only construction costs. It excludes right-of-way acquisition costs by assuming that they are “uniform throughout the county.” Therefore, “…costs included or excluded will not adversely impact results.”

In fact, Right-of-Way (ROW) Acquisition costs are huge and NOT UNIFORM throughout the county. I have documented that ROW costs typically comprise the second most expensive part of flood-control projects.

All Flood Control and partner spending on all capital improvement projects from 1/1/2000 through the end of Q3 2021. Data obtained via FOIA Request from HCFCD.

A quick glance at the Appraisal District website will tell you that land costs vary widely throughout Harris County and change over time.

The cost of buying floodplain land or wetlands for preservation in rural parts of Harris County pales in comparison to land acquisition costs in densely populated parts of the county.

In fact, acquiring land in densely populated areas for flood mitigation often costs more than construction, according to several engineers I consulted.

Compounding Problems?

I worry that other methodological issues may compound each other, not cancel each other out.

Map of Census tracts in Harris County, Texas.

Consider that:

  • Census tract population typically varies by up to 4X (2,000 to 8,000), according to the Census Bureau. This will produce deceptive spatial comparisons.
  • Some Census tracts may comprise dozens of square miles while others comprise a few city blocks. Typically, flood mitigation projects are not considered at the Census-tract level. According to three engineers I consulted, that’s too small in most cases to be workable.
  • Larger Census tracts may contain multiple watersheds, each with independent levels of risk – or individual watersheds with varying levels of risk. In such cases, the formula would average risk. But averaging can mask a serious problem in one area with a non-problem in another. Thus, the formula has a bias in favor of spatially smaller Census tracts.
    Smaller tracts tend to be more uniform in risk, so problems will likely stand out rather than get lost in an average. But in larger watersheds, flood risk will feather out with increased elevation and distance from a river. That will make it extremely difficult to calculate the number of people exposed to varying degrees of risk.
    Averaging takes the simple way out. But averaging risk is like comparing saints and sinners, then declaring “No problem.”
  • The data collection effort for the index omits many sources of funding. So the formula will calculate investment dollars from some entities and areas, but not others. For instance, the formula will NOT measure drainage funding from Harris County Commissioner Precincts, dozens of cities, and 389 municipal utility districts in unincorporated areas. The difficulty of data collection in these areas will produce another spatial bias. Likewise, the FMBI formula will omit the considerable drainage-improvement contributions of reputable private developers. 

No one has tested how these inconsistencies will affect each other. But there’s an even bigger data integrity issue.

Partially Updated Data

HCFCD and its partners invested more than $1.5 billion in flood mitigation between Harvey and the end of 2021. Since 2000, they’ve invested more than $3.5 billion. But as of this writing, new MAAPnext flood maps only reflect the POST-mitigation risk associated with projects in FIVE bayous: Brays, Greens, White Oak, Sims, and Hunting. The Army Corps partnered with HCFCD in those.

Unfortunately, according to a knowledgeable source, HCFCD has not yet updated the risk maps for its own Capital Improvement Projects in other watersheds. So if you ran the allocation formula now, it would compare PRE-mitigation risk in 18 watersheds with POST-mitigation risk in 5. 

Mitigation in those five watersheds totals $439 million out of $1.5 billion since Harvey. So true, current risk is reflected in only 29% of spending since Harvey and 13% in this century. Those percentages will no doubt increase in the future. But if you ran the numbers today, you would compare numbers with PRE- and POST-mitigation risk.

And consider this. With HCFCD spending at the current rate of about $80 million per quarter, “current risk” is a constantly changing target. So we’ll never be able to compare apples to apples in all watersheds anytime soon.

And we want to use this formula to guide future mitigation spending? Using it could send more money back to fix areas we already fixed!

Difficulty of Assigning Investments to Census Tracts

Another challenge: How do you determine which census tract(s) to apportion project benefits among? Example: Addicks and Barker Reservoirs. The Army Corps developed those back in the 1930s to protect downtown Houston…15-20 miles away! 

Do you credit the investment to:

  • All of downtown?
  • People living inside the reservoirs (who have their own census tract)?
  • The current population of the entire Addicks and Barker Watersheds?
  • All census tracts along Buffalo Bayou and parts of White Oak Bayou, our second and third most populous watersheds?

The Corps certainly didn’t build the reservoirs to protect the people living inside them. That’s what all the lawsuits are about!

And virtually all residents of the Addicks and Barker watersheds live upstream from the Corps’ investment, so they will not benefit from the investment either.

Downtown has immense commercial and economic value but relatively few permanent residents. 

So, who gets the benefit? Again, lots of room for interpretation and misplaced assumptions here that numbers can easily mask! Now, multiply this problem times thousands of Census tracts.

Anti-Commercial Bias

The population-based FMBI has a built-in bias against commercial areas that have little to no residential population. For example, consider the cases of Downtown, the Texas Medical Center, and the Port of Houston. Such areas support employment throughout the region, but the formula discriminates against them by giving huge weight to population and omitting actual damage.

No Thresholds Defined

To my knowledge, the task force has never discussed threshhold “benefit” levels that correlate to “needs help” or “doesn’t need help.” The extremes may sometimes be easy to determine. But what about outcomes in the middle? 

Offsetting Variables

Variables in the formula can offset each other as we saw above. In tight races for funding, who gets the next flood-mitigation investment? The area with the lowest investment, highest risk, or largest population? Such quandaries have not yet been addressed. 

No Agreement on Weights of Other Factors

To help make future flood-mitigation decisions, proponents of the formula also suggest weighing (separately) other factors, such as the CDC’s Social Vulnerability Index. It includes the percentage of Low-to-Moderate residents in an area. However, no one has yet discussed the weight given the Benefit Index relative to other factors.

No Consideration of Actual Flood Damage

In deciding where to put flood mitigation projects, engineers traditionally look for damage clusters. It’s that simple. Dollars flow to damage.

Reducing flood damage is a tried and true, measurable way to evaluate projects. So why all the complexity? 

What’s The Point?

What is this formula trying to prove? Is it attempting to develop a new approach to mitigation funding that eliminates a perceived bias in Benefit/Cost Ratios? 

Commissioner Rodney Ellis often talks about how calculating the value of avoided damages in higher value homes disadvantages projects in poorer neighborhoods. That can be true in some instances. Expensive homes can ratchet up benefits (measured in dollars) faster than lower value homes can. And that can result in higher Benefit/Cost Ratios for projects in affluent neighborhoods – assuming density is held constant. But…

One high-value home on an acre would likely appraise less than an apartment building, also on an acre. In Kingwood, I compared the valuations of an expensive single-family home with a large apartment complex one block away. The appraised cost per acre (including structures) of the apartment complex is 4X higher.

Now consider that apartments accommodate almost half of Harris County’s population.

According to the latest census data, 54.9% of Harris County residents live in owner-occupied homes. The rest, 45.1 percent, live in apartments.

Most Americans aspire to and encourage home ownership, in part, because of the stability it fosters in communities. But this formula – because of its emphasis on population density – favors apartment areas over areas with owner-occupied homes. There’s nothing inherently wrong with that. You just need to understand what the formula does.

Difference Between Vertical and Horizontal Density

The Benefit Index favors all areas with dense population. Proponents argue that helping more people is better. I don’t argue with that. However, the generalization masks the financial pain inflicted by a flood on owners vs. renters, and on the people who live at ground level compared to those who live above it. 

Ground floor renters may lose contents in a flood, but they won’t be responsible for making structural repairs. The owner will. 

And many living above the ground floor may find themselves more inconvenienced by flooding than financially devastated. So, is it fair to count all people on all floors when determining who suffers the most pain? 

Five-story apartment buildings crowding Brays Bayou with ground-level parking underneath. HCFCD has no way of knowing how many people live in apartments like this, yet HCFCD will be responsible for compiling the data.

In the proposed formula, higher population will lower the benefit index, making it look as though all renters (almost half the county’s population) suffered more than owners of single-family homes. 

The premise underlying such “equity” arguments is that poor people can least afford floods. But most people in apartments like those shown above won’t make structural repairs as a homeowner would.

No Perfect Formula

No perfect formula exists that’s equally fair to all in all circumstances. That’s why FEMA, HUD and the Army Corps allow consideration of multiple factors when determining which projects to fund. 

The Flood Mitigation Benefit Index focuses totally on population, risk, and past investment. It ignores actual flood damage. 

If we use ANY formula to HELP allocate future flood-mitigation funds, we should all strive to:

  • Understand its built-in biases
  • Maintain high standards for data integrity.

If we want to test a hypothesis of historical discrimination in flood-mitigation funding, there’s a much simpler way. It’s called direct measurement. Simply locate damage centers from past storms and compare funding in the following decade designed to mitigate those areas.

For More Information

For more background on issues with the formula, see my earlier posts:

Or consult Mr. Bloom’s rebuttals.

Posted by Bob Rehak on 7/14/22

1780 Days since Hurricane Harvey