100-Year Flood, 500-Year Flood: Real Risk Probabilities

When the Army Corp of Engineers and NFIP came up with the 100-Year Flood and 500-Year Flood designations, it’s almost as though they wanted to confuse the public. With Hurricane Harvey, much has been written on the meaning of the terms 100-year flood (it means a 1% chance of flooding in a single year), and the term 500-year flood (a 0.2% chance of flooding in a single year). While these basic definitions are correct, they don’t really help homeowners, whose question is: what’s the chance that my house will flood while I own it?

In the case of the 100-year flood zone, this means that the chance of flooding is at least 1% in a single year. But what if you plan to own your home for 30 years? In this case, you have a 99% of NOT flooding each year, but you’ve got to NOT flood for all 30 years. The probability of NOT flooding over 2 years is 0.99 * 0.99, and thus the probability of not flooding over 30 years is 0.99^30, or 74%. This means that the home has a 26% of flooding over the 30 years in question.

Of course, that doesn’t take into account the change in probabilities resulting from a combination of climate change and reckless development in most American cities. According to Kenneth Trenbeth, a scientist at the National Center for Atmospheric Research, “What used to be a 500-year event has become a 50- or 100-year event.” With this in mind, we can lay out the following table of homeowners’ flood risks:

Flood Probability Over 10 Years Flood Probability Over 30 Years
100-year flood zone  10% 26%
100-year flood zone, climate-change adjusted (to 10-year flood) 65% 96%
500-year flood zone 2% 6%
500-year flood zone, climate-change adjusted (to 50-year flood) 18% 45%

The flood risks over 30 years likely exceed many homeowners’ assumptions even before accounting for climate change – the climate-change adjusted risks make flooding within flood zones a virtual certainty! Homeowners in these areas are well advised to buy flood insurance, which is an incredible value as it is priced by the government below fair value. Homeowners not in, but simply near the 100-year floodplain, should realize that THEY are now likely in the true 100-year flood risk area, while their neighbors in the floodplain are likely at much greater risk.

Think that the probabilities can’t possibly have shifted that much? Consider that parts of Houston have had 3 500-year flood events since 2001 – Harvey, the 2016 Tax Day Flood, and Hurricane Allison. The chance of having one such “500-year” flood in 16 years is around 3.2%, but three such events? It’s less than 0.15% if these are really 500 year floods! [1] The reality is that 500-year floods are likely more than 10 times more common than the old statistics indicate, and homeowners should plan accordingly.


[1] The chance of 3 or more 500 year floods is equal to 100% minus the chance of 0, 1, or 2 such floods. The chance of 0 floods is 96.85%, and the chance of exactly 1 flood is roughly 3%, leaving less than 0.15% for the other potential outcomes (which drop off very rapidly because of the 0.2% chance happening multiple times).

List of Warmest Years on Record Globally

9 of the top 10 hottest years globally have occurred over the past decade, when measured using three different global temperature data sets. The top 20 warmest years have all occurred during the last 24 years.

How do the record high temperatures over the spring and summer in the US compare on a global basis? While numerous articles on global temperature trends exist [1], I decided to go to the primary temperature data sources to find out. Below I have created a list of the 20 warmest years on record globally, using three data sets: NASA GISS, the UK Meteorogical Office, and NOAA / UAH [2]. While the three data sets vary in length from 40 to 150 years, the 20 warmest years turn out to have all occurred in the last 24, making it possible to construct an average temperature for the hottest 20 years.

Rank Year Global Avg Temp (F) [3]
1 2010 58.28
2 1998 58.22
3 2005 58.15
4 2007 58.06
5 2002 58.05
6 2009 58.04
7 2003 58.03
8 2006 58.02
9 2011 57.98
10 2004 57.90
11 2001 57.89
12 2008 57.75
13 1995 57.70
14 1997 57.68
15 1999 57.65
16 1990 57.64
17 1991 57.64
18 2000 57.64
19 1988 57.59
20 1987 57.54

Since this is a divisive topic prone to political obfuscation, it’s worth noting that both the NASA Goddard Institute and the UK Meteorological Office officially support the theory of anthropogenic global-warming, while the research scientist responsible for the University of Alabama-Huntsville data set does not support this theory.

[1] This has been a popular topic: Economist, Live Science, ArsTechnica, Science Daily, and Wikipedia

[2] Here are the original data sets:

GISS Data: http://data.giss.nasa.gov/gistemp/tabledata_v3/GLB.Ts.txt and www.movingandstoragesite.com moving and storage

NOAA/UAH: http://vortex.nsstc.uah.edu/data/msu/t2lt/resume builder online/uahncdc.lt

Hadley Meteorological Centre UK: http://www.metoffice.gov.uk/hadobs/hadcrut4/data/download.html#regional_series

[3] The data in this blog post was constructed by averaging data from the three underlying data series. The NASA GISS estimate of global mean baseline temperature of 14 degrees Celsius was used to adjust the temperature deltas provided by the original data series in order to show global mean temperature in Fahrenheit terms here.

Here is my excel spreadsheet with data and calculations.

Will Solar Power Meet World Electricity Demands?

Proponents have looked to solar power as a potential panacea to the world’s current and future energy needs, while critics note that solar power still provides less than 1% of the world’s electricity. While wind power has grown to scale much faster, conventional wind technology has much less capacity to scale than solar power, and the theoretical limits on solar power are significantly higher [1]. When might solar power fulfill the hype and generate much of our electricity? Solar energy has grown at a rapid clip since its infancy in the 1970’s, from 0 to 20GW (nameplate capacity) in 2009. How much of worldwide electricity demand will solar be able to fulfill if it maintains this growth rate?

Total solar power capacity continues to grow at 20-25% per year, a rate of growth it has maintained for decades. It’s not surprising that solar photovoltaic technology is advancing rapidly, as it is a cousin of traditional semiconductor technology. For almost four decades semiconductor technology advanced according to Moore’s Law, with chips roughly doubling in transistor density (and speed) every 18 months. At a 20% annual rate of growth, installed solar capacity would rise from 21 GW in 2009 to almost 6000 GW by 2040. This install base could generate 12 trillion kilowatt-hours of electricity per year, or two-thirds of today’s worldwide electricity consumption [2]. However, the EIA estimates that by 2040 worldwide electricity demand will hit 35 trillion kilowatt-hours!

Even assuming that solar energy installations grow at a 20% clip for three decades, the total install base will not be sufficient to meet world energy demands. Despite the industry’s rapid growth, replacing a hundred years of fossil-fuel based generation capacity by mid-century may be close to impossible. Nonetheless, if solar energy manages to scale on this trajectory, its contribution would still be enormous, and would likely bring total renewable generation to over 50% of all electricity.

Can it be done? Did anyone in the 1960’s believe that a 2010 phone would have more processing capacity than all the world’s computers combined?

[1] From Without The Hot Air – all wind power resources worldwide could supply a significant fraction of total power needs, while solar energy in the Sahara alone could theoretically supply all world energy needs.

[2] The EIA International Energy Outlook shows current worldwide electrical demand of roughly 18 trillion kilowatt-hours, with this figure growing to 35 trillion kWh by 2035 by www.usbgeeks.net.

Hybrid Economics Part II

In part I of this post, I outlined a number of variables that impact the cost-benefit of buying a hybrid-electric vehicle.

First, the spreadsheet model.

To recap, here are the variables included in the model, with the default assumptions made:

  • Price of gasoline = $3/gallon
  • Annual mileage driven = 12k/year
  • Standard-car MPG (mileage of the same car or similar car without hybrid technology) = 20mpg
  • Hybrid MPG / electric MPGe = 100 mpge
  • Risk-free discount rate = 3%
  • Projected annual increase in gasoline prices = 5%
  • Hybrid price premium = $18k
  • Length of car ownership = 8 years

There’s one more important variable to add to this list:

  • Time savings from reducing gas station stops = 300 minutes, or 5 hours per year

Time savings can be a huge hidden savings for upper-middle class and wealthy Americans (those able to afford a car like the Chevy Volt). If the value of a Volt driver’s time is $50/hour (equivalent to a 100k/yr salary), then eliminating a single gas station stop of 10 minutes is worth over $8. Ten minutes may sound long for a stop at the gas station, but is not unrealistic when considering total time lost leaving and re-entering a normal commute.

Using the assumptions provided above, we find that the total fuel and time cost savings of driving a Chevy Volt for eight years are around $9000. Since the Chevy Volt costs $18,000 more than a comparable loaded Chevy Cruze, it’s not yet cost competitive, even with government tax credits and with time savings taken into account.

Key Conclusions:

  • Gas prices of $7 per gallon are required to make the Chevy Volt cost-effective at current prices (without the government tax credit)
  • Once plugin hybrid premiums drop to $9000, they will be cost-competitive.
  • The Nissan Leaf currently offers buyers significant savings WITH the $7500 tax credit according to frontier high speed internet, as the total savings of $16,500 exceeds the $12,000 price premium. Even without the tax credit, the Leaf is very close to being cost-competitive at current pricing.

Hybrid Economics Part I

With the arrival of the Chevy Volt and Nissan Leaf, and plans for many more hybrid and electric vehicles in the works, I’d like to revisit the cost-benefit of purchasing a hybrid (or electric) vehicle. Externalities* (pollution) and cool-factor aside, a hybrid vehicle is a cost-effective purchase only if the total present value of gasoline savings equals the price premium paid for hybrid technology. A number of factors impact the calculation:

  • Price of gasoline
  • Annual mileage driven
  • Standard-car MPG (mileage of the same car or similar car without hybrid technology)
  • Hybrid MPG / electric MPGe
  • Risk-free discount rate
  • Projected annual increase in gasoline prices
  • Hybrid price premium
  • Length of car ownership

In part II of this post, I’ll attach a detailed spreadsheet to analyze this problem. But it’s possible to come up with a quick best-case estimate without a whole lot of math. Assume that gas costs $3 a gallon, that we drive 15,000 miles per year, that a comparable non-hybrid gets 30 MPG, and that the risk-free discount rate (currently in the 3% range) and gas price inflation roughly cancel out. In a year we’ll have to buy 500 gallons of gas for $1500. If we own the car for eight years, that makes $12,000 in maximum possible gas savings – if the hybrid were to use no fuel at all!

The Chevy Volt and Nissan Leaf both appear to cost significantly more than $12,000 above vanilla gasoline competitors. At $40,280, the Chevy Volt is more than 18k more than a loaded Chevy Cruze, and that’s with GM selling at a loss! The Nissan Leaf is similarly 15k more than a maxed-out Nissan Versa. Perhaps this is not surprising, as new technology often commands a price premium, and early adopters may be happy to pay that premium.

In Part II I’ll introduce the complete model, and add one more variable that may tip the balance back in hybrids’ favor. Stay tuned…


*Why leave out externalities like pollution from the analysis? True externalities are outside the traditional economic transaction, and so a car buyer doesn’t take them into account when making a purchasing decision. In reality, a large number of hybrid buyers purchase the vehicles precisely because they value the environmental benefits of the vehicle. But in order to scale past that crowd, hybrids will have to be cost-effective for the rest of consumers – so it makes sense to leave this out environmental benefits here.

Fuel Efficiency: Modes of Transportation Ranked By MPG

Building on a previous post on the energy efficiency of various foods, I decided to create a list of transportation modes by fuel efficiency.  In order to compare vehicles with different passenger capacities and average utilization, I included both average efficiency and maximum efficiency, at average and maximum passenger loads.

The calculations and source data are explained in detail in the footnotes. For human-powered activities, the mpg ratings might appear high, but many calculations omit the fact that a human’s baseline calorie consumption must be subtracted to find the efficiency of human-powered transportation. I have subtracted out baseline metabolism, showing the true efficiencies for walking, running, and biking.

For vehicles like trucks and large ships which primarily carry cargo, I count 4000 pounds of cargo as equivalent to one person. This is roughly the weight of an average American automobile (cars, minivans, SUVs, and trucks).

The pmpg ratings of cars, trucks, and motorcycles are also higher than traditional mpg estimates, since pmpg accounts for the average number of occupants in a vehicle, which according to the Bureau of Transportation Statistics is 1.58 for cars, 1.73 for SUVs, minivans, and trucks, and 1.27 for motorcycles.

List of Transportation Modes By Person-Miles Per Gallon (PMPG)

Transport Average PMPG Max PMPG
Bicycle [3] 984 984
Walking [1] 700 700
Freight Ship [10] 340 570
Running [2] 315 315
Freight Train [7] 190.5 190.5
Plugin Hybrid [5] 110.6 350
Motorcycle [4] 71.8 113
Passenger Train [7] 71.6 189.7
Airplane [9] 42.6 53.6
Bus [8] 38.3 330
Car [4] 35.7 113
18-Wheeler (Truck) [5] 32.2 64.4
Light Truck, SUV, Minivan [4] 31.4 91

[0] I used these conversion factors for all calculations.

[1] Walking: A typical person expends roughly 75 calories to walk a mile in 20 minutes. An American burns about 30 calories just to exist for 20 minutes, so the net expenditure for walking is 45 calories per mile. One gallon of gasoline contains roughly 31,500 kcal, so 45 calories is 0.0014 gallons of gas. Thus the average American has a walking efficiency of 700mpg. This estimate is higher than that given elsewhere – the crucial difference is that you have to subtract out baseline metabolism, since an American consumes over 2100 calories a day just to stay alive.

[2] Running: The calculation is similar to [1]. Here we assume a 6 minute/mile pace, which burns 1088 calories per hour, or 109 calories per mile, and 100 net calories per mile. 100 calories is 0.003 gallons of gas, for a fuel efficiency of 315mpg.

[3] Bicycles: Bicycling at 10mph requires 408 calories per hour, or 40.8 calories per mile, which is 32 net calories per mile. This yield an mpg rating of 984, higher even than walking!

[4] Automobiles: The Bureau of Transportation Statistics has done the heavy lifting for us, calculating BTU per passenger-mile for cars, light trucks, and motorcycles. For cars, the latest (2008) data point is 3501 BTU / passenger-mile, or 0.028 gallons per passenger-mile, which equals 35.7 pmpg (BTS assumes 1.58 passengers on average, so this equates to 22.6 mpg). Using the same BTS data, average pmpg for light trucks is 31.4, and for motorcycles is 71.76. For max pmpg, we use a max passengers of 5 for cars and trucks, and 2 for motorcycles. To do this calculation from the BTS data, we first divide the avg. pmpg by the avg. passenger count, and then multiply by the max in each case.

[5] 18-Wheelers: For 18-wheel rigs, BTS data shows an average diesel mpg of 5.1. This equates to a gasoline mpg of 4.6, using 125,000 btu / 138,700 btu as the gas / diesel energy ratio. The weight limit for trucks on most roads is 80,000 lbs, of which 55,000 might be the max load given a truck weight of 25,000 lbs. To convert load to passengers, I assume 4000 lbs per passenger, since that’s roughly the weight of a passenger vehicle. A 50% (average) loaded truck counts for roughly 7 passengers, and a full load counts for 14. Using these factors, average pmpg is 32.2 and max pmpg is 64.4.

[6] Plugin-Hybrids: With the exception of the Prius Hymotion conversion, plugin hybrids like the Chevy Volt have yet to reach market, and have not yet had a final mpg designation. Consumer Reports achieved 67 mpg with the Hymotion Prius, though Hymotion and many owners claim 100 mpg is possible. Using 70 mpg, and adjusting this by the 1.58 average passenger count, the Hymotion Prius has an average pmpg of 110.6, and a maximum pmpg of 350.

[7] Trains: While all trains have similar underlying efficiencies, passenger trains in the US are much less efficient in practice because of poor utilization. BTS calculates Amtrak efficiency at 1745 BTU per passenger-mile, which equates to 71.6 pmpg. Amtrak traveled 267 million car-miles in 2007, which equals to 16 billion potential passenger miles if the average car holds 60 passengers. In 2007 Amtrak consumed 10.5 trillion BTU of fuel, or 659 BTU per available passenger mile. Amtrak’s max pmpg is therefore 189.7 (if somebody would just ride it).

Freight trains consume 328 BTU to move a ton one mile. Using 4000 lbs of freight equals one passenger, this equals 656 BTU per passenger-mile, or 190.5 pmpg.

[8] Buses: At average passenger loads, buses achieve 3262 BTU per passenger-mile, or 38.3 pmpg. Per BTS data, buses average 6.1 diesel mpg, or 5.5 gas mpg. With a full load of roughly 60 passengers, a max pmpg of 330 is possible. The huge difference in average and max pmpg implies that buses are usually almost empty – perhaps smaller mini-buses should be used by more fleets.

[9] Airplanes: Airplanes flying domestic routes average 2931 BTU per passenger-mile, or 42.6 pmpg. The overall domestic load factor in 2008 was 79.6%, so at max capacity a plane might achieve 53.6 pmpg.

[10] Ships: In a previous post I found that shipping over water (by barge) costs one-third of shipping by rail. This implies that water based shipping is also roughly triple the efficiency in energy terms, since energy is one of the key cost drivers in transportation. This provides a rough estimate of 570 pmpg. According to this post, the world’s largest container ship travels 28 feet on a gallon of residual fuel oil (149,690 BTU or 1.2 gallons of gas). This equals 0.004 mpg. Per Wikipedia, the ship can carry 11,000 14-ton containers, or 77,000 passenger-equivalents using our 4000 lb conversion rate. Thus pmpg is 340 for this ship.

The ROI Payback of Tossing Incandescents For CFLs

After moving into my current home, I discovered that the previous owners had left dozens of light bulbs for the various fixtures in the house. I was happy to know that I wouldn’t have to restock for a while. In the interim, compact fluorescent light bulbs have become inexpensive, and LED bulbs have begun to become economical as well. While I have realized for some time that CFLs are a good investment with a short payback period, I have yet to replace my bulbs. At some level, it feels wrong to throw out all those light bulbs. What is the real return on throwing out a working bulb and replacing it with a CFL?

I calculated the payback period in days when replacing a 60W bulb with a CFL, assuming $0.1 per kWh electricity and $0.97 per CFL, which is what I paid at Home Depot last weekend [1]. I performed the calculation for a variety of usage assumptions, and this graph shows the results:

CFL Payback Period In Days

The payback on moving to CFLs is quite fast, a few weeks for high usage bulbs, and several months for bulbs used only one hour per day.

The first graph begs the question – how frequently does a light bulb need to be used to justify replacing it with an incandescent? Assuming that a 10% return on investment is desired, that the CFL will last 5 years [2], and that electricity costs $0.10 per kWh, I calculate that you should replace any bulb used more than 9 minutes per day [3].

That’s a pretty low bar, lower than I expected. As CFL prices have dropped, and light quality has improved [4], there aren’t many arguments left for sticking with incandescents. And for the lazy, switching to CFLs will decrease the frequency of light bulb changes, resulting in lower effort as well.

Conclusion: Throw out your light bulbs and replace them with CFLs today. The quality of CFL light output is now pretty close to incandescent, and you are burning money every day you wait!

I replaced roughly 40 light bulbs last weekend, in the middle of writing this post. For the most part it’s worked out – the light quality is decent, but the CFLs still take some time to get to full intensity, and I may have to replace a few that flicker due to dimmers on the switches.

Here is my calculations spreadsheet on Google Docs.

[1] While this was a sale price, CFL prices have been falling steadily and the standard price at HomeDepot.com is still only $1.25 per bulb (see the 12 pack of 60W-equivalent TCP brand bulbs available at this writing).

[2] Many CFLs are warrantied for 7-9 years, and claim 8000-12,000 hours of working life. Five years is thus a conservative estimate, but takes into account the fact that CFL quality control is still an issue, so that some percentage of bulbs will be defective.

[3] The calculations in my spreadsheet are linear with respect to purchase price – if you pay $2 for a CFL instead of $1, then you should replace all bulbs used for more than 18 minutes a day, and so on.

[4] That CFL light quality has improved is my personal opinion – look around on the web, and you will find hundreds of articles disparaging CFL light quality. I think they’ve come a long way, however, and the soft-white (2700K) bulbs available now do an acceptable job imitating incandescent soft-white bulbs.