Detailed statistical analysis of weather data from my daily log

[Diesel_Dave]

I finally got the chance to sit down and do some number crunching of the weather data from my daily log.

Here’s some background. On every trip I make to and from work I will resent my factory-installed trip MPG display prior to starting. After arriving at my destination, I record the displayed trip MPG and enter that in my daily log. Later, I go back and pull up the weather data for that time of day at a local weather station via wunderground.com. I record the temperature, barometric pressure, relative humidity, wind speed, & wind direction. From that info, I set up my spreadsheet to calculate other things like specific humidity and well as breaking up the wind into two different components—the portion acting parallel to my direction of travel (head/tail wind) and the portion acting perpendicular (effective crosswind). For example, if I’m headed due north and there’s a SW wind of 10 mph, that counts as a 7.1 mph tailwind and a 7.1 mph crosswind (calculated from the Pythagorean Theorem: c^2 = a^2 +b^2). I’ll also make notes in my daily log of traffic conditions, mods (driving & vehicle).

One thing that I’ve noticed is that weather does seem to have a significant impact. Temperature has been the most noticeable one for me. I clearly do much better on warmer days than colder ones. Wind is also noticeable as well. Days with a strong tailwind are noticeably better, for example. This presents a challenge when trying to determine the effects of different mods (driving or vehicle). Let’s say I made a mod this weekend and then went on to average 5% better mileage this week vs. last week. However, what if the temperature was 10 deg F warmer this week vs. last? Was my improvement due to the mod or due to the weather? This becomes even harder when you have multiple things changing. For example, what if the temperature was 10 deg F warmer, but the crosswinds were 5 mph higher? You can see the difficulty. In a lab we could just remove all these noise variables, but in the real world, we have to live with them.

But, what if I knew the effects of the weather? If I knew that a 10 deg F increase in temperature causes a 5% improvement in FE, then I could correct for that and then see whether my “weather-corrected FE” has actually improved or not.

So I decided to do some statistical regression analysis on my daily log weather data. Here’s what I did: I looked at all my weather data from the last ~15 months (since I moved to where I live now). I then separated morning and evening (I typically do better in the mornings, partially due to the elevation change). I then went through and removed all the days when there was rain or snow. I also removed any days where I used the AC (yes, sometimes I give in and use it—like when it 100 deg F and my wife’s going to be home when I get there). After the screening here’s what I got:



So, my first task was to determine the relative significance of the different variables. This is somewhat challenging because some of them are cross-correlated. For example, specific humidity and temperature are cross-correlated because you can’t have high specific humidity without first having high temperatures. So what I decided to do was this:

Step 1: Do a regression fit of fuel economy with each variable individually.
Step 2: Look at which single variable gives the best fit—this variable is the most significant one.
Step 3: Do a regression fit of fuel economy with two variables at a time—the most significant one and then each of the others one at a time
Step 4: Repeat the process with 3 variables at a time, 4 variables at a time, etc.

So here are the results for the analysis of the morning data. I included the day as a variable as well, because this accounts for the mods I make—I’m getting better as I go along in spite of varying weather conditions. This table shows the average error (%) in the fit:



So let’s pretend I want to guess the mileage that I’m going to get on any given day. With absolutely no information, the best I could do would be to guess that I’m going to get my average mileage (42.9 mpg in this case). That will give me an average absolute error of +/- 12.6%. If I know only the day (and nothing about the weather), I can predict my mileage to within +/- 8.45%. If I know only the temperature, to within +/- 9.08%, etc. So you can see that factors with lower numbers are more significant. Knowing only cross wind speed, for example, only reduces the error from 12.6% to 11.93%.
So the day ended up being the most significant variable, followed closely by the temperature. This is interesting, as it indicates that I am the most significant variable.

Okay so if I look at line 2, this shows me the effect of the other variables AFTER I account for the day. As you can see, temperature is the most significant of the other variables—knowing just the day and the temperature reduces my error all the way to +/-4.72 %.

Moving along to line 3 you can see that tailwind speed and crosswind speed have similar significance. Also note that adding in specific humidity after temperature has been accounted for does make much difference: day & temp give +/- 4.72% vs day, temp, & humidity give +/- 4.71%. This indicates that specific humidity itself doesn’t matter much at all, but it is cross-correlated to temperature.

Lines 5 & 6 show that specific humidity & barometric pressure have a relatively small impact. Without those 2 variables I can predict to within +/- 4.20%--with them included it doesn’t really reduce much further. So there’s not really much sense in including them in the correlation.

Here’s the correlation using the 4 most significant variables:

MPG = 24.7 + 0.0485*Day + 0.223*Temp + 0.287*Tailwind – 0.260*Crosswind

So I improve about 0.5 mpg every 10 days—gotta be pretty happy with that.

Also, each degree F increase in temperature leads to a 0.223 mpg increase. This agrees with a rule of thumb I’ve talked about before: roughly 1% change in FE for every 2 deg F temperature change.

As far as wind goes, a 1 mph tailwind or crosswind has roughly the same effect as a 1 deg F temperature change. Also of note is that tailwind and crosswind have roughly the same magnitude of effect.

Without going into all the details, I also went through the same process with my evening data. It turned out fairly similar, except temperature came out slightly more significant than the day.



Here’s the evening correlation:
MPG = 24.7 + 0.0336*Day + 0.152*Temp + 0.209*Tailwind – 0.150*Crosswind

The coefficients are similar, but slightly different from the morning correlation.

Now I can go though my log and “weather correct” my numbers…sweet!

[JRMichler]

What is the distance and elevation change on your commute? I see that the constant is exactly the same in both cases, 24.7. This implies that the elevation change is not affecting your mileage.

You could run another set of correlations by lumping all data together, with a to/from work variable. I use 1 for to work, and 0 for from work. The resulting coefficient is a direct measure of the effect of direction / elevation change / how tired you are / traffic variables / other confounders.

I regularly drive a route of about 60 miles with net elevation change of 800 feet. In the summer, I normally get 30 to 35 MPG uphill and 35 to 42 MPG downhill. The exact MPG depends on wind and temperature.

I also drive a 4 mile stretch of winding gravel road with 35 foot total elevation change. In the summer, I average about 38 MPG downhill and about 30 MPG uphill.

[Diesel_Dave]

Originally Posted by JRMichler

What is the distance and elevation change on your commute? I see that the constant is exactly the same in both cases, 24.7. This implies that the elevation change is not affecting your mileage.

You could run another set of correlations by lumping all data together, with a to/from work variable. I use 1 for to work, and 0 for from work. The resulting coefficient is a direct measure of the effect of direction / elevation change / how tired you are / traffic variables / other confounders.

I regularly drive a route of about 60 miles with net elevation change of 800 feet. In the summer, I normally get 30 to 35 MPG uphill and 35 to 42 MPG downhill. The exact MPG depends on wind and temperature.

I also drive a 4 mile stretch of winding gravel road with 35 foot total elevation change. In the summer, I average about 38 MPG downhill and about 30 MPG uphill.

My elevation change is only 140 ft over 25 miles. Morning commute is left to right:


I tried to the regressions with morning and evening all together, but I couldn't get anything that would get the average error under +/- 10%.

I've wondered why I do better in the mornings for a long time. I haven't figured out all of it but I think it's a number of small factors. I'm sure the elevation change does make some difference. Also, I plug in the heaters in the morning, but evenings are true cold starts. Also, even though the route is "the same", it's not truly the same. For example, if you have a red light on a hill, it's completely different if you're approaching it from the uphill side vs. the downhill side. Also, there's several right hand turns on the way to work which are left hand turns on the way home--typically it's easier to roll through right hand turns without brakes because you only have to watch one lane of traffic. Also, in the mornings I have less city/neighborhood driving before I get to the highway than I do in the evenings. Also, there's usually heavier traffic in the evenings as everybody's leaving work near the same time--that can lead to less hypermiling flexibility.

[slowmover]

I'm really looking forward to reading this in depth. Have to get up at 0400 to help move a rig out near Cotulla. But what you've done here -- with variables -- is, IMO, central to best use: predictability!!

My very first thought about morning versus evening is the greater oxygen content in the air. Certainly seems to apply here in almost-hell-heat-land. Plus the driver is a little less jagged than he would be at days end.

.

[2000neon]

I think you are second to none with your detailed records and going back with such in depth statistical analysis is nothing short of incredible. It would be an understatement to say that I am impressed.

Fantastic work, not only with the MPG you squeeze out of the truck, but having the numbers to back it up.

[gone-ot]

Diesel Dave -- I immediately thought of this quote from Lord Kelvin:



"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.

• Lecture on "Electrical Units of Measurement" (3 May 1883), published in Popular Lectures Vol. I, p. 73; quoted in Encyclopaedia of Occupational Health and Safety (1998) by Jeanne Mager Stellman, p. 1992"

...it's my philosophy, too, which I summarize by paraphrasing the Cuba Gooding, Jr. quote from the Jerry McGuire movie: "...show me the data..."

[Diesel_Dave]

I hadn't seen that quote before. I love it!

[Diesel_Dave]

Already finding some interesting things. Consider the plot below:

This is 5-day average mileage over several months (date is on the x-axis as month/day). I corrected the data to get the mpg if the temperature was always 60 deg F with no wind.

If I had just been looking at the un-corrected data (red line) going into the fall and winter (Aug through Feb), I would have thought that I was getting worse. But, in reallity, my weather-corrected mileage was getting better that whole time!

Also, I could have looked at that period in late March and thought that somethin I'd done must have caused a big spike in mileage. In reality, it was just a brief spring warm-up that went away.

[Diesel_Dave]

Another interesting way to look at things. These are averages for each month:


Having these weather-corrected numbers has been good recently. It's been getting colder and it's discouraging to see my raw numbers going down, despite my beast efforts. However, I'm keeping good weather-corrected numbers which means when it warms up in the spring I should be able to get even better numbers than I did earlier when it was warmer.

[rancidx]

I did a similar exercise today with the data i've been keeping in the garage on ecomodder...
I threw in the weather data and compiled it all in Tableau... It's not as detailed as what you guys did, but clearly shows that the fuel economy follows the weather (even to the point where you when I was having fun in the snow ).
Unfortunately I have 0 posts so I can't throw in the link....