Drifts 05: effect of temperature on air pressure

[DavorJ]

Here I wanted to see:

1. Whether temperature has any effect on air pressure based on data. It should have as air pressure depends on air density, and density on temperature. (A second analysis based on a derivation from ideal gas equations; Drifts 07: theoretical influences of air pressure #54.)
2. Whether temperature can explain the periodic drift effects seen in some loggers (e.g. Drifts 04: Analysis of differences between one barometer and many others (improved) #51)

1. Temperature effect

Since the barometers are not protected from the sun, the temperature can attain extreme values, and these in turn can have an effect on air pressure measurements. But the temperature distribution seems OK (i.e. apparently not many extremes);

In total 850k measurements have been taken into consideration. The peak is 12 *C for some reason?

Plotting pressure against temperature results in the following:

Red line is the median with 95 % interval. Looking at the dots, there do appear to be more extreme air pressure values around 20 *C, and more lower values around 5 *C. But the median seems quite stable, and only shows a bump under 0 *C. I can not explain it.

The decreasing variance in function of temperature has to do with seasonality; #50 .

Here I added 2 regression lines:

Yellow is based on mean, and blue is based on median regression. Due to outliers, the yellow line is possibly biased. The blue line is more plausible: the higher the temperature, the lower the pressure:

Coefficients:
                  Value       Std. Error  t value     Pr(>|t|)   
(Intercept)        1035.69548     0.02500 41423.62580     0.00000
TEMPERATURE_VALUE    -0.06811     0.00115   -59.40118     0.00000

2. Temperature and drift periodicity of air pressure

This is analysis_06.r. It is the same as #51, but here temperature (blue) is added. There seems to be some correlation on first sight:

But the correlation is not always in the same direction:

And even the peaks do not always match:

This last peak doesn't match with the temperature peak, as the years before. Note though, that mostly they do match (i.e. this is more-or-less a unique case).

So I don't think the temperature can explain the periodicity?

All plots are available here

[DavorJ]

Drifts 17: influence of temperature change on air pressure change

According to theory, daily effects of temperature are removed for pressure reduction to MSL calculation, as suggested here.

Here we look whether a change in temperature within 12h, has any effect on pressure.

No convincing pattern.

Quantile regression suggests a significant, but unconvincing slope: 0.00231 cmH2O/°C (i.e. 100 °C would increase (??) the pressure with 0.2 cmH2O).

The quadratic term makes more sense and is even more significant;

Call: quantreg::rq(formula = PRESSURE_VALUE_DIFF ~ TEMPERATURE_VALUE_DIFF + 
    +I(TEMPERATURE_VALUE_DIFF^2), data = df)

tau: [1] 0.5

Coefficients:
                            Value     Std. Error t value   Pr(>|t|) 
(Intercept)                   0.00000   0.00028    0.00000   1.00000
TEMPERATURE_VALUE_DIFF        0.00453   0.00031   14.78205   0.00000
I(TEMPERATURE_VALUE_DIFF^2)  -0.00107   0.00006  -17.81232   0.00000

Conclusion: change in +/- 20 °C tends to decrease the pressure by 0.5 cmH2O.

Now, as stated here, a change in 20 °C results in about 10 cmH2O pressure reduction error using the hypsometric equation. (If using the barometric formula, it amounts to 8.5 cmH2O change when using an altitude of 1200 m and increasing T_b from 15 °C to 35 °C.)

So the hypsometric/barometric formula is sensitive to temperature changes, but real pressure measured at the station is influenced by temperature changes an order of magnitude less (cf. supra). So usage of average temperature in hypsometric/barometric formula seems mainly to alleviate this undesirable effect where e.g. you could have a station at 1200 m altitude measuring constant pressure during the day and the calculated MSL pressure fluctuating with an amplitude of 10 cmH2o (in case the temperature fluctuates with 20 °C).