Downwelling Infra-Red Radiation and Temperature: Part 2

In Part 1 I showed that:

  • Downwelling infra-red radiation (so called “back radiation”) is real and measurable including at night.
  • It is greatly increased by cloud and humidity,
  • It results from daytime heating of the ground, which then loses heat by conduction, convection, evaporation, and radiation, into the atmosphere where the IR is repeatedly absorbed and re-emitted in all directions by greenhouse gases (including water vapour).
  • A warmer atmosphere from whatever cause, natural or enhanced, will result in greater downwelling IR.

In this post I will look at the relationship between downwelling IR and temperatures at five Australian locations during 2018 (the last year for which complete irradiance data is available.)  Those locations are Alice Springs, Darwin, Rockhampton, Melbourne, and Cape Grim, and are shown on this map.

Fig.1:  Australian stations with solar exposure data

Cape Grim, set on a clifftop above the Southern Ocean, is most exposed to marine influences.  Melbourne, Rockhampton, and Darwin are surrounded by land but are subject to marine influence at times when the wind blows from the ocean.  Alice Springs has a desert climate and the ocean is thousands of kilometres away.  Most examples in this post will come from the Alice.

The Relationship Between Maxima and Minima:

Consider this plot of temperature at Walgett (NSW):

Fig. 2:  Latest weather graph for Walgett 27 – 31 January 2018

During a fine clear day the sun heats the ground which by conduction and convection raises the near-surface air temperature.  The hot ground emits upwelling IR, some of which greenhouse gases in the atmosphere absorb and re-emit in all directions, including towards the earth.  This is downwelling IR (DWIR), which adds to the solar radiation during the day, and slows the loss of heat at night.  The air temperature, and DWIR, peaks usually in the mid to late afternoon.  As the ground cools slowly throughout the evening and night hours, IR continues to be exchanged upwards and downwards, with enough being lost to space for ground and air temperatures to cool to the minimum.  This is usually reached, in fine clear conditions, sometime after sunrise.  And that is usually the time when DWIR also reaches minimum values.

Before I look at the relationship between DWIR and minima, let’s look at plots of maxima and minima.

Fig, 3:  Maxima and Minima at Alice Springs during 2018:

Note that usually (but not always!) peaks in maxima are matched by peaks in minima.  Here’s a closer look at the period from 6 May to 20 July, with minima scaled up by 19 degrees:

Fig. 4:  Maxima and Scaled Minima, 6 May – 20 July 2018

Note that maxima highs and lows precede those of minima by one day NEARLY ALWAYS.  (Sometimes they occur together, and sometimes maxima precedes minima by two days.)  The minimum temperature reflects the previous day’s maximum.  Why?  Due to DWIR, the ground cools slowly.  A hot day generates lots of DWIR, which keeps the ground (and air temperature) warmer next morning.  A cool day means less DWIR available next morning.  However, clouds lower maxima by reflecting sunlight but increase DWIR to keep nights and minima warmer, as we shall see later. The pattern seen above is also seen at Cape Grim, Melbourne, and Rockhampton, but not in Darwin where it is not so clear at all.

The Relationship Between Downwelling IR and Minima:

I used solar irradiance data to find daily (to 9.00 a.m.) minimum DWIR values for 2018 at Alice Springs, Darwin, Rockhampton, Melbourne, and Cape Grim, for comparison with daily temperature minima. 

Fig. 5:  Daily minima for 2018 at all stations

Fig. 6:  Daily minimum DWIR for 2018 at all stations

At all sites, as daily minimum IR increases, daily minimum temperature increases.  However, the strength of the relationship varies.  I calculated derivatives of Tmin and IR to find the daily change in values.  The relationship is strongest at Alice Springs, with a correlation of 0.69, Figure 5:

Fig. 7:  Change in temperature as a function of change in DWIR at Alice Springs.

Melbourne has almost exactly the same correlation (0.68), followed by Cape Grim (0.64) and Rockhampton at 0.61.  However Darwin is much different:

Fig. 8:  Change in temperature as a function of change in DWIR at Darwin.

The reason for this is not as complex as I thought, but first I’ll show a method of showing (and testing) the relationship between DWIR and Tmin more easily.

Converting DWIR to Representative Atmospheric Temperature

From the Bureau’s solar radiation glossary, http://reg.bom.gov.au/climate/austmaps/solar-radiation-glossary.shtml#globalexposure :

Downward infra-red irradianceis related to a `representative (or effective radiative) temperature’ of the Earth’s atmosphere by the Stefan-Boltzmann Law:

E = σ T4

Where: E = irradiance measured [W/m2]
σ = Stefan-Boltzmann constant [5.67 x 10-8 W/m2/K4
T = representative atmospheric temperature [K]

From this we can calculate the daily Representative Atmospheric Temperature (RAT) above each weather station.  Here is a plot of RAT for Alice Springs.

Fig. 9: Representative Atmospheric Temperature and Minima at Alice Springs

RAT is always colder than the surface.  Notice how closely Tmin tracks with RAT. 

To compare them more closely, I scaled up RAT by adding the average monthly difference from Tmin.  Now you can see how closely minimum temperature is related to RAT and thus DWIR.

Fig. 10:  Scaled Representative Atmospheric Temperature and Minima at Alice Springs

Zooming in to the period from 31 March to 4 June:

Fig. 11 :  Scaled RAT and Minima at Alice Springs, 31 March – 4 June 2018

The timing of variations is very close.

Here is a plot of the actual daily difference between minimum surface temperature and Representative Atmospheric Temperature.  I have marked some unusually low and high values for closer inspection..

Fig. 12:  Daily difference between Surface Minima and RATat Alice Springs

What causes these fluctuations?  Returning to actual temperature and calculated RAT, here is the plot for the year to 15 April:

Fig. 13:  RAT and Minima at Alice Springs, 1 January – 15 April 2018

Both Tmin and RAT usually move in unison, rising and falling together.  However, notice at point A there is very little difference between the values, but at point B there is a very large difference.

Here’s the plot for November and December.  A and B have very small differences, while C and D have very large differences.

Fig. 14:  RAT and Minima at Alice Springs, 6 November – 31 December 2018

Cloudy conditions increase downwelling IR.  With no daily cloud data, rainfall will be a proxy for some cloudy days.  (There will be plenty of cloudy days when there is no rain.)  Here is a plot of rainfall and the difference between surface minima and calculated RAT.

Fig. 15:  Rainy weather and Tmin minus RAT at Alice Springs

Rainfall appears to coincide with very low differences when RAT (derived from DWIR) has increased but corresponding Tmin has not increased as much as expected.  Let’s zoom in to look at Points A and B from Figure 13 above.

Fig. 16:  Rainy weather and Tmin minus RAT at Alice Springs, January – April

In fact rain coincides with nearly all of the low differences.  Point B remains anomalously high.  What about November and December?

Fig. 17:  Rainy weather and Tmin minus RAT at Alice Springs, November – December

Here we have a problem.  Points A and B from Figure 14 above line up with rain events.  Instead of being a low difference as expected, point C has a high value coinciding with a small rain event, and D is on its own.  Why?

When RAT is scaled up, the problem (and likely reason) is obvious:

Fig. 18  Scaled RAT and Minima at Alice Springs, December 2018

No IR data is recorded for 11 December.  I suspect that IR values should also be missing for 12 and 13 December.  Moving remaining data for the month two days later removes these strange inconsistencies (and also dramatically improves correlation between IR change and temperature change to above 0.7.)

Which still leaves the odd spike in Figure 13 at point B.

The Exception Proves The Rule

Here is a count of the number of days with no IR data at Alice Springs in 2018.

Fig.19:  Count of days with no data at Alice Springs

There are a few minutes of missing data on nearly every day, but data was completely absent for eight whole days in March, and three days in December.  Did the pyrgeometer stop recording suddenly?  Was it a sudden fault or was it failing gradually?  Figure 20 shows the 31 day centred running correlation between change in DWIR and change in Tmin, with missing days shown.

Fig. 20:  Centred 31 day running correlation between change in DWIR and change in Minima

If all is well, and the relationship between change in DWIR and temperature minima is sound, the correlation between them should be fairly constant.  However, if the pyrgeometer reads incorrectly (or else the temperature probe- another possibility, but not in this case), correlation will suffer.  This is shown in March and December.  From April to September, change in Tmin correlates well with change in DWIR being between 0.8 and 0.9 for nearly the whole time.

Now let’s look at Darwin, which we saw in Figure 8 above was poorly correlated.   The running correlation shows when faults may have occurred.

Fig. 21:  Centred 31 day running correlation between change in DWIR and change in Minima

The dips above coincide with equipment failure in January, March, November and December.  There also appears to be a problem in August – September.

It does not help that the equipment failures occur in rainy, cloudy periods (Wet and Build-up).

Fig. 22:  Rainy weather and Tmin minus RAT at Darwin

In the Dry, with no rain, the difference between Tmin and the RAT (Representative Atmospheric Temperature) still fluctuates wildly.  Here is a plot of the difference for June 2018:

Fig. 23:  Daily difference between Surface Minima and RATat Darwin June 2018

If the relationship is valid, and there are no recording problems, then large differences occur during fine and cloudless conditions and low values indicate cloudy conditions.  The daily total of Global Solar Exposure can also be a metric of cloudiness, because smaller amounts of sunlight reach the ground on cloudy days.   Figure 24 is a plot of the sum total of Global Irradiance in kiloWattminutes per square metre received each day.

Fig. 24: Daily total of Global Irradiance Darwin, June 2018

Apart from 10 – 12 June, the relationship holds.  Darwin’s apparent poor relationship between DWIR and Minima is very probably due to equipment failure.

The apparent exceptions to the “rule” that large differences between minima and Representative Atmospheric Temperature occur in dry, cloud free conditions, and small differences in cloudy conditions, in fact confirm it. 

Conclusion:

  • Downwelling infra-red radiation (so called “back radiation”) is real and measurable including at night.
  • It is greatly increased by cloud and humidity.
  • It results from daytime heating of the ground, which then loses heat by conduction, convection, evaporation, and radiation, into the atmosphere where the IR is repeatedly absorbed and re-emitted in all directions by greenhouse gases (including water vapour).
  • A warmer atmosphere from whatever cause, natural or enhanced, will result in greater downwelling IR.
  • Temperature Maxima highs and lows precede those of minima by one day NEARLY ALWAYS, due to the influence of downwelling IR.
  • Calculating Representative Atmospheric Temperature from downwelling IR using the  Stefan-Boltzman Law provides further insights.
  • The daily minimum RAT is always much colder than minimum temperature.
  • The difference between the two changes with the weather.  Sunny, dry, cloudless weather is associated with large differences, while cloudy weather is associated with small differences.
  • When recording error is accounted for there is very good correlation between downwelling infra-red irradiance and daily minimum temperatures at a range of sites across Australia.
  • In Australia, meteorological equipment can deteriorate for some time and fail completely, resulting in faulty data being included in national databases.
  • Finally, the effect of DWIR on minima is not site dependent.  Both Melbourne and Rockhampton have Urban Heat Island influence but the relationship is similar to that of other sites.  Minima are directly related to DWIR, but DWIR is increased not only by clouds, but also by large trees, nearby buildings, and areas of concrete and bitumen.

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4 Responses to “Downwelling Infra-Red Radiation and Temperature: Part 2”

  1. Geoff Sherrington Says:

    Ken,
    You would have looked at the day on which each 9am minimum was assigned, day before or day after?
    Your work ties in with quite a lot of data from several weeks I spent looking at lagged temperatures, those on day(n) subtracted from day(n+1). Then I looked at correlations of these lagged T differences between sites that are close together, less than 300 km or so. There would be a lot of work to combine the data and see what shakes out.
    Geoff

  2. siliggy Says:

    What an excellent pair of posts Ken. Great work. Worth reading and re-reading multiple times. All useful and very interesting stuff too. So very impressed with how well you have your head around this. Oh and, Fig 7 and 8 are great mate. “Y = Mx + B” and variance. That’s the way to do it! How much of that variance relates to wind speed i wonder?

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