Understanding Time Lag

One of my favorite aspects of writing articles for this website is I am constantly learning new things about the Earth and the climate.  There are so many aspects to understand and there is always more to learn.  Being open to new information is the true nature of the scientific method.  It is also one that has broken down in the global warming debate because so few people are open to contrary findings.

The unexpected new piece of the puzzle that I stumbled across deals with the temperature of the land in different seasons.  It focuses on the United States, but the behaviors described would apply to all regions of the Earth to some degree.  Specifically it deals with how the temperature of the Earth itself varies at different depth over the course of the seasons.  It is also a perfect example of how time lags show up in the climate cycles.

The Inconvenient Skeptic

Time Lag behavior of soil at different depths.

This chart provides the average temperature of the ground at different depths over the course of a year. The surface of the Earth responds identically to the atmosphere above it.  The peak temperature takes place 46 days after the summer solstice.  This would indicate that the surface is receiving more energy than it is losing up until August 6th.  After that the surface of the Earth starts to lose energy at a faster rate than it is gaining energy.

The surface loses energy in two directions.  It loses it to the atmosphere above it and to the cooler ground beneath it.  The rate that it loses energy to the atmosphere is greater than the the ground beneath because there is only thermal conduction available to the ground beneath it.

The 2 foot (0.61 m) depth is only influenced by the temperature of the ground above it and the temperature of the ground below.  It gains energy from whichever is warming and loses to whichever is cooler.  As the surface stops warming and starts to cool, the amount of energy that the 2nd layer gets from the surface decreases.  It reaches the maximum temperature 14 days after the surface does.  At that point it is losing energy to the cooler ground beneath it at the same rate it is gaining from the still warmer ground above it.

The 5ft (1.5m) depth lags even further behind the 2ft mark and reaches the maximum temperature more than a month after the surface reached it’s maximum temperature.  Each lower layer has less of a temperature change though and as a result the 5ft mark has about half the temperature change that the surface has.  At that point it is gaining and losing energy at the same rate, but after that it will lose more than it gains so it will start cooling.

The last depth on the graph is 12 ft (3.6m).  This depth has half the temperature change that the 5ft depth does and the maximum temperature change takes place almost two months after the surface does.  It takes that long for the the soil to respond to the changes in the surface temperature.

This is also why spring temperatures are colder than fall temperatures.  In the spring the Earth is still cold from the winter and the ground is warming up as a result.  In the fall the Earth is still warm and has energy to transfer to the atmosphere.  So the same energy from the Sun results in warmer fall temperatures than spring temperatures.

Due to the lag the deeper into the Earth the less influence it has on the surface temperatures.  Deeper than 5ft the response time is more than a month.  The full depth of the surface influence is about 25 ft (7.6m), but the time lag could be longer than a year at those depths.

The Inconvenient Skeptic

The total depth of temperature change and scale by depth. The positive is caused by summer warmth and the negative is caused by winter cold. It also shows the results for different types of soil.

Here is a chart I created long ago to describe the impact of insolation on the annual temperature cycle.  See how the insolation leads the atmospheric temperature.  This atmosphere and the surface stay in equilibrium, but the depths lag the surface.  This is a clear indication that solar insolation CAUSES the other changes.

The Inconvenient Skeptic

Daily temperature data for Manhattan, Kansas for the year 2006. Compared to the normalize insolation from the sun. In the spring the temperature mostly lies beneath the energy. After the peak energy it tends to be above the energy curve due to the time lag.

It could also be noted that the way that the Earth orbits the sun is what causes the differences in the insolation at different times of the year.  So the true cause of the seasons reverts back to what you learned in school.  The tilt of the Earth causes the seasons.  Of course that might imply that the orbit is also involved in the glacial/interglacial cycle and not CO2 levels.

Posted in Climate and Science Articles - Global Warming and Science Overviews by inconvenientskeptic on March 10th, 2011 at 10:02 pm.


This post has 10 comments

  1. Richard Mar 11th 2011

    I think that one of the most important points is that the atmosphere also demonstrates similar lags.

    When I looked at this previously I noticed that the tMax air temperature at a station lagged the insolation less than the tMin did. That is, the day air temperature rose first, followed by the nightime temperatures later. This would show that the air also demonstrates similar profiles to the ground in response to the insolation curve. Have you noticed this being dealt with in the literature anywhere before?

  2. Retired Dave Mar 11th 2011

    Yes a sequence that all good meteorologists should know about.

    You obviously see the same type of lags each day as the maximum air temperature occurs 2 to 3 hours or more after the local noon. I believe that some researchers have shown such lead time effects with solar activity and mean atmospheric temperatures.

    Understanding the soil depth effects you mention is also crucial on shorter time-scales as well. On a clear, calm night the air temperature plummets at first, then steadies off to become much flatter, then falling much more slowly for the rest of the night. The discontinuity, where the falling air temperature steadies, occurs when the earth surface temperature falls below the sub-soil temperature. At that point the surface is supplied with heat by conduction from below and moderates further falls of the surface temperature, and thus the air in contact with it. Looking at the lags you mention means that this effect can only be in the top few inches of the ground.


    I wasn’t quite sure what you meant. On a clear night/day the temperature of the ground and air often continues to fall for a hour or so after the sun rises. The outgoing energy is for a while still greater than the incoming. The ground should warm first and then transfer heat to the air. As said above the lag between max insolation and max air temp is often 3 hours or so.

    Of course all of this is muddied by cloud, wind and different surfaces.

  3. inconvenientskeptic Mar 11th 2011

    I found the article on soil temperature lag while putting together my earlier time lag articles. I really liked the way that the lag was presented so I put this together.

    When this is put together with the earlier articles about lag it is clear that there is always some system lag in the Earth’s climate, but that lag is generally only a few months.

    That greatly diminishes the idea that it takes decades for the impact of CO2 to be felt.

    And clouds muddy up everything. It is just really hard to quantify the cause and effect with them.

  4. Richard Mar 11th 2011

    The procedure I did was to take the whole of a long record with both tMin and tMax and produce the ‘centre’ for each month for the 12 months of the year. I chose the tMedian for this as the data was skewed negative in the winter and positive in the summer making tMedian a better choice IMHO than tMean. If you then plot those monthly figures you will see that the tMax plot is lagged less than the tMin plot compared to the Insolation that has been supplied at that location.

    This is, of course, quite logical. The energy required to raise the temperature would have to be applied during the daytime first and then this would subsequently pull the nightime temperatures up after it.

    This long term average plot seems to show that the air follows a similar profile to the ground. Indeed I suspect that the plot in Fig 1 could be extended by adding in the air tMax and tMin curves and they would be to the right on the existing curves for the land and larger in range.

    All of them (in a ideal world) would be centered on the same figure, which is the yearly average temperature for that location.

    The great advantage of using ground temperatures is that it will naturallly integrate the insolation curve taking into account all the short term fluctuations both plus and minus. This will then hopefully tend to average out the weather including the clouds!

    I am not sure that ground temperature data is sufficiently available to make this possible over the whole globe though.

  5. inconvenientskeptic Mar 11th 2011

    There is very little difference between ground surface temps and the air right above it. The papers I have found on this topic seem to indicate that it is maybe 1C in most circumstances.

    Of course asphalt and other materials can muck that up, but despite all the roads, most of the Earth is not covered. Plants make them very, very comparable. Since most of the land mass is covered with plants, that is reasonable more most of the land.

    Oceans are different, but they pretty much ensure that the temperature difference is not significant.

  6. Richard111 Mar 11th 2011

    There is a site I used to watch with interest:


    They used to provide a fascinating continuous graph of several levels of air temperature AND levels in the ice at 100mm, 1m and so on. Watching during the SH winter period I saw quite large changes in air temperature and noted the DELAYED change in the ice, mostly out of curiosity. Now I understand the significance of the TIME LAG… and Murphy’s law strikes, they no longer show those graphs. :-(

  7. inconvenientskeptic Mar 12th 2011

    That is an interesting site though. – 57C is impressive. Seems to me that not much ice melt happens at that temperature.

    Glad the delay makes sense. I have been having another active, but old thread about the energy balance. It is the 2 of 3 about the energy balance.

    The energy going into the surface might be more important than I expected. As usual, the more I learn the more there is to learn.

  8. Retired Dave Mar 12th 2011

    Richard and John the Skeptic

    The air is bound to follow the same pattern as the ground, after all it is the ground that both warms and cools the air, mostly by conduction, but also by convection (day) and to a much lesser extent IR radiation.

    So the air close to the ground (1 inch) will pretty much be what the ground tells it to be. During insolation the temp lapse rate from ground to air temperature (measured at around 4 foot 2 inches in a Stevenson Screen) becomes steeply positive with the air in the Screen never getting as warm as the ground. After sundown the ground cools by radiation and the air in contact with it cools as well, eventually setting up a temperature inversion between the screen and the ground often leaving the air 4 to 8 degrees C warmer than the ground.

    As I said earlier the fall in ground temperature overnight (and thus the air temperature as well) by radiation is moderated by heat conducted from the sub-surface soil once the surface is colder than the soil below. It would be interesting to monitor how the heat continues to conduct downwards (as per the OP) while there are conflicting fluxes taking place near the surface.


    I am still not sure what you mean by insolation (obviously a daytime phenomena) pulling temperatures UP over night. Obviously the energy received from the Sun by day is absorbed deeper into the ground and moderates overnight falls.

    Historical note

    The Stevenson Screen was invented by a man called Thomas Stevenson – he was the father of the Scottish author Robert Louis Stevenson who wrote “Treasure Island”, “Kidnapped”, and “Dr Jekyll and Mr Hyde”. I am sure that he would be amazed and proud to find that in most of the world it is still being used 160 years later. He realised that temperatures in different places could not be compared unless they were exposed in the same way.

    The Stevenson Screen seeks to measure air temperature at a common height (although this varies slightly from country to country). The temp sensor must obviously be shielded from the Sun since it is the air temp we want, not the temperature of a thermometer hung in the Sun. The screen is louvred and for accurate air temp measurements air must pass in and out of the box – this does not always happen on calm days and the accuracy of both temperature and humidity readings by wet-bulb suffer. Modern electronic sensors exist that can be exposed in the sun with less than half a degree C inaccuracy.

  9. Richard Mar 12th 2011

    Retired Dave

    The insolation curve I as refering to is the monthly available solar radiation at a given latitude. It has maxima and minima at the solstices and ‘zero’ crossing points at the equinoxes.

    As observed here, that available energy leads the response by the ground as shown in Fig1.

    My observation was that the average (tMedian) of the daytime air temperatures (tMax) in 12 monthly slices (all Jans, Febs, etc) over a long time period also shows a smilar curve to that of Fig1.

    That in turn, leads the average of the nightime tempertures (tMin).

    My supposition is that you could add the two tMax and tMin average air temperature curves to Fig1 with them appearing to the left of the existing ground curves and with a larger range.

  10. Retired Dave Mar 12th 2011


    Thanks – now I get it.

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