ERTH 535: Planetary Climate Change (Spring 2018) Lab Activity #4 (For classes starting Friday, Feb. 23) Dr. Dave Dempsey Dept. of Earth & Climate Sci., SFSU

## Introduction to the Earth's Heat Budget

Objectives:

• Formulate several simple conceptual models of the earth's heat budget.
• Use satellite observations of radiative energy fluxes to test the validity of these models quantitatively.
• Analyze satellite-based radiative flux data sets in several different ways to help raise questions about features, patterns, and differences in the spatial and temporal distributions of these fluxes.
• Begin to pose possible answers to these questions.
• Apply the Stefan-Boltzmann relation to compare emission fluxes of longwave IR radiation at the earth's surface and the top of the atmosphere.

Introduction. In this lab activity you will explore some aspects of the earth's heat budget. Some of the questions below ask you to do or think about things that might not yet have been covered in lecture or the readings. Don't worry about being right or wrong, but pay close attention to why you are right or wrong, and include the insights you gain from this process in your answers.

### Part 1: A Simple Model of Absorbed Solar Energy at the Earth's Surface

(1) Before opening any of the data sets in My World GIS, draw a simple box-and-arrow diagram of the earth's energy system (a qualitative budget) as discussed in class. Include the following components:

 Boxes: Amount of sensible and latent heat energy in the earth's atmosphere & surface (combined in one box) Arrows: Incoming solar radiation, reflected solar radiation, and outgoing (longwave) radiation

(2) We can also construct a budget for solar radiation only (so it doesn't include heat, latent heat, or terrestrial radiation—that is, radiation emitted by the earth). Translate the parts of your box-and-arrow diagram above that deal only with solar radiation into a simple mathematical equation:

Solar Energy Absorbed by the Planet = __________ +/– __________
(where you have to decide if the operator above is "+" or "–").

(3) Both the diagram in (1) and the equation you wrote in (2) are models of the real world, abstract simplifications that, ideally, represent some or all of the essential components of a planet's heat budget.

You can test your budget model using satellite observations in several My World GIS data sets. To this end, using My World GIS, access a plot of absorbed solar radiation, the left-hand side of your budget model in item (2) above, for March 1987, and a plot of the right-hand side of your budget model in (2) above for the same month and year. (See instructions [for Part 1, Item (3)] in the Supplement to Lab Activity #4: My World GIS Instructions.)

(4) Compare the two plots, both by visual inspection and by checking actual values at various locations. Do the satellite observations confirm your model budget equation—that is, are satellite observations consistent with it? (If not, can you identify your error and correct it?)

### Part 2: Spatial Variations in the Earth's Energy Budget

You should have been able to convince yourself that satellite observations largely support a version of the equation in (2) that states that absorbed solar radiation = incoming solar radiation minus reflected solar radiation. An even stronger test of this relation would be to add reflected and absorbed solar radiation together and subtract the results from incoming solar radiation—you should get values close to zero for all cells. (See the My World GIS plot called "Incoming Solar Minus Sum of Absorbed and Reflected Solar March 1987". What is the result?)

Both the qualitative and quantitative forms of your models are useful in their own ways, but both are too general to illuminate a critical aspect of all of earth science: the amounts of solar radiation received, reflected, and absorbed all vary from place to place. In this part of the lab activity, we will consider the data sets more carefully and explore spatial variation within them using both maps and cross-sectional (profile) plots. (Note that we've already done this to a significant degree with incoming solar radiation in the context of understanding the cause of the seasons.)

(5) You have seen incoming solar radiation plots before (in Lab Activity #2: The Seasons). What type of quantity in particular did those plots show (flux, rate, something else)? What were the units of those data?

(6) You should still have the My World GIS "PlanetaryEnergyBudget" project still loaded. (If not, run My World GIS and load it.) In the "Layer List" sub-window, in the "MonAvg_RadiativeBudgetTerms.wwf" panel, click on the "eye" icon in the upper-right corner of the panel. Though the panel is still highlighted, it should now be closed, and the plot in the main window should now show incoming solar radiation for March 1987.

Click on (highlight) the "MonAvg_IncomingSolar.wwf" panel. Pull down the "Layer" menu on the top menu bar and select "Show Data Documentation". How were these data collected?

(7) The intensity of solar radiation on a surface directly facing the sun at the top of the earth's atmosphere depends mainly on the distance from the sun (though also on the output of the sun, which can vary a little bit over time). Why, then, does incoming solar radiation on this plot vary so much with latitude? How can you tell from this plot that monthly-average incoming solar radiation doesn't vary with longitude? (Why not?)

(8) Below is a link to a graph showing plots of three south-to-north insolation profiles (that is, a cross-section from pole to pole along the prime meridian, or 0° longitude, though the plots are identical along other longitudes):

Compare the graphs. We commented on features of similar graphs in Lab Activity #2—see if you can explain any of those features and differences between plots based on what you've learned in the course so far.

### Part 3: Space-Bound Longwave Infrared Radiation

If the earth system as a whole were not to gain or lose energy (and thereby warm or cool), the amount of energy leaving the earth system as longwave infrared radiation must balance the amount of energy that the earth system absorbs.

(9) For the earth as a whole to have a balanced heat budget, which of the following do you think should equal the emission rate (or emission flux) of outgoing (space-bound) longwave IR radiation?

1. the rate (or flux) of incoming solar radiation (i.e., solar radiation arriving at the top of the earth's atmosphere);
2. the rate (or flux) at which reflected solar radiation leaves the earth;
3. the rate (or flux) at which the earth absorbs solar radiation; or
4. some combination of these three.

(10) Now, use satellite observations to test your answer. To do this:

1. For each of the three months of January, March, and July, 1987, find out the global-mean, area-weighted space-bound energy (where "space-bound energy" is the flux of longwave infrared radiation emitted to space by, or "outgoing" from, the earth). (See instructions for Part 3, Item (10)] in the Supplement to Lab Activity #4: My World GIS Instructions.)
2. Do the same for the quantity or quantities that you chose in (9). (See instructions for Part 3, Item (10)] in the Supplement to Lab Activity #4: My World GIS Instructions.)

3. For each month individually, compare the global-mean area-weighted values that you looked up in Steps 1 and 2 above.

Were you correct, or was your answer way off (say, more than 25 Watts/m2 different)? (If you were way off, you probably chose the wrong quantity in (9)!)

(11) Even if you chose the correct quantity, you'll notice that the global mean values are not exactly the same. For each month, did the earth gain more energy than it lost or lose more than it gained? If this difference was real, what do you think it implies about global temperatures during that month?

Now consult the background information about absorbed solar radiation (click on [highlight] the "MonAvg_AbsorbedSolar.wwf" panel in the "Layer List" sub-window, pull down the "Layer" menu on the top menu bar, and select "Show Data Documentation"). Can you be confident that your conclusion about the global temperature trend in March, 1987 was correct? (On what do you base your answer?)

### Part 4: Variations with Latitude of Outgoing Longwave IR Radiation and Absorbed Solar Radiation

(12) Close all of the monthly average radiative energy data panels in the "Layer List" sub-window except "Zonal Average Spacebound Energy 1987", which you should open.

The fields accessible through this panel are zonal averages of monthly average spacebound energy flux fields, where a "zone" is a band of latitudes in a ring around the globe, in this case 2.5° latitude wide (the span of a single cell in the north-south direction). Plots of zonal-average fields should show no east-west variations (because they've been averaged out), though north-south variations remain.

Below is a link to a graph showing three south-to-north profile plots of :

Compare the three profiles. What dominant features do you see on each plot? Can you suggest possible explanations for any of them, based on what you've learned in class so far? What differences between the three profile plots do you see? Can you account for the differences?

(13) Hide the "ZonalAverage_OutgoingLWRadiation" panel (click on the "eye" icon in the panel). Click on (highlight) the "ZonalAverage Absorbed Solar" panel and open it if necessary. As in (12), these absorbed solar data are zonally-averaged.

Below is a link to a graph showing three south-to-north profile plots of:

What dominant features do you see on these plots? Can you suggest possible explanations for any of these features?

Compare the January absorbed solar radiation profile plot with the January outgoing longwave radiation profile plot. Does outgoing longwave radiation approximately balance absorbed solar radiation at each latitude? (That is, are differences between them less than, say, 25 W/m2?) Repeat for March and for July.

If radiative absorption and emission were the only mechanisms by which particular latitude zones could gain and lose energy, what would any imbalances that you see at any particular time imply about what might be happening to the temperature at those locations at that time?

(14) Hide the "ZonalAverage_AbsorbedSolar" panel and open the "ZonalAverag_ OutgoingLWRadiation" panel. Pull down the menu in this panel and select "Annual, Zonal Average Outgoing LW Radiation 1987". This plot shows annual- and zonal-averaged outgoing longwave IR radiation fluxes for 1987—that is, zonal-average outgoing longwave infrared radiation flux data sets averaged across all 12 months of a year.

You can then hide the "ZonalAverage_OutgoingLWRadiation" panel and open the "ZonalAverage_AbsorbedSolar" panel. Pull down the menu in this panel and select "Annual, Zonal Average Absorbed Solar 1987". This plot shows annual-average, zonal-average absorbed solar radiation fluxes for 1987—that is, zonal-average absorbed solar radiation flux data sets averaged across all 12 months of a year.

Below is a link to a graph showing two north-south profile plots of:

What are the dominant features of each plot? Can you suggest possible explanations for them?

Compare the annual-average, zonal-average outgoing longwave radiation profile plot with the corresponding one for absorbed solar radiation. Do the two balance at each latitude? If not, and if the graphs for this particular year are representative of other years, and if radiative absorption and emission are the only mechanisms by which latitude zones on the earth can gain and lose energy, what implication would any imbalances have for temperature at those latitudes over time? Do we in fact observe the behavior that you deduce?

### Part 5: Outgoing Longwave IR Radiation from Top of the Earth's Atmosphere vs. from the Earth's Surface

(15) Look up the area-weighted global, annual average of the spacebound energy (outgoing longwave IR radiation) fluxes and enter it into the table below. (See instructions [for Part 5, Item (15)] in the Supplement to Lab Activity #4: My World GIS Instructions.) We want to compare this value to the area-weighted, global, annual average radiative emission flux from the earth's surface. My World GIS doesn't have the latter data set, but it does have surface temperature data, which we can use to estimate the radiative emission flux from the surface using the Stefan-Boltzmann Law and assuming that the earth's surface behaves like a blackbody (not a bad assumption in the longwave infrared part of the spectrum).

It would be tempting to compute a global, annual-average surface temperature and use that value in the Stefan-Boltzmann Law. Unfortunately, this could be misleading (that is, wrong!). The global, annual-average radiative emission flux does not necessarily equal the flux calculated using a global, annual-average temperature. (Can you explain why not? As a hint, try averaging two different temperatures and calculating the emission flux of an object at that average temperature, and then compute two emission fluxes from the first two temperatures and average the fluxes. Are they different? If so, why?)

Instead, we have to calculate the radiative emission flux in each cell for each month and average all of them together over 12 months to get the annual average and area-weighting them to get the global average. This calculation can be tedious, but fortunately I've done it for you!

### Emission Flux & Effective Radiating Temperature: Earth's Surface vs. Whole Planet

(My World GIS data & Stefan-Boltzmann Law)
Month
(1987)
Area-weighted
Global Average
Spacebound
Emission Flux
(Eplanet)

(W/m^2)
Area-weighted
Global Average
Surface
Emission Flux
(Esfc)

(W/m^2)
Effective
Temperature
of the Planet
(Te)planet

(K)
Effective
Temperature
of the Planet's
Surface
(Te)sfc

(K)
Area-weighted
Global Average
Observed
Temperature
of the Surface
(Tsfc)

(K)
Jan 233.66 386.64 253.4 287.4 285.9
Feb   387.98   287.6 286.1
Mar 233.09 390.28 253.2 288.0 286.6
Apr   395.26   289.0 287.6
May   400.17   289.8 288.7
Jun   400.17 255.9 289.8 289.5
Jul 243.22 406.21   290.9 289.9
Aug   405.03   290.7 289.6
Sep   400.99   290.0 288.8
Oct   394.63   288.8 287.6
Nov   390.42   288.1 286.8
Dec   388.52   287.7 286.4
Annual Avg   395.5 W/m^2     287.8 K

How does the global, annual-average radiative emission flux from the earth's surface compare to the global, annual-average emission flux out the top of the earth's atmosphere to space? If the difference seems significant, what must be happening to account for it?

(16) There is an alternative approach that shows the same discrepancy between the earth as a whole (based on longwave radiation leaving the top of the earth's atmosphere) and the earth's surface. We can calculate a kind of "effective" global, annual-average temperature of the planet from the Stefan-Boltzmann Law using the global, annual-average radiative emission flux out the top of the earth's atmosphere. What "effective" global, annual-average temperature do you get from that calculation? (Enter it in the table above.)

Similarly, we can calculate an "effective" global, annual average temperature of the earth's surface from the Stefan-Boltzmann Law using the global, annual-average radiative emission flux from the surface (entered in the table above). Determine what that temperature is and enter it in the table above.

Finally, we can use My World GIS to calculate an area-weighted global, annual-average surface temperature for 1987, which is entered in the table above. How does this value, and the "effective" global-average temperature of the earth's surface, compare to the "effective" global-average temperature of the planet? Is the difference consistent with your result in (15)? Explain.

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