METR 104: Our Dynamic Weather (w/Lab) Lab Exploration #2: Solar Radiation & Temperature Part IV: A Simple Computer Model Dr. Dave Dempsey Dept. of Geosciences SFSU, Spring 2012

(5 points)
(Lab Section 1: Wed., March 7; Lab Section 2: Fri., March 9)

Learning Objectives. After completing this activity, you should be able to:

• Configure and run experiments with a simple computer model (a STELLA model) that predicts temperature at the earth's surface over a period of several days, driven by absorption of solar radiation and affected by cloud cover (but little or nothing else).
• Evaluate the model based on experience reading meteogram plots of observed temperature patterns and cloud cover over several days at individual locations.
• Begin to describe the role that computer models play in the way that science works in atmospheric science.
Materials Needed. To complete this activity, you will need:
• A computer in TH 604 or 607 with:
• A graph of sun angle (in degrees) vs. time (in hours) over several days at the latitude of Hanford, CA (36.3°N) starting on May 22 (Julian day 142)
• A meteogram showing a typical daily temperature cycle under cloud-free conditions at Hanford, CA (KHJO):

I. Introduction. As noted in Lab #2, Parts II and III, forecasting temperature is one of the most common and useful aspects of weather forecasting. Modern professional weather forecasters typically do it by starting with current and recent observations of weather conditions and applying their understanding of the underlying physical causes of temperature change, in a largely quantitative way, to estimate near-future changes in temperature from current conditions.

One of the most important tools that forecasters and atmospheric scientists use is the computer model. One type of computer weather forecast and research models are based on the known physical relationships between meteorological quantities (temperature, pressure, wind speed, wind direction, humidity, etc.) and external factors that can affect them (solar radiation, topography, land vs. water surface, etc.). These relationships can be expressed mathematically and solved quantitatively using a computer, providing a forecast or scenario of the future state of the atmosphere, given a starting state.

In this lab you'll configure a very simple computer model, run experiments with it, and evaluate it based on your experience reading surface weather observations displayed on meteograms.

II. A Simple Computer Model of Temperature Driven by Solar Heating

Our intuition is that the sun plays a central (though not necessarily the only) role in causing daily temperature variations, as we began to explore in Parts I, II, and III of Lab #2. We've discovered in those previous labs that the intensity of solar radiation depends strongly on the angle of the sun above the horizon (sun angle), which varies with time of day and time of year at any particular location. Cloud cover also affects insolation at the earth's surface.

To test the extent to which the sun (affected by variations in sun angle and cloud cover) controls the earth's surface temperature, we can build a simple computer model based on a well-established, empirical physical law called the Law of Conservation of Energy. (An empirical relationship is based on many and repeated observations of the way the physical world behaves in many, many situations. Empirical relationships stand in contrast to theoretical relationships, which are derived from physical principles or [usually] well informed assumptions about the way the world works that might or might not [yet] be empirically well established.)

One version of the Law of Conservation of Energy describes how objects gain or lose heat and how the temperature of the object responds as a result. It can be written very generally like this:

 The rate at which an object's temperature changes ∝  (is proportional to) The rate at which the heat content of the object changes = Sum of the rates at which the object gains heat by various mechanisms − Sum of the rates at which the object loses heat by various mechanisms

We could apply this relationship to the earth's surface. If we suppose that the surface gains heat by absorbing solar radiation only, then the Law of Conservation of Energy applied to the earth's surface would be written as:

 The rate at which the earth's surface temperature changes ∝  (is proportional to) The rate at which the heat content of a layer of the earth's surface changes = The rate at which the surface absorbs solar radiation

Using this relationship (along with a little more information than is shown here, to convert the proportionality into an "="), if we specify the rate at which the surface absorbs solar radiation, then we can calculate how fast the surface temperature changes. From that, we can estimate what the temperatures will be in the near future (if they are driven only by absorption of solar radiation).

We can run this simple model, compare the results to observed daily temperature cycles, and see how well the model performs. That is, we can evaluate the model's performance. If the model does well, it could be useful for helping us understand better how the atmosphere works and perhaps even for making temperature forecasts. (Further experience and evaluation of the model would be necessary to be sure.) If the model doesn't do well, we have to question any assumptions that underlie the physical relationship as we've applied it above or perhaps take into account physical processes that are important but that we neglected in the relationship.

III. Instructions. Respond in writing to questions posed in sections D and E below, and print a hard copy of the plot that you create in section D. Label the plots clearly with the circumstances of the model run (in particular, the latitude, time of year, cloud cover, nature of the earth's surface). Turn in your written responses and annotated plots at the end of the lab session.

1. Access "Daily Temperature Cycle I", a computer model of the daily temperature cycle written using STELLA modeling software.

• If you are using one of the Mac computers in TH 604 or 607:

1. Locate a file called "DailyTempCycle.I.STM" on the Desktop.
2. Double-click on the DailyTempCycle.I.STM file. This should start STELLA, open the file, and present you with the model interface.

• Or, almost (but not quite) as good, if you are using a Web browser and have an internet connection:

• Your instructor will describe the model features and explain how to configure it, run it, and access and read the model output graphs.

2. Note the default model configuration.

1. In this version of the daily temperature cycle model, you can specify:

• Latitude (in degrees)
• Day of the year (Julian day, expressed as a number from 1 to 365)
• "Surface Type" (land or water)
• "Cloud Cover" (expressed as a percentage of the sky covered by clouds)

By default, the latitude is set to 36°N (the approximate latitude of Hanford, CA); the day of the year is set at 142 (May 22); the surface type is set to "land"; and the cloud cover is set to 0%.

For this lab activity, start out with these default settings (that is, don't change anything yet). Don't run the model yet, either.

3. Make your own prediction of the daily temperature pattern, given how the sun angle varies.

1. You have been provided with a plot of sun angle (in degrees) vs. time (in hours) for several days starting on May 22 at the latitude of Hanford, CA. On this plot, identify nighttime vs. daytime periods and the times of sunrise, sunset, and (solar) noon.

Based on the sun angle, sketch the pattern of temperature that you would expect to see. [The actual temperatures aren't important here, just the pattern of temperature—that is, the time(s) when the temperature is lowest and highest and what it does in between—relative to the sun angle pattern.]

4. Run the model and compare your prediction to the model simulation.

1. Run the model (using the default settings). You should see the same plot of sun angle as in Step C.1 above appear on the first graph (which is Page 1 of three pages of graphs).

2. View the second graph (Page 2). [Click on the lower left-hand corner of the graph, which looks as if the corner has been bent forward slightly.] This graph plots (1) the sun angle (in degrees, the blue line) and (2) temperature (in °F, the red line) simulated by the model.

3. Describe any apparent connections or associations that you can see between temperature (as calculated by the model) and sun angle.

[For example, how does each behave at night? During daylight hours? When is temperature changing and not changing, relative to what the sun angle is or is not doing?]

[You can refine your sense of this as follows: (a) place the cursor on the graph; (b) click and hold the click, so that a vertical line appears on the graph through the location of the cursor; and (c) drag the cursor back and forth, which drags the vertical line with it. Beneath the "Hours" label along the horizontal axis you'll see the time (in hours) corresponding to the cursor's position, and beneath the "Sun Angle deg" and "Temperature F" labels along the top of the graph you'll see the values of these quantities at that hour.]

4. In what ways is the model simulation of temperature similar to what you sketched in Step C.1 above? In what ways is it different?

5. View the third graph (Page 3). It shows (1) the rate at which the surface absorbs solar energy (in Watts, the blue line), and (2) the temperature (in °F, the red line).

In what ways does the model simulation seem reasonable and in what ways does it not? [You should consider surface temperature observations that you've seen plotted on meteograms (for example, on the meteograms accompanying this lab from Hanford, CA, which we first saw in Lab #2, Part II), and your own personal experience with the daily temperature cycle.]

6. Do you have any suggestions about what might be done to improve the model? [By this we don't mean how to improve the graphs, which merely show the model output—we mean the physical processes that are represented in the model and that determine the temperatures that it calculates.]

7. Print a copy of the third graph (Page 3) only.
1. First, pull down STELLA's "File" menu and select "Page Setup", and next to "Orientation", select the landscape mode [the right-hand icon.].
2. Then click on the printer icon in the lower left-hand corner of the graph. You'll get a "Print" dialog box.
3. In the "Print" dialog box, make sure that the printer specified is "coriolis". [If coriolis isn't working, use "downpour".]
4. If the arrow next to the printer name points down, click on it to expand the dialog box.
5. In the expanded dialog box, locate "Pages", click on the "From" button and specify from page 3 to page 3. (That is, you're going to print just one page.)
6. Retrieve your plot from the printer and put your name on it. (You'll turn in this plot along with your responses to the questions in the next two sections, below.)

5. Run the model to see if adding cloud cover or changing the nature of the earth's surface improves the simulation.

1. Specify a cloud cover exceeding 50%. Before you run the model, predict what you expect the temperature pattern to look like. How does your prediction differ from the first model simulation (without clouds) in Step D above. Why?

2. Run the model, and view the plots on Page 3 of the graphs. Compare these plots to those from the simulation in Step D above (where there was no cloud cover). In what way(s) are the simulations different?

[You can address several aspects of the temperature simulations: (a) the temperature values themselves; (b) the daily temperature range from minimum to maximum; and (c) the pattern of temperature, particularly the timing of lows and highs each day and what happens in between.]

Is the model simulation with cloud cover any better—that is, do it's main features resemble the main features of observed daily temperature cycles more closely (such as the one for Hanford, CA ending at 09Z on May 22, 1999)?

3. Specify (a) no cloud cover, but (b) change the surface type from land to ocean.

4. Predict what you expect the temperature pattern to look like. How does your prediction differ from the simulation in Step D above, and why?

5. Run the model, and compare this model simulation to the simulation in Step D above. In what way(s) are the results different?

[Again, you can consider (a) the temperature values themselves; (b) the daily temperature range from minimum to maximum; and (c) the pattern of temperature, particularly the timing of lows and highs each day and what happens in between.]

Is the model simulation any better?

6. If you want, try increasing the cloud cover over the ocean surface to see if that helps. Good luck!

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