METR 104:
Our Dynamic Weather
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:

Materials Needed. To complete this activity, you will need:

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:

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:

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.

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