ERTH 535:
Planetary Climate Change
(Spring 2018)

Solutions to
Problem #1

Dr. Dave Dempsey
Dept. of Earth & Climate Sci.,
SFSU

(5 pts total; due in class Monday., Feb. 12)

  1. [5 pts] In Lab Activity #1: Seasonal Temperature Changes, you examined a color-shaded, global plot of the difference between July and January surface temperatures for a particular year. In our discussion, we identified a number of discernible features of this plot without trying to explain them. (See the summary of discussion of Lab Activity #1, posted on the schedule of class assignments along with Lab Activity #1.)

    Then, in Lab Activity #2: The Seasons, we analyzed both satellite observations of insolation (in My World GIS) and schematic diagrams of the earth at the solstices and equinoxes to try to understand how and why the amount of solar radiation reaching the earth varies (i) with time of year at any particular place; and (ii) with latitude at any particular time of year. (See the partial summary of class discussion of Lab Activity #2: The Seasons, posted on the schedule of class assignments along with Lab Activity #2). To do this, we developed an understanding of how sun angle and length of daylight affect monthly-average insolation.

    Assuming that the monthly-average insolation at any particular place has a strong influence on monthly-average surface temperature at that place, do the following:

    1. Identify which features (of those identified in class) of the July – January surface temperature difference plot might be explained by what we learned in Lab Activity #2. (Some can't!)

      Lab Activity #2 (The Seasons) was about (1) sun angles: how they vary with latitude, time of day, and time of year, and hence (because of the connection between sun angle and insolation) how the intensity of solar radiation varies with latitude, time of day, and time of year on horizontal surfaces at the top of the atmosphere; and (2) length of daylight and how it varies with latitude and time of year, and how it, along with sun angle, affects monthly average insolation. It told us nothing about differences between land and ocean, or between western vs. eastern sides of continents and oceans, or between low and high elevations, or between ocean areas next to high latitude continents and nearby ocean areas. Hence, Lab #2 won't offer any insight into systematic differences in the July minus January temperature difference that might be associated with those particular comparisons.

      That leaves us with the following features that we can reasonably try to relate to concepts established in Lab #2:

      1. The sign of the July minus January temperature difference is positive in the Northern Hemisphere but negative in the Southern Hemisphere. (That is, in the Northern Hemisphere, July is warmer than January, while the opposite is true in the Southern Hemisphere.)

      2. July – January temperature differences are smallest in the low latitudes and largest at higher latitudes.

    2. For each of those features, explain briefly but clearly how we might account for them in terms of seasonal and latitudinal differences in length of daylight and sun angle and their (presumed) influence on monthly average insolation.

      (Note: For your purposes here, use differences in sun angle at solar noon as a surrogate for differences in sun angle at other times of day.)

      For our purposes, we'll assume that monthly average temperatures are closely related in some way to monthly average insolation. [The connection turns out not to be quite as direct as we thinkóthere's more to understanding what controls temperature than just insolationóbut the connection is strong enough to work for our purposes here.]

      1. Positive July minus January difference in insolation (and hence in temperature, by assumption) in the Northern Hemisphere and the opposite in the Southern Hemisphere.

        First, refer to the south-to-north profile plots of monthly average insolation for June and December that we saw in Lab Activity #2: "The Seasons". If the average insolation for January and July are close to those in December and June, respectively, then clearly the insolation in July is greater than it is in January in the Northern Hemisphere and the opposite is true in the Southern Hemisphere. (The two plots cross at the equator.) Hence, this aspect of the July minus January insolation difference pattern is consistent with the temperature difference pattern. Since monthly average insolation depends on both the (noon) sun angle and on the number of hours of daylight averaged over a month, we will see if the sign of the July minus January difference in sun angle and/or in length of daylight have the same pattern as insolation does. If so, we can explain the insolation pattern in terms of (noon) sun angle and/or length of daylight.

        Sun angle. In July, the noon sun angle is close to 66.5° at the equator (its minimum for the year there), increases to 90° near the Tropic of Cancer, and decreases steadily from there to close to 23.5° at the North Pole—not far from their values at the June solstice. In January, while the noon sun angle at the equator is the same as it is in July, from it decreases northward from the equator to an angle of 0° near the Arctic Circle and remains 0° the rest of the way to the North Pole. In other words, at every latitude north of the equator, the noon sun angle is greater in July than in January. Exactly the opposite is true at every latitude in the southern Hemisphere. Hence, at every latitude north of the equator in July, the (positive) difference in sun angle helps make insolation greater in July than it is in January, while the opposite is true everywhere south of the equator.

        Length of daylight. North of the equator in July, the length of daylight is everywhere more than 12 hours, while in January it is everywhere less than 12 hours. (It is exactly 12 hours at the equator.) Hence, at every latitude north of the equator, the (positive) difference in length of daylight also helps make insolation greater in July than it is in January but less in July than in January in the Southern Hemisphere.


      2. Smaller July minus January difference in insolation (and hence in temperature, by assumption) at low latitudes than at high latitudes.

        First, refer to the south-to-north profile plots of monthly average insolation for June and December that we saw in Lab Activity #2: "The Seasons". If the average insolation for January and July are close to those in December and June, respectively, then clearly the difference between the July and January insolation is zero at the equator, increases rapidly with increasing latitude away from the equator at first, then continues to increase with increasing latitude at higher latitudes, though more slowly, all the way to the poles. Hence, this aspect of the July minus January insolation difference pattern is consistent with the temperature difference pattern. Since monthly average insolation depends on both the (noon) sun angle and on the number of hours of daylight averaged over a month, we will see if the magnitude of the July minus January difference in sun angle and/or in length of daylight have the same pattern as insolation does. If so, we can explain the insolation pattern in terms of (noon) sun angle and/or length of daylight.

        Length of daylight. In July, the length of daylight in the summer hemisphere varies from 12 hours at the equator to 24 hours at the pole, while in the winter hemisphere it varies from 12 hours at the equator to 0 hours at the pole. In January the same statements apply but summer and winter hemispheres are reversed. As a result, the July minus January difference in the length of daylight varies systematically from 0 hours at the equator ±24 hours at the poles, consistent with the pattern of increasing July minus January insolation difference with increasing latitude.

        Sun angle.
        At the equator, the noon sun angle is close to 66.5° in both July and January, so the July minus January difference in sun angle is zero there. At the Tropic of Cancer and Tropic of Capricorn, the sun angle varies from close to 90° at the summer solstice to 90° − 23.5° − 23.5° = 43° at the winter solstice, a range of 47°, and between July and January the range is nearly as great. However, from the two Tropics all the way to the Arctic and Antarctic Circles, the July minus January sun angle difference is the same: close to 47°, and from the Arctic and Antarctic Circles to the poles, the July minus January sun angle difference decreases systematically from almost 47° to almost 23.5°. We conclude initially that outside the tropics, the pattern of variation in July minus January sun angle difference with increasing latitude is not consistent with the observed pattern of increasing July minus January insolation difference from low latitudes to high latitudes and hence don't appear to help explain it. Length of daylight would appear to be the dominant factor outside the tropics.

        (The real answer isn't that simple, though, because insolation depends nonlinearly on sun angle—it's a sine functional dependence (that is, the insolation is proportional to the sine of the sun angle, not to the sun angle). As a result, the effect on insolation of a given difference in sun angle is much greater at low sun angles than it is at high sun angles. Hence, seasonal variations in noon sun angle at low latitudes, where noon sun angles are high, have a much smaller impact on insolation than the same variations in noon sun angle do at high latitudes, where noon sun angles are low. Hence, the impact of July minus January differences in sun angle does continue to increase with increasing latitude all the way to the Arctic and Antarctic Circle, if not farther, even though the July minus January difference in sun angle itself doesn't vary between the tropics and the Arctic and Antarctic Circle and even decreases beyond that to the poles.)

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