The map above is a surface temperature map. The boundaries between different colored regions represent isotherms, or curves of constant temperature. There is an isotherm for every 5-degree increment of temperature, and the temperatures of some of the isotherms are indicated in the picture. If we let T(x,y) denote the temperature function of this portion of the surface of North America, then the isotherms are the level curves of T.

The yellow arrows in the picture represent temperature gradients, or gradient vectors of T. Each vector represents a gradient of T, evaluated at the same place where the initial point of the vector is located. Remember that a gradient vector of T at a particular point

  1. is normal to the level curve through that point

  2. points in the direction of the maximum rate of increase of T

  3. has a length (magnitude) which is equal to the rate of increase in that direction.

With these points in mind, can you visualize what the temperature gradient should look like at the northern edge of Lake Superior (the yellow dot by the question mark)? You should be able to decide on an approximate direction for the gradient, as well as an approximate length, in relation to the other two vectors. When you think you've got it, look here.

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