We turn now to a final consideration of some geomorphic properties that apply to the entire study area. A map showing relief relative to terranes was made from digitized data in the DEM 1:250,000 sheet for the Klamath Mountains:

Maximum relief occurs in the central Yolla Bolly terrane. This is also the area (in purple) of highest maximum elevations (3850 ft; 1185 m). Both this height and the ease of downcutting into the shales account for this relief. The lowest areas inland are shown in orange-red. These are valleys, one containing Grants Pass, the largest town in the Klamaths, that are surfaced by Quaternary deposits; the Grant Pass valley is underlain in part by a granitic rock which weathers into a thick "rotten rock" (saprolite) soil and is easily removed to leave a lowlands.

At this point, with some trepidation, we interpose the concept of hypsometery; this is a rather complicated idea and is treated here in a general way because, when applied to the Klamath terranes, some interesting results ensued (but their significance remains unclear).

Hypsometry refers to the distribution of elevations as a function of area occupied by each contour interval within some geographic unit (such as a topographic sheet). This determines the fraction of a surface bounded by specified elevations. These diagrams (from Process Geomorphology, by D.F. Ritter) depict the concept:

The calculation unit is defined as a volume bounded by base and summit planes, of a given area A, and the total height (H) from base to highest elevation. As one moves from the lowest elevation (base) upwards on the map progressively through increasing values of h, all areas within each contour interval are measured. With each successive increase in h, the area increases by some new value of a. This progression is cumulative. When plotted on an x-y diagram, the relative values of h/H and a/A form the hypsometric curve (center right). Note that x and y values are dimensionless, representing proportions of the total area and height; thus for y = 0, all heights are above the datum plane and thus lie within the total area, i.e., x = 1. The area lying below the curve can be calculated as the hypsometric interval (HI). As applied to a drainage basin, HI represents the unconsumed volume as a percentage delimited by base plane, summit plane, and perimeter area.

Various factors influence the shape of the hypsometric curve and its position in the x-y plot - hence its HI value. Direct interpretation of a family of curves, and their possible interrelationships, is not straightforward but some generalizations are warranted. Overall, the HI broadly denotes the degree of uplands dissection. Look at the bottom diagram above. Its top curve can typify a relatively high terrain (keep in mind that the geomorphic unit - the drainage basin - actually consists of both valleys and intervening divides and all slopes between) which may be in the early stages of downward erosion and slope wall development. The lower curve is characteristic of the late stage of erosion marked by broad, low valleys, with occasional higher promontories ("monadnocks"). Of course, various combinations of surfaces can lead to similar curves in proximate positions.

Again, using digitized topographic data, hypsometric curves were produced for individual Klamath terranes and, for several, segments thereof. Hand plots of these are shown in the top diagram; plots for the three aforementioned Yolla Bolly segments are on the bottom.

We do not ask you to grasp in detail the relations among these curves (it is hard to identify some of the terrane symbols), as we ourselves have not derived specific interpretations having obvious meaning. Suffice to comment that the one on top associates with the sliver of Briggs Creek terrane which is one of the highest; the Jj (Smith River) and Jdb (Dry Butte) terranes also have high elevations and rugged topography. But, the Yolla Bolly terrane as a whole (KJd in the top diagram) occupies a lower position in the set of plots. From the bottom diagram, it is evident that there is moderate variation within this terrane itself, although less than the range among all terranes in the top diagram. The three map units - none are actual terranes - with the lowest curves (and thus smallest HI's) are the lowlands associated with the Quaternary coastal plains and inland areas and the granite lowlands.

When the values of HI (in fractions of 1.00) are plotted on the terranes map, some pattern emerges.

The highest values cluster in the central terranes. This suggests that these are also topographic units that have not been significantly downcut towards sea level. Those towards the coast, with lower elevation levels, even though younger (docked later), may have been eroded more completely, although more likely with their stream heights and gradients being closer to sea level, the amount of relief is expected to be less. But, we stop here without further explanation, as the hypsometric data, while tantallizing, are not equivocally interpretable.

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