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23 EPHEMERAL STREAMS lOOO lOO " w w - . ;; o lO " > ~ o 33. ". I 50. 44- -36 45- I .59 1 .57 '52 " .1 I 4 10 11 12 8 STREAM ORDER FIGURE 19.-Relation of stream width to stream order in arro)'os. Number beside point is serial number in appendix:. A second approach to the discharge-order relation makes use of flood-frequency analysis. On streams of small and moderate size in central ~ew Mexico there are only a few gaging stations that have a relatively long period of record. Despite the paucity of data, flood-frequency curves for all gaging stations considcred applicable to the area being studied were obtained from an unpublished study by H. H. Hudson. Also, the records of some additional stations were analyzed by the authors. In eastern streams the bankfull stage is attaincd about once a year, A conservative quantity little affected by the length of record is the average of the highest flood each year of record. This is called the mean annual flood. It has a recurrence interval of 2,3 years, and thus we assume roughly approximates the discharge at bankiull stage, The relation between 2.3-year flood discharge and drainage area for gaging stations in central New Mexico is presented on figure 2l. It is known by hydrologists that the discharge of a flood of a given frequency increases somewhat less rapidly than drainage basin size. It is typical for the relation of flood discharge to drainage area to plot as a 10,000 lOOO Derived Irom wid1h ~5 stfeam 0 order,elatiI)(lJ,nd z wiatl1vsQrelationl 0 ~ . ~ . ~ u 100 " Deli~ed from Q \1 ~ dramlgenea U relationsllId . drlinsgeareavs "' Wllmo/de. ~ ,elations ~ < . ~ 15 lO 1 I I 2 4 6 7 8 lO 11 12 STREAM ORDER FlGURIi: 2O.-Relation of discharge to stream order derived b)' two separate types of anah'Ses. straight line on logarithmic paper, expressed by the equation Q ex: A: \vhe.re k is a constant \vhich for the mean annual flood has a value of between 0.7 and 0.8. The slope of line on figure 21 is consistent with values known from other areas. In drainage basins of the same size, those studied in the West produce floods of about one-fifth the magnitude of the typical one in the East. By combining the discharge-area graph with the order-area graph, discharge call be related to order, The drainage area corresponding to each stream order is read from figure 16, and the value of discharge for an equal drainage area is determined from figure 2l. The resulting plot is shown as the clashed line in figure 20. Thus, the relation between stream order and dis- charge, which is the link between the Horton analysis and hydraulic geometry, has been derived for a central New l",fexico a.rea in two ways which are at least some- what independent, Comparison between the results is indicated by the two lines in figure 20. Only the slopes