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I examine how well drainage area serves as a proxy for discharge in the stream power incision model in the semi-arid climate of central Texas, where precipitation is characterized by infrequent, high intensity, localized storms. The stream power incision model takes the form ε = KAmSn, where: ε is incision rate; K is a dimensional coefficient of erosion; A is drainage area which serves as a proxy for discharge, Q; S is local stream gradient; and m and n are dimensionless exponents. I calculate fluvial incision rates with the model using drainage area, mean peak annual discharge, and 1.0-, 1.5-, and 4.0-year-recurrence-interval floods, which bracket bankfull discharges at fourteen gauging stations in eight detachment-limited, bedrock streams underlain by marls and limestones. I utilize 30m resolution USGS DEM analysis and USGS gauging station data for the W. Nueces, Nueces, Dry Frio, Frio, Sabinal, and Medina Rivers and Seco and Hondo Creeks. The range of values used for the erosional coefficient, K, and exponents, m and n, in the model are published values of K for similar lithologies (mudstones, sandstones) and based on the relationship (m/n) is ∼0.5, with m and n values usually ranging between 0.3-0.5 and 0.6-1.0 respectively.

I compare incision rates calculated using the stream power incision model with every possible combination of drainage area, discharge, local channel slope, K, m, and n to each other and to incision rates I calculate from fluvial terraces in six streams in the field (Nueces, Frio, Sabinal, and Medina Rivers; Seco and Hondo Creeks) with DGPS surveys and published terrace ages. I determine maximum incision of each stream as the difference between the modern stream longitudinal profile and the highest terrace surface and divide that difference by the age range of the terraces to obtain ranges of incision rates from terraces. The ranges of incision rates calculated with the stream power incision model using mean peak annual discharge and 1.5- and 4.0-year-recurrence-interval bankfull discharges fall within the range of incision rates obtained from field and published terrace age data (2.3x10-6 m/yr – 4.3x10-3 m/yr). Incision rates calculated using drainage area closely approximate incision rates calculated using mean peak annual and 4.0-year-recurrence-interval bankfull discharges. I conclude that: (1) the generalized stream power incision model appears to predict incision rates well; (2) drainage area serves as an appropriate proxy for discharge in the stream power incision model where historical discharge data are unavailable; (3) the use of a dominant discharge, though it cannot represent the variability in discharge through time, appears to be a reasonable working assumption; and (4) mean peak annual and 4.0-year-recurrence-interval bankfull discharge values appear to represent the dominant discharge in central Texas streams well. Presumably these conclusions are true for other semi-arid regions on passive margins underlain by similar rock types and subject to similar flooding behavior.


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This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.