Function Of Drainage Area Research Articles

River self-organisation inhibits discharge control on waterfall migration

The action of rivers within valleys is fundamentally important in controlling landscape morphology, and how it responds to tectonic or climate change. The response of landscapes to external forcing usually results in sequential changes to river long profiles and the upstream migration of waterfalls. Currently, models of this response assume a relationship between waterfall retreat rate and drainage area at the location of the waterfall. Using an experimental study, we show that this assumption has limited application. Due to a self-regulatory response of channel geometry to higher discharge through increasing channel width, the bed shear stress at the lip of the experimental waterfall remains almost constant, so there was no observed change in the upstream retreat rate despite an order of magnitude increase in discharge. Crucially, however, the strength of the bedrock material exhibits a clear control on the magnitude of the mean retreat rate, highlighting the importance of lithology in setting the rate at which landscapes respond to external forcing. As a result existing numerical models of landscape evolution that simulate the retreat of waterfalls as a function of drainage area with a fixed erodibility constant should be re-evaluated to consider spatial heterogeneity in erodibility and channel self-organisation.

Variation in hydraulic geometry for stable versus incised streams in the Yazoo River basin – USA

The effects of basin hydrology on hydraulic geometry of channels variability for incised streams were investigated using available field data sets and models of watershed hydrology and channel hydraulics for the Yazoo River basin, USA. The study presents the hydraulic geometry relations of bankfull discharge, channel width, mean depth, cross-sectional area, longitudinal slope, unit stream power, and mean velocity at bankfull discharge as a function of drainage area using simple linear regression. The hydraulic geometry relations were developed for 61 streams, 20 of them are classified as channel evolution model (CEM) Types IV and V and 41 of them are CEM streams Types II and III. These relationships are invaluable to hydraulic and water resources engineers, hydrologists, and geomorphologists involved in stream restoration and protection. These relations can be used to assist in field identification of bankfull stage and stream dimension in un-gauged watersheds as well as estimation of the comparative stability of a stream channel. A set of hydraulic geometry relations are presented in this study, these empirical relations describe physical correlations for stable and incised channels. Cross-sectional area, which combines the effects of channel width and mean channel depth, was found to be highly responsive to changes in drainage area and bankfull discharge. Analyses of cross-sectional area, channel width, mean channel depth, and mean velocity in conjunction with changes in drainage area and bankfull discharge indicated that the channel width is much more responsive to changes in both drainage area and bankfull discharge than are mean channel depth or mean velocity.

Development and Evaluation of Bankfull Hydraulic Geometry Relationships for the Physiographic Regions of the United States

AbstractBankfull hydraulic geometry relationships are used to estimate channel dimensions for streamflow simulation models, which require channel geometry data as input parameters. Often, one nationwide curve is used across the entire United States (U.S.) (e.g., in Soil and Water Assessment Tool), even though studies have shown that the use of regional curves can improve the reliability of predictions considerably. In this study, regional regression equations predicting bankfull width, depth, and cross‐sectional area as a function of drainage area are developed for the Physiographic Divisions and Provinces of the U.S. and compared to a nationwide equation. Results show that the regional curves at division level are more reliable than the nationwide curve. Reliability of the curves depends largely on the number of observations per region and how well the sample represents the population. Regional regression equations at province level yield even better results than the division‐level models, but because of small sample sizes, the development of meaningful regression models is not possible in some provinces. Results also show that drainage area is a less reliable predictor of bankfull channel dimensions than bankfull discharge. It is likely that the regional curves can be improved using multiple regression models to incorporate additional explanatory variables.

Effects of hillslope dynamics and network geometry on the scaling properties of the hydrologic response

This paper investigates the specific contributions of river network geomorphology, hillslope flow dynamics and channel routing to the scaling behavior of the hydrologic response as function of drainage area. Scaling relationships emerged from the observations of geomorphological and hydrological data and were reproduced in previous works through mathematical models, for both idealized self-similar networks and natural basins. Recent literature highlighted that scale invariance of hydrological quantities depends not only on the metrics of the drainage catchment but also on effective flow routing. In this study we employ a geomorphological width function scheme to test the simple scaling hypothesis adopting more realistic dynamic conditions than in previous approaches, specifically taking into account the role of hillslopes. The analysis is based on the derivation of the characteristic distributions of path lengths and travel times, inferred from DEM processing and measurements of rainfall and runoff data. The study area is located in the Tiber River region (central Italy). Results indicate that, while scaling properties clearly emerge when the hydrologic response is defined on the basis of the sole geomorphology, scale invariance is broken when less idealized flow dynamics are taken into account. Lack of scaling appears in particular as a consequence of the catchment to catchment variability of hillslope velocities.

Improved Bankfull Channel Geometry Prediction Using Two-Year Return-Period Discharge1

He, Laien and Gregory V. Wilkerson, 2011. Improved Bankfull Channel Geometry Prediction Using Two-Year Return-Period Discharge. Journal of the American Water Resources Association (JAWRA) 47(6):1298–1316. DOI: 10.1111/j.1752-1688.2011.00567.x Abstract: Bankfull discharge (Qbf) and bankfull channel geometry (i.e., width, Wbf; mean depth, Dbf; and cross-section area, Abf) are important design parameters in stream restoration, habitat creation, mined land reclamation, and related projects. The selection of values for these parameters is facilitated by regional curves (regression models in which Qbf, Wbf, Dbf, and Abf are predicted as a function of drainage area, Ada). This paper explores the potential for the two-year return-period discharge (Q2) to improve predictions of Wbf, Dbf, and Abf. Improved predictions are expected because Q2 estimates integrate the effects of basin drainage area, climate, and geology. For conducting this study, 29 datasets (each representing one hydrologic region) spanning 14 states in the United States were analyzed. We assessed the utility of using Q2 by comparing statistical measures of regression model performance (e.g., coefficient of determination and Akaike’s information criterion). Compared to using Ada, Q2 is shown to be a “clearly superior” predictor of Wbf, Dbf, and Abf, respectively, for 21, 13, and 25% of the datasets. By contrast, Ada yielded a clearly superior model for predicting Wbf, Dbf, and Abf, respectively, for 0, 0, and 14% of the datasets. Our conclusion is that it alongside with developing conventional regional curves using Ada it is prudent to develop regional curves that use Q2 as an independent variable because in some cases the resulting model will be superior.

Analyses of extreme flooding in Austria over the period 1951–2006

AbstractAnalyses of extreme flooding in Austria is performed using daily discharge time series from 27 stations over the period 1951‐2006. The main research questions revolve around: (1) temporal non‐stationarities in the flood record, (2) upper tail and scaling properties of the flood peak records, and (3) relation between magnitude and frequency of flooding and the North Atlantic Oscillation (NAO). Two datasets are derived from the daily discharge time series: annual maximum daily discharge and peaks‐over‐threshold (POT) data. The validity of the stationarity assumption in the annual maximum discharge record is assessed by investigating the presence of abrupt and slowly varying changes using nonparametric tests. The time series are tested for abrupt changes both in the mean and variance of the flood peak distributions by means of the Pettitt test. The presence of monotonic trends is investigated by means of the Mann‐Kendall and Spearman tests. Violations of the stationarity assumption are associated with abrupt rather than gradual changes. These step changes generally involve river regulation through construction of dams or other major engineering works. It is not possible to make conclusive statements about the presence of an anthropogenic climate change signal in the flood peak record. Similar conclusions are obtained when focussing on the frequency of POT floods. The Generalised Extreme Value distribution is used to study the upper tail and scaling properties of annual maximum daily discharge records. The location and scale parameters exhibit power‐law behaviour as a function of drainage area. The shape parameters indicate that the flood peak distributions for Austria have a heavy tail. Non‐stationary modelling of the annual maximum daily discharge and POT time series is used to explore the relation between flood magnitude and frequency and NAO. The results indicate that NAO is a significant covariate in explaining the magnitude and frequency of occurrence of flooding over a large part of Austria. Copyright © 2011 Royal Meteorological Society

Developing channel and floodplain dimensions with limited data: a case study in the Amazon Basin

ABSTRACTThis research builds on the concept of hydraulic geometry and presents a methodology for estimating bankfull discharge and the hydraulic geometry coefficients and exponents for a station using limited data; only stage‐discharge and Landsat imagery. The approach is implemented using 82 streamflow gauging locations in the Amazon Basin. Using the estimated values for the hydraulic geometry relations, bankfull discharge, discharge data above bankfull and upstream drainage area at each site, relationships for estimating channel and floodplain characteristics as a function of drainage area are developed. Specifically, this research provides relationships for estimating bankfull discharge, bankfull depth, bankfull width, and floodplain width as a function of upstream drainage area in the Amazon Basin intended for providing reasonable cross‐section estimates for large scale hydraulic routing models. The derived relationships are also combined with a high resolution drainage network to develop relationships for estimating cumulative upstream channel lengths and surface areas as a function of the specified minimum channel width ranging from 2 m to 1 km (i.e. threshold drainage areas ranging from 1 to 431,000 km2). At the finest resolution (i.e. all channels greater than 2 m or a threshold area of 1 km2), the Amazon Basin contains approximately 4.4 million kilometers of channels with a combined surface area of 59,700 km2. The intended use of these relationships is for partitioning total floodable area (channels versus lakes and floodplain lakes) obtained from remote sensing for biogeochemical applications (e.g. quantifying CO2 evasion in the Amazon Basin). Copyright © 2011 John Wiley & Sons, Ltd.

Analyses of seasonal and annual maximum daily discharge records for central Europe

Summary Annual and seasonal maximum daily discharge time series for 55 stations in central Europe (Germany, Switzerland, Czech Republic, and Slovakia) are used to examine flood frequency from a regional perspective. In this study we examine temporal nonstationarities in the flood peak records, and characterize upper tail and scaling properties of the flood peak distributions. There is a marked seasonality in the flood peak record, with a large fraction of annual maximum flood peaks occurring during the winter in the western part of the study domain, and during the summer in the southern portion of this region. The presence of abrupt and slowly varying changes in the flood time series is examined by means of non-parametric tests. Change-points in the mean and variance of the flood peak distributions are examined using the Pettitt test, while the presence of monotonic patterns is examined by means of Spearman and Mann-Kendall tests. Abrupt changes, rather than monotonic trends are responsible for violations of the stationarity assumption. These step changes can often be associated with anthropogenic effects, such as construction of dams and reservoirs and river training. Given the profound changes that these catchments have undergone, it is difficult to detect a possible climate change signal in the flood peak record. The estimates of the location, scale, and shape parameters of the Generalized Extreme Value distribution are used to examine the upper tail and scaling properties of the flood peak distributions. The location and scale parameters exhibit a power law behaviour when plotted as a function of drainage area, while the shape parameter decreases log-linearly for increasing catchment area. The findings of this study suggest that these records exhibit a heavy tail behaviour.

Downstream variation in bankfull width of wadeable streams across the conterminous United States

Bankfull channel width is a fundamental measure of stream size and a key parameter of interest for many applications in hydrology, fluvial geomorphology, and stream ecology. We developed downstream hydraulic geometry relationships for bankfull channel width w as a function of drainage area A, w = α A β, (DHG wA) for nine aggregate ecoregions comprising the conterminous United States using 1588 sites from the U.S. Environmental Protection Agency's National Wadeable Streams Assessment (WSA), including 1152 sites from a randomized probability survey sample. Sampled stream reaches ranged from 1 to 75 m in bankfull width and 1 to 10,000 km 2 in drainage area. The DHG wA exponent β, which expresses the rate at which bankfull stream width scales with drainage area, fell into three distinct clusters ranging from 0.22 to 0.38. Width increases more rapidly with basin area in the humid Eastern Highlands (encompassing the Northern and Southern Appalachians and the Ozark Mountains) and the Upper Midwest (Great Lakes region) than for the West (both mountainous and xeric areas), the southeastern Coastal Plain, and the Northern Plains (the Dakotas and Montana). Stream width increases least rapidly with basin area in the Temperate Plains (cornbelt) and Southern Plains (Great Prairies) in the heartland. The coefficient of determination ( r 2) was least in the noncoastal plains (0.36–0.41) and greatest in the Appalachians and Upper Midwest (0.68–0.77). DHG wA equations differed between streams with dominantly fine bed material (silt/sand) and those with dominantly coarse bed material (gravel/cobble/boulder) in six of the nine analysis regions. Where DHG wA equations varied by sediment size, fine-bedded streams were consistently narrower than coarse-bedded streams. Within the Western Mountains ecoregion, where there were sufficient sites to develop DHG wA relationships at a finer spatial scale, α and β ranged from 1.23 to 3.79 and 0.23 to 0.40, respectively, with r 2 > 0.50 for 10 of 13 subregions (range: 0.36 to 0.92). Enhanced DHG equations incorporating additional data for three landscape variables that can be derived from GIS—mean annual precipitation, elevation, and mean reach slope—significantly improved equation fit and predictive value in several regions, most notably the Western Mountains and the Temperate Plains. Channel width was also related to human disturbance. We examined the influence of human disturbance on channel width using several indices of local and basinwide disturbance. Contrary to our expectations, the data suggest that the dominant response of channel width to human disturbance in the United States is a reduction in bankfull width in streams with greater disturbance, particularly in the Western Mountains (where population density, road density, agricultural land use, and local riparian disturbance were all negatively related to channel width) and in the Appalachians and New England (where urban and agricultural land cover and riparian disturbance were all negatively associated with channel width).

Regional channel geometry equations: a statistical comparison for physiographic provinces in the eastern US

AbstractRegional stream channel equations are created to solve for a specified discharge or channel dimensions as a function of drainage area. In recent years, regional equations have been developed by the US Geological Survey (USGS) and US Fish and Wildlife Service (USFW), as well as various state agencies for use in the preliminary design of stable channels. The regional equations are created using measured stable channel dimensions. Physiographic provinces have been used as boundaries for the development of these equations due to the perceived roles of climate, geology and physiography in shaping channels. Data collection within each physiographic province has typically been confined to a study area which encompasses parts of one or more states, but not the whole physiographic province. Thus, the use of the equations is restricted to the physiographic province(s) and the state(s) for which they have been developed. The purpose of this study was to determine whether the regional equations are statistically different within a single physiographic province and different between physiographic provinces. The results of the statistical analyses of the regional equations and their associated data showed that the majority of the equations are similar within their respective physiographic provinces. Testing between provinces showed that the Appalachian Plateau, New England and Valley and Ridge provinces have statistically similar equations. Based on the evidence presented in this study, separating regional equations by physiographic regional boundaries is valid. New equations for those data that showed statistical similarity were developed. Copyright © 2008 John Wiley & Sons, Ltd.

Relative size of fluvial and glaciated valleys in central Idaho

Quantitative comparisons of the morphometry of glaciated and fluvial valleys in central Idaho were used to investigate the differences in valley relief and width in otherwise similar geologic and geomorphic settings. The local relief, width, and cross-sectional area of valleys were measured using GIS software to extract information from USGS digital elevation models. Hillslope gradients were also measured using GIS software. Power-law relationships for local valley relief, width, and cross-sectional area as a function of drainage area were developed. Local valley relief in glaciated valleys relates to drainage area with a power-law exponent similar to fluvial valleys, but glaciated valleys are deeper for a given drainage area. Local valley width in glaciated valleys is greater than in fluvial valleys, but the exponent of the power-law relationship to drainage area is similar in both valley types. Local valley cross-sectional area in glaciated valleys increases with drainage area with a power-law exponent similar to fluvial valleys, however, glacial valleys have roughly 80% greater cross-sectional area. Steep valley walls in glaciated basins increase the potential for bedrock landsliding relative to fluvial basins. Both the Olympic Mountains of Washington and valleys in central Idaho show relationships in which glaciated valleys are up to 30% deeper than fluvial valleys despite differences in lithology, tectonic setting, and climate.

Cenozoic river profile development in the Upper Lachlan catchment (SE Australia) as a test of quantitative fluvial incision models

We have used early Miocene valley‐filling basalts to reconstruct fluvial long profiles in the Upper Lachlan catchment, SE Australia, in order to use these as well‐constrained initial conditions in a forward model of fluvial incision. Many different fluvial incision algorithms have been proposed, and it is not clear at present which one of these best captures the behavior of bedrock rivers. We test five different formulations; the ability of these models to reproduce the observed present‐day stream profiles and amounts of incision is assessed using a weighted‐mean misfit criterion as well as the structure of the misfit function. The results show that for all models, parameter combinations can be found that reproduce the amounts of incision reasonably well. However, for some models, these best fit parameter combinations do not seem to have a physical significance, whereas for some others, best fit parameter combinations are such that the models tend to mimic the behavior of other models. Overall, best fit model predictions are obtained for a detachment‐limited stream power model or an “undercapacity” model that includes a river width term that varies as a function of drainage area. The uncertainty in initial conditions does not have a strong impact on model outcomes. The model results suggest, however, that lithological variation may be responsible for variations in parameter values of a factor of 3–5.

Geomorphic and Forest Cover Controls on Monsoon Flooding, Central Nepal Himalaya

Devastating monsoon season floods in the central Nepal Himalaya have been difficult to predict with any precision, reliability, or accuracy. Deforestation is often blamed as the principal cause of flooding. This paper uses field data at 22 stream crossings, together with drainage basin morphometric data and forest cover data, to determine the dominant controls on bank-full discharge from monsoon storms. Results demonstrate that 82 percent of the variation in bank-full discharge can be explained as a function of drainage area alone; forest cover did not add explanatory power. Findings from this study can be used to guide planning for future projects that will be affected by flood hazards in the central Nepal Himalaya, including irrigation, hydropower, and footbridge construction.

Spatial Trends in Pearson Type III Statistical Parameters

Spatial trends in the statistical parameters (mean, standard deviation, and skewness coefficient) of a Pearson Type III distribution of the logarithms of annual flood peaks for small rural basins (less than 90 km 2 ) are delineated using a climate factor, C T ( T = 2-, 25-, and 100-yr recurrence intervals) which quantifies the effects of long-term climatic data (rainfall and pan evaporation) on observed T -yr floods. The statistical parameters are computed from gridded estimates of the geographically varying climate factors and regression models relating at-site T -yr floods as a function of drainage area, climate factor, hydrograph shape, and infiltration. Spatial portrayals, covering a large part of the United States east of the 105th meridian, are presented for averaged statistical parameters and their variability obtained using data from a sample of 200 small basins scattered over 12 states. Maps showing trends in average parameter values demonstrate the geographically varying influence of climate on ...

Test of Hack's slope to bed material relationship in the Southern Eifel Uplands, Germany

AbstractThe local reach gradient of small gravel bed rivers (drainage area 0‐8‐110 km2) in the Eifel, West Germany, is adjusted to transport the river bed sediments. Transport of gravel becomes possible under high flow conditions (Shields entrainment factor ≈‐03).Mean bed material size for riffle sections increases with distance downstream. For small drainage areas channel slope is a negative exponential function of drainage area, while for the larger region the additional influence of bedload size has to be considered.Good agreement with Hack's data (1957) for Virginia and Maryland, U.S.A., is achieved (S = 0.0066 (D50/A)‐ 40., r = 0.67).

100 Frequency Curves of North American Rivers

Frequency curves of maximum annual flood flows on important rivers in North America are given; frequency curves are drawn as straight lines; it was found that inclination of lines is function of drainage area, climate and soil conditions.