On the expected width function for topologically random channel networks
No abstract available.
Journal of Applied Probability↗
Geology topics
Michael R. Karlinger
Publications and source records attributed to Michael R. Karlinger.
Fat fractal scaling of drainage networks from a random spatial network model
An alternative quantification of the scaling properties of river channel networks is explored using a spatial network model. Whereas scaling descriptions of drainage networks previously have been presented using a fractal analysis primarily of the channel lengths, we illustrate the scaling of the surface area of the channels defining the network pattern with an exponent which is independent of the fractal dimension but not of the fractal nature of the network. The methodology presented is a fat fractal analysis in which the drainage basin minus the channel area is considered the fat fractal. Random channel networks within a fixed basin area are generated on grids of different scales. The sample channel networks generated by the model have a common outlet of fixed width and a rule of upstream channel narrowing specified by a diameter branching exponent using hydraulic and geomorphologic principles. Scaling exponents are computed for each sample network on a given grid size and are regressed against network magnitude. Results indicate that the size of the exponents are related to magnitude of the networks and generally decrease as network magnitude increases. Cases showing differences in scaling exponents with like magnitudes suggest a direction of future work regarding other topologic basin characteristics as potential explanatory variables.
Water Resources Research↗
A random spatial network model based on elementary postulates
A model for generating random spatial networks that is based on elementary postulates comparable to those of the random topology model is proposed. In contrast to the random topology model, this model ascribes a unique spatial specification to generated drainage networks, a distinguishing property of some network growth models. The simplicity of the postulates creates an opportunity for potential analytic investigations of the probabilistic structure of the drainage networks, while the spatial specification enables analyses of spatially dependent network properties. In the random topology model all drainage networks, conditioned on magnitude (number of first-order streams), are equally likely, whereas in this model all spanning trees of a grid, conditioned on area and drainage density, are equally likely. As a result, link lengths in the generated networks are not independent, as usually assumed in the random topology model. For a preliminary model evaluation, scale-dependent network characteristics, such as geometric diameter and link length properties, and topologic characteristics, such as bifurcation ratio, are computed for sets of drainage networks generated on square and rectangular grids. Statistics of the bifurcation and length ratios fall within the range of values reported for natural drainage networks, but geometric diameters tend to be relatively longer than those for natural networks.
Water Resources Research↗
Soil CO 2 Flux in the Amargosa Desert, Nevada, during El Nino 1998 and La Nina 1999
Mean annual soil CO2 fluxes from normally bare mineral soil in the Amargosa Desert in southern Nevada, United States, measured with clear and opaque soil CO2-flux chambers (autochambers) were small - <5 millimoles per square meter per day - during both El Nino 1998 and La Nina 1999. The 1998 opaque-chamber flux exceeded 1999 opaque-chamber flux by an order of magnitude, whereas the 1998 clear-chamber flux exceeded 1999 clear-chamber flux by less than a factor of two. These data suggest that above-normal soil moisture stimulated increased metabolic activity, but that much of the extra CO2 produced was recaptured by plants. Fluxes from warm moist soil were the largest sustained fluxes measured, and their hourly pattern is consistent with enhanced soil metabolic activity at some depth in the soil and photosynthetic uptake of a substantial portion of the CO2 released. Flux from cool moist soil was smaller than flux from warm moist soil. Flux from hot dry soil was intermediate between warm-moist and cool-moist fluxes, and clear-chamber flux was more than double the opaque-chamber flux, apparently due to a chamber artifact stemming from a thermally controlled CO2 reservoir near the soil surface. There was no demonstrable metabolic contribution to the very small flux from cool dry soil, which was dominated by diffusive up-flux of CO2 from the water table and temperature-controlled CO2-reservoir up- and down-fluxes. These flux patterns suggest that transfer of CO2 across the land surface is a complex process that is difficult to accurately measure.
Scientific Investigations Report↗
Unit hydrograph approximations assuming linear flow through topologically random channel networks
The instantaneous unit Hydrograph (IUH) of a drainage basin is derived in terms of fundamental basin characteristics ( Z , α, β), where α parameterizes the link (channel segment) length distribution, and β is a vector of hydraulic parameters, Z is one of three basin topological properties, N , ( N , D ), or ( N , M ), where N is magnitude (number of first-order streams), D is diameter (mainstream length), and M is order. The IUH is derived based on assumptions that the links are independent and identically distributed random variables and that the network is a member of a topologically random population. Linear routing schemes, including translation, diffusion, and general linear routing are used, and constant drainage density is assumed. By using ( N , α, β) as the fundamental basin characteristics, asymptotic (for large N ) considerations lead to a Weibull probability density function for the IUH, with time to peak given by t p = (2 N ) ½ α * /β * where α * is mean link length, and β * is a scalar hydraulic parameter (usually average celerity). This asymptotic IUH is identical for all linear routing schemes.
Water Resources Research↗
Regional flood probabilities
The T ‐year annual maximum flood at a site is defined to be that streamflow, that has probability 1/ T of being exceeded in any given year, and for a group of sites the corresponding regional flood probability (RFP) is the probability that at least one site will experience a T ‐year flood in any given year. The RFP depends on the number of sites of interest and on the spatial correlation of flows among the sites. We present a Monte Carlo method for obtaining the RFP and demonstrate that spatial correlation estimates used in this method may be obtained with rank transformed data and therefore that knowledge of the at‐site peak flow distribution is not necessary. We examine the extent to which the estimates depend on specification of a parametric form for the spatial correlation function, which is known to be nonstationary for peak flows. It is shown in a simulation study that use of a stationary correlation function to compute RFPs yields satisfactory estimates for certain nonstationary processes. Application of asymptotic extreme value theory is examined, and a methodology for separating channel network and rainfall effects on RFPs is suggested. A case study is presented using peak flow data from the state of Washington. For 193 sites in the Puget Sound region it is estimated that a 100‐year flood will occur on the average every 4.5 years.
Water Resources Research↗
A note on subtrees rooted along the primary path of a binary tree
Let F n denote the set of rooted binary plane trees with n external nodes, for given T ∈ F n let u i ( T ) be the altitude i node along the primary path of T , and let δ i ( T ) denote the number of external nodes in the induced subtree rooted at u i ( T ). We set δ i ( T ) = 0 if i is greater than the length of the primary path of T . We prove lim n →∞ ∑ i ≤ x / n E n { δ i }/∑ i <∞ E n { δ i } = G ( x ), where E n denotes the average over trees T ∈ F n and where the distribution function G is determined by its moments, for which we present an explicit expression.
Discrete Applied Mathematics↗
Regression estimates for topological‐hydrograph input
Physiographic, hydrologic, and rainfall data from 18 small drainage basins in semiarid, central Wyoming were used to calibrate topological, unit‐hydrograph models for celerity, the average rate of travel of a flood wave through the basin. The data set consisted of basin characteristics and hydrologic data for the 18 basins and rainfall data for 68 storms. Calibrated values of celerity and peak discharges subsequently were regressed as a function of the basin characteristics and excess rainfall volume. Predicted values obtained in this way can be used as input for estimating hydrographs in ungaged basins. The regression models included ordinary least‐squares and seemingly unrelated regression. This latter regression model jointly estimated the celerity and peak discharge. The correlation between residuals of the celerity and peak‐discharge regressions was sufficiently large to de‐, crease the variances of estimated univariate‐model parameters.
Journal of Water Resources Planning and Management↗
Daily water and sediment discharges from selected rivers of the eastern United States; a time-series modeling approach
Time-series models were constructed for analysis of daily runoff and sediment discharge data from selected rivers of the Eastern United States. Logarithmic transformation and first-order differencing of the data sets were necessary to produce second-order, stationary time series and remove seasonal trends. Cyclic models accounted for less than 42 percent of the variance in the water series and 31 percent in the sediment series. Analysis of the apparent oscillations of given frequencies occurring in the data indicates that frequently occurring storms can account for as much as 50 percent of the variation in sediment discharge. Components of the frequency analysis indicate that a linear representation is reasonable for the water-sediment system. Models that incorporate lagged water discharge as input prove superior to univariate techniques in modeling and prediction of sediment discharges. The random component of the models includes errors in measurement and model hypothesis and indicates no serial correlation. An index of sediment production within or between drain-gage basins can be calculated from model parameters.
Water Supply Paper↗
Risk preferences and flood insurance
A detailed theoretical model characterizing the individual's decision to purchase flood insurance is specified and the magnitude of the risk parameter is estimated using data based on transactions of flood insurance purchases. Empirical results for several samples of this subset of the general population indicated that consumers exhibited a relatively uniform degree of risk aversion across various localities where different hydrologic and economic conditions prevailed. While the estimates presented should not be directly extrapolated to the entire population located in a flood prone area, they provide evidence that parameters determining an individual's and/or community's willingness to pay for flood protection can be measured.
American Journal of Agricultural Economics↗