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Abstract: The rainfall–run‐off convolution integral is analytically solved for several models for the elementary hydrograph. These solutions can be combined with available rainfall frequency analyses to predict flood flows along streams for different recurrence intervals, using no free parameters for gauged streams and one estimable parameter for ungauged streams. Extreme discharge magnitudes at gauged sites can be typically estimated within a factor of two of actual records, using no historical data on extreme flows. The flow predictions reproduce several important characteristics of the flood phenomenon, such as the slope of the regression line between observed extreme flows and basin area on the conventional logQ versus logA plot. Importantly, for the models and data sets investigated, the storm duration of greatest significance to flooding was found to approximate the intrinsic transport timescale of the particular watershed, which increases with basin size. Thus, storms that deliver extraordinary amounts of rainfall over a particular time interval will most greatly activate basins whose time constants approximately equal that interval. This theoretical finding is supported by examination of the regional hydrological response to the massive storms of September 14, 2008, and April 28–30, 2017, which caused extraordinary record flooding of basins of about 5–100 km2 and 500–4,000 km2, respectively, but produced few records in basins that were larger or smaller than those ranges. [ABSTRACT FROM AUTHOR]

Flooding in the Mississippi basin has become increasingly uncertain, and a succession of progressively higher, peak annual water levels is observed at many sites. Many record levels set in the central USA by the huge 1993 flood have already been superseded. Methodology developed elsewhere that recognizes trends of river stages is used to estimate present-day flood risk at 27 sites in the Mississippi basin that have >100 years of continuous stage record. Unlike official estimates that are fundamentally based on discharge, this methodology requires only data on river stage. A novel plot linearizes the official flood levels that are indirectly derived from the complex, discharge-based calculations and demonstrates that the neglect of trends has resulted in the effective use of undersized means and standard deviations in flood risk analysis. A severe consequence is that official 'base flood' levels are underestimated by 0.4 to 2 m at many sites in the central USA. [ABSTRACT FROM AUTHOR]

A theoretical, dimensionless rainfall-runoff model was used to simulate the discharge of Wulongdong spring in western Hubei province, South China. The single parameter (time constant τ) in the model is easy to obtain by fitting the recession rate of the observed hydrographs. The model was scaled by simply matching the total annual flow volume of the model to the observed value. Annual distribution of actual evapotranspiration was embedded in the model input to calculate the accumulated deficit of soil moisture before each rain event. Hourly precipitation input data performed better than daily data, defining τ of 0.85 days and returning a Nash-Sutcliffe efficiency of 0.89 and the root mean square error of 0.07. This model offers an effective way to simulate the discharge of karst springs that respond sensitively to rainfall events. The model parameters of a successful simulation can be used to estimate the recharge area and indicate the intrinsic response time of the basin. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

To explore planetary evolution, we provide conductive cooling profiles that account for planet size, phonon diffusivity and various internal heating scenarios. Our new analytical solution for simple cooling of spheres reveals that heat is removed from only Earth's outermost ~1000 km over geological time. Numerical models with decaying heat production show that any upward concentration of radionuclides causes high temperatures at shallow depths, forcing interior temperatures to increase with time while producing a thermal gradient that forbids lower mantle convection. Hence, differentiation drives upper mantle magmatism and tectonics, leaving a quiescent but hot deep interior, while slowly melting the core. [ABSTRACT FROM AUTHOR]

Temporal variations in the head of wells in the alluvial aquifer along the lower Missouri River are accurately simulated by summation of linear differential terms involving daily variations in river stage and effective precipitation. Scaling parameters were optimized using a fourth order Adams-Bashforth-Moulton method, providing predictions for head that are typically accurate within ±1.5 feet (0.5 m) over intervals of 1 to 15 years. Parameter magnitudes represent the product of realistic aquifer properties and geometric factors. [ABSTRACT FROM AUTHOR]

A theoretical hydrograph based on Darcy's law and the diffusion equation has been extended into a predictive model for the discharge of diffuse springs and small rivers from a detailed rainfall record, using only a single free parameter, the basin time constant b. The model accurately predicts the flow variations of natural hydrographs, including the magnitude and timing of peak flow, total flow volume, inflection points, and recession rate, all as a function of effective rainfall amounts, basin area, and the time constant b. Predicted hydrographs for a sharp storm event in an unimpounded basin are compared to results for two common transfer functions, and our more parsimonious model is statistically superior. Modeling of a long-term record in proximal basins illustrates the effect of variations in b. Potential applications of the model include flood prediction, comparative studies of basin response in a regional context, and estimation of actual evapotranspiration. [ABSTRACT FROM AUTHOR]

An extensive base of water quality information emphasizing the effects of land use and hydrology was obtained in the karstified Fountain Creek watershed of southwestern Illinois to help resolve local water quality issues. Agrichemicals dominate the loads of most water quality constituents in the streams and shallow karstic ground water. Only calcium (Ca), magnesium (Mg), Aluminum (Al), and sulfate (SO4) ions are predominantly derived from bedrock or soils, while agrichemicals contribute most of the sodium (Na), potassium (K), chlorine (Cl), nitrate (NO3), fluorine (F), phosphorus (P), and atrazine. Concentrations of individual ions correlate with discharge variations in karst springs and surface streams; highly soluble ions supplied by diffuse ground water are diluted by high flows, while less soluble ions increase with flow as they are mobilized from fields to karst conduits under storm conditions. Treated wastewater containing detergent residues dominates the boron load of streams and provides important subordinate loads of several other constituents, including atrazine derived from the Mississippi River via the public water supply. Average surface water concentrations at the watershed outlet closely approximate a 92:8 mixture of karst ground water and treated wastewater, demonstrating the dominance of ground water contributions to streams. Therefore the karst aquifer and watershed streams form a single water quality system that is also affected by wastewater effluent. [ABSTRACT FROM AUTHOR]

A letter to the editor is presented in response to B. Schaefli and H. V. Gupta's point in the need of useful metrics to analyze and compare the performance of hydrologic models, published in "Hydrological Processes" in 2008.