Jeffrey D. Niemann

Nonlinearity and self‐similarity of rainfall in time and a stochastic model

We use physical arguments and statistical analysis to formulate stochastic models of rainfall intensity in time during intense convective storms. Special attention is given to the issue of multiplicative versus additive model structure and to the type of self-similarity that can be displayed by rainfall under the constraints of stationarity and nonnegativity. We show that some multiscaling models proposed in the past do not satisfy these constraints. Using a set of six high-resolution records, we find that the best fitting models are multiplicative, with a log (rain rate) spectrum of the segmented power type, i.e., of the form |ω| -β , with β that varies in different frequency ranges. Four spectral regimes are identified between scales from a few seconds to several hours. Nowhere do we find a log (rain rate) spectrum of the |ω| -1 type or scaling of the moments, which would be consistent with a conserved multifractal model. Other moment and spectral analyses as well as theoretical arguments lead us to reject also nonconserved multiscaling representations. The stochastic model we finally propose is lognormal with a segmented log spectrum and is not scaling. Two versions of the model are considered, one stationary for the central portion of the storm and the other nonstationary to include the buildup and decay phases. Compared to existing alternatives, the model is very easy to fit to data and to simulate.

Self-similarity and multifractality of fluvial erosion topography: 1. Mathematical conditions and physical origin.

It is suggested that the scaling laws satisfied by fluvial erosion topography and river networks reflect a basic self-similarity or multifractality property of the topographic surface within river basins. By analyzing the symmetries of fluvial topography, we conclude that this self-similarity or multifractality condition should be expressed in a particular way in terms of the topographic increments within subbasins. We then analyze whether self-similar or multifractal topographies can be stationary or transient solutions of dynamic evolution models of the type ∂h/∂t = U − ƒ{β, т}, where U is the uplift rate, ƒ is the fluvial erosion rate, β is a vector of erodibility parameters, and т is hydraulic shear stress. The hydraulic stress on a channel bed is assumed to satisfy т ∝ AmSn, where A is contributing area, S is slope, and m and n are parameters. We allow U to vary randomly in time and β to vary randomly in space and determine conditions on these random functions as well as the parameters m and n under which the topography may remain in a self-similar or multifractal state. Simulation shows that self-similar states are attractive also for non-self-similar boundary and initial conditions.

Method for Assessing Impacts of Parameter Uncertainty in Sediment Transport Modeling Applications

The predictions from a numerical sediment transport model inevitably include uncertainty because of assumptions in the model’s mathematical structure, the values of parameters, and various other sources. In this paper, the writers aim to develop a method that quantifies the degree to which parameter values are constrained by calibration data and the impacts of the remaining parameter uncertainty on model forecasts. The method uses a new multiobjective version of generalized likelihood uncertainty estimation. The likelihoods of parameter values are assessed using a function that weights different output variables on the basis of their first-order global sensitivities, which are obtained from the Fourier amplitude sensitivity test. The method is applied to Sedimentation and River Hydraulics—One Dimension (SRH-1D) models of two flume experiments: an erosional case and a depositional case. Overall, the results suggest that the sensitivities of the model outputs to the parameters can be rather different for er...

Prediction of regional water balance components based on climate, soil, and vegetation parameters, with application to the Illinois River Basin

[1] This paper presents a framework for studying regional water balance in which the physical processes are first described at the local instantaneous scale and then integrated to the annual, basin-wide scale. The integration treats the relative soil saturation (i.e., the soil moisture divided by the porosity) and precipitation intensities as stochastic variables in space and time. A statistical equilibrium characterizes the annual water balance, resulting in a specific relation that predicts the space-time average of soil saturation in terms of soil, climate, and vegetation parameters. Specific relationships are proposed to relate the space-time average soil saturation to runoff, groundwater recharge, and evapotranspiration. This framework is applied to the Illinois River Basin. The shape of the spatial and temporal distributions of soil saturation are determined from observations. The other parameters are determined from the physical characteristics of the basin and calibration procedures. The resulting model is able to reproduce an observed relation between the space-time average soil saturation and precipitation. It is also able to reproduce observed relations between space-time average soil saturation and space-time average evapotranspiration, surface runoff, and groundwater runoff. INDEX TERMS: 1836 Hydrology: Hydrologic budget (1655); 1866 Hydrology: Soil moisture; 1854 Hydrology: Precipitation (3354); 1860 Hydrology: Runoff and streamflow; KEYWORDS: Illinois River, probabilistic methods, soil moisture, water balance

Impacts of surface elevation on the growth and scaling properties of simulated river networks

We investigate the connection between surface elevation and the growth and scaling of river networks. Three planar models (Scheidegger, Eden, and invasion percolation) are first considered. These models develop aggregating networks according to stochastic rules but do not simulate erosion because the network growth is independent of the surface elevation. We show that none of these planar growth models produces scaling results consistent with observations for natural river basins. We then modify the models to include elevation, simulating the effects of fluvial erosion by enforcing the slope-area relationship. The resulting configurations have scaling properties that still depend on the model (Scheidegger, Eden, or invasion percolation) but are closer to natural river networks when compared with those from the planar growth rules. We conclude that inclusion of the vertical dimension in these three models is critical for explaining the formation and regularities of fluvial networks

AutoRAPID: A Model for Prompt Streamflow Estimation and Flood Inundation Mapping over Regional to Continental Extents

This article couples two existing models to quickly generate flow and flood-inundation estimates at high resolutions over large spatial extents for use in emergency response situations. Input data are gridded runoff values from a climate model, which are used by the Routing Application for Parallel computatIon of Discharge (RAPID) model to simulate flow rates within a vector river network. Peak flows in each river reach are then supplied to the AutoRoute model, which produces raster flood inundation maps. The coupled tool (AutoRAPID) is tested for the June 2008 floods in the Midwest and the April-June 2011 floods in the Mississippi Delta. RAPID was implemented from 2005 to 2014 for the entire Mississippi River Basin (1.2 million river reaches) in approximately 45 min. Discretizing a 230,000-km area in the Midwest and a 109,500-km area in the Mississippi Delta into thirty-nine 1° by 1° tiles, AutoRoute simulated a high-resolution (~10 m) flood inundation map in 20 min for each tile. The hydrographs simulated by RAPID are found to perform better in reaches without influences from unrepresented dams and without backwater effects. Flood inundation maps using the RAPID peak flows vary in accuracy with F-statistic values between 38.1 and 90.9%. Better performance is observed in regions with more accurate peak flows from RAPID and moderate to high topographic relief. (KEY TERMS: flooding; computational methods; rivers/streams; AutoRoute; RAPID; AutoRAPID.) Follum, Michael L., Ahmad A. Tavakoly, Jeffrey D. Niemann, and Alan D. Snow, 2017. AutoRAPID: A Model for Prompt Streamflow Estimation and Flood Inundation Mapping over Regional to Continental Extents. Journal of the American Water Resources Association (JAWRA) 53(2):280-299. DOI: 10.1111/1752-1688.12476

Impacts of precipitation and potential evapotranspiration patterns on downscaling soil moisture in regions with large topographic relief

Soil moisture can be estimated at coarse resolutions (>1 km) using satellite remote sensing, but that resolution is poorly suited for many applications. The Equilibrium Moisture from Topography, Vegetation, and Soil (EMT+VS) model downscales coarse-resolution soil moisture using fine-resolution topographic, vegetation, and soil data to produce fine-resolution (10-30 m) estimates of soil moisture. The EMT+VS model performs well at catchments with low topographic relief (≤124 m), but it has not been applied to regions with larger ranges of elevation. Large relief can produce substantial variations in precipitation and potential evapotranspiration (PET), which might affect the fine-resolution patterns of soil moisture. In this research, simple methods to downscale temporal average precipitation and PET are developed and included in the EMT+VS model, and the effects of spatial variations in these variables on the surface soil moisture estimates are investigated. The methods are tested against ground truth data at the 239 km2 Reynolds Creek watershed in southern Idaho, which has 1145 m of relief. The precipitation and PET downscaling methods are able to capture the main features in the spatial patterns of both variables. The space-time Nash-Sutcliffe coefficients of efficiency of the fine-resolution soil moisture estimates improve from 0.33 to 0.36 and 0.41 when the precipitation and PET downscaling methods are included, respectively. PET downscaling provides a larger improvement in the soil moisture estimates than precipitation downscaling likely because the PET pattern is more persistent through time, and thus more predictable, than the precipitation pattern. This article is protected by copyright. All rights reserved.

Impact of Shallow Groundwater on Evapotranspiration Losses from Uncultivated Land in an Irrigated River Valley

In many agricultural regions of the West, decades of intensive irrigation have produced shallow water tables under not only cultivated fields but also the nearby uncultivated land. It is possible that the high water tables under the uncultivated lands are substantially increasing evapotranspiration (ET) rates, which would represent an unnatural and potentially nonbeneficial consumptive use. The objective of this paper is to quantify loss of water that occurs from uncultivated lands in a semiarid irrigated river valley (the Lower Arkansas River Valley in southeastern Colorado). A remote-sensing algorithm is used to estimate actual ET rates on 16 dates on the basis of Landsat satellite images. On the same dates, water table depths, soil moisture values, and soil water salinities are measured at up to 84 wells distributed across three study sites. On the basis of a water balance of the root zone, it is estimated that 78% of the ET is supplied by groundwater upflux at these sites. It is also observed that the...

Reconstruction of hillslope and valley paleotopography by application of a geomorphic model

Many applications in geology require estimation of the depth and thickness of lithologic layers based on limited observations. The boundaries of such layers are typically estimated using Kriging or other estimation methods that produce smooth surfaces. In some cases, however, smooth surfaces may be inappropriate. A boundary that is formed by a preserved hillslope and valley paleotopography, in particular, is expected to exhibit drainage characteristics and inherent roughness that are not consistent with standard estimation methods. This paper discusses the generalization of a technique originally designed to interpolate fluvially eroded topography. The method incorporates a simple river basin evolution model to generate realistic topography and adjusts an erodability parameter in space to match observed elevations. The method is generalized to allow flow to enter from outside the interpolation region, which is a likely scenario when reconstructing paleotopography. The method is then applied to the lower boundary of the Tshirege Member of the Bandelier Tuff, which underlies Los Alamos National Laboratory and Bandelier National Monument in north-central New Mexico. The method produces surfaces with major valleys that are consistent with previous studies. The method is also applied in a framework that estimates the likelihood that any particular point within the interpolation region drains through a specified boundary. Although the surfaces vary between simulations, most portions of the interpolation domain drain through consistent boundaries.

Modeling input errors to improve uncertainty estimates for one-dimensional sediment transport models

Bayesian methods have recently been applied to one-dimensional sediment transport models to assess the uncertainty in model predictions due to uncertainty in the parameter values. However, these approaches neglect any uncertainties in the model inputs, which might play a substantial role. The objective of this research is to include uncertainties in sediment transport model inputs and evaluate their contributions to the overall uncertainty in the model predictions. To accomplish this goal, simple error models are developed for the input data and integrated into an existing Bayesian method. Five types of input data are considered: input discharges, rating curves, vertical and horizontal distances in cross-sections, and benchmark elevations that define the longitudinal profile of the reach. The input errors are modeled using Gaussian distributions, and the means and standard deviations are treated as uncertain parameters that are estimated within the Bayesian framework. The Bayesian approach is coupled to the Sedimentation and River Hydraulics-One Dimension (SRH-1D) model and used to simulate a 23-km reach of the Tachia River in Taiwan. When input uncertainties are included, the prediction ranges change substantially and cover more of the available observations, which suggests the uncertainty is better represented when input errors are considered. The results also indicate that the errors in the benchmark elevations have the largest impact on the uncertainty of the predictions among those considered.