Ricardo Mantilla

A GIS numerical framework to study the process basis of scaling statistics in river networks

A new geographic information system (GIS) numerical framework (NF), called CUENCAS, for flows in river networks is presented. The networks are extracted from digital elevation models (DEMs). The program automatically partitions a basin into hillslopes and channel links that are required to correspond to these features in an actual terrain. To investigate the appropriate DEM resolution for this correspondence, we take a high-resolution DEM at 10-m pixel size, and create DEMs at eight different resolutions in increments of 10 m by averaging. The extracted networks from 10-30 m remain about the same, even though there is a tenfold reduction in the number of pixels. By contrast, the extracted networks show increasing distortions of the original network from 40-90 m DEMs. We show the presence of statistical self-similarity (scaling) in the probability distributions of drainage areas in a Horton-Strahler framework using CUENCAS. The NF for flows takes advantage of the hillslope-link decomposition of an actual terrain and specifies mass and momentum balance equations and physical parameterizations at this scale. These equations are numerically solved. An application of NF is given to test different physical assumptions that produce statistical self-similarity in spatial peak flow statistics in a Horton-Strahler framework.

Generalizing a nonlinear geophysical flood theory to medium‐sized river networks

[i] The central hypothesis of a nonlinear geophysical flood theory postulates that, given space-time rainfall intensity for a rainfall-runoff event, solutions of coupled mass and momentum conservation differential equations governing runoff generation and transport in a self-similar river network produce spatial scaling, or a power law, relation between peak discharge and drainage area in the limit of large area. The excellent fit of a power law for the destructive flood event of June 2008 in the 32,400-km 2 Iowa River basin over four orders of magnitude variation in drainage areas supports the central hypothesis. The challenge of predicting observed scaling exponent and intercept from physical processes is explained. We show scaling in mean annual peak discharges, and briefly discuss that it is physically connected with scaling in multiple rainfall-runoff events. Scaling in peak discharges would hold in a non-stationary climate due to global warming but its slope and intercept would change.

Recurrence plots and unstable periodic orbits

A recurrence plot is a two-dimensional visualization technique for sequential data. These plots are useful in that they bring out correlations at all scales in a manner that is obvious to the human eye, but their rich geometric structure can make them hard to interpret. In this paper, we suggest that the unstable periodic orbits embedded in a chaotic attractor are a useful basis set for the geometry of a recurrence plot of those data. This provides not only a simple way to locate unstable periodic orbits in chaotic time-series data, but also a potentially effective way to use a recurrence plot to identify a dynamical system. (c) 2002 American Institute of Physics.

Scaling relations between riparian vegetation and stream order in the Whitewater River network, Kansas, USA

Riparian communities have been well-studied along individual streams, but not within the context of networks of which streams are a part. To study networks, hydrologists use Horton–Strahler ordering to assign streams to discrete categories in which increasing numerical value (ω) reflects increasing size of the stream and complexity of the network. A key use of this classification method has been to demonstrate scaling relations between hydrogeomorphic variables and order. These relations now provide a foundation to determine how ecological processes are associated with the geometry and topology of river networks. We used geographic information systems (GIS) to map and measure the stream network and riparian vegetation of the Whitewater River basin of eastern Kansas, USA. With the resulting data, we tested if (1) riparian vegetation scaled with order, and (2) riparian vegetation at confluences of two streams differed from that found along constituent streams. Most characteristics of riparian vegetation scaled with order. In confluence zones, density and diversity of riparian vegetation generally were equivalent to that of the largest constituent stream. Scaling relations between riparian vegetation and order provide a framework to quantify the role of riparian vegetation in the water balance of stream networks and a tool to predict area and distribution of riparian vegetation from network topology.

Real-Time Flood Forecasting and Information System for the State of Iowa

AbstractThe Iowa Flood Center (IFC), established following the 2008 record floods, has developed a real-time flood forecasting and information dissemination system for use by all Iowans. The system complements the operational forecasting issued by the National Weather Service, is based on sound scientific principles of flood genesis and spatial organization, and includes many technological advances. At its core is a continuous rainfall–runoff model based on landscape decomposition into hillslopes and channel links. Rainfall conversion to runoff is modeled through soil moisture accounting at hillslopes. Channel routing is based on a nonlinear representation of water velocity that considers the discharge amount as well as the upstream drainage area. Mathematically, the model represents a large system of ordinary differential equations organized to follow river network topology. The IFC also developed an efficient numerical solver suitable for high-performance computing architecture. The solver allows the IF...

Analyzing the effects of excess rainfall properties on the scaling structure of peak discharges: Insights from a mesoscale river basin

Key theoretical and empirical results from the past two decades have established that peak discharges resulting from a single rainfall-runoff event in a nested watershed exhibit a power law, or scaling, relation to drainage area and that the parameters of the power law relation, henceforth referred to as the flood scaling exponent and intercept, change from event to event. To date, only two studies have been conducted using empirical data, both using data from the 21 km2 Goodwin Creek Experimental Watershed that is located in Mississippi, in an effort to uncover the physical processes that control the event-to-event variability of the flood scaling parameters. Our study expands the analysis to the mesoscale Iowa River basin (A = 32,400 km2), which is located in eastern Iowa, and provides additional insights into the physical processes that control the flood scaling parameters. Using 51 rainfall-runoff events that we identified over the 12 year period since 2002, we show how the duration and depth of excess rainfall, which is the portion of rainfall that contributes to direct runoff, control the flood scaling exponent and intercept. Moreover, using a diagnostic simulation study that is guided by evidence found in empirical data, we show that the temporal structure of excess rainfall has a significant effect on the scaling structure of peak discharges. These insights will contribute toward ongoing efforts to provide a framework for flood prediction in ungauged basins.

Classical and generalized Horton laws for peak flows in rainfall-runoff events

The discovery of the Horton laws for hydrologic variables has greatly lagged behind geomorphology, which began with Robert Horton in 1945. We define the classical and the generalized Horton laws for peak flows in rainfall-runoff events, which link self-similarity in network geomorphology with river basin hydrology. Both the Horton laws are tested in the Iowa River basin in eastern Iowa that drains an area of approximately 32 400 km(2) before it joins the Mississippi River. The US Geological Survey continuously monitors the basin through 34 stream gauging stations. We select 51 rainfall-runoff events for carrying out the tests. Our findings support the existence of the classical and the generalized Horton laws for peak flows, which may be considered as a new hydrologic discovery. Three different methods are illustrated for estimating the Horton peak-flow ratio due to small sample size issues in peak flow data. We illustrate an application of the Horton laws for diagnosing parameterizations in a physical rainfall-runoff model. The ideas and developments presented here offer exciting new directions for hydrologic research and education.

Exploring the Effect of Reservoir Storage on Peak Discharge Frequency

AbstractIn this paper, a simple hydrologic example is employed to illustrate the important features of reservoir regulated flood frequency. Despite its practical significance, the estimation of reservoir regulated flood frequency is largely dominated by empirical methodologies containing assumptions that could lead to incorrect results. The goal of this paper is to show by means of a continuous rainfall-runoff simulation how several reservoir variables, including the reservoir storage capacity, the size of release structures, operation rules, and the statistical variability of inflows to the reservoir, quantitatively control the regulated flood frequency. Although the example presented in this paper does not encompass the full complexity of the problem, it reveals important features of the regulated flood frequency. The study also highlights how specific assumptions in the traditional and widely used inflow volume-duration-frequency (VDF)–based methodology could lead to underestimation of flood risk for l...

A Spatial–Dynamical Framework for Evaluation of Satellite Rainfall Products for Flood Prediction

AbstractRainfall maps that are derived from satellite observations provide hydrologists with an unprecedented opportunity to forecast floods globally. However, the limitations of using these precipitation estimates with respect to producing reliable flood forecasts at multiple scales are not well understood. To address the scientific and practical question of applicability of space-based rainfall products for global flood forecasting, a data evaluation framework is developed that allows tracking the rainfall effects in space and time across scales in the river network. This provides insights on the effects of rainfall product resolution and uncertainty. Obtaining such insights is not possible when the hydrologic evaluation is based on discharge observations from single gauges. The proposed framework also explores the ability of hydrologic model structure to answer questions pertaining to the utility of space-based rainfall observations for flood forecasting. To illustrate the framework, hydrometeorologica...

An Initial Assessment of Radar Data Assimilation on Warm Season Rainfall Forecasts for Use in Hydrologic Models

AbstractThe effect of introducing radar data assimilation into the WRF Model to improve high-resolution rainfall forecasts that are used for flash flood forecasting is analyzed. The authors selected 12 heavy rainfall events and performed two WRF 24-h simulations that produced quantitative precipitation forecasts (QPFs) for each, one using the standard configuration in forecast mode (QPF-Cold) and one using radar data assimilated at initialization (QPF-Hot). Simulation outputs are compared with NWS stage IV QPEs for storm placement, area over threshold coverage, and equitable threat scores. The two QPF products and stage IV data are used to force the distributed hydrological model CUENCAS for the same 800 km × 800 km domain centered over Iowa (and to calculate peak flows across the river network). The hydrological model responses to the three products are compared in terms of spatial location and flood intensity. In general, QPF-Hot outperformed QPF-Cold in replicating stage IV QPE statistics. However, QPF...