Charles N. Kroll

Trends in floods and low flows in the United States: impact of spatial correlation

Trends in flood and low flows in the US were evaluated using a regional average Kendalls S trend test at two spatial scales and over two timeframes. Field significance was assessed using a bootstrap methodology to account for the observed regional cross-correlation of streamflows. Using a 5% significance level, we found no evidence of trends in flood flows but did find evidence of upward trends in low flows at the larger scale in the Midwest and at the smaller scale in the Ohio, the north central and the upper Midwest regions. A dramatically different interpretation would have been achieved if regional cross-correlation had been ignored. In that case, statistically significant trends would have been found in all but two of the low flow analyses and in two-thirds of the flood flow analyses. We show that the cross-correlation of flow records dramatically reduces the effective number of samples available for trend assessment. We also found that low flow time series exhibit significant temporal persistence. Even when the serial correlation was removed from the time series, significant trends in low flow series were apparent, though the number of significant trends decreased.

Regional geohydrologic‐geomorphic relationships for the estimation of low‐flow statistics

Many investigators have sought to develop regional multivariate regression models which relate low-flow statistics to watershed characteristics. Normally, a multiplicative model structure is imposed and multivariate statistical procedures are employed to select suitable watershed characteristics and to estimate model parameters. Since such procedures have met with only limited success, we take a different approach. A simple conceptual stream-aquifer model is extended to a watershed scale and evaluated for its ability to approximate the low-flow behavior of 23 unregulated catchments in Massachusetts. The conceptual watershed model is then adapted to estimate low-flow statistics using multivariate regional regression procedures. Our results indicate that in central western Massachusetts, low-flow statistics are highly correlated with the product of watershed area, average basin slope and base flow recession constant, with the base flow recession constant acting as a surrogate for both basin hydraulic conductivity and drainable soil porosity.

Quantifying DEM Uncertainty and its Effect on Topographic Parameters

Digital elevation models (DEMs) are representations of topography with inherent errors that constitute uncertainty. DEM data are often used in analyses without quantifying the effects of these errors. This paper describes a Monte Carlo methodology for evaluation of the effects of uncertainty on elevation and derived topographic parameters. Four methods for representing DEM uncertainty that utilize metadata and spatial characteristics of a DEM are presented. Seven statistics derived from simulation results were used to quantify the effect of DEM error. When uncertainty was quantified by the average relative absolute difference, elevation did not deviate. The range of deviation across the four methods for slope was 5 to 8 percent, 460 to 950 percent for derived catchment areas and 4 to 9 percent for the topographic index. This research demonstrates how application of this methodology can address DEM uncertainty, contributing to more responsible use of elevation and derived topographic parameters, and ultimately results obtained from their use.

Estimation of Moments and Quantiles using Censored Data

Censored data sets are often encountered in water quality investigations and streamflow analyses. A Monte Carlo analysis examined the performance of three techniques for estimating the moments and quantiles of a distribution using censored data sets. These techniques include a lognormal maximum likelihood estimator (MLE), a log-probability plot regression estimator, and a new log-partial probability-weighted moment estimator. Data sets were generated from a number of distributions commonly used to describe water quality and water quantity variables. A “robust” fill-in method, which circumvents transformation bias in the real space moments, was implemented with all three estimation techniques to obtain a complete sample for computation of the sample mean and standard deviation. Regardless of the underlying distribution, the MLE generally performed as well as or better than the other estimators, though the moment and quantile estimators using all three techniques had comparable log-space root mean square errors (rmse) for censoring at or below the 20th percentile for samples sizes of n=10, the 40th percentile for n=25, and the 60th percentile for n=50. Comparison of the log-space rmse and real-space rmse indicated that a log-space rmse was a better overall metric of estimator precision.

Estimation of baseflow recession constants

Hydrograph recession constants are required in rainfall-runoff models, baseflow augmentation studies, geohydrologic investigations and in regional low-flow studies. The recession portion of a streamflow hydrograph is shown to be either an autoregressive process or an integrated moving average process, depending upon the structure of the assumed model errors. Six different estimators of the baseflow recession constant are derived and tested using thousands of hydrograph recessions available at twenty-three sites in Massachusetts, U.S. When hydrograph recessions are treated as an autoregressive process, unconditional least squares or maximum likelihood estimators of the baseflow recession constant are shown to exhibit significant downward bias due to the short lengths of hydrograph recessions. The precision of estimated of hydrograph recession constants is shown to depend heavily upon assumptions regarding the structure of the model errors. In general, regression procedures for estimating hydrograph recession parameters are generally preferred to the time-series alternatives. An evaluation of the physical significance of estimates of the baseflow recession constant is provided by comparing regional regression models which relate low-flow statistics to three independent variables: drainage area, basin slope and the baseflow recession constant. As anticipated, approximately unbiased estimators of the baseflow recession constant provide significant information regarding the geohydrologic response of watersheds.

Development of regional regression relationships with censored data

When no discharge record is available for a site, a regional regression relationship can be used to estimate low-flow quantiles. Problems arise in the derivation of such models when some at-site quantile estimates are reported as zero. One concern is that quantile estimates reported as zero may be in the range from zero to the measurement threshold. A second concern is that a logarithmic transformation cannot be used with zero quantile estimates, so traditional log linear least squares estimators cannot be computed. This paper uses visual examples and Monte Carlo simulation to compare the performance of techniques for estimating the parameters of a regional regression model when some at-site quantile estimates are zero. Ordinary least squares (OLS) techniques employed in practice include adding a small constant to all at-site quantile estimates (denoted OLSC), or neglecting all observation reported as zero (denoted OLSD). OLSC and OLSD performed poorly compared to the use of a Tobit model, which is a maximum likelihood estimator (MLE) procedure that represents the below threshold estimates as a range from zero to the threshold level. For a small amount of censoring, the OLSD method can be acceptable. A weighted Tobit model that accounts for the heteroscedasticity of the residuals in the regression model provided relatively little gain over the ordinary Tobit model.

Development of a distributed air pollutant dry deposition modeling framework.

A distributed air pollutant dry deposition modeling system was developed with a geographic information system (GIS) to enhance the functionality of i-Tree Eco (i-Tree, 2011). With the developed system, temperature, leaf area index (LAI) and air pollutant concentration in a spatially distributed form can be estimated, and based on these and other input variables, dry deposition of carbon monoxide (CO), nitrogen dioxide (NO(2)), sulfur dioxide (SO(2)), and particulate matter less than 10 microns (PM10) to trees can be spatially quantified. Employing nationally available road network, traffic volume, air pollutant emission/measurement and meteorological data, the developed system provides a framework for the U.S. city managers to identify spatial patterns of urban forest and locate potential areas for future urban forest planting and protection to improve air quality. To exhibit the usability of the framework, a case study was performed for July and August of 2005 in Baltimore, MD.

The value of streamflow record augmentation procedures in low-flow and flood-flow frequency analysis

Abstract Streamflow record augmentation procedures exploit the cross-correlation among streamflows at two or more streamgages to obtain improved estimates of the mean and variance of the flows at a short-record gage. Recent improvements in these procedures provide unbiased estimates of the mean and variance of the flows at the short-record site which always have equal or lower variance than simple at-site sample estimates. Essentially, record augmentation procedures increase the effective record length at a short-record site in proportion to the additional length of the nearby longer record and the cross-correlation of the concurrent streamflows at the two sites. An experiment documents the effective increase in record lengths on a site-by-site basis and on a regional basis using a network of 23 streamgages in or near Massachusetts. The increases in effective record lengths owing to the use of streamflow record augmentation procedures are substantial for the very-short-record sites for both flood-flow and low-flow statistics. However, the serial correlation associated with both flood-flow and low-flow sequences reduces those gains considerably.

Modeling of air pollutant removal by dry deposition to urban trees using a WRF/CMAQ/i-Tree Eco coupled system

A distributed adaptation of i-Tree Eco was used to simulate dry deposition in an urban area. This investigation focused on the effects of varying temperature, LAI, and NO2 concentration inputs on estimated NO2 dry deposition to trees in Baltimore, MD. A coupled modeling system is described, wherein WRF provided temperature and LAI fields, and CMAQ provided NO2 concentrations. A base case simulation was conducted using built-in distributed i-Tree Eco tools, and simulations using different inputs were compared against this base case. Differences in land cover classification and tree cover between the distributed i-Tree Eco and WRF resulted in changes in estimated LAI, which in turn resulted in variations in simulated NO2 dry deposition. Estimated NO2 removal decreased when CMAQ-derived concentration was applied to the distributed i-Tree Eco simulation. Discrepancies in temperature inputs did little to affect estimates of NO2 removal by dry deposition to trees in Baltimore.

Influences of wood preservation, lumber size, and weather on field leaching of red pine lumber.

Alkaline copper quaternary (ACQ) is a widely used wood preservative. This study evaluated leachate volume generation and contaminant leaching from ACQ-treated lumber during rainfall events in comparison to untreated lumber. The influences of wood preservation with ACQ, lumber size, and weather on leachate generation ratio and contaminant concentrations in wood leachate were investigated with four red pine lumber piles exposed to natural weather conditions. The average volumetric ratio of leachate to rainfall was significantly higher for the large-lumber piles (0.62) compared with the small-lumber piles (0.35). Less leachate was generated in the ACQ-treated lumber piles (0.42) than the untreated lumber piles (0.55). Leachate volume could be predicted with rainfall depth, air temperature, and wetted lumber surface area. Lumber size did not make a statistically significant difference in leachate quality except for zinc concentration. The average copper concentrations were 4034 μg/L in the leachate from the ACQ-treated lumber piles and 87 μg/L in the leachate from the untreated lumber piles. Moreover, ACQ treatment significantly increased leaching of arsenic and total dissolved solids. Copper concentration in leachate from ACQ-treated lumber can be predicted with rainfall intensity, the time interval between two consecutive leachate-generating events, rain copper concentration, and rain pH.