George M. Hornberger

How much complexity is warranted in a rainfall-runoff model?

Development of mathematical models relating the precipitation incident upon a catchment to the streamflow emanating from the catchment has been a major focus of surface water hydrology for decades. Generally, values for parameters in such models must be selected so that runoff calculated from the model “matches” recorded runoff from some historical period. Despite the fact that the physics governing the path of a drop of water through a catchment to the stream involves complex relationships, evidence indicates that the information content in a rainfall-runoff record is sufficient to support models of only very limited complexity. This begs the question of what limits the observed data place on the allowable complexity of rainfall-runoff models. Time series techniques are applied for estimating transfer functions to determine how many parameters are appropriate to describe the relationship between precipitation and streamflow in the case where data on only precipitation, air temperature, and streamflow are available. Statistics from an “information matrix” provide the clues necessary for determining allowable model complexity. Time series models are developed for seven catchments with widely varying physical characteristics in different temperate climatic regimes to demonstrate the method. It is found that after modulating the measured rainfall using a nonlinear loss function, the rainfall-runoff response of all catchments is well represented using a linear model. Also, for all catchments a two-component linear model with four parameters is the model of choice. The two components can be interpreted as defining a “quick flow” and “slow flow” response of the given catchment. The method therefore provides a statistically rigorous way to separate hydrographs and parameterize their response behavior. The ability to construct reliable transfer function models for describing the rainfall-runoff process offers a new approach to investigate empirically the controls of physical catchment descriptors, land use change, climate change, etc., on the dynamic response of catchments through the extensive analysis of historical data sets.

Hydrological controls on dissolved organic carbon during snowmelt in the Snake River near Montezuma, Colorado

A quantitative understanding of the factors controlling the variation of dissolved organic carbon (DOC) in headwater streams is of scientific concern for at least two reasons. First, quantifying the overall carbon budgets of lotic systems is needed for a fundamental understanding of these systems. Second, DOC interacts strongly with other dissolved substances (heavy metals in particular) and plays an important role in the transport of contaminants.In the Snake River near Montezuma, Colorado, measurements of DOC from 1980 to 1986 show rapid decreases in concentration from a peak very early in the snowmelt period. Peak DOC concentrations occur approximately one month prior to peak discharge in the stream. The decline in DOC with time is approximately exponential, suggesting that a simple flushing mechanism can explain the response. We examined hydrological mechanisms to explain the observed variability of DOC in the Snake River by simulating the hydrological response of the catchment using TOPMODEL and routing the predicted flows through a simple model that accounted for temporal changes in DOC. Conceptually the DOC model represents a terrestrial (soil) reservoir in which DOC builds up during low flow periods and is flushed out by infiltrating meltwaters. The model reproduces the main features of the observed variation in DOC in the Snake River and thus lays the foundation for quantitatively linking hydrological processes with carbon cycling through upland catchments. Model results imply that a significant fraction of the soils in the Snake River catchment contribute DOC to the stream during peak discharge. Our work represents one of the first attempts to quantitatively describe the hydrological controls on DOC dynamics in a headwater stream. These controls are studied through the model by imposing mass balance constraints on both the flux of water through the various DOC source areas and the amount of DOC that can accumulate in these areas.

Aggregating Fine‐Scale Ecological Knowledge to Model Coarser‐Scale Attributes of Ecosystems

As regional and global scales become more important to ecologists, methods must be developed for the application of existing fine-scale knowledge to predict coarser-scale ecosystem properties. This generally involves some form of model in which fine-scale components are aggregated. This aggregation is necessary to avoid the cumulative error associated with the estimation of a large number of parameters. However, aggregation can itself produce errors that arise because of the variation among the aggregated components. The statistical expectation operator can be used as a rigorous method for translating fine-scale relationships to coarser scales without aggregation errors. Unfortunately this method is too cumbersome to be applied in most cases, and alternative methods must be used. These alternative methods are typically partial corrections for the variation in only a few of the fine-scale attributes. Therefore, for these methods to be effective, the attributes that are the most severe sources of error must be identified a priori. We present a procedure for making these identifications based on a Monte Carlo sampling of the fine-scale attributes. We then present four methods of translating fine-scale knowledge so it can be applied at coarser scales: (1) partial transformations using the expectation operator, (2) moment expansions, (3) partitioning, and (4) calibration. These methods should make it possible to apply the vast store of fine-scale ecological knowledge to model coarser-scale attributes of ecosystems.

Response characteristics of DOC flushing in an alpine catchment

The spatial distribution of source areas and associated residence times of water in the catchment are significant factors controlling the annual cycles of dissolved organic carbon (DOC) concentration in Deer Creek (Summit County, Colorado). During spring snowmelt (April–August 1992), stream DOC concentrations increased with the rising limb of the hydrograph, peaked before maximum discharge, then declined rapidly as melting continued. We investigated catchment sources of DOC to streamflow, measuring DOC in tension lysimeters, groundwater wells, snow and streamflow. Lysimeter data indicate that near-surface soil horizons are a primary contributor of DOC to streamflow during spring snowmelt. Concentrations of DOC in the lysimeters decrease rapidly during the melt period, supporting the hypothesis that hydrological flushing of catchment soils is the primary mechanism affecting the temporal variation of DOC in Deer Creek. Time constants of DOC flushing, characterizing the exponential decay of DOC concentration in the upper soil horizon, ranged from 10 to 30 days for the 10 lysimeter sites. Differences in the rate of flushing are influenced by topographical position, with near-stream riparian soils flushed more quickly than soils located further upslope. Variation in the amount of distribution of accumulated snow, and asynchronous melting of the snowpack across the landscape, staggered the onset of the spring flush throughout the catchment, prolonging the period of increased concentrations of DOC in the stream. Streamflow integrates the catchment-scale flushing responses, yielding a time constant associated with the recession of DOC in the stream channel (84 days) that is significantly longer than the time constants observed for particular locations in the upper soil.

Bacterial transport in porous media: Evaluation of a model using laboratory observations

The factors that control the transport of bacteria through porous media are not well understood. The relative importance of the processes of dispersion, of immobilization of bacterial cells by various mechanisms (deposition), and of subsequent release of these trapped cells (entrainment) in describing transport has not been elucidated experimentally. Moreover, the variability of the phenomenological coefficients used to model these processes, given changes in such primary factors as grain size, organism, and ionic strength of the water, is unknown. We report results of fitting solutions of an advection-dispersion equation, modified to account for deposition and entrainment, to breakthrough curves from packed sand columns using two sizes of sand, two ionic strengths of the carrier solution, and two organisms with different sizes. A solution to the advection-dispersion equation including three processes, that is, dispersion, deposition, and entrainment, provides a match to the data that is superior to that achieved by solutions ignoring one of the processes. Fitted values of the coefficient describing deposition vary in a consistent manner with the control variables (organism, grain size, and ionic strength) and are generally within one order of magnitude of those predicted on the basis of theory.

Comparison of hydrochemical tracers to estimate source contributions to peak flow in a small, forested, headwater catchment

Three-component (throughfall, soil water, groundwater) hydrograph separations at peak flow were performed on 10 storms over a 2-year period in a small forested catchment in north-central Maryland using an iterative and an exact solution. Seven pairs of tracers (deuterium and oxygen 18, deuterium and chloride, deuterium and sodium, deuterium and silica, chloride and silica, chloride and sodium, and sodium and silica) were used for three-component hydrograph separation for each storm at peak flow to determine whether or not the assumptions of hydrograph separation routinely can be met, to assess the adequacy of some commonly used tracers, to identify patterns in hydrograph-separation results, and to develop conceptual models for the patterns observed. Results of the three-component separations were not always physically meaningful, suggesting that assumptions of hydrograph separation had been violated. Uncertainties in solutions to equations for hydrograph separations were large, partly as a result of violations of assumptions used in deriving the separation equations and partly as a result of improper identification of chemical compositions of end-members. Results of three-component separations using commonly used tracers were widely variable. Consistent patterns in the amount of subsurface water contributing to peak flow (45-100%) were observed, no matter which separation method or combination of tracers was used. A general conceptual model for the sequence of contributions from the three end-members could be developed for 9 of the 10 storms. Overall results indicated that hydrochemical and hydrometric measurements need to be coupled in order to perform meaningful hydrograph separations.

EFFECTS OF CLIMATE CHANGE ON FRESHWATER ECOSYSTEMS OF THE SOUTH‐EASTERN UNITED STATES AND THE GULF COAST OF MEXICO

The south-eastern United States and Gulf Coast of Mexico is physiographically diverse, although dominated by a broad coastal plain. Much of the region has a humid, warm temperate climate with little seasonality in precipitation but strong seasonality in runoff owing to high rates of summer evapotranspiration. The climate of southern Florida and eastern Mexico is subtropical with a distinct summer wet season and winter dry season. Regional climate models suggest that climate change resulting from a doubling of the pre-industrial levels of atmospheric CO 2 may increase annual air temperatures by 3-4°C. Changes in precipitation are highly uncertain, but the most probable scenario shows higher levels over all but the northern, interior portions of the region, with increases primarily occurring in summer and occurring as more intense or clustered storms. Despite the increases in precipitation, runoff is likely to decline over much of the region owing to increases in evapotranspiration exceeding increases in precipitation. Only in Florida and the Gulf Coast areas of the US and Mexico are precipitation increases likely to exceed evapotranspiration increases, producing an increase in runoff (...)

On the Use of Linearized Langmuir Equations

Soil Sci. Soc. Am. J. 71:1796–1806 doi:10.2136/sssaj2006.0304 Received 30 Aug. 2006. *Corresponding author (carl.bolster@ars.usda.gov).

Eutrophication in peel inlet—I. The problem-defining behavior and a mathematical model for the phosphorus scenario

Abstract The utilization of a mathematical model at an early stage of research on an environmental problem, the causes of which are poorly understood, is usually infeasible because of a lack of data. If the problem of interest is generically similar to others that have been reported in the literature however, a considerable amount of applicable information may be available and, if so, the parameters of a simulation model may be specified via a priori statistical distributions. Monte Carlo experiments can then be utilized to examine whether the model is able to simulate the salient qualitative aspects of the problem-defining behavior. The ultimate objective of such an approach is to identify areas of critical uncertainty in knowledge of the system and thereby to derive information that may be useful in focusing the next phase of research. The problem of cultural eutrophication in Peel Inlet, Western Australia, where the system behavior of interest is the excessive growth of the alga Cladophora , is amenable to such treatment. A phosphorus-based model provides one feasible explanation of this nuisance algal problem.

The influence of mineralogy and solution chemistry on the attachment of bacteria to representative aquifer materials.

Abstract The rate and extent of bacterial attachment to mineral surfaces (chips of quartz, muscovite, limestone, and Fe-hydroxide-coated quartz and muscovite) was investigated by counting the numbers of bacterial cells (Lula-D, an indigenous groundwater organism) associated with each surface over time. The degree of attachment of cells to mineral surfaces was correlated with the sign of the surface charge as estimated from literature values for the isoelectric point; attachment of the negatively charged bacteria was much greater to the positively charged surfaces of limeston, Fe-hydroxide-coated quartz, and Fe-hydroxide-coated muscovite than to the negatively charged surfaces of clean quartz and clean muscovite. Batch experiments determined that the numbers of bacteria attached to the clean muscovite increased with increasing ionic strength of the solution, and the numbers attached to clean quartz were greater at pH 5 than at pH 7. In columns of clean quartz sand under saturated flow conditions, bacteria initially broke through at 1 pore volume but continued to elute for at least 7 pore volumes. Columns of Fe-hydroxide-coated sand retained more of the bacteria added to the columns (99.9% vs 97.4%), and the elution of cells ceased after the primary breakthrough. The results indicate that surface interactions between the mineral grains in an aquifer and the bacterial cells must play an essential role in determining the movement of bacteria through saturated porous media.