Nils Christophersen

Modelling streamwater chemistry as a mixture of soilwater end-members - An application to the Panola Mountain catchment, Georgia, U.S.A.

Abstract Streamwater chemistry at Panola Mountain research catchment, Georgia, U.S.A., is explained as a mixture of representative soilwater solutions that are considered to be temporally invariant to a first approximation. The selection of three end-members from all sampled soil waters is evaluated by comparing the observed and predicted streamwater concentration of six solutes (alkalinity, sulfate, sodium, magnesium, calcium and dissolved silica), which are assumed to mix conservatively, and by assessing the consistency of the implied hydrograph separation with the hydrological mechanisms that are believed to be operating in this catchment. The percentage of variation in the streamwater solute concentrations explained by the end-member mixing analysis (EMMA) ranges from 82 to >97%, and the hydrograph separation is, intuitively, physically reasonable. If the correct end-members have been identified, the streamwater chemical response to different levels of acidic deposition can be predicted by examining the change in each end-member under different loads; no hydrological model is required. If a traditional hydrochemical model, which is driven by rainfall quantity and quality, is desired, this analysis provides an indication of the model structure that would be necessary to reproduce both streamwater and soilwater chemistry.

Modelling streamwater chemistry as a mixture of soilwater end-members-a step towards second-generation acidification models

Abstract In present acidification models, soilwater characteristics, though modelled, are seldom checked against field observations. Given that such data are now collected as part of many catchment studies, a technique is developed whereby stream water can be predicted as a mixture of the observed soilwater classes or end-members. Provided that a sufficient set of end-members has been identified, a least-squares technique can be used to estimate the contribution to the stream from each end-member, whenever streamwater samples have been taken. For two catchments, Birkenes in southern Norway and Plynlimon in Mid-Wales, the analysis indicates that the soilwater end-members observed to date are insufficient to explain streamwater chemistry. However, properties of the missing soil waters have been identified, thus facilitating future field work. When an adequate set of soilwater end-members has been established, long-term predictions of changes in streamwater chemistry reduce to the problem of predicting the fate of each end-member. Thus, a separate hydrological submodel is not needed, since the mixing patterns are derived from the end-member analysis.

Multivariate analysis of stream water chemical data: The use of principal components analysis for the end‐member mixing problem

Traditional multivariate data analysis techniques, such as principal components analysis (PCA), have often been used in an attempt to identify source solutions from potential mixtures, such as stream water. Artificial data, generated from conservative mixing of known source solutions in random proportions, are employed to demonstrate that PCA should be used only to determine the rank of the mixture and not to determine the composition of the source solutions. The rank of the mixture is related to the number of source solutions. Unambiguous identification of the source solution compositions from the mixture alone is impossible; thus it is necessary that potential source solutions be derived from independent measurements. In the case of stream water, possible source solutions are groundwater and soil water from different horizons. A multivariate screening procedure is presented for the evaluation of these potential source solutions.

Dissolved organic carbon fractions in soil and stream water during variable hydrological conditions at Birkenes, southern Norway

Spatial and temporal variations in the composition of dissolved organic carbon (DOC) in stream and soil water of the acidified Birkenes catchment were studied during summer and autumn 1990. Hydrophobic and hydrophilic acids were the dominant fractions in the soils (dominated by podzols and peats) and brook, accounting for ∼90% of total DOC. The podzol displayed a vertical gradation of DOC fractions, with hydrophobic acids dominating in the O horizon (∼65%) and hydrophilic acids dominating in the E and B horizons (∼60%). In the bogs, hydrophilic acids were the dominant fraction at all depths. Temporal variations in the relative contributions of the various DOC fractions were most pronounced in the podzol O horizon and the brook during successive autumn rainstorms, and small in the mineral soils and bogs. In the brook, DOC increases at peak discharge were dominated by hydrophilic acids. If stream water was assumed to be a conservative mixture of water from the podzol O and B horizons and from the deeper layers in the bog surrounding the stream, 92% of the variability in the concentration of hydrophobic and hydrophilic acids in the stream could be explained. This mixing analysis suggested that base flow largely originated in the deeper layers of the bogs, while peak flow was primarily made up of B horizon (∼50–65%) and O horizon (∼35–50%) water.

A Critique of Models for Freshwater and Soil Acidification

Four types of models quantifying effects of acid deposition on freshwaters are reviewed. These include Henriksens empirical model, an adsorption isotherm model, soil-oriented charge balance models (Reuss-Johnson, Birkenes, MAGIC, ILWAS), and the Trickle Down model. Emphasis is on an assessment of critical assumptions; no attempt has been made to run the various models and compare results. The models range from simple to very complex and from empirical to highly process oriented. The various types have all proven useful and there has been a significant convergence concerning key processes. The importance of anion mobility, sulfate adsorption, ion exchange, dissolution of Al bearing minerals and weathering seems to be accepted by most workers. Future model improvement, however, relies to a large extent on further checking against observations.

VARIATIONS IN CONCENTRATIONS OF AQUEOUS ALUMINIUM AND OTHER CHEMICAL SPECIES DURING HYDROLOGICAL EPISODES AT BIRKENES, SOUTHERNMOST NORWAY

Abstract Concentrations of H + , aluminium species, total fluoride, silica, TOC, and major cations and anions were measured in stream- and soil water in the Birkenes catchment during base-flow and high discharge hydrological episodes from 1984 to 1986. Snow and meltwater were also sampled before and during the spring snowmelt seasons. During all the rainfall and snowmelt hydrological events for the five field periods analysed, the H + concentration increased with flow, whereas inorganic monomeric aluminium, Al i (including Al 3+ ), increased with flow only during episodes preceded by relatively low flow periods; during subsequent events Al i remained nearly constant or even decreased. Concentrations of Al i and H + in soil water sampled under saturated conditions were generally stable over time compared to the variations for these species in streamwater. The considerable fluctuations observed for chloride Cl − and sulphate SO 2− 4 concentrations illustrated that displacement of soil water occurred. The results confirm the importance of hydrological factors in determining episodic aluminium response. Large variations in the saturation indices show that equilibrium with either Al(OH) 3 (gibbsite) or Al 2 Si 2 O 5 (OH) 4 (kaolinite, halloysite) cannot control aluminium concentrations in streamwater at Birkenes; the same is true for Al(OH)SO 4 (jurbanite) although the saturation index for this mineral is less variable. Most probably, different controlling mechanisms predominate in the different soil layers, producing different chemical signatures which are picked up in the stream to varying degrees depending on hydrological conditions.

Water Flow Paths and the Spatial Distribution of Soils and Exchangeable Cations in an Acid Rain‐Impacted and a Pristine Catchment in Norway

The dynamic pattern of soil water transport is a major factor in determining the chemistry of streamwater. In the acidified Birkenes catchment (southernmost Norway) the streamwater chemistry is, to a first approximation, explained by mixing solutions from the forest floor, the B horizon and the deep peat, in various proportions depending on the hydrological conditions. Paradoxically, a direct physical contact between the forest floor and the B horizon on the one hand and the stream on the other is lacking, as the stream banks largely consist of peats. To investigate this paradox, soils and their levels of exchangeable cations were studied in a 100 m × 100 m grid. Results indicate that the exchange sites of the surface peat along the stream are significantly enriched in Al, probably due to return flow of Al-rich B horizon water. This view is supported by the similarity of the solution chemistry in surface peats and B horizons. Exchangeable base cations dominate in the forest floor upslope. Forest floor solutions, an important component of streamwater during intensive storms, are depleted in Al and may bypass the A-enriched surface peats via ephemeral flow channels. A parallel study in a pristine catchment in mid-Norway shows a similar accumulation of Al in return flow areas. This indicates that acid deposition is not a prerequisite for elevated levels of exchangeable Al in the surface organic layers of return flow areas.

Regularized local linear prediction of chaotic time series

Abstract Local linear prediction, based on the ordinary least squares (OLS) approach, is one of several methods that have been applied to prediction of chaotic time series. Apart from potential linearization errors, a drawback of this approach is the high variance of the predictions under certain conditions. Here, a different set of so-called linear regularization techniques, originally derived to solve ill-posed regression problems, are compared to OLS for chaotic time series corrupted by additive measurement noise. These methods reduce the variance compared to OLS, but introduce more bias. A main tool of analysis is the singular value decomposition (SVD), and a key to successful regularization is to damp the higher order SVD components. Several of the methods achieve improved prediction compared to OLS for synthetic noise-corrupted data from well-known chaotic systems. Similar results were found for real-world data from the R-R intervals of ECG signals. Good results are also obtained for real sunspot data, compared to published predictions using nonlinear techniques.

Monte Carlo filters for non-linear state estimation

It is shown through a simple mathematical formula that Monte Carlo computations of Bayesian filter estimates do not demand many repetitions. A general algorithm is constructed, and its performance on difficult problems demonstrated.

Inorganic aluminium-hydrogen ion relationships for acidified streams; the role of water mixing processes

Abstract Streamwaters draining acidified catchments usually exhibit large fluctuations in aluminium and hydrogen ion concentrations which are positively correlated with flow: stormflow waters are mainly derived from waters passing through the upper acidic and aluminium bearing soil zones; baseflow waters are derived from the lower soil/groundwater zones where inorganic reactions prevail and hydrogen ions generated in the upper soil horizons are consumed. In several cases these variations in streamwater chemistry cannot be explained by solubility control of a single mineral phase such as microcrystalline or natural gibbsite. Here, for three such catchments, the controlling mechanisms are explored in terms of both conservative and non-conservative two-component mixing of upper soil and ground waters. For this exercise linear concentration plots are the best tools; the commonly used log-log plots lead to a confounded picture masking important insights.