Ice in the Environment: Proceedings of the 16th IAHR International Symposium on Ice Dunedin, New Zealand, 2nd–6th December 2002 International Association of Hydraulic Engineering and Research

SMALL TEMPORAL SCALE WINTER DISSOLVED OXYGEN PROCESSES

Kathleen D. White1 and Jeffrey P. Laible2

ABSTRACT Diurnal fluctuations of dissolved oxygen (DO), along with changes in river microbiol-ogy during winter, have been observed in an intermittently ice-covered, relatively nutri-ent-rich river in Vermont during two winter seasons. The diurnal cycling of DO that persists during the ice-covered period appears to be related to photosynthetically active radiation (PAR). A finite element model (FEM) based on the analytical expressions for DO concentration developed by Streeter and Phelps (1925) was extended to explore the relationship between DO and PAR. Observed diurnal DO cycling in open water condi-tions on the LaPlatte River was replicated using a model that included the effects of PAR and effects of air temperature, indicting the importance of photosynthetic activity in rivers during winter. The FEM results suggest that the reaeration coefficient Kr is not negligible as reported by several modelers, and probably lies between about 0.5 and 0.75 d-1. INTRODUCTION Dissolved oxygen (DO) is required for aerobic biological processes in rivers. The DO in a river system is consumed in aerobic respiration as the terminal electron acceptor in the oxidation of organic and nitrogenous material and by the oxygen demand exerted by the benthic community. The opposing processes of photosynthesis and respiration often re-sult in a typical diurnal cycle. DO processes in ice-covered rivers have received little attention in part because the saturation concentration of DO in water is inversely related to water temperature. The higher saturation levels in winter due to low water tempera-ture require very high levels of oxygen depletion before the concentration of DO falls to critical levels. However, research has documented the occurrence of wintertime oxygen deficits in ice-covered rivers (Gamble, 1971; McBean et al., 1979; Brekhovskikh and Volpian, 1991; James et al., 1992). Researchers have also reported small-scale diurnal fluctuations of DO during winter in ice-covered rivers (Simonsen and Harremoes, 1978; White and Melloh, 1999). Despite these observations, water quality models neglect the

1 Research Hydraulic Engineer, U.S. Army Engineer Research and Development Center, Cold Re-

gions Research and Engineering Laboratory, 72 Lyme Rd., Hanover, NH 03755-1290, phone 603-646-4187; Kathleen.D.White@erdc.usace.army.mil.

2 Professor, Department of Civil and Environmental Engineering, 217 Votey Hall, University of Vermont, Burlington, VT 05405-0156

effects of reaeration and deoxygenation at the low temperatures occurring during winter, resulting in uncertainty about model results for the winter period. Recent high temporal resolution DO measurements in an intermittently ice-covered river in Vermont during two winter seasons indicates that the diurnal cycling of DO that persists during the ice-covered period appears to be related to photosynthetically active radiation (PAR) (White et al., 2002; White, 2002). These results confirmed observations made earlier in a different Vermont river (White and Melloh, 1999). This paper reports on the use of the high temporal resolution data to explore coefficients of reaeration and deoxygenation used in the numerical modeling of DO. STREETER-PHELPS MODEL Variations of the equations developed by Streeter and Phelps (1925) are commonly used to calculate DO in rivers downstream from wastewater point sources (e.g. Thomann and Mueller, 1987). The three major water quality simulation models used in the United States — the Enhanced Stream Water Quality Model (QUAL2E, Brown and Barnwell, 1987), CE-QUAL-W2 (Cole and Buchak, 1995), and the Water Quality Analysis Simu-lation Program (WASP6, Ambrose et al., 2001) — are all based on modifications of the fundamental equations developed by Streeter and Phelps. The Streeter-Phelps equations can be written as a set of coupled first-order equations that describe the change in oxygen deficit with distance:

0ddLu K Ldx

+ = (1)

( ) 0d r sdCu K L K C Cdx

+ - - = (2)

where u is velocity, L is the biochemical oxygen demand (also known as the ultimate BOD, or BODL), x is distance, Kd is the coefficient defining the rate of deoxygenation, Cs is the saturation concentration of DO, C is the concentration of DO at distance x, and Kr is the coefficient defining the rate of reaeration. Equations (1) and (2) represent coupled first-order equations that are commonly solved by numerical modeling techniques such as the finite difference method or the finite element method. In this case, the finite element method (FEM) was selected. The basic formulation for the coupled first-order equations used to model the Streeter-Phelps equations is:

[ ] [ ]{ } { } { }0cu k c sx

∂∂

Ï ¸ + - =Ì ˝Ó ˛

(3)

where s is a source or sink term (e.g., photosynthesis, sediment oxygen demand, input from tributary). For the FEM, Equations (1) and (2) can be represented in the form of equation (3) as:

0 00 0

0 0d

d r r s

Ku dL LK K K Cu dC CÈ ˘ Ï ¸È ˘Ï ¸ Ï ¸ Ï ¸

+ - =Ì ˝ Ì ˝ Ì ˝ Ì ˝Í ˙Í ˙Î ˚Ó ˛ Î ˚Ó ˛ Ó ˛Ó ˛

(4)

where KrCs represents a source term for oxygen due to reaeration.

The results of the FEM can be compared to an analytical solution derived by assuming, as Streeter and Phelps (1925) did, that the oxygen demand of the organic matter de-creases linearly with time. The analytic equation for the oxygen saturation deficit at any time after the introduction of a given waste is thus given by:

( )00

d r rK t K t K td

r d

K LD e e D eK K

− − −= − +−

(5)

where D0 is the initial dissolved oxygen deficit in the river in mg L-1. White (1999) validated the FEM for one reach of the St. John River, ME, having two subreaches. More recently, data for two reaches of the Ohio River, also having two subreaches, were used to validate the FEM (White, 2002). Following validation, the FEM was used to examine factors contributing to changes in DO concentration. The FEM model results show that varying Kr has a significant impact on estimated DO lev-els (White, 2002). Similar results were obtained by Brekhovskikh and Volpian (1991) and Adrian and Alshawabkeh (1997).

APPLICATION OF FEM TO LAPLATTE RIVER DATA High-temporal resolution water quality data utilized in this paper were collected from late fall 1999 through spring 2000 and again from late fall 2000 through spring 2001 on the LaPlatte River at Hinesburg, VT. Detailed descriptions of the site, instrumentation, data, and analysis, can be found in White (2002). The FEM validation above was car-ried out with spatial data, while application of the model to LaPlatte River data requires that Equation (4) be modified by substitution of dx/dt for u, allowing computation of variables over time rather than distance. This assumption assumes relatively constant velocity. After examination of data from a USGS gage located downstream from Hines-burg at Shelburne Falls, VT, White (2002) concluded that this requirement was met dur-ing the period December through March of water years 2000 and 2001. Most water quality models include specialized sink and source terms to account for the impacts of photosynthesis, respiration, sediment oxygen demand, and other physical processes affecting oxygen levels. However, in practice these sink and source terms are often neglected due to limited data, with the result that all of the physical processes af-fecting dissolved oxygen are included in the reaeration coefficient Kr and deoxygenation coefficient Kd. Reported values for Kd in ice-covered conditions do not vary widely (White, 2002). Because of the general agreement for the order of deoxygenation coeffi-cients, the reaeration coefficient Kr was selected for further examination of the impacts of microbial processes on winter water quality through application of the FEM to LaPlatte River data. While the literature regarding reaeration coefficients is extensive, little research has been done regarding appropriate values at low temperatures in natural rivers. QUAL2E (Brown and Barnwell, 1987), CE-QUAL2-W2 (Cole and Buchak, 1995), and WASP6 (Ambrose et al., 2001) all use temperature adjustment factors to account for decreased biological activity in cold water. QUAL2E allows Kr to be input or to be determined using the equations of O’Connor and Dobbins (1956), Churchill et al. (1962), Owens et al. (1964), and others. WASP6 calculates Kr using the equations of O’Connor and Dob-bins (1956), Churchill et al. (1962), Owens et al. (1964).

Both CE-QUAL-W2 (Cole and Buchak, 1995) and QUAL-2E (Brown and Barnwell, 1987) provide for the presence of an ice cover, however CE-QUAL-W2 apparently uses the ice cover in hydrodynamic calculations and does not directly link it to reaeration. Brown and Barnwell (1987) assume that the ice cover will decrease reaeration and sug-gest that its presence can be accounted for by multiplying Kr by a coefficient between 0.05 and 1.0. Reported reaeration coefficients for ice-covered conditions are summa-rized in Table 1.

Table 1: Summary of reported reaeration coefficients.

Reaeration coefficient Kr (d-1) Source

0.3 Streeter and Phelps (1925)

0 McBean et al. (1979)

0 MacDonald et al. (1989)

0.05 Weslowski ice-covered (1996)

0.2 Weslowski open-water (1996)

0.001 Pietroniro et al. (1998)

0 Brekhovskikh and Volpian (1991) The effects of varying reaeration coefficients can be evaluated by comparing computed DO and observed DO. However, use of a constant Kr in the FEM will not reflect diurnal cycling. Diurnal changes in DO can be accounted for by using some function such as a sine or cosine to drive changes in Kr, an approach used by Adrian and Alshawabkeh (1997). Using a mathematical forcing function may provide good fit, but does not shed light on the physical processes involved. Use of measured data to account for variations in DO would accomplish this. Because the observed changes in DO at the LaPlatte River site are thought to occur as a result of photosynthesis and respiration, PAR and temperature are the likely variables to examine. The diurnal cycling of the measured data clearly shows some relationship between DO and PAR (Figure 1). Correlations between observed variables (White, 2002) indicated that including the effects of PAR when computing DO could reflect the contribution of photosynthetic activity. It appeared most practical to modify the Kr term rather than add an additional source or sink term to equation (4), since changes in the level of reaeration would be the primary result of changes in photosynthesis. After numerical experimentation and comparison to the observed data, a simple linear relationship was chosen to account for these effects in the FEM:

Kpar = αPtl + Kr (6) where Kpar is the reaeration coefficient at time t modified to reflect PAR and α is a coef-ficient describing the relationship between DO and PAR at time t – l (Ptl ) where l is a specified lag time. Based on numerical experiments, the lag time appears to range from

0 for open-water conditions to about 3 hr for late ice-covered period conditions. To ac-count for expected daily fluctuations in BOD, the model assumed a conservative con-stant input of 8 mg L-1, a value selected based on the reported monthly BOD samples of the Hinesburg wastewater treatment plant. Initial values of Kr = 0.3 d-1 and Kd = 0.06 d-1

were selected after reviewing the work of Streeter and Phelps (1925) and McBean et al. (1979). The initial DO level of the model is set to be the same as the observed for that date and time.

Figure 1: Water quality data measurements for winter 1999–2000.

Use of Equation (6) provided acceptable results during the open water periods, but did not mimic the smaller and more random DO fluctuations that occur during the ice-covered periods. After numerical experimentation, Equation (6) was modified to ac-count for air temperature: Kpar = αPtl +βTtl + Kr (7) where β is a coefficient describing the relationship between DO and air temperature at time t–l (Ttl). Results using Equation (7) were improved during the ice-covered period.

For example, agreement between modeled and observed DO is quite good for the late ice-covered period of winter 1999–2000 using Kr = 0.75 d-1, Kd = 0.12 d-1, PAR l = 0.01 d, α = 0.02, β = –0.2, and temperature l = 1 d (Figure 2), especially compared to using a constant value of Kr. The model results indicate that the inclusion of PAR and air temperature in Kr does af-fect computed DO levels in a way that more closely replicates observed diurnal cycling of DO. This is particularly noticeable on 6 and 12 February, when decreases in air tem-perature are followed by relatively large increases in DO in both observed and com-puted DO.

Figure 2: Observed PAR and air temperature and observed vs. computed DO during the late ice-covered period, 1 to 15 February 2000, LaPlatte River, VT. For comparison, DO computed using constant Kr = 0.75 d-1 in Equation (4) is also shown. The coefficients associated with minimum error in applying the model to various peri-ods during the sampling period indicate that a reaeration coefficient of about 0.5d-1 to 0.75 d-1 could be used to model wintertime conditions similar to those observed in the LaPlatte River. This is two to three times the values suggested by Streeter and Phelps (1925) for the Ohio River (average Kr = 0.3) and Weslowski (1996) for open water con-ditions on the Red River of the North near Fargo, ND (average Kr = 0.2). Weslowski found that his model significantly under-predicted DO levels at two locations under ice-covered conditions, and went so far as to suggest that the measurements could be out-liers or simply incorrect. However, the results of this study indicate that for these reaches, his reaeration coefficient (0.05) may have been an order of magnitude too low. CONCLUSIONS The purpose of this study was to investigate riverine DO during winter, particularly the ice-covered period, with emphasis on processes impacting reaeration and deoxygena-tion. Several knowledge gaps regarding these processes in ice-affected rivers exist. For example, the relative impacts of water temperature, photosynthesis, and respiration on

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