Steady-state dissolved oxygen model of the Willamette River, Oregon

By Stuart W. McKenzie, Walter G. Hines, David A. Rickert, and Frank A. Rinella

GEOLOGICAL SURVEY CIRCULAR 715-J United States Department of the Interior

FOREWORD

v

Factors for converting English units to the International System of Units (SI) are given below to four significant figures. However, in the text the metric equivalents are shown only to the number of significant figures consistent with the values for the English units.

STEADY-STATE DISSOLVED-OXYGEN MODEL OF THE WILLAMETIE RIVER, OREGON.

The summertime DO (dissolved-oxygen) regimen of the Willamette River, Oregon is presently dominated by basinwide secondary treatment, low-flow augmentation, nitrification, and a benthic-oxygen demand in Portland Harbor. The entire regimen and all sources and sinks of DO were recently described in detail in a companion report (Hines and others, 1977), which is hereafter referred to as Circular 715-1.

Using the information presented in 715-I as a basis, the present report describes a mathematical model that quantitatively simulates the low-flow DO regimen of the Willamette. Discussion focuses on the description, formulation, and testing of the model, referred to hereafter as the WIRQAS (Willamette Intensive River Quality Assessment Study) Model. The final goal of the model is the development of a practical management tool useful for assessing the impacts on river DO of planning and management alternatives. The impact assessment phase of the modeling effort will be subsequently described in

J1 As used here, formulation and testing deal with four major elements of model development:

Before dealing with these elements, it is helpful to introduce the conceptual basis of the WIR-QAS Model. In doing so it is convenient to consider first a general conceptual model of river self-purification processes. Then, as a means for specifying the configuration of the WIRQAS Model, the general model is modified for compatibility with the physical and biochemical characteristics of the Willamette River system.

Because of the technical detail of the following section, some readers may wish to proceed directly to the section entitled "Formulation of the WIRQAS DO Model."

The understanding and explanation of the DO regimen of rivers involves the consideration of several complex physical, chemical, and biological processes. One approach for describing such a system is the development of a conceptual model. In other words, one seeks to formulate an integrated, rational set of concepts that satisfactorily describe the "real" system. Mathematics are used to provide an internally consistent, rigorous definition of the concepts and to allow a quantitative simulation.

Through more than 50 years of empirical observation and thought, a rich conceptual model of the river DO regimen has evolved. This general model incorporates a description of five self-purification processes (Circ. 715-I, Supp. A):

1. Configuration
2. Calibration
3. Verification (validation)
4. Sensitivity analysis
5. Carbonaceous deoxygenation
6. Nitrification
7. Benthic-oxygen demand
8. Plant photosynthesis and respiration
9. Atmospheric reaeration

For purposes of modeling, these processes can be considered as DO sources (producers) and sinks (consumers); the sources being photosynthesis and reaeration, the others being DO sinks.

Based on the need to quantitatively simulate the five self-purification processes, a number of mathematical DO models have been developed. One model, now in widespread use, was originally described by Bella and Dobbins (1968). Their model was based on the classic Streeter-Phelps (1925) equations for carbonaceous deoxygenation and atmospheric reaeration, plus terms for the other DO sources and sinks. The model also includes equations for simulating the transport characteristics of the river, including the inflow and outflow of water, DO, and oxygendemanding materials. The mathematical framework of the Bella-Dobbins model is shown in equation 1:

a(AC) + a(UAC) = j (AE ac) +K A(C -C)

where A = area of stream cross section perpendicu-

c = average DO concentration in cross sec-

u = average cross-sectional velocity in the

E = longitudinal dispersion coefficient, K2 = atmospheric reaeration rate (loge), Cs = oxygen saturation in water at the prevail-

Kl = carbonaceous deoxygenation rate (loge), = BODult concentration (from carbona-

Kn = nitrogenous deoxygenation rate (loge), N = nitrogenous oxygen demand (a function

= oxygen added by photosynthesis per unit

R = oxygen consumed by aquatic plant respi-

B = oxygen demand by benthal deposits per ax ax ax

ceous material) in cross section,

of ammonium- and nitrite-ion concentration) in cross section,

ration per unit area,

J2 Db = oxygen added along the stream by

= time, and x = distance in the longitudinal direction.

In order to obtain values for L and N to use in equation 1 (L and N are constantly undergoing first-order decay along the course of the river in the x-direction), it is necessary to first solve equations 2 and 3:

a(:tL) a(A!ax) + a(~~L) -Kl(AL) + ALa(2)

a(AN) a(AEax) + a(AUN) -K (AN)

where La = rate of BODutt addition along the stream by inflows, Na =rate of addition of nitrogenous-oxygen de-

and all other terms are as defined in equation 1.

The DO model described by equations 1-3 is based upon the idealized concept of a one-dimensional stream. That is, variations in velocity, concentrations, and process-rate coefficients are assumed to occur only in the longitudinal direction (x), and not in the horizontal or vertical directions. Equations 1-3 are derived using the laws of conservation of mass and momentum by performing a mass balance for a time interval, dt, on a stream segment of cross-sectional area, A, and length, dx (see fig. lA). As dt and dx approach infinitesimally small values, the three partial differential equations that describe the temporal and spatial distribution of C, L, N, P, R, B, and Db are obtained.

In many applications, the assumption of a onedimensional stream is reasonable and scientifically sound. This is so because data-averaging techniques can be used to "smooth out" local and short-term nonhomogeneity in the vertical and horizontal dimensions.

The application of equations 1-3 to an actual river situation usually involves a fixed reference frame known as the Eulerian system (fig. lA). With this system, the river is divided into short segments by establishing numerous cross-sectional planes normal to the direction of flow. unit area,

mand along the stream by inflows, AN

a J3 where V = average velocity ~ average time-of-travel Q = streamflow A= cross-sectional area

Consistent with the Velz-Lagrangian system, the WIRQAS Model was applied to the river between RM's 86.5 to 5.0 under conditions of summer low flow. As described elsewhere (Gleeson, 1972; Circular 715-1), no significant DO problems have occurred upstream of RM 86.5, nor have problems been noted at times other than during the summer. RM 5.0 is the approximate location of the lowest DO concentration in the Willamette during low-flow conditions. Below this point, mixing with Columbia River water (Circular 715-1, figs. 21 & 22) causes a rapid increase in DO concentrations.

A key consideration in the configuration of any DO model is the method by which the quantitative definition of streamflow, channel morphology, and water temperature is accomplished. These river characteristics determine the "immediate environment" (Hines and others, 1976) of the river within which the self-purification processes occur and are largely controlled.

For the WIRQAS Model, streamflow data were obtained from direct measurements made routinely at U.S. Geological Survey gaging stations on tributaries and the main-stem Willamette River. (See Circular 715-1, section on "Streamflow.") The Survey streamflow gage at Salem (fig. 2) was used as the reference gage. Flow measured at Salem was routed downstream on the basis of times-of-travel calculated by the volumetric-displacement technique. Measured inflows from tributaries and waste-water outfalls were simply added to the mainstem flow to obtain a cumulative flow at any downstream location. During summer low-flow periods no major diversions occur in the segment of interest, RM 86.5-5.0. Water losses from evaporation, riverto-groundwater seepage, and irrigation are small, and they were considered to be balanced by the small volume of unmeasured surface and ground-water inflows.

J6 Definition of channel geometry was accomplished as follows:

1. In the Tidal Reach (RM's 0-26.5), recently

compiled (1972) channel geometry (width and depth) maps were available from the Portland District, U.S. Army Corps of Engineers. Soundings on these maps are referenced to a specific river-discharge and tidal condition. This facilitated adjustments to obtain channel geometry data consistent with the discharge and tidal conditions encountered during model calibration and verification.

2. In the Newberg Pool (RM's--26.5-52.0), new

channel geometry data were obtained by making cross-sectional traverses in a boat equipped with a recording fathometer. The traverses were made at longitudinal intervals of approximately 0.2 mi during periods of low flow in the summer and early fall of 1973. Auxiliary staff gages were installed to develop stage-discharge ratings.

3. As described in Circular 715-1, the Up-

stream Reach (RM's 52.0-187) is shallow, meandering, and characterized by year-to-year shifts in channel shape. Therefore, for the modeled portion, a detailed definition of channel geometry with the recording fathometer was considered of dubious value. Consequently, time-of-travel values for use in the model were calc~lated on the basis of dye-tracer data reported by Harris (1968). Generalized values for average cross-sectional depth, cross-sectional area, and segment volume were obtained using the continuity equation (equation 7) in conjunction with width measurements made from high-resolution aerial photos taken under known conditions of streamflow.

Once compiled, the channel geometry data for the three reaches were collated so as to define relatively homogeneous 0.2-1.0 mi segments for which representative values of depth, width, and channel volume could be assigned. The averaged values were those actually used in the model for computational purposes. Besides channel geometry data, the location of waste-water outfalls and tributaries was used as a criterion for establishing river segment boundaries. In all, 260 discrete segments were established between RM's 86.5 and 5.0.

Water-temperature data were obtained from measurements made during the course of data

II

collection for model calibration and verification. Average daily temperatures were used in the model as calculated from individual values having a maximum range at any site of ± 3°C.

Calibration is the procedure whereby model parameters are quantified and adjusted so that model outputs (for a specified set of input data such as streamflow, water temperature, and waste-water loads) approximate a set of observed DO and BOD data. The quantification of model parameters and the range within which they can be realistically adjusted should be based primarily on field and laboratory data, an understanding of the particular river system, and sound professional judgment. For the calibration to be credible, it should not be based on arbitrary parameter optimization routines and computerized curve fitting (see Hines and others, 1975). This means that parameter values should be similar to and consistent with (though not necessarily identical to) thoae values calculated f1·om field and laboratory studies of the river system. Further, if adjustments of parameters are necessary to make model outputs approximate observed data, they should be readily explainable.

Model parameters, input data, and other pertinent information related to the calibration of the WIRQAS Model are summarized in table 1. The model parameter values were developed from the results of the synoptic studies reported in Circular 715-1. Specifically, the model calibration involved data on flow, waste-water loading, and measured in-river parameters from the synoptic studies of August 6, 7 and 12-14, 1974. As discussed in Circular 715-1, the 1974 data were used for calibration because the nitrogen and BOD results were of better quality than those obtained in 1973.

Streamflow in the Willamette River was low (approximately 6,760 ft3/s at Salem) and steady during the early-August 1974 calibration period. On the basis of precalibration sampling (see Rickert and others, 1976), BOD, nitrogen, and DO concentrations in the river and waste-water effluents were also stable on a daily average basis.

J8 Using the information in table 1, a model computer run was made to produce a predicted DO profile of the Willamette River between RM's 86.5 and 5.0. The predicted profile is compared in figure 3 with the ranges and averages of the measured calibration data. In general, there is good agreement between the two profiles; the largest discrepancy occurs at RM 72 where the predicted DO concentration is 5 percent lower than the daily average.

A further calibration check was made by comparing results of predicted and measured loads of ultimate BOD (BODuit). As shown in figure 4, the two profiles compare reasonably well, except in the segment between RM's 13 to 7 where measured loads are approximately 27,000 lb/d higher than predicted. As described elsewhere (Circular 715-1, in the section on "Anomalously High BOD in the Tidal Reach") oxygen-demanding benthic materials are suspected as one major cause of this discrepancy.

A third, though somewhat limited, calibration check involved the comparison of predicted and measured nitrogen concentrations (Circular 715- 1, fig. 14) in the zone of active nitrification (RM's 86.5-55.2). As noted in table 1 and explained in

the WIRQAS Model incorporates an effective nitrification rate that does not generate segmentto-segment predictions for nitrate-, nitrite-, and ammonia-N concentrations. However, a predicted ammonia-N concentration can be obtained at RM 55 by flow routing and decaying the cumulative loadings from above this point. On this basis, the WIRQAS Model predicted an ammonia-N concentration of 0.36 mg/L at RM 55, whereas the measured value was 0.22 mg/L. Considering the likelihood of ammonia-N losses to algal assimilation, this is considered a reasonable check.

Table 2 presents a reach-by-reach accounting of changes in the concentration (mg/L) and mass (lb-02/d) of DO in the Willamette during calibration conditions. In terms of oxygen loss, the percentages over the 81.5 mi are nitrification-38 percent, carbonaceous deoxygenation-4 7 percent, and benthic demand-15 percent. All the nitrogenous demand occurs in the Upstream Reach, and all the benthic demand occurs in low- -------------

JlO

er Portland Harbor (RM's 12.8-5.0). In contrast, the carbonaceous demand is spread over the entire 81.5 mi. In assessing the relative importance of carbonaceous deoxygenation, the reader should note (as explained in Circular 715-1) that about one-half of the exerted demand originates from near natural, nonpoint-source loads of tributary streams. Such loads are not amenable to treatment.

Verification, by definition, implies the "proof of truth" of the model. However, Bella (1969) cautioned that model verification should not be thought of in these absolute terms. All models have limitations and specific domains of applicability. Thus, model verification is more realistically described as a means for validating or substantiating the model's predictive power under a specific set of environmental conditions. In practice, verification should involve the use of a calibrated model (that is, the same model parameters developed during calibration) and a new set of observed data. Some of the new data establish the initial and boundary conditions necessary to "start" and "run" the model. The remainder serve as an independent set of observations for comparison with model predictions.

Verification data for the WIRQAS Model were obtained from synoptic studies conducted during a prolonged low-flow period of late July to mid August 1973 (Circular 715-1, fig. 10 and table 4). As was the case for the calibration period, stable hydrologic and waste-water loading conditions made the Velz-Lagrangian modeling approach compatible with its underlying steady-state assumptions.

Table 3 summarizes the model parameters, input data, and other information used in verification of the WIRQAS Model. Note that in keeping with the described requirement for verification, the model parameter values for items 1-5 are identical with those used for calibration (see table 1).

Based on the information in table 3, a predicted DO profile was generated by the WIRQAS Model. The predicted profile is compared in figure 5 with average measured DO values from the synoptic studies of July 24-26 and August 15-18, 1973. The two profiles are in good agreement

J11 throughout the 81.5 mi segment. The largest difference occurs at RM 28.6 where the predicted DO saturation is 4 percent lower than the daily average.

The in-river 1973 data for BODult and ammonia- N were considered too poor to be used as a basis for additional model verification. However, we consider the model to be fully verified for future use by the closeness of fit between the predicted and measured DO profiles (fig. 5).

tered with the 1973 data for BODult and nitrogen.

Sensitivity analysis is concerned with changes in model outputs that result from variations in model parameters and data inputs. In most cases, the primary concern is with the identification of those factors that are most important in controlling model outputs. For example, a pertinent question to ask in the sensitivity analysis of the WIRQAS Model is "What is the impact,·in terms of predicted DO concentrations, if (with all other variables held constant) water temperatures were 3°C higher or lower than those used in calibration?" By inserting the changed values of water temperature into the model and making a run on the computer, one can observe whether the impact on predicted DO concentrations is small or large. If small, the model is said to be "insensitive" to water temperature (at least in the analyzed range). If the impact is large, it suggests that water temperature is an important control of the DO regimen.

Sensitivity analyses such as the one described above have at least two general categories of use. First, they help to identify those factors that deserve most attention in model formulation. This is to say, sensitivity analysis can lead the investigator to spend more time and effort on those data and parameters that are most important to the model's simulatory and predictive capability. Perhaps of equal importance is a second use. Sensitivity analysis can lead to a better recognition of the management alternatives that are most efficient and practical for controlling riverquality problems. Only the first type of sensitivity analysis is addressed here, because a subse- -------------------

J12

ffi 90

A chronic problem with the configuration of river DO models appears to be a failure to develop models that are both simple and conceptually satisfying. In an earlier paper, Hines (Hines and others, 1975) suggests that this situation is at least partly attributable to the proliferation of the "general case" model. That is, in an attempt to make DO models capable of handling all conceivable river conditions (presumably in the name of conceptual satisfaction), complex math-

J15 ematical configurations have been used. Such models are often proposed for steady-state application. However, the conceptual simplicity and explanatory power offered by the steady-state concept has all too often been lost in dealing with the complexity of the "general case" model.

A second, chronic problem with DO models lies in the methods and data that are used for calibration and verification. In applying steady-state models, it has been common practice among modelers having little field experience to

calibrate and (supposedly) verify with data that, even in the most optimistic sense, were not collected during steady-state conditions. This is evident in that many discussions of river DO models deal with steady-state only in the context of the river's transport and waste-loading regimes. Thus, for example, a 2- or 3-day stability in average daily streamflow and waste loads is commonly erroneously cited as proof of a steady-state condition. Worse yet is the case wherein numerous measurements of streamflow and waste loads have been made during a hydrologically variable 1- or 2-month period, and then, averaged and used as data for calibration and verification of a steady-state model. These exam-

pies reflect a lack of fundamental understanding as to what constitutes a steady-state DO regimen.

What does determine a steady-state condition for rivers? In our view, steady state involves nothing less than a short-term ecological stability of the river. In addition to a stable transport and waste-loading regimen, this ecological steady state ~ust reach a day-to-day constancy in biochemical processes and reaction rates at any given cross section. The attainment of such a steady state entails, in turn, an antecedent stability of the river's "immediate environment" (Hines and others, 1976) as reflected primarily by streamflow, water temperature, and channelmorphology conditions. This antecedent constancy is necessary for the river's chemical and biological subsystems to adjust to the surrounding environment-that is, to get "used to" (or to come to a dynamic equilibrium wiih) the immediately surrounding environment.

Without the antecedent stability of the river environment, measurements used for calibration and verification are unlikely to reflect a steady-state DO regimen. Consequently, even if model predictions "fit" the observed calibration or verification data, the model is likely to be determin-

J17 istically erroneous. Invariably, such a model will be a poor explanatory and predictive tool.

The WIRQAS modeling effort was designed to overcome the problems described above. With regard to the problem of extraneous mathematical complexity, simple algorithms were devised. The algorithms incorporate the Velz (1970) bookkeeping-type DO accounting system in conjunction with a Lagrangian moving-reference frame. The resulting configuration is extremely simple, yet applicable to simulation of the low-flow DO regimen of the Willamette River.

To provide reliable data for calibration and verification, a series of intensive field and laboratory studies was conducted during the summers of 1973 and 1974 (Circular 715-1). Importantly, in keeping with the notion of steady state, the two independent sets of data were collected under extended low-flow, high-temperature conditions. During the study periods, the Willamette River DO regimen was in a state of relative ecological stability and, thus, compatible with the underlying assumptions of the steady-state concept. Moreover, DO depletion was maximum during these low-flow, steady-state conditions,

thus making the periods the "critical condition" for basing the design of waste treatment and river-management plans.

Calibration and verification of the WIRQAS DO Model involved comparison of model predictions with measured data. With minor exceptions, good agreement was found between predictions and observations. Agreement was particularly good between predicted and measured percent DO saturation (figs. 3 and 5). Nowhere over the modeled 81.5 mi of river were there differences of more than 5 percent saturation.

Based on the DO calibration and verification results, the WIRQAS Model appears to be a valid mathematical description of the summertime, steady-state DO regimen of the Willamette River between RM's 86.5-5.0.

Sensitivity analysis suggests that the WIR-QAS DO Model is relatively insensitive to changes in water temperature (fig. 8), BOD loading (fig. 10), carbonaceous deoxygenation rate (fig. 11), and nitrification rate (fig. 13). The model is relatively sensitive to changes in streamflow (fig. 6), the initial DO concentration at RM 86.5 (fig. 7), ammonia-N loading upstream of RM 55 (fig. 12), and benthic-oxygen demand in Portland Harbor (fig. 15). Based on

J19 comparative reaeration computations (fig. 9), the model is also sensitive to the method of calculating reaeration. The WIRQAS Model employs the Velz (1970) reaeration calculation method. This method resulted in good agreement between predicted and observed data (figs. 3 and 5), while the other methods shown_ in figure 9 did not. Reasons for the differences in predicted DO profiles based on the various reaeration computation methods await further research.

Based on the results discussed in this report and in Circular 715-1, the WIRQAS DO Model is considered to be a reliable simulatory and predictive tool, subject to the following conditions and limitations:

a:

a:

z

a:

z

Without oxygen demand w

u a:

~flj

o...,.Y.

z

en en J24 J25 Table 5 is an example of the computer printout of the WIRQAS DO Model. The illustrated printout includes 29 columns of information that were used to calibrate the model at the first five river cross sections between RM's 86.5 and 84.0. Columns 1 through 11 together with input coefficients for kr and kn provide the information necessary to initiate and drive the model. Columns

ceous deoxygenation, whereas columns 17-21 summarize similar calculations for nitrification. Columns 22-29 complete the printout by listing reaeration calculations and a summary of DO gains and losses.

To aid the reader, column 1, which shows the section boundary stations, has been included at the left of each part of the table. The reader should note that the first seven columns of the printout includes double spacing for each station, whereas the rest of the columns have single spacing. The double spacing is necessitated by the river segment averaging calculations listed in columns 2, 5, 6, and 7.

The model begins at RM 86.5 and the startup is handled by treating the conditions at this station as those from an inflowing tributary. Values in each column are exactly as observed on the original printout sheets; there has been no rounding to selected significant figures.

A complete explanation of each column is presented on the following pages.

Column 1. STATION is the station location in river miles as measured from the mouth. These values correspond with the Willamette River Mile Index as established by the Hydrology Subcommittee, Columbia Basin Interagency Committee (June, 1963). Column 2. WATER TEMP is water temperature in degrees Celsius. The temperature values are used in adjusting self-purification process rate coefficients. Note that the model calculates and uses an average water temperature for each river segment. Column 3. TIME PASS is the cumulative time-of-passage in days from the first station to the downstream station of interest. Time-of-passage between two successive stations is calculated by the equation: 0.0611(A) (x) (8) . Time of passage (days) = Q ,

A = cross-sectional area (ft2)

x = length of segment (mi)

Q = discharge (ft3/s) Column 4. TRIB DIS is a listing of tributary and waste-water discharges (ft3/s) into Willamette River. The model can use discharge values to the nearest 0.01 ft3/s, whereas the printout values in column 4 are rounded to the nearest whole ft3/s. The value shown, for station 86.50 is the inflowing discharge of the mainstem Willamette River (6,760 ft3/s). The model uses the discharge at Salem as the index flow and routes flow downstream accounting for inflqwing tributary and waste-water discharges. Column 5. EFF DEP is the effective depth (ft) at each cross section. Effective depth is calculated by dividing the cross-sectional area, column 7, by the water-surface width (required as input to the program but not printed). Note that the model calculates and uses an average effective depth for each river segment. Column 6. RIV VOL is the volume of water between stations, in millions of gallons. The river volume may be calculated from

RIV VOL = 0.0394(A)(x) (9)

where A and x are as defined for equation 8.

Note that the model calculates and uses an average volume for each river segment. Column 7. AREA is the cross-sectional area in ft2. Areas were determined by field measurement or from existing channel maps provided by the U.S. Army Corps of Engineers and the U.S. Coast Guard. Note that the model calculates and uses an average area for each river segment. Column 8. IM DEM provides for a listing for inflowing loads of "immediate" oxygen demand (see Velz, 1970) in units of population equivalents. One population equivalent (PE) is defined as

J27 Column 9. DIS BOD is the load, in PE, of the

Column 10. SLUDGE is the oxygen demand, in

Column 11. NBOD is the inflowing nitrogenous

as follows:

NBOD(PE) = (4.33)(160 mg/L)(25.0 ft3/s) (i~~;~)

Column 12. kr is the temperature corrected

Column 13. COD DIS is the inflowing load of No immediate demands occur in the modeled· river segment.

ultimate carbonaceous biochemical-oxygen demand for each inflowing tributary or waste-water discharge. For station 86.50, the tributary discharge is equal to the Willamette in-river load of 363,912 PE. This value is calculated from

PE =(discharge) (BODult concentration)

(conversion factor)

= (6,760 ft3/s) (2.4 mg/L) (1.

PE's, at specific stations due to benthic deposits. Benthic demand was found to be significant only in the Portland Harbor area (not included in table 5).

oxygen demand, in PE's, from each tributary or waste-water discharge. Nitrification occurs only between stations 86.50 and 55.20. The oxygen demand of ammonia is calculated as follows: PE = (unit 0 2 demand of NH4-N) (NH4-N concentration) (discharge) (conversion factor) For example, at station 85.00, the NBOD is

in-river rate of carbonaceous deoxygenation (day-1.) Values of kr at 20°C are input to the model and corrected for actual water temperature by the expression:

where Tis the average temperature between stations as listed in column 2.

calculated by adding the values for IM DEM (column 8) and DIS BOD (column 9). Column 14. COD RESUS is the residual BODult load, in PE's, remaining at each station. COD RES US is equal to the BODult load remaining after the total load at the upstream station (TOT COD, column 15) has been satisfied at the specified deoxygenation rate (kr column

12) for the incremental time-of-passage between successive stations (calculated from column 3). For further details, see Circular 715-1, p. 40.

Column 15. TOT COD is the total BODult load, in PE's, remaining at each station. TOT COD is equal to the residual load remaining in the · river (COD RESUS, column 14) plus the inflowing load (COD DIS, column 13). Column 16. T COD SAST is the cumulative load of satisfied BODult , in PE's. Column 17. kn is the in-river rate of nitrification (day-1) at 20° C. Significant nitrification· occurs only between stations 86.50 and 55.20. During calibration and verification conditions, the average daily water temperatures in this river segment were essentially 20°C; therefore, no temperature corrections were made for kn. Column 18. NOD DIS is the inflowing nitrogenous-oxygen demand, in PE's, from each tributary or waste-water discharge. This column is identical to column 11 (NBOD). The data are repeated here so all computations related to nitrogenous demand appear as a unit in the printout (columns 17-21). . Column 19. NOD RESUS is the residual nitrogenous-oxygen demand, in PE's, remaining at each station. NOD RESUS is equal to the nitrogenous-oxygen demand remaining after the total demand at the upstream station (TOT NOD, column 20) has been satisfied at the specified nitrification rate (kn,column 17) for the incremental time-of-passage between successive stations (calculated from column 3). For further details, see Circular 715-1, p. 42. Colu~n 20. TOT NOD is the total nitrogenous-oxygen demand, in PE's, remaining at each station. TOT NOD is equal to the residual load remaining in the river (NOD RESUS, column

19) plus the inflowing load (NOD DIS, column 18).

Column 21. T NOD SAST is the cumulative load of satisfied nitrogenous-oxygen demand, in PE's. Column 22. TOT SAST is the cumulative total satisfied oxygen demand, BODult and nitrogenous, in PE's. For a specific station, TOT SAST is the sum ofT COD SAST (column 16) plus T NOD SAST (column 21). Column 23. TOT RAST is the cumulative total DO, in PE's, resulting from inflowing tributaries and waste-water discharges. Column 24. PE AT SAT is the amount of DO, in PE's, that would be in the river if the water were oxygen saturated at the temperature listed in column 2. Column 25. NET is the DO, in PE's, remaining after the BODult and nitrogenous demands have been subtracted. NET equals TOT RAST (column 23) minus TOT SAST (column 22). Column 26. REAERATION is the DO added, in PE's, due to atmospheric reaeration within each river segment. Column 27. DO BAL is the amount of oxygen, in PE's, in the river after reaeration has been added. DO BAL equals NET (column 25) plus the cumulative reaeration which is found by summing successive values of REAERA TION (column 26). Column 28. PCT SAT is the DO concentration in percent saturation. PCT SAT equals DO BAL (column 27) divided by PEAT SAT (column

24) times 100.

Column 29. MG/L CONC is DO concentration in mg/L. MG/L CONC is calculated as follows:

For example, at station 86.50 the DO in mg/L is as follows: DO (DO BAL (PE)

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