Prepared in cooperation with the Bureau of Reclamation

Macrophyte and pH Buffering Updates to the 

Klamath River Water-Quality Model Upstream of 

Keno Dam, Oregon

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2013–5016
Front cover: Photograph showing Jessica Asbill-Case and Garrett Steensland, 

Bureau of Reclamation, examining macrophyte samples from the Link River 

to Keno Dam reach of the Klamath River, Oregon. (Photograph by Bureau of 

Reclamation field crew, 2011.)

Back cover (top left): Photograph of a Curlyleaf pondweed (Potamogeton crispus) 

sample from the Link River to Keno Dam reach of the Klamath River, Oregon.

(Photograph by Bureau of Reclamation field crew, 2011.)

Back cover (top right): Photograph of a Common waterweed (Elodea canadensis) 

sample from the Link River to Keno Dam reach of the Klamath River, Oregon.

(Photograph by Bureau of Reclamation field crew, 2011.)

Back cover (bottom left): Photograph of a Small pondweed (Potamogeton pusillus) 

sample from the Link River to Keno Dam reach of the Klamath River, Oregon.

(Photograph by Bureau of Reclamation field crew, 2011.)

Back cover (bottom right): Photograph of a Coontail (Ceratophyllum demersum) 

sample from the Link River to Keno Dam reach of the Klamath River, Oregon.

(Photograph by Bureau of Reclamation field crew, 2011.)
Macrophyte and pH Buffering Updates to the 

Klamath River Water-Quality Model Upstream of 

Keno Dam, Oregon

By Annett B. Sullivan and Stewart A. Rounds, U.S. Geological Survey; Jessica R. Asbill-Case, 

Bureau of Reclamation; Michael L. Deas, Watercourse Engineering, Inc.

Prepared in cooperation with the Bureau of Reclamation

Scientific Investigations Report 2013–5016

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013

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Suggested citation:

Sullivan, A.B., Rounds, S.A., Asbill-Case, J.R., and Deas, M.L., 2013, Macrophyte and pH buffering updates to the 

Klamath River water-quality model upstream of Keno Dam, Oregon: U.S. Geological Survey Scientific Investigations 

Report 2013-5016, 52 p.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope .......................................................................................................................................3

Macrophytes...................................................................................................................................................3

Field Methods........................................................................................................................................4

Field Results...........................................................................................................................................4

Model Initial Conditions.......................................................................................................................7

Model Rates and Coefficients ............................................................................................................7

Enhanced pH Buffering and Nonconservative Alkalinity........................................................................8

General Alkalinity Equations...............................................................................................................9

Acid Dissociation Chemistry.............................................................................................................10

Final Equation of Alkalinity with Enhanced pH Buffering.............................................................12

Acid Dissociation Constants for Water, Carbonic Acid, Ammonium, and Phosphoric Acid..13

Acid Dissociation Constants and Site Densities for Organic Matter.........................................13

Theoretical Alkalinity Titration Curves ...................................................................................15

Optimization of Organic Matter Parameters .........................................................................16

Recalculation of Boundary Conditions for Total Inorganic Carbon............................................17

Activity Corrections............................................................................................................................20

Nonconservative Alkalinity ...............................................................................................................20

Summary of Updated Model Calibration..................................................................................................21

Acknowledgments.......................................................................................................................................42

Supplementary Material.............................................................................................................................42

References Cited..........................................................................................................................................42

Appendix A. CE-QUAL-W2 Macrophyte Code Changes........................................................................45

Appendix B. CE-QUAL-W2 pH and Alkalinity Code Changes ...............................................................46
iv

Figures

1. Map showing location of the study reach and sampling locations in Link 

River to Keno Dam reach of the Klamath River, Oregon. WWTP, wastewater 

treatment plant .............................................................................. 2

2. Graph showing mid-channel Secchi depth for the June, August, and 

October 2011 macrophyte sampling events in the Link River to Keno Dam 

reach of the Klamath River, Oregon ...................................................... 4

3. Graphs showing estimated dry weight biomass for the most commonly 

identified macrophytes at June, August, and October 2011 sampling events 

in the Link River to Keno Dam reach of the Klamath River, Oregon .................. 6

4. Graph showing a summation of site densities for two hypothetical Gaussian

distributions of pKa values.................................................................. 14

5. Graphs showing example titration curves of four theoretical titration curves 

and measured data from the Link River to Keno Dam reach of the Klamath 

River, Oregon................................................................................. 18

6. Graphs showing modeled macrophyte biomass along the Link River to Keno

Dam reach of the Klamath River, Oregon, on two selected dates ..................... 22

7. Graphs showing modeled daily average dissolved-oxygen production sources

and consumption sinks in the Link River to Keno Dam reach of the Klamath 

River, Oregon, in 2008 ..................................................................... 22

8. Graphs showing modeled and measured pH at the Klamath River, Oregon,

Railroad Bridge site in summer and fall 2007, without and with the new 

enhanced CE-QUAL-W2 pH buffering ................................................... 24

9. Graphs showing modeled and measured pH at the Klamath River, Oregon, 

Keno site in summer and fall 2007,without macrophytes and with macrophytes ... 24

10. Graphs showing measured and modeled hourly pH during calendar years 

2006, 2007, 2008, and 2009 for sites in the Link River to Keno Dam reach of the 

Klamath River, Oregon ..................................................................... 26

11. Graphs showing measured and modeled hourly dissolved-oxygen

concentrations during calendar years2006, 2007, 2008, and 2009 for sites 

in the Link River to Keno Dam reach of the Klamath River, Oregon .................. 30

12. Graphs showing measured and modeled algae, nutrients, organic matter, 

and bottom sediment during calendar years 2006, 2007, 2008, and 2009 for sites 

in the Link River to Keno Dam reach of the Klamath River, Oregon .................. 34
v

Tables

1. Submergent species identified at June 27–July 7, August 15–19, and 

October 11–13, 2011 sampling events in the Link River to Keno Dam reach 

of the upper Klamath River, Oregon ...................................................... 5

2. Macrophyte parameters in the updated water-quality model for the Link 

River to Keno Dam reach of the Klamath River, Oregon .............................. 8

3. Acid dissociation constants for water, carbonic acid, ammonium, and

phosphoric acid used in the model of the Link River to Keno Dam reach 

of the Klamath River, Oregon............................................................... 13

4. Dissolved organic-matter acid dissociation constants and site densities 

for the Link River to Keno Dam reach of the Klamath River, Oregon, resulting 

from two best-fit optimizations of 24 measured alkalinity titration curves............ 17

5. Parameter values changed as a result of calibration updates to the

water-quality model for the Link River to Keno Dam reach of the Klamath 

River, Oregon................................................................................. 21

6. Enhanced pH buffering input parameters in the water-quality model for the 

Link River to Keno Dam reach of the Klamath River, Oregon........................... 21

7. Goodness-of-fit statistics averaged over all calibration sites for the updated

model of the Link River to Keno Dam reach of the Klamath River, Oregon ......... 25
vi

Conversion Factors, Datums, and Abbreviations

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

cubic inches (in.3) 0.01639 liter (L)

SI to Inch/Pound

Multiply By To obtain

micron (μm) 0.00003937 inch (in)

millimeter (mm) 0.03937 inch (in)

meter (m) 3.281 foot (ft) 

square meter (m2) 1,550.0 square inch (in2)

gram (g) 0.03527 ounce, avoirdupois (oz)

kilogram (kg) 2.205 pound avoirdupois (lb)

liter (L) 33.82 ounce, fluid (fl oz)

liter (L) 0.2642 gallon (gal)

milliliter (mL) 0.03382 ounce, fluid (fl oz)

liter (L) 61.02 cubic inch (in3) 

cubic meter (m3) 35.31 cubic foot (ft3)

cubic meter (m3) 264.2 gallon (gal) 

milligram per liter (mg/L) 1.0 parts per million (ppm)

Watt (W) 3.41 British thermal unit per hour (BTU/h)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32.

Concentrations of chemical constituents in water are given either in milligrams per liter (mg/L), 

which is approximately equivalent to parts per million (ppm), or micrograms per liter (μg/L), 

which is approximately equivalent to parts per billion (ppb).

Datums

Elevation refers to distance above the vertical datum. A local vertical datum (UKLVD) is used, 

established by the Bureau of Reclamation. For the purpose of this report, the conversion is 

UKLVD – 1.78 ft = NGVD29.

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).
vii

Abbreviations Ka acid dissociation constant < less than ≤ less than or equal to

DOC dissolved organic carbon > greater than ≥ greater than or equal to

pK

a acid dissociation constant

MAE mean absolute error

POC particulate organic carbon

POM particulate organic matter

SRP soluble reactive phosphorus

TMDL total maximum daily load

USGS U.S. Geological Survey
This page intentionally left blank.
Macrophyte and pH Buffering Updates to the 

Klamath River Water-Quality Model Upstream of 

Keno Dam, Oregon

By Annett B. Sullivan1, Stewart A. Rounds1, Jessica R. Asbill-Case2, and Michael L. Deas3

Abstract

A hydrodynamic, water temperature, and water-quality 

model of the Link River to Keno Dam reach of the upper 

Klamath River was updated to account for macrophytes 

and enhanced pH buffering from dissolved organic matter, 

ammonia, and orthophosphorus. Macrophytes had been 

observed in this reach by field personnel, so macrophyte field 

data were collected in summer and fall (June−October) 2011 

to provide a dataset to guide the inclusion of macrophytes in 

the model. Three types of macrophytes were most common: 

pondweed (Potamogeton species), coontail (Ceratophyllum 

demersum), and common waterweed (Elodea canadensis). 

Pondweed was found throughout the Link River to Keno 

Dam reach in early summer with densities declining by 

mid-summer and fall. Coontail and common waterweed were 

more common in the lower reach near Keno Dam and were 

at highest density in summer. All species were most dense 

in shallow water (less than 2 meters deep) near shore. The 

highest estimated dry weight biomass for any sample during 

the study was 202 grams per square meter for coontail in 

August. Guided by field results, three macrophyte groups were 

incorporated into the CE-QUAL-W2 model for calendar years 

2006–09. The CE-QUAL-W2 model code was adjusted to 

allow the user to initialize macrophyte populations spatially 

across the model grid.

The default CE-QUAL-W2 model includes pH 

buffering by carbonates, but does not include pH buffering 

by organic matter, ammonia, or orthophosphorus. These 

three constituents, especially dissolved organic matter, are 

present in the upper Klamath River at concentrations that 

provide substantial pH buffering capacity. In this study, 

CE-QUAL-W2 was updated to include this enhanced 

buffering capacity in the simulation of pH. Acid dissociation 

constants for ammonium and phosphoric acid were taken 

1

U.S. Geological Survey

2

Bureau of Reclamation

3

Watercourse Engineering, Inc.

from the literature. For dissolved organic matter, the number 

of organic acid groups and each group’s acid dissociation 

constant (Ka) and site density (moles of sites per mole 

of carbon) were derived by fitting a theoretical buffering 

response to measured upper Klamath River alkalinity titration 

curves. The organic matter buffering in the Klamath River 

was modeled with two monoprotic organic acids: carboxylic 

acids with a mean pKa of 5.584 and site density of 0.1925, 

and phenolic organic acids with a mean pKa of 9.594 and 

site density of 0.6466. Total inorganic carbon concentrations 

in the model boundary inputs were recalculated based 

on the new buffering equations. CE-QUAL-W2 was also 

adjusted to allow the simulation of nonconservative alkalinity 

caused by nitrification, denitrification, photosynthesis, and 

respiration. The Klamath River model was recalibrated after 

the macrophyte and pH buffering updates producing improved 

predictions for pH, dissolved oxygen, and particulate carbon.

Introduction

The Klamath River flows about 255 mi (410 km) from 

the outlet of Upper Klamath Lake to the Pacific Ocean 

through southern Oregon and northern California. The first 

1-mile reach downstream of Upper Klamath Lake (from Link 

River Dam to near sampling site 11507501; fig. 1) is named 

Link River; the Klamath River proper begins at the mouth 

of Link River. Stage in the next 20 miles is controlled by 

Keno Dam (fig. 1). Water quality in the Link River to Keno 

Dam reach has been designated as “water quality limited” for 

exceeding ammonia toxicity and dissolved oxygen criteria 

year-round, and pH and chlorophyll a criteria in summer 

(Oregon Department of Environmental Quality, 2007). A Total 

Maximum Daily Load (TMDL) plan for this reach of the 

Klamath River (Oregon Department of Environmental Quality, 

2010) was approved by the U.S. Environmental Protection 

Agency in May 2012. Water temperature allocations have also 

been established for point and nonpoint sources in this reach, 

due to the water temperature TMDL below Keno Dam.
2 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

tac12-0791_fig 01

Ady Canal

West Canal 

A

Canal

Canal

Canal

North

Klamath

Klamath

Strait

River

Wocus

Drainage

Lake

Ewauna

Spring

Lake

UPPER

KLAMATH

LAKE

Round

Lake

140

140

140

39

39

39

66

66

97

97

420451121510000 Sampling site

EXPLANATION

Upper

Klamath

Basin

OREGON

CALIFORNIA

Wocus

Pelican

City

Midland

Keno

Klamath

Falls

Keno 

Dam

Altamont

Keno

11509370

Keno

Outflow

Keno Gage

11509500

KRS 12a

420615121533600

Link River

11507501

Link River

11507500

Pelican

Marina

Klamath Falls

WWTP

Columbia

Forest

Products

South Suburban

WWTP

Miller Island

420853121505500

Railroad Bridge

421209121463000

Klamath Straits

420451121510000

Lost River 

Diversion Channel

421015121471800

Link River

Dam

121°55' 121°50' 121°45'

42°

15'

42°

10'

42°

05'

0 1 2 3 4 5 MILES

0 1 2 3 4 5 KILOMETERS

Figure 1. Location of the study reach and sampling locations in Link River to Keno Dam reach of the Klamath River, Oregon. 

WWTP, wastewater treatment plant.
Macrophytes 3

Water quality in this reach is affected by hydrology, 

atmospheric conditions, tributaries and upstream inputs, 

withdrawals, instream biogeochemistry, and biota. Mechanistic 

computer models such as CE-QUAL-W2 (Cole and Wells, 

2008) include many of these processes that affect water 

quality, and the models are regularly used to provide insights 

on the relative importance, rates, and other characteristics of 

the processes. Models can also be used to make predictions 

about the effects of system changes on water quality. The 

Klamath River TMDL was based in part on a CE-QUAL-W2 

model for the years 2000 and 2002 (Tetra Tech, Inc., 2009; 

Rounds and Sullivan, 2009; Rounds and Sullivan, 2010).

The U.S. Geological Survey (USGS), Bureau of 

Reclamation (Reclamation), and Watercourse Engineering, 

Inc. (Watercourse) initiated a project in 2006 that led to an 

improved understanding of water-quality processes in the 

Link River to Keno Dam reach of the Klamath River. Two 

years of field data were collected in 2007 and 2008, with 

additional experimental work to investigate the characteristics 

of flow, suspended matter settling, and dissolved oxygen 

and organic matter dynamics (Sullivan and others, 2008, 

2009, 2010; Poulson and Sullivan, 2010; Deas and Vaughn, 

2011). Continuous water-quality monitoring at 12 sites by 

Reclamation in 2006–09 contributed valuable time-dense 

data for model calibration and for helping to understand 

water-quality dynamics in the system. A CE-QUAL-W2 

model was constructed for years 2006–09 based on 

these extensive datasets and an improved understanding 

of instream processes (Sullivan and others, 2011). This 

USGS-Watercourse-Reclamation model (henceforth simply 

called the USGS model) was originally configured to simulate 

stage, flow, water velocity, ice cover, water temperature, 

specific conductance, inorganic suspended sediment, three 

algal groups, total nitrogen, total phosphorus, particulate 

nitrogen, particulate carbon, sediment organic matter, 

dissolved oxygen, dissolved organic carbon, and dissolved 

nitrate, ammonia, and orthophosphorus. In CE-QUAL-W2, 

orthophosphorus is used to model bioavailable phosphorus, 

which is often measured as soluble reactive phosphorus (SRP), 

orthophosphate, or dissolved phosphorus.

CE-QUAL-W2 is a two-dimensional model used to 

simulate variability from upstream to downstream and from 

the river surface to the channel bottom. The third dimension, 

from bank to bank, is considered to be well mixed in this 

model. The USGS upper Klamath River model grid consists 

of 102 segments that connect together in the direction of flow; 

segments average 1,009 ft (308 m) in length. Each segment 

represents a cross-sectional shape of the river channel, with 

stacked layers of varying width from the river surface to the 

channel bottom. Vertical layers are 2 ft (0.61 m) in height. The 

model runs on a variable time step that can be as short as one 

second, but produces output for all constituents for all layers 

in each segment at a user-chosen time interval, often hourly.

During the initial construction of the USGS model, the 

hypothesis was developed that macrophytes (rooted aquatic 

plants) may be an important contributor to the nutrient, 

pH, and oxygen cycling in the Klamath River; however, 

no macrophyte field data were available. Further, model 

development suggested that pH buffering by organic matter, 

orthophosphorus, and ammonia, or a combination of these, 

may be important in this reach, but CE-QUAL-W2 did not 

include equations to account for those forms of buffering. 

Thus, the model published in 2011 (Sullivan and others, 2011) 

did not simulate macrophytes and was not calibrated for pH. 

This study describes macrophyte field data and the addition 

of macrophytes to the model, the addition of enhanced pH 

buffering to CE-QUAL-W2, and recalibration of the upper 

Klamath River model for the years 2006–09.

Purpose and Scope

The purpose of this work was to update the USGS 

upper Klamath River model by (1) including macrophytes 

based on data collected in summer and fall (June−October), 

(2) incorporating dissolved organic matter, phosphoric 

acid, and ammonia buffering into the simulation of pH, and 

(3) recalibrating the CE-QUAL-W2 model for 2006–09. The 

updated model can simulate stage, flow, water velocity, ice 

cover, water temperature, specific conductance, inorganic 

suspended sediment, total nitrogen, particulate nitrogen, 

nitrate, ammonia, total phosphorus, orthophosphorus, 

particulate carbon, dissolved organic carbon, organic matter 

in the sediment, three algal groups, three macrophyte groups, 

dissolved oxygen, and pH.

The model covers the 19.6 mi (31.5 km) reach of 

the Klamath River from the end of Link River, near site 

11507501, to Keno Dam. This reach includes several point 

sources as well as inflows from the Klamath Strait Drain and 

seasonal withdrawals or inflows from the Lost River Diversion 

Channel and withdrawals through the North and Ady Canals. 

The purpose of this report is to document the changes to the 

model and illustrate the importance of macrophytes and pH 

buffering in this reach of the Klamath River.

Macrophytes

Macrophytes participate in the cycles of many 

water-quality constituents of surface waters including 

nutrients, organic matter, oxygen, and pH. CE-QUAL-W2 is 

capable of modeling macrophytes, but before incorporating 

them into the Link River to Keno Dam model, it was 

necessary to collect field data on the species present and 

their distribution spatially and temporally. The macrophyte 

field work was completed in summer and fall 2011 by a 

Reclamation field crew.
4 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

Field Methods

Three macrophyte sampling events in the Link River 

to Keno Dam reach of the Klamath River were conducted in 

2011: June 27 to July 7, August 15 to 19, and October 11 to 

13. Cross-section sampling was conducted by boat at mile or 

half-mile intervals. The sampling proceeded from upstream 

to downstream for the first and last sampling periods and 

downstream to upstream for the second sampling period. 

At each location the crew sampled macrophytes at both the 

left and right banks, moving from shore towards mid-channel. 

Samples were taken at 0.4 m, 1.2 m, 2 m, to a maximum 

sampling depth of 2.8 m. In addition to water depth, distance 

from shore was noted. Macrophytes were sampled with a rake 

technique (Rich Miller, Portland State University Center for 

Lakes and Reservoirs, oral commun., May 2011) that had been 

applied successfully in other studies (Kenow and others, 2007; 

Cashatt and Bruce, 2009; Owens and others, 2010; Hauxwell 

and others, 2010). A total of 765 rake samples were collected 

during the three sampling events. Each sample was collected 

by lowering a two-sided rake, with depth markings on the 

handle, to the specified depth, twisting the rake 180 degrees 

and pulling the macrophyte sample up to the surface. Total 

percentage of rake head coverage by the macrophytes was 

estimated (Cashatt and Bruce, 2009). Then macrophytes were 

removed from the rake head and separated into species. The 

approximate percentage of rake head coverage for each species 

was estimated from the total rake head coverage and the 

prevalence of each species. New species were photographed 

when first identified. Three Secchi‐disk readings were taken 

at each cross-section location: one mid-channel, one between 

mid-channel and the left bank, and one between mid-channel 

and the right bank.

The CE-QUAL-W2 model simulates macrophyte 

dry-weight concentrations in the river, so dry weights were 

determined for a subset of samples. First, plant material for an 

individual species at a selected rake sampling was weighed wet, 

with sediment rinsed off and excess water removed. That plant 

material was then air dried for 7 days in the arid Klamath Falls 

climate, weighed again, then placed in a drying oven at 105°C 

for an additional 8 hours and weighed a final time. Most water 

weight was lost during air drying, with total weight decreasing 

an average of 91 percent. Oven drying reduced the weight of the 

air-dried sample only slightly more, for an average total weight 

loss from wet to dry of 92 percent. Numerous small snails were 

dispersed throughout the macrophyte material and were not 

removed during this analysis; the presence of the snails may 

cause the macrophyte material in this study to dry differently 

than pure vegetative material.

A relation between species dry weight and percentage rake 

coverage was developed for a subset of rake samples, including 

data from all species except for filamentous green algae:

2 dry weight 0.2005 rake coverage 0.81 = × = R (1)

with dry weight in grams and rake coverage determined as 

a percentage. This relation was then applied to all samples. 

Dry weights were divided by the sampling rake area to 

obtain estimates of dry weight biomass per square meter 

of sediment surface (grams per square meter; g/m2). This 

macrophyte biomass areal concentration estimate was used to 

put bounds on modeled macrophyte biomass concentrations 

during model calibration. Quantitative macrophyte sampling 

is inherently difficult, due in part to spatial patchiness and 

temporal variability (Mark Sytsma, Portland State University 

Center for Lakes and Reservoirs, oral commun., May 2011). 

Because the data collection occurred during one year, 

inter-annual variability of macrophyte density and species 

distribution is not known at this time.

Field Results

Mid-channel Secchi-disk values were highest in the 

June−July sampling (fig. 2), averaging 1.3 m, compared to 

August (averaging 0.8 m) and October (averaging 0.6 m). 

Water-column dissolved and particulate organic matter and 

algae, which contribute to light extinction, increase from 

spring into summer in this reach (Sullivan and others, 2008, 

2009, 2011).

June

August

October

0.0

0.4

0.8

1.2

1.6

233 238 243 248 253

Mid−channel Secchi depth, in meters

River mile

Keno Dam

Link River

Figure 2. Mid-channel Secchi depth for the June

(June 27–July 7), August (August 15–19), and October

(October 11–13) 2011 macrophyte sampling events 

in the Link River to Keno Dam reach of the Klamath 

River, Oregon.
Macrophytes 5

Macrophyte species identified during the sampling 

trips are shown in table 1. Of these, the four most 

commonly identified species were curlyleaf pondweed 

(Potamogeton crispus), small pondweed (Potamogeton 

pusillus), coontail (Ceratophyllum demersum), and common 

waterweed (Elodea canadensis). Small pondweed was not 

distinguished with certainty from the similar leafy pondweed 

(Potamogeton foliosus); the plant was one of those two 

thin-leafed pondweeds.

Pondweeds were distributed throughout the reach in 

June–July, were less common in August, and rare in October 

(fig. 3). This was expected, since curlyleaf pondweed is a cool 

weather strategist (Nichols and Shaw, 1986). It can overwinter 

as an entire plant, flower in early spring, and begin to decline 

in early summer. The plant is noted to be an indicator species 

of eutrophic conditions (Nichols and Shaw, 1986). Curlyleaf 

pondweed is a non-native species and has some competitive 

advantages over native species in that it begins growing earlier 

in the year and its wider leaves may shade native pondweeds 

(Vanessa Morgan, Portland State Center for Lakes and 

Reservoirs, oral commun., September 2012). Both pondweed 

species were found throughout the reach, but curlyleaf 

pondweed biomass was higher in the upstream part of the Link 

River to Keno Dam reach.

Common waterweed was at its highest density at the 

furthest downstream section of the reach, near Keno Dam 

(fig. 3). Like pondweed, common waterweed can overwinter 

as an entire plant and is an indicator species of eutrophic 

conditions (Nichols and Shaw, 1986). Coontail also was found 

in its highest biomass in the lower part of the study reach 

(fig. 3) and was found in both summer and fall samplings. 

Coontail has no true roots and either floats freely or is 

anchored by modified leaves (Hough and others, 1989). 

Maximum estimated dry weight biomass for any sampled 

species was 202 g/m2 for coontail during the August sampling.

All macrophytes were most common in the shallowest 

near-shore environments, less common at a depth of 2 m, and 

rarely found in deeper waters. This distribution is likely due 

to the high light extinction in the reach; substrate differences 

may also be contributing factors. In the nearby Lost River 

basin, Eilers (2005) found attached macrophytes uncommon 

below 1.5 m and theorized that light extinction was a limiting 

factor for that depth distribution.

Extensive populations of snails, often <1 mm, were 

distributed within the macrophyte plant material and were 

especially notable in August and October. Snail density 

and diversity were both high with Physids, Planorbids, and 

Lymaeids identified within the samples (Robyn Draheim, 

Portland State University Center for Lakes and Reservoirs, 

oral commun., September 2011).

Table 1. Submergent species identified at June 27–July 7, August 15–19, and October 11–13, 2011 

sampling events in the Link River to Keno Dam reach of the upper Klamath River, Oregon.

[Abbreviation: –, not applicable]

Common name Species name Origin

Percent of total

samples with

species present

Autumnal water-starwort Callitriche hermaphroditica native 0.5

Coontail Ceratophyllum demersum native 27.6

Common waterweed Elodea canadensis native 22.7

Yellow water flag Iris pseudacorus non-native 0.1

Common water nymph Najas guadalupensis native 0.3

Water cress Nasturtium officinale native 0.1

Curlyleaf pondweed Potamogeton crispus non-native 21.0

Small pondweed Potamogeton pusillus native 35.7

Hardstem bulrush Schoenoplectus acutus native 0.7

Giant burweed Sparganium eurycarpum native 0.4

Cattail Typha sp. native 0.1

Horned pondweed Zannichelia palustris native 6.4

Filamentous green algae – native 18.7
6 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

tac12-0791_fig 03 Estimated biomass, in grams per square meter Keno Dam

Link River

Keno Dam

Link River

Keno Dam

Link River

0

50

100

150

200

250

0

50

100

150

200

250

0

50

100

150

200

250

233 238 243 248 253 233 238 243 248 253 233 238 243

River mile River mile River mile

248 253

October

June June June

August August August

October October

Coontail Common Waterweed Pondweed

Figure 3. Estimated dry weight biomass for the most commonly identified macrophytes at June (June 27–July 7), August

(August 15–19), and October (October 11–13) 2011 sampling events in the Link River to Keno Dam reach of the Klamath 

River, Oregon.
Macrophytes 7

Model Initial Conditions

The default implementation of CE-QUAL-W2, 

version 3.6, initializes each macrophyte species homogenously 

across the reach, giving the same density to all cells in 

the grid. However, field results showed distinct trends in 

the distribution of macrophytes both longitudinally along 

the river and with depth. The longitudinal spatial trends 

probably persist for more than a year, given that some of 

the macrophyte species observed in the Klamath River 

can overwinter as entire plants and propagation can occur 

from existing stem fragments (Nichols and Shaw, 1986). 

The CE-QUAL-W2 macrophyte code was changed to give 

the user the option to initialize macrophyte populations 

with a nonuniform longitudinal and vertical distribution 

(appendix A). Using this new capability, all cells were 

initialized on January 1 with a small population of each 

species, and then selected cells were initialized with higher 

density. Pondweed was initialized with higher density across 

all model segments at shallow depths <2 m. Coontail was 

initialized with higher density at shallow depths in model 

segments 65 to 102 (just upstream of the Klamath Strait 

Drain inflow [segment 69] to Keno Dam [segment 102]). 

Common waterweed (Elodea canadensis) was initialized 

at higher densities at shallow depths in segments 86 to 102 

(downstream of the KRS12a monitoring site [segment 78] to 

Keno Dam). After this initialization on day 1, macrophytes 

were simulated according to the macrophyte model parameters 

and local conditions.

Model Rates and Coefficients

The CE-QUAL-W2 macrophyte algorithms consist of 

one section that simulates water-quality effects and another 

that simulates hydrodynamic effects. Because hydrodynamics 

were already simulated well by the original model (Sullivan 

and others, 2011), macrophyte hydrodynamic effects were 

turned off in the revised upper Klamath River model through 

a choice of values for the model parameters CDDRAG, DWV, 

and ANORM. The water-quality effects of macrophytes 

were included in the updated model. The model can simulate 

multiple submerged species of macrophytes. Based on results 

from the field sampling, the three most prevalent macrophyte 

groups were incorporated into the upper Klamath River model:

1. Pondweeds

2. Coontail

3. Common waterweed

Macrophyte growth, respiration, and mortality/excretion 

are simulated by CE-QUAL-W2. Growth is from the channel 

bottom upwards through model layers and can be limited 

by light, water temperature, carbon dioxide, ammonia, and 

orthophosphorus. Nutrients can be obtained from the water 

column and from the sediment; the fraction obtained from the 

sediment is set by the user. When nutrients are obtained from 

the sediment, that nutrient supply is assumed to be infinite. 

While CE-QUAL-W2 models the growth and water-quality 

effects of macrophytes well, it is important to remember 

that some macrophtye ecological effects, such as possible 

inhibitory effects on algal growth (Koerner and Nicklisch, 

2002), are not yet coded into the model.

Rates and coefficients are required for each macrophyte 

group (table 2). Default CE-QUAL-W2 rates were modified as 

guided by the characteristics of the species in each group. For 

instance, the temperature parameters for the pondweed group 

were adjusted so that maximum growth rates were during 

spring and early summer, with reduced growth in mid-summer 

to match the field observation that pondweed density is 

highest early in the year and declines in summer. Macrophyte 

senescence is not modeled directly by CE-QUAL-W2, but 

adjustment of temperature parameters that are tied to mortality 

can help to simulate such seasonal patterns. Light saturation 

parameters were reduced from the default values in order 

to allow for the growth of macrophytes in this light-limited 

reach of the Klamath River. Macrophytes can adapt to low 

light conditions by changing their respiration, photosynthetic 

pigments, and morphology (Barko and Smart, 1981; Barko 

and others, 1981). The macrophyte respiration oxygen 

stoichiometry was increased to 1.5 from the default 1.1 to 

account for respiration from snails (found densely within 

macrophytes), which was not modeled separately. Because 

coontail does not have true roots, its parameters were set so 

that all nutrients were obtained from the water column only; 

the other two groups were able to obtain nutrients from both 

the sediment and the water column. Macrophyte growth was 

not limited by nutrients when the half-saturation constants 

for nutrient-limited growth were set to zero; other studies and 

macrophyte models have noted that growth is limited more 

by light and temperature than by nutrients (Barko and Smart, 

1981; Berger and Wells, 2008).
8 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

Enhanced pH Buffering and 

Nonconservative Alkalinity

In most freshwater systems, alkalinity is dominated 

by bicarbonate and carbonate; other constituents are either 

unimportant or have only a minor effect on alkalinity and 

the shape of the alkalinity titration curve (Hem, 1985; 

Stumm and Morgan, 1996; Rounds, 2006). In some systems, 

however, other constituents such as ammonia, organic matter, 

phosphoric acid, silicic acid, and boric acid, depending on 

their concentration, can have substantive acid/base properties. 

None of these other constituents were integrated into the 

default equations that the unmodified CE-QUAL-W2 model 

uses to calculate pH. Although neglecting such effects is 

appropriate for many natural waters, that approach may 

lead to significant errors in the prediction of pH under 

certain conditions.

Dissolved organic matter, ammonia, and orthophosphorus 

at times are present in sufficiently large concentrations in the 

upper Klamath River to provide a substantial pH buffering 

capacity. For the purpose of modeling acid/base behavior, it 

was assumed that the orthophosphorus measured in the river 

could be represented by phosphoric acid and its conjugate 

bases. The necessity to include organic matter, ammonia, and 

phosphoric acid in the CE-QUAL-W2 pH equations and code 

was noted during the initial construction and calibration of 

the USGS upper Klamath River model (Sullivan and others, 

2011), which recommended inclusion of these factors before 

pH calibration could be completed. Thus in this study, pH 

buffering effects of organic matter, ammonia, and phosphoric 

acid were incorporated into CE-QUAL-W2 for use in the 

upper Klamath River model. This required a review of the 

literature and modification of the CE-QUAL-W2 source code. 

Source code changes are documented in appendix B.

Table 2. Macrophyte parameters in the updated water-quality model for the Link River to Keno Dam reach of the Klamath River, 

Oregon.

[Abbreviations: °C, degrees Celsius; g/g, gram per gram; m2/g, square meter per gram; g/m3, gram per cubic meter; 1/day, per day; POM, particulate organic 

matter; W/m2, Watt per square meter]

Parameter Pondweed Coontail Common 

waterweed Description

EXM 0.005 0.005 0.005 Light extinction due to macrophytes, m2/g

MG 0.28 0.37 0.31 Maximum macrophyte growth rate, 1/day

MR 0.07 0.09 0.09 Maximum macrophyte respiration rate, 1/day

MM 0.06 0.07 0.06 Maximum macrophyte mortality rate, 1/day

MSAT 6 3 7 Light saturation intensity at maximum photosynthetic rate, W/m2

MHSP 0.0 0.0 0.0 Macrophyte half-saturation for phosphorus limited growth, g/m3

MHSN 0.0 0.0 0.0 Macrophyte half-saturation for nitrogen limited growth, g/m3

MHSC 0.0 0.0 0.0 Macrophyte half-saturation for carbon limited growth, g/m3

MPOM 0.7 0.7 0.7 Fraction of macrophyte biomass converted to POM when macrophytes die

LRPMAC 0.2 0.2 0.2 Fraction of POM which originates as dead macrophytes becoming labile POM

PSED 0.8 0.0 0.8 Fraction of phosphorus uptake by macrophytes obtained from sediments

NSED 0.8 0.0 0.8 Fraction of nitrogen uptake by macrophytes obtained from sediments

MBMP 40 40 40 Threshold macrophyte concentration for which growth is moved to the above layer, g/m3

MMAX 108 108 108 Maximum macrophyte concentration, g/m3

CDDRAG 0.0 0.0 0.0 Macrophyte drag coefficient

MT1 9 14 14 Lower temperature parameter for rising rate function, °C

MT2 15 24 24 Upper temperature parameter for rising rate function, °C

MT3 19 27 27 Lower temperature parameter for falling rate function, °C

MT4 26 35 35 Upper temperature parameter for falling rate function, °C

MK1 0.05 0.05 0.05 Fraction of rate at MT1

MK2 0.99 0.99 0.99 Fraction of rate at MT2

MK3 0.99 0.99 0.99 Fraction of rate at MT3

MK4 0.10 0.01 0.01 Fraction of rate at MT4

MP 0.004 0.004 0.004 Stoichiometric equivalent between phosphorus and biomass, g/g

MN 0.054 0.054 0.054 Stoichiometric equivalent between nitrogen and biomass, g/g

MC 0.50 0.52 0.50 Stoichiometric equivalent between carbon and biomass, g/g

O2MR 1.5 1.5 1.5 Oxygen stoichiometry for macrophyte respiration

O2MG 1.4 1.4 1.4 Oxygen stoichiometry for macrophyte primary production
Enhanced pH Buffering and Nonconservative Alkalinity 9

In addition, previous versions of CE-QUAL-W2 have 

assumed that alkalinity is largely unaffected by chemical and 

biological reactions and responds only to changes in inputs 

and transport. While alkalinity is largely a conservative 

quantity, it is not entirely conservative. Reactions such 

as ammonia nitrification and nitrate denitrification, as 

well as photosynthesis and respiration, can have small 

effects on alkalinity. As a result of changes made to this 

version of CE-QUAL-W2, the user is allowed to specify 

whether alkalinity is to be simulated as a conservative or a 

nonconservative quantity. 

General Alkalinity Equations

Alkalinity is a measure of the amount of base that is 

present in a system relative to a reference solution of carbon 

dioxide in water. Alkalinity typically is measured through an 

acidimetric titration of a water sample and subsequent analysis 

to determine the final equivalence point (see Rounds, 2006, 

for USGS methods). Alkalinity can be divided into several 

components, depending on which acid/base constituents are 

included in its computation:

carb am OM

c

P

am

P

arb is the baseline alkalinity due to carbonic

acid species and water,

Alk Alk Alk Alk Alk

whe

is the a

re

Alk is the total sampl

lkalinity due to ammoni

e

a

 alkalinity,

Alk

A ,

is the alkalinit

lk

Alk y

= + + + +...

AlkOM

refers to

 due to phosph

 alkalinity fr

oric

acid species,

is the

om other species at low

 alkalinity due t

concentration and

o organic matter, a

 not considered h

nd

ere.

...

(2)

The alkalinity due to carbonic acid and water is 

straightforward to compute because alkalinity is defined as the 

excess base relative to a solution of carbon dioxide in water:

2 Alk [HCO ] 2[CO ] [O carb 3 3 H H ] ] [ − − −+ =++ − (3)

where the square brackets indicate concentrations of the 

various species in moles per liter, and alkalinity is in units of 

equivalents per liter. The derivation of the above equation can 

be found in many aquatic chemistry textbooks (Pankow, 1991; 

Stumm and Morgan, 1996; Drever, 1997). For ammonia, 

because the transition between the acid form (ammonium, 

NH 4

+ ) and the base form (NH3) occurs at a pH of about 

9.3, and because the final equivalence point of an alkalinity 

titration typically occurs below a pH of 5, any ammonia 

that is present in the sample will be titrated with acid 

and included in the measured alkalinity, resulting in the 

following contribution:

Alk [NH ] am 3 = (4)

 Phosphoric acid (H3PO4) is a triprotic acid that can 

exist in four forms, depending on the pH, if the various 

polyphosphate structures are neglected. When considering 

how to account for these species in an alkalinity computation, 

determining which of these species predominate at the pH 

of the final equivalence point of an alkalinity titration is 

necessary. Because the first and second acid dissociations of 

phosphoric acid occur near pH 2.1 and 7.2, it is reasonable 

to assume that H2PO 4

− is by far the predominant form of 

phosphoric acid present at the end of an alkalinity titration, 

which typically is in the pH range of 5.5–4.2; therefore, the 

contribution of these species to a measured alkalinity is:

3

2 3 Alk [HPO 2[PO [H P P4 4 4 ] ] ] O − − = +− (5)

Finally, the contributions of organic matter to alkalinity 

must be included. This is not straightforward because natural 

organic matter consists of large, complex, and largely 

uncharacterized chemical structures that have multiple acid/

base groups, including a range of carboxylic and phenolic 

groups of varying acidity. Many researchers have studied the 

acid/base properties of dissolved organic matter and found 

that those properties, while not characterized exactly, can be 

approximately represented through the use of a mixture of 

multiple simple acids or a distribution of acidities (Perdue and 

others, 1984; Gherini and others, 1985; Bonn and Fish, 1991; 

Tipping, 1994). However, many natural organic acids have 

acidities such that the acid group either would not be titrated 

or would only be partially titrated in a typical alkalinity 

titration. This complication can be resolved by assuming that 

the chemistry of carbonic acid dominates the sample near the 

final equivalence point, despite the presence of other acid/base 

species, and thereby is the predominant factor determining the 

equivalence point of the titration. Historically, many alkalinity 

titrations were deemed to be complete (at the equivalence 

point) when the sample had been titrated to a pH of 4.5. 

While this fixed-endpoint technique is no longer the primary 

method used by many organizations such as the USGS, it 

remains true that titrations of natural water samples typically 

result in an equivalence point in the pH range of 4.2–5.5. 
10 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

For all but the most dilute samples, the use of a pH 4.5 

equivalence point normally results in only small percentage 

errors in the computed sample alkalinity. Assuming a pH 

4.5 equivalence point also greatly simplifies the task of 

determining the contribution of organic matter to alkalinity:

( ) a n

OM i sample pH i pH 4.5

1

a

i sample pH

i pH 4.5

[A ] [A ]

[A ] is the concentration of the base form of 

a generic a

Alk

wh

cid (HA) at the sample pH, 

and,

[A ] is the 

ere

n is the number of simulated acid grou s,

c

p

i

− −

=

=

−

−

=

= ∑ −

oncentration that would occur at

 a pH of 4.5

(6)

This concentration difference represents the amount of 

these bases that would be titrated in an alkalinity titration if 

that titration were terminated at pH 4.5, and therefore it is a 

reasonable estimate of the contribution of these acid groups to 

the sample alkalinity.

Putting all of these terms together, the sample alkalinity 

can be represented as

 

( ) a

2

3 3 3

2 3

4 4 34

n

i i pH 4.5

1

Alk [ HCO 2[CO [OH [H [NH

[HPO 2[PO H PO

[A

] ] ]] ]

]

[

][ ]

] ] A

i

− − −+

− −

− −

=

=

= + + −+

+ +

−

−

+∑

(7)

Acid Dissociation Chemistry

The alkalinity equation (7) can be written only 

as a function of acid dissociation constants and a few 

concentrations that are simulated by the CE-QUAL-W2 

model. Consider a single monoprotic acid that dissociates and 

reassociates in the following reaction:

HA H A + −  + (8)

The acid dissociation constant for this reaction is defined as:

a

a

{

is the acid dissociation constant, and the

curly braces indicate the "activity" of

the various species i

{H }{

n mo

A } K

HA}

where

K

les per liter.

+ −

= (9)

The activity of a species is approximately the same as its 

concentration in dilute freshwater samples. Activity corrections 

for more saline water can be handled through the definition of a 

mixed acid dissociation constant:

HA

HA

A

A

'

a a

is the activity coefficient for HA, and 

is the ac

{H }[A ] K K

[

tivity co

HA]

whe

efficient

r

 . Ao

e

− f r 

−

+ −

−

γ = = γ

γ

γ

(10)

Knowing the value of the acid dissociation constant allows 

the concentration of A- to be written as a function of the total 

concentration of the acid and base forms of this constituent:

'

a T T '

a

K [A ] A where A [A ]

{H }

A

K

[H ] − −

+ = = +

+

(11)

This equation can be rearranged after realizing that, just as 

pH = –log10{H +} and {H+}=10–pH,

( ) '

a ' '' pK

a 10 a a pK log K and K 10− = − = (12)

The concentration of A– then can be written in terms of pH and 

the acid group’s pKꞌa:

'

a

'

a T TT ' (pK pH) a

'

a

K 1 1 [A ] A A A

{H } K {H } 1 10 1

K

−

+ + − = = = + + +

    (13)

For organic matter that is represented as a mixture of 

monoprotic acids, this representation is particularly useful 

because it can be evaluated easily for both the sample pH and 

a pH of 4.5, which is the assumed pH of the endpoint of the 

alkalinity titration. 

For a diprotic acid such as carbonic acid, it is relatively 

simple to define similar functions. The total inorganic carbon 

concentration is given by:

* 2 C [H CO [HCO [CO T 23 3 3 ] ]] − − = ++ (14)

where the first term includes carbonic acid as well as dissolved 

carbon dioxide:

*

2 3 2 3 2 (aq) [H CO [H CO [CO ] ]] = + (15)

Mass balances as well as use of the acid dissociation constants 

reveal that:
Enhanced pH Buffering and Nonconservative Alkalinity 11

2 *

23 T 2 ' ''

1 12

{H } [H CO C

{H } K {H } K K

]

+

+ + = + +

(16)

'

1

3 T 2 ' ''

1 12

K {H } [HCO C

{H } K {H } K

]

K

+ −

+ + = + +

(17)

' ' 2 1 2

3 T 2 ' ''

1 12

K K [CO C

{H } K {H

]

} KK

−

+ + = + +

(18)

where the acid dissociation constants of carbonic acid are given by:

*

2 3

3

' 3 3 H CO

1 11 * *

2 3 HCO 2 3

{H }[HCO {H }{HCO K K where K

[H C

] }

O ] − { } H CO

+ − γ + −

= = = γ (19)

3

2

3

2 2 ' 3 3 HCO

2 22

3 3 CO

{ }[ ] H CO { }{ } H CO K K where 

[ ]

K

HCO {HCO }

−

−

+ − + −

− −

γ = = = γ (20)

Similar relations can be written for ammonia:

'

am 3 T ' T 4 3

am

K

[NH N where N [NH [NH

{H }

]

K

] ] +

+ = = +

+

(21)

NH4

NH3

' 3 3 am am am

4 4

{H }[NH ] {H NH } K }{

[ ]

K where K

NH { } NH

+ + +

+ +

γ

= = = γ (22)

For phosphoric acid, the relevant equations are:

2 3

T 34 24 4 4 P [H PO ] [H PO [HPO [PO ] ] ] − −− =+++ (23)

3

34 T 3 ' 2 '' '' '

P1 P1 P2 P1 P2 P3

{H } [H PO P

{H } K {H } K K {H } K K K

]

+

++ + = ++ +

(24)

' 2

P1

24 T 3 ' +2 ' ' ' ' '

P1 P1 P2 P1 P2 P3

K {H } [H PO P

{H } K {H } K K {H } K K K

]

+ −

+ + = ++ +

(25)

' ' 2 P1 P2

4 T 3 ' 2 '' '' '

P1 P1 P2 P1 P2 P3

K K {H } [HPO P

{H } K {H } K K {H } K K

]

K

+ −

++ + = ++ +

(26)
12 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

'' ' 3 P1 P2 P3

4 T 3 ' 2 '' '''

P1 P1 P2 P1 P2 P3

KK K [PO P

{H } K {H } K K {H } K K K

] −

++ + = ++ +

(27)

3 4

2 4

' 2 4 H PO 2 4

P1 P1 P1

3 4 H PO 3 4

{H }[H PO ] {H }{H PO } K K where K

[H PO ] − {H PO }

+ − + − γ = = = γ

(28)

2 4

2

4

2 2 ' 4 4 H PO

P2 P2 P2

2 4 HPO 2 4

{H }[HPO ] {H }{HPO } K K where K

[H PO ] {H PO }

−

−

+ − + −

− −

γ = = = γ (29)

2

4

3

4

3 3 ' 4 4 HPO

P3 P3 P3 2 2

4 4 PO

{H }[PO ] {H }{PO } K K where K

[HPO ] {HPO }

−

−

+ − + −

− −

γ = = = γ (30)

Finally, for water the acid dissociation constant and relevant equations are:

' w w w OH

K K {H }[OH ] where K {H }{OH } −

+ − + − = = = γ (31)

'

w

H

K {H } [OH and [H {H } ] ] +

+ − +

+ = = γ (32)

Final Equation of Alkalinity with Enhanced pH Buffering

Substituting relations for the various species concentrations into the master equation for 

sample alkalinity results in the following equation: 

a

' '

a a i i

' ' ' ' '

1 12 w am T T 2 ' '' + '

1 1 2 H am

' ' ''' 3

P1 P2 P1 P2 P3

T 3 ' 2 '' '''

P1 P1 P2 P1 P2 P3

n

T (pK pH) (pK 4.5 1

K {H } 2K K K K {H } Alk C N

{H } K {H } K K {H } {H } K

K K {H } 2K K K {H } P

{H } K {H } K K {H } K K K

1 1 A

1 10 1 10

i

i

+

+ +

+ + +

+ +

++ +

− − =

+ = +−+

+ + γ +

  + −

+  

  ++ +

+δ −

+ +

∑ )

T

where

A

values represent the site 

is the total conce

density for acid g

ntration of organic carbon in moles 

roup in units of moles of 

acid gr

per liter, 

oups per mole of carbon

an

.

d

i i

   

 

δ

(33)

Without the enhanced buffering by ammonia, phosphoric acid, and organic matter, the equation 

would be far simpler, including only the terms before NT.
Enhanced pH Buffering and Nonconservative Alkalinity 13

Acid Dissociation Constants for Water, Carbonic 

Acid, Ammonium, and Phosphoric Acid

The acid dissociation constants for water, carbonic 

acid, ammonium, and phosphoric acid can be represented as 

a function of water temperature according to the following 

equation:

( ) ( ) 3 5

10 1 2 4 10 2 log K T log T T T

where

T is the absolute water temperature in kelvin

(T t( C) 273.15), and

the coefficients are given by the value

table 3

s in

.

°

a a

=+ + + + aa a

= +

(34)

These equations generally predict the values of the various 

acid dissociation constants to within at least three significant 

digits relative to published measurements.

Acid Dissociation Constants and Site Densities 

for Organic Matter

When using the enhanced pH buffering modifications 

to CE-QUAL-W2 for organic matter, the model requires 

the user to provide the number of acid groups (na) used to 

represent the acid/base properties of the organic matter, the 

site density for each of those groups, and their pK values. 

Table 3. Acid dissociation constants for water, carbonic acid, ammonium, and phosphoric acid used in the model of the Link River to 

Keno Dam reach of the Klamath River, Oregon.

Acid 

dissociation 

constant

Coefficient

Reference

a1 a2 a3 a4 a5

Kw -283.971 -0.05069842 13,323.0 102.24447 -1,119,669.0 Stumm and Morgan (1996)

K1 -356.3094 -0.06091964 21,834.37 126.8339 -1,684,915 Stumm and Morgan (1996)

K2 -107.8871 -0.03252849 5,151.79 38.92561 -563,713.9 Stumm and Morgan (1996)

Kam -0.09018 0 -2,729.92 0 0 Emerson and others (1975)

KP1 4.5535 -0.013486 -799.31 0 0 Bates (1951)

KP2 5.3541 -0.019840 -1,979.5 0 0 Bates and Acree (1943)

KP3 -12.38 0 0 0 0 Dean (1985); KP3 without temperature dependence

The user can specify either an explicit mixture of monoprotic 

acids, or a Gaussian distribution of monoprotic acids that are 

characterized by a mean pK value and a standard deviation 

around that mean. The input options are described with the 

code modifications in appendix B.

If the user specifies that a distribution of organic acid 

groups is to be used, then the model interprets the number of 

acid groups as the number of distributions to simulate. For 

example, the user could specify two groups, where one group 

is used to represent carboxylic acids with a mean pK of 4.5 

and a standard deviation around that mean of 1.2, and a second 

group to represent phenolic groups with a mean pK of 9.6 and 

a standard deviation around that mean of 1.0. The model then 

constructs Gaussian distributions of those pK values from 

0 to 14 and sums them together to assign a distribution of site 

densities. A Gaussian distribution of pK values with a mean μ 

and standard deviation σ is defined by the following equation:

( )2

j

j 2

j

j

is the fraction of organic matter ligands

occurring in the i

1 pK

dpK 2 2

where

dpK and

characterized by an acid dissociation

constant pK centered in the inter

nterval 

val

of

 dp . K

f exp

f

  − μ   = −  σπ σ    

(35)
14 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

The model truncates this distribution by considering 

27 pKj values from 0.5 to 13.5 at intervals of 0.5. To account 

for the truncation, the above equation is normalized such that:

( )

( )

( )

( )

2

j

2

j 2

n

n 2

2

j

2

2

n

n 2

n

1 pK dpK 2 2

1 pK dpK 2 2

pK

2

pK

2

where

n goes from 1 to 27, and the values range

from 0.5 to 13.5 at inte

 pK

exp

f

exp

exp

exp

  − μ   − σπ σ       =     − μ     − σπ σ      

  − μ   −

  σ     =     − μ     −

  σ    

∑

∑

rvals of 0.5.

(36)

A truncated Gaussian distribution of these fractions is 

computed for each of the user-defined distributions (i=1 to 

na), and those distributions are then summed to determine the 

final site density for the 27 simulated pKj values (fig. 4). The 

site density for each of the 27 acid groups, therefore, is:

δ δ δ

μ

σ

j

n

j

n

j i

i

2

n

n

a a

pK

pK

= =

−

( ) − 



















− = =

∑ ∑

∑ i

i

i

i f

exp

exp

1 1

2

2

 ( ) −



































































μ

σ

i

i

2 2

2 (37)

Sum of two distributions

Carboxyl groups

Phenolic groups

0

0.005

0.010

0.015

0.020

0.025

0.51.01.52.02.53.03.54.04.55.05.56.06.57.07.58.08.59.09.5

10.010.511.011.512.012.513.013.5

Site density, in moles of acid groups per mole of carbon 

pKa

Figure 4. Summation of site densities for two hypothetical Gaussian distributions of pKa values. 
Enhanced pH Buffering and Nonconservative Alkalinity 15

Theoretical Alkalinity Titration Curves

Theoretical alkalinity titration curves can be compared to measured titration curves to derive the number of organic acid 

groups and their site density and pKa values for use as model parameters. During an acidimetric titration, small increments 

of a known concentration of acid are added to the sample, and the pH after each addition is recorded. Each increment of acid 

decreases the alkalinity of the original sample until it becomes zero at the final equivalence point. A simple mass balance 

indicates that: 

 o o ta t

t o

V Alk V C Alk 

(V V )

− = +

 (38)

t

t

o

a

o

is the alkalinity at any time during the titration,

is the original sample alkalinity,

is the concentration (normality) of the acid titrant,

is the original sample volume, and

where

Alk

Alk

V is t

C

V

he total volume of acid added at any point during the titration.

This equation can be combined with the equation for alkalinity above, using an assumption that the acid titrant does not 

include any carbonates, phosphates, ammonium, or organic matter, and then solved for the volume of acid added as a function of 

pH to produce a theoretical titration curve:

 o o

o o

' ' ' ' '

o 1 12 w am t ' o T 2 ' '' T '

w 1 1 2 H am a H

' ' ''' 3 n

P1 P2 P1 P2 P3

T T 3 ' 2 '' '''

P1 P1 P2 P1 P2 P3 1

V K {H } 2K K K K {H } V Alk C N

K {H } {H } K {H } K K {H } {H } K C

{H }

K K {H } 2K K K {H } P A

{H } K {H } K K {H } K K K i

+

+

+ +

+ ++ + +

+

+ +

++ + =

  + = −   −+−

  + + γ + + −

γ

  + − − −  

  ++ +

a

' '

a a i i (pK pH) (pK 4.5)

1 1

1 10 1 10

i − −

 

δ −  

  + +

∑

 (39) 

where the “o” subscripts on Alk, CT, NT, PT, and AT indicate the concentrations in the original sample prior to the beginning of 

the titration.

If the concentrations of ammonia-plus-ammonium (NT), soluble reactive phosphorus (PT), and organic carbon (AT) in the 

original sample are known, then this theoretical titration curve can be used to fit a set of measured titration curves to determine 

the set of na, δi, and pKa values that best represent the contributions of organic matter to the sample alkalinity.

' K1

{H }+

               

' K1

{H }+

               
16 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

Optimization of Organic Matter Parameters

An optimization program was written to find the set 

of site density and pK values for dissolved organic matter 

that provide the best fit for a set of 24 experimentally 

measured titration curves for water samples (0.45 μm filtered) 

collected from Link River, Klamath River at Miller Island 

(two depths), Klamath River at Keno (two depths), and the 

Klamath Strait Drain in June, July, August, and September 

2007. Those samples also supported an investigation of 

biochemical oxygen demand in the Klamath River (Sullivan 

and others, 2010). Alkalinity titrations for these samples 

were performed according to USGS protocols (Rounds, 

2006), and split samples were sent to the USGS National 

Water Quality Laboratory to determine the concentrations of 

ammonia-plus-ammonium and soluble reactive phosphorus. 

Split samples were sent to a USGS organic carbon laboratory 

in Boulder, Colorado for analysis of dissolved organic 

carbon concentrations. Titration curves were analyzed using 

the USGS Alkalinity Calculator (http://or.water.usgs.gov/

alk/) to determine sample alkalinity; results from many 

samples included a warning message that the shape of the 

titration curve was not entirely consistent with the shape of 

a theoretical titration curve based only on the chemistry of 

carbonic acid. This suggested that some other constituent 

(other than hydroxide, bicarbonate, and carbonate) had acid/

base properties and was being titrated.

An iterative approach was implemented in which a set 

of site density and pK values was chosen, the total inorganic 

carbon concentration for each sample was computed using 

equation 42 provided below, and theoretical Vt

 values 

were computed for every pH in the experimental alkalinity 

titrations. The mean sum of squared differences between the 

experimental and theoretical Vt values was computed for each 

individual titration, and then the mean squared difference was 

computed for the set of all 24 titrations.

Using that mean squared difference as an objective 

function to minimize, the optimization program utilized 

Powell’s conjugate direction-set method as described by Press 

and others (1989) to find the parameter values that provided 

the best fit to the experimental titration curves. Because the 

parameter space can include local minima for the objective 

function, an attempt was made to find the global minimum and 

therefore the best fit to the data by running the optimization 

program 100 times with a wide variety of randomized initial 

parameter values. Results from the 100 optimizations then 

were analyzed to determine the best set of parameter values.

Two sets of optimizations were attempted. In the first, it 

was assumed that the acid groups associated with dissolved 

organic matter could be approximated with two Gaussian 

distributions of pKa values—one to represent carboxylic 

acid groups and one to represent phenolic or amine groups, 

after the method of Perdue and others (1984). The carboxylic 

group was likely to have a mean pKa in the range of 3.5–6, 

while the phenolic group was likely to have a mean pKa in 

the range of 9–11. Note that the algorithm programmed into 

CE-QUAL-W2 (see appendix B for code changes), as well as 

the algorithm used in the optimization routine, uses a truncated 

Gaussian distribution (0.5 ≤ pKa ≤ 13.5) and discretizes the 

distribution at 0.5 unit intervals; a smoother version could be 

used, but this coarser representation of the distribution should 

be adequate and is computationally faster.

Setting na to 2, the optimization program was asked to 

find the best values for six parameters: two site densities, two 

mean pKa values, and a standard deviation about each of the 

two mean pKa values. After 100 optimizations with different 

initial conditions, the results yielded good information to 

set the mean pKa values to 5.50 and 9.74, but the standard 

deviation and site density for the phenolic group proved more 

difficult to optimize.

The problem with characterizing the phenolic groups 

is that the experimental titration curves begin at the pH of 

the sample and then decrease as acid is added. The highest 

pH from the 24 samples was 9.58, making it impossible to 

know the shape of the experimental titration curve at higher 

pH values. To more accurately determine a distribution of 

phenolic pKa values, those higher pH values are needed. 

Perhaps future alkalinity titrations could be performed by first 

adding a known amount of base to increase the sample pH 

(and alkalinity) and thereby provide an experimental titration 

curve at the high end of the pH range, but this dataset lacked 

such data and therefore was insufficient to fully characterize 

the phenolic acid groups associated with dissolved organic 

matter. An additional titration curve with an initial sample pH 

of 10.78 was later tested with the optimized model parameters, 

and the agreement was good, but more titration curves with 

high pH are needed.

When fitting a site density, mean pKa, and standard 

deviation about that pKa for the phenolic groups, it was found 

that the lack of high pH data in the titration curves meant 

that somewhat similar fits could be constructed using higher 

site densities along with a higher mean pKa and a wider 

distribution (larger standard deviation). In that way, just 

the lower tail of the pKa distribution was being used in the 

comparison of theoretical and experimental titration curves. 

Despite this problem, a best fit was found by using the mean 

pKa values from the initial 6-parameter optimization and 

following up with a 4-parameter optimization to find the best 

combination of site density and pKa standard deviation values 

that accompany those mean pKa inputs (table 4). The results 

indicated that the best-fit standard deviation values were quite 

small, around 0.05 units. This is somewhat counterintuitive, 

given what is known about the complex and variable structure 

of natural organic material and the accompanying range in 

acidities of its functional groups (Perdue and others, 1984; 

Bonn and Fish, 1991; Perdue and Ritchie, 2003). A more 

narrow distribution of acidities could be consistent with a 

single predominant source of dissolved organic matter to 
Enhanced pH Buffering and Nonconservative Alkalinity 17

these samples. However, dissolved organic matter in the 

Klamath River system is likely to have multiple sources, 

such as wetlands, algae, or woody debris from historical and 

current mill operations. Further investigation into the sources 

of organic matter in the Klamath River system would help to 

better understand the variability of that material and its effect 

on pH buffering.

A second optimization was designed to test whether 

two monoprotic acids with no distribution of associated 

acidities could be used to fit the organic-matter portion of the 

experimental titration curves. After all, with the rather small 

pKa standard deviations found in the first optimization, the 

fitted Gaussian distribution of pKa values was almost identical 

to just two monoprotic acids. In this second optimization, 

only four organic-matter parameters were fitted using the 

theoretical titration curve: two site densities and two pKa

values. The results were quite similar to and slightly better 

than the results from the first optimization, with a mean 

absolute volume error of about 10.1 counts per titration 

(800 counts to 1 mL of acid volume). The mean absolute 

volume error from the first optimization (6 parameters) was 

about 10.2 counts per titration.

Erring on the side of simplicity, it was decided to 

model the pH buffering of dissolved organic matter in the 

Klamath River using just two monoprotic acids and the 

parameters listed in table 4 for optimization #2. Although 

this is a simple approach, the resulting theoretical titration 

curves do a remarkably good job of fitting the experimental 

titration curves. Three examples from the 24 fitted datasets 

are shown in figures 5A, B, and C, in which the measured 

titration curves (points) are compared against four different 

theoretical titration curves. The simplest theoretical titration 

curve accounts only for the chemistry of carbonic acid and 

water, in which hydroxide, carbonate, and bicarbonate are the 

only entities that can be titrated. Successive theoretical curves 

then add the effects of ammonia, phosphates, and dissolved 

organic matter. In most of the Klamath River samples having a 

high pH, the carbonate-only theoretical titration curve failed to 

capture the shape of the measured titration curve, particularly 

for the higher-pH part of the curve. Adding in the effects 

of ammonia often helped when ammonia concentrations 

were high (close to or higher than 1.0 mg/L as nitrogen) 

and the sample pH was above 8.5. Phosphates rarely had a 

visible effect on the theoretical titration curve for the range 

of phosphate concentrations in these samples. Dissolved 

organic matter had a far more important and substantive effect 

on the theoretical titration curve for these samples and was 

instrumental in capturing the shape of the measured titration 

curve. Clearly, for these Klamath River samples, dissolved 

organic matter appears to be an important constituent that 

can buffer the pH of the river when algal blooms consume 

carbonic acid and force the pH to levels of 8 and above. 

Although the nature of the dissolved organic matter is likely 

to change over the course of a season and as a function of 

its various sources, representing its buffering with a pair of 

monoprotic acids in the model calculations appears to be a 

good first step in capturing that process.

Recalculation of Boundary Conditions for Total 

Inorganic Carbon

With the inclusion of organic matter, orthophosphorus, 

and ammonia into the internal CE-QUAL-W2 calculations 

of pH, it is also necessary to adjust the concentration of total 

inorganic carbon in the model input files. Prior to the enhanced 

buffering updates, the concentration of total inorganic carbon 

for the inflows into the model was calculated from field 

measurements of pH, sample titrations to measure alkalinity, 

and an assumption that the alkalinity is predominantly due to 

bicarbonate, carbonate, and hydroxide. When that is the case, 

the alkalinity equation was simplified:

2

carb 3 3 Alk Alk [HCO 2[CO [OH [H ] ] ] ] − − −+ ≈ = + +− (40)

and the determination of the total inorganic carbon 

concentration was relatively straightforward once the values of 

the acid dissociation constants for carbonic acid are known:

2 ' '' '

1 12 w T ' ' '

1 12 H

{H } K {H } K K K {H } C Alk

K {H } 2K K {H } +

+ + +

+ +

+ +   =   − +

+ γ   (41)

Table 4. Dissolved organic-matter acid dissociation constants 

and site densities for the Link River to Keno Dam reach of the 

Klamath River, Oregon, resulting from two best-fit optimizations of 

24 measured alkalinity titration curves.

[Abbreviations: pKa, acid dissociation constant; std. dev., standard deviations; 

–, not applicable]

Acid group Model parameter

Optimization 

number 1

(2 acid 

distributions)

Optimization 

number 2

(2 monoprotic 

acids)

1

(Carboxylics)

Site density 0.1751 0.1925

pKa

 mean 5.502 5.584

pKa

 std. dev. 0.047 –

2

(Phenolics)

Site density 0.5828 0.6466

pKa

 mean 9.738 9.594

pKa

 std. dev. 0.050 –
18 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

Figure 5. Example titration curves of four theoretical titration 

curves and measured data from the Link River to Keno Dam reach 

of the Klamath River, Oregon. DOC, dissolved organic carbon. 

(A) In this sample at Miller Island July 17, 2007, alkalinity was 

52.8 mg/L as CaCO3, ammonia concentration was 1.1 mg/L as N, 

phosphate concentration was 0.171 mg/L, and DOC concentration 

was 11.1 mg/L. Ammonia had a visible effect on the theoretical 

titration curve, but organic matter was important in capturing 

the shape of the measured curve. (B) In this sample at Link River 

August 14, 2007, alkalinity was 44.2 mg/L as CaCO3, ammonia 

concentration was 0.068 mg/L as N, phosphate concentration 

was 0.104 mg/L, and DOC concentration was 11.4 mg/L. Ammonia 

had little effect on the shape of the curve because the ammonia 

concentration was low, but organic matter was important to the 

shape of the titration curve. (C) In this sample at Keno August 14, 

2007, alkalinity was 65.2 mg/L as CaCO3, ammonia concentration 

was 1.01 mg/L as N, phosphate concentration was 0.165 mg/L, and 

the DOC concentration was 12.5 mg/L. Because the sample pH 

was less than 8.0, ammonia and organic matter had little effect on 

the high end of the titration curve, but organic matter had a slight 

effect on the lower part of the curve.

tac12-0791_fig 05a

Measured

Carbonates only

Carbonates, ammonia

Carbonates, ammonia, phosphates

Carbonates, ammonia, phosphates, DOC

pH

Volume of acid added, counts

4

5

6

7

8

9

0 100 200 300 400 500 600

A

tac12-0791_fig 05b

Measured

Carbonates only

Carbonates, ammonia

Carbonates, ammonia, phosphates

Carbonates, ammonia, phosphates, DOC

pH

Volume of acid added, counts

4

5

6

7

8

9

10

0 100 200 300 400 500

B

Measured

Carbonates only

Carbonates, ammonia

Carbonates, ammonia, phosphates

Carbonates, ammonia, phosphates, DOC

4

5

6

7

8

0 100 200 300 400 500 600 700

pH

Volume of acid added, counts

C
Enhanced pH Buffering and Nonconservative Alkalinity 19

Activating the enhanced pH buffering routines in CE-QUAL-W2 means that, to the extent that such enhanced buffering is 

important compared to that provided by bicarbonate and carbonate, the boundary condition total inorganic carbon concentration 

must be computed by taking into account the contributions of Alkam, AlkP, and AlkOM if those are activated in the model. Taking 

all three into account, the equation for CT becomes:

 

a

' '

a a i i

2 ' '' ' '

1 12 w am T T ' ' ' '

1 1 2 H am

' ' ''' 3 n

P1 P2 P1 P2 P3

T T 3 ' 2 '' ''' (pK pH) (pK 4.5) P1 P1 P2 P1 P2 P3 1

{H } K {H } K K K K H C Alk N

K {H } 2K K {H } {H } K

K K H 2K K K {H } 1 1 P A

{H } K {H } K

{ }

K {H } K K K 1 10

{

10

}

1 i

i

+

+ + +

+ ++

+ +

++ + − − =

+ + = −+−

+ + γ

  + − −  −δ −

  ++ + + +

∑    

 

 (42)

If neglecting activity corrections in a freshwater system, a slightly simpler equation results:

a a i i

2

1 12 w am T T +

1 1 2 am

3 n

P1 P2 P1 P2 P3 T T 3 2 (pK pH) (pK 4.5)

P1 P1 P2 P1 P2 P3 1

T

[] [] [ ]

[ ] [] []

[ ] [ ]

[] [

H K H KK K K C Alk H N

K H 2K K H H K

K K H 2K K K H 1

] []

is t

1 P A

H K H KK H KKK 1 10 1 10

where

C he total

a

i

i

+ + +

+ +

+ +

++ + − − =

+ + = − +−

+ +

  + −   −   −δ −     ++ +   + +

∑

1

2

 inorganic carbon concentration (in moles per liter; multiply result by 12,011

to obtain milligrams per liter),

is the first acid dissociation constant for carbonic acid (table 3),

is the secon

K

K d acid

w

am

P1

 dissociation constant for carbonic acid (table 3),

is the acid dissociation constant for water (table 3),

is the acid dissociation constant for ammonium (table 3),

is the first acid dissocia

K

K

K tion

P2

P3

 constant for phosphoric acid (table 3),

K is the second acid dissociation constant for phosphoric acid (table 3),

K is the third acid dissociation constant for phosphoric acid 

Alk i

(tab

s th

le 3),

e alk 3

T

T

is the concentration of ammonia and ammonium 

alinity in equivalents per liter [(Alk in milli

in moles per liter [(ammonia+ammonium

in mg/L)/1

grams per liter CaCO )/50,0

4,006.74],

is the conce

4

n

4],

N

P trat

a

T

ion of SRP in moles per liter [(SRP in milligrams per liter)/30,973.762],

is the number of monoprotic acid groups, or the number of distributions of those groups,

used to represent organic matter,

n

A is the total organic matter concentration in moles of carbon per liter. Depending on model

options either [(DOC in milligrams per liter)/12,011] or [(DOC+POC in milligrams per

 liter)/12,011],

is the sit i δ

i

i i

a

a a

e density for acid group , in moles of sites per mole of carbon,

is the acid dissociation constant of the th acid group for organic matter,

is the negative logarithm, b

K

pK Kase 10, of (for distri

i

i

-pH

bution option (DIST), use 0.5, 1.0, 1.5,

..., 13.0, 13.5),

pH is the pH of 

H is the hydrogen ion concentration, defi

the water, an

ned as 

d

[ ] 10 . +

 (43)

' K1

{H }+

               

' K1

{H }+

               

' K1

{H }+

               

' K1

{H }+

               
20 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

For organic matter, if the user chooses to represent the 

organic acids with a distribution of pK values, the details of 

the final distribution of pK values is needed. The ph_buffering.

opt model output file from a test run with the organic matter 

inputs provides the overall site densities for a range of pK 

values to use with organic matter. The site density is the moles 

of acid/base groups per mole of carbon. For the distribution 

(DIST) option, 27 pK values from 0.5 to 13.5, at 0.5-unit 

increments, are used to characterize the final distribution and 

need to be accounted for in the calculation of CT.

The calculation of total inorganic carbon concentrations 

from these equations can be used if the acid dissociation 

constants and site densities for organic matter have been 

determined, as in the upper Klamath River, or in different 

systems if the buffering provided by organic matter was 

smaller and could be ignored. It is best when simulating 

organic-matter buffering to analyze a series of alkalinity 

titration curves in advance of the modeling to estimate values 

for the organic matter site densities and pKa values. Otherwise, 

using these values as calibration parameters would require 

that the boundary conditions for CT be recomputed whenever 

the organic-matter parameter values that affect pH buffering 

are modified.

Activity Corrections

The PH_CO2 subroutine in CE-QUAL-W2 (appendix B) 

includes activity correction calculations for most of the 

inorganic constituents included in the computations. Most 

of that code was left unchanged in this version, with the 

exception that some additional constituents not included in the 

default implementation were given activity corrections. Ionic 

strength was estimated in the default code based on simulated 

values of total dissolved solids or salinity. A form of the 

extended Debye-Hückel equation was used in the default code 

to estimate activity coefficients for bicarbonate, carbonate, 

hydroxide, and the hydrogen ion (H+). In this version, 

additional activity coefficients were computed for ammonia, 

ammonium, and the various phosphate species based on the 

existing equations and a set of ion size and charge factors 

tabulated for the Debye-Hückel equation by Stumm and 

Morgan (1996).

Nonconservative Alkalinity

Previous versions of CE-QUAL-W2 assumed that 

alkalinity is largely unaffected by chemical and biological 

reactions and responds only to changes in inputs, transport, 

and mixing. While alkalinity is largely a conservative 

quantity, it is not entirely conservative. Reactions such as 

ammonia nitrification and nitrate denitrification as well 

as photosynthesis and respiration can have small effects 

on alkalinity. A summary of these effects was provided by 

Stumm and Morgan (1996) in their aquatic chemistry text (see 

table 4.5, page 173). The following reactions have effects on 

alkalinity:

• Utilization of ammonium during photosynthesis 

results in a decrease in alkalinity: 14 equivalents of 

alkalinity for every 16 moles of ammonium used. 

(Note: This stoichiometry was applied despite the fact 

that this equation is not balanced in H.)

2

2 44 2

106 263 110 16 2

106CO 16NH HPO 108H O

C H O N P 107O 14H

+ −

+

+++

→ ++

• Utilization of nitrate during photosynthesis results in 

an increase in alkalinity: 18 equivalents of alkalinity 

for every 16 moles of nitrate used.

 

2

2 34 2

106 263 110 16 2

106CO 16NO HPO 122H O 18H

C H O N P 138O

−− + +++ +

→ +

• Production of ammonium during respiration results in 

an increase in alkalinity: 14 equivalents of alkalinity 

for every 16 moles of ammonium produced. (Note: 

This stoichiometry was applied despite the fact that 

this equation is not balanced in H.)

 

106 263 110 16 2

2

2 44 2

C H O N P 107O 14H

106CO 16NH HPO 108H O

+

+ −

+ +

→ +++

• Nitrification of ammonium results in a decrease in 

alkalinity: 2 equivalents of alkalinity for every 1 mole 

of ammonium consumed.

NH 2O NO H O 2H 4 2 32

+ −+ +→ + +

• Denitrification of nitrate (to nitrogen gas) results in 

an increase in alkalinity: 1 equivalent of alkalinity per 

1 mole of nitrate consumed.

2 3 222 5CH O 4NO 4H 5CO 2N 7H O − + + +→ ++

As a result of changes made in this version of CE-QUAL-W2, 

the user is allowed to specify whether alkalinity is to be 

simulated as a conservative or a nonconservative quantity 

(see appendix B).
Summary of Updated Model Calibration 21

Summary of Updated Model Calibration

After macrophytes and enhanced pH buffering were 

incorporated into the upper Klamath River model, the model 

was recalibrated by adjusting selected parameter values to 

obtain a good match between measured data and model output. 

Most parameters were unchanged from the original model 

calibration and remain as documented by Sullivan and others 

(2011). Those parameters that were adjusted are shown in 

table 5. The new macrophyte parameters, as used in the upper 

Klamath River model, are shown in table 2 and the enhanced 

buffering parameters are shown in table 6.

During macrophyte calibration, the macrophyte field 

data were used to provide insight into the general patterns 

of density, spatial and temporal distributions of biomass, 

and macrophyte species characteristics. The model was 

not calibrated directly to the macrophyte field data because 

the macrophyte field data were collected in a different year 

(2011) than the model years (2006–09). Examples of the 

modeled distribution of the three macrophyte groups through 

the model domain on July 2 and August 17 for model year 

2007 are shown in figure 6. Although most constituents in 

CE-QUAL-W2 are laterally averaged across the channel, 

macrophytes are modeled in a quasi three-dimensional mode 

so that macrophytes can be modeled at different depths from 

bank to bank across a model segment (Berger, 2000; Berger 

and Wells, 2008; Cole and Wells, 2008). As in the field data, 

the modeled pondweed density was highest in early summer 

and diminished by August, whereas coontail and common 

waterweed were simulated with a higher density in late 

summer and were more common in the downstream reaches 

near Keno Dam.

Macrophytes affect the cycles of oxygen, nutrients, 

organic matter, and pH. In the updated model, the total 

annual production of dissolved oxygen by macrophytes is 

approximately the same order of magnitude as that by algae 

(fig. 7). Oxygen consumption by respiration is higher in 

macrophytes compared to algae, due in part to the fact that 

the macrophyte oxygen respiration parameter was adjusted 

to account for the large population of snails within the 

macrophytes. Dissolved oxygen production and consumption 

by macrophytes begins earlier in the year than oxygen 

production and consumption by algae, largely because the 

pondweed macrophytes are early season species, whereas the 

largest algal blooms occur in late June and early July.

Table 5. Parameter values changed as a result of calibration updates to the water-quality model for the Link River to Keno Dam reach 

of the Klamath River, Oregon. 

[Abbreviations: °C, degrees Celsius; g, gram; 1/day, per day]

Parameter Original value Updated value Description

AG, blue-green 3.09 2.3 Maximum algal growth rate for blue-green algae, 1/day

AT1, blue-green 12 13 Lower temperature parameter for rising rate function for blue-green algae, °C

AT3, blue-green 35 30 Lower temperature parameter for falling rate function for blue-green algae, °C

CO2R 1.2 0.1 Sediment carbon dioxide release rate, fraction of sediment oxygen demand

Table 6. Enhanced pH buffering input parameters in the water-quality model for the Link River to Keno Dam reach of the Klamath River, 

Oregon.

[Abbreviations: pKa, acid dissociation constant; OM, organic matter; POM, particulate matter]

Parameter Value Description

PHBUFC ON Option to use enhanced buffering routines

NCALKC ON Option to use nonconservative alkalinity algorithms

NH4BUFC ON Specifies whether ammonia/ammonium is included in pH buffering

PO4BUFC ON Specifies whether phosphoric acid is included in pH buffering

OMBUFC ON Specifies whether organic matter is included in pH buffering

OMTYPE MONO MONO specifies discrete pKa

 values

NAG 2 Number of organic acid/base groups to model

POMBUFC OFF Specifies whether POM is included in OM buffering

SDEN1 0.1925 Site density for organic group 1, in moles of acid/base sites per mole of carbon in OM

SDEN2 0.6466 Site density for organic group 2, in moles of acid/base sites per mole of carbon in OM

PK1 5.584 The pKa values (negative log10 of the acid dissociation constant)

PK2 9.594 The pKa

 values (negative log10 of the acid dissociation constant)
22 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

tac12-0791_fig 06 Biomass, in grams per square meter Keno Dam

Link River

Keno Dam

Link River

Keno Dam

Link River

0

25

50

75

100

0

25

50

75

100

July 2, 2007 July 2, 2007 July 2, 2007

August 17, 2007 August 17, 2007 August 17, 2007

Coontail Common Waterweed Pondweed

105 90 75 60 45 30 15 0

Model segment

105 90 75 60 45 30 15 0

Model segment

105 90 75 60 45 30 15 0

Model segment

Figure 6. Modeled macrophyte biomass along the Link River to Keno Dam reach of the Klamath River, Oregon, on two 

selected dates. CE-QUAL-W2 provides macrophyte output at different depths across each segment cross section.

Reaeration

Algal production

Macrophyte production

SOD, First order

POM decay

DOM decay

Macrophyte

respiration

Algal respiration

SOD, Zero order

Nitrification

A B

−10,000

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

Dissolved oxygen source, in kilograms per day

2008

J F M M J J A S O DN A

2008

J F M M J J A S O DN A 0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

Dissolved oxygen sink, in kilograms per day

Figure 7. Modeled daily average dissolved-oxygen production (A) sources and consumption (B) sinks in the Link River to 

Keno Dam reach of the Klamath River, Oregon, in 2008. DOM, dissolved organic matter; POM, particulate organic matter; SOD, 

sediment oxygen demand.
Summary of Updated Model Calibration 23

pH buffering by ammonia, phosphates, and dissolved 

organic matter was enabled in the recalibrated model, but 

buffering by particulate organic matter was disabled (table 6). 

Particulate organic matter, much of it derived from dying 

algae, may have some acid/base properties, but being enclosed 

in particles likely inhibits its reactivity with the bulk river 

water. Algae and macrophyte material may also have acid/

base properties, such as cell walls with carboxyl groups 

(Chojnacka, 2010), but this buffering was also assumed to 

be small relative to buffering by dissolved organic matter. 

Nonconservative alkalinity was turned on, and two monoprotic 

acids were used to simulate the dissolved organic matter 

buffering—one to represent carboxylic acids and one to 

represent phenolic and amine groups together.

The enhanced pH buffering algorithms had a notable 

effect on modeling pH in summer and fall. Without the 

enhanced buffering, the modeled pH was generally lower 

and subject to larger daily variability compared to measured 

pH (fig. 8). The addition of macrophytes also improved pH 

modeling, especially in the lower part of the reach near Keno 

Dam where macrophytes were more abundant (fig. 9). With 

both macrophytes and enhanced pH buffering implemented, 

the model was able to simulate pH well with mean absolute 

errors (MAE) of ≤0.34 for years 2006–09 (fig. 10; table 7). 

The inclusion and calibration of pH in the upper Klamath 

River model will now allow model scenarios to examine the 

effect of management and other system changes on pH, which 

is a water-quality limited constituent in this reach. 

The updates to the model affected the error statistics 

of other constituents modestly. The most improved error 

statistics were for dissolved oxygen, with an average 

MAE improvement of 0.1 mg/L, and particulate carbon, 

with an average MAE improvement of 0.2 mg/L. Average 

error statistics for other constituents were essentially the 

same compared to the original USGS model (Sullivan 

and others 2011). In addition to the model performance 

metrics included in table 7, measured and modeled pH and 

dissolved oxygen time series are shown in figures 10A–D

and 11A–D, respectively, for calendar years 2006–09. Algae, 

nutrients, organic matter, and bottom sediment are shown 

in figures 12A–D for the calendar years 2006–09. Modeled 

temperature and specific conductance are not shown here; 

those plots are available in the original USGS Klamath River 

model report (Sullivan and others, 2011).

When interpreting measured/model comparison plots and 

error statistics, remember that model output and measured data 

are at the same time and location but not at the exact same 

scale. For example, measurements from a continuous monitor 

probe represent a small volume near the probe tip. Model 

output is from an entire model cell that might have dimensions 

of 1,000 ft×500 ft×2 ft near-surface. Measured data and 

model output should show the same large-scale temporal and 

spatial patterns, but some mismatch at smaller scales can be 

expected as a result of these different scales.

The USGS upper Klamath River model has already been 

used to analyze water-quality effects of system changes in 

several preliminary model scenarios (Sullivan and others, 

2011, 2012). The predictive improvements provided by the 

updated model will benefit future analyses of water-quality 

scenarios and help improve the understanding of water-quality 

processes in this reach of the Klamath River. 
24 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

7

8

9

10

11

pH

Measured

Model, without macrophytes

7

8

9

10

11

Jun Jul Aug Sep Oct

pH

2007

Measured

Model, with macrophytes

A

B

Figure 9. Modeled and measured pH at the Klamath River, Oregon, Keno site in summer and 

fall 2007, (A) without macrophytes and (B) with macrophytes. To illustrate just the effect of 

macrophytes, neither of the model runs shown includes enhanced pH buffering.

tac12-0791_fig 08

Measured

Model, without enhanced buffering

Measured

Model, with enhanced buffering

7

8

9

10

11

pH

7

8

9

10

11

Jun Jul Aug Sep Oct

pH

2007

A

B

Figure 8. Modeled and measured pH at the Klamath River, Oregon, Railroad Bridge site in 

summer and fall 2007, (A) without and (B) with the new enhanced CE-QUAL-W2 pH buffering. 

To illustrate just the effect of the enhanced pH buffering, neither of the model runs shown 

includes macrophytes.
Summary of Updated Model Calibration 25

Table 7. Goodness-of-fit statistics averaged over all calibration sites for the updated model of the Link 

River to Keno Dam reach of the Klamath River, Oregon.

[Abbreviations: °C. degrees Celsius; <, less than; μm3/mL, cubic micrometers per milliliter; mg/L, milligrams per liter; 

rl, reporting level; ×, times]

Constituent Unit Data type

Range of 

measured 

values

Year Mean 

error

Mean 

absolute 

error

Root mean 

square error

Water temperature °C hourly 0–28

2006 -0.03 0.55 0.70

2007 0.06 0.63 0.78

2008 0.17 0.63 0.80

2009 -0.17 0.58 0.72

Dissolved oxygen mg/L hourly 0–20

2006 -0.02 0.98 1.37

2007 0.70 1.23 1.70

2008 -0.18 0.95 1.36

2009 -0.65 1.27 1.71

pH hourly 7–11

2006 -0.14 0.26 0.36

2007 -0.04 0.30 0.39

2008 -0.02 0.25 0.33

2009 -0.20 0.34 0.46

Ammonia mg/L grab <rl–1.7 2007 0.00 0.12 0.16

2008 -0.11 0.22 0.28

Nitrate mg/L grab <rl–0.8 2007 0.01 0.03 0.03

2008 0.01 0.03 0.03

Particulate nitrogen mg/L grab 0.06–4.0 2007 -0.21 0.29 0.49

2008 -0.17 0.25 0.39

Total nitrogen mg/L grab 0.6–5.9 2007 0.03 0.40 0.59

2008 -0.08 0.42 0.52

Orthophosphorus mg/L grab 0.01–0.27 2007 0.01 0.03 0.04

2008 0.00 0.02 0.03

Total phosphorus mg/L grab 0.06–0.50 2007 0.01 0.05 0.07

2008 0.00 0.04 0.05

Blue-green algae μm3/mL grab 0–113×106 2007 -4.7×106 7.6×106 14.9×106

2008 -2.2×106 3.4×106 5.8×106

Particulate carbon mg/L grab 0.5–18 2007 0.07 1.09 1.72

2008 0.41 1.31 1.89

Dissolved organic 

carbon mg/L grab 5–14

2007 0.37 0.72 1.12

2008 -0.39 0.71 0.88
26 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

tac12-0791_fig 10a

Railroad Bridge – top

Railroad Bridge – bottom

Miller Island – top

Miller Island – bottom

KRS12a – top

KRS12a – bottom

Keno – top

Keno – bottom

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

12

6

12

6

12

6

12

6

12

6

12

6

12

6

12

6

Measured

Modeled

pH

A. 2006

Figure 10. Measured and modeled hourly pH during calendar years (A) 2006, (B) 2007, (C) 2008, and (D) 2009 for 

sites in the Link River to Keno Dam reach of the Klamath River, Oregon. Top results were from 1 meter below the river 

surface; bottom results were from 1 meter above the channel bottom.
Summary of Updated Model Calibration 27

tac12-0791_fig 10b

Railroad Bridge – top

Railroad Bridge – bottom

Miller Island – top

Miller Island – bottom

KRS12a – top

KRS12a – bottom

Keno – top

Keno – bottom

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

12

6

12

6

12

6

12

6

12

6

12

6

12

6

12

6

Measured

Modeled

pH

B. 2007

Figure 10.—Continued
28 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

tac12-0791_fig 10c

Railroad Bridge – top

Railroad Bridge – bottom

Miller Island – top

Miller Island – bottom

KRS12a – top

KRS12a – bottom

Keno – top

Keno – bottom

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

12

6

12

6

12

6

12

6

12

6

12

6

12

6

12

6

Measured

Modeled

pH

C. 2008

Figure 10.—Continued
Summary of Updated Model Calibration 29

tac12-0791_fig 10d

Railroad Bridge – top

Railroad Bridge – bottom

Miller Island – top

Miller Island – bottom

KRS12a – top

KRS12a – bottom

Keno – top

Keno – bottom

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

pH

12

6

12

6

12

6

12

6

12

6

12

6

12

6

12

6

Measured

Modeled

D. 2009

Figure 10.—Continued
30 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

tac11-0791_fig 11a

Railroad Bridge – top

Railroad Bridge – bottom

Miller Island – top

Miller Island – bottom

KRS20a – top

KRS20a – bottom

Keno – top

Keno – bottom

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Dissolved oxygen, in milligrams per liter

20

0

20

0

20

0

20

0

20

0

20

0

20

0

20

0

Measured

Modeled

A. 2006

Figure 11. Measured and modeled hourly dissolved-oxygen concentrations during calendar years (A) 2006, (B) 2007, 

(C) 2008, and (D) 2009 for sites in the Link River to Keno Dam reach of the Klamath River, Oregon. Top results were from 

1 meter below the river surface; bottom results were from 1 meter above the channel bottom.
Summary of Updated Model Calibration 31

tac11-0791_fig 11b

Railroad Bridge – top

Railroad Bridge – bottom

Miller Island – top

Miller Island – bottom

KRS20a – top

KRS20a – bottom

Keno – top

Keno – bottom

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Dissolved oxygen, in milligrams per liter

20

0

20

0

20

0

20

0

20

0

20

0

20

0

20

0

Measured

Modeled

B. 2007

Figure 11.—Continued
32 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

tac11-0791_fig 11c

Railroad Bridge – top

Railroad Bridge – bottom

Miller Island – top

Miller Island – bottom

KRS20a – top

KRS20a – bottom

Keno – top

Keno – bottom

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Dissolved oxygen, in milligrams per liter

20

0

20

0

20

0

20

0

20

0

20

0

20

0

20

0

Measured

Modeled

C. 2008

Figure 11.—Continued
Summary of Updated Model Calibration 33

tac11-0791_fig 11d

Railroad Bridge – top

Railroad Bridge – bottom

Miller Island – top

Miller Island – bottom

KRS20a – top

KRS20a – bottom

Keno – top

Keno – bottom

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Dissolved oxygen, in milligrams per liter

20

0

20

0

20

0

20

0

20

0

20

0

20

0

20

0

Measured

Modeled

D. 2009

Figure 11.—Continued
34 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

tac12-0791 fig12a1

Blue-green algae, in cubic

microns per milliliter

0

1.2E+8

0

1.2E+8

0

1.2E+8

Below Keno Dam

Bottom

Top

Diatoms, in cubic

microns per milliliter

0

6.1E+6

0

6.1E+6

0

6.1E+6 Bottom

Top

Other algae, in cubic

microns per milliliter

0

6.1E+6

0

6.1E+6

0

6.1E+6 Bottom

Top

Total nitrogen, in 

milligrams per liter

Chlorophyll-a, in

micrograms per liter

0

600

0

0

7.0

7.0

600

0

600

0

7.0

0

7.0

Bottom

Top

Bottom

Top

Particulate nitrogen, 

in milligrams per liter

0

5.0

0

5.0

0

5.0 Bottom

Top

Nitrate+nitrite, in

milligrams per liter

0

1.4

0

1.4 Bottom

Top

Keno KRS12a Miller Railroad Bridge

Apr.Jan. July Oct.

0

1.4

Apr.Jan. July Oct.

Measured

Modeled

Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

A. 2006

Figure 12. Measured and modeled algae, nutrients, organic matter, and bottom sediment during calendar years (A) 2006, 

(B) 2007, (C) 2008, and (D) 2009 for sites in the Link River to Keno Dam reach of the Klamath River, Oregon. Top results were from 

0.5 meters below the river surface; bottom results were from 1 meter above the channel bottom.
Summary of Updated Model Calibration 35

Figure 12.—Continued

tac12-0791 fig12a2

Ammonia, in milligrams

per liter

0

2.0

0

2.0

0

2.0

Below Keno Dam

Bottom

Top

Total phosphorus, in

milligrams per liter

0

0.5

0

0.5

0

0.5 Bottom

Top

Orthophosphorus, in

milligrams per liter

0

0.3

0

0.3

0

0.3 Bottom

Top

Dissolved organic

carbon, in milligrams

per liter

Particulate carbon, in

milligrams per liter

0

20

0

0

7.0

25

20

0

2t0

0

25

0

25

Bottom

Top

Bottom

Top

Bottom sediment, 

in milligrams per liter

0

180

0

180 Bottom

Top

Keno KRS12a Miller Railroad Bridge

Measured

Modeled

Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

A. 2006—Continued
36 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

tac12-0791 fig12b1

Blue-green algae, in cubic

microns per milliliter

0

1.2E+8

0

1.2E+8

0

1.2E+8

Below Keno Dam

Bottom

Top

Diatoms, in cubic

microns per milliliter

0

6.1E+6

0

6.1E+6

0

6.1E+6 Bottom

Top

Other algae, in cubic

microns per milliliter

0

6.1E+6

0

6.1E+6

0

6.1E+6 Bottom

Top

Total nitrogen, in 

milligrams per liter

Chlorophyll-a, in

micrograms per liter

0

600

0

0

7.0

7.0

600

0

600

0

7.0

0

7.0

Bottom

Top

Bottom

Top

Particulate nitrogen, 

in milligrams per liter

0

5.0

0

5.0

0

5.0 Bottom

Top

Nitrate+nitrite, in

milligrams per liter

0

1.4

0

1.4 Bottom

Top

Keno KRS12a Miller Railroad Bridge

Apr.Jan. July Oct.

0

1.4

Apr.Jan. July Oct.

Measured

Modeled

Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

B. 2007

Figure 12.—Continued
Summary of Updated Model Calibration 37

tac12-0791 fig12b2

Ammonia, in milligrams

per liter

0

2.0

0

2.0

0

2.0

Below Keno Dam

Bottom

Top

Total phosphorus, in

milligrams per liter

0

0.5

0

0.5

0

0.5 Bottom

Top

Orthophosphorus, in

milligrams per liter

0

0.3

0

0.3

0

0.3 Bottom

Top

Dissolved organic

carbon, in milligrams

per liter

Particulate carbon, in

milligrams per liter

0

20

0

0

7.0

25

20

0

2t0

0

25

0

25

Bottom

Top

Bottom

Top

Bottom sediment, 

in milligrams per liter

0

180

0

180 Bottom

Top

Keno KRS12a Miller Railroad Bridge

Measured

Modeled

Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

B. 2007—Continued

Figure 12.—Continued
38 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

tac12-0791 fig12c1

Blue-green algae, in cubic

microns per milliliter

0

1.2E+8

0

1.2E+8

0

1.2E+8

Below Keno Dam

Bottom

Top

Diatoms, in cubic

microns per milliliter

0

6.1E+6

0

6.1E+6

0

6.1E+6 Bottom

Top

Other algae, in cubic

microns per milliliter

0

6.1E+6

0

6.1E+6

0

6.1E+6 Bottom

Top

Total nitrogen, in 

milligrams per liter

Chlorophyll-a, in

micrograms per liter

0

600

0

0

7.0

7.0

600

0

600

0

7.0

0

7.0

Bottom

Top

Bottom

Top

Particulate nitrogen, 

in milligrams per liter

0

5.0

0

5.0

0

5.0 Bottom

Top

Nitrate+nitrite, in

milligrams per liter

0

1.4

0

1.4 Bottom

Top

Keno KRS12a Miller Railroad Bridge

Apr.Jan. July Oct.

0

1.4

Apr.Jan. July Oct.

Measured

Modeled

Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

C. 2008

Figure 12.—Continued
Summary of Updated Model Calibration 39

tac12-0791 fig12c2

Ammonia, in milligrams

per liter

0

2.0

0

2.0

0

2.0

Below Keno Dam

Bottom

Top

Total phosphorus, in

milligrams per liter

0

0.5

0

0.5

0

0.5 Bottom

Top

Orthophosphorus, in

milligrams per liter

0

0.3

0

0.3

0

0.3 Bottom

Top

Dissolved organic

carbon, in milligrams

per liter

Particulate carbon, in

milligrams per liter

0

20

0

0

7.0

25

20

0

2t0

0

25

0

25

Bottom

Top

Bottom

Top

Bottom sediment, 

in milligrams per liter

0

180

0

180 Bottom

Top

Keno KRS12a Miller Railroad Bridge

Measured

Modeled

Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

C. 2008—Continued

Figure 12.—Continued
40 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

tac12-0791 fig12d1

Blue-green algae, in cubic

microns per milliliter

0

1.2E+8

0

1.2E+8

0

1.2E+8

Below Keno Dam

Bottom

Top

Diatoms, in cubic

microns per milliliter

0

6.1E+6

0

6.1E+6

0

6.1E+6 Bottom

Top

Other algae, in cubic

microns per milliliter

0

6.1E+6

0

6.1E+6

0

6.1E+6 Bottom

Top

Total nitrogen, in 

milligrams per liter

Chlorophyll-a, in

micrograms per liter

0

600

0

0

7.0

7.0

600

0

600

0

7.0

0

7.0

Bottom

Top

Bottom

Top

Particulate nitrogen, 

in milligrams per liter

0

5.0

0

5.0

0

5.0 Bottom

Top

Nitrate+nitrite, in

milligrams per liter

0

1.4

0

1.4 Bottom

Top

Keno KRS12a Miller Railroad Bridge

Apr.Jan. July Oct.

0

1.4

Apr.Jan. July Oct.

Measured

Modeled

Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

D. 2009

Figure 12.—Continued
Summary of Updated Model Calibration 41

tac12-0791 fig12d2

Ammonia, in milligrams

per liter

0

2.0

0

2.0

0

2.0

Below Keno Dam

Bottom

Top

Total phosphorus, in

milligrams per liter

0

0.5

0

0.5

0

0.5 Bottom

Top

Orthophosphorus, in

milligrams per liter

0

0.3

0

0.3

0

0.3 Bottom

Top

Dissolved organic

carbon, in milligrams

per liter

Particulate carbon, in

milligrams per liter

0

20

0

0

7.0

25

20

0

2t0

0

25

0

25

Bottom

Top

Bottom

Top

Bottom sediment, 

in milligrams per liter

0

180

0

180 Bottom

Top

Keno KRS12a Miller Railroad Bridge

Measured

Modeled

Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct. Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

Apr.Jan. July Oct.

D. 2009—Continued

Figure 12.—Continued
42 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

Acknowledgments

Funding for this study was provided by the Bureau 

of Reclamation. Dean Snyder (U.S. Geological Survey) 

conducted the alkalinity analyses. Mariah Tilman, Garrett 

Steensland, Gunter Schanzenbacher, April Tower, and Tracy 

McGovern (Bureau of Reclamation) assisted with macrophyte 

field work. Discussions with Rick Carlson and Jason Cameron 

(Bureau of Reclamation), Steven Gherini (Tetra Tech) and 

Chris Berger and Scott Wells (Portland State University) 

were helpful. Thanks to Mark Sytsma, Vanessa Morgan, Rich 

Miller, and Robyn Draheim (Portland State University Center 

for Lakes and Reservoirs) for advice on macrophyte sampling 

and assistance with macrophyte and snail identification.

Supplementary Material

Macrophyte field sampling results are provided in 

spreadsheet form at: http://or.water.usgs.gov/proj/keno_reach/

data.html.

References Cited

Barko, J.W., Adams, M.S., and Clesceri, N.L., 1981, 

Environmental factors and their consideration in the 

management of submersed aquatic vegetation: A review: 

Journal of Aquatic Plant Management, v. 24, p. 1–10.

Barko, J.W. and Smart, R.M., 1981, Comparative influences 

of light and temperature on the growth and metabolism of 

selected submersed freshwater macrophytes: Ecological 

Monographs, v. 51, p. 219–235.

Bates, R.G., 1951, First dissociation constant of phosphoric 

acid from 0°C to 60°C—Limitations of the electromotive 

force method for moderately strong acids: Journal of 

Research of the National Bureau of Standards, v. 47, 

p. 127–134.

Bates, R.G., and Acree, S.F., 1943, pH values of certain 

phosphate−chloride mixtures, and the second dissociation 

constant of phosphoric acid from 0° to 60°C: Journal 

of Research of the National Bureau of Standards, v. 30, 

p. 129–155.

Berger, C.J., 2000, Modeling macrophytes of the Columbia 

Slough: Portland, Oregon, Portland State University, Ph.D. 

Dissertation, 278 p.

Berger, C.J., and Wells, S.A., 2008, Modeling the effects of 

macrophytes on hydrodynamics: Journal of Environmental 

Engineering, v. 134, p. 778–788.

Bonn, B.A., and Fish, William, 1991, Variability in the 

measurement of humic carboxyl content: Environmental 

Science and Technology, v. 25, p. 232–240.

Cashatt, D.N., and Bruce, L.J., 2009, Aquatic plant sampling, 

in Schultz, R.D., ed., Standard gear and techniques 

for fisheries surveys in Iowa: Des Moines, Iowa, Iowa 

Department of Natural Resources Completion Report, 

186 p.

Chojnacka, K., 2010, Biosorption and bioaccumulation—

The prospects for practical applications: Environment 

International, v. 36, p. 299–307.

Cole, T.M., and Wells, S.A., 2008, CE-QUAL-W2—A twodimensional, laterally averaged, hydrodynamic and waterquality model, version 3.6: U.S. Army Corps of Engineers, 

Instruction Report EL-08-1 [variously paged].

Dean, J.A., 1985, Lange’s handbook of chemistry (13th ed.): 

New York, McGraw-Hill, p. 5–16.

Deas, M.L., and Vaughn, J., 2011, Keno Reservoir particulate 

study 2008—Technical memorandum prepared for the 

Bureau of Reclamation, Klamath Basin Area Office, April 

2011: Davis, California, Watercourse Engineering, Inc., 

38 p.

Drever, J.I., 1997, The geochemistry of natural waters—

Surface and groundwater environments (3d ed.): New 

Jersey, Prentice-Hall, 436 p.

Eilers, J.M., 2005, Aquatic vegetation in selected sites of the 

Lost River, OR and CA: MaxDepth Aquatics, Inc., prepared 

for Tetra Tech, Inc., January 2005, 18 p.

Emerson, K.R., Russo, C., Lund, R.E., and Thurston, R.V., 

1975, Aqueous ammonia equilibrium calculations—Effect 

of pH and temperature: Journal of the Fisheries Research 

Board of Canada, v. 32, p. 2379-2383.

Gherini, S.A., Mok, L., Hudson, R.J.M., Davis, G.F., Chen, 

C.W., and Goldstein, R.A., 1985, The ILWAS model—

Formulation and application: Water, Air, and Soil Pollution, 

v. 26, p. 425–459.

Hauxwell, J., Knight, S., Wagner, K., Mikulyuk, A., Nault, M., 

Porzky, M., and Chase, S., 2010, Recommended baseline 

monitoring of aquatic plants in Wisconsin—Sampling 

design, field and laboratory procedures, data entry and 

analysis, and applications: Wisconsin Department of 

Natural Resources Bureau of Science Services PUB-SS 

2010, 47 p.
References Cited 43

Hem, J.D., 1985, Study and interpretation of the chemical 

characteristics of natural water (3d ed.): U.S. Geological 

Survey Water-Supply Paper 2254, p. 105–111. (Also 

available at http://pubs.usgs.gov/wsp/wsp2254/.)

Hough, R.A., Fornwall, M.D., Negele, B.J., Thompson, R.L., 

and Putt, D.A., 1989, Plant community dynamics in a 

chain of lakes—Principal factors in the decline of rooted 

macrophytes with eutrophication: Hydrobiologia, v. 173, 

p. 199–217.

Kenow, K.P., Lyon, J.E., Hines, R.K., and Elfessi, A., 2007, 

Estimating biomass of submersed vegetation using a 

simple rake sampling technique: Hydrobiologia, v. 575, 

p. 447–454.

Körner, S., and Nicklisch, A., 2002, Allelopathic growth 

inhibition of selected phytoplankton species by submerged 

macrophytes: Journal of Phycology, v. 38, p. 862–871.

Nichols, S.A., and Shaw, B.H., 1986, Ecological life histories 

of the three aquatic nuisance plants Myriophyllum 

spicatum, Potamogeton crispus and Elodea canadensis: 

Hydrobiologica, v. 131, p. 3–21.

Oregon Department of Environmental Quality, 2007, Oregon’s 

2004/2006 integrated report: Oregon Department of 

Environmental Quality Web page, accessed November 16, 

2007, at http://www.deq.state.or.us/wq/assessment/rpt0406.

htm.

Oregon Department of Environmental Quality, 2010, Upper 

Klamath and Lost River subbasins; total maximum 

daily load (TMDL) and water quality management plan 

(WQMP), accessed December 2010, at http://www.deq.

state.or.us/WQ/TMDLs/klamath.htm

Owens, C.S., Smart, R.M., Williams, P.E., and Spickard, M.R., 

2010, Comparison of three biomass sampling techniques on 

submersed aquatic plants in a northern tier lake: U.S. Army 

Corps of Engineers Report ERDC/TN APCRP-EA-24, 

July 2010, 9 p.

Pankow, J.F., 1991, Aquatic chemistry concepts: Chelsea, 

Michigan, Lewis Publishers, 673 p.

Perdue, E.M., Reuter, J.H., and Parrish, R.S., 1984, A 

statistical model of proton binding by humus: Geochimica 

et Cosmochimica Acta, v. 48, p. 1257–1263.

Perdue, E.M., and Ritchie, J.D., 2003, Dissolved organic 

matter in freshwaters: Treatise on Geochemistry, v. 5, 

p. 273–318.

Poulson, S.R., and Sullivan, A.B., 2010, Assessment of 

diel chemical and isotopic techniques to investigate 

biogeochemical cycles in the upper Klamath River, Oregon, 

USA: Chemical Geology, v. 269, p. 3–11.

Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, 

W.T., 1989, Numerical recipes—The art of scientific 

computing (FORTRAN version): Cambridge, Cambridge 

University Press, 702 p.

Rounds, S.A., 2006, Alkalinity and acid neutralizing capacity 

(version 4), in National field manual for the collection of 

water-quality data, Wilde, F.D., and Radtke, D.B., eds.: 

U.S. Geological Survey Techniques of Water-Resources 

Investigations, book 9, chap. A6, section 6.6, 53 p. (Also 

available at http://water.usgs.gov/owq/FieldManual/

Chapter6/section6.6/.)

Rounds, S.A., and Sullivan, A.B., 2009, Review of Klamath 

River total maximum daily load models from Link River 

Dam to Keno Dam, Oregon: U.S. Geological Survey 

Administrative Report, 37 p. (Also available at http://

or.water.usgs.gov/proj/keno_reach/download/klamath_

river_model_review_final.pdf.)

Rounds, S.A., and Sullivan, A.B., 2010, Review of revised 

Klamath River total maximum daily load models from Link 

River Dam to Keno Dam, Oregon: U.S. Geological Survey 

Administrative Report, 32 p. (Also available at http://

or.water.usgs.gov/proj/keno_reach/download/klamath_

model_rereview_final.pdf.)

Stumm, Werner, and Morgan, J.J., 1996, Aquatic chemistry—

Chemical equilibria and rates in natural waters (3d ed.): 

New York, John Wiley and Sons, 1,022 p.

Sullivan, A.B., Deas, M.L., Asbill, J., Kirshtein, J.D., Butler, 

K., and Vaughn, J., 2009, Klamath River water quality data 

from Link River Dam to Keno Dam, Oregon, 2008: U.S. 

Geological Survey Open-File Report 2009–1105, 25 p. 

(Also available at http://pubs.usgs.gov/of/2009/1105/.)

Sullivan, A.B., Deas, M.L., Asbill, J., Kirshtein, J.D., Butler, 

K., Stewart, M.A., Wellman, R.E., and Vaughn, J., 2008, 

Klamath River water quality and acoustic Doppler current 

profiler data from Link River Dam to Keno Dam, 2007: 

U.S. Geological Survey Open-File Report 2008–1185, 24 p. 

(Also available at http://pubs.usgs.gov/of/2008/1185/.)

Sullivan, A.B., Snyder, D.M., and Rounds, S.A., 2010, 

Controls on biochemical oxygen demand in the upper 

Klamath River, Oregon: Chemical Geology, v. 269, p. 

12–21, doi: 10.1016/j.chemgeo.2009.08.007.
44 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

Sullivan, A.B., Rounds, S.A., Deas, M.L., Asbill, J.R., 

Wellman, R.E., Stewart, M.A., Johnston, M.W., and 

Sogutlugil, I.E., 2011, Modeling hydrodynamics, water 

temperature, and water quality in the Klamath River 

upstream of Keno Dam, Oregon, 2006–09: U.S. Geological 

Survey Scientific Investigations Report 2011–5105, 70 p. 

(Also available at http://pubs.usgs.gov/sir/2011/5105.)

Sullivan, A.B., Rounds, S.A., Deas, M.L., and Sogutlugil, 

I.E., 2012, Dissolved oxygen analysis, TMDL model 

comparison, and particulate matter shunting—Preliminary 

results from three model scenarios for the Klamath River 

upstream of Keno Dam, Oregon: U.S. Geological Survey 

Open-File Report 2012–1101, 30 p. (Also available at http://

pubs.usgs.gov/of/2012/1101.)

Tetra Tech, Inc., 2009, Klamath River model for TMDL 

development, Prepared for U.S. Environmental Agency 

Region 9 and 10, Oregon Department of Environmental 

Quality, and North Coast Regional Water Quality Control 

Board, December 2009: 196 p., accessed May 20, 2011, at 

http://www.deq.state.or.us/wq/tmdls/docs/klamathbasin/

uklost/KlamathLostAppendixC.pdf.

Tipping, E., 1994, WHAM—A chemical equilibrium model 

and computer code for waters, sediments, and soils 

incorporating a discrete site/electrostatic model of ionbinding by humic substances: Computers and Geosciences, 

v. 20, p. 973–1023.
Appendix A 45

The most important macrophyte code changes related to initial conditions are included here. Other minor code changes also 

were made, including an expansion of macrophyte model flux outputs. For the definitive list of changes, users should compare new 

and old source code files.

Normal macrophyte initialization is invoked by setting MACWBCI to a value ≥0. With the new code changes, however, if 

MACWBCI is set to a value ≤ -1.0, a longitudinal set of initial concentrations is read from the longitudinal profile input file for 

every cell in the grid. The cell concentrations are read in units of grams per cubic meter, the same units used for MACWBCI. The 

model reads initial concentrations for each macrophyte group separately and in order, with one line per segment, and the initial 

concentrations for each layer read from KT to KB (left to right) as 8-character floating point inputs. This is the same input format as 

other longitudinal inputs; the macrophyte initial concentrations are placed at the end of that input file.

New variables include LONG_MACROPHYTE() and MACCI(). LONG_MACROPHYTE() is a logical, “true” when the user 

asks to read initial macrophyte concentrations from a longitudinal profile file. MACCI() is a real array holding the longitudinal 

initial concentrations. The longitudinal concentrations are read and initial macrophyte concentrations and masses are set in the 

init‐cond.f90 source-code file:

 DO I=cus(jb),ds(jb)

 IF (LONG_MACROPHYTE(JW,M)) READ (LPR(JW),’(//(8X,9F8.0))’) (MACCI(K,I,M),K=KT,KB(I)) ! SR 12/21/11

 depkti=ELWS(i)-el(kti(i)+1,i)

 if(depkti.ge.thrkti)then

 kticol(i)=.true.

 jt=kti(i)

 else

 kticol(i)=.false.

 jt=kti(i)+1

 end if

 je=kb(i)

 DO j=jt,je

 if(j.le.kt)then

 k=kt

 else

 k=j

 end if

 IF (LONG_MACROPHYTE(JW,M)) THEN ! SR 12/21/11

 MACRC(J,K,I,M) = MACCI(K,I,M) ! SR 12/21/11

 ELSE ! SR 12/21/11

 macrc(j,K,I,m) = macwbci(jw,m)

 END IF ! SR 12/21/11

 SMACRC(J,K,I,M) = MACRC(J,K,I,M) ! SR 12/21/11

 END DO

 END DO

Macrophyte initializations are also dealt with in the layeraddsub.f90 and w2_36_gen.f90 source files.

Appendix A. CE-QUAL-W2 Macrophyte Code Changes
46 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

The most important code changes made to the CE-QUAL-W2 pH and alkalinity routines are included in this section. For a 

definitive list of all changes, those who are interested should compare the new and old source files electronically.

The enhanced pH buffering routines and the nonconservative alkalinity algorithms can be turned on or off by the user 

through two new global input parameters in the control file on the MISCELL card; that modified card is shown below:

MISCELL NDAY PHBUFC NCALKC

 100 ON ON

The PHBUFC variable (ON/OFF) controls the use of the enhanced pH buffering routines; the NCALKC variable (ON/OFF) 

controls the use of the nonconservative alkalinity algorithms.

If the enhanced pH buffering routines are turned on, then the model will read a new input file named “ph_buffering.npt” that 

takes the following form:

Enhanced pH Buffering Input File for CE-QUAL-W2

BUFTYPE NH4BUFC PO4BUFC OMBUFC

 ON ON ON

OM TYPE OMTYPE NAG POMBUFC

 DIST 2 OFF

DENSITY SDEN SDEN SDEN SDEN SDEN SDEN SDEN SDEN SDEN

 0.14 0.10

pK VALS PK PK PK PK PK PK PK PK PK

 4.5 9.6

STD DEV PKSD PDSD PDSD PDSD PDSD PDSD PDSD PDSD PDSD

 1.2 1.0

--------------------------------------------------------------------------------

Input Variables:

 NH4BUFC ON/OFF, specifies whether ammonia/ammonium is included in pH buffering

 PO4BUFC ON/OFF, specifies whether phosphoric acid is included in pH buffering

 OMBUFC ON/OFF, specifies whether organic matter is included in pH buffering

 OMTYPE DIST or MONO

 where DIST specifies one or more Gaussian distributions of pKa values,

 or MONO specifies a collection of discrete pKa values

 NAG the number of acid/base groups to model, either as the means of

 Gaussian distributions of pKa values or as discrete monoprotic acids

 POMBUFC ON/OFF, specifies whether POM is included in OM buffering

 where ON indicates that OM buffering includes both DOM and POM

 OFF indicates that OM buffering includes only DOM

 SDEN site density, in moles of acid/base sites per mole of carbon in OM

 PK the pKa values (negative log10 of the acid dissociation constant),

 specified either as the mean of a distribution or a discrete value

 PKSD the standard deviation for a Gaussian distribution of pKa values

 (ignored when specifying an OMTYPE of MONO)

Appendix B. CE-QUAL-W2 pH and Alkalinity Code Changes
Appendix B 47

When the model is run with the enhanced pH buffering capability turned on, the code will generate a new output file named 

“ph_buffering.opt” based on the new inputs from the ph_buffering.npt file. The object is to echo some of the inputs and provide the 

user with information on the distribution of site densities and pKa values for the organic matter acids. The following is the output 

that corresponds to the input file shownabove:

Enhanced pH buffering output file

Ammonia buffering: ON

Phosphate buffering: ON

OM buffering: ON

POM buffering: OFF

OM buffer type: DIST

Inputs:

Group Site density pKa std.dev.

 1 0.1400 4.500 1.200

 2 0.1000 9.600 1.000

Modeled:

Group Site density pKa

 1 0.0001 0.500

 2 0.0003 1.000

 3 0.0010 1.500

 4 0.0027 2.000

 5 0.0058 2.500

 6 0.0107 3.000

 7 0.0164 3.500

 8 0.0213 4.000

 9 0.0233 4.500

 10 0.0213 5.000

 11 0.0165 5.500

 12 0.0107 6.000

 13 0.0060 6.500

 14 0.0033 7.000

 15 0.0032 7.500

 16 0.0059 8.000

 17 0.0110 8.500

 18 0.0167 9.000

 19 0.0199 9.500

 20 0.0184 10.000

 21 0.0133 10.500

 22 0.0075 11.000

 23 0.0033 11.500

 24 0.0011 12.000

 25 0.0003 12.500

 26 0.0001 13.000

 27 0.0000 13.500
48 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

The “ph_buffering.npt” input file is read by using new code in the input.f90 source file, including the following:

! Initialize variables for enhanced pH buffering ! entire section ! SR 01/01/12

 IF (CONSTITUENTS .AND. PHBUFC == ’ ON’) THEN

 OPEN (298,FILE=’ph_buffering.npt’,STATUS=’OLD’)

 READ (298,’(///8X,3A8)’) NH4BUFC, PO4BUFC, OMBUFC

 READ (298,’(//8X,A8,I8,A8)’) OMTYPE, NAGI, POMBUFC

 ALLOCATE (SDENI(NAGI),PKI(NAGI),PKSD(NAGI))

 READ (298,’(//(:8X,9F8.0))’) (SDENI(J), J=1,NAGI)

 READ (298,’(//(:8X,9F8.0))’) (PKI(J), J=1,NAGI)

 READ (298,’(//(:8X,9F8.0))’) (PKSD(J), J=1,NAGI)

 CLOSE (298)

 AMMONIA_BUFFERING = NH4BUFC == ’ ON’

 PHOSPHATE_BUFFERING = PO4BUFC == ’ ON’

 OM_BUFFERING = OMBUFC == ’ ON’

 POM_BUFFERING = POMBUFC == ’ ON’ .AND. OM_BUFFERING

 IF (OM_BUFFERING) THEN

 SDENI = ABS(SDENI)

 IF (OMTYPE == ’ DIST’) THEN

 IF (ANY(PKSD <= 0)) THEN

 WARNING_OPEN = .TRUE.

 WRITE (WRN,’(A)’) ’WARNING -- PKSD inputs in the ph_buffering.npt file must be greater than zero.’

 WRITE (WRN,’(A/)’) ’Please fix your inputs. For now, PKSD values of zero will be set to 1.’

 END IF

 DO JA=1,NAGI

 IF (PKSD(JA) <= 0) PKSD(JA) = 1.0

 END DO

 NAG = 27

 ALLOCATE (SDEN(NAG),PK(NAG),FRACT(NAG))

 SDEN = 0.0

 DO J=1,NAG

 PK(J) = 0.5*J

 END DO

 DO JA=1,NAGI

 SUM = 0.0

 DO J=1,NAG

 FRACT(J) = EXP(-0.5*(((PK(J)-PKI(JA))/PKSD(JA))**2))

 SUM = SUM+FRACT(J)

 END DO

 DO J=1,NAG

 SDEN(J) = SDEN(J)+SDENI(JA)*FRACT(J)/SUM

 END DO

 END DO
Appendix B 49

 ELSE

 ALLOCATE (SDEN(NAGI),PK(NAGI))

 NAG = NAGI

 SDEN = SDENI

 PK = PKI

 OMTYPE = ’ MONO’

 END IF

 END IF

 OPEN (299,FILE=’ph_buffering.opt’,STATUS=’UNKNOWN’)

 WRITE (299,’(A/)’) ’Enhanced pH buffering output file’

 WRITE (299,’(2A)’) ’Ammonia buffering: ’, ADJUSTL(TRIM(NH4BUFC))

 WRITE (299,’(2A)’) ’Phosphate buffering: ’, ADJUSTL(TRIM(PO4BUFC))

 WRITE (299,’(2A)’) ’OM buffering: ’, ADJUSTL(TRIM(OMBUFC))

 IF (OM_BUFFERING) THEN

 WRITE (299,’(2A)’) ’POM buffering: ’, ADJUSTL(TRIM(POMBUFC))

 WRITE (299,’(2A)’) ’OM buffer type: ’, ADJUSTL(TRIM(OMTYPE))

 WRITE (299,’(/A/A)’) ’Inputs:’,’Group Site density pKa std.dev.’

 DO JA=1,NAGI

 IF (OMTYPE == ’ DIST’) THEN

 WRITE (299,’(1X,I3,5X,F8.4,4X,F6.3,3X,F6.3)’) JA, SDENI(JA), PKI(JA), PKSD(JA)

 ELSE

 WRITE (299,’(1X,I3,5X,F8.4,4X,F6.3,3X,A)’) JA, SDENI(JA), PKI(JA), ’ N/A’

 END IF

 END DO

 WRITE (299,’(/A/A)’) ’Modeled:’,’Group Site density pKa’

 DO JA=1,NAG

 WRITE (299,’(1X,I3,5X,F8.4,4X,F6.3)’) JA, SDEN(JA), PK(JA)

 END DO

 END IF

 CLOSE (299)

 ELSE

 AMMONIA_BUFFERING = .FALSE.

 PHOSPHATE_BUFFERING = .FALSE.

 OM_BUFFERING = .FALSE.

 POM_BUFFERING = .FALSE.

 END IF
50 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

In the water-quality.f90 source file, the PH_CO2 subroutine was modified to include the optional buffering by ammonia, 

phosphoric acid, and organic matter. The modified code is:

ENTRY PH_CO2 ! Enhancements added for buffering by ammonia, phosphate, and OM ! SR 01/01/12

! pH and carbonate species

 DO I=IU,ID

 DO K=KT,KB(I)

 T1K = T1(K,I)+273.15

 CART = TIC(K,I)/12011. ! SR 01/01/12

 ALKT = ALK(K,I)/50044. ! SR 01/01/12

 AMMT = NH4(K,I)/14006.74 ! SR 01/01/12

 PHOST = PO4(K,I)/30973.762 ! SR 01/01/12

 OMCT = (LDOM(K,I)+RDOM(K,I))*ORGC(JW)/12011. ! moles carbon per liter from DOM ! SR 01/01/12

 IF (POM_BUFFERING) OMCT = OMCT + (LPOM(K,I)+RPOM(K,I))*ORGC(JW)/12011. ! SR 01/01/12

!**** Ionic strength

 IF (FRESH_WATER(JW)) S2 = 2.5E-05*TDS(K,I)

 IF (SALT_WATER(JW)) S2 = 1.47E-3+1.9885E-2*TDS(K,I)+3.8E-5*TDS(K,I)*TDS(K,I)

!**** Debye-Huckel terms and activity coefficients

 SQRS2 = SQRT(S2)

 DH1 = -0.5085*SQRS2/(1.0+1.3124*SQRS2)+4.745694E-03+4.160762E-02*S2-9.284843E-03*S2*S2

 DH2 = -2.0340*SQRS2/(1.0+1.4765*SQRS2)+1.205665E-02+9.715745E-02*S2-2.067746E-02*S2*S2

 DH3 = -4.5765*SQRS2/(1.0+1.3124*SQRS2) ! extended Debye-Huckel for PO4 ! SR 01/01/12

 DHH = -0.5085*SQRS2/(1.0+2.9529*SQRS2) ! extended Debye-Huckel for H+ ion ! SR 01/01/12

 H2CO3T = 10.0**(0.0755*S2)

 HCO3T = 10.0**DH1

 CO3T = 10.0**DH2

 PO4T = 10.0**DH3 ! SR 01/01/12

 HT = 10.0**DHH ! activity coefficient for H+ ! SR 01/01/12

 HPO4T = CO3T ! tabled values similar to those for carbonate ! SR 01/01/12

 OHT = HCO3T ! tabled values similar to those for bicarbonate ! SR 01/01/12

 H2PO4T = HCO3T ! tabled values similar to those for bicarbonate ! SR 01/01/12

 NH4T = HCO3T ! tabled values similar to those for bicarbonate ! SR 01/01/12

 NH3T = H2CO3T ! neutral species, set coefficient to same as that for carbonic acid ! SR 01/01/12

 H3PO4T = H2CO3T ! neutral species, set coefficient to same as that for carbonic acid ! SR 01/01/12

!  Temperature adjustment

 KW = 10.0** (-283.971 -0.05069842*T1K +13323.0/T1K +102.24447*LOG10(T1K) -1119669.0/(T1K*T1K))/OHT

 K1 = 10.0**(-356.3094 -0.06091964*T1K +21834.37/T1K +126.8339 *LOG10(T1K) -1684915 /(T1K*T1K))*H2CO3T/HCO3T

 K2 = 10.0**(-107.8871 -0.03252849*T1K + 5151.79/T1K + 38.92561*LOG10(T1K) - 563713.9/(T1K*T1K))*HCO3T/CO3T

 KAMM = 10.0**(-0.09018 -2729.92/T1K)*NH4T/NH3T ! SR 01/01/12

 KP1 = 10.0**(4.5535 -0.013486*T1K -799.31/T1K)*H3PO4T/H2PO4T ! Bates (1951) ! SR 01/21/12

 KP2 = 10.0**(5.3541 -0.019840*T1K -1979.5/T1K)*H2PO4T/HPO4T ! Bates and Acree (1943) ! SR 01/21/12

 KP3 = 10.0**(-12.38) *HPO4T/PO4T ! Dean (1985) ! SR 01/01/12
Appendix B 51

!**** pH evaluation

 PHT = -PH(K,I)-2.1

 IF (PH(K,I) <= 0.0) PHT = -14.0

 INCR = 10.0

 DO N=1,3

 F = 1.0

 INCR = INCR/10.0

 ITER = 0

 DO WHILE (F > 0.0 .AND. ITER < 12)

 PHT = PHT+INCR

 HION = 10.0**PHT

 F = CART*K1*(HION+2.0*K2)/(HION*HION+K1*HION+K1*K2)+KW/HION-ALKT-HION/HT ! SR 01/01/12

 IF (AMMONIA_BUFFERING) THEN ! SR 01/01/12

 F = F + AMMT*KAMM/(HION+KAMM) ! SR 01/01/12

 END IF ! SR 01/01/12

 IF (PHOSPHATE_BUFFERING) THEN ! SR 01/01/12

 F = F + PHOST*( KP1*KP2*HION + 2*KP1*KP2*KP3 - HION*HION*HION ) &

 /( HION*HION*HION + KP1*HION*HION + KP1*KP2*HION + KP1*KP2*KP3) ! SR 01/01/12

 END IF ! SR 01/01/12

 IF (OM_BUFFERING) THEN ! SR 01/01/12

 DO JA=1,NAG ! SR 01/01/12

 F = F + OMCT*SDEN(JA)*( 1.0/(1.0+HION*(10.0**PK(JA))) - 1.0/(1.0+(10.0**(PK(JA)-4.5))) ) ! SR 01/01/12

 END DO ! SR 01/01/12

 END IF ! SR 01/01/12

 ITER = ITER+1

 END DO

 PHT = PHT-INCR

 END DO

!  pH, carbon dioxide, bicarbonate, and carbonate concentrations

 HION = 10.0** PHT

 PH(K,I) = -PHT

 CO2(K,I) = TIC(K,I)/(1.0+K1/HION+K1*K2/(HION*HION))

 HCO3(K,I) = TIC(K,I)/(1.0+HION/K1+K2/HION)

 CO3(K,I) = TIC(K,I)/((HION*HION)/(K1*K2)+HION/K2+1.0)

 END DO

 END DO

RETURN
52 Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon

In the water-quality.f90 source file, a new ALKALINITY subroutine was added to realize the nonconservative components of 

alkalinity. The new code is:

!********************************************************************************************************************

!** A L K A L I N I T Y **

!********************************************************************************************************************

ENTRY ALKALINITY ! entire subroutine added ! SR 01/01/12

! According to Stumm and Morgan (1996), table 4.5 on page 173:

! Utilization of ammonium during photosynthesis results in an alkalinity decrease: 14 eq. alk per 16 moles ammonium

! Utilization of nitrate during photosynthesis results in an alkalinity increase: 18 eq. alk per 16 moles nitrate

! Production of ammonium during respiration results in an alkalinity increase: 14 eq. alk per 16 moles ammonium

! Nitrification of ammonium results in an alkalinity decrease: 2 eq. alk per 1 mole ammonium

! Denitrification of nitrate (to nitrogen gas) results in an alkalinity increase: 1 eq. alk per 1 mole nitrate

! Alkalinity is represented as mg/L CaCO3 (MW=100.088). CaCO3 has 2 equivalents of alk per mole.

! Nitrogen has an atomic mass of 14.00674. These numbers account for the factor of 50.044/14.00674 used below.

 DO I=IU,ID

 DO K=KT,KB(I)

 ALKSS(K,I) = (50.044/14.00674) * ( 14./16.*(NH4AP(K,I)+NH4EP(K,I)+NH4ZR(K,I)+NH4MR(K,I)-NH4MG(K,I)) &

 + 18./16.*(NO3AG(K,I)+NO3EG(K,I)) &

 - 2.*NH4D(K,I) + NO3D(K,I) + NO3SED(K,I)*(1-FNO3SED(JW)) )

 END DO

 END DO

RETURN
Publishing support provided by the U.S. Geological Survey 

Publishing Network, Tacoma Publishing Service Center

For additional information contact:

Director, Oregon Water Science Center

U.S. Geological Survey

2130 SW 5th Avenue

Portland, Oregon 97201

http://or.water.usgs.gov
Sullivan and others— Macrophyte and pH Buffering Updates to the Klamath River Water-Quality Model Upstream of Keno Dam, Oregon—Scientific Investigations Report 2013–5016