United States

Department of 

Agriculture

Forest Service

Northern 

Research Station

General Technical

Report NRS-71

Approaches for Estimating 

Critical Loads of Nitrogen 

and Sulfur Deposition for 

Forest Ecosystems on 

U.S. Federal Lands

Linda H. Pardo
Visit our homepage at: http://www.nrs.fs.fed.us/

Published by: For additional copies:

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 Fax: (740)368-0152

September 2010 Email: nrspubs@fs.fed.us

The Author

LINDA H. PARDO is an environmental engineer with the U.S. Forest Service’s Northern 

Research Station at Burlington, Vermont.

Abstract

Projected emissions of sulfur and nitrogen are expected to have continuing negative impacts 

on forests, in spite of reductions in sulfur emissions as a result of SO2

 control programs. Sulfur 

and nitrogen emissions present serious long-term threats to forest health and productivity 

in the United States. This report is intended to explain the differences in approaches for 

calculating critical loads for forest ecosystems in Europe, Canada, and the United States; it 

is directed to air quality regulators and Federal Land Managers (FLMs) in the United States, 

and addresses concerns particular to U.S. Federal lands. The paper describes the basic mass 

balance approach for calculating critical loads, presents the various critical thresholds, and 

explains the assumptions inherent in the calculation and data selection procedure. The input 

necessary from FLMs in the process of estimating the critical load is described.

Manuscript received for publication 3 March 2006
Contents

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

 Purpose ............................................................................................................... 1

 Critical Load History ............................................................................................ 1

 Types of Approaches for Critical Load Calculations ............................................ 4

Steady-state Approach: In-depth Review............................................................ 7

 Base Cation Depletion ......................................................................................... 7

 Nitrogen Saturation .............................................................................................. 8

 Calculation of Critical Loads ................................................................................ 8

 Similarities and Differences in Approaches ....................................................... 11

Critical Thresholds Related to Ecosystem Effects........................................... 11

 Thresholds for Estimating Acceptable ANC Leaching ....................................... 11

 Note on Thresholds for Aquatic Critical Loads: ANC ......................................... 13

 Thresholds for Estimating Acceptable N Leaching ............................................ 13

 Thresholds for Estimating Acceptable Soil N Accumulation .............................. 14

 Summary ........................................................................................................... 14

Data Necessary for Critical Loads Calculations ............................................... 14

 Atmospheric Deposition ..................................................................................... 16

 Forest Type/Nutrient Removal ........................................................................... 16

 Soil Mineral Weathering .................................................................................... 17

 Leaching Losses ................................................................................................ 17

 Additional Data Issues ....................................................................................... 17

Selecting the Method .......................................................................................... 17

 Selecting the Critical Threshold ......................................................................... 17

 Selecting the Data Method/Models .................................................................... 18

 Comparing Results ............................................................................................ 18

Next Steps: Toward National Scale Critical Loads Calculations .................... 19

Acknowledgments ............................................................................................... 20

Literature Cited .................................................................................................... 20

Additional Web Resources ................................................................................. 24

Glossary ............................................................................................................... 24

1

INTRODUCTION

Purpose

The objective of this paper is to provide resource 

managers an overview of the critical loads approach for 

estimating acceptable levels of sulfur (S) and nitrogen 

(N) deposition to forest ecosystems. Acceptable levels 

of deposition will protect vulnerable ecosystems and 

allow restoration of impaired ecosystems (Blett 2004). 

Projected emissions of sulfur and nitrogen are expected 

to have continuing negative impacts on forests, in spite of 

reductions in sulfur emissions as a result of SO2 control 

programs. Sulfur and nitrogen emissions present serious 

long-term threats to forest health and productivity in 

the United States. This paper is intended to explain the 

differences in critical loads approaches used in Europe, 

Canada, and the United States for forest ecosystems; it 

is directed to air quality regulators and U.S. Federal land 

managers (FLMs) and addresses concerns particular to 

U.S. Federal lands.

The focus of this paper is on the steady-state mass balance 

methods that have been used most broadly to calculate 

critical loads. Many researchers have calculated critical 

loads using variations of the same approach. This paper 

seeks to clarify the differences in those approaches. The 

two key variations are in selecting the critical threshold (a 

particular pH, for example) and in dealing with missing 

data. These topics are addressed in Sections 3 and 4. 

The paper describes the basic mass balance approach 

for calculating critical loads, presents the various critical 

thresholds, and explains the assumptions inherent in 

the calculation and data selection procedure. The input 

necessary from FLMs in the process of estimating the 

critical load is described. Critical loads for aquatic 

ecosystems are not addressed in this paper.

Critical Load History

Background

The critical load approach has been used in Europe to 

identify levels of deposition expected to cause harmful 

ecological effects. The United Nations Economic 

Commission for Europe (UNECE) convention on 

Long-range Transboundary Air Pollution (LR TAP) 

(U.N. Econ. Com. for Europe 2007) resulted in maps of 

critical loads being generated for Europe by 1995 (Posch 

et al. 1995). Those maps have been modifi ed (Posch et 

al. 2001) and the resulting critical loads have been used 

to regulate emissions through the 1999 Gothenburg 

Protocol via the UNECE Convention on LRTAP. 

Projected emissions reductions in Europe of 63 percent 

for SO2 and 41 percent for NOx by 2010 are estimated 

to protect 78 million hectares, reducing the area of 

exceedance from 93 million hectares in 1990 to 15 

million hectares by 2010 (U.N. Econ. Com. for Europe 

2000).

Critical Load Defi nition

The critical load is the level of deposition below which 

signifi cant harmful ecological effects do not occur (see 

Sidebar 1). This defi nition is used in Europe (UBA 

1996). A current defi nition used by FLMs is “the 

threshold deposition of pollutants at which harmful 

effects on sensitive receptors begins to occur” (Blett 

2004). Both of these defi nitions indicate that to protect 

ecosystems deposition must be below the critical load; 

they are, therefore, essentially interchangeable. Another 

defi nition was used in the FLMs Air Quality Related 

Values Work Group (FLAG) Phase One program 

(National Park Service 2000) that “the critical load is 

the level of deposition above which detrimental effects 

occur”. In this case, the critical load is the maximum 

acceptable deposition level. For example, using the 
2

fi rst two defi nitions, if the critical load is 10 kg/ha/

yr, that means that if the deposition is 10 kg/ha/yr, it 

will harm the ecosystem. Using the third defi nition, 

if the deposition is 10 kg/ha/yr, the ecosystem will be 

protected. For reasons of scientifi c clarity and legal 

defensibility, it is important to be consistent about how 

the critical load is defi ned. Because of the historic use 

of the fi rst defi nition in Europe, and because of the way 

empirical critical loads are set (based on the deposition 

level where detrimental effects are observed), it is 

preferable to defi ne the critical load using either of the 

fi rst two defi nitions—that the critical load is above the 

acceptable level of deposition.

Target Load Defi nition

The critical load is a value that is based on scientifi c 

information about expected ecosystem response to a 

given deposition level. The target load is set by policy 

makers (land managers or air regulators) to meet their 

objectives. In selecting the target load, the policy maker 

may consider economic cost of emissions reductions, 

timeframe, and other matters. The target load may be 

higher than the critical load. For example, the target 

load may be chosen to protect 95 percent of forest 

lands, as has been done in Europe. The target load may 

be lower than the critical load if a very sensitive area 

is to be protected in the short term, generally, in cases 

where current deposition exceeds the critical load. For 

federal resources, the target load would be somewhat 

below the critical load to be consistent with federal 

resource protection mandates (Porter et al. 2005). For 

areas where the critical load has been exceeded, air 

regulatory agencies may choose an “interim target load” 

higher than the critical load, as a progress goal toward 

the critical load (Porter et al. 2005, Skeffi ngton 1999). 

The process for selecting the critical load and target 

load is illustrated in Figure 1. The critical load is not a 

time-dependent value; the target load, in contrast, can 

take into account the timeframe for a desired ecosystem 

condition or recovery (see Sidebar 2).

Sidebar 1.—Roles of Federal Land 

Managers and Research Scientists in 

Setting Critical Loads

Defi ned by researchers with direction from FLMs

Detrimental, Harmful—used to describe a 

condition of the ecosystem where normal nutrient 

cycling processes have been disrupted in such a 

way that the ecosystem can no longer maintain 

its health and productivity. For pristine class I 

areas, this may also include change from “natural” 

(pre-industrial) condition.

Defi ned by FLMs with input from researchers

Signifi cant—this is a decision by the FLM about 

what sort of effect is considered large enough 

to be of importance. For example, what would 

be considered a small change (not signifi cant) 

in an intensively managed ecosystem, may be 

considered signifi cant in a class I area.

Acceptable—Acceptable levels of deposition are 

levels that will protect vulnerable ecosystems and 

allow restoration of impaired ecosystems.

Sidebar 2.—Time and the Critical Load

The concept that the critical load is a steadystate property can be confusing. This means that 

the critical load is based on the capacity of the 

ecosystem to buffer deposition inputs. Inherent in 

the critical load calculation is the assumption that 

all the processes in the ecosystem are at steady 

state, and that the critical load is, therefore, not 

a function of time. An example of steady state is 

a bathtub with the water running and the drain 

plug open, with the fl ow set so that the level of the 

water is unchanging (also see Fig. 2.A).

The steady-state assumption means that fewer 

data are necessary to calculate the critical load. 

Alternatively, if we have enough information to 

describe the rates of the physical, chemical and 

biological processes, we can estimate the time 

until a given condition is reached. This process 

is dynamic modeling, which can yield valuable 

information about time to damage and time to 

recovery if the necessary input data are available. 

Time to recovery (and to damage) are important 

factors in policy and management decisions and 

are used to set target loads rather than critical 

loads.
3

Procedure and roles

The application of critical loads requires interaction 

between policy makers, air quality regulators, federal 

land managers, and scientists. The policy makers create 

the context for enforcement and select the target loads or 

interim target loads based on the critical loads that the 

research scientists have calculated. Federal land managers 

(and air quality regulators) interact with the scientists 

calculating critical loads at several points (Fig. 1). First, 

they identify the regions of concern. Next, they identify 

any particularly sensitive receptors (or areas of an 

ecosystem) of concern; they may be called upon to provide 

data for critical load calculations. Finally, given the critical 

load calculations, they determine the target load.

The research scientists calculating critical loads identify 

the appropriate critical threshold to protect the sensitive 

receptor or area of an ecosystem. They assemble the data 

available for the sites, then they use the best available 

method (based on the data availability) for calculating 

the critical load. In some cases, a range of critical loads 

may be calculated to refl ect the heterogeneity of the 

site or uncertainty in calculation methods. In these 

cases, scientists work with the FLM to determine the 

most appropriate critical load to address the FLMs’ 

goals. It is the manager’s role to determine what change 

is unacceptable and the role of research scientists to 

determine at what level of deposition that change is likely 

to occur.

Identify ecosystems of concern 

Identify sensitive receptors 

Confirm critical threshold 

Propose critical threshold

Identify available data

Evaluate critical load 

Determine target load 

Determine critical load

Select best method based on data 

availability and critical threshold 

FLM activity

Research 

Joint activity

Improve data 

Figure 1.—Flowchart of FLM involvement in the process of calculating critical loads.
4

Inputs from FLMs

To be sure that critical loads are calculated and presented 

in a way that is most useful, FLMs’ input is necessary at 

several stages in the process (Fig. 1). Calculating critical 

loads requires that assumptions be made to convert 

available site data into the simple form required for the 

critical load calculations. These assumptions may include 

utilizing data from other sites or from the literature when 

site-specifi c data are not available. It may also include 

calculating averages of vegetation or soil data, since many 

sites include multiple species and some include multiple 

soil types.

Federal land managers’ input is necessary prior to making 

critical load calculations. Federal land managers need 

to determine the spatial extent of the site for which 

the critical load is to be calculated. A site could be a 

plot, a stand, or a watershed. The scale of the site has 

a signifi cant impact on the assumptions necessary to 

calculate the critical load. Federal land managers also 

must decide whether the critical load should be presented 

as a mean for the area or should be given as a range of 

values from the least to most sensitive areas. And, if 

the critical load is presented for the most sensitive area, 

what is the scale on which that is defi ned? A watershed, 

a stand, a plot, a tree? Further, the FLM may identify 

certain sensitive species of concern, as the critical load 

would normally be calculated for the existing forest type 

(based on a mean of the species present). This broad 

approach could overlook a species with greater sensitivity. 

The same is true for sites with mixed soil types: generally 

the critical load would be calculated based on the areaweighted average of the two soil types. If one soil were 

considerably more sensitive, the calculated critical load 

using the mean soil type might be too high and not 

protect the sensitive soil type. Finally, the FLM can assist 

in the selection of sites that are representative of the 

ecosystems of concern for which critical load calculations 

would be made.

Types of Approaches for Calculations 

of Critical Loads

There are three main approaches for calculating critical 

loads. Empirical approaches are based on observations 

of response of an ecosystem or ecosystem component 

(e.g., foliage, lichens, soil) to a given, observed deposition 

level. Empirical critical loads then are calculated for the 

site where the data were obtained and, generally, they are 

applied to similar sites where such data are not available.

Simple mass balance approaches are based on 

estimating the net loss or accumulation of nutrients based 

on inputs and outputs of the nutrient of concern (e.g., 

base cations, nitrogen). Simple mass balance methods 

are steady-state models that calculate the critical load 

of deposition to an ecosystem over the long term (i.e., 

one rotation in land managed for timber, 100+ years 

in wilderness). They are used at sites with moderate to 

intensive data availability.

Dynamic models use a mass balance approach 

expanded by incorporating internal feedbacks—such as 

accumulation of N in the system, or exchange of base 

cations between soil and soil solution from year to year. 

Dynamic models can predict time to damage and time 

to recovery. Dynamic models are typically used at sites 

where intensive data are available.

Data availability drives the selection of the type of 

approach for calculating critical loads. For sites where 

little or no data are available, empirical approaches must 

be based on data from similar or comparable sites. For 

sites with a moderate to intensive level of data available, 

simple mass balance approaches are used. Most dynamic 

models may be used only at sites with substantial 

data that, generally, must range over some period of 

time. However, a highly tested dynamic model can be 

subsequently applied to an adjacent region with more 

sparse data (e.g., Chen and Driscoll 2005). Each type 

of critical load calculation may yield a different critical 

load value for the same site because of the different 

assumptions involved. Each type of critical load may be 

calculated for the overall ecosystem or for a particular 

ecosystem component (if data for that component are 

available).

Field observation-based approaches

Empirical critical loads are determined by using literature 

or fi eld observations of detrimental ecological effect and 

noting the deposition level at which the effect occurred. 

The lowest deposition level at which a response occurs 
5

is considered the critical load. In cases where there is a 

variation in the level of deposition that causes a given 

response, a range for the critical load often is reported. 

An example of empirical critical loads that are widely 

applied is the European summary of empirical critical 

loads for N (Bobbink et al. 2003). This paper includes 

a table of ecosystem types and their respective empirical 

critical load for N. The utility of empirical critical loads is 

that they can be used to determine the critical load based 

on the best available information for that ecosystem type 

when data are not available at a given site.

Advantages of empirical critical loads are simplicity and 

ease of use (they require no calculation), and applicability 

over a broad set of conditions. Empirical critical loads 

also can be set for different ecosystem types if data are 

available. The main conceptual advantage of empirical 

critical loads is that, under the best circumstances, 

they link ecosystem response to deposition. They are 

particularly useful for setting critical loads for nutrient N, 

which are diffi cult to model.

Disadvantages of empirical critical load calculations are 

primarily due to a lack of quantitative understanding 

of the empirical observations. This approach is based 

on observed cause and effect responses rather than 

understanding of a process or mechanism. Thus, it is 

diffi cult to be certain of the level of deposition that 

causes a given response. Further, since the observations of 

ecological response to a given deposition level are based 

on past scenarios, they may not show the breadth of 

response possible in the future. For example, if a response 

is observed at a given deposition level (or fertilization 

level) after a certain number of years, it is possible that 

a lower deposition over a longer period of time would 

cause the same detrimental effect. This would mean that 

the empirical critical load was too high. For example, N 

deposition of 25 kg/ha/yr for 7 years may cause excess 

nitrate leaching, and therefore, the critical load would 

be set at 25 kg/ha/yr. However, at another site (or even 

the same site), N deposition of 15 kg/ha/yr for 15 years 

might cause the same response.

Another pitfall of the empirical approach is that the 

observed response may be unique to the site at which 

it was measured (because of particular site history, soil 

thickness, etc.) and may not be representative of the 

ecosystem type in general. In this case, the critical load 

might be too high, which would put sensitive areas at 

risk. On the other hand, the critical load might be too 

low, which would not be of great concern for class I areas 

where the mandate is to err on the side of protecting 

the land. Class I areas include national parks, wilderness 

areas, monuments, and other areas of special national and 

cultural signifi cance above a size criterion and in existence 

as of August 7, 1977. They are protected, under the 

Clean Air Act, more stringently than other areas.

In Europe, empirical critical loads have been proposed 

both for acidity (UBA 2004, Chapter 5) and for nutrient 

N (Bobbink et al. 2003, UBA 2004). In the United 

States, because of the nonlinear behavior of acid-base 

processes, and heterogeneity of ecosystems, it is less 

useful to propose empirical critical loads for acidity. For 

nutrient N, however, it is useful to estimate empirical 

critical loads for different categories of ecosystems. 

Several recent summaries of effects of N deposition on 

ecosystems provide useful information about possible 

empirical critical loads for nutrient N (Aber et al. 2003, 

Bobbink et al. 2003, Driscoll et al. 2003a, Fenn et al. 

2003a, 2003b). These assessments are being compiled 

to generate empirical critical loads for N for ecoregions 

in the United States (Pardo et al., in press).1 For some 

ecosystem types where data for calculating critical loads 

are sparse (e.g., arid ecosystems), it may be advantageous 

to estimate empirical critical loads based on the best 

understanding of impacts in those or similar ecosystems 

elsewhere, rather than to attempt to model them.

Steady-state Approaches

Steady-state approaches are based on scientifi c 

understanding of ecosystem processes. These approaches 

also are called simple mass-balance methods. They utilize 

the best available data for estimating the net loss or 

accumulation in the ecosystem of the nutrient of concern.

The advantage of mass balance equations is that they 

are scientifi cally based on the mass balance concept—

that if you deplete the ecosystem pool of an essential 

1For further information see http://nrs.fs.fed.us/clean_air_water/

clean_water/critical_loads/.
6

nutrient, such as base cations, ultimately it will harm the 

forest (Fig. 2). By contrast, if you have too large a net 

accumulation of N in the system, it will be detrimental 

for the forest ecosystem. The mass balance is based on 

ecosystem processes and can be applied at different sites, 

taking into account site condition.

The disadvantages of the mass-balance approach are 

the requirements for extensive data that are not readily 

available; considerable uncertainty about the critical 

thresholds for ecosystem response used; and lack of 

information about time until the expected ecosystem 

response or the timeframe for recovery. Further, steadystate models cannot describe any individual site well, 

as they do not incorporate suffi cient detail or include 

ecosystem processes.

Nonetheless, simple mass-balance models often are 

considered the best available model for estimation of 

critical loads across large regions. These approaches may 

provide the maximum return for the level of information 

they require. This is the approach that was used to 

generate maps for Europe (Posch et al. 2001).

Dynamic Modeling Approaches

Dynamic modeling approaches were developed to address 

the inability of steady-state models to assess time to 

ecological damage or time to recovery. These dynamic 

models give a more realistic representation of change in 

an ecosystem by taking into account that response to 

one change does not occur immediately throughout the 

whole ecosystem. Instead, a change in deposition can 

cause a change in chemistry over some period of time; 

this change in chemistry causes a subsequent change in 

biology over time.

The advantages of dynamic models are that they include 

a more realistic representation of the complexity of 

ecosystems and that the results allow assessment of the 

time for a particular ecosystem effect to occur. Many of 

the impacts associated with air pollution involve these 

nonsteady-state conditions; recovery from these impacts 

also involves nonsteady-state conditions.

The disadvantages of dynamic models are that the models 

may have very large data requirements, take a fairly long 

time (and high level of expertise) to apply to a given 

site, and that some models may describe a particular 

ecosystem type or site very well, but may not be 

applicable to a wide variety of sites. A general diffi culty in 

dynamic modeling is fi nding the balance between having 

the model describe a particular system very well (which 

dynamic models may do, but steady-state models cannot) 

and having the model be useable at a broad range of sites. 

Typically, dynamic models have not been applied over 

broad areas for terrestrial ecosystems. One exception is 

INPUTS OUTPUTS

A. Inputs = Outputs DEPOSITION OTHER INPUTS

INPUTS OUTPUTS

B. Outputs > Inputs

Net Loss

DEPOSITION OTHER INPUTS

INPUTS OUTPUTS

C. Inputs > Outputs

Net Accumulation DEPOSITION OTHER INPUTS

LEACHING LOSS BIOMASS EXPORT

BIOMASS EXPORT LEACHING LOSS

BIOMASS EXPORT LEACHING LOSS

Figure 2.—Mass Balance Approach. 

This is a conceptual schematic for 

any quantity of interest. Specifi c 

examples are shown in Fig. 3. Other 

inputs refers to any inputs in addition 

to deposition, such as mineral 

weathering or nitrogen fi xation. 

Biomass export refers to removal by 

harvesting (which is zero for class I 

areas) and loss from fi re. Leaching 

loss refers to export in solution from 

the soil; for a watershed this would 

include stream export.
7

the Very Simple Dynamic model being developed in 

Europe (http://www.pbl.nl/en/themasites/cce/methods_

and_models/vsd-model/index.html), which is discussed 

on page 19. Dynamic models may be applied over broad 

areas with little data, but not without compromising the 

quality of the results. In such cases, as in any calculation 

of critical loads, better quality and fi ner resolution of 

input data will yield more accurate results.

Since the critical load concept is essentially a steadystate concept, an appropriate application would be to 

combine a steady-state estimation of the critical load 

with a dynamic modeling estimation of time to damage 

or recovery (see Sidebar 2). In this case, it is important 

to ensure that the assumptions and conditions of the 

dynamic model are consistent with those of the steadystate model.

STEADY-STATE APPROACH: 

IN-DEPTH REVIEW

This section explores the steady-state approach in more 

detail, because it is the methodology most likely to be 

used initially by FLMs based on the level of site data 

generally available. The steady-state approach also is 

called the simple or steady-state mass balance approach. 

It is based on the concept that if outputs from an 

ecosystem exceed inputs, you will have a net loss from 

the ecosystem (Fig. 2). On the other hand, if inputs 

to the ecosystem exceed outputs, you will have a net 

accumulation in the ecosystem (Fig. 2C). Simple mass 

balance methods are steady-state models that calculate 

the critical load of deposition to an ecosystem over the 

long term (i.e., one rotation or several cutting cycles, 

depending on the management, or 100+ years for 

wilderness).

The main inputs to the ecosystem include atmospheric 

deposition and weathering of mineral soil; the outputs 

from the ecosystem include leaching losses and biomass 

removal (Fig. 2A). Leaching losses may be estimated 

from water moving downward through the soil or, for 

watersheds, from export of the stream draining the 

watershed. To calculate a critical load, one needs to 

defi ne the ecosystem of concern. In this paper, we explain 

calculating the critical load for the forest ecosystem—

from the trees down through the soil. Although we 

discuss various conditions in one part of the ecosystem or 

another, we do not calculate a critical load to protect that 

component, but to protect the whole forest ecosystem 

including that component. (Protect, in this context, 

means to prevent harmful ecological effects.)

Base Cation Depletion

One result of acidic deposition is the acidifi cation of 

soils and surface water (Driscoll et al. 2001, Reuss and 

Johnson 1985). As acidic deposition moves through 

the ecosystem, there is exchange between the acidifying 

hydrogen ion (that entered the ecosystem with sulfate 

and nitrate) and base cations (calcium (Ca), magnesium 

(Mg), sodium, (Na), potassium (K)). When sulfate 

and nitrate exit the ecosystem, they take these base 

cations with them, leaving the hydrogen ion (H+) in the 

ecosystem. There are several consequences of the removal 

of base cations from the ecosystem and the accumulation 

of H+ in the soil, soil solution, and surface water: the 

acidifi cation of soils and surface water; the potential 

mobilization of aluminum (Al), which can be toxic for 

plants and animals; and the net loss or depletion of base 

cations, which are essential plant nutrients.

These three chemical changes then impact the biological 

components of the ecosystem. There can be direct 

effects of the increased acidity (Driscoll et al. 2001). 

The most broadly described concern is that from 

Al toxicity for aquatic (Cronan and Schofi eld 1990, 

Driscoll et al. 1984, Driscoll et al. 2003b) and forest 

(Cronan and Grigal 1995, Sverdrup and Warfvinge 

1993b) ecosystems. The depletion of base cations is of 

increasing concern (Driscoll et al. 2001, Federer et al. 

1989). Without an adequate supply of base cations, trees 

are susceptible to toxicity from Al in excessively acidic 

environments and from nutritional defi ciency of base 

cations. Consequences of base cation depletion include 

reduced cold tolerance and increased winter injury 

(DeHayes et al. 1999, Schaberg et al. 2000), crown 

dieback (Wilmot et al. 1995), increased susceptibility 

to pest and disease (McLaughlin and Wimmer 1999), 

reduced regeneration, reduced growth and increased 

mortality (Schaberg et al. 2002), and species composition 

changes.
8

To calculate a critical load for acid deposition inputs 

(or acidity), we calculate a mass balance on the base 

cations necessary to neutralize the acid input. If we revise 

Figure 2 in the context of base cation mass balance, the 

inputs are base cation (BC) deposition and soil mineral 

weathering; the losses are BC in biomass removed and 

leaching (Fig. 3A).

Nitrogen Saturation

In addition to nitrogen’s role as an acidifying compound, 

there is concern about excess input of nitrogen in 

the ecosystem and N saturation. This excess nitrogen 

initially will accumulate in soil and subsequently be lost 

via leaching. While increased nitrogen may increase 

productivity in many terrestrial ecosystems (which are 

typically N limited) this is not necessarily desirable in 

protected ecosystems, where natural ecosystem function is 

desired. Excess nitrogen can lead to nutrient imbalances 

in trees, understory species, nonvascular plants (lichens), 

or mycorrhizal fungi; changes in composition of these 

species; and ultimately to declines in forest health (Aber 

et al. 1998, Driscoll et al. 2003a, Fenn et al. 2003b).

If we revise Figure 2 in terms of N saturation 

concerns (Fig. 3B), the inputs for the mass balance 

are atmospheric deposition of N, N fi xation (where 

signifi cant), and the N losses are via leaching, biomass 

removed, accumulation of N in soil, and gaseous 

losses of N (denitrifi cation and volatilization, where 

signifi cant).

Calculation of Critical Loads

Federal land managers need values for critical loads for 

N and S deposition. To determine the critical load for 

N and the critical load for S, we need to determine the 

critical load for N and S inputs combined (i.e., for the 

total acid inputs to the ecosystem). Once the critical 

load for S+N is determined, we must apportion that 

critical load into a S portion and a N portion—in other 

words, to determine how much of the acid input may 

enter the ecosystem as S and how much as N. The N 

input component is the sum of ammonium and nitrate 

deposition. Once the critical load for S+N is calculated, 

there are many possible combinations of N and S 

deposition that would be acceptable (Sidebar 3).

$%$6(&$7,21

,13876$1'2873876

OUTPUTS

BC

WEATHERING

BC

DEPOSITION

BC

LEACHING

BIOMASS

EXPORT

INPUTS

N LEACHING

INPUTS OUTPUTS

B. NITROGEN 

INPUTS AND OUTPUTS

N FIXATION

N DEPOSITION

N GASEOUS LOSS

 N BIOMASS

 EXPORT

Figure 3.—Mass Balance Approach: A. Base Cations (BC), and B. Nitrogen. Two examples 

of how the mass balance approach uses various types of site-specifi c data on chemical and 

biological inputs and outputs. In both cases, outputs are greater than inputs; the difference 

is used in the calculation to determine whether critical loads have been exceeded. A. In this 

example, there is a net loss of BC (outputs>inputs). B. In this example, there is also a net 

output of N from the ecosystem. Biomass export could be via fi re or harvesting.
9

One source of confusion in calculating critical loads 

comes from the fact that N deposition has two main 

consequences: it can acidify the ecosystem, and it can 

lead to plant nutrient imbalances. Sulfur deposition, in 

contrast, only acidifi es the ecosystem. Determining the 

critical load for N, therefore, is a three-step process. First, 

we calculate the critical load for N to address concerns of 

acidifi cation, then we calculate the critical load for N to 

address concerns of excess nutrient N. Finally, we use the 

lower value as the critical load for N.

Process for Calculating the Critical Load for S+N 

(Acidity)

Calculating critical loads for S and N requires several 

steps. First, we calculate the critical load for acidity—for 

the total S + N deposition (note that this is the value 

people use when they calculate a critical load only for 

S—actually, they calculate the critical load for acidity).

The next step is to calculate a critical load for N nutrient. 

This is the level of N deposition that would lead to plant 

nutrient imbalances and, in some cases, to changes in 

species composition and biodiversity. In some cases, the 

critial load for N nutrient is much lower than the critial 

load for acidity (Fig. 4A). In those cases, the critial load 

for N nutrient is taken as the critical load for N, and 

the critical load for S is calculated by taking the critial 

load for N+S and subtracting critial load for N (so the 

total S and N critical loads add up to the critial load for 

for S+N). When the critial load for N nutrient is high 

(Fig. 4B), and when the critial load for N nutrient is 

greater than the critial load for acidity (Fig. 4C), then 

the calculation of critial load for S and critial load for 

N is more complicated. In these cases, there are many 

possible combinations of S and N deposition that would 

be permissible (combine to equal the critial load for S+N; 

Fig. 4B and C).

Process for Estimating the Critical Load for N 

Nutrient

The critical load for N nutrient is sometimes referred 

to as the critial load for N eutrophication. However, 

the term critial load for N nutrient is usually preferred 

because eutrophication implies a concern with effects 

only in aquatic ecosystems. In many calculations 

for critical loads, the critical load for N nutrient is 

Sidebar 3.—Critical Loads and Target Loads for Acidity, Sulfur, Nitrogen, 

N Nutrient

The critical load is the level of deposition below which no harmful ecological effects occur.

The target load is the level of deposition set by policymakers to protect a given area of 

sensitive ecosystem components. The target load may be higher or lower than the critical 

load based on considerations of economic cost of emissions reductions, timeframe, and other 

matters.

Critical loads and target loads can be calculated for different inputs: acidity (N and S combined), 

S, N, or N nutrient (to address detrimental effects caused by excess N and N saturation).

The critical load for acidity is the total deposition of acidity inputs to the ecosystem (S and N 

combined); it is sometimes referred to as critical load S+N.

The critical load for S is the total deposition of S to the ecosystem; when no critical load for N 

is calculated, the critical load for S is equal to the critical load for acidity.

The critical load for N nutrient is the deposition of N to an ecosystem below which no harmful 

effects of N saturation occur.

The critical load for N is the total deposition of N to the ecosystem. The critical load N is either 

simply the critical load for N effects from acidifi cation which is calculated by subtracting the S 

deposition from the critical load acidity. Preferably, a critical load N nutrient is calculated and the 

critical load N used will be the lower of the two.
10

Figure 4.—Calculation of critical loads for S and N is a muti-step process. Critical loads are calculated 

separately for acidity and nutrient N in forest ecosystems (boxes on left). The calculated critical load for 

acidity can be made up various proportions of N:S deposition (boxes on right). The critical load for N 

should not exceed the critical load for nutrient N. (A) critical load for N nutrient is much less than critical 

load for acidity; in this case, the critical load for N nutrient is signifi cantly less than the critical load for 

acidity, so the critical load for N is set to equal the critical load of N nutrient. Once the critical load for 

N is defi ned, then the critical load for S is simply the difference between the critical load for acidity and 

the critical load for N. (B) critical load for N nutrient is similar to critical load for acidity; in this case, there 

are many possible combinations of acceptable values for the critical load for N and the critical load for 

S, as long as the critical load for N does not exceed the critical load for N nutrient. Some of the possible 

combinations are shown. (C) critical load for N nutrient is greater than critical load for acidity; in this case, 

there also are many possible combinations of acceptable values for the critical load for N and the critical 

load for S; any combination of N and S that adds up to critical load for S+N is acceptable. The upper limit 

for critical load for N is the critical load for S+N. Some of the possible combinations are shown.

A

Critical load

Possible Scenario

Critical load

B

Critical load

Possible Scenarios

Critical load

C

Critical load

Critical load acidity

Critical load N nutrient

Possible Scenarios

Critical load

Critical load N

Critical load S
11

overlooked. Initially, this occurred because of a lack of 

understanding about the potential harm that excess N 

deposition could do to ecosystems, and because concerns 

were only about acidifi cation and focused on sulfur. 

With SO2 abatement legislation, sulfur emissions and 

deposition have decreased signifi cantly (Butler et al. 

2001, Driscoll et al. 2001). This decrease in S, combined 

with increases of N deposition in some places, has made 

N increasingly signifi cant (Fenn et al. 2003a). Another 

reason that critical loads for N nutrient were not initially 

calculated is that internal cycling of nitrogen makes the 

effects of N deposition diffi cult to predict and model. 

However, it is very important that the critical load for N 

nutrient be calculated. In some locations, consequences 

of N deposition are far more signifi cant than from 

acidifi cation (Fenn et al. 2003b).

Similarities and Differences in 

Approaches

It is critical for FLMs to understand when using and 

evaluating critical loads that all of the steady-state 

approaches are based on a mass balance on the forest 

ecosystem (Fig. 2). Fundamentally, the approaches are all 

the same: they compare inputs to and outputs from the 

ecosystem. However, the approaches differ in two ways: 

in determining the critical thresholds and in estimating 

and modeling data that are not available. The following 

two sections address these issues in detail.

CRITICAL THRESHOLDS RELATED 

TO ECOSYSTEM EFFECTS

One of the challenges in estimating critical loads is 

relating the ultimate biological or ecosystem effect 

to some measurable quantity—often a chemical 

characteristic. This chemical characteristic is referred 

to as a critical threshold. For aquatic ecosystems, this 

can be more straightforward—a given pH or acid 

neutralizing capacity (ANC) can cause a detrimental 

response in a certain population. In terrestrial ecosystems, 

setting critical thresholds is more diffi cult because 

of the complexity of nutrient cycling and the spatial 

heterogeneity of these ecosystems (UBA 2004). Different 

critical thresholds will lead to different critical loads. 

In general, the critical threshold that best addresses the 

receptor of concern is selected (for example, for some 

receptors a decrease in pH would be the problem, for 

some receptors, an increase in the Al concentration). A 

receptor might be a particular organism (salamander, 

lichen, tree species) or it might be an ecosystem 

compartment (soil, trees, etc.). When several critical loads 

are calculated using different receptors, the lowest value is 

generally used as the critical load. This is a key point for 

FLMs: their input is needed on what ecosystem effects 

are of particular concern and whether there are specifi c 

receptors of exceptional concern within the ecosystem.

The following sections detail the different parameters 

that have been used to set critical threshold values. The 

main values that need to be set in the mass balance 

equations are: (1) acceptable ANC leaching rate; (2) 

acceptable N leaching rate; and (3) acceptable N 

accumulation rate in soil. A more detailed, technical 

explanation can be found in the Mapping Manual (UBA 

2004, Section 5.3.2.2).

Thresholds for Estimating Acceptable 

ANC Leaching

One of the critical thresholds in the mass-balance 

equation used for critical load calculations is the 

acceptable ANC leaching rate—or the loss of acid 

neutralizing capacity that is acceptable over the 

long term. In aquatic systems, the acceptable ANC 

concentration may be set directly because data are 

available that link ANC concentration directly to 

indicator organism health. In terrestrial ecosystems, 

however, organism or ecosystem health are not linked 

directly with ANC concentration, but are related to other 

chemical parameters such as pH or Al that are linked to 

ANC leaching. These chemical parameters (e.g., pH, Al 

concentration) can be used to calculate ANC leaching, 

so if the chemical parameter is set to a given value (the 

critical threshold), the value of ANC leaching calculated 

based on the critical threshold is the acceptable ANC 

leaching rate.

To determine what that ANC value would be, we 

must take into account information about soil pH 

and exchange between Al and H+. The procedure for 

determining the acceptable ANC leaching rate is to 

identify the sensitive receptor, select a chemical criterion, 
12

and fi nally, determine what the critical threshold for 

that criterion would be based on past research and 

understanding (Aherne and Farrell 2002). Typical values 

for critical thresholds are given in Table 1.

Aluminum Concentration

The main critical thresholds that have been used are 

aluminum concentration or the base-cation-to-aluminum 

ratio, BC:Al, in soil solution. At certain levels, Al can be 

toxic to plants (Sverdrup and Warfvinge 1993b). There 

is tremendous variability in how ecosystems actually 

respond to given Al concentrations, making it diffi cult 

to develop an Al threshold. Ecosystem response depends 

heavily on site condition, which can vary widely: one 

ecosystem well below the threshold may appear to thrive 

while another may show signs of clear decline (Cronan 

and Grigal 1995). All of the equations involving a critical 

value for Al rely on a defi ned relationship between Al and 

H+ concentration based on equilibrium with the mineral 

gibbsite (Al(OH)3). A fi xed ratio of Al to H+ is used 

to predict Al concentration based on pH. This value is 

determined observationally or from the literature (Table 

1). Because these data are not widely available, a single 

literature-derived value is usually used (UBA 2004, Table 

5-11, p.V-22).

Base Cation to Aluminum Ratio

Aluminum concentration has been used extensively as a 

critical threshold in aquatic ecosystems. But in terrestrial 

ecosystems, it has been observed that the abundance of 

Al relative to base cations (BC) is more important. For 

example, Al values may be high, but if BC values are 

also high, plant health is not compromised. In contrast, 

relatively low Al values may be detrimental if BC values 

are very low. In this case, the acceptable ANC leaching 

rate is determined by the critical BC:Al ratio and the 

gibbsite ratio of Al:H+ (Table 1).

Calcium to Aluminum Ratio

Research (summarized by Cronan and Grigal 1995) 

has suggested that the most signifi cant ratio is that of 

calcium to aluminum, and not simply the ratio of total 

base cations to aluminum. In this case, a critical threshold 

just for Ca:Al ratio is used. Thus, the acceptable ANC 

leaching value is determined by the critical Ca:Al ratio 

and the gibbsite ratio of Al:H+.

One complicating factor in determining what that critical 

Ca:Al ratio should be is the range of ecosystem response 

to a given Ca:Al ratio. Recent research has made some 

advances in explaining the variability in tree response to 

high Ca:Al in soil solution. Instead of measuring total 

foliar Ca to determine whether a tree has a Ca defi ciency, 

as was done in the past, researchers have separated 

out functionally important Ca, known as membraneassociated calcium or mCa (DeHayes et al. 1999). The 

variability in tree response to low Ca:Al in soil solution 

is greatly reduced when the functionally signifi cant plant 

Ca pool is measured rather than the largely structurally 

bound total Ca. Further, this research suggests that the 

Ca content of the plant prior to exposure may control 

the plant’s susceptibility to Al toxicity—plants with high 

levels of Ca may sequester the toxic Al, minimizing any 

detrimental effects on the plant (Borer et al. 2004). While 

this mCa value is useful for explaining the relationship 

between soil solution Ca:Al ratio and plant Ca defi ciency 

Table 1.—Critical thresholds used to calculate acceptable ANC leaching rate

Critical threshold Typical value Receptor Ecological response Comments

Aluminum 

concentration

0.2 meq/L soils Protection of drinking water 

(groundwater) to EPA standard 

of 5-20 μeq/L

BC:Al ratio 1 mol/mol soils fi ne root damage a more conservative value is 10

Ca:Al ratio 1 mol/mol soils fi ne root damage a more conservative value is 10

pH 4.0 soils loss of Al from soil 

complex; BC depletion

4.2 also is used

Base saturation No decrease soils further BC depletion; 

subsequent nutrient 

defi ciency

Implies that current condition is 

acceptable
13

(and subsequent declines in plant health), the data are 

diffi cult to obtain, and, therefore, not widely available.

pH

For soils high in organic matter, using a criterion based 

on H+ concentration is recommended (UBA 2004). 

In this case, the acceptable ANC leaching value is 

determined by the critical pH (or H+ concentration) 

and the gibbsite ratio of Al:H+. Because organic matter 

forms compounds with Al in solution, the gibbsite ratio 

must be adjusted for these types of soil (Hall et al. 2001, 

van der Salm and de Vries 2001; see UBA 2004, Table 

5-11, p. V-22). If the gibbsite ratio is not modifi ed, the 

calculations will overestimate available toxic Al and give a 

falsely low value for the critical load.

Base Saturation

To move away from the threshold concept, the New 

England Governors/Eastern Canadian Premiers (NEG/

ECP) Forest Mapping Group decided the critical 

criterion would be no change in base saturation (NEG/

ECP 2001). This criterion avoids a precise threshold as 

a basis for setting the critical load. Base saturation (BS) 

is a measure of the available (exchangeable) BC in the 

soil system as a fraction of the maximum BC potentially 

available. High base saturation (greater than about 20 

percent) means that base cations are abundant; low base 

saturation (less than about 10 percent) means that base 

cations are less available and the soil is more susceptible 

to detrimental effects from acidic deposition.

This approach may appeal to FLMs, because it is based 

on limiting human-induced change, which may be 

more aligned with the FLMs’ mandate than selecting 

a particular critical threshold. The base saturation 

approach, however, is not without complexity. Using 

“no decrease in base saturation” as the criterion does 

not necessarily give you equivalent results in terms of 

ecosystem condition. For example, if you have two 

ecosystems, one with a BS of 25 percent and one with a 

BS of 4 percent and you prevent a decrease in BS, you 

end up with two ecosystems that meet the criterion, 

but clearly these ecosystems are not equally buffered. 

The ecosystem with the BS of 25 percent is much less 

susceptible to detrimental effects from acidic deposition 

than the ecosystem with the BS of 4 percent. However, 

from the FLM perspective, with the focus on preventing 

this change to the ecosystem, the base saturation criterion 

may be adequate. On the other hand, this approach 

does not account for any loss of base saturation due to 

acidifi cation in the past, it simply prevents further loss.

Note on Thresholds for Aquatic 

Critical Loads: ANC

The following section is included for information and to 

compare aquatic with terrestrial critical loads. For aquatic 

ecosystems, the critical threshold is the ANC, which is 

set directly (rather than calculated, as above). Generally, 

the acceptable ANC value ranges from 0-50 μeq/L (see 

Pembroke 2003, DuPont et al. 2005, UBA 2004, section 

5.4.1.4, pages V-32-V-33). Lower values of ANC (0 

or 20 μeq/L) usually are set to protect against chronic 

acidifi cation; higher values of ANC (50 μeq/L or in some 

cases higher) are usually set to protect against episodic 

acidifi cation.

Thresholds for Estimating 

Acceptable N Leaching

The acceptable N leaching rate is the allowable loss of 

nitrogen from the ecosystem, usually via streamwater. 

Like the acceptable ANC leaching rate, this rate is 

determined to be acceptable over the long term. Excess 

leaching of N is a sign of N saturation (Aber et al. 1989, 

Stoddard 1994). This is a value used in critical load 

equations and is not a measured value. Typical values for 

critical thresholds are given in Table 2.

Nitrate Concentration

The critical threshold for nitrate concentration exported 

from the ecosystem may range from 0.2-0.4 mg N/L. 

At those levels, nutrient imbalances have been observed 

in coniferous and deciduous forest stands (van Damm 

1990). To determine the critical leaching rate, the critical 

concentration is multiplied by the actual stream fl ow rate.

Nitrate leaching

The nitrate leaching term also may be determined 

directly, if it is not possible to determine it using the 

critical nitrate concentration. Typically values ranges 

from 0-5 kg N/ha/yr, depending on stand type, age, and 

management (Gundersen 1992). For example, acceptable 
14

N leaching rates would increase in the following 

sequence: tundra < boreal coniferous < temperate 

coniferous < temperate deciduous (Grennfelt and 

Thörnelöf 1992).

Thresholds for Estimating Acceptable 

Soil N Accumulation

The acceptable N accumulation is the amount that can 

be added to the soil N pool each year without ultimately 

leading to elevated N losses. This value varies widely as 

a function of soil type and age, species composition, and 

past land-use history; it is diffi cult to determine. Values 

typically used for the threshold for acceptable soil N 

accumulation range from 0.2-1 kg N/ha/yr, although 

some conservative estimates set the value at 0 (Table 2).

Summary

The diffi culty in identifying an abiotic threshold value 

that will lead to a given biological concern is caused by 

lack of understanding of the mechanisms that regulate 

ecosystem dynamics (processes), and also, in cases where 

the mechanism is understood, the extreme variability in 

response of different ecosystems to the same deposition 

level. Also, for acid-sensitive sites it might be diffi cult 

to separate out N nutrient effects from N acidifi cation 

effects. This points out an important scientifi c gap in 

understanding the mechanisms of detrimental effects 

of atmospheric deposition on forest ecosystems. If 

deposition is extremely high (such as 150 kg N/ha/

yr), we know we will see a response, and if deposition 

is extremely low (1 kg N/ha/yr) we know we will not 

see a response. The task at hand, then, is to fi gure out 

when we will start seeing effects, if deposition ranges 

approximately from 5-25 kg N/ha/yr. This is not to say 

that there are not biological measures of damage from 

atmospheric deposition, but that the measures in forest 

ecosystems tend to be of fairly severe damage. In the 

United States, ecosystems usually experience moderate 

levels of deposition. An early indicator that would tell us 

that the trees are at risk, not that they are already severely 

damaged, would be more useful to land managers.

DATA NECESSARY FOR 

CALCULATIONS OF CRITICAL 

LOADS

The data used to calculate critical loads can have an 

impact on the critical load value calculated. Therefore, in 

some cases, it may not be legitimate to compare results 

that are based on different data assumptions. The most 

signifi cant variation between different applications of the 

steady-state mass balance method is in the selection of 

the critical threshold. The second most signifi cant factor 

is how the inputs and outputs of the mass balance are 

estimated. Which data are used is generally a function 

of data availability: when measured data are available, 

differences in critical loads between sites should primarily 

refl ect actual differences in characteristics of each site 

and not incorporate the uncertainty of modeled input 

data. Measured data, however, may include variation 

resulting from differences in measurement method; often 

such differences may be systematic. When measured 

data are not available, the inputs need to be estimated 

either by category or modeling. In these cases there are 

many different approaches that can be used. The data 

requirements include information about soil, vegetation, 

deposition, and surface waters/leaching. The data 

requirements are summarized in Table 3.

Table 2.—Critical thresholds for nitrogen

Critical threshold Typical value Receptor

Ecological 

response Comments

Nitrate concentration in 

soil solution

0.2-0.4 mg N/L coniferous, 

deciduous 

forests

nutrient 

imbalances

Acceptable N leaching 

(soil solution)

0-5 kg N/ha/yr higher N leaching can 

indicate N saturation

Acceptable soil N 

accumulation

0.2-1 kg N/ha/yr soil N leaching, 

acidifi cation

a more conservative 

value is 0
15

It is important to note that in Europe there are some 

signifi cant differences (from the U.S. scenario) that 

drove the development of calculation methods for critical 

loads. First, in terms of vegetation, the stands typically 

are much more homogeneous—fewer species, many 

more single-species stands, many plantations. A second 

difference is that most stands in Europe are intensively 

managed and harvested. Wilderness on the scale of the 

United States does not exist in Europe. This means 

the data assumptions may be more straightforward in 

Europe and data may be more readily available (species 

composition, stand age, rotation length, etc.). In all 

cases, the better the quality and reliability of the data 

used in the critical loads calculations, the more reliable 

the results. This holds true for dynamic models as well as 

steady-state models.

Table 3.—Summary of data needed for calculations of critical loads using the steady-state mass 

balance approach. Data from individual sites are usually preferable to modeled or extrapolated data.

Site description data

Mandatory

Optional

Atmospheric/climate data

Mandatory

Optional

Latitude and longitude

Elevation

Size of site

Land-use history

Disturbance history

County

x

x

xb

xb

xb

xb

Deposition (N, S, Ca, Mg, K, Na)

Precipitation volume (long-term)

Mean annual temperature (long-term)

Mean annual evapotranspiration 

Runoff

xa

xa

xa

xa

xa

Soil data Tree and forest data

Number of soil pits/site

Mineralogy

Soil profi le descriptions

Soil depth

Soil texture

Soil bulk density

Course fragments

Parent material 

Organic matter percent

Soil series

Extractable nutrients (Ca, Mg, K, Na)

Cation exchange capacity

Base saturation

Volumetric soil moisture

Lysimeter data, DON, DOC

pH

x

xa

xd

xd

xd

xc

xc

xc

xc

xc

xc

xc

xb

xb

xb

xb

xb

xb

xb

Stand composition

DBH (diameter at breast height)

Nutrient concentration (N, Ca, Mg, K) 

 by biomass fraction by species

Annual biomass removal rate

Biomass by species 

Average height by species

MAI (mean annual increment)

Volume

Nutrient uptake by species

Nutrient ratios

x

x

xc

xc

xc

xb

xb

xb

xb

xb

Forest health data Stream water data

Foliage transparency

Crown density

Dieback

Insect damage and disease

Areas of forest decline

Vegetation structure

Other (lichens, ...)

xb

xb

xb

xb

xb

xb

xb

Size of catchment

Stream water chemistry

Stream water fl ux

xb

xb

xb

aData may be modeled in some regions if models are available

bData helpful for interpreting results

cData may be calculated or come from (regional) values reported in the literature

dNecessary for making critical loads calculations using the criterion of “no decrease in base saturation” 
16

The purpose of this section is to explain how the different 

assumptions used in assembling data can cause differences 

in critical loads values and to present some of the most 

common approaches for estimating data. The subsequent 

sections address the major components of the critical 

loads calculations.

Atmospheric Deposition

Atmospheric deposition data are often available for wet 

deposition, but infrequently available for dry deposition, 

and rarely available for cloud/fog inputs. Also, dry 

deposition is highly uncertain, spatially heterogeneous, 

and rarely tested using multiple approaches. (Even when 

measured values are available for dry deposition, models 

need to be used to transform the measured concentrations 

into loads of dry deposition, and these models may not 

be parallel). Our purpose here, however, is not to present 

an exhaustive list of the differences in measurement 

and estimation methods, but to give an overview of the 

types of approaches used to determine the atmospheric 

deposition that is necessary for calculating the exceedance 

of the critical load. The exceedance of the critical load is 

the actual deposition minus the critical load.

Two approaches are used to estimate total deposition 

in the absence of measured values: fi xed ratios of total 

deposition:wet deposition and modeling. Using fi xed 

ratios is generally discouraged by atmospheric deposition 

specialists, however, it is very simple and therefore, 

practical. Ratios could be based on CASTNet (Clean 

Air Status and Trends Network; http://www.epa.gov/

castnet) and NADP (National Atmospheric Deposition 

Program; http://nadp.sws.uiuc.edu) data. Note that fi xed 

dry:wet deposition ratios may not be realistic, at least 

for the northeastern United States, because decreases in 

SO2 concentration appear to be reducing the dry:wet 

deposition ratio (Chen and Driscoll 2004). The modeling 

approach can be very useful (e.g., ClimCalc) (Ollinger 

et al. 1993), in that one can generate a value at any site 

regardless of whether any data exist for that site. Other 

regional models include a model of wet deposition for 

the eastern United States (Grimm and Lynch 2004), 

and of deposition in the Rocky Mountains (Nanus et al. 

2003). Such models are usually regional and vary in their 

ability to capture extremes in deposition (as a function 

of elevation, distance from edge, aspect, and inclusion of 

cloud and fog inputs). These models may have numerous 

drawbacks, however, including time period modeled or 

data too sparse to interpolate well between measurement 

points.

Approaches that do not adequately account for dry, 

cloud and fog inputs will result in an underestimation 

of the exceedance: not all sites where the actual 

deposition exceeds the critical load will be identifi ed. 

Some method of estimating total (wet + dry + cloud) 

deposition is therefore needed to interpret critical loads 

meaningfully. Fixed ratios will underestimate deposition 

when cloud and fog inputs are very high, probably 

at sites where inputs occur in a few large events (for 

example, arid or seasonally dry areas). Fixed ratios may 

overestimate deposition in some deciduous stands, high 

precipitation areas, and low-lying areas. Fixed ratios are 

also problematic when there is a shift in vegetation from 

hardwood to conifer or if there are marked variations in 

elevation. If fi xed ratios are based on S deposition, they 

will not be adequate for predicting N deposition.

In summary, it is important to estimate deposition as 

accurately as possible, because underestimation will cause 

too few susceptible sites to be identifi ed (sites where the 

actual deposition exceeds the critical load).

Forest Type/Nutrient Removal

In forests that are harvested, it is necessary to defi ne a 

term for biomass removal. In class I or wilderness areas, 

the biomass removal term would include only biomass 

removed by fi re. Note that large-scale forest disturbances, 

such as blow-down, insect, or disease outbreaks, would 

not be treated as biomass removal because the bulk of 

the biomass remains on the site. It is also necessary to 

determine the forest type for estimating total deposition 

and for identifying susceptibility.

The nutrient removal term can include considerable 

uncertainty in the species composition, estimated 

biomass, estimated nutrient concentration, and estimated 

biomass removed. Estimating the nutrients removed with 

biomass requires fi rst determining the biomass removed 

and then the concentration of nutrients in the biomass 

(which is a function of species composition).
17

Biomass Removal Estimates

If forest harvesting rates are unknown, it may be possible 

to obtain county level information and use that as a crude 

estimate of biomass removed. Actual biomass records that 

can be extrapolated to the future are preferable.

For class I or wilderness areas, it is necessary to have 

information about the frequency and intensity of fi re.

Nutrient Concentration Estimates

To estimate nutrient removal, the nutrient concentration 

is multiplied by biomass removal (generally by tree 

compartment: stem, branch, bark, foliage). For the 

northeastern United States, Pardo et al. (2005) developed 

a tree chemistry database to use when site-specifi c data 

are not available. It might be a useful step to develop 

such a database for the whole country.

If biomass removal is overestimated, the critical load 

for acidity will be too low, and the critical load for N 

nutrient will be too high (not adequately protective).

Soil Mineral Weathering

Mineral weathering is very signifi cant for sites where 

there are concerns about acidifi cation because of 

the role weathering plays in buffering acidic inputs. 

However, there is considerable uncertainty in 

estimating weathering rates. There are several different 

approaches for estimating the mineral weathering. 

The most sophisticated is the Profi le model (Sverdrup 

and Warfvinge 1993a), which has extensive data 

requirements, including a comprehensive measurement 

of minerals present in each soil horizon (mineralogy). 

A simpler approach is to assign the soils to categories 

based on substrate type and to calculate weathering using 

a regression equation based on soil texture, depth, and 

mean annual temperature. Finally, in the absence of even 

soil texture data, the simplest method involves selecting 

categories of soil weathering based on bedrock type, 

adjusted for precipitation, vegetation type, soil texture, 

soil drainage, BC deposition (UBA 2004, Section 5.2.2.).

Underestimating the weathering will cause the critical 

load to be too low; overestimating weathering will cause 

the critical load to be high.

Leaching Losses

Leaching loss terms in the critical loads equations (as 

discussed previously on pages 11-13) are values that are 

set at a level determined to be acceptable over the long 

term. These values are not measured data.

Additional Data Issues

Nitrogen fi xation inputs and denitrifi cation (gaseous 

N loss) losses often are assumed to be negligible and 

therefore excluded from critical loads calculations. 

However, they should be included at sites where they are 

signifi cant.

For some problematic land types, these assumptions/

calculations break down. For example, if a large fraction 

of the land is wetlands, ignoring reduction processes and 

the production of organic acids may be problematic.

Also, lands that were previously in agriculture or 

experienced a severe fi re will retain large quantities of N. 

For these sites, the acceptable soil N accumulation may 

be considerably larger than the range reported (Table 2).

SELECTING THE METHOD

Selecting the Critical Threshold

The two factors that drive the selection of the method to 

use for calculating critical loads are the critical threshold 

and data availability. The critical threshold is selected 

based on which receptor is to be protected. In addition, 

management goals and defensibility may be considered 

in selecting the critical threshold. For class I or wilderness 

areas, it is important to identify any sensitive receptors 

of concern to ensure that the whole ecosystem will 

be protected. The critical load for each ecosystem 

component may be different, and there may be ecosystem 

components more (or less) sensitive than the one for 

which data are available. If data are not available that link 

a given receptor to a particular chemical criterion and 

critical threshold, the critical threshold must be selected 

from those for which there is information. The critical 

load would then be presented to the FLM with the 

information about which receptor was used (soil, etc.). 

Then the FLM would decide about how to set the target 

load, based on the sensitive receptor of concern.
18

Selecting the Data Method/Models

The next step is to determine how the data will be 

synthesized or modeled to generate the input and output 

values necessary for the calculations. The goal is to use 

the best data available at a given site. Therefore, when 

intensive data are available for a site, those would be 

used (Table 3). If fewer data are available, the missing 

data need to be modeled or estimated. In either case, it 

is necessary to document which default variables were 

used as input, which site-specifi c data were used, which 

data were estimated or extrapolated from other sites, and 

which critical thresholds were used. Finally, when very 

few data are available, a categorical approach would be 

used (see UBA 2004, Section 5.2.2; Pardo and Duarte 

2006).

Comparing Results

Several scenarios will result in having multiple critical 

loads values to compare. Different values for the critical 

load may be generated if critical loads are calculated 

for different ecosystem components, different critical 

thresholds, or for individual parameters (for each tree 

species, rather than using a weighted mean species 

composition, or for each soil type, rather than the average 

soil), using different models to calculate input and output 

values for the mass balance equation, or using steadystate and dynamic modeling.

Critical Thresholds and Ecosystem Components

One example of different critical thresholds and 

ecosystem components being used is in comparing 

the European approach used by the International 

Cooperation Programme (ICP) on Mapping and 

Modelling Critical Loads and Levels and Air Pollution 

Effects, Risks and Trends to the approach used in 

calculating critical loads for Eastern Canada and New 

England by the New England Governors/Eastern 

Canadian Premiers Forest Mapping Project (NEG/ECP 

2001). The ICP approach uses the critical threshold of 

BC:Al in soil solution equal to 1 (mol/mol) to protect 

roots from Al toxicity, while the NEG/ECP approach 

uses a critical threshold of no change in base saturation 

to protect the soil from depletion of base cations. In both 

cases, the goal is to protect the forest ecosystem. In the 

ICP case, the receptor is plant roots, in the NEG/ECP 

case, the receptor is the soil. The NEG/ECP result is 

more conservative, but may result in greater variation in 

the ultimate ecosystem condition because of the variation 

in current base saturation (as discussed on page 13).

Most sensitive receptors

In some cases there is an especially sensitive species. 

Rather than calculate a single critical load (based on the 

site average) for a site with multiple tree species, it may 

be appropriate to calculate the critical load based on 

that individual species. The critical load for the average, 

based on the species composition, might not protect 

that sensitive species. This is another point when input 

from FLMs is needed. While it can be helpful to have 

information about the most sensitive tree species, it may 

not be useful for the FLM to be presented with several 

critical loads for a site (and if different types of soils are 

present, the number of critical loads calculated would 

increase). Therefore, depending on the objective of the 

FLMs, they may request the critical load for the average 

conditions, for the most sensitive combination, or for 

the range.

Federal land managers also need to provide input on the 

issue of the scale on which the critical load is calculated. 

Clearly, as discussed previously, the scale on which the 

critical load is calculated will have an impact on its value. 

In general, as the resolution gets coarser, the critical 

load will increase because the small fraction of the most 

sensitive ecosystems will have relatively less impact than 

when those ecosystems are evaluated separately.

Dynamic Models

Dynamic models can provide useful information about 

the time to damage and to recovery. They must be 

used in combination with a steady-state assessment of 

the critical load. Available dynamic models are used to 

evaluate the critical load for acidity.

Dynamic models vary greatly in their complexity and 

ease of use. Some of these models are simple extensions 

of the steady-state method, other models are processbased models that incorporate site data, and others are 

mixed. One of the challenges of using a dynamic model 

to calculate critical loads for forest ecosystems is to model 

both the soil chemistry and the forest vegetation growth 
19

and response accurately. Often a soil model and a tree 

model are linked. Examples of linked models include 

PnET-BGC (Gbondo-Tugbawa et al 2001, GbondoTugbawa and Driscoll 2002, Gbondo-Tugbawa et 

al. 2002), Century-MAGIC, SAFE , and DayCent/

PHREEQC.

The Very Simple Dynamic Model (VSD) was developed 

by the International Cooperation Programme (ICP) 

Mapping and Modelling Group. The VSD model was 

intentionally kept simple so that it could be applied at 

many sites, and it might be an interesting tool for FLMs 

to use for broad-scale critical loads calculations.

One of the biggest challenges in the forest growth 

component is accurately capturing the complexity of N 

cycling. At this point, few dynamic models are used to 

evaluate the critical load for N nutrient, however PnETBGC has been used in this way (Backx 2004).

Some caution is necessary in comparing dynamic models 

with steady-state mass balance models without checking 

that the assumptions are the same. It also is important 

to note that the critical load does not vary with time 

(Sidebar 4). Occasionally, modeling results are presented 

in which a target load (for achieving a certain condition 

in a certain period of time) is presented loosely as a 

critical load.

NEXT STEPS: TOWARD NATIONAL- SCALE CALCULATIONS 

OF CRITICAL LOADS

While the focus of national critical loads calculations 

would be to identify the areas likely to be the most 

susceptible to impacts from atmospheric deposition, it 

also would be useful for identifying critical gaps in the 

data and in developing priorities for monitoring at these 

sites.

Making critical loads calculations on the national scale 

in the United States would present many challenges. 

It is critical to develop a protocol for making these 

calculations so that the process is standardized across the 

country. Because of the heterogeneity of ecosystems and 

variation of deposition and because of the variability in 

data available, this process needs to allow for multiple 

approaches based on the best available data at each site. 

In the absence of measured site data, which is usually 

preferable if the data are of good quality, a protocol 

would specify the order of preference of different 

approaches for calculating or estimating values based on 

ecosystem type and data available.

The European ICP Mapping Manual (UBA 2004) can 

serve as a model for a standard method for calculating 

critical loads for the United States (see web resources 

page). However, alterations to that protocol are necessary 

to make it suitable for use as a federal land management 

tool in the United States. These alterations should focus 

on achieving greater standardization in the process, 

especially concerning the selection of the critical threshold 

and the procedure for fi lling in gaps in data. In Europe, 

the selection of the critical threshold and procedure for 

manipulating data to generate the inputs necessary for 

critical load calculations were at the discretion of each 

country, and were, therefore, made in many different 

ways. Such nonuniformity would not be desirable for 

federal land management in the United States.

Sidebar 4.—Differentiating Critical Loads from 

Target Loads

The critical load is a property of the ecosystem and is independent of 

time. A target load can take time into consideration (for example, the 

time to achieve a certain condition). The critical load does not depend 

on the current condition of the ecosystem; the target load must take 

that into account. When “critical loads” are presented for different 

time periods for an ecosystem, these are actually target loads.
20

ACKNOWLEDGMENTS

I thank Rock Ouimet and Natasha Duarte for review 

of an earlier version of the manuscript. I appreciate the 

thoughtful reviews of C.T. Driscoll and the extensive 

reviews and discussion of T. Blett.

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24

GLOSSARY

Acid neutralizing capacity, ANC—A measure of the 

ability of a solution to neutralize acid imputs.

Base cations—Calcium (Ca2+), magnesium (Mg2+), 

sodium (Na+) and potassium (K+); elements or ions with 

a positive charge (cations) that can neutralize acids.

Base saturation, BS—A way of measuring the base 

cations available to plants. Given as the percentage of 

potential cation exchange sites that have exchangeable 

base cations on them and is expressed as a percentage of 

the total cation exchange capacity.

Categorical approach—Used when very few or no data 

are available at a site. It is an empirical approach which 

classifi es the site into one of several categories associated 

with a value or range of values for each parameter in 

the critical load equation (for example BC weathering, 

nutrient removal, etc.).

Cation exchange—The interchange between a cation 

(positively charged ion) in solution and another cation on 

the surface of soil particles.

Cation exchange capacity, CEC—A measure of the 

total exchangeable cations that a soil can absorb.

Critical load, CL —The level of deposition below which 

signifi cant harmful ecological effects do not occur (see 

Sidebar 1, page 2).

Critical load for acidity—The total deposition of 

acidity inputs to the ecosystem (S and N combined); it is 

sometime referred to as the critical load for S+N.

Critical load for N—The total deposition of N to 

the ecosystem. The critical load for N may simply be 

the critical load for N effects from acidifi cation which 

is calculated by subtracting the S deposition from the 

critical load for acidity. Preferably, a critical load for N 

nutrient is calculated and the critical load for N used will 

be the lower of the two.

Critical load for N nutrient—The deposition of N to 

an ecosystem below which no harmful effects caused 

by excess N (N saturation) occur. These effects include 

elevated N availability and leaching, plant nutrient 

imbalances, changes in species composition,

 and other detrimental impacts on ecosystem health.

Critical load for S—The total deposition of S to the 

ecosystem; when no critical load for N is calculated, the 

critical load for S is equal to the critical load for acidity.

Clean Air Status and Trends Network (CASTNet): http://www.epa.gov/castnet

Critical load resources for Federal land managers: http://nrs.fs.fed.us/clean_air_water/clean_water/critical_loads/

Empirical nitrogen critical loads for natural and 

 semi-natural ecosystems: 2002 update: 

http://www.icpmapping.org/cms/zeigeBerich/13/related_

documents.html

ICP Forests information: http://www.icp-forests.org

ICP Forests manual: http://www.icp-forests.org/Manual.htm

ICP Forests reports: http://www.icp-forests.org/Reports.htm

ICP Forests assessment: http://www.icp-forests.org/pdf/review.pdf

ICP Mapping and Modelling: http://www.icpmapping.org

Long-range Transboundary Air Pollution Convention: http://www.unece.org/env/lrtap

National Atmospheric Deposition Program: http://nadp.sws.uiuc.edu

PROFILE soil chemistry model: http://www2.chemeng.lth.se/models/profi le/index.shtml

Very Simple Dynamic (VSD) soil acidifi cation model: http://www.pbl.nl/en/themasites/cce/methods_and_models/

vsd-model/index.html

ADDITIONAL WEB RESOURCES
25

Critical threshold—A chemical characteristic (usually 

easily measurable) that is related to the ultimate 

biological or ecosystem effect of concern. For example, 

in aquatic systems, a given acid neutralizing capacity 

(critical threshold) may be related to fi sh mortality (the 

biological effect of interest).

DBH—Diameter at breast height. DBH is used to 

measure tree size and to estimate tree biomass.

Denitrifi cation—A microbial process that converts 

nitrogen to a gaseous form which can then be exported 

from the ecosystem.

DOC—Dissolved organic carbon

DON—Dissolved organic nitrogen

Dynamic model—Computer models that incorporate 

internal feedbacks, such as accumulation of N in the 

system, or exchange of base cations between soil and soil 

solution from year to year, and allow for the prediction of 

time to damage and time to recovery.

Empirical critical load—Based on observations of 

response of ecosystem or ecosystem component (e.g., 

foliage, lichens, soil) to a given, observed deposition level. 

Empirical critical loads can be calculated for the site 

where the data were obtained; usually, they are applied to 

similar sites where such data are not available.

Exceedance—The exceedance of the critical load is the 

actual deposition minus the critical load.

FLM—Federal Land Manager

Gibbsite equilibrium—The relationship or 

exchange between aluminum and hydrogen ion (H+) 

concentration is based on equilibrium with the mineral 

gibbsite. A fi xed ratio of aluminum to hydrogen ion 

is used—this ratio is KGibb. Mathematically, this is 

expressed as: [Al3+]crit = KGibb x [H+]crit The ratio, KGibb, 

is used to predict Al concentration based on pH. KGibb is 

determined observationally or from the literature.

Mean annual increment—A measure of the net increase 

in biomass of a tree or forest.

Mass balance—An approach used to determine the 

status of an ecosystem by comparing the inputs to 

the system and the outputs from the system. A mass 

balance can be calculated for any quantity of interest, for 

example, water, nitrogen, etc.

Sensitive receptor—A part of the ecosystem of concern 

to FLMs. The sensitive receptor might be a particular 

organism (salamander, lichen, tree species) or an 

ecosystem compartment (soil, trees, etc.).

Simple mass balance model—Based on estimating the 

net loss or accumulation of nutrients based on inputs 

and outputs of the nutrient of concern (e.g., base cation, 

nitrogen).

Steady state—A condition of an ecosystem where inputs 

are matched by output; there is no net change in a system 

at steady state.

Target load—The level of deposition set by 

policymakers to protect a given area of sensitive 

ecosystem components. The target load may be higher 

or lower than the critical load based on considerations of 

economic cost of emissions reductions, timeframe, and 

other matters.

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The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on 

the basis of race, color, national origin, age, disability, and where applicable, sex, marital status, familial 

status, parental status, religion, sexual orientation, genetic information, political beliefs, reprisal, or because 

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Pardo, L.H. 2010. Approaches for estimating critical loads of N and S deposition 

for forest ecosystems on U.S. federal lands. Gen. Tech. Rep. NRS-71. Newtown 

Square, PA: U.S. Department of Agriculture, Forest Service, Northern Research 

Station. 25 p.

Projected emissions of sulfur and nitrogen are expected to have continuing negative 

impacts on forests, in spite of reductions in sulfur emissions as a result of SO2

control programs. Sulfur and nitrogen emissions present serious long-term threats to 

forest health and productivity in the United States. This report is intended to explain 

the differences in approaches for calculating critical loads for forest ecosystems in 

Europe, Canada, and the United States; it is directed to air quality regulators and 

Federal Land Managers (FLMs) in the United States, and addresses concerns 

particular to U.S. Federal lands. The paper describes the basic mass balance 

approach for calculating critical loads, presents the various critical thresholds, and 

explains the assumptions inherent in the calculation and data selection procedure. 

The input necessary from FLMs in the process of estimating the critical load is 

described.

KEY WORDS: base cation depletion, nitrogen saturation, simple mass balance model
www.nrs.fs.fed.us