Development and Assessment of Odor Footprint Tools from Air Dispersion Modeling: A Case Study in North Dakota

Abstract

As livestock production continues to consolidate into fewer but larger operations, odor complaints from neighboring communities have become a major challenge to industry growth, making the establishment of appropriate odor setback distances essential. This paper reiterates the development procedure of odor footprint tools for setback determination based on AERMOD, a regulatory air dispersion model, using North Dakota as an example. Specifically, we developed North Dakota Odor Footprint Tool (NDOFT), an Excel-based calculator designed to estimate odor setback distances between animal production facilities and surrounding communities. The tool utilizes county-specific meteorological data to predict odor concentrations at various distances and directions relative to an established annoyance threshold of 75 OU m⁻³. Setback distances are determined based on the percentage of time during which modeled odor concentrations remain below this threshold, corresponding to annoyance-free frequencies ranging from 91% to 99%. Facility characteristics, including livestock types, source areas, and odor control measures, are incorporated to enable scenario-based assessments. The influence of complex terrain on setback determination was also evaluated, revealing that no simple correction factors adequately capture terrain effects for valleys and hilltops. Overall, the use of county-specific meteorological inputs substantially improves the accuracy of predicted setback distances compared with area-representative approaches, providing an updated and more robust framework for odor setback planning and environmental evaluation. This work is expected to guide future efforts in developing and refining odor setback tools.

1. Introduction

The growing demand for animal products, driven by rising living standards and evolving consumer expectations, has accelerated consolidation and intensification within the livestock industry across the U.S. Midwest [1,2]. While this transition improves production efficiency and economic viability, it also introduces various environmental challenges [3]. Among these, odor emerges as a prominent concern, influencing the quality of life of nearby residents and prompting a growing number of complaints [4,5,6]. Increased public awareness of odor and air quality issues has further intensified opposition to the siting of new animal production facilities and the expansion of existing ones [7].

One of the most widely used strategies for mitigating odor nuisance is the establishment of setback distances that separate animal production facilities from neighboring communities. However, determining appropriate setback distances is complicated, as odor emissions and resulting impacts vary with factors such as animal species, facility types, manure management practices, meteorological conditions, terrain, and location of neighboring communities [8,9]. These factors can substantially influence odor dispersion patterns and, therefore, the frequency and severity of odor nuisance.

Several states rely on prescriptive approaches, such as lookup tables or fixed minimum distances, to establish odor-related setback requirements based on animal type, herd size, or facility characteristics [10,11]. For instance, in North Carolina, regulations specify fixed minimum separation distances for certain operations, particularly swine farms with waste lagoons requiring buffers from residences, schools, and water bodies [12]. Missouri applies a similar framework but generally imposes more stringent requirements for large concentrated animal feeding operations (CAFOs) [13,14,15]. Ohio mandates minimum distances for large facilities, with requirements determined by animal units and facility characteristics [16]. While these prescriptive approaches are straightforward and easy to implement, they do not explicitly account for local meteorological conditions despite their significant impact on odor dispersion. Consequently, setback distances derived from such approaches may be overly conservative—placing unnecessary economic constraints on producers—or insufficiently protective of neighboring communities [17].

An alternative and more scientifically grounded approach involves simulating odor dispersion around animal production facilities. INPUFF, a single source Gaussian puff model historically adopted by the U.S. Environmental Protection Agency (EPA), has been used to create odor setback tools in states such as Minnesota and Michigan. AERMOD, a more complicated, EPA-approved regulatory air dispersion model, has been applied in Nebraska and South Dakota to support similar tool development [18,19,20]. By incorporating emission source characteristics, meteorological data, terrain features, and receptor locations, AERMOD enables more site-specific estimates of potential odor impacts. Consequently, it has been widely used in agricultural research and, in some cases, voluntarily adopted in large-scale livestock development projects to evaluate potential odor and other air quality impacts [14,21].

Despite their robustness, both INPUFF and AERMOD require extensive input data, technical expertise, and licensing fees, which limits their accessibility for many stakeholders. To address these challenges, the odor footprint tools in Nebraska and South Dakota divide each state into several meteorological areas. For each area, simplified AERMOD modeling was used to establish relationships between odor setback distances and overall odor emissions across radial directions (e.g., north, east, south, and west) [18,19]. These simplifications rely on assumptions on terrain, source type, plume rise, and other dispersion-related factors. The resulting tools allow average users to generate setback estimates without specialized modeling skills.

Minnesota and Michigan employ a related but distinct approach for tool development. Instead of creating zone-specific relationships, their tools statistically summarize modeling results from multiple scenarios to formulate statewide empirical equations for distance determination [22]. The Michigan version further refines this approach by allowing adjustments based on county- and direction-specific meteorological conditions. Although these tools are practical and user-friendly, they share certain limitations, such as reduced zonal or radial directional resolution, which can introduce uncertainty into setback distance estimates.

Compared with neighboring states, livestock production in North Dakota remains relatively less developed. As the state seeks to grow its livestock sector, odor management challenges are expected to become increasingly critical. However, producers, community members, and government officials have limited experience with siting large-scale animal operations. Consequently, there is a clear need for a practical odor setback tool to support planning and decision-making. Such a tool would help balance livestock development with community acceptance and support the sustainable growth of animal agriculture.

Although advanced dispersion models such as AERMOD are available, their routine application in odor management in North Dakota is unlikely due to practical constraints, including data requirements, technical expertise, and computational demands. Simplified odor footprint tools tailored to state-specific meteorological and terrain conditions offer a more accessible alternative. In this context, a key question arises: how can a simplified, regionally adapted odor setback tool be developed using AERMOD-based simulations while maintaining both practical usability and a reasonable representation of local meteorological and terrain influences? Therefore, the goal of this study was to develop a North Dakota-specific odor footprint tool (NDOFT) that leverages AERMOD-based simulations while maintaining usability for producers, planners, and Extension practitioners. The specific objectives were to: (1) conduct AERMOD simulations of odor dispersion using county-specific meteorological data; (2) develop an Excel-based, user-friendly calculator for estimating odor setback distances under varying facility characteristics; and (3) evaluate the performance, limitations, and practical applicability of the resulting tool. This work is intended to inform future development and refinement of odor setback tools.

2. Tool Formulation

2.1. Tool Overview

NDOFT is an Excel-based odor footprint tool developed to estimate direction-specific odor setback distances for planned or existing animal production facilities. The formulation of NDOFT follows a workflow-based framework that links dispersion modeling, data processing, and tool implementation (Figure 1). AERMOD modeling was conducted using county-specific meteorological data, simplified terrain assumptions, and assumed odor emission rates to predict ground-level odor concentrations in multiple directions. The model outputs were subsequently processed to derive odor annoyance-free curves, which establish the relationship between setback distances and odor emission rates for a given odor annoyance management goal. These mathematical relations were then incorporated into a streamlined, Excel-based calculator. Key parameters involved in the formulation of NDOFT are defined in

Table 1. Definitions and units of key parameters used in this study.

Parameter	Description	Unit
Odor concentration	Modeled odor concentration in ambient air	OU m−3
Odor emission factor	Odor emission rate per unit surface area	OU ft−2 s−3
Plan area	Surface area of an odor-emitting source/unit	ft2
Total odor emission rate	Total emission rate from the entire operation	OU s−1
Annoyance-free frequency	Percentage of hours with modeled odor concentrations below 75 OU m−3	%
Meteorology	Hourly meteorological variables	—

. Detailed descriptions of model configuration, data processing, and tool implementation are provided in the following sections.

2.2. Modeling Configuration and Process

2.2.1. Modeling Considerations

Odor is not a single, regulated air pollutant; rather, it arises from a mixture of various odorous chemicals in gases and particulates. The dispersion of these chemicals is governed by the same physical processes, including advection and turbulent diffusion that control the transport of typical air pollutants. Some odorous compounds may undergo photolysis under sunlight in the atmosphere, with certain oxygenated compounds exhibiting relatively rapid photochemical decay [23]. However, because communities affected by livestock odors are often located in close proximity to animal production facilities, atmospheric photochemical degradation of odorants can often be neglected. Consequently, odor dispersion can, in principle, be modeled using air dispersion models that build on the law of conservation of mass.

Air dispersion models rely on the principle of mass conservation, which requires a quantifiable and additive entity to be transported through the modeling domain. Odor, however, is typically assessed as an integrated human sensory response. Among common odor metrics (e.g., odor intensity, persistence, and hedonic tone), only the threshold concentration—measured via olfactometry using the dilution-to-threshold method and expressed in odor units per cubic meter (OU m⁻³)—provides a mass-consistent surrogate suitable for AERMOD modeling.

AERMOD requires three categories of input data: emission source characteristics, meteorological conditions, and receptor locations. As a tool derived from AERMOD modeling, NDOFT similarly depends on these inputs and represents odors using threshold concentrations. Full-scale AERMOD simulations can be complex and highly site-specific due to variability in source geometry, building downwash, and terrain effects. To enable consistent and computationally efficient implementation, a set of simplifying assumptions was adopted, as described below [18,19].

For emission sources, NDOFT assumes that:

(1)

Odor emissions from animal houses, feedlots, and manure storage units are constant over time and occur at the ground level;

(2)

An animal farm consisting of multiple houses, lots, and manure storage units can be represented as a single point source for modeling purposes;

(3)

No nearby buildings or major physical obstructions exist that would substantially alter odor dispersion patterns.

This single-point-source assumption was adopted to keep NDOFT practical as a statewide screening tool. Because facility layouts and source distributions vary widely, defining one standard geometry for all operations is not practical. This approximation is most appropriate when individual odor-emitting units are close to one another relative to the source-receptor distance. For very large or spatially distributed operations, especially when receptors are located near the facility boundary, site-specific AERMOD modeling with explicit source geometry is recommended. In detailed AERMOD applications, individual emission sources can be explicitly represented using spatially resolved source configurations (e.g., multiple point, area, or volume sources). However, such approaches require site-specific data and modeling expertise that are not practical for a generalized, user-oriented screening tool.

For meteorological conditions, it assumes that:

(1)

Historical meteorological data are representative of typical weather patterns and therefore suitable for simulating odor dispersion; and

(2)

For farms in each county, historical meteorological conditions can be represented using data from the nearest local weather station when available; otherwise, conditions can be approximated using the Weather Research and Forecasting (WRF) model outputs generated for the county’s geographic center.

For receptors representing neighboring communities, it assumes that:

(1)

Receptors are located at ground level; and

(2)

Both emission sources and receptors are situated on flat terrain.

2.2.2. Model Inputs

AERMOD modeling involved four types of inputs: meteorological data, terrain data, emission source specification, and receptor layout. In addition, output options were predefined to extract ground-level odor concentration percentiles required for subsequent establishment of odor-free annoyance curves.

(1)

Meteorology

Both surface and upper-air meteorological datasets are required by AERMOD. Surface meteorological data describes near-ground conditions (e.g., wind speed, wind direction, temperature, humidity, and solar radiation), whereas upper-air data provide vertical profiles governing atmospheric stability, mixing height, and plume behavior.

In this study, county-level surface meteorological data covering the period Jan 2021–Dec 2023 were compiled from NOAA’s Integrated Surface Dataset (ISD) for counties with operational weather stations. For counties without local stations, surface meteorological conditions for the same period were extracted from WRF model outputs at the county geographic center. Notably, the use of WRF-derived meteorological fields as input to AERMOD has been commonly adopted in regions where representative surface observations are sparse or unavailable [24]. A three-year meteorological dataset was used in this study. While current regulatory guidance for AERMOD applications recommends five consecutive years of meteorological data, the selected period reflects common practice in non-regulatory and screening-level assessments, particularly where data availability is limited. This choice also ensures consistency across counties included in the analysis, as longer continuous records were not uniformly available for all locations.

Upper-air meteorological data for the same period were obtained from NOAA’s Integrated Global Radiosonde Archive (IGRA), using the Bismarck station as the representative upper-air source for the state. The availability and sources of surface meteorological data for each county are summarized in Table S1. Both surface and upper-air datasets were subsequently processed using the AERMET meteorological preprocessor, the standard preprocessing system for AERMOD applications. Meteorological data was processed using AERMET View, V13.0 (Lakes Environmental Software, Waterloo, ON, Canada). The generated county-specific surface (SFC) and upper air (PFL) meteorological files were then used as model inputs for AERMOD View, V13.0 (Lakes Environmental Software, Waterloo, ON, Canada).

(2)

Terrain

Terrain data is required for regulatory AERMOD modeling. However, incorporating complex terrain information into Excel-based odor setback tools presents practical challenges. Consequently, and consistent with other existing odor setback tools, NDOFT assumes flat terrain surrounding animal production facilities, including neighboring communities. This assumption is appropriate for many sites in the Midwest, including North Dakota, where landscapes are predominantly flat. Nonetheless, since terrain can influence odor dispersion and, thus, setback distance determination, the potential effects of representative terrain conditions were further evaluated in Section 3.

(3)

Source characteristics

A single POINT source was used to represent an entire facility (i.e., consolidated from multiple barns, lots, and manure storage units), consistent with the simplifying assumptions described in Section 2.2.1. A computational reference of 0.5 g s⁻¹ was applied as a unit emission rate. This value was not interpreted as a physical pollutant mass but was treated as an equivalent odor emission rate (50 × 10⁴ OU s⁻¹) for scaling purposes, since odor is not included as a pollutant option in AERMOD. It is important to note that AERMOD simulations were conducted using this unit emission only. Consistent with the Gaussian dispersion formulation of AERMOD, modeled pollutant concentrations are linearly proportional to the point source emission rate. This proportionality was verified through additional model runs using a range of emission rates. Other POINT source characteristics included a release height of 0 m, a stack inside diameter of 10 m, a gas exit temperature of 20 °C, and a gas exit velocity of 0.1 m s⁻¹. Under these conditions, plume rise due to momentum and thermal buoyancy was negligible, which is representative of odor plumes emitted from most odor-emitting units on animal farms.

(4)

Receptor grids

Receptors were defined using a ground-level uniform polar receptor network to obtain direction-specific concentration patterns. Eight directional radials were specified at 45° increments, and receptors were placed at 20 m spacing along each radial from the origin out to 10,000 m, resulting in 4000 receptor points per county. This receptor design supports direct extraction of setback-vs-odor-emission relationships (i.e., odor annoyance-free curves) along each direction while maintaining computational efficiency.

(5)

Output options

To support odor management, a set of annoyance-free frequency targets (91%, 94%, 96%, 97%, 98%, and 99%) was selected as management objectives. Here, annoyance-free frequency refers to the proportion of time during which modeled odor concentrations remain below the odor threshold (75 OU m⁻³) at receptor locations, as detailed in Section 2.3.2. Accordingly, AERMOD output options were configured to report ground-level odor concentrations at the corresponding percentiles (91%, 94%, 96%, 97%, 98%, and 99%), consistent with the selected odor annoyance management objectives for the April–October period. Consistent with existing odor footprint tools, the April-October period was selected because livestock odor nuisance most commonly occurs during warmer months in the U.S. Midwest, when elevated temperatures and increased ventilation rates enhance the volatilization and release of odorants [18,22].

2.3. Data Processing and Metric Definition

2.3.1. Model Outputs

AERMOD simulations generated ground-level odor concentration outputs at all receptor locations at each selected percentile (91%, 94%, 96%, 97%, 98%, or 99%). County-specified meteorological data was used; therefore, for each county, AERMOD produced five separate output files corresponding to these predefined concentration percentiles at the unit emission rate (50 × 10⁴ OU s⁻¹).

2.3.2. Definition of Annoyance-Free Frequency

Odor annoyance is commonly evaluated using psychophysical odor intensity scales that relate human perception to ambient odor levels. On the widely used 0–5 odor intensity scale, an intensity level of 2 corresponds to a distinct and clearly noticeable odor and has been used in livestock odor setback studies as the boundary between faint or generally non-annoying odor and odor levels that may cause annoyance. Previous studies indicate that, for animal production facilities, this perception level corresponds to an odor concentration of approximately 75 OU m⁻³. Consequently, this value has been widely adopted in livestock odor setback calculations and related odor footprint tools as a practical threshold for unacceptable odor impact [6,8,13]. Notably, the threshold is based on field measurements conducted in Minnesota more than 25 years ago, a region with livestock systems and rural landscapes comparable to those in North Dakota. Although changes in production practices may have altered odor characteristics to some extent, such changes are expected to be limited, and the use of this threshold represents a reasonable approximation in the absence of more recent, region-specific data.

Based on this threshold, annoyance-free frequency is defined as the proportion of time during which modeled ground-level odor concentrations at a given receptor location remain below 75 OU m⁻³. Since the time resolution of AERMOD is 1 h, the annoyance-free frequency (AFF) can be expressed as:

$$\mathrm{A}\mathrm{F}\mathrm{F}=1-{\displaystyle \frac{{\mathrm{N}}_{\mathrm{e}\mathrm{x}\mathrm{c}\mathrm{e}\mathrm{e}\mathrm{d}}}{{\mathrm{N}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}}$$

(1)

where ${\mathrm{N}}_{\mathrm{e}\mathrm{x}\mathrm{c}\mathrm{e}\mathrm{e}\mathrm{d}}$ represents the number of modeled hours during which odor concentrations exceed 75 OU m⁻³, and ${\mathrm{N}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ denotes the total number of modeled hours within the specified analysis period.

2.3.3. MATLAB-Based Data Processing

MATLAB R2025b (Mathworks Inc., Natick, MA, USA) was employed to post-process AERMOD output files and determine direction-specific odor setback distances at a selected odor management objective (91%, 94%, 96%, 97%, 98%, or 99% annoyance-free frequency).

To evaluate setback distances across a broader range of emission scenarios without rerunning AERMOD, modeled concentrations derived from the unit emission rate (50 × 10⁴) were linearly scaled to represent higher odor emission rates. Scaled odor emission rates intentionally ranged from 50 × 10⁴ to 10,000 × 10⁴ OU s⁻¹, covering odor emission scenarios representative of small- to very large-scale animal production facilities.

For each odor annoyance-free frequency and wind direction, setback distance was again defined as the radial distance at which the odor concentration decreased to the 75 OU m⁻³ threshold. Distances were determined by identifying threshold-crossing intervals between adjacent receptors, followed by interpolation to estimate the corresponding distance. When concentrations at the nearest receptor (20 m) were below the threshold, the setback distance was assigned a value of zero; however, this did not occur in the simulations. When concentrations at the outermost receptor remained above the threshold, the setback distance was estimated by extrapolation.

2.3.4. Construction of Annoyance-Free Curves

The MATLAB-based data processing in Section 2.3.3 yields direction-specific setback distances for discrete odor emission rates at selected odor annoyance-free frequencies. To facilitate practical application, these discrete results were organized into annoyance-free curves that describe the relationship between odor emission rates and the required setback distance for a given wind direction and odor management objective.

For each county and radial direction, odor annoyance-free curves present how setback distances increase with odor emission rates at multiple odor management objectives (91–99%). Directional differences among the curves reflect prevailing wind effects and the associated directional variability of odor dispersion. Figure 2 shows the annoyance-free curves for Cass County across eight directions. Each curve defines the minimum separation distance required to ensure that modeled odor concentrations remain below the odor annoyance threshold. These curves allow setback distances to be determined for any odor emission rates of up to 10,000 × 10⁴ OU s⁻¹.

It should be noted that the setback distances generated by NDOFT inherently contain uncertainty arising from multiple sources, including variability in meteorological inputs, assumptions in terrain representation, and the use of generalized odor emission and control factors. These uncertainties propagate through the dispersion modeling process and are reflected in the resulting annoyance-free curves. Because of the nonlinear nature in which setback distance is determined (based on the percentage of time that concentrations exceed a threshold), these uncertainties cannot be expressed through a simple analytical relationship. Consequently, the setback distances provided by NDOFT should be again interpreted as planning-level estimates rather than precise predictions of odor impact.

2.4. Excel Tool Implementation

2.4.1. Total Odor Emission Rate (TOER)

TOER represents the sum of odor emissions from all odor-emitting units within an animal facility and is intended to characterize the facility’s overall odor emission strength in a form that can be directly applied in the odor annoyance-free curves (Figure 2).

The odor emission rate (OER) for an individual odor-emitting component is calculated as below:

$$\mathrm{O}\mathrm{E}\mathrm{R}=\mathrm{O}\mathrm{d}\mathrm{o}\mathrm{r} \mathrm{e}\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}\times \mathrm{P}\mathrm{l}\mathrm{a}\mathrm{n} \mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}\times \mathrm{O}\mathrm{d}\mathrm{o}\mathrm{r} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{l} \mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}$$

(2)

where OER characterizes the per footage odor emission rate for a given source type, plan area is the footage of the odor-emitting surface, and odor control factor accounts for emission mitigation by on-farm management practices.

This formulation allows odor emissions to be estimated across different source types, including animal housing, manure storage units, and open feedlot surfaces, and facility sizes, while accounting for the effects of odor control technologies. The odor emission factors, source classifications, and odor control factors used in this study were derived from previously published odor measurement and modeling research conducted during the development of the Odor From Feedlots–Setback Estimation Tool (OFFSET) [22,25]. These parameters have also been adopted in subsequent tools, including Michigan OFFSET, the South Dakota Odor Footprint Tool (SDOFT), and the Nebraska Odor Footprint Tool (NDOT) [18].

For a given facility, the total odor emission rate (TOER) is calculated as the sum of odor emission rates from all contributing sources on the site:

$$\mathrm{T}\mathrm{O}\mathrm{E}\mathrm{R}=\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{O}\mathrm{E}\mathrm{R}}_{\mathrm{i}}$$

(3)

where $\mathrm{n}$ is the total number of odor-emitting units within the facility. The adopted odor emission factors, odor control factors, and source specifics can be found in Ref. [22]. Notably, these odor emission and control factors were adopted from existing setback tools in Minnesota and South Dakota and have not yet been locally validated using North Dakota-specific measurements, due in part to funding and resource constraints. Their applicability may therefore vary with housing design, manure management, maintenance, and operational practices. Accordingly, the calculated TOER and setback distances should be interpreted as planning-level estimates, and future site-specific measurements will help refine these parameters for North Dakota conditions.

The calculated TOER can be manually intersected with the odor annoyance-free curves (Figure 2) to obtain setback distances for selected odor management targets. However, to facilitate practical application, these calculations were implemented using Excel-based setback calculators.

2.4.2. Creation of an Excel-Based Calculator

In this Excel-based calculator, the annoyance-free curves obtained from MATLAB processing were tabulated for each wind direction and county and stored collectively in a hidden worksheet for backend lookup. The TOER calculation, however, was implemented in a user-interface worksheet (Figure 3), following the same layout as SDOFT. In this worksheet, the user first selects the county in which the animal production facility is located, enabling the calculator to retrieve the county-specific odor annoyance-free curves for setback determination.

Determination of TOER for a given facility involves four steps. First, the user specifies the source type of each odor-emitting unit (e.g., swine barns, poultry barns, manure storage units). Second, the user selects the corresponding source subtypes (labeled “Housing Type & Manure Storage” in the interface). Based on these selections, the tool retrieves the appropriate odor emission rate (OER) from a lookup table stored in a separate hidden worksheet. Third, the user specifies the plan area of each odor-emitting unit. As in SDOFT, only the length and width of rectangular units are accepted as inputs for simplicity; for non-rectangular units, equivalent length and width values can be entered to preserve the correct plan area. Lastly, the user specifies the odor control practices in place, prompting the calculator to retrieve the associated odor control factors from another hidden worksheet. The user-interface worksheet allows inclusion of up to five odor-emitting units, and TOER is calculated as the sum of emissions from these units.

Based on the TOER and the county-specific annoyance-free curves, the calculator automatically calculates setback distances across eight compass directions. The calculation results are presented in both tabular forms and a polar chart (Figure 3). The user can further select a target odor management objective (91–99% annoyance-free) to streamline visualization of setback distances in difference directions.

3. Tool Assessment

3.1. Tool Assessment Tasks

3.1.1. Implication of Wind Roses

Wind speed and wind direction are two primary meteorological parameters governing odor dispersion and therefore play a central role in determining direction-specific setback distances. To assess whether county-level wind characteristics are reflected in the setback distances produced by NDOFT, wind roses were generated for counties in North Dakota.

Wind roses summarize the distribution of wind direction and wind speed over a specified time period and provide insight into prevailing wind and dispersion conditions. In this study, wind roses were created using the WRPlot View module within the AERMOD View software based on the same meteorological datasets retrieved used in the NDOFT simulations. These wind roses were then used to qualitatively evaluate the relationship between dominant wind patterns and the directional variability of modeled setback distances.

3.1.2. Influence of Complex Terrain

In the current version of NDOFT, all sources and receptors are assumed to be located on flat terrain, resulting in AERMOD simulations over an idealized level surface. While this assumption reflects typical siting conditions in North Dakota, it does not explicitly represent real-world topographic variability.

To examine the potential influence of complex terrain on setback distance estimates, digital elevation data retrieved from the U.S. Geological Survey (USGS) National Map were used for simulations in Billings, McKenzie, and Cass counties (Table S2), representing three characteristic terrain types: hill, valley, and flat, respectively. Receptor locations were placed at representative positions within each terrain type, and the associated terrain data were pre-processed with AERMAP before being applied for AERMOD modeling. Setback distances derived from these terrain-specific simulations were then compared with those calculated by NDOFT to assess the influence of terrain on setback determination and the practical applicability of the flat-terrain assumption. In this analysis, the “flat” terrain case represents relatively level topography derived from Cass County elevation data, rather than the perfectly flat surface assumed in NDOFT simulations. To ensure comparability, the same farm input used in Figure 3 was applied across all simulations.

3.1.3. Influence of County-Specific Meteorology

In the Minnesota OFFSET, the entire state was assumed to share uniform meteorological conditions. In contrast, the South Dakota SDOFT and Nebraska NOFT tools divide each state into several meteorological areas based on wind roses to reduce computational complexity. To assess the potential influence and benefit of employing country-specific meteorology, North Dakota’s 53 counties were grouped into three major meteorological areas using the same classification criteria as in SDOFT (Figures S1 and S2).

This regionalization was conducted using principal component analysis (PCA) of historical wind rose data obtained from the North Dakota Agricultural Weather Network (NDAWN) database, which consists of over 90 stations statewide. It should be noted that this grouping was not intended to be exact, and the resulting meteorological areas do not closely align with North Dakota’s three geographic (topographic) regions (Red River Valley, Drift Prairie, and Missouri Plateau).

Based on the PCA results, one county with representative wind conditions was selected for each meteorological area (Mountrail County for Area 1, Billings County for Area 2, and La Moure County for Area 3). Two additional counties were selected in each area, and setback distances were calculated using NDOFT and the same farm input used in Figure 3. Differences in predicted setback distances among counties within the same region were then examined. Specifically, Divide County and Ward County were selected from Area 1, McKenzie County and Burleigh County were from Area 2, and Sioux County and Cass County from Area 3.

3.2. Tool Assessment Results

3.2.1. Implication of Wind Roses

This section examines the relationship between wind patterns and NDOFT-predicted setback distances using wind rose analysis. Figure 4 presents wind roses and corresponding setback distances calculated by NDOFT for Cass, McKenzie, and Mercer counties during the 2021–2023 period, based on the same facility characteristics shown in Figure 3. Wind roses were generated using the WRPlot View module within the AERMOD View software. The variability observed across scenarios also reflects cumulative uncertainties associated with meteorological inputs, emission parameterization, and terrain assumptions, all of which influence odor plume dispersion and therefore the derived setback distances.

As shown in Figure 4a, the prevailing wind direction in Cass County is from the south, indicating that southerly winds occur most frequently. Consistent with this pattern, the greatest predicted setback distance occurs north of the facility. This observation aligns with the common expectation that frequent and persistent winds can transport odors farther in the downwind direction (Figure 4d). A similar correspondence between prevailing wind direction and maximum setback distance is observed for McKenzie County (Figure 4b,e). In contrast, Mercer County exhibits a different pattern. Although northwesterly winds dominate the wind rose (Figure 4c), the maximum setback distances are predicted to the northeast of the facility (Figure 4f). This mismatch indicates that prevailing wind direction alone is insufficient to guide the siting of animal production facilities and suggests that additional meteorological factors influence directional variability in setback distances.

Atmospheric dispersion is governed not only by the mean wind field but also by turbulence intensity, boundary-layer mixing height, and atmospheric stability, which collectively control the vertical and horizontal dispersion of odor plumes [26,27]. Rather than traveling strictly along the mean wind direction, odor plumes undergo continuous turbulent diffusion, resulting in horizontal and vertical dispersion that occurs perpendicular to the wind direction and cannot be inferred from wind roses alone [20]. Vertical mixing is especially sensitive to boundary-layer conditions and may be suppressed during stable stratification or temperature inversions, leading to elevated near-surface odor concentrations [28,29]. In addition, local terrain-induced circulations, such as slope flows and valley-channeling effects, can further alter plume trajectories and redistribute odor concentrations, producing downwind impact patterns that differ from those suggested by synoptic wind statistics [30]. Collectively, these processes explain the discrepancies observed between wind rose patterns and the directional distribution of setback distances, and underscore the importance of dispersion modeling for odor-based planning and facility siting.

The observed relationships between wind patterns and setback distances are influenced by the internal formulation of AERMOD, particularly the derivation of planetary boundary layer (PBL) parameters through AERMET. As atmospheric stability is represented using continuous boundary-layer scaling parameters (e.g., Monin–Obukhov length), rather than discrete stability classes, the resulting dispersion behavior may not always align with simplified expectations.

3.2.2. Influences of Terrain

This section evaluates the influence of terrain on NDOFT-predicted setback distances. As shown in Figure 5 and Table S3, setback distances predicted for Cass County differed only slightly (by on average 0.4%) between the idealized flat-terrain case assumption (Figure 5a) and simulations incorporating real-world relatively flat terrain (Figure 5b,c). The close agreement between these cases indicates that odor dispersion patterns simulated under idealized flat terrain are highly comparable to those under real-world relatively flat conditions. Because much of North Dakota is characterized by gently sloping or flat topography and animal production facilities are typically sited on level ground, these results support the applicability of NDOFT for facility planning under such terrain conditions.

In contrast, simulations incorporating representative hilly terrain in Billings County demonstrate that terrain can alter odor dispersion patterns and associated setback distances. The changes in the resulting setback distances depend on the relative position of the animal production facility within the terrain. When the facility was located at the hilltop, predicted setback distances were smaller (by an average of 8.5%) than those estimated by NDOFT across all directions and annoyance-free frequencies (Figure 5d,e; Table S3). A similar trend was observed for the leeward-slope facility, where most setback distances were reduced (by an average of 6.0%) relative to NDOFT predictions, with differences generally between 0.3% and 29.2%, except for a few directions exhibiting minor increases (0.4–3.3%; Figure 5f; Table S3). When the facility was located on the windward slope, terrain exhibited stronger effects (Figure 5g). Although setback distances in most directions remained comparable to or slightly smaller (by an average of 9.6%) than those predicted by NDOFT, markedly smaller setback distances occurred toward the southeast at the 99% annoyance-free frequency (by 29.3%) and toward the southwest at the 98% frequency (by 42.9%). These reduced setback distances can be attributed to enhanced turbulence and the resulting increased odor dispersion induced by complex terrain.

The most pronounced terrain effects were observed in McKenzie County, which is characterized by broad valley terrain. Facilities were placed at the valley bottom on the leeward slope, and on the windward slope, respectively (Figure 5m). Relative to NDOFT predictions, setback distances simulated for these source locations decreased (by on average 22.3%, 14.7%, and 11.5%, respectively) with particularly large reductions observed in the northeast (NE) direction. When the facility was located at the valley bottom, the NE-direction setback distance decreased by 48.4–69.8%, depending on the target odor management objective (Table S3). For the leeward-slope facility, NE-direction reductions ranged from 16.2% to 45.0%; while for the windward-slope facility, NE-direction reductions varied from 12.7% to 40.4%. This pattern is largely attributed to prevailing but relatively gentle southwesterly winds (Figure 4b), which make the NE sector the dominant downwind dispersion direction. Under valley conditions, plumes released from valley bottoms are frequently forced upslope, leading to plume lifting, enhanced vertical mixing, and rapid dilution—phenomena widely reported in dispersion studies over complex terrain [30]. A similar but weaker reduction pattern occurs for leeward-slope and windward-slope sources, where flow sheltering, terrain-induced turbulence, and localized recirculation promote vertical mixing and reduce sustained near-surface transport.

Overall, these terrain-induced differences are consistent with known modifications of plume behavior and atmospheric dispersion over complex terrain. Hills and valleys are known to generate terrain-induced turbulence and localized circulations that enhance vertical mixing and dilution, often reducing near-surface concentrations downwind of elevated sources [30,31,32]. Previous computational fluid dynamics and mesoscale modeling studies demonstrate that complex topography can substantially modify local wind fields and dispersion patterns in terrain-influenced environments [33,34]. Such terrain-following airflow and plume–terrain interactions are incorporated within the AERMOD formulation for complex terrain dispersion [20,35]. While the general influence of terrain on dispersion may appear intuitive, its implications for simplified odor footprint tools are not always straightforward under mildly complex terrain conditions. The clarification is included to improve interpretability for both technical and non-technical users.

It is important to note that, for practical reasons, AERMOD simulations and comparisons could not be conducted for all possible combinations of terrain configurations, source locations, and odor emission rates. Consequently, it remains uncertain whether the patterns observed in these case studies—namely, that complex terrain often results in reduced odor setback distances—hold universally across all conditions. It is unlikely that a consistent or generic relationship between terrain configuration and setback distance can be established across different counties, source locations, and wind directions. As a result, terrain effects cannot be represented by a simple correction factor for implementation in a generalized, Excel-based setback calculator. Nonetheless, our comparison results suggest that NDOFT serves as a reasonable, if not conservative, starting point for setback determination under the typical terrain conditions encountered in North Dakota.

Notably, these findings are inconsistent with the recommendations for using the Nebraska NOFT under complex terrain conditions, which suggest applying a margin factor of 10% for farms located on hills and 20% for those situated in valleys [36]. However, this inconsistency does not imply that either study is incorrect. Rather, the observed differences in terrain effects likely reflect fundamental differences in terrain characteristics and meteorological conditions between Nebraska and North Dakota.

Therefore, NDOFT should be used primarily as a screening-level planning tool for sites located on relatively flat or gently rolling terrain where sources and receptors are not separated by major terrain features. In areas with complex terrain, such as valley settings, steep slopes, escarpments, or substantial source-receptor elevation differences, NDOFT results should be interpreted with caution and should not be used as the sole basis for siting decisions. In such cases, particularly when sensitive receptors are located near the predicted setback boundary or when terrain complexity may influence plume rise and dispersion, site-specific AERMOD modeling with terrain processing is recommended.

3.2.3. County-Specific vs. Area-Representative Meteorology

This section compares the use of county-specific versus area-representative meteorological data for estimating odor setback distances. As shown in Figure 6, two counties from each meteorological area were selected for comparison. In Area 3 (Figure S2), where terrain is predominantly flat, only minor differences in overall setback patterns were observed between simulations using county-specific and area-representative meteorological inputs. However, when evaluated at the individual setback scale—by compass direction and odor annoyance-free threshold—calculated setback distances differed by up to 32% in Sioux County and 58% in Cass County.

More pronounced differences were observed in Area 1, which represents southwestern North Dakota, where calculated setback distances differed by as much as 443% in Divide County and 416% in Ward County relative to Mountrail County. The greatest variability occurred in Area 2, where many counties include prominent escarpments (e.g., the Pembina and Missouri escarpments). In this area, substantial differences were observed even in overall setback patterns, with calculated setback distances differing by up to 287% in McKenzie County and 150% in Burleigh County relative to Billings County.

Overall, these results indicate that substantial differences can occur in calculated setback distances among counties located within the same meteorological area. This suggests that grouping counties solely based on wind roses and using a single representative data set to characterize an entire region may introduce substantial uncertainty.

The differences in setback distances between counties within the same area, particularly those in Figure 6e,h, are likely attributable to variations in meteorological conditions such as temperature, humidity, precipitation, and cloud cover, all of which influence atmospheric dispersion [20,29]. A key limitation of the area classification method is that it relies solely on wind speed and wind direction while neglecting other meteorological variables that can significantly influence plume rise, turbulence, mixing height, and accordingly dispersion. Thus, although regional grouping can simplify the modeling process and improve computational efficiency, its limitations cannot be ignored [30,31].

For counties lacking ground-based observations, AERMOD simulations in this study relied on surface meteorological data generated by the WRF model. While WRF data provide spatially continuous meteorological inputs, some studies have reported notable uncertainties in near-surface wind speeds and planetary boundary layer heights, which can propagate into dispersion modeling results [37,38,39]. The availability of more representative surface meteorological data would help reduce modeling uncertainty and further enhance the robustness of odor footprint assessments [40,41].

4. Conclusions

This study developed and evaluated NDOFT, an Excel-based calculator that determines odor setback distances for animal production facilities across eight compass directions. Three main conclusions were drawn. First, calculated setback distances exhibit strong directional variability and are influenced by more than prevailing wind patterns alone, underscoring the importance of full air dispersion modeling that accounts for multiple meteorological factors when evaluating odor setbacks. Second, the use of county-specific meteorological data can produce substantially different setback estimates compared with approaches based on regionally representative inputs. Third, the flat-terrain assumption underlying NDOFT is generally appropriate for North Dakota’s predominantly level landscapes. In areas of complex topography, NDOFT produced conservative setback estimates (i.e., greater than necessary) in the scenarios evaluated, and site-specific AERMOD modeling may still be necessary because terrain effects cannot be adequately captured by generalized correction factors. Like other odor footprint tools, NDOFT is intended for planning and siting of animal production facilities rather than regulatory permitting. Future work should focus on improving meteorological representativeness in data-sparse counties, evaluating the sensitivity of setback distances to longer historical meteorological records, and exploring hybrid modeling approaches to better address odor dispersion in complex terrain.