Uncertainty resulting from constant bulk density assumption when interpreting soil nutrient concentrations

Soil nutrient concentrations are often expressed as parts per million (ppm) in soil test reports. For incorporation into nutrient management decisions, ppm‐based concentrations have to be converted into pounds per acre, and a conversion factor (multiplier) of 2.0 is typically recommended universally to do so. However, this conversion factor stems from an assumed value of bulk density (ρb) corresponding to silt loam soil and is invariant to any deviation beyond assumed ρb. Here, we quantify and evaluate the potential ramifications of assuming a constant ρb value on calculating soil nitrogen credits. A true dynamic conversion factor that is sensitive to variation in ρb ranges between 1.28 and 2.68 for soils across US cropland. Failure to account for this dynamic conversion factor was shown to result in an underestimation of soil N credits by up to 40%. In addition to spatial variation, management‐induced changes in ρb are also important to incorporate into the conversion factor.


INTRODUCTION
Effective on-farm nutrient management is aimed at optimizing nutrient use efficiency and profitability while mitigating nutrient losses.A primary method to accurately determine nutrient (especially nitrogen [N]) application rates for agronomic crops is the use of simple but effective tools that account for yield goals and nutrient availability, uptake, and credits (Ransom et al., 2020;Rodriguez et al., 2019).These tools are based on local experimental assessments and are offered through university extension programs to be intended for simplified use by growers.
A major input to these algorithms is residual soil nutrient concentration, the rate equivalent of which is subtracted from potential nutrient requirements.Residual soil concentrations are recommended to be measured from representative soil samples using standardized laboratory procedures (Hergert, 1987).It is common for growers to have a commercial soil laboratory test of these samples, with resulting soil test reports often reporting concentrations as parts per million (ppm).The ppm units are then converted into rate units (lb ac −1 ) by multiplying with a conversion factor of 2.0, as recommended by guidance provided by several university extension programs (Hannan, 2018;Jones & Olson-Rutz, 2019;Kaiser, 2018;LaBarge, 2022;Landschoot, 2022;Liu et al., 2023;Reiter, 2020).However, it is rare to encounter guidance materials that explain how this conversion factor is derived and the assumptions therein, which has led to a notion that the factor remains universally applicable.In reality, the conversion factor (2.0) is a simplification based on a bulk density (ρ b ) of 1.33 g cm −3 (representative of a silt loam soil) and a soil depth of 17.06 cm (0.56 ft) employed to represent an acre furrow slice (Equation 1).The volume of an acre furrow slice is 6.91E+08 cm 3 (Landschoot, 2022).Since the conversion factor is applied to ppm units and allows interpretation of soil nutrient concentrations in lb ac −1 , the denominator in Equation (1) (454,711,812) is a coefficient that accounts for unitary conversions, allowing its direct use with commonly reported units in applied settings.
The assumption of ρ b value in Equation ( 1) is a critical determinant of whether a conversion factor of 2.0 would apply or not.Any deviation from the assumed value can hamper the "universal" application of the conversion factor of 2.0.Natural deviations in soil structure and hence ρ b are commonly encountered at fine spatial scales (Mzuku et al., 2005), but also across soil landscapes (Chaney et al., 2019;Miller & White, 1998).More importantly, soil health practices within the climate-smart soil management framework are aimed at improving soil structure, and these strategies' outcomes are typically measured and evaluated using ρ b (Bagnall et al., 2022(Bagnall et al., , 2023;;Lehmann et al., 2020).As soil structure improves in a given field, lower values of ρ b are anticipated and observed (Byrnes et al., 2018;Lang & Russell, 2020;Logsdon & Karlen, 2004;Topa et al., 2021), resulting in deviations from the conversion factor of 2.0, translating into uncertainty for accurately assessing residual soil nutrient rates.Such scenarios present challenges for estimating appropriate application rates for fertilization, potentially leading to underestimation or overestimation and eventually manifesting as crop nutrient stress and environmental pollution, respectively.In this study, we quantify the uncertainty in estimating N credits from residual soil N as a consequence of failure to account for (i) spatial variation in ρ b and (ii) temporal improvement in ρ b for the deduction of the conversion factor.

MATERIALS AND METHODS
We used large-scale datasets of depth-specific soil characteristics to delineate natural spatial variation in surface  (Hengl, 2018) were obtained at depths of 0 and 10 cm, hosted on Google Earth Engine (Gorelick et al., 2017).These datasets are based on measurements by various institutions and research organizations globally (e.g., USDA NCSS in the United States), compiled and mapped at 250 m spatial resolution with machine learning-based methods.The global datasets were subset for spatial extent of the conterminous United States (CONUS).The ρ b for the furrow slice (0-17 cm) was represented using the mean of ρ b at 0 and 10 cm.In doing this, we assume that vertical soil heterogeneity between 10 and 17 cm is negligible because of the relatively small vertical separation.Nevertheless, the conversion factors deduced from Equation (1) were based on the volume of acre furrow slice.The resulting ρ b at each 250 m grid cell was input to Equation (1) and the corresponding conversion factor was deduced.These raster calculations were performed in RStudio (R Core Team, 2023).ρ b and the conversion factors were mapped for the CONUS using ArcMap 10.7 (Environmental Systems Research Institute [ESRI], 2024).To visualize the potential uncertainty associated with using an assumed ρ b of 1.33 g cm −3 , we also mapped the percent deviation of spatially dynamic conversion factor from the assumed value (2.0) subset for regions with cropland acreage in the United States.
The rasters were subset based on a discrete cropland/noncropland developed using 250 m moderate resolution imaging spectroradiometer imagery (Pittman et al., 2010).
To quantify uncertainty propagation into soil N credits, we used Equation (2), which is recommended and used by commercial labs and university extension materials: Using increments 1 ppm apart in a range of practically encountered residual soil N (ppm) values and dynamic conversion factors that account for measured ρ b (Equation 1), we developed a lookup matrix for readers to understand the resulting impacts on soil N credits.We also developed an RShiny app intended for users to calculate soil N credit based on user-defined values of ρ b and soil nutrient concentrations (ppm).

Uncertainty in N credits estimation resulting from overlooking spatial variation in ρ b
The dynamic conversion factor demonstrates significant spatial variation (0.10-2.71) across CONUS.Considering cropland acreage within CONUS only, the factor varied between 1.28 and 2.68, implying a significant deviation from the assumption of 2.0 (Figure 1a).As per Equation (1), this deviation is solely a function of natural spatial variation in surface ρ b , which varied between 0.84 and 1.77 g cm −3 across US croplands.Simplifying Equation (1), every 0.1 g cm −3 increase in ρ b results in the need for increasing the conversion factor by 0.15.Upon analyzing the 250 m datasets for deviation in conversion factor, we found that conversion factors greater than 2.0 were applicable for most of the cropland within the United States.Use of an assumed conversion factor (2.0), which is lower in most regions than what should be used site-specifically based on locally measured ρ b (Figure 1a), will result in underestimating soil N credits.When interpreting a given ppm value of soil nutrient concentration, the degree of underestimation encountered is proportional to the difference between the true versus assumed conversion factor (Figure 1b).Because the overall N-related health and environmental costs of corn production in the United States are not only the highest but exceed farmer profits by a large margin (Goodkind et al., 2023), these findings hold the most relevance for the area under corn production.Based on 2023 USDA survey estimates, we find that about 95% of the area under corn production is subject to risk for underestimating soil N credits, while the remainder of the acreage (5%) is subject to risk of overestimation.When estimates of soil N credits are lower than actual, the likelihood that N will be overapplied is high, even when following scientific N recommendation guidelines for decision-making (Mulvaney et al., 2006).While overapplication of N will not cause any yield penalties, it would result in loss of revenue from the additional fertilizer cost that was not required.Moreover, excess N is extremely likely to be lost via hydrological and non-hydrological pathways, causing environmental pollution and increasing the environmental cost of production (Meisinger & Delgado, 2002).Vulnerability to economic and environmental risks, however, is not only limited to the area under corn but also persists for other agronomic and specialty cropping systems for which nutrient management decisions are based on test-reported soil N credits.

Management-induced ρ b change and implications for soil N credits
As with natural spatial variation, ρ b is also impacted by management.It has been evaluated to be responsive and sensitive to changes in a wide range of management practices aimed at building soil health (Azooz & Arshad, 2001;Bagnall et al., 2022;Castellini et al., 2019;Soane et al., 2012;Strudley et al., 2008;Singh et al., 2023).Rightfully so, ρ b has been included as a standard dynamic soil property to be measured for all soil survey pedons (Wills et al., 2017).As soil health improves, any significant reductions in ρ b should be accounted for in soil N credit calculations.There is strong experimental evidence F I G U R E 2 A lookup matrix that shows soil nitrogen credits (lb ac −1 ) available under a gradient of bulk density (ρ b ) and nitrate-N (NO 3 -N) concentration values reported in parts per million (ppm).The matrix is based on Equations ( 1) and ( 2). of reduction in ρ b because of no tillage (Blanco-Canqui et al., 2009), cover crops (Chalise et al., 2019), manure application (Blanco-Canqui et al., 2015), biochar application (Rogovska et al., 2014), and crop rotation (Aller et al., 2017).In contrast, ρ b increase can occur as a consequence of soil compaction (Abu-Hamdeh, 2003).The impact of management-induced change in ρ b on soil nutrient outcomes can be visualized using Figure 2, which presents a matrix of soil N credits (lb ac −1 ) calculated under different combinations of ρ b (g cm −3 ) and NO 3 -N concentrations (ppm) along a realistic gradient.

Incorporating site-specific ρ b
Measurement of ρ b (using either disturbed or undisturbed soil samples) is a readily available procedure at commercial labs, and increasingly so because of growing voluntary carbon markets.When soil nutrient concentration tests are accompanied with ρ b measurements, test reports should use the measured ρ b to quantify soil nutrient credits rather than using the silt loam assumption (1.33 g cm −3 ).At the least, producers/commercial labs should do their due diligence in using a best estimate of ρ b value specific to their site of sampling, even when laboratory measurements are not conducted.For instance, a texture-specific ρ b can be a better assumption than a universal one, and this capability is incorporated in the University of Nebraska-Lincoln (UNL) Nitrogen Algorithm (Shapiro et al., 2019).Tools such as SSURGO (U.S.Department of Agriculture [USDA], 2024) can be instrumental in such cases, where users can look up ρ b values for their sites free of cost.These initial estimates can be refined further by using repeated soil sampling and laboratory procedures in the future.Although tracking temporal change in ρ b may be challenging given the uncertainty involved in sampling, within-field soil heterogeneity, handling, and determination techniques (Han et al., 2016;Nemes et al., 2010;Sharma et al., 2020;Xu et al., 2016), it is expected that over sufficient time, a decent estimate and trajectory of ρ b can be elucidated.

A simple web application to interpret ppm-based soil nutrient concentrations
In order to simplify the practical use of site-specific conversion of soil N concentrations into soil N credits, we have developed a simple web application (https://agrohydrology. shinyapps.io/Soil_N_credits/).The web application is based on the R programming language (R Core Team, 2023) and the Shiny package (Chang et al., 2019), which is a highly favored open-source tool for developing user-centric tools.The structure of the Shiny application consists of Shiny user interface and Shiny server.The user interface requests two inputs from the user: (1) NO 3 -N concentration (ppm) and (2) ρ b (g/cm 3 ).The user-specified values are used as inputs to Equations ( 1) and ( 2) within the Shiny server to output soil N credits (lb ac −1 ).The web application calculates the conversion factor based on user-specified ρ b instead of relying on an assumed conversion factor.

CONCLUSION
This analysis serves to highlight the uncertainty that can be expected in calculating soil N credits when relying on an assumed conversion factor that is insensitive to variation in ρ b .Soil diversity in US croplands necessitate that ρ b is well represented when converting soil nutrient concentrations reported as ppm into lb ac −1 .A failure to account for spatial change in ρ b can result in underestimating soil N credits by up to 40% in some regions.Use of a dynamic ρ b value under scenarios of management-induced soil health improvement is also discussed.Greater transparency in equation structures and mathematics behind simple multipliers involved in calculations may help in avoiding uncertainties.While simplifications and assumptions in calculations promote usability, users should visualize and understand the accuracy tradeoffs associated with these assumptions for optimal nutrient management on farms.We have deployed an online web-based application to convert soil nutrient concentrations reported in ppm into soil N credits based on Equations ( 1) and (2) (https://agrohydrology.shinyapps.io/Soil_N_credits/).

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Soil test reports often express nutrient concentrations as parts per million.• A constant multiplier of two is suggested to infer ppm as lb ac −1 based on a bulk density (ρ b ) assumption.• Accounting for ρ b variation, the multiplier should be 1.28-2.68for US cropland soils.• Use of assumed conversion factor results in up to 40% underestimation of soil N credits.• Management-induced change in ρ b should be accounted for in the multiplier.layer ρ b across the conterminous United States.The ρ b data

F
Spatial variation in (a) conversion factor derived (using Equation1) from site-specific surface bulk density.This conversion factor allows effectively interpreting nutrient concentrations reported as parts per million (ppm) in soil reports as lb ac −1 .(b) Degree of under or overestimation of soil nitrogen credits when a conversion factor (2.0) based on a constant bulk density is used compared to site-specific estimates (as shown in[a]).The calculation of conversion factor shown in (a) was based on average of bulk density estimates at 0 and 10 cm, and assumes negligible vertical heterogeneity between 10 and 17 cm (remainder of the furrow slice).