How to Estimate Statistically Detectable Trends in a Time Series: A Study of Soil Carbon and Nutrient Concentrations at the Calhoun LTSE

Abstract

Core Ideas Detecting change depends on soil variability, sampling effort and desired confidence. We illustrate detectable rates of change using data from the Calhoun Long‐Term Soil‐Ecosystem experiment. The sampling intensity needed to detect change varied with soil depth and chemical element. Experience at this LTSE can be used to improve long‐term soil monitoring designs. Quantifying rates of change in soil carbon and nutrients is essential to understanding the global carbon cycle as well as to guiding local management decisions. However, change in soils can be nonlinear, difficult to detect, and dependent on the depth of soil examined. The purpose of this study was to demonstrate how to quantify uncertainty in detection of soil change, which has major implications for the design of soil monitoring projects. We analyzed soils collected over five decades from a long‐term soil‐ecosystem experiment in the South Carolina Piedmont of the United States. We estimated the minimum detectable change (MDC) using a dataset of soil carbon, nitrogen, calcium, magnesium, and potassium concentrations at four soil depths (0–7.5, 7.5–15, 15–35, and 35–60 cm). Changes over time in the log‐transformed concentration at each soil depth were fit with one of three response shapes (linear, exponential, and quadratic) with the best model fit determined by a corrected AIC. The MDC analyses were conducted using repeated‐measures models. For soil depths in which elemental change was quadratic, we conducted MDC analyses separately on the decreasing and increasing limbs. We also used paired t tests to analyze the MDCs based on only the first and last sample dates. Greater sampling intensity was needed to detect equivalent proportional changes in elements at intermediate depths than at shallower or deeper depths. Our study demonstrates the importance of considering the pattern and rate of the expected change, and how that may vary by element and depth, when designing and evaluating soil monitoring studies.

Soil organic carbon is not just for soil scientists: measurement recommendations for diverse practitioners

“…Though SOC data are deemed useful for many disciplines (Vicca et al 2018), data sets describing changes in SOC pools over decadal and centennial timescales are relatively rare (Richter et al 2007). These data sets reveal how the power to detect change depends on sampling intensity in time and space, and on parameter variability at discrete depths (Mobley et al 2019). Networks often struggle to balance standardized data collection across diverse environments with the unstandardized approaches often exhibited by hypothesis-driven research (Richter et al 2018).…”

“…Spatial heterogeneity in soil properties at scales ranging from millimeters to kilometers presents a challenge for characterizing mean soil properties and detecting changes over time and across space (Webster and Oliver 2001, Mobley et al 2019). Soil‐sampling strategies thus must account for spatial variation in soil attributes.…”

“…However, variance does not always scale linearly with area, making it difficult to prescribe the number of samples needed to estimate the mean with precision. For example, past and present land use can alter the magnitude and dominant scale of spatial variability of soil properties (Robertson et al 1993, Bennett et al 2005, Fraterrigo et al 2005, Mobley et al 2019). Whenever possible, variance should be directly measured for a site (i.e., by sampling without compositing) and used to determine the number of samples needed for estimating the mean and variance within a specified confidence interval.…”

Soil production and the soil geomorphology legacy of Grove Karl Gilbert

“…The soils, too, have rapidly developed O horizons under pine (Pinus spp.) and pine-hardwood stands and accumulated soil organic matter in surficial A horizons as well (Mobley et al, 2015(Mobley et al, , 2019Richter & Markewitz, 2001;Richter, Markewitz, Trumbore, & Wells, 1999). In the Holcombe's Branch floodplains, the youthful soils are classified as Entisols, specifically Fluvents, and are mapped by the NRCS in a Cartecay-Toccoa series mapping unit, a series mapped on about 350,000 ha of the Piedmont (Cartecay: coarse-loamy, mixed, semiactive, nonacid, thermic Aquic Udifluvents; Toccoa: coarse-loamy, mixed, active, nonacid, thermic Typic Udifluvents).…”

Corrigendum to: How to estimate statistically detectable trends in a time series: A study of soil carbon and nutrient concentrations at the Calhoun LTSE

“…The first equation in the section titled Statistical Analysis ( page S135 ; Mobley et al, 2019), which calculates the minimum detectable change, was incorrect. The correct equation appears as below: …”