A new model integrating short- and long-term aging of copper added to soils

<div><p>Aging refers to the processes by which the bioavailability/toxicity, isotopic exchangeability, and extractability of metals added to soils decline overtime. We studied the characteristics of the aging process in copper (Cu) added to soils and the factors that affect this process. Then we developed a semi-mechanistic model to predict the lability of Cu during the aging process with descriptions of the diffusion process using complementary error function. In the previous studies, two semi-mechanistic models to separately predict short-term and long-term aging of Cu added to soils were developed with individual descriptions of the diffusion process. In the short-term model, the diffusion process was linearly related to the square root of incubation time (t^1/2), and in the long-term model, the diffusion process was linearly related to the natural logarithm of incubation time (lnt). Both models could predict short-term or long-term aging processes separately, but could not predict the short- and long-term aging processes by one model. By analyzing and combining the two models, we found that the short- and long-term behaviors of the diffusion process could be described adequately using the complementary error function. The effect of temperature on the diffusion process was obtained in this model as well. The model can predict the aging process continuously based on four factors—soil pH, incubation time, soil organic matter content and temperature.</p></div

The measured E values (E_m) versus the E values predicted by erfc model (E_p) for short-term data.

<p>The measured E values (E_m) versus the E values predicted by erfc model (E_p) for short-term data.</p

Average Cu labile pool (E value as fraction of total added Cu) in 17 short-term soil samples as a function of incubation time and temperature (vertical lines represent the standard errors).

<p>Average Cu labile pool (E value as fraction of total added Cu) in 17 short-term soil samples as a function of incubation time and temperature (vertical lines represent the standard errors).</p

The measured E values (E_m) versus the predicted E values of the erfc model (E_p).

<p>The measured E values (E_m) versus the predicted E values of the erfc model (E_p).</p

The measured E values and predicted E values of field-contamination soil samples.

<p>Vertical lines represent standard errors where they exceed the height of columns.</p

Soil pH, temperature (K), time (year, since soil field-contamination with Cu salts), soil organic carbon content (w/w%), total Cu (mg kg^-1), measured E values (E_m, fraction).

<p>Soil pH, temperature (K), time (year, since soil field-contamination with Cu salts), soil organic carbon content (w/w%), total Cu (mg kg^-1), measured E values (E_m, fraction).</p

The estimated values of parameters, R² and RMSE in erfc model.

<p>The estimated values of parameters, R² and RMSE in erfc model.</p