Input data¶

Input data must be passed to the fragmentmnp.FragmentMNP model class. Examples are given in the fragmentmnp.examples module:

>>> from fragmentmnp.examples import minimal_data, full_data
>>> minimal_data
{'initial_concs': [42.0, 42.0, 42.0, 42.0, 42.0, 42.0, 42.0], 'density': 1380, 'k_frag': 0.01}
>>> full_data
{'initial_concs': [42.0, 42.0, 42.0, 42.0, 42.0, 42.0, 42.0], 'density': 1380, 'k_frag': 0.01,
'theta_1': 0.0, 'k_diss': 0.0, 'k_diss_gamma': 1.0}

The minimal_data contains only required variables, whilst full_data includes variables that have defaults. Here we take a look at the schema for this data dict.

initial_concs: Required, list of positive floats with length equal to n_size_classes, units: kg/m3.; The intial mass concentration in each model size class.
density: Required, float, units: kg/m3.; The density of the polymer being modelled.
k_frag: Required, float or iterable with length equal to n_size_classes, units: s^-1.; Either a scalar representing the average fragmentation rate \(k_\text{frag}\) across the size classes, or the full \(k_\text{frag}\) distribution for all size classes. \(k_\text{frag}\) is defined as the fraction of the mass of a particular size class that fragments each second. If a scalar (average) is provided, theta_1 and k_frag_tau are used to calculate the size- and time-dependent distribution. If a size class distribution is given, any value given for theta_1 is ignored.

theta_1: Optional, float, default: 0.; Surface energy empirical parameter \(\theta_1\), which dictates how \(k_\text{frag}\) varies with particle size. \(k_\text{frag}\) varies as \(d^{2\theta_1}\), meaning that if \(\theta_1 = 0\), the same \(k_\text{frag}\) is used across size classes, and if \(\theta_1 > 0\), \(k_\text{frag}\) is larger for larger size particles. theta_1 is ignored if a distribution is given for k_frag.

k_frag_tau: Optional, float, default: 0.; Fragmentation rate time-dependence parameter \(\tau\), which dictates how \(k_\text{frag}\) varies over time. \(k_\text{frag}\) varies as \(t^\tau\), where \(t\) is the model timestep index, meaning that if \(\tau = 0\) (the default), \(k_\text{frag}\) is constant in time. If \(\tau < 0\), \(k_\text{frag}\) decreases in time, and vice-versa. Note that this dependence is on the timestep index, rather than the actual time.
k_diss: Optional, float, default: 0.; Either the average (median) dissolution rate \(k_\text{diss}\) across the size classes, or the full \(k_\text{diss}\) distribution for all size classes. \(k_\text{diss}\) describes the rate of loss to “dissolved” organics from each size class. If an average (scalar) is given, how this average is distributed across size classes is determined by the k_diss_scaling_method in the model configuration. If a distribution is given, the k_diss_scaling_method is ignored.
k_diss_gamma: Optional, float, default: 1.; If the config option k_diss_scaling_method is set to surface_area and an average (scalar) k_diss is given in input data, then k_diss_gamma \(\gamma\) is an empirical parameter that scales how dependent the distribution of k_diss across size classes is on the particle surface area to volume ratio. In short, \(k_\text{diss} \propto s^\gamma\), where \(s\) is the surface area to volume ratio. In other words, if \(\gamma = 1\), k_diss scales directly with the surface area to volume ratio, and if \(\gamma = 0\), k_diss is constant across size classes (i.e. it has the same effect as setting k_diss_scaling_method to constant). If a distribution is given for k_diss, then k_diss_gamma is ignored.

fsd_beta: Optional, float, default: 0.; \(\beta\) is an empirical parameter that controls the dependence of the fragment size distribution fsd on particle diameter. The split of fragmented mass amongst daughter size classes is scaled as \(\propto d^\beta\), where \(d\) is the particle diameter. Thus, if \(\beta = 0\) (the default), there is an even split amongst daughter size classes, if \(\beta < 0\), a greater proportion of the mass goes to smaller size classes, and if \(\beta > 0\), a greater proportion of the mass goes to larger size classes. See Fragment size distribution for more information on the fragment size distribution matrix.

Units

Strictly speaking, the FRAGMENT-MNP model is unit-agnostic. As long as the units of data specified in input data are consistent, then the units of variables output by the model will match these. For example, if you specify initial_concs and density with units of mg/m³, then output concentrations will be in mg/m³.

However, we strongly recommend you stick to SI units to avoid the chance of mistakes being made. Hence this page gives unit recommendations in SI units.