Adjusted size distributions and renamed test files accordingly.

Calculations/size_distribution.py

@@ -137,13 +137,92 @@ def lognormal_number_distribution(number_concentration: float,
     from air pollution to climate change. John Wiley & Sons. isbn: 1118947401.
 
     """
-    dNdlogdp = (number_concentration
-                / (standard_deviation * np.sqrt(2 * np.pi)
+    dNddp = (number_concentration
+                / (np.log(standard_deviation) * particle_diameter * np.sqrt(2 * np.pi)
                    )
-                * np.exp(- (np.log10(particle_diameter) - np.log10(median_particle_diameter))**2
-                         / (2 * np.log10(standard_deviation)**2)
+                * np.exp(- (np.log(particle_diameter) - np.log(median_particle_diameter))**2
+                         / (2 * np.log(standard_deviation)**2)
                          )
                 )
+    return dNddp
+
+def lognormal_number_distribution_natural_scale(number_concentration: float,
+                                                standard_deviation: float,
+                                                median_particle_diameter: float,
+                                                particle_diameter: npt.ArrayLike) -> npt.ArrayLike:
+    """
+    Lognormal number distribution with median diameter and
+    standard deviation, both on log-scale. Log is related to
+    the decadal logarithm. Definition taken from [1]_.
+
+    Parameters
+    ----------
+    number_concentration : float
+        Total number concentration of particles.
+    standard_deviation : float
+        Standard deviation..
+    median_particle_diameter : float
+        Median diameter.
+    particle_diameter : npt.ArrayLike
+        Particle diameter of a given size distribution.
+
+    Returns
+    -------
+    npt.ArrayLike
+        Lognormal number distribution based on the median
+        particle diameter and the standard deviation,
+        both on the log-scale.
+
+    References
+    ----------
+    [1] Seinfeld, J. H. and S. N. Pandis (2016). Atmospheric chemistry and physics:
+    from air pollution to climate change. John Wiley & Sons. isbn: 1118947401.
+
+    """
+    dNdlndp = lognormal_number_distribution(number_concentration,
+                                            standard_deviation,
+                                            median_particle_diameter,
+                                            particle_diameter) * particle_diameter
+    return dNdlndp
+
+
+def lognormal_number_distribution_log_scale(number_concentration: float,
+                                            standard_deviation: float,
+                                            median_particle_diameter: float,
+                                            particle_diameter: npt.ArrayLike) -> npt.ArrayLike:
+    """
+    Lognormal number distribution with median diameter and
+    standard deviation, both on log-scale. Log is related to
+    the decadal logarithm. Definition taken from [1]_.
+
+    Parameters
+    ----------
+    number_concentration : float
+        Total number concentration of particles.
+    standard_deviation : float
+        Standard deviation..
+    median_particle_diameter : float
+        Median diameter.
+    particle_diameter : npt.ArrayLike
+        Particle diameter of a given size distribution.
+
+    Returns
+    -------
+    npt.ArrayLike
+        Lognormal number distribution based on the median
+        particle diameter and the standard deviation,
+        both on the log-scale.
+
+    References
+    ----------
+    [1] Seinfeld, J. H. and S. N. Pandis (2016). Atmospheric chemistry and physics:
+    from air pollution to climate change. John Wiley & Sons. isbn: 1118947401.
+
+    """
+    dNdlogdp = lognormal_number_distribution(number_concentration,
+                                             standard_deviation,
+                                             median_particle_diameter,
+                                             particle_diameter) * np.log(10) * particle_diameter
     return dNdlogdp
 
 

test.py → test_Calculations_size_distributions.py

@@ -7,32 +7,37 @@ Created on Sun Nov 24 00:07:14 2024
 """
 
 import numpy as np
+import pandas as pd
+import math
 import matplotlib.pyplot as plt
 import os
 from pathlib import Path
 os.chdir(Path(__file__).parent)
 from Calculations import size_distribution as sd
 
+plot_path = Path(__file__).parent.joinpath('test_results/Calculations')
+plot_path.mkdir(exist_ok=True, parents=True)
+
 # Test size distributions and create suitable plots.
 # Generate three modes of a size distribution in urban areas.
 
 particle_diameter = np.geomspace(1e-3, 10, 500)  # µm
 
-number_size_distribution_nucleation = sd.lognormal_number_distribution(
+number_size_distribution_nucleation = sd.lognormal_number_distribution_log_scale(
     number_concentration=7100,
-    standard_deviation=10**0.232,
+    standard_deviation=np.exp(0.232),
     median_particle_diameter=0.0117,
     particle_diameter=particle_diameter)
 
-number_size_distribution_aitken = sd.lognormal_number_distribution(
+number_size_distribution_aitken = sd.lognormal_number_distribution_log_scale(
     number_concentration=6320,
-    standard_deviation=10**0.250,
+    standard_deviation=np.exp(0.250),
     median_particle_diameter=0.0373,
     particle_diameter=particle_diameter)
 
-number_size_distribution_coarse = sd.lognormal_number_distribution(
+number_size_distribution_coarse = sd.lognormal_number_distribution_log_scale(
     number_concentration=960,
-    standard_deviation=10**0.204,
+    standard_deviation=np.exp(0.204),
     median_particle_diameter=0.151,
     particle_diameter=particle_diameter)
 
@@ -41,13 +46,13 @@ number_size_distribution_coarse = sd.lognormal_number_distribution(
 dlogdp = np.diff(np.log10(particle_diameter)).mean()
 number_concentration_nucleation = (number_size_distribution_nucleation
                                    * dlogdp).sum()
-print(number_concentration_nucleation)
+assert math.isclose(7100, number_concentration_nucleation)
 number_concentration_aitken = (number_size_distribution_aitken
                                * dlogdp).sum()
-print(number_concentration_aitken)
+assert math.isclose(6320, number_concentration_aitken)
 number_concentration_coarse = (number_size_distribution_coarse
                                * dlogdp).sum()
-print(number_concentration_coarse)
+assert math.isclose(960, number_concentration_coarse)
 
 # %%
 fig, ax = plt.subplots()
@@ -57,13 +62,40 @@ ax.plot(particle_diameter,
         number_size_distribution_aitken, label='Aitken')
 ax.plot(particle_diameter,
         number_size_distribution_coarse, label='Coarse')
-# ax.plot(particle_diameter,
-#         number_size_distribution_aitken + number_size_distribution_nucleation,
-#         label='Total')
+ax.plot(particle_diameter,
+        number_size_distribution_aitken
+        + number_size_distribution_nucleation
+        + number_size_distribution_coarse,
+        label='Total')
+
+ax.set_xlabel(r'$d_\mathrm{p}$ / µm')
+ax.set_ylabel(r'd$N$/dlog$d_\mathrm{p}$ / cm${-3}$')
 
 ax.set_xscale('log')
-# ax.set_yscale('log')
+ax.legend()
+fig.savefig(plot_path.joinpath('test_sd.png'))
+
+# %% Testing calculations of surface and volume distributions
+total_sd = (number_size_distribution_aitken
+            + number_size_distribution_nucleation
+            + number_size_distribution_coarse)
+total_sd = pd.DataFrame(total_sd, index=particle_diameter).T
+
+fig, (ax, ax2, ax3) = plt.subplots(3, 1, sharex=True)
+ax.plot(particle_diameter,
+        total_sd.iloc[0, :],
+        label='Number')
+ax2.plot(particle_diameter,
+         sd.surface_distribution(total_sd).iloc[0, :],
+         label='Surface')
+ax3.plot(particle_diameter,
+         sd.volume_distribution(total_sd).iloc[0, :],
+         label='Volume')
 
-# ax.set_ylim(1e-3, 1e4)
+for name, axis in zip(('N', 'S', 'V'), (ax, ax2, ax3)):
+    axis.set_ylabel(fr'd${name}$/dlog$d_\mathrm{{p}}$ / cm${-3}$')
+    axis.set_xscale('log')
+    axis.legend()
+ax3.set_xlabel(r'$d_\mathrm{p}$ / µm')
 
-ax.legend()
\ No newline at end of file
+fig.savefig(plot_path.joinpath('test_sd_NSV.png'))