PMF Output Validation Example¶

This notebook demonstrates how to use the OutputValidator class to validate PMF results against reference profiles and ratio criteria.

In [1]:

import sys
import os
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

# Import the OutputValidator class
from PMF_toolkits.validation import OutputValidator
from PMF_toolkits import PMF

# Set plotting style
plt.style.use('seaborn-v0_8-whitegrid')
%matplotlib inline
plt.rcParams['figure.figsize'] = (12, 6)

# Suppress warnings
import warnings
warnings.filterwarnings('ignore')

import sys import os import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns # Import the OutputValidator class from PMF_toolkits.validation import OutputValidator from PMF_toolkits import PMF # Set plotting style plt.style.use('seaborn-v0_8-whitegrid') %matplotlib inline plt.rcParams['figure.figsize'] = (12, 6) # Suppress warnings import warnings warnings.filterwarnings('ignore')

1. Initialize the validator¶

First, we'll initialize the validator with a site name and data directory. The validator can work with both single-site and multi-site PMF outputs.

In [2]:

# Define data directory
data_dir = "single_site"  # Path to PMF output files
site_name = "GRE-fr"      # Site name

# Create a validator
validator = OutputValidator(
    site=site_name, 
    bdir=data_dir,
    reference_dir="reference_data"  # Path to reference data files (Source_reference_profiles.csv and Ratio.xlsx)
)

# Load PMF data (happens automatically when needed)
print(f"Validator initialized for site: {site_name}")

# Define data directory data_dir = "single_site" # Path to PMF output files site_name = "GRE-fr" # Site name # Create a validator validator = OutputValidator( site=site_name, bdir=data_dir, reference_dir="reference_data" # Path to reference data files (Source_reference_profiles.csv and Ratio.xlsx) ) # Load PMF data (happens automatically when needed) print(f"Validator initialized for site: {site_name}")

Initialized XlsxReader for site 'GRE-fr' with multisites=False
Total variable set to: PM10recons
Successfully read base profiles with shape (36, 11)
Found multiple 'Factor Contributions' sections, using first section
Successfully read base contributions with shape (125, 11)
Successfully read base bootstrap with 101 runs
Loading base uncertainty summary from: single_site\GRE-fr_BaseErrorEstimationSummary.xlsx
Read base DISP swap data: {'Mineral dust': 0, 'Industrial': 0, 'Aged sea salt': 0, 'Biomass burning': 0, 'Nitrate-rich': 0, 'MSA-rich': 0, 'Sea/road salt': 0, 'Sulfate-rich': 0, 'Secondary biogenic oxidation': 0, 'Primary biogenic': 0, 'Primary traffic': 0}
Successfully read base uncertainties summary with shape (396, 12)
Successfully read constrained profiles with shape (36, 11)
Found multiple 'Factor Contributions' sections, using first section
Successfully read constrained contributions with shape (125, 11)
Successfully read constrained bootstrap with 101 runs
Loading constrained uncertainty summary from: single_site\GRE-fr_ConstrainedErrorEstimationSummary.xlsx
Read constrained DISP swap data: {'Mineral dust': 0, 'Industrial': 0, 'Aged sea salt': 0, 'Biomass burning': 0, 'Nitrate-rich': 0, 'MSA-rich': 0, 'Sea/road salt': 0, 'Sulfate-rich': 0, 'Secondary biogenic oxidation': 0, 'Primary biogenic': 0, 'Primary traffic': 0}
Successfully read constrained uncertainties summary with shape (396, 10)
Successfully read: 8/8 components
Validator initialized for site: GRE-fr

In [3]:

validator.load_source_profiles()

validator.load_source_profiles()

Out[3]:

	Id	Name	Specie	Relative Mass	Uncertainty	Analythical Method	Uncertainty Method	Specie Id	Particle Size	Original Name	...	Reference	Country	Place	Test Year	Profile Type	Sampling Method	Latitude	Longitude	Cas	Symbol
0	1	Cement	Aluminum	0.018609	0.003790	NaN	95% confidence interval	292.0	PM10	CEMENT	...	Larsen,2012,10.1016/j.atmosenv.2011.12.038	Italy	Po Valley, Valtelline	2008.0	C	Form bibliography	45.4773	9.1815	7429-90-5	Al
1	1	Cement	Antimony	0.000012	0.000008	NaN	95% confidence interval	296.0	PM10	CEMENT	...	Larsen,2012,10.1016/j.atmosenv.2011.12.038	Italy	Po Valley, Valtelline	2008.0	C	Form bibliography	45.4773	9.1815	7440-36-0	Sb
2	1	Cement	Arsenic	0.000015	0.000003	NaN	95% confidence interval	298.0	PM10	CEMENT	...	Larsen,2012,10.1016/j.atmosenv.2011.12.038	Italy	Po Valley, Valtelline	2008.0	C	Form bibliography	45.4773	9.1815	7440-38-2	As
3	1	Cement	Cadmium	0.000008	0.000004	NaN	95% confidence interval	328.0	PM10	CEMENT	...	Larsen,2012,10.1016/j.atmosenv.2011.12.038	Italy	Po Valley, Valtelline	2008.0	C	Form bibliography	45.4773	9.1815	7440-43-9	Cd
4	1	Cement	Calcium	0.386055	0.020188	NaN	95% confidence interval	329.0	PM10	CEMENT	...	Larsen,2012,10.1016/j.atmosenv.2011.12.038	Italy	Po Valley, Valtelline	2008.0	C	Form bibliography	45.4773	9.1815	7440-70-2	Ca
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
8798	291	Sulphate	Elemental Carbon	0.024104	0.006470	NaN	standard deviation	797.0	PM10	Sulphate	...	Cesari et al., 2016, doi.org/10.1016/j.atmosre...	Italy	Civitavecchia, Torrevaldaliga Nord	2014.0	D	Constrained PMF5 was run on an unified dataset...	42.1269	11.7583	7440-44-0	EC
8799	291	Sulphate	Bromine	0.000254	0.000027	NaN	standard deviation	810.0	PM10	Sulphate	...	Cesari et al., 2016, doi.org/10.1016/j.atmosre...	Italy	Civitavecchia, Torrevaldaliga Nord	2014.0	D	Constrained PMF5 was run on an unified dataset...	42.1269	11.7583	10097-32-2	Br
8800	291	Sulphate	Potassium ion	0.005016	0.001238	NaN	standard deviation	2302.0	PM10	Sulphate	...	Cesari et al., 2016, doi.org/10.1016/j.atmosre...	Italy	Civitavecchia, Torrevaldaliga Nord	2014.0	D	Constrained PMF5 was run on an unified dataset...	42.1269	11.7583	24203-36-9	K+
8801	291	Sulphate	Calcium ion	0.000000	0.000000	NaN	standard deviation	2303.0	PM10	Sulphate	...	Cesari et al., 2016, doi.org/10.1016/j.atmosre...	Italy	Civitavecchia, Torrevaldaliga Nord	2014.0	D	Constrained PMF5 was run on an unified dataset...	42.1269	11.7583	14127-61-8	Ca2+
8802	291	Sulphate	Magnesium ion	0.000367	0.001149	NaN	standard deviation	2772.0	PM10	Sulphate	...	Cesari et al., 2016, doi.org/10.1016/j.atmosre...	Italy	Civitavecchia, Torrevaldaliga Nord	2014.0	D	Constrained PMF5 was run on an unified dataset...	42.1269	11.7583	22537-22-0	Mg2+

8803 rows × 21 columns

2. Check Species Ratios¶

Species ratios can be valuable indicators of source types. For example, the OC/EC ratio helps differentiate between different combustion sources.

In [4]:

# Calculate OC/EC ratio for a specific factor
factor_name = 'Biomass burning' # validator.pmf.profiles[0]  # Use first available factor
print(f"Using factor: {factor_name}")

try:
    # Calculate OC/EC ratio
    ratio = validator.calculate_ratio(factor_name, "Levoglucosan", "Mannosan")
    if np.isnan(ratio):
        print("Could not calculate OC/EC ratio (one or both species not found or zero value)")
    else:
        print(f"OC/EC ratio for {factor_name}: {ratio:.2f}")

    # Compare with reference values
    ratio_result = validator.compare_ratio(factor_name, "OC*", "EC")
    if ratio_result.get("success", False):
        print("\nFound matching source type(s):")
        for match in ratio_result["matches"]:
            print(f"- {match['Source']} (expected range: {match['Min']:.2f}-{match['Max']:.2f})")
    else:
        print("\nNo matching source types found for this ratio")
except Exception as e:
    print(f"Error during ratio calculation: {str(e)}")
    
    # Show available species for debugging
    print("\nAvailable species:")
    print(validator.pmf.species)

# Calculate OC/EC ratio for a specific factor factor_name = 'Biomass burning' # validator.pmf.profiles[0] # Use first available factor print(f"Using factor: {factor_name}") try: # Calculate OC/EC ratio ratio = validator.calculate_ratio(factor_name, "Levoglucosan", "Mannosan") if np.isnan(ratio): print("Could not calculate OC/EC ratio (one or both species not found or zero value)") else: print(f"OC/EC ratio for {factor_name}: {ratio:.2f}") # Compare with reference values ratio_result = validator.compare_ratio(factor_name, "OC*", "EC") if ratio_result.get("success", False): print("\nFound matching source type(s):") for match in ratio_result["matches"]: print(f"- {match['Source']} (expected range: {match['Min']:.2f}-{match['Max']:.2f})") else: print("\nNo matching source types found for this ratio") except Exception as e: print(f"Error during ratio calculation: {str(e)}") # Show available species for debugging print("\nAvailable species:") print(validator.pmf.species)

Using factor: Biomass burning
OC/EC ratio for Biomass burning: 8.93

Found matching source type(s):
- Biomass burning (expected range: 3.00-10.60)
- Biomass burning (expected range: 2.30-17.70)
- Traffic (expected range: 1.34-3.70)

In [5]:

# Calculate ratios for a specific factor
factor_name = 'Biomass burning'  # validator.pmf.profiles[0]  # Use first available factor
print(f"Using factor: {factor_name}")

try:
    # Calculate Levoglucosan/Mannosan ratio (typical for biomass burning source identification)
    levo_manno_ratio = validator.calculate_ratio(factor_name, "Levoglucosan", "Mannosan")
    if np.isnan(levo_manno_ratio):
        print("Could not calculate Levoglucosan/Mannosan ratio (one or both species not found or zero value)")
    else:
        print(f"Levoglucosan/Mannosan ratio for {factor_name}: {levo_manno_ratio:.2f}")
        
    # Also calculate OC/EC ratio (another important marker for combustion sources)
    oc_ec_ratio = validator.calculate_ratio(factor_name, "OC*", "EC")
    if np.isnan(oc_ec_ratio):
        print("Could not calculate OC/EC ratio (one or both species not found or zero value)")
    else:
        print(f"OC/EC ratio for {factor_name}: {oc_ec_ratio:.2f}")

    # Compare OC/EC ratio with reference values
    ratio_result = validator.compare_ratio(factor_name, "OC*", "EC")
    if ratio_result.get("success", False):
        print("\nFound matching source type(s) for OC/EC ratio:")
        for match in ratio_result["matches"]:
            print(f"- {match['Source']} (expected range: {match['Min']:.2f}-{match['Max']:.2f})")
    else:
        print("\nNo matching source types found for OC/EC ratio")
        
    # Compare Levoglucosan/Mannosan ratio with reference values
    levo_ratio_result = validator.compare_ratio(factor_name, "Levoglucosan", "Mannosan")
    if levo_ratio_result.get("success", False):
        print("\nFound matching source type(s) for Levoglucosan/Mannosan ratio:")
        for match in levo_ratio_result["matches"]:
            print(f"- {match['Source']} (expected range: {match['Min']:.2f}-{match['Max']:.2f})")
    else:
        print("\nNo matching source types found for Levoglucosan/Mannosan ratio")
        
except Exception as e:
    print(f"Error during ratio calculation: {str(e)}")
    
    # Show available species for debugging
    print("\nAvailable species:")
    print(validator.pmf.species)

# Calculate ratios for a specific factor factor_name = 'Biomass burning' # validator.pmf.profiles[0] # Use first available factor print(f"Using factor: {factor_name}") try: # Calculate Levoglucosan/Mannosan ratio (typical for biomass burning source identification) levo_manno_ratio = validator.calculate_ratio(factor_name, "Levoglucosan", "Mannosan") if np.isnan(levo_manno_ratio): print("Could not calculate Levoglucosan/Mannosan ratio (one or both species not found or zero value)") else: print(f"Levoglucosan/Mannosan ratio for {factor_name}: {levo_manno_ratio:.2f}") # Also calculate OC/EC ratio (another important marker for combustion sources) oc_ec_ratio = validator.calculate_ratio(factor_name, "OC*", "EC") if np.isnan(oc_ec_ratio): print("Could not calculate OC/EC ratio (one or both species not found or zero value)") else: print(f"OC/EC ratio for {factor_name}: {oc_ec_ratio:.2f}") # Compare OC/EC ratio with reference values ratio_result = validator.compare_ratio(factor_name, "OC*", "EC") if ratio_result.get("success", False): print("\nFound matching source type(s) for OC/EC ratio:") for match in ratio_result["matches"]: print(f"- {match['Source']} (expected range: {match['Min']:.2f}-{match['Max']:.2f})") else: print("\nNo matching source types found for OC/EC ratio") # Compare Levoglucosan/Mannosan ratio with reference values levo_ratio_result = validator.compare_ratio(factor_name, "Levoglucosan", "Mannosan") if levo_ratio_result.get("success", False): print("\nFound matching source type(s) for Levoglucosan/Mannosan ratio:") for match in levo_ratio_result["matches"]: print(f"- {match['Source']} (expected range: {match['Min']:.2f}-{match['Max']:.2f})") else: print("\nNo matching source types found for Levoglucosan/Mannosan ratio") except Exception as e: print(f"Error during ratio calculation: {str(e)}") # Show available species for debugging print("\nAvailable species:") print(validator.pmf.species)

Using factor: Biomass burning
Levoglucosan/Mannosan ratio for Biomass burning: 8.93
OC/EC ratio for Biomass burning: 3.58

Found matching source type(s) for OC/EC ratio:
- Biomass burning (expected range: 3.00-10.60)
- Biomass burning (expected range: 2.30-17.70)
- Traffic (expected range: 1.34-3.70)

Found matching source type(s) for Levoglucosan/Mannosan ratio:
- Biomass burning (expected range: 3.00-10.00)
- Biomass burning (expected range: 2.00-33.30)

3. Compare with Reference Profiles¶

Now we'll compare our PMF factors with reference profiles from the literature.

In [6]:

# Calculate similarity metrics for a factor
metrics = validator.calculate_similarity_metrics(factor_name)
# Display the top 5 best matches
print(f"Top 5 matches for {factor_name} by Pearson Distance (PD):")
display(metrics.sort_values('PD').head(5))

# Find similar sources using thresholds
similar_sources = validator.find_similar_sources(
    factor_name,
    pd_threshold=0.4,   # Maximum Pearson Distance
    sid_threshold=0.8,  # Maximum Standardized Identity Distance
    min_species=5       # Minimum number of shared species
)

print(f"\nMatching sources (PD < 0.4, SID < 0.8, shared species >= 5):")
display(similar_sources)

# Calculate similarity metrics for a factor metrics = validator.calculate_similarity_metrics(factor_name) # Display the top 5 best matches print(f"Top 5 matches for {factor_name} by Pearson Distance (PD):") display(metrics.sort_values('PD').head(5)) # Find similar sources using thresholds similar_sources = validator.find_similar_sources( factor_name, pd_threshold=0.4, # Maximum Pearson Distance sid_threshold=0.8, # Maximum Standardized Identity Distance min_species=5 # Minimum number of shared species ) print(f"\nMatching sources (PD < 0.4, SID < 0.8, shared species >= 5):") display(similar_sources)

Top 5 matches for Biomass burning by Pearson Distance (PD):

	Reference ID	Reference Name	Place	Particle Size	SID	PD	Shared Species	Common Species
46	47	Exhaust	Copenhagen	PM2.5	0.706569	0.001265	8	Aluminum, Arsenic, Iron, Manganese, Rubidium, ...
196	210	Ship auxiliary engine at 25% load	sea	PM2.5	0.948225	0.003945	12	Antimony, Cadmium, Calcium, Copper, Elemental ...
50	51	Exhaust	Copenhagen	PM10	0.762362	0.004222	6	Arsenic, Iron, Rubidium, Selenium, Vanadium, Zinc
184	187	Oak closed fireplace	Wien	PM10	0.635842	0.005711	20	Aluminum, Ammonium, Chloride ion, Chromium, Co...
274	290	Traffic	Civitavecchia, Torrevaldaliga Nord	PM10	0.776520	0.008727	15	Aluminum, Ammonium, Copper, Elemental Carbon, ...

Matching sources (PD < 0.4, SID < 0.8, shared species >= 5):

	Reference ID	Reference Name	Place	Particle Size	SID	PD	Shared Species	Common Species
46	47	Exhaust	Copenhagen	PM2.5	0.706569	0.001265	8	Aluminum, Arsenic, Iron, Manganese, Rubidium, ...
50	51	Exhaust	Copenhagen	PM10	0.762362	0.004222	6	Arsenic, Iron, Rubidium, Selenium, Vanadium, Zinc
184	187	Oak closed fireplace	Wien	PM10	0.635842	0.005711	20	Aluminum, Ammonium, Chloride ion, Chromium, Co...
274	290	Traffic	Civitavecchia, Torrevaldaliga Nord	PM10	0.776520	0.008727	15	Aluminum, Ammonium, Copper, Elemental Carbon, ...
7	8	Closed fireplace Wood Burning	Po Valley, Valtelline	PM10	0.784574	0.051953	23	Aluminum, Ammonium, Antimony, Arsenic, Cadmium...
67	68	Ceramic Pottery factories (wood burning)	Bailén	PM2.5	0.791825	0.053067	18	Arsenic, Cadmium, Calcium, Chromium, Copper, E...
21	22	Closed fireplace Beech Combustion	Valtelline	TSP	0.696905	0.077837	15	Aluminum, Calcium, Chromium, Copper, Elemental...
270	286	Biomass Burning	Civitavecchia, Torrevaldaliga Nord	PM10	0.798382	0.082389	15	Aluminum, Ammonium, Copper, Elemental Carbon, ...
20	21	Closed fireplace Pine Combustion	Valtelline	TSP	0.761043	0.085149	17	Aluminum, Ammonium, Calcium, Chromium, Copper,...
238	252	Olive pit	Aveiro	PM10	0.748922	0.089406	15	Aluminum, Arsenic, Calcium, Chromium, Copper, ...
66	67	Ceramic Pottery factories (wood burning)	Bailén	PM10	0.792151	0.098616	19	Arsenic, Cadmium, Calcium, Chromium, Copper, E...

4. Visualize Similarity Diagram¶

Create a source similarity diagram to visualize how the factor compares with reference profiles.

In [7]:

# Plot similarity diagram
fig = validator.plot_similarity_diagram(factor_name, max_sources=10)
plt.tight_layout()
plt.show()

# Plot similarity diagram fig = validator.plot_similarity_diagram(factor_name, max_sources=10) plt.tight_layout() plt.show()

5. Working with Multiple Factors¶

Let's check all factors in our PMF solution.

In [8]:

# Get list of factors from the PMF object
factors = validator.pmf.profiles

# Process each factor
for factor in factors:
    print(f"\n========== {factor} ==========")
    
    # Get best match by Pearson Distance
    metrics = validator.calculate_similarity_metrics(factor)
    best_match = metrics.sort_values('PD').iloc[0]
    
    print(f"Best match: {best_match['Reference Name']}")
    print(f"PD: {best_match['PD']:.3f}, SID: {best_match['SID']:.3f}, Shared species: {best_match['Shared Species']}")
    
    # Check key species ratios
    if "OC" in validator.pmf.species and "EC" in validator.pmf.species:
        oc_ec = validator.calculate_ratio(factor, "OC", "EC")
        print(f"OC/EC ratio: {oc_ec:.2f}")
        
    if "K+" in validator.pmf.species and "SO42-" in validator.pmf.species:
        k_so4 = validator.calculate_ratio(factor, "K+", "SO42-")
        print(f"K+/SO4 ratio: {k_so4:.3f}")

# Get list of factors from the PMF object factors = validator.pmf.profiles # Process each factor for factor in factors: print(f"\n========== {factor} ==========") # Get best match by Pearson Distance metrics = validator.calculate_similarity_metrics(factor) best_match = metrics.sort_values('PD').iloc[0] print(f"Best match: {best_match['Reference Name']}") print(f"PD: {best_match['PD']:.3f}, SID: {best_match['SID']:.3f}, Shared species: {best_match['Shared Species']}") # Check key species ratios if "OC" in validator.pmf.species and "EC" in validator.pmf.species: oc_ec = validator.calculate_ratio(factor, "OC", "EC") print(f"OC/EC ratio: {oc_ec:.2f}") if "K+" in validator.pmf.species and "SO42-" in validator.pmf.species: k_so4 = validator.calculate_ratio(factor, "K+", "SO42-") print(f"K+/SO4 ratio: {k_so4:.3f}")

========== Mineral dust ==========
Best match: Salt
PD: 0.000, SID: 0.629, Shared species: 10
K+/SO4 ratio: 0.084

========== Industrial ==========
Best match: Traffic
PD: 0.046, SID: 0.830, Shared species: 14
K+/SO4 ratio: 0.419

========== Aged sea salt ==========
Best match: Exhaust
PD: 0.001, SID: 0.946, Shared species: 6
K+/SO4 ratio: 0.768

========== Biomass burning ==========
Best match: Exhaust
PD: 0.001, SID: 0.707, Shared species: 8
K+/SO4 ratio: 2.112

========== Nitrate-rich ==========
Best match: Ship auxiliary engine at 75% load
PD: 0.000, SID: 0.945, Shared species: 10
K+/SO4 ratio: 0.037

========== MSA-rich ==========
Best match: Tyre wear on road dust
PD: 0.001, SID: 1.229, Shared species: 12
K+/SO4 ratio: 0.016

========== Sea/road salt ==========
Best match: Ship auxiliary engine at 25% load
PD: 0.002, SID: 0.810, Shared species: 12
K+/SO4 ratio: 0.055

========== Sulfate-rich ==========
Best match: Ship auxiliary engine at 50% load
PD: 0.002, SID: 0.928, Shared species: 11
K+/SO4 ratio: 0.022

========== Secondary biogenic oxidation ==========
Best match: Exhaust
PD: 0.000, SID: 0.882, Shared species: 6
K+/SO4 ratio: 0.000

========== Primary biogenic ==========
Best match: Salt
PD: 0.001, SID: 0.643, Shared species: 10
K+/SO4 ratio: 0.336

========== Primary traffic ==========

2025-04-25 14:13:43,184 - PMF_toolkits.validation - WARNING - Denominator species 'SO42-' has zero or NaN value, cannot calculate ratio

Best match: Exhaust
PD: 0.000, SID: 0.803, Shared species: 6
K+/SO4 ratio: nan

6. Extract Regression Diagnostics¶

R² values for each species can help evaluate how well the PMF model explains the observations.

In [9]:

# Extract regression diagnostics
r2_data = validator.read_regression_diagnostics()

if not r2_data.empty:
    # Display R² values
    print("R² values for species in the PMF solution:")
    display(r2_data)
    
    # Plot species with low R² values (<0.6)
    low_r2_species = r2_data[r2_data["r^2"] < 0.6].index
    
    if len(low_r2_species) > 0:
        print(f"\nSpecies with low R² values (<0.6):")
        for species in low_r2_species:
            print(f"- {species}: {r2_data.loc[species, 'r^2']:.3f}")
else:
    print("Regression diagnostics not available in the PMF output file")

# Extract regression diagnostics r2_data = validator.read_regression_diagnostics() if not r2_data.empty: # Display R² values print("R² values for species in the PMF solution:") display(r2_data) # Plot species with low R² values (<0.6) low_r2_species = r2_data[r2_data["r^2"] < 0.6].index if len(low_r2_species) > 0: print(f"\nSpecies with low R² values (<0.6):") for species in low_r2_species: print(f"- {species}: {r2_data.loc[species, 'r^2']:.3f}") else: print("Regression diagnostics not available in the PMF output file")

R² values for species in the PMF solution:

2	Intercept	Slope	SE	r^2	Stat	P Value
Species
PM10recons	0.073399	0.989945	1.116572	0.982175	0.079762	0.404203
OC*	-0.042199	0.993941	0.476667	0.947379	0.032954	0.999231
EC	0.063121	0.90835	0.175888	0.960257	0.078551	0.423492
Cl-	0.001415	0.973778	0.014889	0.988755	0.146554	0.009313
NO3-	-0.045585	1.029101	0.155301	0.996481	0.109547	0.099549
SO42-	0.379642	0.674983	0.284731	0.854757	0.056431	0.820898
Na+	0.001703	0.986245	0.012505	0.990259	0.071988	0.536277
NH4+	0.030592	0.928837	0.117288	0.984147	0.05354	0.866141
K+	0.011217	0.871335	0.024529	0.944353	0.048939	0.92565
Mg2+	0.001897	0.856315	0.003	0.911967	0.052991	0.874103
Ca2+	0.002535	0.907594	0.086758	0.879913	0.059661	0.765173
MSA	0.000768	0.965917	0.00318	0.984831	0.242553	0.000001
Levoglucosan	-0.005927	1.018592	0.058862	0.974291	0.145609	0.009978
Mannosan	0.000451	0.957836	0.006375	0.97578	0.069218	0.587163
Polyols	0.000872	0.976074	0.005427	0.983208	0.149971	0.007229
Cellulose	0.016219	0.439206	0.020104	0.48922	0.044577	0.964969
3-MBTCA	0.000359	0.817166	0.003097	0.856201	0.11533	0.071925
Phthalic	0.001779	0.391278	0.00131	0.658752	0.045562	0.957611
Pinic	0.000387	0.805255	0.001974	0.762246	0.044394	0.96624
Al	0.017669	0.56433	0.02395	0.824992	0.071916	0.537577
As	0.000038	0.805123	0.000107	0.848041	0.041311	0.983292
Cd	0.000439	0.592505	0.000865	0.603945	0.089033	0.274944
Cr	0.000026	0.516929	0.000034	0.612272	0.100871	0.157066
Cu	0.000476	0.902072	0.001952	0.918537	0.051098	0.899859
Fe	0.011588	0.922492	0.032574	0.970968	0.061176	0.737725
Mn	0.000951	0.742165	0.002494	0.853568	0.122602	0.046669
Mo	0.000285	0.242142	0.000279	0.377606	0.063794	0.689095
Ni	0.000196	0.64386	0.000322	0.687599	0.090439	0.258252
Pb	0.000302	0.844148	0.001493	0.911103	0.069691	0.578384
Rb	0.000009	0.941812	0.000074	0.951278	0.065866	0.650077
Sb	0.000712	0.021423	0.000525	0.037679	0.094837	0.210862
Se	0.000133	0.546149	0.000098	0.64242	0.060642	0.74748
Sn	0.000638	0.620514	0.000691	0.627257	0.063265	0.699007
Ti	-0.000165	1.009001	0.001216	0.882881	0.085063	0.326218
V	0.000103	0.548661	0.000164	0.786945	0.082404	0.363993
Zn	0.003263	0.787337	0.009368	0.893123	0.091387	0.247424

Species with low R² values (<0.6):
- Cellulose: 0.489
- Mo: 0.378
- Sb: 0.038