# staRdom: Versatile Software for Analyzing Spectroscopic Data of Dissolved Organic Matter in R

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- Calculating fluorescence peaks and indices (tutorials S1 and S2) [47],
- Calculating common absorbance (slope) indices:
- ◦
- absorbance at 254 nm (a254) [43],
- ◦
- absorbance at 300 nm (a300) [50],
- ◦
- ratio of absorbance at 250 to 365 nm (E2:E3) [51],
- ◦
- ratio of absorbance at 465 to 665 nm (E4:E6) [52],
- ◦
- spectral slope within log-transformed absorption spectra range (S
_{275–295}, S_{350–400}, S_{300–700}) and the ratio of S_{275–295}to S_{350–400}(SR) [44], - ◦
- the wavelength distribution of absorption spectral slopes [53] and
- ◦
- user-defined values and slopes can be extracted or calculated from the absorbance spectra.

#### 2.1. Data Import

#### 2.2. Data Preprocessing

#### 2.3. PARAFAC Analysis

#### 2.3.1. Calculation of a PARAFAC Model from EEM Data

_{ijk}is the value of the ith sample, the jth emission wavelength, and the kth excitation wavelength. Here, e

_{ijk}is the respective residuum, i.e., data not modeled by PARAFAC components. a (samples), b (emission), and c (excitation) are matrices (also called modes) with N columns and multiple rows, equal to the numbers of samples, emission wavelengths, or excitation wavelengths, respectively. The matrices resulting from a multiplication of the vectors b

_{f}and c

_{f}show the PARAFAC components, resemble EEMs, and can, therefore, be interpreted easily.

#### 2.3.2. Identification of Outliers

#### 2.3.3. Model Evaluation

_{4}C

_{6}T

_{3}): the data are split into four subsets (A, B, C, and D) and recombined to compare one half of the data to the other in different combinations (AB–CD, AD–BC, AC–BD) [32]. The comparison is done visually by plots showing the spectral loadings (splithalf_plot, Figure 8) and by calculating Tucker’s congruence coefficient [65] (TCC) or shift- and shape-sensitive congruence [66] (SSC, splithalf_tcc). Subsets can be automatically generated or manually defined.

#### 2.4. Export and Further Interpretation of Results

#### 2.5. Toolbox Comparison

^{−6}and 1 × 10

^{−9}for drEEM and between 1 × 10

^{−8}and 1 × 10

^{−11}for staRdom, in steps of 1 × 10

^{−1}. Different convergence criteria were necessary because the toolboxes use different methods to monitor convergence, as shown in Equations (2) and (3). Due to this difference, when identical convergence criteria are supplied in the function inputs to both staRdom and drEEM, then drEEM return models with a smaller modeling error.

_{n}—sum-of-squared-error of nth iteration

## 3. Results and Discussion

#### 3.1. Number of Initializations

#### 3.2. Convergence Criterion

^{−6}in drEEM and 1 × 10

^{−8}in staRdom. As the results in this study are based on model errors, these differences do not further influence any results of the shown PARAFAC models.

#### 3.3. Influence of Missing Data

#### 3.4. Time until Model Convergence

#### 3.5. Outlier Calculation and Split-Half Validation

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Distributions of calculation times for models of five datasets, using staRdom and drEEM on different CPU architectures (CPU speed improves from left to right), with the model specifications defined in Table 3.

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**Figure 2.**An excitation–emission matrices (EEM) sample as measured, untreated (original) and after spectral correction with correction factors, blank subtraction with ultra-pure water, and inner-filter effect correction using absorbance data.

**Figure 3.**The same EEM sample as in Figure 2 after Raman normalization, scatter removal (Rayleigh 1st and 2nd order, Raman 1st and 2nd order), wavelength range reduction, manual noise removal, and interpolation of missing data.

**Figure 4.**Comparing preliminary (outliers still included) and final models with 5 and 6 components. The components were normalized according to their maximum fluorescence (Fmax). Comp. = Component.

**Figure 5.**Outlier identification in a PARAFAC model using the leverage of emission and excitation wavelengths as well as samples.

**Figure 6.**Residuals of 6 samples; E and F were identified as outliers using the leverage and, thus, were excluded from the model calculation.

**Figure 7.**Components’ loadings from PARAFAC models (

**a**) without and (

**b**) with previous normalization. Diagonally: distributions of the loadings; lower triangle: regression curve between components; and upper triangle: Pearson correlation coefficient between components.

**Figure 8.**Split-half validation of a PARAFAC model. Emission spectra: full line; excitation spectra: dashed line; colors according to models using different sample sub-sets.

**Figure 9.**Similarity of PARAFAC models derived using staRdom and drEEM, using different numbers of random initializations and different convergence criteria. Similarity is measured as minimum TCC: the higher the TCC, the more similar are the components.

**Table 1.**List of selected staRdom functions and the step of the analysis scheme (Figure 1) that are most probably used.

Step of the Analysis | staRdom Functions Used | Purpose of the Function |
---|---|---|

import raw data | eem_read | load EEM data |

absorbance_read | load absorbance data | |

check data consistency | eem_checkdata | check presence and names of samples |

view data | ggeem | create single plots |

eem_overview plot | create multiple plots | |

correct biases | abs_blcor | absorbance baseline correction |

eem_spectral_cor | EEM spectral correction | |

eem_remove_blank | subtract blank sample | |

eem_ife_correction | inner-filter effect correction | |

eem_raman_normalisation,eem_raman_normalisation2 | normalize EEM data to Raman units | |

remove scatter | eem_rem_scat | remove Rayleigh and Raman scattering of 1^{st} and 2^{nd} order |

eem_setNA | remove noise manually | |

eem_interp | interpolate missing data | |

synchronize sample wavelength | eem_red2smallest | remove all wavelengths that are not present in all samples |

eem_extend2largest | create all wavelengths present in any sample in all samples | |

correct for sample dilution | eem_dilution | multiply EEM data by a dilution factor |

smooth data | eem_smooth | smooth EEM data |

normalize | no dedicated function, argument normalise = TRUE in eem_parafac | normalize EEM data |

fluorescence peaks and indices | eem_biological_index | calculate BIX |

eem_coble_peaks | calculate Coble peaks | |

eem_fluorescence_index | calculate FI | |

eem_humification_index | calculate HIX | |

absorbance indices | abs_parms | calculate absorbance indices, spectral slopes, and selected ratios |

calculate PARAFAC model (preliminary and final) | eem_parafac | calculate PARAFAC models |

view PARAFAC models | eempf_compare | compare PARAFAC models (with different numbers of components) visually |

eempf_comp_load_plot | plot single PARAFAC models | |

identify outliers | eempf_leverage | calculate the leverage of each sample and wavelength |

eempf_leverage_plot | plot leverages | |

eempf_leverage_ident | manually select samples in leverage plots | |

remove outliers | eem_exclude | remove samples and wavelengths from the data set |

evaluate model | eempf_convergence | extract convergence behavior of a model |

eempf_cortable, eempf_corplot | show correlation between components | |

eempf_corcondia | calculate the core consistency | |

sensitivity analysis | splithalf, splithalf_plot | calculate and plot a split-half validation |

interpret the results | eempf4analysis | export table with component loadings |

eempf_report | create an analysis report in html format | |

eempf_openfluor | export data for openfluor.org |

Name | Number of | % | Description | Reference | |||
---|---|---|---|---|---|---|---|

Comps ^{1} | Samples | Em ^{2} | Ex ^{3} | NA ^{4} | |||

Amino3 | 3 | 5 | 201 | 61 | 0 | Pure amino acids | [31] |

Fjord6 | 6 | 191 | 91 | 44 | 16.6 | Solid-phase extracts of DOM from three arctic fjords | [68] |

Headwater4 | 4 | 235 | 151 | 43 | 0 | Headwater streams, and agricultural catchments, Denmark and Uruguay | [20] |

PortSurvey6 | 6 | 206 | 73 | 42 | 9.5 | port and oceanic marine samples (USA, Pacific coast), drEEM tutorial dataset | [54] |

Pure5 | 5 | 60 | 50 | 40 | 0 | Pure substances with added artificial noise | unpublished |

RioEx4 | 4 | 58 | 97 | 111 | 0 | Photodegradation experiment of solid-phase extracted DOM | [69] |

^{1}components of the PARAFAC model,

^{2}emission wavelengths,

^{3}excitation wavelengths,

^{4}missing data.

Name | Software | Convergence Criterion | Initializations | Relative Error | Minimum TCC |
---|---|---|---|---|---|

Amino3 | staRdom | 1 × 10^{−8} | 10 | 1.000069 | 1.0000 |

drEEM | 1 × 10^{−8} | 10 | 1.000000 | 1.0000 | |

Headwater4 | staRdom | 1 × 10^{−9} | 10 | 1.000010 | 1.0000 |

drEEM | 1 × 10^{−7} | 10 | 1.000002 | 1.0000 | |

PortSurvey6 | staRdom | 1 × 10^{−11} | 30 | 1.000042 | 0.9997 |

drEEM | 1 × 10^{−7} | 10 | 1.000039 | 0.9997 | |

Pure5 | staRdom | 1 × 10^{−10} | 40 | 1.000071 | 0.9993 |

drEEM | 1 × 10^{−7} | 10 | 1.000056 | 0.9993 | |

RioEx4 | staRdom | 1 × 10^{−10} | 30 | 1.000022 | 0.9999 |

drEEM | 1 × 10^{−7} | 20 | 1.000015 | 1.0000 |

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## Share and Cite

**MDPI and ACS Style**

Pucher, M.; Wünsch, U.; Weigelhofer, G.; Murphy, K.; Hein, T.; Graeber, D. staRdom: Versatile Software for Analyzing Spectroscopic Data of Dissolved Organic Matter in R. *Water* **2019**, *11*, 2366.
https://doi.org/10.3390/w11112366

**AMA Style**

Pucher M, Wünsch U, Weigelhofer G, Murphy K, Hein T, Graeber D. staRdom: Versatile Software for Analyzing Spectroscopic Data of Dissolved Organic Matter in R. *Water*. 2019; 11(11):2366.
https://doi.org/10.3390/w11112366

**Chicago/Turabian Style**

Pucher, Matthias, Urban Wünsch, Gabriele Weigelhofer, Kathleen Murphy, Thomas Hein, and Daniel Graeber. 2019. "staRdom: Versatile Software for Analyzing Spectroscopic Data of Dissolved Organic Matter in R" *Water* 11, no. 11: 2366.
https://doi.org/10.3390/w11112366