# Metric for Automatic Machine Translation Evaluation
based on Universal Sentence Representations

Hiroki Shimanaka†
&Tomoyuki Kajiwara†‡
†Graduate School of Systems Design, Tokyo Metropolitan University, Tokyo,
Japan
<EMAIL_ADDRESS><EMAIL_ADDRESS>
‡Institute for Datability Science, Osaka University, Osaka, Japan
<EMAIL_ADDRESS>
&Mamoru Komachi†

###### Abstract

Sentence representations can capture a wide range of information that cannot
be captured by local features based on character or word N-grams. This paper
examines the usefulness of universal sentence representations for evaluating
the quality of machine translation. Although it is difficult to train sentence
representations using small-scale translation datasets with manual evaluation,
sentence representations trained from large-scale data in other tasks can
improve the automatic evaluation of machine translation. Experimental results
of the WMT-2016 dataset show that the proposed method achieves state-of-the-
art performance with sentence representation features only.

##  1 Introduction

This paper describes a segment-level metric for automatic machine translation
evaluation (MTE). MTE metrics having a high correlation with human evaluation
enable the continuous integration and deployment of a machine translation (MT)
system. Various MTE metrics have been proposed in the metrics task of the
Workshops on Statistical Machine Translation (WMT) that was started in 2008.
However, most MTE metrics are obtained by computing the similarity between an
MT hypothesis and a reference translation based on character N-grams or word
N-grams, such as SentBLEU Lin and Och (2004), which is a smoothed version of
BLEU Papineni et al. (2002), Blend Ma et al. (2017), MEANT 2.0 Lo (2017), and
chrF++ Popović (2017), which achieved excellent results in the WMT-2017
Metrics task Bojar et al. (2017). Therefore, they can exploit only limited
information for segment-level MTE. In other words, MTE metrics based on
character N-grams or word N-grams cannot make full use of sentence
representations; they only check for word matches.

We propose a segment-level MTE metric by using universal sentence
representations capable of capturing information that cannot be captured by
local features based on character or word N-grams. The results of an
experiment in segment-level MTE conducted using the datasets for to-English
language pairs on WMT-2016 indicated that the proposed regression model using
sentence representations achieves the best performance.

The main contributions of the study are summarized below:

  * •

We propose a novel supervised regression model for segment-level MTE based on
universal sentence representations.

  * •

We achieved state-of-the-art performance on the WMT-2016 dataset for to-
English language pairs without using any complex features and models.

Figure 1: Outline of Skip-Thought.

Figure 2: Outline of InferSent.

Figure 3: Outline of our metric.

##  2 Related Work

DPMFcomb Yu et al. (2015a) achieved the best performance in the WMT-2016
Metrics task Bojar et al. (2016). It incorporates 55 default metrics provided
by the Asiya MT evaluation toolkit111http://asiya.lsi.upc.edu/ Giménez and
Màrquez (2010), as well as three other metrics, namely, DPMF Yu et al.
(2015b), REDp Yu et al. (2015a), and ENTFp Yu et al. (2015a), using ranking
SVM to train parameters of each metric score. DPMF evaluates the syntactic
similarity between an MT hypothesis and a reference translation. REDp
evaluates an MT hypothesis based on the dependency tree of the reference
translation that comprises both lexical and syntactic information. ENTFp Yu et
al. (2015a) evaluates the fluency of an MT hypothesis.

After the success of DPMFcomb, Blend222http://github.com/qingsongma/blend Ma
et al. (2017) achieved the best performance in the WMT-2017 Metrics task Bojar
et al. (2017). Similar to DPMFcomb, Blend is essentially an SVR (RBF kernel)
model that uses the scores of various metrics as features. It incorporates 25
lexical metrics provided by the Asiya MT evaluation toolkit, as well as four
other metrics, namely, BEER Stanojević and Sima’an (2015), CharacTER Wang et
al. (2016), DPMF and ENTFp. BEER Stanojević and Sima’an (2015) is a linear
model based on character N-grams and replacement trees. CharacTER Wang et al.
(2016) evaluates an MT hypothesis based on character-level edit distance.

DPMFcomb is trained through relative ranking of human evaluation data in terms
of relative ranking (RR). The quality of five MT hypotheses of the same source
segment are ranked from 1 to 5 via comparison with the reference translation.
In contrast, Blend is trained through direct assessment (DA) of human
evaluation data. DA provides the absolute quality scores of hypotheses, by
measuring to what extent a hypothesis adequately expresses the meaning of the
reference translation. The results of the experiments in segment-level MTE
conducted using the datasets for to-English language pairs on WMT-2016 showed
that Blend achieved a better performance than DPMFcomb (Table 2). In this
study, as with Blend, we propose a supervised regression model trained using
DA human evaluation data.

Instead of using local and lexical features,
ReVal333https://github.com/rohitguptacs/ReVal Gupta et al. (2015a, b) proposes
using sentence-level features. It is a metric using Tree-LSTM (Tai et al.,
2015) for training and capturing the holistic information of sentences. It is
trained using datasets of pseudo similarity scores, which is generated by
translating RR data, and out-domain datasets of similarity scores of
SICK444http://clic.cimec.unitn.it/composes/sick.html. However, the training
dataset used in this metric consists of approximately 21,000 sentences; thus,
the learning of Tree-LSTM is unstable and accurate learning is difficult
(Table 2). The proposed metric uses sentence representations trained using
LSTM as sentence information. Further, we apply universal sentence
representations to this task; these representations were trained using large-
scale data obtained in other tasks. Therefore, the proposed approach avoids
the problem of using a small dataset for training sentence representations.

##  3 Regression Model for MTE Using Universal Sentence Representations

The proposed metric evaluates MT results with universal sentence
representations trained using large-scale data obtained in other tasks. First,
we explain two types of sentence representations used in the proposed metric
in Section 3.1. Then, we explain the proposed regression model and feature
extraction for MTE in Section 3.2.

| cs-en | de-en | fi-en | ro-en | ru-en | tr-en
---|---|---|---|---|---|---
WMT-2015 | 500 | 500 | 500 | - | 500 | -
WMT-2016 | 560 | 560 | 560 | 560 | 560 | 560
Table 1: Number of DA human evaluation datasets for to-English language
pairs888en: English, cs: Czech, de: German, fi: Finnish, ro: Romanian, ru:
Russian, tr: Turkish in WMT-2015 Stanojević et al. (2015) and WMT-2016 Bojar
et al. (2016).

###  3.1 Universal Sentence Representations

Several approaches have been proposed to learn sentence representations. These
sentence representations are learned through large-scale data so that they
constitute potentially useful features for MTE. These have been proved
effective in various NLP tasks such as document classification and measurement
of semantic textual similarity, and we call them universal sentence
representations.

First, Skip-Thought555https://github.com/ryankiros/skip-thoughts Kiros et al.
(2015) builds an unsupervised model of universal sentence representations
trained using three consecutive sentences, such as $s_{i-1}$, $s_{i}$, and
$s_{i+1}$. It is an encoder-decoder model that encodes sentence $s_{i}$ and
predicts previous and next sentences $s_{i-1}$ and $s_{i+1}$ from its sentence
representation $\vec{s_{i}}$ (Figure 3). As a result of training, this encoder
can produce sentence representations. Skip-Thought demonstrates high
performance, especially when applied to document classification tasks.

Second, InferSent666https://github.com/facebookresearch/InferSent Conneau et
al. (2017) constructs a supervised model computing universal sentence
representations trained using Stanford Natural Language Inference (SNLI)
datasets777https://nlp.stanford.edu/projects/snli/ Bowman et al. (2015). The
Natural Language Inference task is a classification task of sentence pairs
with three labels, entailment, contradiction and neutral; thus, InferSent can
train sentence representations that are sensitive to differences in meaning.
This model encodes sentence pairs $u$ and $v$ and generates features by
sentence representations $\vec{u}$ and $\vec{v}$ with a bi-directional LSTM
architecture with max pooling (Figure 3). InferSent demonstrates high
performance across various document classification and semantic textual
similarity tasks.

###  3.2 Regression Model for MTE

In this paper, we propose a segment-level MTE metric for to-English language
pairs. This problem can be treated as a regression problem that estimates
translation quality as a real number from an MT hypothesis $t$ and a reference
translation $r$. Once $d$-dimensional sentence vectors $\vec{t}$ and $\vec{r}$
are generated, the proposed model applies the following three matching methods
to extract relations between $t$ and $r$ (Figure 3).

  * •

Concatenation: $(\vec{\mathstrut\smash[t]{t}},\vec{\mathstrut\smash[t]{r}})$

  * •

Element-wise product:
$\vec{\mathstrut\smash[t]{t}}*\vec{\mathstrut\smash[t]{r}}$

  * •

Absolute element-wise difference:
$|\vec{\mathstrut\smash[t]{t}}-\vec{\mathstrut\smash[t]{r}}|$

Thus, we perform regression using $4d$-dimensional features of
$\vec{\mathstrut\smash[t]{t}}$, $\vec{\mathstrut\smash[t]{r}}$,
$\vec{\mathstrut\smash[t]{t}}*\vec{\mathstrut\smash[t]{r}}$ and
$|\vec{\mathstrut\smash[t]{t}}-\vec{\mathstrut\smash[t]{r}}|$.

##  4 Experiments of Segment-Level MTE for To-English Language Pairs

We performed experiments using evaluation datasets of the WMT Metrics task to
verify the performance of the proposed metric.

| cs-en | de-en | fi-en | ro-en | ru-en | tr-en | Avg.
---|---|---|---|---|---|---|---
SentBLEU Bojar et al. (2016) | 0.557 | 0.448 | 0.484 | 0.499 | 0.502 | 0.532 | 0.504
Blend Ma et al. (2017) | 0.709 | 0.601 | 0.584 | 0.636 | 0.633 | 0.675 | 0.640
DPMFcomb Bojar et al. (2016) | 0.713 | 0.584 | 0.598 | 0.627 | 0.615 | 0.663 | 0.633
ReVal Bojar et al. (2016) | 0.577 | 0.528 | 0.471 | 0.547 | 0.528 | 0.531 | 0.530
SVR with Skip-Thought | 0.665 | 0.571 | 0.609 | 0.677 | 0.608 | 0.599 | 0.622
SVR with InferSent | 0.679 | 0.604 | 0.617 | 0.640 | 0.644 | 0.630 | 0.636
SVR with InferSent + Skip-Thought | 0.686 | 0.611 | 0.633 | 0.660 | 0.649 | 0.646 | 0.648
Table 2: Segment-level Pearson correlation of metric scores and DA human
evaluations scores for to-English language pairs in WMT-2016 (newstest2016).

###  4.1 Setups

#### Datasets.

We used datasets for to-English language pairs from the WMT-2016 Metrics task
Bojar et al. (2016) as summarized in Table 8. Following Ma et al. Ma et al.
(2017), we employed all other to-English DA data as training data (4,800
sentences) for testing on each to-English language pair (560 sentences) in
WMT-2016.

#### Features.

Publicly available pre-trained sentence representations such as Skip-
Thought55footnotemark: 5 and InferSent66footnotemark: 6 were used as the
features mentioned in Section 3. Skip-Thought is a collection of
4,800-dimensional sentence representations trained on 74 million sentences of
the BookCorpus dataset Zhu et al. (2015). InferSent is a collection of
4,096-dimensional sentence representations trained on both 560,000 sentences
of the SNLI dataset Bowman et al. (2015) and 433,000 sentences of the MultiNLI
dataset Williams et al. (2017).

#### Model.

Our regression model used SVR with the RBF kernel from scikit-
learn999http://scikit-learn.org/stable/. Hyper-parameters were determined
through 10-fold cross validation using the training data. We examined all
combinations of hyper-parameters among $C\in\\{0.01,0.1,1.0,10\\}$,
$\epsilon\in\\{0.01,0.1,1.0,10\\}$, and $\gamma\in\\{0.01,0.1,1.0,10\\}$.

There are three comparison methods: Blend Ma et al. (2017), DPMFcomb Yu et al.
(2015a), and ReVal Gupta et al. (2015a, b), as described in Section 2. Blend
and DPMFcomb are MTE metrics that exhibited the best performance in the
WMT-2017 Metrics task Bojar et al. (2017) and WMT-2016 Metrics task,
respectively. We compared the Pearson correlation of each metric score and DA
human evaluation scores.

###  4.2 Result

As can be seen in Table 2, the proposed metric, which combines InferSent and
Skip-Thought representations, surpasses the best performance in three out of
six to-English languages pairs and achieves state-of-the-art performance on
average.

###  4.3 Discussion

These results indicate that it is possible to adopt universal sentence
representations in MTE by training a regression model using DA human
evaluation data. Since Blend is an ensemble method using combinations of
various MTE metrics as features, our results show that universal sentence
representations can consider information more abundantly than a complex model.
Since ReVal is also based on sentence representations, we conclude that
universal sentence representations trained on a large-scale dataset are more
effective for MTE tasks than sentence representations trained on a small or
limited in-domain dataset.

###  4.4 Error Analysis

We re-implemented Blend101010http://github.com/qingsongma/blend Ma et al.
(2017) and compared the evaluation results with the proposed metric.111111The
average Pearson correlation of all language pairs after re-implementing Blend
was 0.636, which is a little lower than the value reported in their paper.
However, we judged that the following discussion will not be affected by this
difference.

We analyzed 20% of the pairs of MT hypotheses and reference translations (112
sentence pairs $\times$ 6 languages = 672 sentence pairs) in descending order
of DA human score in each language pair. In other words, the top 20% of MT
hypotheses that were close to the meaning of the reference translations for
each language pair were analyzed. Among these, only Blend estimates the
translation quality as high for 70 sentence pairs, and only our metric
estimates the translation quality as high for 88 sentence pairs.

#### Surface.

Among pairs estimated to have high translation quality by each method, there
were 26 pairs in Blend and 42 pairs in the proposed method with a low word
surface matching rate between MT hypotheses and reference translations. This
result shows that the proposed metric can evaluate a wide range of sentence
information that cannot be captured by Blend.

#### Unknown words.

There were 26 MT hypotheses consisting of words that were treated as unknown
words in Skip-Thought or InferSent that were correctly evaluated in Blend. On
the other hand, there were 26 MT hypotheses that were correctly evaluated in
the proposed metric. This result shows that the proposed metric is affected by
unknown words. However, it is also true that there are some MT hypotheses
containing unknown words that can be correctly evaluated. Therefore, we
analyzed further by focusing on sentence length. There were 17 MT hypotheses
consisting of words that were treated as unknown words by either Skip-Thought
or InferSent with a short length (15 words or less) that were correctly
evaluated in Blend. However, in the proposed metric, there were only two MT
hypotheses that were correctly evaluated. This result indicates that the
shorter the sentence, the more likely is the proposed metric to be affected by
unknown words.

##  5 Conclusions

In this study, we tried to apply universal sentence representation to MTE
based on the DA of human evaluation data. Our segment-level MTE metric
achieved the best performance on the WMT-2016 dataset. We conclude that:

  * •

Universal sentence representations can consider information more
comprehensively than an ensemble metric using combinations of various MTE
metrics based on features of character or word N-grams.

  * •

Universal sentence representations trained on a large-scale dataset are more
effective than sentence representations trained on a small or limited in-
domain dataset.

  * •

Although a metric based on SVR with universal sentence representations is not
good at handling unknown words, it correctly estimates the translation quality
of MT hypotheses with a low word matching rate with reference translations.

Following the success of InferSent Conneau et al. (2017), many works Wieting
and Gimpel (2017); Cer et al. (2018); Subramanian et al. (2018) on universal
sentence representations have been published. Based on the results of our
work, we expect that the MTE metric will be further improved using these
better universal sentence representations.

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[1,2]Craig R. Walton

[1]Department of Earth Sciences, Institute für Geochemie und Petrologie, ETH
Zürich, NW D 81.2, Clausiusstrasse 25, Zürich, 8092, Switzerland

2]Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge,
CB3 OHA, United Kingdom

3]Department of Earth Sciences, Merton College, University of Oxford, Oxford,
OX1 4JD, United Kingdom

4]Department of Earth Sciences, University of Bergen, Bergen, NO-5020, Norway

5]School of Physical Sciences, Open University, Walton Hall,Milton Keynes, MK7
6AA, United Kingdom

6]Department of Earth Sciences, University of Cambridge, Downing
Street,Cambridge, CB2 3EQ, United Kingdom

# Cosmic dust fertilization of glacial prebiotic chemistry on early Earth

<EMAIL_ADDRESS>Jessica K. Rigley<EMAIL_ADDRESS>Alexander Lipp  Robert Law  Martin D. Suttle  Maria Schönbächler  Mark Wyatt
Oliver Shorttle  *  [  [  [  [  [

###### Abstract

Earth’s surface is deficient in available forms of many elements considered
limiting for prebiotic chemistry. In contrast, many extraterrestrial rocky
objects are rich in these same elements. Limiting prebiotic ingredients may
therefore have been delivered by exogenous material; however, the mechanisms
by which exogeneous material may be reliably and non-destructively supplied to
a planetary surface remains unclear. Today, the flux of extraterrestrial
matter to Earth is dominated by fine-grained cosmic dust. Whilst this material
is rarely discussed in a prebiotic context due to its delivery over a large
surface area, concentrated cosmic dust deposits are known to form on Earth
today due to the action of sedimentary processes. Here, we combine empirical
constraints on dust sedimentation with dynamical simulations of dust formation
and planetary accretion to show that localised sedimentary deposits of cosmic
dust could have accumulated in arid environments on early Earth – in
particular glacial settings that today produce cryoconite sediments. Our
results challenge the widely held assumption that cosmic dust is incapable of
fertilising prebiotic chemistry. Cosmic dust deposits may have plausibly
formed on early Earth and acted to fertilise prebiotic chemistry.

###### keywords:

origin, life, cosmic, dust

##  1 Introduction

The origin of life on Earth probably resulted from interacting solid, liquid,
and gaseous reservoirs of bioessential elements in reactive molecular forms
[1]. Experimental work demonstrates that high to moderate concentrations (mM
to 100’s mM) of simple species (e.g., HCN, $\mathrm{PO_{4}^{3-}}$, and
$\mathrm{HSO_{3}^{-}}$) can produce high yields of biologically-relevant
molecules such as nucleic acids, lipids, and peptides [2] [3] [4] [5] [6].
However, a remaining gap in understanding the geological context of prebiotic
chemistry on Earth is the mechanisms by which concentrated feedstocks were
produced [7].

Common terrestrial rocks are relatively poor in reactive and/or soluble forms
of the key elements mentioned above: phosphorus (P), sulfur (S), nitrogen (N),
and carbon (C). Indeed, life on Earth is engaged in fierce competition for the
limited endogenous bioavailable reservoirs of these elements. Complex
enzymatic machinery has evolved in response to this challenge, such that life
can extract these species from the environment even when they occur in limited
concentration or in largely inert chemical form. The pre-enzymatic world of
prebiotic chemistry must have initially lacked such mechanisms to enhance the
availability of key species. However, certain processes in Earth’s early
history may have gone part or all of the way towards solving this apparent
paradox. One such possibility is the accretion and surficial sedimentary
sorting of cosmic dust (here defined as grains of size $\mathrm{<3\;mm}$).

Cosmic dust is comprised of the mineral grain aggregates produced by
collisions between asteroids [8] and/or the sublimation and disintegration of
comets [9] (Fig. 1a). Such particles produced further from the Sun can then
drift inwards due to Poynting-Robertson (P-R) drag and be accreted by Earth.
Cosmic dust contains bioessential elements (for terrestrial life), e.g., P, S,
N, and C, at concentrations well above that of Earth’s crust [10, 11, 12].
Many cosmic dust grains represent nearly pristine samples of their parent body
objects, which appear to span comets (volatile-rich outer Solar System
materials) and asteroids (a mixture of early-formed differentiated objects and
relatively late-formed and/or small-to-moderate sized undifferentated objects,
of both outer and inner Solar System origin) [13, 11].

In contrast to larger objects, the flux of cosmic dust to Earth is essentially
constant on yearly timescales. Moreover, some fraction of cosmic dust grains
pass relatively gently through the Earth’s atmosphere, thereby retaining a
greater fraction of primitive CHNS than do large (e.g., bolide-type) impactors
[14, 15, 16, 17]. The continuous and mostly non-destructive accretion of
cosmic dust across planetary surfaces suggests a significant advantage over
discrete and violent episodes of bioessential element delivery by larger
impactors, potentially greatly improving the chances of the successful entry
of extraterrestrial matter into prebiotic chemistry.

Cosmic dust is accreted across the Earth’s entire surface area, such that it
is initially dilute in terms of mass per unit area relative to discrete
delivery events by larger objects [18]. On this basis, the prebiotic
importance of cosmic dust has previously been questioned [19, 18]. However,
there are many planetary processes that can concentrate fine grained materials
from across large surface areas to form concentrated deposits, e.g., aeolian,
fluvial, and glaciogenic sorting mechanisms, which produce dunes, beaches, and
moraines, respectively. Indeed, these mechanisms are known to operate today to
locally concentrate cosmic dust by up to 1000-fold relative to the global
baseline; on the basis of which, cosmic dust has been proposed to be relevant
to the origin of life [20, 21, 22, 23, 24, 25]. Despite these possible links,
there are no existing quantitative models of the supply to and surface cycling
of cosmic dust on early Earth.

Here, we use astrophysical simulations and geological models to quantify both
the flux and compositions of cosmic dust accreted to the surface of early
Earth (Fig. 1a). We combine these results with geological models of subaerial
concentration in a range of environments (Fig. 1b-c). Using our results, we
assess the possible utility of cosmic dust deposits on early Earth for
fertilising prebiotic chemistry.

##  2 Results

Estimating early dust accretion fluxes

We simulate cosmic dust accretion to Earth during the first 500 million years
after the Moon-forming impact at 4.51 Ga [26]. Numerical models (see Methods)
were used to simulate the generation, interplanetary transport, and
terrestrial accretion flux of dust produced by two compositionally distinct
parent body populations: Jupiter-family comets (JFCs) and asteroids (Fig. 1).
Asteroidal dust is considered as the sum of dust generated by Main Belt
asteroids and unstable planetesimals located in planet-forming regions (see
Methods).

Comparing the results of our numerical model to estimates of present day
cosmic dust accretion flux to Earth, we find that total early cosmic dust
accretion fluxes would have been on the order of 100-to-10,000-fold higher
than observed today, depending on the value chosen to represent the modern
flux (Fig. 2–3) [27]. These elevated dust fluxes arise mainly from (i) a more
massive main asteroid belt leading to higher rates of collisional grinding
[28], (ii) dynamical perturbation of the asteroid belt and injection of
cometary objects by giant planet migration [9], and (iii) the collisional
erosion of the population of rocky objects left over from planet formation,
which had yet to be depleted.

Our simulations suggest that early cosmic dust fluxes would have been
dominated by fragments of the dynamically unstable asteroid population and
comets, with a relatively minor contribution by the Main Belt (Supplementary
Fig. 3). Short-lived spikes in the proportion of cometary material in the
cosmic dust accretion flux occur as a result of the scattering of large or
long-lived comets, with these spikes lasting for on the order of one to
several Myr. The timing of these cometary dust spikes has no special
sigificance in the models, simply reflecting a particular realisation of a
semi-random history. Critically, this means that intervals of high-flux comet-
dominated dust supply could have occurred at any point during the first 500
Myr of Earth history.

Grain size frequency distributions for the mean mass accretion flux of all
three cosmic dust sources are bimodal between 1 and 3000 $\mathrm{\mu m}$,
peaking at around 1–10 and 100–500 $\mathrm{\mu m}$ (Supplementary Fig. 1).
These distributions are ultimately very similar to those arriving at Earth’s
atmosphere and observed in cosmic dust deposits today [29, 13, 10], with a
somewhat larger contribution by particles larger than 500 $\mathrm{\mu m}$.
Overall, our model predicts an early cosmic dust flux that differs mainly in
having a higher total mass per unit time and distinct compositional make-up
compared with that observed today. However, like today [30], and with great
relevance for prebiotic chemistry, volatile-rich dust grains – including
$>\;$65$\%$ cometary material at some points – are expected to have dominated
the cosmic dust flux to early Earth (Fig. 2b).

Occurrence and composition of cosmic dust deposits

The final concentration of cosmic dust in a sedimentary deposit will depend on
dust input rate, endogenous sediment supply, and local dust concentration
mechanisms. Using our estimates of dust accretion fluxes to prebiotic Earth,
we construct a model to predict the proportion of dust within coeval
unconsolidated sediments (see Methods; Fig. 1c). We consider a range of end-
member sedimentary environments: glacier surfaces, hot deserts, and deep-sea
sediments. The proportion of cosmic dust by mass, the relative proportions of
types of cosmic dust, and their chemical compositions and degrees of
alteration have been measured for all of these environments on Earth today,
allowing us to ground truth our calculations (Supplementary Table 1). We use
the resulting empirically-derived scaling factors to estimate both the total
cosmic dust concentration by mass and relative abundance of cosmic dust-types
within sediments on early Earth as a function of early dust flux relative to
modern (Fig. 3).

Many aspects of early Earth remain uncertain. To obtain meaningful results, we
assume that all early Earth environmental parameters are equivalent to present
day except the rate of cosmic dust accretion. This minimises sources of
uncertainty that would otherwise be difficult or impossible to constrain,
i.e., allowing us to test the prebiotic relevance of dust supply in one well
constrained early Earth scenario.

We further assume that the concentration mechanisms operating in these
environments will operate with the same efficiency at all accreted mass fluxes
of dust considered in our work, i.e., sedimentary environments are far from
being dust saturated. We focus on environments where high cosmic dust
concentrations are achieved without a high degree of fractionation with
respect to different categories of dust. This allows us to assume that
differences in the compositional make-up of the accreted cosmic dust
translates directly into the resulting estimated compositions of putative
early Earth cosmic dust deposits [31, 13]. Furthermore, although the presence
of vegetation in modern-day environments strongly affects sedimentation
mechanisms and early Earth would have lacked such interferences, the modelled
environments in our study are essentially absent of any vegetation, such that
our all-else-being-equal approach is applicable.

To interpret our results, we must normalise our values for early Earth cosmic
dust accretion flux to a reference value for the modern top-of-atmosphere dust
accretion flux. We compare to a range of conservative values for the top of-
modern-atmosphere dust accretion flux: a high value of 100 t/d and a low value
of 10t/d [27]. Given that our model for predicting the proportion of cosmic
dust in early sediments is pegged to present day systems, using lower values
to represent the modern dust flux renders our predicted early dust flux
relatively higher and hence predicts higher cosmic dust proportions in early
sedimentary systems (Fig. 3).

We find that cosmic dust represents a minor component of deep ocean sediments
even at the highest dust accretion rates estimated by our model (Fig. 3).
Meanwhile, cosmic dust may have represented $>$ 50 % of sediments in desert
and glacial settings given the same cosmic dust fluxes. The highest
concentrations ($>$ 80 %) would have occurred within glacial ablation zones in
cryoconite-type sediments (Fig. 3), just as these sediments contain the
highest reported cosmic dust concentrations today [20]. Cryoconite forms on
Earth today in small (metre-to-centimetre) melt-water pools on the surface of
retreating ice-sheets, with dust components non-destructively introduced by
wind-driven transport [32]. Compositionally, cosmic-dust-rich analogues of
these sedimentary environments would represent a unique and compelling
environment for fostering prebiotic chemistry.

We can gain an insight into this plausible prebiotic utility by exploring the
likely chemical compositions of putative cosmic sediments. This is achieved by
combing estimates of the contributions of cometary versus asteroidal dust with
estimates of their respective average C, N, P, and S concentrations
(Supplementary Table 1). Whilst other arid environments are plausible settings
for concentrated deposits of cosmic dust, e.g., hot deserts (Fig. 3), we focus
here on glaciogenic cosmic sediments – the environment we expect to be richest
in cosmic dust for any given dust accretion flux (Fig. 3–4). Moreover, glacial
environments are unusual in being generally arid yet always having the
capacity to generate liquid water, unlike hot arid environments. Our results
show that continuous accretion of cosmic dust and concentration in glaciogenic
settings could have generated sediments enrichmented in bioessential elements
relative to average Upper Continental Crust [33] by up to 100-fold.

These enrichments peak for S, N, and C during episodes of enhanced cometary
delivery. The highest amplitude comet-delivery spikes that our model predicts
result in around 2-fold higher concentrations of N and C in the cyroconite
sediments than achieved during background cosmic dust accretion. The highest
possible enrichments may be obtained in the timeframe immediately following
the collisional breakup of parent body objects. These episodes of enhanced
delivery (million-year timescales) may outpace background cosmic dust fluxes
by around 1 order of magnitude [34] (Fig. 3–4), yielding equivalently enriched
sediment compositions. Given the rarity of parent body break up events over
the last 4 billion years, ground truth constraints on the impact of post-
break-up dust fluxes on concomitant proportions by mass of cosmic dust in
terrestrial sediments are hard to establish. However, our estimate of peak
fluxes of around 10,000x modern, lasting on the order of millions of years, is
supported by observations of cosmic dust, micrometeorite, and fossil meteorite
abundance in Ordovician sediments [35, 34], which record the aftermath of the
L chondrite parent body disruption event at 474 $\pm$ 22 Ma [36].

Our results highlight that cosmic dust-rich deposits would have formed most
readily in environments of low endogenous sediment production on early Earth
over much of its early history, with exceptionally high cosmic dust
concentrations developing in the aftermath of individual parent body break-up
events. In particular, we find that cosmic dust proportions would have been
high in glacial settings – specifically, cryoconite fields within glacial
ablation zones (Fig. 3–4). Here, cosmic sediments ($>$ 50 % cosmic dust by
mass fraction) would have formed, enriched with respect to average crustal
rocks both in terms of the fraction of bioessential elements in reduced form
and the overall concentration of those elements. This outcome is robust, given
that early sources of cometary material were chemically comparable to the
comets sampled by recent missions [37] and unmelted carbonaceous
micrometeorites [38, 13] (Supplementary Table 1).

##  3 Discussion

In principle, cosmic dust rich cryoconite is a compelling scenario for
prebiotic chemistry (Fig. 5). However, there are also caveats that should be
highlighted. A possible challenge for the prebiotic relevance of our scenario
is that many ice sheet surfaces undergoing melting are semi-permeable and
connected to a wider supraglacial drainage system [39] (Fig. 5). Cryoconite
most often forms in the ablation zone of glaciers, where ice dynamics or the
continual development of the supraglacial drainage system typically preclude
permanent or even multi-annual cryoconite holes. As such, prebiotically
interesting species leached from dust-rich deposits in cryoconite holes may
drain along with melt water to the level of the water table (Fig. 5a) – and be
diluted in the process [39].

In contrast, the dry valleys of Antarctica shelter cryoconite holes which form
with an ice surface lid and cold surrounding ice limiting lateral water
transport. These result from the particular and unique conditions of the dry
valleys: extreme aridity and cold, with surface melting possible for only
brief periods in summer. Solar radiation heats low-albedo inclusions within
the ice which melt the ice around them in a local greenhouse effect, despite
the icy lid [32] (Fig. 5b). Here, biogeochemical recycling results in the
waters of cryoconite holes becoming 100-fold enriched in bioavailable forms of
limiting nutrients relative to surrounding ecosystems [32]. Abundant life
occurs in such systems mostly supported by leached nutrients from the
sedimentary dust deposits at the base of the cryoconite holes [40]. In a
prebiotic Earth scenario, we may therefore expect similar cosmic-sediment-
filled environments to form on the surface of impermeable ice lids,
abiotically-enriched in prebiotic feedstock.

Nonetheless, even Dry Valleys type cryoconite deposits are subject to
transport through ice dynamics of up to 20 m/yr [41], precluding long-term
formations. However, the regular destabilisation of cryoconite sediments
directly supplies meltwater and sedimentary material to endorheic proglacial
lakes (Fig. 5c). Indeed, ecosystems in these closed proglacial lakes are known
to depend on fertilisation by cryoconite-derived nutrients [42, 32]. Glacier
margins therefore provide settings capable of both locally concentrating
cosmic dust and initiating closed system aqueous prebiotic chemistry with the
products of cosmic dust dissolution/leaching.

Both cosmic-dust-rich cryoconite sediments and endorheic proglacial lakes
would appear to have many attractive properties for both initiating and
sustaining prebiotic chemistry. These environments would represent networks of
icy prebiotic chemical ‘reactors’, replete with the known advantages of ice-
hosted prebiotic chemistry: freeze-thaw wet-dry cycles (annual–daily) [43],
low water-rock ratios, potential for UV irradiation as well as UV shielding
[44, 3], and the ability to exchange over weekly-to-yearly timescales with
other cosmic-dust-filled reactors [20] – analogous to the stream intersection
models envisaged by Sutherland [45] and Rimmer [46].

The geochemistry of cosmic-dust-rich sediments provides unique advantages over
and above glacial settings hosting sediments of solely terrestrial geochemical
character. In particular, identifying soluble early Earth sources of P and S
is a long running challenge [47, 48]. Prebiotic chemistry directly initiating
after exposure of cosmic dust deposits to liquid water in e.g., cryoconite
holes or proglacial lakes would have had access to reactive P- and S-rich
materials of a very fine grain size, namely:

  * •

P (up to 1500 ppm) – schreibersite ($\mathrm{Fe_{3}P}$), apatite
($\mathrm{Ca_{5}PO_{4}[OH,Cl,F]}$), merrillite
($\mathrm{Ca_{9}NaMg(PO_{4})_{7}}$) [49];

  * •

S (up to 5 wt%) – troilite (FeS), pyrrhotite ($\mathrm{Fe_{1-x}S}$),
pentlandite $\mathrm{(Fe,Ni)_{9}S_{8}}$, pyrite $\mathrm{(FeS_{2})}$,
chalcopyrite $\mathrm{(Cu,Fe)S_{2}}$, sulfonic acids, [50, 51].

These materials are analogous to the powders used to accelerate dissolution of
chemical reagents in a laboratory setting – often with a grain size of tens to
hundreds of microns, similar to the size distribution of cosmic dust particles
[31, 13]. Such fine particles sizes aid with dissolution and hence with
sustaining high throughput of key species for prebiotic chemistry. Indeed,
glacial meltwater discharge zones are known today to yield among the highest
known fluvial fluxes of reactive and particulate phosphate on Earth [52].

Some non-trivial fraction of the P content of early cryoconite sediments would
have been speciated as phosphide (perhaps around 50%) [49]. The action of
ultra-violet light combined with dissolved $\mathrm{H_{2}S\;and\;HS^{-}}$
species has been shown to be capable of oxidising species released during
phosphide corrosion in water, forming phosphate [53] – a key constituent in
and catalyst for prebiotic chemistry [54]. Sulfide and its derivative oxidised
species (e.g., bisulfite) have further been shown to assist the prebiotic
syntheses of nucleic acids [3] and many components of central carbon
metabolism [55]. Given the apparent scarcity of high throughput sources of
fine grained sulfide, phosphate, and phosphide on Earth [47, 48], we suggest
that cosmic dust sedimentation in glacial systems provides a highly relevant
geological feedstock for prebiotic chemistry.

Our results show that Antarctic-like ice sheets on prebiotic Earth would have
plausibly given rise to aerially extensive regions of cryoconite-hosted cosmic
dust-rich deposits and derivative proglacial lakes, with many attractive
properties for prebiotic chemistry. Our results therefore highlight a
particular environmental context for dust-fed scenarios for prebiotic
chemistry, linking the relevance of the scenario to the climate of early
Earth. This provides a helpful line of reasoning by which our scenario can be
falsified on planetary climatic grounds alone. At present, it is unclear
whether or not the glacial environments needed to forge concentrated cosmic
dust deposits would have been common on early Earth. Glaciers are known to
have formed up to 2.5 billion years ago on Earth [56]. Recent models also
suggest a cold early Earth [57], coincident with the timeframe explored in our
study and which could support our scenario.

With regard to C and N, we suggest that cosmic dust may also have been a
stockpiling agent for prebiotic chemistry, rather than a direct participant.
Alongside the arrival of single large impactors [58], cosmic dust sedimentary
cycling may be a plausible mechanism by which to involve C- and N-rich
cometary matter in prebiotic chemistry. Whilst the soluble component of cosmic
dust will be liberated rapidly during interaction with liquid water, much of
the C and N content of cosmic dust arrives in the form of mostly insoluble and
inert species. These include N-bearing kerogen (largely poly-HCN),
N-heterocycles, amino acids, amines, amides, purines, polar species,
aromatics, hydroxy, dicarboxylic, and carboxylic acids [59].

Instead of suggesting irrelevance to prebiotic chemistry, the inert character
of many of these species strongly implies their capacity to accumulate over
time. In settings with low rates of terrestrial sediment deposition – glacier
surfaces, for example – cosmic dust could have built up sedimentary blankets
with around 0.2 wt% N and 5 wt% C (Fig. 4c). Transport fractionation of
organics relative to silicate phases could have generated still greater C- and
N-enrichment. A pure nitrogenous kerogen sedimentary end-member would have
around 3 wt% N and 70 wt% C [60]. Indeed, extreme organic C enrichments are
observed in cryoconite sediments with increasing distance inland across the
Greenland ice sheet albation zone – at least in part due to transport
fractionation of organic materials [61]. A key caveat is that such sediment
compositions are only possible assuming that atmospheric entry of dust through
a reducing anoxic atmosphere promotes minimal loss of N, in contrast to the
substantial (90–99%) loss observed during entry through Earth’s present day
oxidising atmosphere (Fig. 4c) [62].

Stockpiling mechanisms are commonly invoked in proposed scenarios for
cyanosulfidic prebiotic chemistry [45]. The thermal processing e.g., meteorite
impacts [45] or melting into magma chambers [63] of inert CN-rich and
relatively H-poor reducing sediments could have supplied prebiotically
relevant concentrations of HCN to overlying aqueous environments [64]. Such a
mechanism of continuous HCN supply could be made possible by an intermediate
stage of sedimentary sorting and stockpiling of dust-derived inert CN-bearing
organics. Via a cosmic dust sedimentation and heating pathway – closely
analogous to volcanic remobilisation of sedimentary organic C on Earth today
[64] – the requisite starting ingredients for cyanosulfidic prebiotic
chemistry could plausibly have been delivered, concentrated, and liberated to
clement environments for the origin of life.

We have discussed different geological mechanisms to separately supply P + S
and C + N from cosmic dust to prebiotic chemistry. However, whilst these
mechanisms operate across different spatial scales and timescales, they are
not mutually exclusive. Thermally processed deposits of exogenous organic
matter may have degassed HCN into lake systems fed by glacial meltwater rich
in P and S sourced from locally dissolving cosmic dust. Taken together with
recent findings from geology, astronomy, and prebiotic chemistry, our results
provide support for the fertilisation of prebiotic chemistry by cosmic dust on
early Earth. Furthermore, cosmic dust is potentially a widespread and flexible
planetary fertiliser, being accreted in quantities that may be assessed by
observation [65, 9] to potentially habitable exoplanets.

##  4 Methods

###  4.1 Cosmic dust deposit model parameters

Cosmic dust grains in pristine modern sedimentary systems appear to derive
mainly from undifferentiated carbonaceous-chondrite- and/or cometary precursor
bodies [66, 67]. Cosmic dust that appear to originate from differentiated
asteroids represent less than 5 percent by mass of all cosmic dust in most
deposits [68]. The compositional disparity between modern cosmic dust
accretion fluxes and predicted early fluxes must be considered in interpreting
the significance of our results for supplying bioessential elements to early
Earth’s surface. Bridging this gap requires us to make assumptions both about
the parent bodies of cosmic dust falling to Earth today and how those
precursor objects are represented in our simulations.

We assume that all cometary material is well represented by the compositions
of unmelted micrometeorites and apparently cogenetic carbonaceous chondrite
meteorites [68]. Dust sourced from asteroids is conservatively assumed to
sample differentiated precursor bodies. Cosmic dust grains sourced from
differentiated material is considered to represent an equal mixture of crust-
and core- material, and to be well represented by the compositions of
silicate- and iron-type grains arriving on Earth, today [69]. These
assumptions inform the values in Supplementary Table 1.

Particle diameter exerts a strong control on the survival of cosmic dust
during atmospheric entry (Supplementary Fig. 1). The majority of particles
with sizes $\mathrm{<\;0.1\;mm}$ survive to the Earth’s surface with minimal
heating [29] and empirical studies demonstrate they retain a significant
proportion of their temperature-sensitive organic matter [15]. We estimate the
proportion of early accreted material that survives unaltered versus that
which melts and that which vaporises using the results of Love and Brownlee
[29] (Supplementary Fig. 1). Again, we take an all-else-being-equal approach
to justify this approach, where the atmosphere of early Earth is considered to
be of similar mass to today.

Our findings are robust to uncertainties regarding the assumed composition of
the terrestrial sedimentary component. Whilst we plot all results relative to
and assuming a modern day average Upper Continental Crust for terrestrial
sediment within the modelled early dust deposits, different choices would
result in higher reduced fractions and/or nutrient enrichment factors. This is
because estimated early crustal compositions that differ from modern average
Upper Continental Crust are instead more similar to Earth’s mantle [33] –
thereby containing lower concentrations of P, S, C, and N, and resulting in
their stronger relative enrichment in early cosmic dust-rich sedimentary
deposits. We have not modelled the leaching of bioessential elements from dust
during sedimentary transport. This assumption is valid for the arid conditions
and aeolian transport mechanisms operating in the desert and glacial settings
that favour cosmic dust deposit formation.

Whilst stochastic and relatively short-lived on geological timescales (several
Myr), intervals of comet-dominated dust supply occur with high probability in
any given simulation run. These intervals are also sufficiently long-lived to
allow complete cycling of cosmic dust through all of the surface environments
that we consider [23, 13]. Therefore, whilst background dust supply provides
notable enrichments, our results highlight that stochastic large cometary
breakup events are crucial for producing dust-rich sediments with the highest
concentrations of bioessential elements.

###  4.2 Estimating cosmic dust abundance within early sediments

We take an all-else-being-equal approach to assess the potential for cosmic
sediment formation on early Earth. Critically, we assume that the deposition
flux of dust in a given environment directly scales with the flux accreted to
Earth, i.e., that processes acting to concentrate dust operate with equal
efficiency at higher dust accretion rates. This assumption is defensible
because maximum sediment loading is expected to be extremely low in the low
sedimentation environments that we consider, even given much higher early
cosmic dust accretion fluxes.

Given these assumptions, we can set up a linear relationship between the
cosmic dust accretion flux to early Earth relative to the at-atmosphere flux
estimated today ($\epsilon_{x}$) and the ratio of cosmic dust mass per unit
mass of sediment in a given sedimentary system ($\delta$, $\mathrm{kg/kg}$).
As cosmic dust fluxes increase, total sediment within the system of interest
will increase. To track this, we must include as a constant the original mass
of terrestrial sediment mass per unit mass of sediment $(1-\delta)$ in the
sedimentary system. The fraction of cosmic dust in the putative early
sedimentary system ($f_{dust}$) is then given by

$f_{dust}=\frac{\delta_{modern}\;\epsilon_{x}}{\delta_{modern}\;\epsilon_{x}+(1-\delta_{modern})}.$
(1)

The principal parent body sources are considered to be asteroids and comets,

$f_{dust}=\frac{\sum_{x=cometary,asteroidal}F_{x}\;\delta_{modern}\;\epsilon_{x}}{\sum_{x=cometary,asteroidal}F_{x}\;\delta_{modern}\;\epsilon_{x}+(1-\delta_{modern})}.$
(2)

We can calculate the concentration of a given element in the early sedimentary
deposit ($\gamma$) as as mixture of the chemical compositions ($\beta$)
(Supplementary Table 1) [89, 88, 90, 38, 62, 15, 33, 87, 25, 13] of endogenous
sediment (E) and cosmic dust as follows,

$\gamma=\frac{\sum_{x=cometary,asteroidal}F_{x}\;\delta_{modern}\;\epsilon_{x}\;\beta_{x}+(1-\delta_{modern})\;\beta_{E}}{\sum_{x=cometary,asteroidal}F_{x}\;\delta_{modern}\;\epsilon_{x}\
+(1-\delta_{modern})}.$ (3)

The proportion of the early dust sedimentation flux made up by each cosmic
dust class will have also been partially determined by the effects of
atmospheric entry. Volatiles may also be preferentially lost during
atmospheric entry heating of dust grains [38, 14, 15]. We use empirical
observations of the volatile chemistry of cosmic dust particles to inform our
calculations, which show that S, C, and P are largely conserved during entry,
even if they may be to some extent chemically reorganised [70]. In contrast, a
large fraction of nitrogen is lost from cosmic dust particles during
atmospheric entry, largely due to degradation by oxidation [62]. Entry into an
anoxic and possibly reducing early atmosphere, relevant for early Earth, may
have been far less efficient for destabilising and removing nitrogen from dust
grains – an end-member scenario for which we consider here.

Since cosmic dust vaporisation during atmospheric entry is heavily dependent
on particle size [29], we examined whether the size frequency distribution of
early dust accretion fluxes predicted by our model differs to that observed
today. We use the results of Love and Brownlee [29] to estimate the proportion
of all cosmic dust that is vaporized versus melted/survived unaltered during
atmospheric entry today. In order to facilitate like-for-like comparison
between our results and those of Love and Brownlee [29], we generate
continuous distributions of accreted mass as a function of grain size from
histograms of mean mass accreted per grain size bin. We interpolate between
the centre point of each bin. These continuous distributions are then used to
predict the fraction of early cosmic dust grains that vaporize ($f_{v}$)
during entry for each source population (Supplementary Fig. 1).

Overall, the size distributions of material arriving at the top of the
atmosphere and arriving at the surface after entry are essentially similar to
those observed today [13]. However, the exact abalation behaviour may differ
for each population based on mineralogical and entry velocity differences [16,
10]. To largely eliminate this uncertainty, we proceed with our approach of
anchoring to empirical observations. We compare the flux estimate of cometary
versus asteroidal dust arrivin at Earth’s surface to top of atmosphere flux
estimates to obtain an empirical value for ($f_{v}$). Similarly, we use
empirical observations of unmelted to melted dust particles to estimate the
fraction that experiences melting during entry ($f_{m}$), and compositional
analyses to estimate the fraction of volatiles lost during entry from both
unmelted and melted particles ($f_{loss}$). This approach then yields,

$\gamma=\frac{\sum_{x=cometary,asteroidal}\;(1-f_{v})\;(\theta_{x}\;\beta_{x}\;f_{m}\;f_{loss}+\;\theta_{x}\;\beta_{x}\;(1-f_{m}))\;+\;(1-\delta_{modern})\;\beta_{E}}{\sum_{x=cometary,asteroidal}\;(1-f_{v})\;(\theta_{x}\;\beta_{x}\;f_{m}\;f_{loss}+\;\theta_{x}\;\beta_{x}\;(1-f_{m}))+(1-\delta_{modern})},$
(4)

where $\theta_{x}$ is equivalent to $F_{x}\;\delta_{modern}\;\epsilon_{x}$.

Uncertainty on the measured masses of cosmic dust per kg of sediment is
obtained from literature reports. These literature reports were conducted at
different times, in different places, and using different methods to both
obtain sediment and to filter cosmic dust from the material. Ultimately,
uncertainty on the proportion of cosmic dust in the sediment is trivial
compared to that introduced by assumptions made during the construction of the
dust flux model. For example, rounding up reported 2$\;\sigma$ uncertainty on
cosmic sediment fraction to the nearest interval, uncertainties of around 10
$\%$ characterise the majority of measurements. Details of the values of all
parameters used in our model for cosmic sediment composition can be found in
Supplementary Table 1.

###  4.3 Numerical model of collisional dust generation and transport to Earth

We simulated the distributions of dust produced by two compositionally
distinct parent body populations: Jupiter-family comets (JFCs) and asteroids.
Asteroids were treated as the sum of two dynamically distinct populations:
relatively stable Main Belt objects and rapidly depleted unstable
planetesimals leftover from planet formation. For each population, the overlap
of the dust grain orbits with Earth was used to calculate the resulting fluxes
of cosmic dust accreted onto Earth.

Intrinsic to this model are assumptions about the history of the Solar System
and its formation. For the start time of our models, we use the Moon-forming
impact. Models in the literature suggest that this occurred early, $\sim
50-100$ Myr after the formation of CAIs [71, 72, 73]. We assume the Moon-
forming impact occurred at 50 Myr, which is time zero of our simulations. We
also assume that the giant planet instability occurred early [74, 75].
Simulations were run for 500 Myr for each source population.

We modelled the distributions of dust produced by each source population
separately using a kinetic model [76] which follows the evolution of a
population of particles in terms of their orbital elements and sizes. The
numbers of particles in bins of particle size, pericentre, and eccentricity
evolve due to several forces. Destructive collisions between particles remove
particles that collide and produce smaller fragments; P-R drag causes
particles to lose angular momentum and drift towards the Sun; and radiation
pressure acts radially outwards on small particles.

Comets

The dust produced by JFCs was simulated using the model of [77], which was
originally created to model the production of the present zodiacal cloud via
spontaneous fragmentation of comets. We updated the model to allow comets to
be scattered in at a variable rate. In the early Solar system, comets should
be scattered inwards at a much higher rate than today. The rate of comet
scattering was extrapolated from N-body simulations which followed the
distribution of JFCs throughout the 4.5 Gyr history of the Solar system [78].
The input rate of comets was found to be tens to hundreds of times higher in
the first 500 Myr of the Solar system than the present rate, declining with
time (Supplementary Fig. 2). This cometary model gives the distribution of
dust produced by comets with time, which was then input into the kinetic model
to find how the dust evolves after it is released from the comets.

Asteroids

For the asteroid belt, the kinetic model was initialised with bodies with the
size distribution [79] of the current belt, going from diameters of 1 to 1000
km. The initial orbits of asteroids were assumed to be those of the present
main belt (JPL Small-Body Database
(https://ssd.jpl.nasa.gov/tools/sbdb_query.html). The initial mass of the
asteroid belt and its subsequent evolution is poorly constrained. While
collisional evolution of asteroids will slowly deplete the overall mass of the
belt, it is likely that the dynamical evolution of planets dominated depletion
of the asteroids (e.g. [80]). Based on [81], we assume that following the
giant planet instability, the asteroid belt had a mass four times higher than
its present mass ($\sim 5\times 10^{-4}~{}\mathrm{M}_{\oplus}$ [82, 83]), and
lost half of its mass over the subsequent 100 Myr by depletion of unstable
resonances. We therefore initialised the model with a mass of $2\times
10^{-3}~{}\mathrm{M}_{\oplus}$ of asteroids. The asteroids then evolve in the
kinetic model by collisional evolution, producing dust, which further evolves
due to collisions and radiation forces.

Rapidly depleted asteroids

Similarly, the collisional evolution of asteroids leftover from terrestrial
planet formation was traced with the kinetic model. The size distribution was
assumed to be the same as the current asteroid belt [79]. The orbits of these
asteroids are taken from N-body simulations [84] which were run to find the
bombardment history of early Earth from rapidly depleted objects. The total
initial mass of rapidly depleted asteroids was chosen using an iterative
process in order to match the observation that 0.005 $M_{\oplus}$ [85] of
highly siderophile elements (HSEs) should have been accreted to Earth during
the Late Veneer from rapidly depleted asteroids. The number of rapidly
depleted asteroids present in the inner Solar system decreases roughly
exponentially with time due to a combination of ejection from the system by
Jupiter, accretion onto Earth, and collisional evolution. The N-body
simulations give the dynamical depletion of bodies with time, while our
kinetic model gives the collisional depletion. By calculating the mass of
asteroids accreted onto Earth when taking into account both the dynamical and
collisional depletion, we found that an initial mass of
$0.065~{}\mathrm{M}_{\oplus}$ of asteroids leftover after terrestrial planet
formation led to $0.005~{}\mathrm{M}_{\oplus}$ of asteroids being accreted by
Earth. We initialised this mass of asteroids in the kinetic model on the
orbits from the N-body simulations. The model then accounted for the
collisional depletion of asteroids, which produced smaller bodies and thus
dust, and the dynamical depletion of asteroids, which removed bodies from the
simulation according to the evolution found by the N-body results. The model
therefore gave the distribution of dust produced by the collisional evolution
of rapidly depleted asteroids leftover from planet formation.

Having found the distribution of dust in the inner Solar system with time
using the kinetic model, we then found the accretion rates of dust from each
source population onto the early Earth as a function of time. The rate of each
orbit overlapping with the Earth was found with the method of [86], which was
multiplied by the population of dust on each orbit to give the cosmic dust
flux to Earth with time from each source.

  * Data availability

All relevant data needed to evaluate the findings of the manuscript are
included in the figures or in supplementary electronic materials.

  * Code availability

Details of specific codes used to perform simulations are available upon
request.

  * Acknowledgments

C.R.W. acknowledges NERC and UKRI for support through a NERC DTP studentship,
grant number NE/L002507/1; financial support from the Cambridge Leverhulme
center for Life in the Universe; funding support from Trinity College
(Cambridge) in the form of a Junior Research Fellowship; funding support from
ETH Zürich and the NOMIS formation in the form of a research fellowship. Dr
Dougal Ritson is thanked for their comments on an early version of the
manuscript.

  * Contributions

C.R.W. conceived of the project, performed meta-data curation and analysis,
and geological modelling. J.K.R. wrote the numerical model and performed all
astrophysical simulations. O.S. and M.W. supervised the project. All authors
contributed to the writing and editing of the manuscript text and figures.

  * Competing Interests

The authors declare no competing interests.

Figure 1: Delivery dynamics, atmospheric entry, and terrestrial sedimentation
of cosmic dust. A schematic illustration of factors considered in this study
related to the formation of terrestrial sediments rich in cosmic dust. a)
Dynamical sources of cosmic dust grains. Comets (undifferentiated) scattered
inward from the Outer Solar System disintegrate to produce dust particles.
Asteroids predominantly generate dust through collisions. b) Atmospheric entry
of cosmic dust involves partial melting ($f_{m}$) and partial vaporisation
($f_{v}$), both of which influence the final mass of cosmic dust per unit mass
of total sediment in a given sedimentary environment ($f_{dust}$,
$\mathrm{kg/kg}$). c) The relative abundance of cosmic dust within terrestrial
sediments is set by the local sedimentation rates of cosmic dust versus
terrestrial (endogeneous) sediment, with dust proportion therefore being
maximised in areas of low endogeneous sediment production and the action of
local sedimentary concentration mechanisms.

Figure 2: Interplanetary dust particle accretion flux to early Earth. a) Total
flux and individual fluxes of different cosmic dust populations - divided on
the basis of parent body type. b) Proportions of the total cosmic dust
accretion flux represented by each population over time. Boundaries between
the proportion of each dust source are demarcated with solid black lines.

Figure 3: Predicted proportion by mass of cosmic dust within sediments, which
varies with the ratio of early to modern accreted dust flux. A conservatively
high reference value for modern dust accretion is shown in (a). An
optimistically low reference value is shown in (b). The predicted proportion
of dust within terrestrial sediments varies as a function of local
environmental processes/conditions that preferentially concentrate dust
relative to terrestrial sediment [31, 87, 25]. Dust can be expected to
represent a higher concentration of overall sediment in environments with low
local endogenous sediment generation rates and where dust concentration
mechanisms are active, e.g., sediment traps on glaciers, versus e.g., deep
ocean sediments, where endogenous sedimentation rates are high and
concentration mechanisms are ineffective (Fig. 1c). Individual data points,
coloured according to their associated simulation time-step, indicate the
average sediment compositions predicted by our simulations. The shaded region
indicates the broad range of possible elevated dust fluxes that may
transiently occur following individual large parent body collisions, which
would translate into extremely cosmic-dust-rich sedimentary compositions in
the context of our model.

Figure 4: a–d) Predicted chemical composition and utility for prebiotic
chemistry of dust-rich sediments on early Earth. Results are plotted for the
absolute concentration of each element relative to the observed average
concentration of emergent Upper Continental Crust on Earth, today [33].
Results plotted are obtained using a modern day dust flux of 10 t/d [27]. In
c), both oxidising and reducing atmosphere scenarios are shown, due to the
strong consequences for N-bearing organic molecule survival during entry under
reducing conditions.

Figure 5: Schematic illustration of cryoconite sedimentary deposit rich in
cosmic dust. a) Open air deposits may exist above the local water table,
whereas dilute deposits lie in it. However, from a prebiotic chemistry
perspective, both will suffer from nutrient leaching into a wider volume of
diffuse water in the variably porous ice sheet. b) This is not the case for
icy-lid cryoconite deposits, which are encased on all sides by weakly porous
ice to cold impermeable ice. c) Regardless of their setting, cryoconite
deposits are inherently unstable and most will be destabilised and drained
within multi-annual timescales. Drained meltwater and cryoconite sediments
will be transported in part to proglacial endorheic lakes, where longer term
stockpiling of dust-derived species may occur.

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Supplementary Figure 1: Grain size distribution for the mean accretion flux of
cosmic dust per type, before and after atmospheric entry. Simulations predict
the mean mass accreted for a given size bin, plotted as a histogram, and
normalised in the case of each dust source to the maximum accretion flux among
all bins. Smoothed distributions plot an interpolation between the centre-
point of each bin. The bimodal distribution predicted by our numerical model
for a) main belt asteroid, b) comet, and c) rapidly depleted asteroid sourced
dust arriving at Earth’s atmosphere undergoes a process of ablation that
destroys larger grains with progressively greater efficiency. Results are
unitless, being normalised to the highest accretion flux as a function of a
grain size for each class of dust.

Parameter | Symbol | Value (units) | Reference
---|---|---|---
Nitrogen in cometary dust | $--$ | 2500 (ppm) | [38]
Carbon in cometary dust | $--$ | 50,000 (ppm) | [38]
Sulfur in cometary dust | $--$ | 90,400 (ppm) | [88]
Phosphorus in cometary dust | $--$ | 1000 (ppm) | [89]
Nitrogen in asteroidal dust | $--$ | 1500 (ppm) | [89]
Carbon in asteroidal dust | $--$ | 30,000 (ppm) | [89]
Sulfur in asteroidal dust | $--$ | 60,000 (ppm) | [89]
Phosphorus in asteroidal dust | $--$ | 1000 (ppm) | [49]
Nitrogen in upper continental crust | $--$ | 83 (ppm) | [33]
Carbon in upper continental crust | $--$ | 500 (ppm) | [90]
Sulfur in upper continental crust | $--$ | 600 (ppm) | [33]
Phosphorus in upper continental crust | $--$ | 600 (ppm) | [33]
Cosmic dust fraction in glacial trap | $\delta_{modern}$ | $1.52E-03$ | [13]
Cosmic dust fraction in deep sea sediments | $\delta_{modern}$ | $7.00E-07$ | [87]
Cosmic dust fraction in arid aeolian sediments | $\delta_{modern}$ | $8.00E-04$ | [25]
Melted dust fraction in glacial trap | $f_{m}$ | $0.57$ | [13]
Vaporised dust fraction | $f_{v}$ | $0.9$ | [13]
Volatile loss fraction (N), unmelted | $f_{loss}$ | $0.9$ | [15, 62]
Volatile loss fraction (N), melted | $f_{loss}$ | $0.99$ | [15, 62]

Supplementary Table 1: Parameters used in estimating cosmic dust deposit
compositions. All compositional values for meteoritic components are model
values, i.e., chosen to be representative of a group, rather than fully
quantitative average compositions. Such an assessment would require compiling
lines of evidence from different techniques, classes of meteoritic material,
and forms of samples. Determining unbiased average compositions is an ongoing
challenge in cosmochemistry and is beyond the scope of the present study.
Noting this, we have chosen indicative and conservative values for parameters,
on the basis of published literature.

Supplementary Figure 2: The rate at which comets are input into the inner
Solar system throughout the simulations. Data is plotted relative to the rate
at which JFCs are scattered inward in the present Solar system. Results from
our simulations are plotted for the first 500 Myr of Solar System history.

Supplementary Figure 3: Main belt fraction of asteroidal dust accreted to
early Earth. Results from our simulations are plotted for the first 500 Myr of
Solar System history.