Figure 5 A

EC OCM SO4 Si NO3 Na

Complete case Posterior estimate 1.28692933 -0.46007670 -1.04279285 1.44459409 1.22761531 0.23238397

Posterior interval Lower bound 0.3402020 -1.4450386 -1.9836220 0.5969304 0.3803867 -0.5593048

Posterior interval Upper bound 2.2460586 0.5503927 -0.1159751 2.3539157 2.1031885 1.0229177

All case Posterior estimate 0.63484363 -0.03966882 -1.46058708 0.81438963 0.40455322 -0.39578879

Posterior interval Lower bound 0.04055138 -0.71524659 -2.16479587 0.20138336 -0.21626236 -0.99329072

Posterior interval Upper bound 1.2392670 0.6643089 -0.7453204 1.4225731 1.0198128 0.2052672

Figure 5 B

EC OCM SO4 Si NO3 Na

Complete case Posterior estimate 0.003653686 -0.079300809 0.382435986 -0.228295217 -0.131582725 0.583053756

Posterior interval Lower bound -0.320051278 -0.442955537 0.086573908 -0.529145215 -0.402117205 0.310079390

Posterior interval Upper bound 0.346107471 0.283244765 0.681555716 0.068724441 0.142766829 0.864455785

All case Posterior estimate 0.03970781 -0.09463931 0.33239610 -0.33314601 -0.10948036 0.39192535

Posterior interval Lower bound -0.1821599 -0.3430556 0.0966060 -0.5533934 -0.3183361 0.1807518

Posterior interval Upper bound 0.25644027 0.14323883 0.56771231 -0.11984849 0.10325578 0.60804049
Figure S3 Top

EC OCM SO4 Si NO3 Na

Complete case Posterior estimate 1.2512002 -0.5503317 -5.5023940 3.0922887 1.7994882 0.9925164

Posterior interval Lower bound -0.4570725 -3.4168728 -7.7534311 1.0719010 0.5000372 -0.3629058

Posterior interval Upper bound 3.038339 2.389117 -3.196035 5.122473 3.089580 2.381205

All case Posterior estimate 0.7228563 -0.1269402 -1.5950565 1.1736683 1.3760288 0.5403980

Posterior interval Lower bound -0.154639533 -1.129246937 -2.640329875 0.270110302 0.491432515 -0.377120852

Posterior interval Upper bound 1.6410636 0.9008576 -0.5418079 2.0901508 2.2976141 1.4244734

Figure S3 Bottom

EC OCM SO4 Si NO3 Na

Complete case Posterior estimate -0.28396599 -0.57199131 -2.32322967 1.71719173 0.05412797 0.28355702

Posterior interval Lower bound -1.2984086 -2.3477964 -3.7807429 0.4829483 -0.7108196 -0.5345123

Posterior interval Upper bound 0.7854928 1.2334817 -0.8229682 2.9623396 0.8407057 1.1062598

All case Posterior estimate -0.5497356 0.4282163 -0.7677222 0.9428480 -0.1113610 -0.4310982

Posterior interval Lower bound -1.1008655 -0.2165922 -1.4125939 0.3796295 -0.6669681 -0.9826114

Posterior interval Upper bound -0.00365727 1.05456036 -0.09939811 1.51250194 0.45122952 0.13401784
Figure S4 Top

EC OCM SO4 Si NO3 Na

Complete case Posterior estimate -0.4224613 0.1278761 0.2821726 -0.4756639 -0.6905350 0.3890341

Posterior interval Lower bound -1.00578597 -0.49710465 -0.22516565 -0.99521677 -1.14077096 -0.08893162

Posterior interval Upper bound 0.15911346 0.76019491 0.81049267 0.03132724 -0.23307536 0.88319084

All case Posterior estimate 0.007368805 0.030494346 0.260254712 -0.666459061 -0.645651900 0.324205282

Posterior interval Lower bound -0.39784881 -0.42451967 -0.18047252 -1.05833903 -1.02277373 -0.03635381

Posterior interval Upper bound 0.4300448 0.4939300 0.7041889 -0.2687262 -0.2675757 0.7115996

Figure S4 Bottom

EC OCM SO4 Si NO3 Na

Complete case Posterior estimate 0.178687056 -0.171099059 0.466330116 -0.189742856 -0.002907371 0.594344174

Posterior interval Lower bound -0.1971655 -0.5802714 0.1204770 -0.5287679 -0.3190268 0.2817072

Posterior interval Upper bound 0.5684775 0.2299798 0.8053780 0.1462131 0.3081527 0.9112408

All case Posterior estimate 0.068049146 -0.151358191 0.443677750 -0.281520184 -0.004450573 0.346770610

Posterior interval Lower bound -0.1776330 -0.4290548 0.1778341 -0.5229382 -0.2330231 0.1239068

Posterior interval Upper bound 0.31947731 0.13285332 0.70354454 -0.03516217 0.23020872 0.57967133