1
Supporting Information
2
3
Estimates of flux influence subtracted from observations
4
The change in the mole fraction of CO2, integrated over the time frame of interest, was
5
simulated by multiplying surface fluxes, F, by footprints, H:
6
7
DCO2 = H(FNBE + FBB + Ffossil + Focean )+ DCO2 BKG + e
Eqn. S1
8
9
F indicates a net CO2 flux between the atmosphere and surface. Subscripts NBE, BB,
10
fossil, and ocean refer to surface reservoirs exchanging CO2 with the atmosphere: net
11
biome exchange, emissions from biomass burning, emissions from fossil fuel burning,
12
and net ocean-atmosphere flux, respectively. The CO2 mole fraction of air entering the
13
domain, or “background” is CO2 BKG. The error term ε represents uncertainty in ΔCO2.
14
15
The influences of FBB, Ffossil, and Focean were subtracted from the observations before
16
solving for FNBE. Fossil fuel and ocean CO2 fluxes were from Carbon-Tracker 2013 era-
17
interim (CT2013_ei) output (CarbonTracker CT2013B; Peters et al., 2007). Biomass
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burning emissions estimates were from a global inversion for CO with the TM5 global
19
chemistry transport model in a 4Dvar system using satellite observations from the
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Infrared Atmospheric Sounding Interferometer (IASI) and observations from the same
21
flights (Krol et al., 2013; Gatti et al., 2014; van der Laan-Luijkx et al., 2015). We used
22
scenario F1 (van der Laan-Luijkx et al., 2015), which resulted in the best match to
23
atmospheric observations of CO. Their analysis ended after 2011, so we used their
1
24
scenario F3 for 2012. Fig. S3 shows results of inversions run with 3 other fire emissions
25
models from (Wiedinmyer et al., 2011; Kaiser et al., 2012; van der Laan-Luijkx et al.,
26
2015). Model differences in Region 4 in August 2010 are mainly attributable to F3,
27
which showed the worst match to atmospheric observations in that year (van der Laan-
28
Luijkx et al., 2015).
29
30
Fossil fuel and ocean flux influences (and related uncertainties) were small in the domain.
31
We accounted for two sources of uncertainty in biomass burning: the spread between
32
available fire emissions estimates and uncertainty arising from the conversion of CO
33
inversion results to CO2 emissions. These sources of error were included in R, as
34
described in the section describing model data mismatch.
35
36
Choice of prior FNBE and test of assumptions therein
37
Process-based models do not consistently reproduce plot level and eddy-flux observations
38
of the seasonality of net ecosystem exchange in the Amazon (Saleska et al., 2003; Baker
39
et al., 2009; Gonçalves et al., 2013). We estimated prior FNBE in a manner as independent
40
as possible from bottom-up model estimates of FNBE magnitude, seasonality and
41
interannual variability. Prior flux for each 1º by 1º grid cell and for each year of the
42
inversion was equal to the 2011 annual mean diurnal cycle in that grid cell as calculated
43
in SiBCASA (Schaefer et al., 2008; van der Velde et al., 2014), with the mean subtracted
44
to make the diurnal (and therefore seasonal and annual) sum neutral. We used the same
45
diurnal cycle for all years so that model results would be as independent as possible from
46
prior assumptions regarding year-to-year changes in sink strength, and 2011 has been
2
47
previously demonstrated to represent a “normal” year with respect to Amazon carbon and
48
climate (e.g. Gatti et al., 2014). Fig. S5 shows the mean diurnal cycle constructed as
49
described for the central Amazon, as well as the neutral, annual-mean NBE diurnal cycle
50
calculated with CASA-GFEDv3.1, and seasonal variability of the diurnal cycle from both
51
models.
52
53
Synthetic data studies have highlighted the importance of a realistic prior diurnal cycle in
54
NBE for approximation of s (Huntzinger et al., 2011), because different prior estimates of
55
the diurnal cycle can produce different recovered fluxes, especially in the near field. If
56
our assumption of a time invariant diurnal cycle is incorrect (e.g. (Schaefer et al., 2008;
57
van der Velde et al., 2014)), the possibility that it would add errors to posterior fluxes is
58
mitigated in our approach by three factors: 1) we adjust fluxes at small scales in space (1º
59
by 1º) and time (3-hourly), such that the diurnal cycle can be adjusted in the model, an
60
important factor for model success identified by (Huntzinger et al., 2011), 2) we add
61
uncertainty in the diurnal cycle to prior flux covariance (described below), and 3) we
62
aggregate posterior fluxes to large regions to avoid over-interpretation of near-field
63
fluxes, also an important factor identified by (Huntzinger et al., 2011).
64
65
In addition to the possibility that an unrealistic prior diurnal cycle can affect inversion
66
results, if seasonal variability (or a non-neutral mean) exists in s for FNBE, then seasonally
67
invariant (or neutral) sp could be a biased prior, which would violate the assumption of
68
zero-mean prior error (Rodgers, 2000). We applied two tests to examine whether our
69
results would be robust to the possibility of a biased or unrealistic prior: we ran the
3
70
inversion with 1) priors from two biosphere models, both with time-varying diurnal
71
cycles and 2) doubled prior uncertainty. The first test is described in this section, and the
72
second is described in the following section.
73
74
We solved for posterior NBE in an inversion with sp equal to 1) CASA-GFEDv3.1 NBE
75
and 2) SiBCASA NBE (van der Velde et al., 2014). The results of these two inversions
76
are compared with the main study results (“This Study”) in Figure S5. SiBCASA and
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CASA-GFED showed predictable, but disagreeing seasonality in sp. ŝ agreed between the
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two test inversions and the main study result in many parts of the record. ŝ agreed except
79
in those parts of the record where sp from SiBCASA and CASA-GFEDv3.1 were strongly
80
negative, usually in the dry season. In those cases, the posterior was invariably adjusted
81
to a less negative result, indicating that the priors were too negative (Fig. S5). This
82
finding supports the value of using a prior flux estimate that does not have strong prior
83
assumptions of seasonal changes in sink and source strength in regions like Amazon,
84
where such information is not known. It also suggests that, if our neutral prior is biased or
85
unreal, it still agrees with the posterior results from inversions using process-model-based
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priors at times when process-model-based priors are not themselves biased.
87
88
It is important to examine whether the use of a time-neutral prior could “wash out”
89
seasonality in the posterior result. As will be shown in the next section, we find that the
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prior errors assigned to NBE are large enough to allow for significant seasonality, should
91
its expressions be evident in the atmospheric data, yet that seasonality does not emerge in
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the model even when tested with doubled uncertainty. This leaves the possibility that if
4
93
observational constraint was too low, full NBE variability would not be detectable. We
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attempt to avoid this potentiality by interpreting our results within the observational
95
degrees of freedom. Finally, it is important to note that NBE seasonality on large scales
96
in the Amazon is not well known, so we suggest that the importance of not using a
97
seasonal biosphere prior outweighs any gains that could be made from introducing prior
98
seasonality that has not been substantiated using data.
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Prior flux uncertainty estimates and sensitivity of results to this choice
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The square root of prior flux variance for the year 2010 is shown in Fig. S6.
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103
To be sure that our findings of relatively low NBE variability, and a lack of discernable
104
NBE seasonality are real signals and not an artifact of our methodology, we explore
105
several possible methodological factors that could create this result. First, we test whether
106
our uncertainties are too small, given a neutral prior NBE estimate, and whether prior
107
uncertainty impacts the seasonality of the posterior result. (A related discussion of our
108
use of a neutral prior can be found above in the section titled “Choice of prior FNBE and
109
test of assumptions therein”.) Second, we investigate whether keeping prior flux
110
uncertainty, Q, constant through time (aside from diurnal variability), impacts the
111
seasonality of posterior NBE. Third, we investigate whether a time invariant diurnal cycle
112
in the prior impacts the time variability of posterior NBE.
113
114
Does a neutral prior affect posterior NBE variability?
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115
To investigate whether our choice of a neutral prior results in an inability of the inversion
116
to produce realistic seasonal variability in posterior NBE, we test the sensitivity of the
117
result to prior flux uncertainty by doubling the square root of prior flux variance, σ, and
118
inverting for fluxes (e.g. (Law et al., 2002)). We find that monthly, Regional NBE does
119
not change markedly (Fig. S7). This suggests that our prior uncertainty estimate is high
120
enough for ŝ to approximate s and/or that sp is a reasonable enough estimate of s (i.e. not
121
biased) that approximation of s was possible within the prescribed uncertainty bounds,
122
given the constraints of the data. It is, of course, possible that the data are not sufficient
123
for detection of fluxes at the time and space scales of our interpretation, despite the
124
degrees of freedom implied by footprints and sampling.
125
126
Does constant Q in time affect posterior NBE variability?
127
We ask whether our choice not to vary prior flux uncertainty in time affects the
128
seasonality of posterior NBE. The choice not to vary Q through time was made because
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of a lack of independent data to identify the seasonal cycle of flux uncertainties in the
130
Amazon. Figure S5 shows the results of three inversion runs: two have different
131
biosphere models as the prior and one has a neutral prior, but all three use the same
132
constant Q through time. As Figure S5 shows, monthly and seasonal variability in NBE
133
emerges in all three cases, but in periods where the biosphere prior is strongly negative or
134
positive, posterior NBE tends to look more like its prior than the other inversion
135
posteriors. This finding suggests that time variability in prior flux uncertainty is a lower
136
order control on posterior NBE than the choice of prior. This result underscores the
137
importance of conservative (i.e. large) prior uncertainty estimates, so that the neutral
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138
prior used in our inversion can deviate from neutral. Inversions with strong seasonality
139
in prior NBE result in posterior NBE that also has strong seasonality, despite none of
140
these tests using prior NBE uncertainty with time variability. In other words, the absence
141
of seasonal variability in prior NBE uncertainty does not appear to impact posterior NBE
142
seasonality.
143
144
Does a time invariant prior diurnal cycle affect posterior NBE?
145
We also investigate whether having no seasonal variability in the diurnal cycle (in the
146
NBE prior) affects the seasonality of posterior NBE. Figure S5 shows the range in the
147
mean diurnal cycle between four 3-month periods for two biosphere models (panel B).
148
From this figure, it is clear that the seasonal variability in the diurnal cycle within one
149
model is generally smaller than the difference in diurnal cycle between models. If the
150
absence of seasonal variability in the diurnal cycle were to cause seasonal biases in the
151
posterior NBE result, then we would expect to see consistent seasonal differences in the
152
posterior NBE in inversions using these two biosphere models as prior NBE. On the
153
contrary, the posterior NBE results agree at some points in time and disagree at other
154
points in time, but there is no consistent bias or offset between them in any season. That
155
is, there is no season in which the CASA-GFEDv3.1 posterior NBE or the SiBCASA
156
posterior NBE is consistently more or less variable (more or less close to neutral flux of
157
NBE equal to zero) than the other. These findings suggest that the diurnal cycle prior, and
158
seasonal variability in the diurnal cycle of the prior, likely do not impact the NBE result
159
strongly enough to alter NBE seasonality, or that prior flux uncertainty estimates are
7
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large enough that the prior diurnal cycle variability is not a primary control on posterior
161
NBE seasonality.
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Model Data Mismatch Estimates for CO2
164
Transport Uncertainty
165
Transport uncertainty was calculated by comparing transport from two different
166
Lagrangian particle dispersion models: Flexpart and Hysplit. Convection and buoyancy
167
of air masses during transport represent key sources of uncertainty in modeling
168
atmospheric transport in the Amazon (Fu et al., 1999). Flexpart uses a convective
169
parameterization scheme that redistributes particles in the vertical column based on
170
temperature and humidity (Emanuel & Zivkovic-Rothman, 1999). We use Hysplit
171
without convective parameterization; vertical motion fields of the meteorological input
172
data mix particles vertically (Draxler & Hess, 1998). Therefore, by comparing air
173
transport modeled with and without convective parameterization, we hope to capture the
174
largest source of uncertainty in atmospheric transport in the Amazon.
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To perform this comparison, we first multiply an estimate of land CO2 fluxes (SiBCASA
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biosphere fluxes + GFEDv3.1 fire fluxes) by H from Flexpart and H from Hysplit. We
177
then calculate the square of the standard deviation of differences in atmospheric CO2
178
simulated by the two transport models at each site and at each 500 m altitude increment.
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We estimate transport uncertainty as the square of this value, and impose a maximum of
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64 ppm2 based on (Miller et al., 2015).
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Biomass Burning Uncertainty
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Two sources of uncertainty in pre-subtracted CO2 from biomass burning emissions were
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incorporated into R: from differences in biomass burning estimates (Wiedinmyer et al.,
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2011; Kaiser et al., 2012; van der Laan-Luijkx et al., 2015) and from emissions ratio of
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CO:CO2 (van Leeuwen et al., 2013). We estimated BB model uncertainty by examining
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the spread between three estimates: F5, F4, and the mean of F1 and F2 from
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(Wiedinmyer et al., 2011; Kaiser et al., 2012; van der Laan-Luijkx et al., 2015).
189
Specifically, we calculated BB variance in one-week blocks (all 3-hourly timesteps in a
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given week were assigned the same variance), as the square of the standard deviation of
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all 3-hourly values in that week, from all three BB estimates (thus sampling the spread of
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7 days × 8 steps/day × 3 models = 168 values). We estimated BB uncertainty arising from
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conversion of CO fluxes to CO2 fluxes by propagating uncertainty in the CO:CO2
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emissions ratio used by (van der Laan-Luijkx et al., 2015) to convert optimized CO to
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fluxes of CO2. CO emissions factors and standard deviations were from ((van Leeuwen et
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al., 2013); GFED-AKAGI EF scenario), with 0.5º by 0.5º space and monthly time
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resolution. Annual, biome averaged values of CO2 emissions factors and standard
198
deviations were from (Akagi et al., 2011; van Leeuwen et al., 2013). The relative errors
199
arising from BB model spread and CO to CO2 conversion were summed in quadrature.
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The square root of that value was multiplied by biomass burning emissions and squared
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to calculate the variance in biomass burning emissions.
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All sources of model data mismatch were summed in quadrature to calculate R, and are
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shown in Fig. S8. Transport model differences were higher in 2012 for unknown reasons,
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resulting in higher model data mismatch, on average, and consequent higher flux
206
uncertainty in 2012 compared with 2010 and 2011.
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Prior Background CO2 Estimates
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Background CO2, or boundary condition, is a source of uncertainty in regional
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atmospheric inversions. We created an observationally-constrained CO2 background in
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three steps: 1) we created a background CO2 prior using output from global inversion
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models, 2) we processed the background CO2 prior using atmospheric observations from
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near the domain boundary that were not used in the inversion, and 3) we optimized the
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CO2 background in the inversion. The first two steps are described in this section, and the
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third step is described in the following section.
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We created a first guess background CO2 “curtain” using 3-dimensional “slices” from 4-
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dimensional atmospheric CO2 mole fraction fields from a global inversion. The 4-D
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fields were from CT2013_ei, and were sampled at 30º W longitude with 2º latitudinal
220
resolution, 34 vertical pressure levels, and 3-hourly time resolution.
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Next, we processed the curtain to match available observations, expanding on the
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methods of (Lauvaux et al., 2012). We removed biases between the curtain and
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atmospheric observations at two NOAA/ESRL Global Monitoring Division network sites
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that measure CO2 several times weekly near the dominant inflow to the domain
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(Ascension Island – ASC, and Ragged Point Barbados – RPB, Fig. 1).
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We fit smoothed curves to the data at ASC and RPB (“data curves”) using the CCGVU
229
program (Thoning et al., 1989), with a short-term filter cutoff value of 2.5 days. Next, we
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did weighted fitting of the curtain to match either the ASC “data curve” or the RBP “data
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curve” by convex combination of the curtain and the data curve. Weighting was based on
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spatial proximity (vertical and latitudinal) of the background CO2 grid cell in question
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and either ASC or RPB. The increase in the weighting of the values towards in-situ
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observations increased exponentially with vertical and horizontal proximity to the
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observation site, with a decay length scale of 1000 km. The choice of 1000 km represents
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the expectation that air mass sources in the tropics may vary on synoptic scales of ~3
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times this order (Madden & Julian, 1972). Bias removal between the smoothed
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background CO2 and observation data occurred every three hours. Above 4 km height,
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the curtain was no longer adjusted to match in-situ observations.
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The curtain was fitted to either the ASC “data curve” or the RPB “data curve” based on
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the monthly mean latitude of the ITCZ; curtain values at latitudes north of the ITCZ were
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adjusted to match the RPB curve, and curtain values at latitudes south of the ITCZ were
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adjusted to match the ASC curve. We estimated the monthly mean latitude of the ITCZ at
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-30º longitude using NCEP Reanalysis monthly mean surface v-wind (Kalnay et al.,
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1996).
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Before processing the prior background CO2 curtain, the mean difference between the
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curtain and observations (CT2013_ei – Observations) at ASC was 0.19 ppm in 2010, 0.52
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ppm in 2011 and 0.51 ppm in 2012. At RBP, before-processing biases were -0.08 ppm in
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2010, 0.57 ppm in 2011 and 0.41 ppm in 2012. The mean difference after processing was
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< 0.05 ppm at all sites and all years.
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Background CO2 Uncertainty and Optimization
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We optimized the CO2 background in the state vector, sp (Eqn. 3). Prior background CO2
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for each observation was calculated by sampling the processed curtain using particle
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backtrajectories from Flexpart. At each receptor point, or observation location and time,
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Flexpart transported 10,000 particles, or infinitesimally small air parcels, backwards in
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time using GFS meteorological data. We calculated the mean backtrajectory at 1º by 1º
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and 3-hour resolution.
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For mean particle trajectories that left the domain via the eastern boundary (Fig. 1) we
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sampled the processed background CO2 curtain at the altitude and time that the particle
264
exited the domain. For particles that did not leave the domain after 7 days back in time,
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we sampled the 4-dimensional mole fraction fields (CT2013_ei) at the mean end point
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location and time recorded.
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We account for two sources of “background CO2 construction” uncertainty in estimating
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the prior background CO2 estimate. (“Background CO2 sampling” uncertainty is in the
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model data mismatch term, R.)
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σ2 BG = σ2obs-curtain + σ2endpointCT-curtainCT,
Eqn. S2
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σ2obs-curtain is the standard deviation of differences between observations and the curtain at
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three sites: ASC and RPB (described above) and Fortaleza (FTL; located at 3.52º S,
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38.28º W). Standard deviations are calculated for all years available at each site (for
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example, sampling took place at Fortaleza from late 2000 to early 2003). σ2obs-curtain was
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calculated as the standard deviation of residuals around the smoothed curves fitted to the
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data at the appropriate site, equivalent to the stochastic CO2 “weather” at the domain
280
boundary. When backtrajectory end points were at altitudes higher than 1000 m, we
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compared the curtain to observations made at FTL, because that measurement campaign
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produced vertical profiles using aircraft sampling. When backtrajectory endpoints were at
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altitudes lower than 1000 m, we compared the curtain to observations made at ASC and
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RPB, using the meridional position of the ITCZ to determine the appropriate site.
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The second estimate of background CO2 sampling error was σ2endpointCT-curtainCT, calculated
287
as the standard deviation of the difference between 1) the CT2013_ei CO2 mole fraction
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at the Lagrangian particle backtrajectory endpoint and 2) the CT2013_ei CO2 mole
289
fraction at the closest point in space to the curtain. This source of error was only added to
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observations for which mean particle backtrajectories did not intersect the domain
291
boundary.
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The mean value of σobs-curtain was 1.44 ppm in 2010, 1.43 ppm in 2011, and 1.40 ppm in
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2012, and the mean value of σendpointCT-curtainCT was 0.21 ppm in 2010, 0.26 ppm in 2011,
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and 0.12 ppm in 2012.
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Degrees of Freedom and Aggregation of Results
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We estimated the signal degrees of freedom to determine the number of independent
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pieces of information available for interpretation of fluxes and background CO2.
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Although we solve the inversion with 1º by 1º and 3-hourly resolution over the Amazon
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Basin (1487 grid cells x 2920 time steps = over 4.3 million fluxes in the state vector), the
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number of observations in each yearlong batch inversion (n < 1000) did not justify
303
interpretation of fluxes at such high resolution. One way to estimate how many individual
304
pieces of information were provided by the observations (and therefore how many
305
individual pieces of information we were justified in interpreting) is the signal degrees of
306
freedom (d.o.f.) (Rodgers, 2000). Signal d.o.f. is calculated as:
307
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signal d.o.f. = trace((QHT (HQHT + R)-1 )H)
Eqn. S3
309
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The signal degrees of freedom were 206 in 2010, 171 in 2011 and 173 in 2012. Of that,
311
113 contributed to constraining background CO2 in 2010, 83 in 2011, and 61 in 2012. To
312
interpret fluxes with monthly time resolution, we were left with 7-9 degrees of freedom
313
over which to interpret the spatial flux signals in each month. We initially aggregated
314
fluxes to 17 5º by 7º regions. We then examined similarities and differences between
315
fluxes in those regions and aggregated again to a conservative choice of 5 regions, chosen
316
based on 1) latitude and 2) common climate and ecosystem types. The northern-most
317
region (Region 1) is in the Northern Hemisphere; Regions 2-5 are in the Southern
318
Hemisphere. Regions 2-4 span a climatic gradient of wet-to-dry, and timing of rainy
319
season onset and end (e.g. (Marengo et al., 2011; Restrepo-coupe et al., 2013)). The
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division between Regions 2-4 and Region 5 follows the latitude of a strong gradient in
321
the number of months of precipitation per year (Restrepo-coupe et al., 2013). Study sites
322
south of that latitude band also show stronger seasonality in daytime photosynthetic
323
active radiation (Restrepo-coupe et al., 2013).
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To confirm that 5-region division of space and monthly division of time were appropriate
326
choices, we calculated the posterior correlations between regions at the monthly time
327
step. Low correlations should indicate that independently grouped flux information is
328
indeed independently constrained by the available observations. The upper right part of
329
Table S1 shows prior and posterior flux correlations, on average, between regions. The
330
posterior spatial correlation coefficients were very low (≤ 0.1), which justifies our
331
interpretation of signals at the regional scale. Table S1 shows percent uncertainty
332
reduction for annual mean and regional fluxes, as well as distances between adjacent
333
region centers, and Fig. S9 shows prior and posterior correlation coefficients between
334
Region 3 and other regions through time. Correlations of uncertainties between months
335
were not calculated, but the prior temporal correlation length implies some independence
336
between months.
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Choice of Transport Model: Comparison of Hysplit and Flexpart
339
We used a separate transport model, Hysplit, to compare the sensitivity of our inversion
340
model result to choice of transport model. Hysplit was run with 0.5-degree Global Data
341
Assimilation System (GDAS) meteorology (Draxler & Hess, 1998), and 10-day (the
342
decision of the group who ran the model) back trajectories. Hysplit and Flexpart rely on
15
343
different methods for modeling of convection (as described above). We constructed a
344
completely separate inversion using Hysplit, with all calculations, including background
345
CO2 construction and footprint creation, generated independently.
346
347
We found that different transport models resulted in different magnitude of total net land
348
CO2 fluxes, such that estimates of NBE differed depending on the transport model used.
349
Fig. S10 shows that Flexpart resulted in more positive net emissions than Hysplit; the
350
results from the two models bracketed the estimates of NBE found by (Gatti et al., 2014)
351
and (van der Laan-Luijkx et al., 2015) for the years available.
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Critically, the time variability of NBE was very similar between inversions with Flexpart
354
and Hysplit. Fig. S10 shows that the time rate of change (month-on-month) of NBE in the
355
central Amazon is very similar between the two models. This indicates that, while the
356
choice of transport model may influence recovered flux magnitude, the ability of the
357
inversion to recover meaningful information about the time evolution of NBE and
358
therefore the NBE response to climate variability is robust to choice of transport model. It
359
is for this reason that we focus our interpretation of results on direction of change rather
360
than on absolute magnitude or sign of fluxes.
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In order to determine which transport model more realistically relates the magnitudes of
363
surface fluxes and atmospheric trace gas signals, we performed a test using the optimized
364
fire emissions of CO from (van der Laan-Luijkx et al., 2015) that produced the best fit to
365
CO observations (F1). We convolved footprints from either Flexpart of Hysplit with F1
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366
plus an estimate of non-biomass burning sources of CO (biogenesis, soil emissions and
367
soil oxidation) of 27 mg m-2 day-1 (Gatti et al., 2010), and added background CO that was
368
calculated in the same manner as for the CO2 background. We assumed that the timing
369
and magnitude of the F1 fire emissions were close to reality, such that multiplication of
370
footprints from each transport model with fire flux data would help us determine which
371
performed better. We compared model performance for all four continental sites (ALF,
372
RBA, SAN, and TAB) and at two altitude levels: 0 – 2.5 km and 2.5 – 5 km (Table S2).
373
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Annually, at all sites, the mean bias (i.e. simulated CO minus observed CO) was similar
375
between Flexpart and Hysplit for 2010 and 2011 (Flexpart performed slightly better at
376
higher altitudes), but the standard deviation of the bias was almost always higher from
377
Hysplit (Table S2) at all sites and both altitude bins. This result suggested that Flexpart
378
was more capable of capturing surface signals arising from fluxes than Hysplit in what
379
was our only independent measure of measurement sensitivity to fluxes.
380
We therefore focused our investigation and results on Flexpart. In 2011, both models
381
over-estimated CO mole fractions at every site and every altitude bin, except for Flexpart
382
at the ALF 0 – 2.5 km bin (where the bias was 0 ppb), which suggests that either absolute
383
flux magnitude from F1, background CO2, or non-biomass burning sources may have
384
been incorrect, or that both transport models contain systematic biases. Since we cannot
385
rule out the possibility of systematic biases in transport, we focus, where possible, on
386
time evolution and variability of NBE rather than exclusively focusing on the absolute
387
magnitude of NBE. The finding that the time evolution of NBE (i.e. month-on-month
388
NBE) agrees very well between Hysplit and Flexpart gives us confidence that, in spite of
17
389
the impacts different treatments of convection may have on final recovered flux
390
magnitude, the impacts on seasonality and variability in response to climate are robust.
391
392
Calculation of Cumulative Water Deficit (CWD)
393
A given month’s CWD value (CWDn) is equal to the previous month’s CWD value
394
(CWDn-1), plus the current month’s precipitation (Pn), minus average monthly
395
evapotranspiration (which does not change month-to-month). Evapotranspiration is set to
396
100 mm month-1 for each month, which is the mean value of evapotranspiration measured
397
in various seasons and locations across the Amazon (Aragão et al., 2007 and citations
398
therein), and CWD is reset to 0 in December of every year. If monthly precipitation
399
exceeds evapotranspiration, CWD is set to zero. We standardize CWD by subtracting the
400
long-term (1998-2013) climatological monthly mean and dividing by the long-term
401
(1998-2013) climatological monthly standard deviation.
402
403
Calculation of the Supply-Demand Drought Index (SDDI)
404
SDDI is calculated in several steps, following (Touma et al., 2015). First, the Z value is
405
calculated by 1) removing the seasonality of the hydrologic monthly deficit (precipitation
406
– potential evapotranspiration) with the stratified sampling technique, and 2)
407
standardizing the deficit using the mean and standard deviation of the deficit time series
408
(1979-2013). SDDI is then calculated iteratively: a given month’s SDDI value (SDDIn) is
409
equal to that month’s Z value (Zn) added to a fraction (0.897) of the previous month’s
410
SDDI value (SDDIn-1) (Rind et al., 1990; Touma et al., 2015).
411
18
412
Solar-induced Fluorescence (SIF)
413
SIF is an electromagnetic emission in the 650-800 nm range, originating from plant
414
photosynthetic machinery, and it is theoretically linearly correlated with electron
415
transport rate of the photosynthetic activity (Zhang et al., 2014). Theoretical and
416
experiment studies (van der Tol et al., 2009; Zarco-Tejada et al., 2013) demonstrate that
417
under normal temperature range and normal light conditions (e.g. most satellite overpass
418
times), SIF is linearly correlated with GPP and co-varies with GPP under environmental
419
stresses. At canopy and ecosystem scales, SIF is found to be better correlated with and
420
more closely track the seasonality of the measured GPP from the eddy covariance flux
421
data than other available GPP products and reflectance-based vegetation index (Guanter
422
et al., 2014; Joiner et al., 2014).
423
424
The SIF data used here are retrieved near the λ=740nm far-red fluorescence emission
425
peak from the Global Ozone Monitoring Experiment-2 (GOME-2) instrument onboard
426
Eumetsat’s MetOp-A satellite. GOME-2 is in a sun-synchronous orbit with overpass at
427
about 09:30AM local time, near the window of peak daily photosynthesis at these
428
latitudes. The SIF algorithm (Joiner et al., 2013) disentangles three spectral components
429
near the peak of the far-red chlorophyll fluorescence emission feature: atmospheric
430
absorption (due to water vapor), surface reflectance, and fluorescence radiance. The
431
derived GOME-2 SIF (version 26, level 3) covers from 2007-present, and the data from
432
2007 to 2012 has been used in this study. The SIF data has been cloud filtered, and the
433
data with the effective cloud fraction (fc)>0.4 have been eliminated, where fc was
434
computed from the black-sky 16 day gridded filled land surface albedo product from
19
435
Aqua MODIS (MOD43B3) at 656 nm (Schaaf et al., 2002). Using more or less stringent
436
criteria on cloud filtering within a moderate range did not substantially alter the derived
437
spatial and temporal patterns of SIF (Joiner et al., 2013). All SIF data with SZA > 70°
438
were also eliminated. The current version of SIF has not incorporated any sun-sensor
439
geometry correction, but we find that its multi-year mean seasonal cycle is highly
440
consistent with that of the BRDF-corrected MAIAC EVI (Fig. S11), which provides
441
confidence of using these data in our analysis. It should be noted, however, that we did
442
not remove the seasonal cycle of Photosynthetically Active Radiation (PAR), which
443
would result in a more directly comparable measure to EVI. We did not correct for PAR
444
for three reasons: 1) we were interested in the signal of GPP more than the comparability
445
of SIF to EVI, and 2) cloud cover in the Amazon is high enough that the standard
446
correction for PAR (division by the cosine of the solar zenith angle) could have resulted
447
in errors from diffusion of incoming light by clouds, and 3) variation in the solar zenith
448
angle is smaller near the equator. The SIF data have been gridded to 0.5° spatial
449
resolution and monthly time resolution, with estimated errors of 0.1-0.2 mW/m2/nm/sr
450
(Joiner et al., 2013).
451
452
Enhanced Vegetation Index (EVI)
453
EVI is an index of landscape-integrated vegetation greenness (Huete et al., 2006) and
454
photosynthetic capacity (Sellers et al., 1992), which is related to the photosynthetic
455
potentials under ideal environmental conditions, and thus EVI reflects an inherent
456
vegetation photosynthetic property. EVI has been found to correlate with independent
457
ground-based measures of photosynthesis from eddy flux towers across multiple biomes
20
458
(Rahman et al., 2005; Sims et al., 2006; Kuhn & et al., 2007; Huete et al., 2008), though
459
the direct linkage between EVI and photosynthesis rate (or gross primary production,
460
GPP) in tropical evergreen forests is more complicated and is an ongoing research topic,
461
as leaves in tropical rainforests are year-around present. Here we refer to EVI as
462
photosynthetic capacity at tropical forest regions. We use the EVI version from the Multi-
463
Angle Implementation of Atmospheric Correction algorithm (MAIAC) (Lyapustin et al.,
464
2012). The MAIAC EVI incorporates both rigorous BRDF correction and stricter cloud,
465
atmosphere and aerosol corrections (Lyapustin et al., 2012). In particular, MAIAC is an
466
advanced algorithm that uses time series analysis and a combination of pixel- and image-
467
based processing to improve accuracy of cloud detection, aerosol retrievals, and
468
atmospheric correction based on MODIS calibrated and geolocated (L1B) measurements
469
(Lyapustin et al., 2011a, 2011b, 2012). MAIAC provides a suite of gridded 1km
470
atmospheric and surface products including bidirectional reflectance factors (BRF, also
471
called "surface reflectance"), albedo, and Ross-Thick Li-Sparse (RTLS) (Lucht et al.,
472
2000) BRDF model parameters in 7 land bands. The data were downloaded from
473
ftp://ladsweb.nascom.nasa.gov/MAIAC/. We calculated both MAIAC BRDF-corrected
474
EVI. The BRDF correction normalizes BRF from a given view geometry to the fixed
475
geometry of nadir view and 45° sun zenith angle using the retrieved BRDF model, and
476
then normalized EVI is computed from these values. The retrieval error for EVI is
477
estimated to be 0.04-0.06 mW/m2/nm/sr (Hilker et al., 2012).
478
479
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Fig. S1. Frequency histograms of the local time of day (in hours since 00:00) for each
sample from all sites (ALF, RBA, SAN, and TAB) in 2010, 2011, and 2012.
26
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635
636
637
638
639
640
641
642
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Fig. S2. Central Amazon (Region 3) climate and NBE. Top panel: red dots show daily
maximum 6-hourly temperature from the NCEP-NCAR Reanalysis, with long-term mean
(1981-2010) (black line) and 1-σ standard deviation (grey shading) (Adler et al., 2003).
Second panel: red dots and lines show monthly mean temperature anomalies from the
long-term mean climatology (1981-2010) from NCEP-NCAR Reanalysis (Kalnay et al.,
1996). Third panel: blue dots show monthly precipitation from the Global Precipitation
Climatology Project (GPCP) with long-term mean (1981-2010) (black) and 1-σ standard
deviation (grey shading) (Kalnay et al., 1996). Bottom panel: a monthly standardized
drought index that incorporates both temperature and precipitation (SDDI) (teal) (Touma
et al., 2015).
27
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648
649
650
651
Fig. S3. NBE solved in an inversion with influences from fire emissions estimates of
(Wiedinmyer et al., 2011; Kaiser et al., 2012; van der Laan-Luijkx et al., 2015)
subtracted from the atmospheric observations in Regions 3 (top panel) and 4 (bottom
panel).
28
652
653
654
655
656
657
658
659
Fig. S4. Panel (a) is reproduced with permission from Figure 4 (their panel c) of (Nepstad
et al., 2004), showing maximum plant available water at 10 m rooting depth across the
Amazon Basin, estimated using soil texture profiles and soil water parameters. Panel (b)
is reproduced with permission from Figure 3 of (Fan et al., 2013) showing hydrologic
model results for water table depth.
29
660
661
662
663
664
665
666
667
668
669
670
Fig. S5. (a) Solid line with circles marking 3-hourly values: the average diurnal cycle for
the year 2011, as calculated with the SiBCASA model, averaged over Region 3 (the
central Amazon). Dotted line without 3-hourly markers: is the equivalent calculation
using CASA-GFEDv3.1 biosphere CO2 fluxes. (b) Seasonal mean diurnal cycles for 2011
(JFM: January-March, AMJ: April-June, JAS: July-September, OND: OctoberDecember), for SiBCASA (solid lines) and CASA-GFEDv3.1 (dashed lines). (c) Region
3 (central Amazon) prior (dotted lines) and posterior (solid lines) NBE with priors from
two different models (CASA-GFEDv3.1 in blue and SiBCASA in green) as well as the
prior and posterior fluxes presented in the main body of this study (gold).
30
671
672
673
674
675
676
Fig. S6. Prior flux (NBE) uncertainty for the year 2010, which equals the sum in
quadrature of annual maximum monthly heterotrophic respiration and the standard
deviation of differences in the annual mean diurnal cycle calculated with SiBCASA and
CASA-GFED.
31
677
678
679
680
Fig. S7. Monthly NBE for each region (as in Fig. 3); results as for the main results of this
work (black lines and posterior uncertainty) and for an inversion run with prior flux
uncertainty, σ, doubled (red lines and posterior uncertainty).
32
681
682
Fig. S8. Model Data Mismatch (R) in units of ppm2 for each year (all sites).
33
683
684
685
686
Fig. S9. Monthly mean correlation between Region 3 and Regions 1, 2, 4, and 5 (Fig. 3).
Solid lines are prior correlation and dotted lines are posterior correlation.
34
687
688
689
690
691
Fig. S10. (a) Net ecosystem exchange and biomass burning are shown for each year of
the inversion, 2010-2012, as well as for each year of the studies of (Gatti et al., 2014) and
(van der Laan-Luijkx et al., 2015), 2010-2011. (b) Month-on-month NBE for each
Region, calculated with Flexpart (black line) and Hysplit (gray line).
35
692
693
694
695
696
697
698
699
Fig. S11. Spearman correlations of the mean seasonal cycles between SIF and MAIAC
EVI with BRDF correction (MAIAC EVIn). (a) Shows the spatial patterns of
correlations, and (b) shows the corresponding histograms of the correlations. The red
areas in the histograms indicate the proportion of grids with statistically significant
correlation at the p-value of 0.1, while the black areas are statistically insignificant at the
same p-value level.
36
700
701
702
703
704
705
706
707
Table S1.
Table shows, on the diagonal, percent annual mean error reduction by the inversion (from
Q to Vŝ) in each Region as defined in Fig. 2. Above the diagonal (upper right) shows
prior (italics) and posterior (bold) annual mean flux correlation coefficients (expressed as
percent) between Regions for each year of the study, 2010-2012. Below the diagonal
(lower left) show approximate distance in km between the centers of each of the 5
Regions.
Region 1
Region 2
Region 1
2010:
2010:
7% error reduction
2011:
5% error reduction
2012:
5% error reduction
Region 3
2010:
2%
1%
2011:
6%
4%
2011:
2%
1%
2012:
2011:
2012:
Region 2
Distance Between
Region Centers:
1800 km
2011:
2012:
2012:
2010:
2010:
2011:
2011:
2012:
Region 3
Distance Between
Region Centers:
1100 km
4%
2%
2012:
0%
0%
2010:
Distance Between
Region Centers:
900 km
4%
2%
0%
0%
10%
8%
2010:
20% error reduction
2011:
16% error reduction
2012:
18% error reduction
1%
0%
0%
0%
10%
8%
2012:
1%
0%
5%
3%
10%
7%
2011:
1%
0%
5%
3%
6%
5%
2010:
Region 5
2010:
5%
3%
6%
4%
2%
1%
2010:
3% error reduction
2011:
3% error reduction
2012:
3% error reduction
Region 4
2010:
4%
3%
2010:
7%
3%
2011:
8%
4%
2011:
7%
4%
2012:
8%
4%
2012
7%
4%
8%
5%
Region 4
2010:
Distance Between
Region Centers:
1200 km
Distance Between
Region Centers:
2500 km
Distance Between
Region Centers:
1400 km
2010:
23% error reduction
2011:
20% error reduction
2012:
24% error reduction
3%
1%
2011:
3%
1%
2012:
Region 5
3%
1%
Distance Between
Region Centers:
1600 km
Distance Between
Region Centers:
1300 km
Distance Between
Region Centers:
800 km
708
709
710
37
Distance Between
Region Centers:
1600 km
2010:
15% error reduction
2011:
16% error reduction
2012:
12% error reduction
711
712
713
714
715
716
Table S2.
Summary of comparisons between transport model ability to simulate vertical
concentrations of CO given estimates of biomass burning and background CO. Residuals
(modeled – observed) for two altitude bins (0 – 2.5 km and 2.5 – 5 km) are shown for
each site. Units are ppb CO.
Flexpart 2010 (all sites all altitudes):
Hysplit 2010 (all sites all altitudes):
Flexpart 2011 (all sites all altitudes):
Hysplit 2011 (all sites all altitudes):
-11 ± 84 ppb
4 ± 104 ppb
17 ± 74 ppb
31 ± 88 ppb
717
2010:
Alta Floresta (ALF) Rio Branco (RBA)
Santarém (SAN)
Tabatinga (TAB)
Flexpart: 0 – 2.5 km
-41 ± 81 ppb
-33 ± 126 ppb
-4 ± 36 ppb
-19 ± 86 ppb
Hysplit: 0 – 2.5 km
-26 ± 110 ppb
-23 ± 121 ppb
14 ± 41 ppb
-16 ± 136 ppb
Flexpart: 2.5 – 5 km
-12 ± 83 ppb
19 ± 104 ppb
9 ± 24 ppb
4 ± 94 ppb
Hysplit: 2.5 – 5 km
9 ± 109 ppb
52 ± 123 ppb
22 ± 31 ppb
31 ± 105 ppb
Santarém (SAN)
Tabatinga (TAB)
4 ± 40 ppb
2011:
Alta Floresta (ALF) Rio Branco (RBA)
Flexpart: 0 – 2.5 km
0 ± 76 ppb
10 ± 118 ppb
7 ± 77 ppb
Hysplit: 0 – 2.5 km
22 ± 79 ppb
37 ± 140 ppb
21 ± 73 ppb
2 ± 52 ppb
Flexpart: 2.5 – 5 km
28 ± 58 ppb
57 ± 87 ppb
27 ± 36 ppb
13 ± 38 ppb
Hysplit: 2.5 – 5 km
45 ± 72 ppb
58 ± 98 ppb
52 ± 86 ppb
15 ± 45 ppb
718
719
38