Climate variations can have profound impacts on marine
ecosystems and the socioeconomic systems that may depend upon them.
Temperature, pH, oxygen (O2) and net primary production (NPP) are
commonly considered to be important marine ecosystem drivers, but the
potential predictability of these drivers is largely unknown. Here, we use a
comprehensive Earth system model within a perfect modeling framework to
show that all four ecosystem drivers are potentially predictable on global
scales and at the surface up to 3 years in advance. However, there are
distinct regional differences in the potential predictability of these
drivers. Maximum potential predictability (>10 years) is found
at the surface for temperature and O2 in the Southern Ocean and for
temperature, O2 and pH in the North Atlantic. This is tied to ocean
overturning structures with “memory” or inertia with enhanced predictability
in winter. Additionally, these four drivers are highly potentially
predictable in the Arctic Ocean at the surface. In contrast, minimum
predictability is simulated for NPP (<1 years) in the Southern
Ocean. Potential predictability for temperature, O2 and pH increases
with depth below the thermocline to more than 10 years, except in the
tropical Pacific and Indian oceans, where predictability is also 3 to
5 years in the thermocline. This study indicating multi-year (at surface)
and decadal (subsurface) potential predictability for multiple ecosystem
drivers is intended as a foundation to foster broader community efforts in
developing new predictions of marine ecosystem drivers.
Introduction
Marine organisms and ecosystems are strongly influenced by seasonal- to
decadal-scale climate variations, challenging the sustainable management of
living marine resources (Drinkwater et al.,
2010; Lehodey et al., 2006). Anomalies in temperature, pH, O2 and
nutrients are important drivers of such climate-induced ecosystem variations (Gattuso
et al., 2015; Gruber, 2011). Therefore, skillful predictions of these marine
ecosystem drivers have considerable potential for use in marine resource
management (Gehlen
et al., 2015; Hobday et al., 2016; Payne et al., 2017; Tommasi et al.,
2017).
The primary tools for investigating how marine organisms and ecosystems
change on seasonal to decadal timescales are Earth system models, where
prognostic equations are implemented for biogeochemical cycles. These models
are capable of representing both natural variability and transient changes
in the marine ecosystem drivers (Bopp
et al., 2013; Frölicher et al., 2016). Recently, Earth system models
have been used to explore and quantify the predictability of marine
biogeochemical tracers. Most of the studies focus on predicting the ocean
uptake of carbon (Li et al.,
2016, 2019; Lovenduski et al., 2019; Séférian et al., 2018).
To date, only a few studies have investigated the predictability of marine
ecosystem drivers (Chikamoto
et al., 2015; Park et al., 2019; Séférian et al., 2014a). An
intriguing finding of these studies is that marine biogeochemical drivers
may be more predictable than their physical counterparts. Séférian et al. (2014a), for example, showed that net primary productivity (NPP) has greater
predictability than sea surface temperature (SST) in the eastern equatorial
Pacific. They hypothesized that SST is strongly influenced by high-frequency
surface fluxes, whereas NPP is more directly impacted by thermocline
adjustment processes that determine the rate at which nutrients are brought
into the ocean's euphotic layer. Thus, biogeochemical predictions may hold
great promise and highlight the need for further investigation. Changes in
ecosystem drivers have impacts not only on the surface ocean but also over upper
ocean waters spanning the euphotic zone and below, making it important to
understand more broadly how ecosystem drivers vary over a range of depths.
To our knowledge there is no comprehensive assessment of potential
predictability of marine ecosystem drivers at the global scale spanning
multiple depth horizons and a comparison of the relative predictability
among them.
In this study, we assess the potential predictability of the four marine
ecosystem drivers using “perfect model” simulations of a comprehensive Earth
system model. We address the following three questions:
To what extent are marine ecosystem drivers predictable at the global scale?
What are the regional and depth-dependent characteristics of potential
predictability?
Which underlying physical and biogeochemical processes prescribe or limit
the potential predictability of marine ecosystem drivers?
This study is organized as follows. First, we introduce the model and
methods used to assess the potential predictability in marine ecosystem
drivers. Subsequently, the temporal sequencing of potential predictability
over global scales for the four marine ecosystem drivers are identified and
evaluated for regional differences in potential predictability horizons.
Both surface and subsurface manifestations are presented to assess the
origin of potential predictability. Finally, we also identify the
mechanistic controls on the limits to potential predictability and conclude
with a discussion and summary section.
MethodsEarth system model: GFDL-ESM2M
For this study we conducted a new 240-member ensemble suite of simulations
of 10-year duration each with the Earth system model ESM2M developed at the
Geophysical Fluid Dynamics Laboratory (GFDL) of the National Oceanic and
Atmospheric Administration (NOAA; Dunne
et al., 2012, 2013). The GFDL-ESM2M is a fully coupled carbon cycle–climate
model. The physical core of the model is based on the physical coupled model
CM2.1 (Delworth
et al., 2006). The atmospheric model AM2 has a horizontal resolution of
2∘ latitude × 2.5∘ longitude with 24 vertical levels (Anderson
et al., 2004). The land model simulates land water, energy and the carbon cycle,
and it has the same horizontal resolution as the atmospheric component. The
ocean model MOM4p1 (Griffies, 2012) has 50 vertical levels of
varying thickness and a nominal horizontal resolution of 1∘
latitude × 1∘ longitude, increasing towards the Equator to up to
1/3∘. The sea ice model includes full ice dynamics, three
thermodynamic layers and five ice thickness categories and is defined on the
same grid as the ocean model (Winton, 2000).
Ocean biogeochemistry and ecology is simulated by the Tracers Of
Phytoplankton with Allometric Zooplankton version 2.0
(TOPAZ2; Dunne et al., 2013).
TOPAZ2 represents 30 prognostic tracers to describe the cycles of carbon,
phosphorus, silicon, nitrogen, iron, alkalinity, oxygen and lithogenic
material as well as surface sediment calcite. TOPAZ2 includes three
phytoplankton functional groups: small (mostly prokaryotic pico- or
nanoplankton), diazotroph (fixing nitrogen from the atmosphere) and large
phytoplankton. TOPAZ2 only implicitly simulates zooplankton activity. The
growth of phytoplankton depends on the level of photosynthetically active
irradiance, nutrients (e.g., nitrate, ammonium, phosphate and iron) and
temperature (see Sect. 2.3.2 and Appendix A).
Previous studies have shown that the GFDL-ESM2M captures the observed
large-scale biogeochemical patterns (Dunne
et al., 2012, 2013). The GFDL CM2.1 skillfully simulates primary modes of
natural climate variability (Wittenberg et al., 2006) and has
been extensively applied to assess seasonal and multiannual climate
predictions (Meehl et al.,
2013; Park et al., 2019).
Perfect model framework
We estimated potential predictability within a perfect model experiment.
By perturbing the initial conditions of the GFDL-ESM2M and quantifying the
spread of initially close model trajectories, the limit of initial
condition predictability was assessed. The underlying assumption is that we
have a perfect model (e.g., the model accurately represents all physical and
biogeochemical processes relevant to assess marine ecosystem drivers at
adequate temporal and spatial resolution) and nearly perfect initial conditions
and that we exclude the role for external forcing in determining or limiting
predictability. Specifically, we first performed a 300-year preindustrial
control simulation (black line in Fig. 1), which is branched off a
preexisting quasi-steady-state 1000-year preindustrial control simulation.
Using this 300-year preindustrial control simulation to provide initial
conditions, six 40-member ensemble simulations of 10-year duration each are
performed. Each ensemble simulation starts at different times in the control
simulation: 1 January in years 22, 64, 106, 170, 232 and 295. The six distinct initialization dates for the individual large
ensemble simulations were randomly selected from the 300-year preindustrial
control simulation. This was intended to average across biases that may
result from predictability being different across different phases of climate
modes (e.g., different El Niño–Southern Oscillation phase states) within
the preindustrial simulation. Note that the last ensemble exceeds the
control simulation by 5 years. Each of the six ensembles consists of 40
ensemble members with micro-perturbations to oceanic initial states but with
the same atmospheric, land, ocean biogeochemical, sea ice and iceberg
initial conditions. Specifically, for each ensemble member, i=1, 2,
..., 40, an infinitesimal temperature perturbation δ is
added to a single grid cell in the Weddell Sea at 5 m depth, similar to the
approach described in Wittenberg et al. (2014) and Palter et al. (2018):
δi=0.0001∘C×i+12:for odd i-i2:for even i.
Thus, the range of perturbations is evenly spread from -0.002
to 0.002 ∘C with the unperturbed control case in the center with
zero perturbation. As stated above, our model setup encompasses 240 ensemble
members, each of 10-year duration and thus 2400 years of model integration in
addition to the 300-year-long control simulation. While our perturbation
method is in no way optimal in terms of, for example, sampling the likely
range of atmospheric–ocean–biogeochemical errors, it is sufficient to
generate ensemble spread on the timescales of interest. After just 4 d
of simulation time subsequent to the micro-perturbations for each cluster of
40 starting points, the SSTs of all surface ocean grid cells are numerically
different from the SST of the control simulation, underscoring the rapidity
with which divergences due to nonlinearities in the model express
themselves. The method applied here mirrors that of Griffies
and Bryan (1997a), Msadek et al. (2010), and Wittenberg et al. (2014) and
emphasizes the amplitude (but not the phase) of perturbations to identify
potential predictability. Our perturbation method produces ensemble
experiments likely to give the upper limit of the model predictability,
hence the term potential predictability. Nevertheless, it warrants
mentioning here that studies have been published arguing that predictability
in the real world for some variables may even be larger than estimated with
the perfect modeling framework within an Earth system model in cases where
the ratio of the predictable mode to model noise is underestimated (Eade et al., 2014; Kumar et al., 2014).
Illustration of the model setup and the calculation of the
predictability time horizon. (a) Simulated global mean SST of the 300-year
reference control simulation (black line) and of the six 10-year-long 40
ensemble simulations (red lines). (b) Global mean SST anomaly (i.e.,
deviation from the control simulation) for the ensemble simulation starting
in the year 170. The thick red line indicates the period over which SST is
predictable (i.e., PPP ≥0.183), and thin red lines indicate the
period over which SST is unpredictable (i.e., PPP <0.183). The
dashed horizontal lines indicate 1 standard deviation of the control
simulation, and the vertical line indicates the predictability time horizon.
Analysis methods
We calculate the potential predictability for the four marine ecosystem
drivers: temperature, pH, O2 and NPP. In the following, NPP is always
integrated over the upper 100 m, whereas temperature, pH and O2 are
analyzed at different depth levels. In addition to identifying the upper
limits of predictability of these variables within the Earth system model,
an equally important objective is to identify the relative predictability of
the four variables under consideration.
Assessment of potential predictability
The prognostic potential predictability (PPP) is the main metric used in
this study to assess predictability. The PPP is the ratio between the
variance among the ensemble members at a given time t after the
initialization and the temporal variance of an undisturbed control
simulation. The PPP is calculated following Griffies and Bryan (1997b) and Pohlmann et al. (2004):
PPPt=1-1NM-1∑j=1N∑I=1MXijt-X‾jt2σc2,
where Xij is the value of a given variable for the jth ensemble and
ith ensemble member, X‾j is the mean of the jth ensemble over all
ensemble members, σc2 is the variance of the control
simulation, N is the total number of different ensemble simulations (N=6)
and M the number of ensemble members (M=40). The variance of the control
simulation is calculated for each month of the year separately to exclude
the seasonality from the natural variability, i.e., only the natural
variability at that month in the seasonal cycle is considered. PPP equal to
unity constitutes perfect predictability. An F test is applied to estimate a
significant difference between the ensemble variance and the variance of the
control run. With N=6 and M=40, predictability is achieved with a 95 %
confidence level when PPP ≥0.183.
The predictability time horizon is defined as the lead time at which PPP
falls below the predictability threshold (Fig. 1b). To calculate global
means, all metrics are first calculated at each individual grid cell and
then averaged with area weighting over the global ocean.
Taylor deconvolution method to identify mechanistic controls of
predictability
To understand the processes behind the simulated predictability, we applied
a first-order Taylor-series deconvolution method to decompose the normalized
ensemble variance of pH, O2 and NPP into contributions from their
physical and biogeochemical driver variables:
σf2≅∑i=1n∂f∂xiσxi2+2∑i<j∂f∂xi∂f∂xjCovxixj,
where σ denotes the standard deviation among the ensemble members of
the different variables. Specifically, the Taylor deconvolution method is
applied to decompose the normalized ensemble variance for f of pH,
O2 and NPP into the contribution from their physical and biogeochemical
drivers by expressing the ensemble variance and the variance of the control
run from Eq. (2) in terms of Eq. (3). The partial derivatives in
Eq. (3) are calculated at the point p=x, where x
is the mean value of the corresponding driver variables over the entire
control simulation.
The changes in pH are attributed to changes in temperature, salinity, total
alkalinity (Alk) and total dissolved inorganic carbon (DIC). Here, we
assume that variations in phosphate and silicate are negligible.
Dissolved oxygen (O2) is decomposed into an oxygen solubility component
O2sol and an apparent oxygen utilization (AOU) component using (e.g., Frölicher et al., 2009)
O2=O2sol-AOU.O2sol is the solubility of oxygen, which depends nonlinearly on
temperature and salinity (Garcia and Gordon,
1992). The difference between diagnosed O2sol and simulated
O2 is AOU. Variations in AOU reflect changes in oxygen consumption and
ocean ventilation. Earlier studies demonstrated that changes in AOU are
typically associated with changes in ventilation, as simulated changes in
the remineralization rates of organic material and in associated O2
consumption are relatively small (Gnanadesikan et al., 2012).
NPP can be decomposed into the contributions from the three phytoplankton
groups simulated in the TOPAZ2 model:
NPP=NPPSm+NPPDi+NPPLg,
where NPPSm, NPPDi and NPPLg are the contributions from
small, diazotroph and large phytoplankton, respectively. At any time t the
NPP for all phytoplankton groups “phyto” is given by the phytoplankton stock
Pphyto times the phytoplankton growth rate μphyto:
NPPphytot=μphyto(t)⋅Pphyto(t).
The growth rate μSm of the small phytoplankton is parameterized using
a maximum growth rate μmax, which is limited by nutrients Nlim,
light Llim and temperature Tf (see Appendix A for further
details):
μ=μmax⋅Nlim⋅Llim⋅Tf.
Note that grazing, sinking and other loss processes impact phytoplankton
stock, but these processes in TOPAZ2 are only a function of steady-state
growth and biomass implicit grazing formulation, and they exert no separate
dynamic control. Therefore they do not require separate consideration.
ResultsPotential predictability at the ocean surface
The change in globally averaged annual PPP over time is very similar for all
four marine ecosystem drivers at the surface, i.e., the PPP decreases
exponentially over lead time for all four drivers (solid thick lines in
Fig. 2). After 3 years, the PPP falls below the predictability
threshold (dashed line in Fig. 2), indicating that the global
predictability time horizon is about 3 years for all four ecosystem
drivers. The seasonality in PPP (solid thin lines in Fig. 2) as well as
the differences among the four drivers are very small at the global scale.
Globally averaged prognostic potential predictability (PPP) for
all four marine ecosystem drivers at the surface, except for NPP which is
integrated over the top 100 m. Monthly mean (thin lines) and annual mean
(thick lines) values of PPP are shown. The horizontal black dashed line
represents the predictability threshold. If PPP is above (below) the
predictability threshold, the driver is potentially predictable
(unpredictable) as indicated with the arrows on the right-hand side. The PPP
has first been calculated at each grid cell and then averaged globally.
Predictability time horizon for (a) SST, (b) surface pH, (c) surface O2 and (d) NPP integrated over the top 100 m using PPP as a
predictability measure. The red contour lines in panel (d) indicate the annual
mean total nitrogen production in moles of nitrogen per kilogram per year averaged over
the 300-year preindustrial control simulation to highlight regions with low
and high NPP. In panel (d) regions north of 69∘ N and south of
69∘ S have been excluded since NPP is zero during wintertime
there.
At the regional scale, the predictability time horizon shows distinct
structured patterns and also large differences between each of the four
different marine ecosystem drivers (Fig. 3). In general, SST (Fig. 3a),
surface pH (Fig. 3b) and surface O2 (Fig. 3c) share similar
predictability time horizon patterns with short predictability time horizons
(1–2 years) between 20 and 40∘ in both hemispheres,
intermediate predictability time horizons (3–5 years) in the tropical
oceans, and long predictability time horizons (>10 years) in the
North Atlantic between 40 and 70∘ N, in the Southern
Ocean between 40 and 65∘ S (except for surface pH)
and in the Arctic Ocean. Interestingly, the potential predictability time
horizon of surface pH is short relative to SST and surface O2 in the
Southern Ocean but longer over both the Caribbean and the eastern
subtropical North Pacific relative to SST. The Caribbean and the eastern
North Pacific are both regions of importance for resource management, given
the high density of neighboring human populations.
The NPP predictability time horizon pattern (Fig. 3d) is fundamentally
different from the patterns of the other three ecosystem drivers. NPP has
long predictability time horizons (6–10 years) in the midlatitudes, where
the annual mean NPP is generally small (indicated with contour lines in
Fig. 3d), but very short predictability time horizons of 0–1 years in the
Southern Ocean, the North Atlantic and the Pacific, as well as short
predictability time horizons of 1–3 years in the tropical oceans, where
annual mean NPP is high (Fig. 3d). The spatial pattern of the
predictability time horizon and the sequencing of predictability among the
ecosystem drivers is very similar when using two other metrics for potential
predictability, indicating that our results do not depend on the
predictability metric used (Appendix B).
PPP for all four ecosystem drivers averaged over 17 different
biomes at the surface, except for NPP, which is integrated over the top 100 m.
Monthly means are shown as thin lines, and annual means are shown as thick lines. The
horizontal dashed black lines in each panel represent the predictability
threshold. The lower right panel shows the boundaries and the geographical
location of biomes 1 to 17.
We further average the local potential predictability across 17
biogeographical biomes (Fig. 4) to highlight the pronounced seasonal cycle
in predictability for some variables in particular biomes. The biomes
capture patterns of large-scale biogeochemical function at the basin scale
and are defined by distinct SSTs, maximum mixed-layer depths, maximum ice
fractions and summer chlorophyll concentrations (Fay and
McKinley, 2014). As shown in Fig. 4, potential predictability exhibits
strong seasonality for SST, surface O2 and surface pH in the North
Atlantic (biomes 8, 9, 10 and 11), in the Southern Ocean (biomes 15 and 16)
and in the subtropical/subpolar gyre boundary region of the North Pacific
(biome 3). In all these biomes, predictability is higher during the cold
season (boreal and austral winter) and lower during the warm season. The
biomes with high seasonality in PPP are also the regions which generally
show larger predictability in the annual mean. The PPP values of SST and surface
O2 have almost identical seasonal amplitudes, while the seasonal
amplitude of the surface pH is generally smaller compared to SST and surface
O2 seasonal amplitude. Interestingly, the PPP for NPP generally shows
no large differences amongst the seasons, except in biome 8, which is
influenced by seasonal sea ice retreat and growth. Figure 4 also reveals other
interesting characteristics of PPP. For example, the changes in PPP over
lead time are very small, but they fluctuate around the predictability threshold
for NPP in biome 10 and for SST and O2 in biome 8, making the
predictability horizon in some biomes for some variables very sensitive to
small changes in PPP. In addition, the PPP for NPP in the eastern equatorial
Pacific (biome 6) shows large interannual variations with lead time,
indicating that even more ensemble members are needed to robustly assess the
predictability there. The PPP for SST in biome 17 (around Antarctica) is
even negative, indicating a higher variance simulated in the ensemble
simulations than simulated in the 300-year preindustrial control simulation.
The role of the subsurface ocean in the potential predictability of
marine ecosystem drivers
Next, we assess the predictability time horizon for temperature, O2 and
pH in the top 1000 m (Figs. 5 and 6). In theory, the subsurface ocean
should be expected to be predictable longer than the surface layer, as the
subsurface is not directly coupled to the high-frequency and relatively
unpredictable variability of the atmosphere. Indeed, the potential
predictability for temperature, oxygen and pH rapidly increases with depth
at the global scale (Fig. 5a–c). Below 300 m, the predictability time
horizon of all three ecosystem drivers exceeds a decade; i.e., the PPP is
still larger than the predictability limit (depth levels with no hatching in
Fig. 5a–c). Interestingly, the PPP at depth changes more rapidly with time
for temperature than for O2 and pH. In fact, the PPP for temperature is
constant below 500 m for a given year; i.e., the PPP value does not change
with depth. This is different for O2 and pH, for which the PPP
increases with all depth levels. Clearly, the overall increasing potential
predictability with depth can be attributed to the increasing disconnection
of the deeper ocean with the surface ocean (see also Sect. 3.3). However,
the biogeochemical processes lead to enhanced predictability below 500 m for
O2 and pH, relative to temperature.
PPP depth profiles for the top 1000 m for ocean temperature,
oxygen and pH at the (a–c) global scale and (d–f) in the North Atlantic. The
PPP is shown as monthly means. The light gray hatching indicates a PPP value
below the predictability threshold. The North Atlantic is defined as the
ocean area between 40 and 60∘ N in the North
Atlantic. Note that the variance over the control simulation for pH is zero
for approximately 0.4 % of grid cells at subsurface, which leads to an
undefined PPP value there (see Eq. 2). Such grid cells have been excluded
here.
The global mean picture of Fig. 5a–c obscures some interesting seasonal
features at the regional scale, which are highlighted in Fig. 5d–f for the
North Atlantic. Even though the North Atlantic is among the regions with the
largest potential predictability at the ocean surface, the predictability at
1000 m depth for pH and O2 is smaller in the North Atlantic than the
global average at the same depth (Fig. 5d–f), especially in boreal winter.
For example, the PPP in winter of year 3 for pH is 0.6 at the global scale
at 400 m depth (Fig. 5b) but only 0.3 in the North Atlantic (Fig. 5e).
The strong connection in the Atlantic between the ocean surface and the
upper 1000 m in winter increases the predictability but at the same time
decreases the potential predictability within the subsurface. Interestingly,
this effect is also visible for temperature but confined to the upper few
hundred meters. The reason is that anomalies from the ocean surface do not
penetrate as deep for pH and O2 as they do for temperature.
Spatial pattern of the predictability time horizon at (a–c) 300 m
and (d–f) 1000 m depth for (a, d) ocean temperature, (b, e) pH and (c, f) dissolved oxygen.
Figure 6 shows the spatial pattern of the predictability time horizon for
ocean temperature, O2 and pH at 300 m (panels a–c) and 1000 m (panels d–f) depth,
respectively. Although the predictability time horizon is close to 10 years
below 300 m on global average, there are specific regions with a reduced
predictability time horizon. At 300 m, these regions are the tropical
Pacific, the Indian Ocean and parts of the Southern Ocean (Fig. 6a–c). In
the equatorial Pacific and Indian Ocean averaged over 20∘ N and
20∘ S, the predictability is 4 years for temperature and 7 years for
O2 and pH. For temperature and O2, the
predictability time horizon drops to values lower than 5–6 years in the eastern
equatorial Atlantic. At 1000 m depth (Fig. 6d), the spatial pattern of
temperature predictability time horizon is similar to the one at 300 m.
Large parts of the equatorial Pacific and the Indian Ocean still show
relatively short predictability time horizons. This is not the case for
O2 and pH, for which the predictability time horizon largely increases
at 1000 m depth compared to 300 m depth in the eastern equatorial Pacific
and in the Indian Ocean as well as in the Southern Ocean, so that the
predictability time horizon of both O2 and pH is up
to 10 years almost everywhere. Only the western equatorial Pacific (for pH) and the central
equatorial Pacific (for O2) are characterized by reduced potential
predictability at 1000 m (predictability time horizons lower than 8 years).
Deconvolution into physical and biogeochemical control processes
The predictability patterns and timescales presented in the previous
sections are investigated next for their underlying dynamical and/or
biogeochemical controls. For SST, we compare our findings with previous
studies that attributed SST predictability to particular processes. In order
to understand the dynamical and biogeochemical control processes of O2,
pH and NPP and to quantify their contribution, we apply a Taylor
deconvolution method (see Sect. 2.3.2). It is important to note that a large
contribution of a particular driver to the potential predictability of
O2, pH and NPP does not imply a long predictability time horizon of
that driver. In addition, the contribution of a process depends not only on
its potential predictability (captured by the variance terms in Eq. 3)
but also on the potential interaction with the other drivers (covariance
terms in Eq. 3).
Sea surface temperature
The long predictability time horizon of SST in the North Atlantic between
40 and 70∘ N (Fig. 3a) is consistent with previous
findings (Boer,
2004; Collins et al., 2006; Griffies and Bryan, 1997a; Pohlmann et al.,
2004). The SST in the North Atlantic experiences low-frequency variability
that is linked to the Atlantic Meridional Overturning Circulation (AMOC; Buckley and Marshall, 2016). In GFDL-ESM2M, the
AMOC experiences strong low-frequency variability, consistent with Msadek et al. (2010), and its
predictability time horizon is about 9 years (Fig. C1). Similarly, the
Southern Ocean surface waters are also strongly connected to the deep ocean (Morrison et al., 2015), and slow subsurface ocean
processes there give rise to decadal predictability in SST (Marchi et al.,
2019; Zhang et al., 2017). In CM2.1, the peak in the power spectrum of deep
convection in the Weddell Sea is simulated to lie between 70 and 120 years (Zhang et al., 2017). In the North
Atlantic and the Southern Ocean, the potential predictability is enhanced
during the winter period (Fig. 4), as the surface waters are especially
well connected with the deep ocean during the cold season. The long SST
predictability time horizon in the Arctic Ocean is due to the overall
low-frequency variability in SST there, because these waters are permanently
covered by sea ice in the preindustrial ESM2M control simulation and cannot
exchange heat (and carbon) with the atmosphere. This is not the case around
the Antarctic continent, where sea ice almost vanishes during austral summer
in ESM2M, allowing the surface ocean to exchange heat and carbon with the
atmosphere. Therefore, the influence of high-frequency atmospheric
variability is large, which leads to diminished predictability time horizons
around Antarctica. Moderate predictability time horizons in SST of about 3
to 5 years are simulated in the tropical oceans associated with the coupled
atmosphere–ocean system (Boer, 2004).
Dissolved oxygen
To understand the processes that give rise to the O2 predictability
pattern, we use a Taylor deconvolution method (see Sect. 2.3.2) to further
split the O2 predictability into respective O2sol and AOU
contributions. Figures 7 and 8 show the predictability time horizon of
O2 (identical to patterns shown in Figs. 3c and 6c), O2sol,
AOU and their covariance (panels a, b, c and d) as well as their percentage
contribution to the normalized ensemble variance (panels e, f and g) for the
surface (Fig. 7) and 300 m depth (Fig. 8). The percentage contribution
is defined as the value of a given variance term (first term on the right-hand side of the equal sign in Eq. 3) or covariance term (second term
on the right-hand side in Eq. 3), divided by the sum of all absolute
variance and covariance values. By combining the information from
panels e, f and g (i.e., percentage contribution to total predictability) with the
information from panels a, b, c and d (i.e., predictability time horizon), we can
attribute the local predictability of O2 to O2sol, AOU
or the covariance. For example, if both the percentage contribution and the predictability time horizon of a particular variable are high, then the
O2 predictability is high. If the percentage contribution is generally
low for a particular variable, then this variable does not contribute to the
overall short or long predictability time horizon of O2.
Spatial pattern of the (a–d) predictability time horizons and
(e–g) contribution of different terms to the predictability of oxygen at the
surface. (a–d) Predictability time horizon for (a)O2, (b)O2sol, (c) AOU and (d) covariance between O2sol and
AOU. (e–g) Percentage contributions of (e)O2sol, (f) AOU and (g) covariance between O2sol and AOU relative to the sum of all terms.
Red shading in panels (e)–(g) represents positive absolute values of the variance and
covariance terms. The percentage contributions are shown as averages over
the entire 10 years of the simulations. The percentage contributions do not
change substantially over the 10 years (always within ±5 % of the
10-year averages).
The largest contribution to the normalized variance in O2 at the
surface stems from O2sol (Fig. 7) with a globally averaged
contribution of 58 %, followed by AOU with 23 % and the covariance
between O2sol and AOU contributing 19 %. Thus, the
O2sol predictability time horizon pattern (Fig. 7b) is almost
identical to the O2 predictability time horizon pattern (Fig. 7a or
Fig. 3c), i.e., long predictability time horizons in the North Atlantic,
Southern Ocean and Arctic and short predictability time horizons in the
midlatitudes. As O2sol at the ocean surface is mainly controlled
by temperature (Garcia and Gordon, 1992), it is
not surprising that the time horizon pattern of surface O2
predictability (Figs. 7a and 3c) is also almost identical to the time
horizon pattern of SST predictability (Fig. 3a). In the Arctic Ocean and
around Antarctica, however, AOU (Fig. 7f) is almost solely responsible for
the normalized variance of O2. As a result, the predictability time
horizon of O2 (Fig. 7a) is similar to the AOU predictability time
horizon (Fig. 7c) in these two regions. The covariance between
O2sol and AOU overall plays a minor role (Fig. 7g).
Same as Fig. 7, but at 300 m depth.
The picture is quite different at 300 m depth (Fig. 8), where the largest
contribution percentage-wise to the normalized variance of O2 stems
from AOU (64 % on global average), with minor contributions from
O2sol (13 %) and the covariance between O2sol and AOU
(23 %). Therefore, the pattern of the AOU predictability time horizon
(Fig. 8c) is similar to the pattern of the O2 predictability time
horizon (Fig. 8a). Exceptions are found in the eastern equatorial Pacific,
where the covariance dominates (Fig. 8g), and the northern North Atlantic,
where O2sol dominates (Fig. 8e). The dominance of AOU in
explaining subsurface O2 predictability is also the reason why O2
predictability generally increases with depth (Fig. 5c), which is not the
case for temperature (Fig. 5a).
pH
The predictability characteristics of pH are decomposed into its primary
drivers in the marine carbonate system, namely temperature, salinity, DIC
and Alk (Fig. 9). Even though the total normalized ensemble variances from
the Taylor deconvolution are only approximations of the total real ensemble
variances due to nonlinearities in carbonate chemistry, the values of the
Taylor deconvolution are always within ±2 % of the real values,
giving us confidence in the appropriateness of the Taylor deconvolution
method for pH.
Spatial pattern of the (a–f) predictability horizons and (g–k) contribution of different terms to the predictability of pH at the surface.
(a–f) Predictability time horizon for (a) pH, (b) SST, (c) Alk, (d) DIC, and
the covariance between (e) Alk and DIC and (f) DIC and SST. (g–k) Percentage contributions of (g) SST, (h) Alk, (i) DIC, and covariance of (j) ALK and DIC and (k) DIC and SST relative to the sum of all terms. Red
shading in panels (g)–(k) represents positive absolute values of the variance and
covariance terms. The percentage contributions are shown as averages over
the entire 10 years of the simulations. The percentage contributions do not
change substantially over the 10 years (always within ±5 % of the
10-year averages). Note that the terms that do not contribute to pH
predictability such as sea surface salinity and the covariances between sea
surface salinity and all other terms as well as the covariance between SST
and Alk are not shown here.
At the surface, the largest contribution percentage-wise stems from the
covariance between Alk and DIC (Fig. 9j; with 26 % globally averaged),
followed by DIC (Fig. 9i; 22 %), Alk (Fig. 9h; 15 %), the covariance
between SST and DIC (Fig. 9k; 14 %), and SST (Fig. 9g; 9 %). All
other possible contributors such as sea surface salinity and its covariances
(including the covariance between SST and Alk) are not discussed further, as
their contributions are below 5 %. The pH predictability time horizon at
the surface is mainly determined by Alk and DIC and to a lesser extent SST.
The long predictability time horizon of pH in the North Atlantic, the Arctic
Ocean and the eastern North Pacific and the short predictability time
horizon in the tropical regions (Figs. 9a and 3c) are mainly
determined by DIC and Alk and the covariance between DIC and ALK. SST plays
a role for parts of the North Atlantic. The predictability of pH in the
Southern Ocean is mainly determined by DIC, SST and their covariance. Even
though SST exhibits enhanced predictability in the Southern Ocean in
relation to pH, the short predictability time horizon of DIC and the
covariance of DIC and SST lead to the overall diminished predictability
time horizon for pH relative to SST there.
Same as Fig. 9, but at 300 m depth.
The pH predictability time horizon at 300 m depth (Fig. 10a) is mainly
determined by DIC (accounts for 44 % on a global scale; Fig. 10j) and to a
lesser extent by the covariance between DIC and SST (19 %; Fig. 10k) and
the covariance between Alk and DIC (15 %; Fig. 10j). Interestingly, the
relatively short pH predictability time horizon of about 5 years in the western
equatorial Pacific and the northern Indian Ocean is also mainly determined
by DIC (Fig. 10d, i) and the covariance between DIC and SST (Fig. 10f, k). The
short predictability time horizon of pH in the South Pacific is caused by
the covariance between SST and DIC. Again, salinity plays a negligible role
(not shown).
Net primary production
To understand the drivers that may set the upper limits of NPP
predictability, we first split the NPP into the contributions from small-phytoplankton production (NPPSm), large-phytoplankton production
(NPPLg) and production by diazotrophs (NPPDi; see Sect. 2.3.2
and Appendix A). The largest contribution (i.e., the most important driver of
NPP potential predictability) stems from NPPSm (65 % averaged
globally; Fig. 11). The second most important contributor is the
covariance between NPPSm and NPPLg (19 %) followed by NPPLg
(9 %). Diazotrophs and all other covariances have only a small impact on
the predictability of NPP (less than 5 %; not shown in Fig. 11). The
large dominance of NPPSm is not unexpected as the small-phytoplankton
production overall dominates the total phytoplankton production in ESM2M (Dunne
et al., 2013; Laufkötter et al., 2015). NPPSm accounts for 84 %
of the total NPP at global scales, whereas NPPLg and NPPDi only
account for 14 % and 2 %, respectively.
Spatial pattern of the (a–d) predictability horizons and (e–g) contribution of different terms to the predictability of NPP integrated over
the top 100 m. (a–d) Predictability time horizon for (a) NPP, (b) large-phytoplankton production NPPLg, (c) small-phytoplankton production
NPPSm, and (d) the covariance between NPPLg and NPPSm. (e–g) Percentage contributions of (e) NPPLg, (f) NPPSm, and (g) covariance of NPPLg and NPPSm relative to the sum of all terms.
Red shading in panels (e)–(g) represents positive absolute values of the variance and
covariance terms. The percentage contributions are shown as averages over
the entire 10 years of the simulations. The percentage contributions do not
change substantially over the 10 years (always within ±5 % of the
10-year averages). Note that the terms that do not substantially contribute to
NPP predictability such diazotrophs (NPPDi) and the covariances
between NPPDi and all other terms are not shown here.
On regional scales, NPPSmdetermines the
predictability of NPP almost everywhere (Fig. 11f). Exceptions are the eastern equatorial
Pacific and the higher northern latitudes, where NPPLg (Fig. 11e) and
the covariance between NPPLg and NPPSm (Fig. 11g) also play a
substantial role. Interestingly, the NPPLg (Fig. 11b) has overall a
longer predictability time horizon than NPP (Fig. 11a) and NPPSm
(Fig. 11c).
Spatial pattern of the (a–d) predictability horizons and
(e–g) contribution of different terms to the predictability of small-phytoplankton production (NPPSm) integrated over the top 100 m. (a–d) Predictability time horizon for (a) NPPSm, (b) small-phytoplankton
stock, (c) growth rate of small phytoplankton, and (d) the covariance
between the stock and the growth rate of small phytoplankton. (e–g) Percentage contributions of (e) stock, (f) growth rate, and (g) covariance
of stock and growth rate relative to the sum of all terms. Red shading in
panels (e)–(g) represents positive absolute values of the variance and covariance
terms. The percentage contributions are shown as averages over the entire 10 years of the simulations. The percentage contributions do not change
substantially over the 10 years (always within ±5 % of the 10-year
averages).
To understand the drivers of small-phytoplankton predictability, we further
deconvolve NPPSm into growth rate and small-phytoplankton stock (Fig. 12; Eq. 6 in Sect. 2.3.2). The deconvolution suggests that the
largest contribution to the potential predictability on a global scale stems
from the small-phytoplankton stock (51 %) followed by the growth rate
(31 %) and the covariance between stock and growth rate (18 %). Between
40∘ S and 40∘ N, the NPPSm predictability is almost
solely determined by the small-phytoplankton stock, with the exception of
the eastern equatorial Pacific, where the growth rate is more important.
Also, the short NPPSm predictability time horizon in the North Atlantic
mainly originates from the variance of the stock, indicated by the short
predictability time horizons of the stock compared to the growth rate there.
As we stated previously, NPP has a relatively short potential predictability
time horizon over the Southern Ocean compared to the other ecosystem drivers
(Fig. 3d). Our analysis shows that small phytoplankton (Fig. 11) and
especially the growth rate of the small phytoplankton (Fig. 12) are
important for setting this local minimum.
Spatial pattern of the (a–e) predictability horizons and (f–i) contribution of different terms to the predictability of the small-phytoplankton growth at the surface. (a–e) Predictability time horizon for
(a) growth rate of small phytoplankton, (b) nutrient limitation, (c) temperature limitation, (d) light limitation, and (e) the covariance between
the temperature and nutrient limitation. (f–i) Percentage contributions of
(f) nutrient limitation, (g) temperature limitation, (h) light limitation,
and (i) covariance between temperature and nutrient limitation relative to
the sum of all terms. Red shading in panels (f)–(i) represents positive absolute
values of the variance and covariance terms. The percentage contributions
are shown as averages over the entire 10 years of the simulations. The
percentage contributions do not change substantially over the 10 years (always
within ±5 % of the 10-year averages). Note that the terms that do not
substantially contribute to NPP predictability covariances between
temperature and light and nutrients are not shown here. The hatching in panel (f) indicates the limiting nutrients as obtained from the 300-year-long
preindustrial control simulation.
We further deconvolute the drivers of the surface growth rate predictability
of small phytoplankton into their temperature, nutrient and light limiting
factors (see Eq. 7 in Sect. 2.3.2; Fig. 13). As the limiting factors are
not saved routinely as three-dimensional fields, we focus here on the growth
rate and its limiting factors at the surface. Note that the growth rate
predictability time horizon at the surface (Fig. 13a) may differ from the
growth rate predictability time horizon integrated over the top 100 m
(Fig. 12c), especially in the Southern Ocean and the North Atlantic. At
the surface and at the global scale, the largest contribution stems from the
nutrient limitation term (50 %) followed by the temperature limitation
term (25 %) and the covariance between the temperature and nutrient
limitations (13 %). At the regional scale, the nutrient limitation term
clearly dominates at midlatitudes (Fig. 13f). In GFDL-ESM2M, the
subtropical gyres are mainly iron limited (hatching in Fig. 13f), and
therefore iron fundamentally constrains the predictability of the growth
rate of small phytoplankton there. Exceptions are the boundary region
between the subtropical and subpolar gyre in the North Pacific (nitrate
limited) as well as the tropical Atlantic (phosphate and nitrate) and the
northern Indian Ocean (phosphate). GFDL-ESM2M's overall strong iron
limitation is in contrast to the findings of Moore et al. (2013), who suggest that nitrogen is the limiting nutrient in the
subtropical gyres. GFDL-ESM2M is a fully coupled Earth system model and
assesses iron limitation through the ability to synthesize chlorophyll. In
contrast, Moore et al. (2013) use
observation-driven parameterizations of phytoplankton growth and assess iron
limitation through nutrient uptake alone. The temperature limitation term is
dominant in the higher latitudes and the eastern equatorial Pacific (Fig. 13g). The light limitation term only plays a substantial role (up to 20 %)
around Antarctica and close to the Arctic sea ice edge (Fig. 13h). The
simulated long predictability time horizon for NPP in the midlatitudes can
therefore be attributed to the long predictability time horizon of the
nutrient limitation, especially given that the growth rate predictability at the
surface is similar to the growth rate predictability integrated over the top
100 m in this region. At latitudes north of 40∘ N and south of
40∘ S, the temperature limitation is the most important
contributor. Therefore, the predictability time horizon pattern of the
growth rate strongly resembles the one for SST in these regions. In the
Southern Ocean, however, the growth rate predictability time horizon at the
surface is much longer than the growth rate predictability integrated over the
top 100 m, indicating that a process other than temperature (e.g., light
limitation) may limit predictability there.
Discussion and conclusion
We set out three goals for this study: (a) assessing the global
characteristics of potential predictability for temperature, pH, O2 and
NPP, as a mean to identify an upper bound on our ability to predict
conditions for marine ecosystems; (b) assessing regional and depth-dependent
characteristics of potential predictability; and (c) identifying the
potential mechanisms that limit or increase predictability for the different
marine ecosystem drivers. This was pursued within a perfect modeling
framework using a comprehensive Earth system model.
The analysis revealed that on global scales the predictability time horizon
of each variable is surprisingly similar, i.e., 3 years for all four
marine ecosystem drivers (Fig. 2; first goal), despite the fact that the
regional processes operating are different over a range of scales (second
and third goal). This is unexpected, as the ocean processes that sustain the
disparate divers should not be expected to have identical memory as pertains
to predictability. For example the relatively long predictability time
horizon identified for SST and surface O2 over the subpolar North
Atlantic (the SST to be consistent with Griffies
and Bryan, 1997a, b; Boer, 2000; Collins et al., 2006; Keenlyside et al., 2008) and
the Southern Ocean (consistent
with Zhang
et al., 2017 and Marchi et al., 2019) is not reflected in NPP. Likewise,
the long predictability time horizon of NPP in the subtropical gyres is not
simulated for other ecosystem drivers, and the short predictability time
horizon of surface pH in the Southern Ocean is reflected in neither SST nor surface O2.
Our results suggesting the same global predictability time horizon for all
four ecosystem drivers are not inconsistent with time of emergence
diagnostics for transient climate warming scenarios where pH (early
emergence) and NPP (late emergence) behave oppositely (Frölicher
et al., 2016; Rodgers et al., 2015; Schlunegger et al., 2019). Time of
emergence is defined as the ratio (large for pH and small for NPP) of the
anthropogenic forced change to the background internal variability.
Comparing our results with the time of emergence analysis is therefore
complicated by the presence of the anthropogenic forced signal in scenario
projections. In fact it is the presence of the large invasion flux for
CO2 that renders acidification the most rapidly emergent of the drivers
under anthropogenic perturbations, in particular relative to NPP. The
similarities between the analyses of predictability and emergence timescales
lie in the noise, which is expected to include not only modes of climate
variability such as El Niño–Southern Oscillation (ENSO) but also higher-frequency variability such as
cloud cover that may impact NPP for both cases.
Our study complements earlier studies which suggested that marine ecosystem
drivers may be predictable on multi-annual timescales. In contrast to
earlier studies (Chikamoto
et al., 2015; Park et al., 2019; Séférian et al., 2014b), rather
than focusing on a single ecosystem driver, we compare and contrast the
potential predictability of four marine ecosystem drivers and also evaluate
the processes behind their respective predictability limits. We find that in
contrast to SST, these ecosystem drivers depend on a complex interplay
between physical and biogeochemical underlying processes. For O2, the
importance of subsurface AOU reveals a complex interplay between nonlocal
circulation and biological consumption, whereas at the surface O2 is
mainly determined by the predictability of SST. For NPP, the growth rate of
the small phytoplankton in the Southern Ocean is important for setting the
local minimum in predictability time horizon there. The predictability time
horizon of surface pH is mainly determined by a complex interplay between
DIC and Alk predictability in the low latitudes and DIC, Alk and temperature
predictability in high latitudes. Interestingly, we find longer
predictability time horizons for SST than for NPP in the equatorial Pacific,
which is in contrast to findings of Séférian et al. (2014a). Importantly, this may be indicative of a potential model dependency
of the relationship between ecosystem driver predictability. Séférian et al. (2014b)
attributed longer NPP predictability time horizons to the idea that the
nutrient supply processes that modulate NPP are themselves regulated by
thermocline wave adjustment processes, without sizable modulation by
surface fluxes. This was framed as being in contrast to the case of SST,
where air–sea fluxes reflecting higher-frequency variations act to reduce
the predictability of SST. In ESM2M, the predictability time horizon for SST
in the eastern equatorial Pacific (biome 6 in Fig. 4) is approximately 3.5 years, modestly longer than the predictability time horizon for NPP of
approximately 3 years. In ESM2M, NPP is only weakly correlated with changes in
upwelling and nutrient supply in the eastern tropical Pacific (as was shown
in Fig. 2 of Kwiatkowski et al., 2017). This is confirmed
by our analysis showing that nutrient limitation is not the dominant term
for explaining the predictability of NPP there. This indicates that less
predictable processes occurring over shorter timescales, such as temperature
and/or light level variations, influence NPP predictability.
Even though we consider our conclusion to be robust, a number of potential
caveats warrant discussion. These include the (i) ensemble design of the
perfect model simulations (e.g., initialization and number of ensemble
members) and (ii) the impact of model formulation and biases. For the first
of these caveats, our simulations are all initialized with SST perturbations
applied to a single grid cell in the Weddell Sea, and therefore a different
spatial perturbation strategy may give different results. However, as the
signal at the ocean surface spreads very rapidly (i.e., after 4 d all
grid cells at the ocean surface are perturbed) our results are insensitive
to the spatial initialization method, at least in the upper ocean. Second,
all ensemble simulations start on 1 January of the corresponding
simulation year. It has been shown that the forecast skill of seasonal
predictions may depend strongly on the way the models are initialized. ENSO
forecasts, for example, have a much lower predictability if they are
initialized before and through spring (Webster and Yang, 1992). However,
as our focus is on annual to decadal timescales, this effect is less
important for our analysis. Third, we have employed only six starting points
for our 40-member ensemble simulation. Even though all six ensemble
simulations branched off at different El Niño–Southern Oscillation
states of the preindustrial control simulation, our choice of six
macro-perturbations may still introduce aliasing issues that could bias our
results. Although the computing resources at our disposal for this study did
not allow for expanding the number of starting points, we recommend that
future studies with CMIP-class models should expand the number of
initialization points to further explore the sensitivity of the results to
the starting point of the ensembles.
The second caveat in our study is that we only used one single Earth system
model and that our results might depend on the model formulation and
resolution. Even though the GFDL-ESM2M model achieves sufficient fidelity in
its preindustrial states (Bopp
et al., 2013; Dunne et al., 2012, 2013; Laufkötter et al., 2015), it is
well known that CMIP5-generation models have imperfect representation of
biogeochemical and physical processes as well as variability over a range of
timescales, ranging from weather variability to ENSO variability (Frölicher
et al., 2016; Resplandy et al., 2015) to decadal variability (England et al., 2014; McGregor et al.,
2014). Different physical and biogeochemical parameterizations within a
given model may change the length of the predictability time horizon. For
example, TOPAZ2 represents a hypothetically optimal phytoplankton
physiology; namely the model assumes that the fastest growing phytoplankton
group always wins in all environments via the upper limit in growth rates.
In addition, TOPAZv2 represents a steady-state ecosystem, such that there
are no time lags between primary production and the grazing response. In the
subsurface, the remineralization of particles is set to reproduce the
vertical scale of the nutricline on the timescale of sinking particles, and
the sinking particle velocity is fast. All three factors may tend to
decrease the memory associated with the real-world surface ecosystem and
minimize predictability. For the case of weather prediction, it has been
argued that the inclusion of stochastic parameterizations increases potential
predictability (Palmer and Williams, 2008). To our
knowledge, this remains unexplored for marine biogeochemistry and ecosystem
drivers. In any case, it would be necessary to repeat our predictability
experiments with a set of different Earth system models including different
parameterizations of biogeochemical and/or physical ocean processes to
investigate the dependence of our result on the model representation (Séférian et al., 2018), in parallel with
broader efforts to further evaluate noise characteristics of these models.
Additionally, the ocean model resolution of GFDL-ESM2M is rather coarse and
cannot represent the critical scales of small-scale structures of
circulation. Predictability studies using high-resolution ocean models with
improved process representations are therefore needed to explore potential
predictability, especially at the local scale. However, it is currently
impossible in many cases to constrain the simulated variability in
biogeochemical drivers, especially for the ocean subsurface, with
observations due to limited data availability (Frölicher
et al., 2016; Laufkötter et al., 2015).
Currently, no global coupled physical–biogeochemical seasonal to decadal
forecast system is yet operational (Tommasi et al.,
2017). However, our study suggests great promise that
physical–biogeochemical forecast systems may have the potential to provide
useful information to a wide group of stakeholders, such as, for example,
for the management of fisheries (Dunn et
al., 2016; Park et al., 2019). Our study therefore underscores the need to
further develop integrated physical–biogeochemical forecast systems.
Especially in regions with long predictability time horizons, such as the
North Atlantic (for temperature, O2 and pH), the Southern Ocean (for
temperature and O2) and midlatitudes (for NPP), installing and
maintaining a spatially and temporally dense physical and biogeochemical
ocean observing system would have the potential to significantly improve the
effective predictability of marine ecosystem drivers.
The NPP in TOPAZ2, defined as the phytoplankton nitrogen production, is
individually described for all phytoplankton groups i by the product of a
phytoplankton growth rate μi and the amount of nitrogen in the
plankton group Ni (see Table A1 for numerical values of parameters used in TOPAZ2):
NPPi=μi⋅Ni.
The growth rate of the small-phytoplankton group is given by a maximum
growth rate times the limiting factors of nutrients Nlim, light
Llim and temperature Tf:
μSm=μmax′1+ζ⋅Nlim⋅Llim⋅Tf.
The temperature limitation factor is
Tf=expkepp⋅T.
The nutrient limitation factor is
Nlim=minNFe,NPO4,NNO3+NNH4,
with iron limitation
NFe=QFe:N2QFe:N2+KFe:N2
with
QFe:N=minQFe:Nmax,FeSmNSm,
with phosphate limitation
NPO4=QP:NQP:Nmax
with
QP:N=minQP:Nmax,PSmNSm,
with nitrate limitation
NNO3=NO3NO3+KNO3⋅1+NH4KNH4,
and with ammonium limitation
NNH4=NH4NH4+KNH4.
The light limitation factor is
Llim=1-exp-αθIRRNlimTfμmax
with
θ=θmax-θmin1+θmax-θminαIRRmem/2NlimTfμmax+θmin
and
θmin=max0,θminnolim-θminlim⋅Nlim+θminlim,
where IRR describes the photosynthetically active radiation
and IRRmem is the irradiation memory over the last 24 h.
TOPAZ2 parameters for small phytoplankton.
ParameterValueUnitsDescriptionζ0.1Photorespiration losskepp0.063∘C-1Temperature coefficient for growthα2.4×10-5⋅2.77×1018/g C (g Chl)-1 m2 W-1 s-1Light harvest coefficient6.022×1017μmax′1.5×10-5s-1Maximum growth rate at 0 ∘Cθminnolim0.01g Chl (g C)-1Minimum Chl : C without nutrient limitationθminlim0.001g Chl (g C)-1Minimum Chl : C with complete nutrient limitationθmax0.04g Chl (g C)-1Maximum Chl : CKNO32×10-6mol N kg-1NO3 half-saturation coefficientKNH42×10-7mol N kg-1NH4 half-saturation coefficientKFe:N12×10-6⋅106/16mol Fe (mol N)-1Half-saturation coefficient of iron deficiencyQFe:Nmax46×10-6⋅106/16mol Fe (mol N)-1Maximum Fe : N limitQP:Nmax0.1458mol P (mol N)-1Maximum P : N limit
Potential predictability may depend on the choice of the predictability
metric (Hawkins et al., 2016). Therefore, we
calculate two additional metrics to assess the robustness of our results:
the normalized root-mean-square error (NRMSE) and the intra-ensemble anomaly
correlation coefficient (ACCI). The NRMSE is similar to the PPP but
uses standard deviations instead of variances and compares every ensemble
member to every other member of that ensemble, thereby increasing the
effective sample size (Collins et al., 2006):
NRMSEt=1-Xijt-Xkj(t)2i,j,k≠i2σc2.〈⋅〉 means that we sum over the listed indices and divide by the degrees of
freedom. The intra-ensemble anomaly correlation coefficient (ACCI) is a
measure for the correlation between the anomaly of all ensemble members of
an ensemble averaged over all ensembles and is regularly used for assessing
operational predictions (Goddard et
al., 2013). The anomaly is defined as the deviation of a given value from
the climatological mean μj (i.e., the mean over the control run) over
the jth ensemble period.
ACCIt=Xijt-μjXkj(t)-μji,j,k≠iXijt-μj2i,j
While PPP and NRMSE estimate predictability by comparing the spread of the
ensembles to the natural variability from the control simulation, the
anomaly correlation coefficients include the phase alignment of the
ensembles and the control simulation. We again use a F test for NRMSE and a
t test for ACCI to estimate the predictability threshold.
SST predictability time horizon calculated with different
metrics. Spatial pattern of the predictability horizon for sea surface
temperature using (a) PPP, (b) NRMSE and (c) ACCI. Note that we assume
an arbitrary predictability threshold for ACCI so that the emerging
pattern matches the PPP predictability best. This allows us to compare the
relative differences in predictability.
Figure B1 compares the two additional metrics applied to SST with the PPP
metric. We introduce an artificial predictability threshold for ACCI
in such a way that the emerging pattern matches the predictability time
horizon best. This allows us to compare the relative differences in
predictability between the metrics best. The predictability pattern for SST
obtained from all three metrics is very similar. In particular the patterns
obtained using PPP and NRMSE are nearly identical. This can be expected
since both the PPP and the NRMSE estimate potential predictability by
analyzing the ensemble spread. The ACCI shows some small differences from
PPP and NRMSE, especially in the Southern Ocean and the North Pacific.
(a) Simulated annual mean AMOC maximum of the 300-year-long
preindustrial control simulation. The blue line indicates the 10-year running
mean. (b) Monthly mean (thin line) and annual mean (thick line) prognostic
potential predictability for the AMOC maximum. The horizontal black dashed
line represents the predictability threshold.
Data availability
The GFDL-ESM2M simulations are available upon request.
Author contributions
TLF, KBR, LR and CCR designed the study. TLF set up the ensemble
simulations and KBR performed the simulations. JD is the lead developer of TOPAZ2. LR performed most of the
analysis. TLF wrote the initial manuscript. All authors contributed
significantly to the writing of the paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Thomas L. Frölicher and Luca Ramseyer acknowledge support from the Swiss National Supercomputing Centre (CSCS). The authors thank Friedrich Burger for discussions on the
Taylor deconvolution method and Natacha Le Grix for discussion on the
TOPAZ2 model code.
Financial support
This research has been supported by the Swiss National Science Foundation (grant no. PP00P2_170687), the EU H2020 (grant no. 821003) and the Institute for Basic Science (grant no. IBS-R028-D1).
Review statement
This paper was edited by Stefano Ciavatta and reviewed by Mark Baird and one anonymous referee.
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