2.1 Model setup

We used a GOA configuration of the three-dimensional physical Regional Oceanic Model System (ROMS; Shchepetkin and McWilliams, 2005). ROMS is a free-surface, hydrostatic primitive equation and finite volume (Arakawa C-grid) ocean circulation model. The vertical discretization is based on a terrain-following coordinate system (50 depth levels), with increased resolution towards the surface and the bottom of the ocean. Due to shallower bathymetry, the shelf and coastal areas have higher vertical resolution. For example, in the shallowest areas (depth = 0.5 m), the vertical spacing is 0.01 m, whereas in the deepest water, the vertical spacing is 5 m in surface waters, expanding smoothly to over 300 m near the bottom. The horizontal resolution is eddy-resolving at 4.5 km, which resolves regional coastal upwelling scales. The grid covers a large coastal area from the southern tip of Prince of Wales Island in the southeast to west of Sand Point in the middle of the Aleutian Islands (Fig. 1). The current model configuration is based on Danielson et al. (2016), although with a larger grid extent and a lower horizontal resolution to accommodate the computationally intense ecosystem model. Our GOA-COBALT domain is based on Coyle et al. (2012), although it includes the Alexander Archipelago. Experiments with the Coyle et al. (2012) model have shown that the model had insufficient near-surface vertical mixing, leading to overly fresh water at the surface, which is challenging to mix down. In order to improve on our surface mixing, we added the parameterization of Li and Fox-Kemper (2017). They looked to large-eddy simulations (LESs) to study the effects of unresolved Stokes drift driven by surface waves and the resulting Langmuir circulation on the vertical mixing in a variety of stratification regimes. Their parameterization is now being routinely used in global climate simulations (e.g., Adcroft et al., 2019).

The biogeochemical model used for this study is a modified version of the Carbon, Ocean Biogeochemistry and Lower Trophic (COBALT) marine ecosystem model, which has been applied on a global scale in conjunction with the Earth system model from the Geophysical Fluid Dynamics Laboratory (GFDL) (Stock et al., 2014). Only recently, COBALT was coupled to ROMS and modified with an additional coastal chain-forming diatom to better represent biogeochemical processes and properties in highly productive coastal regions (3PS-COBALT, Van Oostende et al., 2018). 3PS-COBALT resolves the cycles of nitrogen, carbon, phosphate, silicate, iron, calcium carbonate, oxygen, and lithogenic material with 36 state variables. The model contains small phytoplankton that are grazed by microzooplankton; a medium phytoplankton that can be consumed by small copepods; and a larger, chain-forming diatom, which can only be grazed by large copepods and krill. Light, temperature, the most limiting nutrient, and metabolic costs are used to calculate primary productivity for each phytoplankton group. The chlorophyll-to-carbon ratio is dynamic and is based on light (Manizza et al., 2005) and nutrient limitations. Iron limitation depends on an internal cell quota and nitrate and phosphate limitations are simply dependent on their ambient concentrations in the seawater. The currency of biomass and productivity in the model is nitrogen. Organic nitrogen is converted into organic carbon following the Redfield ratio of 106 : 16 (Redfield et al., 1963). DIC and TA are state variables and dictate the inorganic carbon system. Like all other tracer concentrations in the model, these two variables are affected by diffusion, horizontal and vertical advection, and sources minus sink terms that include net primary production, CaCO₃ formation and dissolution both in the water column and sediments, detritus remineralization in the water column and sediments, zooplankton respiration, and atmosphere–ocean CO₂ fluxes. The Chl-a-specific initial slope of the photosynthesis–light curve and the iron-scavenging coefficient onto sinking detritus were both adjusted to better represent the GOA biogeochemistry and ecosystem (Table 1). All other constants are based on Van Oostende et al. (2018).

Table 1Summary of the definitions, abbreviations, values, and units of the model parameters adjusted from Van Oostende et al. (2018) to better represent the ecosystem in higher northern latitudes (Strom et al., 2010). $a=\mathrm{365.25}\cdot \mathrm{24}\cdot \mathrm{3600}$, and b=4.5998.

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2.2 Initial conditions, boundary conditions, and forcing

Physical initial and boundary conditions for currents, ocean temperature, salinity, and sea surface height were taken from the Simple Ocean Data Assimilation ocean/sea ice reanalysis 3.3.1 (SODA, Carton et al., 2018, available as 5-day averages). After a model spin-up of 10 years, the hindcast simulation (1980 to 2013) was forced at the surface with 3-hourly winds, surface air temperature, pressure, humidity, precipitation, and radiation from the Japanese 55-year Reanalysis (JRA55-do) 1.3 project (Tsujino et al., 2018). The atmospheric fields were used to compute surface stresses and fluxes using a bulk flux algorithm (Large and Yeager, 2008). Precipitation was solely counted as a negative salt flux and did not change any volume or dilute any other tracers, such as DIC and TA. Along its coastal boundary, freshwater was brought in from numerous rivers and tidewater glaciers. This was done with a point-source river input via exchange of mass, momentum, and tracers through the coastal wall at all depths (Danielson et al., 2020). A hydrological model provided riverine input at a 1 km resolution and at a daily time step (Beamer et al., 2016). The hydrological model was based on a suite of weather, energy balance, snow/ice melt, soil water balance, and runoff routing models forced with Climate Forecast System Reanalysis data (Saha et al., 2010). The reanalysis data were regridded from their 0.2 degree resolution to the 1 km hydrological model grid using MicroMet (Liston and Elder, 2006). Nutrient, DIC, and TA concentrations in the freshwater were based on available observations and are summarized in Table 2. As found in other freshwater data (Rheuban et al., 2019), DIC concentrations were higher than TA, showing that the freshwater discharging into the GOA is quite acidic (Stackpoole et al., 2016, 2017).

Table 2Table listing riverine dissolved inorganic carbon, total alkalinity, nitrate, dissolved iron, dissolved oxygen, and temperature values. When seasonal observations were available, the variables followed a seasonal cycle. These variables are listed with their minimum, mean, and maximum levels. The values of all other variables were initialized at a very small number (<0.0001).

^* Aguilar-Islas et al. (2015) observed a maximum of 10 nmol kg⁻¹ dFe in nearshore waters with a salinity of 25. In order to model high nearshore dFe values (see Fig. 2), riverine dFe was set to 30 nmol kg⁻¹.

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DIC and TA initial conditions for the hindcast simulation were extracted from the mapped version 2 of the Global Ocean Data Analysis Project (GLODAPv2.2016b, Lauvset et al., 2016) data set. GLODAP DIC data, which were referenced to 2002, were normalized to 1980 using the anthropogenic CO₂ estimates for the GOA by Carter et al. (2017). Carter et al. (2017) suggest two different rates of the depth-dependent increase of anthropogenic CO₂ per year for the period from 1980 to 1999 and for the period from 2000 to the present. The anthropogenic CO₂ increase for the corresponding time period was added (or subtracted) in monthly increments from the reference year. A seasonal cycle was added to the surface based on Takahashi et al. (2014). Following Hauri et al. (2013), DIC and TA were assumed to vary throughout the upper 200 m of the water column, but they were attenuated proportional to the seasonal variations of temperature across depth. Each year, DIC boundary conditions increased as a result of anthropogenic CO₂ increase, following estimates for the region made by Carter et al. (2017). Nitrate, phosphate, oxygen, and silicate initial conditions were taken from the World Ocean Atlas 2013 (Garcia et al., 2013). All other variables were initialized based on a climatology from a GFDL-COBALT simulation (1988–2007) forced by Common Ocean-ice Reference Experiment (CORE-II) data, as described in Stock et al. (2014). Atmospheric pCO₂ was forced with monthly means derived from the Mauna Loa CO₂ record (https://www.esrl.noaa.gov/gmd/ccgg/trends/data.html, last access: 22 January 2018).

3.1 Physics

The model domain is strongly influenced by freshwater coming from hundreds of glacier-fed rivers and tidewater glaciers that ring the GOA. Our approach of using a hindcast simulation from a highly resolved land hydrography model (Beamer et al., 2016) to force the freshwater input was recently evaluated through comparison to salinity, temperature, velocity, and dynamic height observations (Danielson et al., 2020). The findings of Danielson et al. (2020) are summarized in the following paragraph. The influence of the springtime freshet is well reproduced by the model, with low salinities (∼26 PSU) in the nearshore upper 10–20 m of the water column (r∼0.5–0.6, p∼0.05). While the correlation between salinity observations and model output is only slightly weaker in summertime, the model has difficulty in reproducing small-amplitude salinity variations between October and March, when riverine input is lowest and the signal-to-noise ratio of salinity is small. Temperature is particularly well modeled in the first half of the year, with the highest correlations (r∼0.9, p<0.05) in the middle of the water column. The model is also able to skillfully reproduce monthly dynamic height anomalies in summer, fall, and winter (not shown). Overall, the freshwater fluxes used in this study are more realistic than in previous studies because they are derived from a temporally and spatially highly resolved hindcast simulation forced with meteorological reanalysis data sets. Compared with previous studies (Royer, 1982; Wang et al., 2004; Hill et al., 2015; Siedlecki et al., 2017), this current model configuration is better able to reproduce low salinity levels in coastal areas across the GOA and can, therefore, more adequately reproduce the Alaska Coastal Current (Danielson et al., 2020).

3.2 Nutrients and Chl-α

High concentrations of biologically available dFe prevail across the inner to mid GOA shelf due to the dFe-rich input of glacially fed rivers (Aguilar-Islas et al., 2015; Wu et al., 2009; Lippiatt et al., 2010). While these shelf areas are low in NO₃, they border the NO₃-rich and dFe-poor waters off the shelf (Martin et al., 1989). The spatial variability of these two limiting nutrients orchestrate the phytoplankton community composition, with diatom-dominated areas in the dFe-rich nearshore environment and small phytoplankton in dFe-depleted offshore areas (Strom et al., 2010). Here, we first evaluate the modeled spatial variability of surface dFe, NO₃, and Chl-α by comparing them to in situ and satellite observations (Aguilar-Islas et al., 2015; Lippiatt et al., 2010; Crusius et al., 2017; MODIS-Aqua Ocean Color Data, NASA Goddard Space Flight Center, Ocean Ecology Laboratory, 2014).

Figure 2Observed (left) and GOA-COBALT-simulated (middle) surface dissolved iron (a, dFe, nmol kg⁻¹) and nitrate (b, NO₃, µmol kg⁻¹) concentrations. The right panel shows the difference between the observed and modeled (a) dFe and (b) NO₃. The observations were made in July, August, and September (Aguilar-Islas et al., 2015; Lippiatt et al., 2010; Crusius et al., 2017). The model output is based on a mean of modeled July, August, and September values from a 1980 to 2013 climatology. dFe and NO₃ are plotted on a log scale.

dFe observations along a transect near the Copper River estuary suggest that coastal surface concentrations can reach up to 9.4 nmol kg⁻¹ in mid to late summer west of Prince William Sound (Fig. 2a), when glacial melt and riverine input are highest. These surface concentrations decrease rapidly with distance from shore, with levels of <1 nmol kg⁻¹ near the shelf break and beyond. The horizontal surface dFe gradient across the shelf, with high dFe concentrations in coastal areas and dFe levels near depletion offshore, was simulated well by the model. For example, the model shows dFe values of up to 8 nmol kg⁻¹ (Fig. 2a) in some coastal areas and low concentrations (<0.5 nmol kg⁻¹) at the shelf break. Overall, the model slightly underestimates dFe along the coast, except for the area surrounding Copper River and near the shelf break, despite the relatively high dFe riverine boundary condition (Table 2).

The low observed surface summertime values of NO₃ in coastal areas are simulated well by the model. Observed NO₃ values range up to 5.4 µmol kg⁻¹ (with the exception of a few outliers in southeast Alaska), and modeled surface NO₃ concentrations reach a maximum of 4.3 µmol kg⁻¹ (Fig. 2b).

The modeled spring phytoplankton bloom starts in April and coarsely matches with the timing of the satellite-observed spring bloom (Fig. 3). Simulated surface Chl-α then ranges between 3 and 4 µg kg⁻¹ across the entire shelf, with some nearshore areas reaching surface Chl-α levels of 5 µg kg⁻¹. However, satellite images suggest that Chl-α concentrations are more patchy in April than shown by the model, with lower concentrations across the shelf (1–2 µg kg⁻¹). While peak observed Chl-α concentrations between 7 and 9 µg kg⁻¹ are localized in southeast Alaska in May, simulated Chl-α levels of 5 µg kg⁻¹ are more widespread along the coast, with peak concentrations of 6 to 7 µg kg⁻¹ in some select areas. In July through August, simulated Chl-α levels slowly taper off, although some nearshore areas still reach peak concentrations of 6 µg kg⁻¹. In September, on-shelf modeled Chl-α concentrations are <3 µg kg⁻¹. In summary, observed Chl-α concentrations are lower than suggested by the model across the shelf and the domain throughout the summer. With the exception of November through February, when modeled Chl-α concentrations are <1 µg kg⁻¹, standing stock Chl-α concentrations are also overestimated by a factor of 2 by the model throughout the year.

Figure 3Monthly climatology (1980–2013) for satellite-based (left, MODIS) and GOA-COBALT-simulated (middle) surface Chl-α concentrations for (a) March, (b) April, (c) May, (d) July, and (e) September. The right panel shows the difference between MODIS and GOA-COBALT surface Chl-α concentrations. (Source for MODIS data: MODIS-Aqua Ocean Color Data, NASA Goddard Space Flight Center, Ocean Ecology Laboratory, 2014.)

3.3 Model skill to simulate spring and fall oceanographic conditions

Inorganic carbon observations in the GOA have been collected every spring and fall along the historic Seward Line since 2008 (Evans et al., 2013). Here, we compare May and September monthly means of our 2008–2012 model output to the publicly available shipboard observations made in May and September of the corresponding years. To do so, the model output was sampled at the closest grid point to every Seward Line station. The model output and observations were then interpolated onto the same grid and averaged across all years for May and September.

In May, observations and model output clearly show the influence of freshwater on the coastal water properties, including inorganic carbon chemistry (Fig. 4). In nearshore surface areas, waters are cold, fresh, and low in TA and DIC. The influence of freshwater is visible throughout the transect but with slowly increasing values of salinity, DIC, and TA with distance from the coast. The model generally reproduces these patterns well, although with slightly higher values for all three parameters across the transect. For example, observed surface salinity ranges between 31.4 at 59.8^∘ N and 32.2 at the end of the transect (Fig. 4b). TA varies between 2143 and 2170 µmol kg⁻¹, and DIC varies between 1965 and 2017 µmol kg⁻¹ (Fig. 4c, d). Simulated ranges of these parameters are similar (salinity from 31.7 to 32.4, TA from 2163 to 2203 µmol kg⁻¹, and DIC from 2009 to 2038 µmol kg⁻¹). The largest biases in salinity (S_bias=0.6), alkalinity (TA_bias=35 µmol kg⁻¹), and DIC (DIC_bias=46 µmol kg⁻¹) are found around 59.6^∘ N. The overestimation of salinity suggests that the freshwater influence is overly weak, leading to the modeled overestimation of TA and DIC. However, the bias in DIC relative to the bias in TA is largest in the grid cell closest to the coast, which leads to an underestimation of modeled pH and Ω_arag of up to 0.09 and 0.29, respectively (Fig. 4e, f). The bias of surface pH and Ω_arag vanishes with distance from the coast. The larger difference in DIC relative to TA near the coast is likely due to an underestimation of biological carbon drawdown, leading to the underestimation of pH and Ω_arag in nearshore surface waters. At depth farther offshore, salinity-, DIC-, and TA-enriched waters are visible on the shelf. As a result, the springtime in situ aragonite saturation horizon (depth where Ω_arag=1) is shallower offshore than nearshore (Fig. 4f). Observations suggest that with a depth of the aragonite saturation horizon of about 200 m, the seafloor on the shelf up to 59.1^∘ N is undersaturated with respect to aragonite. The model underestimates the aragonite saturation horizon depth slightly. However, because the model's bathymetry is shallower than the observed depth at this particular location (gray areas in Fig. 4), modeled bottom water masses across the shelf are not undersaturated with respect to Ω_arag north of 59^∘ N.

Figure 4Visual comparison of vertical sections of (a) temperature (^∘C), (b) salinity, (c) total alkalinity (TA, µmol kg⁻¹), (d) dissolved inorganic carbon (DIC, µmol kg⁻¹), (e) pH, and (f) the aragonite saturation state (Ω_arag) of climatologies (2008–2012) of observations made along the Seward Line in May (left, Evans et al., 2013), the corresponding monthly model output (middle), and the difference between observed and GOA-COBALT-simulated variables (right). The model output was sampled at locations where observations were made. Observations and model points were then vertically and horizontally interpolated onto the same grid and averaged across the years 2008 to 2012. The gray area depicts the observed sampling depth in the left panel and the seafloor in the model output. The black line in panel (f) indicates Ω_arag=1.

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In September, nearshore surface waters are warm (∼ 11 ^∘C) and much fresher than in spring (Fig. 5a, b). The observed surface salinity is as low as 27.6 at 59.8 ^∘C and increases to 32 salinity units at the end of the transect. Modeled surface salinity ranges between 26.3 and 31.8. It is important to note that observed surface salinity at the station closest to the coast is also as low as 26.8, but it is masked out in this point-by-point comparison. As a result of this bias in salinity, modeled nearshore TA and DIC concentrations in the upper 30 m are underestimated by ∼30 and ∼20 µmol kg⁻¹, respectively (Fig. 5c, d). Because the model is likely underestimating the magnitude of late-season phytoplankton blooms, the bias in DIC is slightly smaller than in TA. Modeled Ω_arag underestimates observations by <0.2 in this area (Fig. 5f). At depth, the model output aligns well with observations. Both observations and model output suggest that bottom waters across the Seward Line transect are undersaturated with respect to aragonite in fall. Observations also show an intermediate maximum in DIC at about 150 m depth, which leads to an even shallower aragonite saturation horizon (Fig. 5d). This small-scale feature may be due to remineralization at mid depth and is not simulated by the model. Overall, the model does a reasonable job of simulating the spatial patterns of salinity, TA, DIC, pH, and Ω_arag in spring and fall, with statistically significant (p value < 0.05) Pearson correlation coefficients of between 0.82 and 0.97 (Fig. 6a, b). The model overestimates springtime temperature along the surface and around 100 m offshore, which is reflected in a slightly lower Pearson correlation coefficient of 0.62. The Pearson correlation coefficients (Pcc) and their corresponding p values were calculated based on the climatologies presented in Figs. 4 and 5. All standard deviations and correlation coefficients between the observed and modeled variables are summarized using Taylor Diagrams in Fig. 6.

Figure 5Visual comparison of vertical sections of (a) temperature (^∘C), (b) salinity, (c) total alkalinity (TA, µmol kg⁻¹), (d) dissolved inorganic carbon (DIC, µmol kg⁻¹), (e) pH, and (f) the aragonite saturation state (Ω_arag) of climatologies (2008–2012) of observations made along the Seward Line in September (left, Evans et al., 2013), the corresponding monthly model output (middle), and the difference between observed and GOA-COBALT-simulated variables (right). The model output was sampled at locations where observations were made. Observations and model points were then vertically and horizontally interpolated onto the same grid and averaged across the years 2008 to 2012. The gray area depicts the observed sampling depth in the left panel and the seafloor in the model output. The black line in panel (f) indicates Ω_arag=1.

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Figure 6Taylor diagrams (Taylor, 2001) of model-simulated temperature, salinity, total alkalinity (TA, µmol kg⁻¹), dissolved inorganic carbon (DIC, µmol kg⁻¹), pH, and the aragonite saturation state (Ω_arag) compared to observations made along the Seward Line in (a) May and (b) September across the upper 300 m (Figs. 4, 5). Climatologies of the averaged modeled monthly means of May and September are compared to climatologies of observed conditions during spring and fall cruises in the years 2008 through 2012. The distance from the origin is the normalized standard deviation of the modeled parameters. The azimuth angle shows the correlation between the observations and the modeled output, whereas the distance between the model point and the red observation point shows the normalized root mean square misfit between the modeled and observed data.

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3.4 Model skill to simulate interannual variability

The GOA oceanography undergoes large interannual to decadal variability as a result of the El Niño–Southern Oscillation (ENSO), the Pacific Decadal Oscillation (PDO), and other climate modes of variability that drive changes in freshwater flux, water temperature, and winds (Whitney and Freeland, 1999; Hare and Mantua, 2000). These physical changes are likely translated into the inorganic carbon chemistry. Here, we investigate the model's skill to simulate interannual features, comparing Hovmöller plots of observations made in May and September between 2008 and 2012 and modeled monthly means of the corresponding time and location for temperature, salinity, TA, and DIC (Figs. 7, 8). We also calculate the monthly observed and modeled anomalies for May and September, based on the observed and modeled 5-year monthly mean of each variable (Figs. 9, 10). In the following, we will describe observations of years that stand out within this 5-year record and determine whether these features were captured by the model.

Figure 7Hovmöller plots showing the observed (left) and modeled monthly mean (right) surface (a) temperature (^∘C), (b) salinity, (c) total alkalinity (TA, µmol kg⁻¹), and (d) dissolved inorganic carbon (DIC, µmol kg⁻¹) in May along the Seward Line between 2008 and 2012. Gray areas show missing data.

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Figure 8Hovmöller plots showing the observed (left) and modeled monthly mean (right) surface (a) temperature (^∘C), (b) salinity, (c) total alkalinity (TA, µmol kg⁻¹), and (d) dissolved inorganic carbon (DIC, µmol kg⁻¹) in September along the Seward Line between 2008 and 2012. Gray areas show missing data.

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Figure 9Hovmöller plots showing the observed (left) and modeled (center) monthly anomalies from the 5-year mean (2008–2012) of surface (a) temperature (^∘C), (b) salinity, (c) total alkalinity (TA, µmol kg⁻¹), and (d) dissolved inorganic carbon (DIC, µmol kg⁻¹) in May along the Seward Line. Gray areas show missing data. The right column shows plots of observed vs. modeled monthly anomalies for the corresponding parameter. Different marker types are used to indicate different years. The marker legend is given in the left column. The root mean square error (RMSE), the Pearson correlation coefficient (Pcc), and the p value for the observed and modeled interannual monthly anomalies are listed in Table 3.

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Figure 10Hovmöller plots showing the observed (left) and modeled (center) monthly anomalies from the 5-year mean (2008–2012) of surface (a) temperature (^∘C), (b) salinity, (c) total alkalinity (TA, µmol kg⁻¹), and (d) dissolved inorganic carbon (DIC, µmol kg⁻¹) in September along the Seward Line. Gray areas show missing data. The right column shows plots of observed vs. modeled monthly anomalies for the corresponding parameter. Different marker types are used to indicate different years. The marker legend is given in the left column. The root mean square error (RMSE), the Pearson correlation coefficient (Pcc), and the p value for the observed and modeled interannual monthly anomalies are listed in Table 3.

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The observed and modeled springtime surface temperatures show large interannual variability (Figs. 7a, 9a). Within the 5-year-long record, 2008 was a particularly cold spring, with surface temperatures of around 5 ^∘C. The model also simulated May 2008 as the coldest spring, but it overestimated the temperature by approximately 1 ^∘C. In May 2010, observed sea surface temperatures were particularly high (> 6 ^∘C) across the shelf, which was well reflected by the model. While the model also suggested high temperatures in the previous spring, the observations do not show a particularly warm spring in 2009. The modeled and observed interannual variability of surface temperatures in May are statistically significantly correlated with a Pcc of 0.54 (Table 3). The interannual variability in salinity is visible by how far the freshwater penetrates into the open ocean. For example, observations suggest that freshwater penetrated farther offshore in 2010 than in other years (Fig. 7b), which was not reflected by the model.

Table 3Table listing the root mean square error (RMSE), the Pearson correlation coefficient (Pcc), and the p value between the observed and modeled interannual variability at the surface. The RMSE, Pcc, and the corresponding p value were based on observed and modeled monthly anomalies from a temporal mean of May or September (2008–2012) along the Seaward Line transect. Statistically significant Pcc values and the corresponding p values are indicated in bold. The anomalies are shown in Figs. 9 and 10.

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The anomalous warm sea surface temperatures observed in spring 2010 remained persistent into fall, with temperatures around 13 ^∘C across the whole transect (Figs. 8a, 10a). This anomalously warm fall was well simulated by the model. Overall, the modeled interannual variability of fall surface temperatures correlated well with the observations (Pcc = 0.87, $p=<\mathrm{0.05}$). Interestingly, in the anomalously warm fall of 2010, observations suggest anomalously high salinities penetrating closer to the nearshore than in other years, which was not reflected by the model (Figs. 8b, 10b). However, observed lower salinities mid transect in 2012 were also simulated by the model, which directly translated into TA and DIC (Fig. 8c, d). Overall, there was no clear interannual pattern in observed or simulated salinity, TA, and DIC between 2008 and 2012 (panels b–d in Figs. 7–10), and no statistically significant correlation between the observed and modeled spring and fall anomalies (Table 3).